{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_69093/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_69093","id":"gutenberg_69093","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/69093","summary":null,"tags":["Category: History - Other","Category: Philosophy & Ethics","Science -- Philosophy"],"text":"HISTORY\nOF\nSCIENTIFIC IDEAS.\n\n\n\nVOLUME I.\n\n\n\n\nCambridge;\nPRINTED BY C. J. CLAY, M.A.\nAT THE UNIVERSITY PRESS.\n\n\n\nHISTORY\nOF\nSCIENTIFIC IDEAS.\n\nBY WILLIAM WHEWELL, D.D.,\nMASTER OF TRINITY COLLEGE, CAMBRIDGE, AND\nCORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.\n\n\n\nBEING THE FIRST PART OF THE PHILOSOPHY\nOF THE INDUCTIVE SCIENCES.\n\n\n\n_THE THIRD EDITION._\n\nIN TWO VOLUMES.\n\n\n\u039b\u0391\u039c\u03a0\u0391\u0394I\u0391 \u0395\u03a7\u039f\u039d\u03a4\u0395\u03a3 \u0394I\u0391\u0394\u03a9\u03a3\u039f\u03a5\u03a3I\u039d \u0391\u039b\u039b\u0397\u039b\u039fI\u03a3\n\n\nVOLUME I.\n\n\n\nLONDON:\nJOHN W. PARKER AND SON, WEST STRAND.\n1858.\n\n\n\n{{v}}\nPREFACE TO THIS EDITION.\n\n\n\nTHE Chapters now offered to the Reader were formerly\npublished as a portion of _The Philosophy of the Inductive\nSciences, founded upon their History_: but the nature and\nsubject of these Chapters are more exactly described by the\npresent title, _The History of Scientific Ideas_. For this\npart of the work is mainly historical, and was, in fact,\ncollected from the body of scientific literature, at the\nsame time that the _History of the Inductive Sciences_ was\nso collected. The present work contains the history of\nScience so far as it depends on _Ideas_; the former work\ncontains the same history so far as it is derived from\n_Observation_. The leading features in _that_ were Theories\ninferred from Facts; the leading features of _this_ are\nDiscussions of Theories tending to make them consistent with\nthe conditions of human thought.\n\nThe Ideas of which the History is here given are mainly the\nfollowing:\n_Space_, _Time_, _Number_, _Motion_, _Cause_, _Force_,\n_Matter_, _Medium_, _Intensity_, _Scale_, _Polarity_,\n_Element_, _Affinity_, _Substance_, _Atom_, _Symmetry_,\n_Likeness_, _Natural Classes_, _Species_, _Life_,\n_Function_, _Vital Forces_, _Final_ {vi} _Causes_,\n_Historical Causation_, _Catastrophe and Uniformity_, _First\nCause_.\n\nThe controversies to which the exact fixation of these Ideas\nand their properties have given occasion form a large and\nessential part of the History of Science: but they also form\nan important part of the Philosophy of Science, for no\nPhilosophy of Science can be complete which does not solve\nthe difficulties, antitheses, and paradoxes on which such\ncontroversies have turned. I have given a survey of such\ncontroversies, generally carried from their earliest origin\nto their latest aspect; and have stated what appeared to me\nthe best solution of each problem. This has necessarily\ninvolved me in much thorny metaphysics; but such metaphysics\nis a necessary part of the progress of Science. The human\nmind deriving its knowledge of Truth from the observation of\nnature, cannot evade the task of determining at every step\nhow Truth is consistent with itself. This is the Metaphysics\nof Progressive Knowledge, and this is the matter of this\npresent History.\n\nOf the remaining part of what was formerly published as the\nPhilosophy of the Inductive Sciences, an additional part,\ndescribed in the Introduction to the present work, will\nshortly be published.\n\nTRINITY LODGE,\n_May_ 24, 1858.\n\n\nERRATUM, p. 157, l. 11 from top, _for_ sciences\n_read_ science.\n\n\n\n\nCONTENTS\nOF\nTHE FIRST VOLUME.\n\n\n PAGE\nPREFACE v\n\nPART I.\nOF IDEAS.\n\n\nINTRODUCTION 3\n\nBOOK I.\n\nOF IDEAS IN GENERAL.\n\nCHAP. I. OF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY 23\n\n_Sect._ 1. _Thoughts and Things_ --\n 2. _Necessary and Experiential Truths_ 25\n 3. _Deduction and Induction_ 27\n 4. _Theories and Facts_ 29\n 5. _Ideas and Sensations_ 30\n 6. _Reflexion and Sensation_ 33\n 7. _Subjective and Objective_ 35\n 8. _Matter and Form_ 38\n 9. _Man the Interpreter of Nature_ 41\n 10. _The Fundamental Antithesis is inseparable_ 43\n 11. _Successive Generalization_ 49\n{viii}\n\nCHAP. II. OF TECHNICAL TERMS 54\n\n _Art._ 1. Examples.\n 2. Use of Terms.\n\nCHAP. III. OF NECESSARY TRUTHS 57\n\n _Art._ 1. The two Elements of Knowledge,\n 2. Shown by necessary Truths.\n 3. Examples of necessary Truths in numbers.\n 4. The opposite cannot be distinctly conceived.\n 5. Other Examples.\n 6. Universal Truths.\n\nCHAP. IV. OF EXPERIENCE 65\n\n _Art._ 1. Experience cannot prove necessary Truths,\n 2. Except when aided by Ideas.\n\nCHAP. V. OF THE GROUNDS OF NECESSARY TRUTHS 69\n\n _Art._ 1. These Grounds are Fundamental Ideas.\n 2. These are to be reviewed.\n 3. Definitions and Axioms.\n 4. Syllogism,\n 5. Produces no new Truths.\n 6. Axioms needed.\n 7. Axioms depend on Ideas:\n 8. So do Definitions.\n 9. Idea not completely expressed.\n\nCHAP. VI. THE FUNDAMENTAL IDEAS ARE NOT DERIVED FROM EXPERIENCE 76\n\n _Art._ 1. No connexion observed.\n 2. Faculties implied in observation.\n 3. We are to examine our Faculties.\n\nCHAP. VII. OF THE PHILOSOPHY OF THE SCIENCES 81\n\n Sciences arranged according to Ideas.\n{ix}\n\nBOOK II.\n\nTHE PHILOSOPHY OF THE PURE SCIENCES.\n\nCHAP. I. OF THE PURE SCIENCES 88\n\n _Art._ 1. Geometry, Arithmetic, Algebra,\n 2. Are not Inductive Sciences:\n 3. Are Mathematical Sciences.\n 4. Mixed Mathematics.\n 5. Space, Time, Number.\n\nCHAP. II. OF THE IDEA OF SPACE 91\n\n _Art._ 1. Space is an Idea,\n 2. Not derived from Experience,\n 3. As Geometrical Truth shows.\n 4. Space is a Form of Experience.\n 5. The phrase not essential.\n\nCHAP. III. OF SOME PECULIARITIES OF THE IDEA OF SPACE 95\n\n _Art._ 1. Space is not an Abstract Notion.\n 2. Space is infinite.\n 3. Space is real.\n 4. Space is a Form of Intuition.\n 5. Figure.\n 6. Three Dimensions.\n\nCHAP. IV. OF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE 98\n\n _Art._ 1. Geometry.\n 2. Definitions.\n 3. Axioms.\n 4. Not Hypotheses.\n 5. Axioms necessary.\n 6. Straight Lines.\n 7. Planes.\n 8. Elementary Geometry.\n\nCHAP. V. OF SOME OBJECTIONS WHICH HAVE BEEN MADE TO THE\n DOCTRINES STATED IN THE PREVIOUS CHAPTER 107\n\n _Art._ 1. How is Geometry hypothetical?\n 2. What was Stewart's view?\n{x}\n 3. 'Legitimate filiations' of Definitions.\n 4. Is a Definition a complete explanation?\n 5. Are some Axioms Definitions?\n 6. Axiom concerning Circles.\n 7. Can Axioms become truisms?\n 8. Use of such.\n\nCHAP. VI. OF THE PERCEPTION OF SPACE 117\n\n _Art._ 1. Which Senses apprehend Space?\n 2. Perception of solid figure.\n 3. Is an interpretation.\n 4. May be analysed.\n 5. Outline.\n 6. Reversed convexity.\n 7. Do we perceive Space by Touch?\n 8. Brown's Opinion.\n 9. The Muscular Sense.\n 10. Bell's Opinion.\n 11. Perception includes Activity.\n 12. Perception of the Skyey Dome.\n 13. Reid's Idomenians.\n 14. Motion of the Eye.\n 15. Searching Motion.\n 16. Sensible Spot.\n 17. Expressions implying Motion.\n\nCHAP. VII. OF THE IDEA OF TIME 131\n\n _Art._ 1. Time an Idea not derived from Experience.\n 2. Time is a Form of Experience.\n 3. Number.\n 4. Is Time derived from Motion?\n\nCHAP. VIII. OF SOME PECULIARITIES IN THE IDEA OF TIME 134\n\n _Art._ 1. Time is not an Abstract Notion.\n 2. Time is infinite.\n 3. Time is a Form of Intuition.\n 4. Time is of one Dimension,\n 5. And no more.\n 6. Rhythm.\n 7. Alternation.\n 8. Arithmetic.\n{xi}\n\nCHAP. IX. OF THE AXIOMS WHICH RELATE TO NUMBER 138\n\n _Art._ 1. Grounds of Arithmetic.\n 2. Intuition.\n 3. Arithmetical Axioms,\n 4. Are Conditions of Numerical Reasoning\n 5. In all Arithmetical Operations.\n 6. Higher Numbers.\n\nCHAP. X. OF THE PERCEPTION OF TIME AND NUMBER 141\n\n _Art._ 1. Memory.\n 2. Sense of Successiveness\n 3. Implies Activity.\n 4. Number also does so.\n 5. And apprehension of Rhythm.\n Note to Chapter X. 145\n\nCHAP. XI. OF MATHEMATICAL REASONING 147\n\n _Art._ 1. Discursive Reasoning.\n 2. Technical Terms of Reasoning.\n 3. Geometrical Analysis and Synthesis.\n\nCHAP. XII. OF THE FOUNDATIONS OF THE HIGHER MATHEMATICS 151\n\n _Art._ 1. The Idea of a Limit.\n 2. The use of General Symbols.\n 3. Connexion of Symbols and Analysis.\n\nCHAP. XIII. THE DOCTRINE OF MOTION 156\n\n_Art._ 1. Pure Mechanism.\n 2. Formal Astronomy.\n\nCHAP. XIV. OF THE APPLICATION OF MATHEMATICS TO THE INDUCTIVE\n SCIENCES 159\n\n _Art._ 1. The Ideas of Space and Number are clear from\n the first.\n 2. Their application in Astronomy.\n 3. Conic Sections, &c.\n 4. Arabian Numerals.\n 5. Newton's Lemmas.\n 6. Tides.\n 7. Mechanics.\n 8. Optics.\n 9. Conclusion.\n{xii}\n\nBOOK III.\n\nTHE PHILOSOPHY OF THE MECHANICAL SCIENCES.\n\nCHAP. I. OF THE MECHANICAL SCIENCES 171\n\nCHAP. II. OF THE IDEA OF CAUSE 173\n\n _Art._ 1. Not derived from Observation,\n 2. As appears by its use.\n 3. Cause cannot be observed.\n 4. Is Cause only constant succession?\n 5. Other reasons.\n\nCHAP. III. MODERN OPINIONS RESPECTING THE IDEA OF CAUSE 178\n\n _Art._ 1. Hume's Doctrine.\n 2. Stewart and Brown.\n 3. Kant.\n 4. Relation of Kant and Brown.\n 5. Axioms flow from the Idea.\n 6. The Idea implies activity in the Mind.\n\nCHAP. IV. OF THE AXIOMS WHICH RELATE TO THE IDEA OF CAUSE 184\n\n _Art._ 1. Causes are Abstract Conceptions.\n 2. First Axiom.\n 3. Second Axiom.\n 4. Limitation of the Second Axiom.\n 5. Third Axiom.\n 6. Extent of the Third Axiom.\n\nCHAP. V. OF THE ORIGIN OF OUR CONCEPTIONS OF FORCE AND MATTER 205\n\n _Art._ 1. Force.\n 2. Matter.\n 3. Solidity.\n 4. Inertia.\n 5. Application.\n{xiii}\n\nCHAP. VI. OF THE ESTABLISHMENT OF THE PRINCIPLES OF STATICS 212\n\n _Art._ 1. Object of the Chapter.\n 2. Statics and Dynamics.\n 3. Equilibrium.\n 4. Measure of Statical Forces.\n 5. The Center of Gravity.\n 6. Oblique Forces.\n 7. Force acts at any point of its Direction.\n 8. The Parallelogram of Forces\n 9. Is a necessary Truth.\n 10. Center of Gravity descends.\n 11. Stevinus's Proof.\n 12. Principle of Virtual Velocities.\n 13. Fluids press equally.\n 14. Foundation of this Axiom.\n\nCHAP. VII. OF THE ESTABLISHMENT OF THE PRINCIPLES OF DYNAMICS 235\n\n _Art._ 1. History.\n 2. The First Law of Motion.\n 3. Gravity is a Uniform Force.\n 4. The Second Law of Motion.\n 5. The Third Law of Motion.\n 6. Action and Reaction in Moving Bodies.\n 7. D'Alembert's Principle.\n 8. Connexion of Statics and Dynamics.\n 9. Mechanical Principles grow more evident.\n 10. Controversy of the Measure of Force.\n\nCHAP. VIII. OF THE PARADOX OF UNIVERSAL PROPOSITIONS\n OBTAINED FROM EXPERIENCE 263\n\n _Art._ 1. Experience cannot establish necessary Truths;\n 2. But can interpret Axioms.\n 3. Gives us the Matter of Truths.\n 4. Exemplifies Truths.\n 5. Cannot shake Axioms.\n 6. Is this applicable in other cases?\n\nCHAP. IX. OF THE ESTABLISHMENT OF THE LAW OF UNIVERSAL\n GRAVITATION 272\n\n _Art._ 1. General course of the History.\n{xiv}\n 2. Particulars as to the Law.\n 3. As to the Gravity of Matter.\n 4. Universality of the Law.\n 5. Is Gravity an essential quality?\n 6. Newton's Rule of Philosophizing.\n 7. Hypotheses respecting Gravity.\n 8. Do Bodies act at a distance?\n\nCHAP. X. OF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS 279\n\n _Art._ 1. Nature of the Process\n 2. Among the Ancients.\n 3. Kepler, &c.\n 4. Lord Monboddo, &c.\n 5. Schelling, &c.\n 6. Common usage.\n 7. Effect of Phrases.\n 8. Contempt of Predecessors.\n 9. Less detail hereafter.\n 10. Mechanico-Chemical Sciences.\n 11. Secondary Mechanical Sciences.\n\n\nBOOK IV.\n\nTHE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES.\n\nCHAP. I. OF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED 293\n\n _Art._ 1. Of Primary and Secondary Qualities.\n 2. The Idea of Externality.\n 3. Sensation by a Medium.\n 4. Process of Perception of Secondary Qualities.\n\nCHAP. II. ON PECULIARITIES IN THE PERCEPTIONS OF THE\n DIFFERENT SENSES 302\n\n _Art._ 1. Difference of Senses.\n\n_Sect._ I. _Prerogatives of Sight._\n _Art._ 2. Position.\n 3. Distance.\n{xv}\n_Sect._ II. _Prerogatives of Hearing._\n _Art._ 4. Musical Intervals.\n 5. Chords.\n 6. Rhythm.\n\n_Sect._ III. _The Paradoxes of Vision._\n _Art._ 7. First Paradox.\n 8. Second Paradox.\n 9. The same for near Objects.\n 10. Objections answered.\n\n_Sect._ IV. _The Perception of Visible Figures._\n _Art._ 11. Brown's Opinion.\n\nCHAP. III. SUCCESSIVE ATTEMPTS AT THE SCIENTIFIC\n APPLICATION OF THE IDEA OF A MEDIUM 322\n\n _Art._ 1. Introduction.\n 2. Sound.\n 3. Light.\n 4. Heat.\n\nCHAP. IV. OF THE MEASURE OF SECONDARY QUALITIES 333\n\n_Sect._ I. _Scales of Qualities in General._\n _Art._ 1. Intensity.\n 2. Quantity and Quality.\n\n_Sect._ II. _The Musical Scale._\n _Art._ 3. Musical Relations.\n 4. Musical Standard.\n\n_Sect._ III. _Scales of Colour._\n _Art._ 5. The Prismatic Scale.\n 6. Newton's Scale.\n 7. Scales of Impure Colours.\n 8. Chromatometer.\n\n_Sect._ IV. _Scales of Light._\n _Art._ 9. Photometer.\n 10. Cyanometer.\n\n_Sect._ V. _Scales of Heat._\n _Art._ 11. Thermometers.\n 12. Their progress.\n 13. Fixed Points.\n 14. Concordance of Thermometers.\n 15. Natural Measure.\n 16. Law of Cooling.\n{xvi}\n 17. Theory of Exchanges.\n 18. Air Thermometer.\n 19. Theory of Heat.\n 20. Other Instruments.\n\n_Sect._ VI. _Scales of other Quantities._\n _Art._ 21. Tastes and Smells.\n 22. Quality of Sounds.\n 23. Articulate Sounds.\n 24. Transition.\n\n\nBOOK V.\n\nOF THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES.\n\nCHAP. I. ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA\n OF POLARITY 359\n\n _Art._ 1. Introduction of the Idea.\n 2. Magnetism.\n 3. Electricity.\n 4. Voltaic Electricity.\n 5. Light.\n 6. Crystallization.\n 7. Chemical Affinity.\n 8. General Remarks.\n 9. Like _repels_ like.\n\nCHAP. II. OF THE CONNEXION OF POLARITIES 371\n\n _Art._ 1. Different Polar Phenomena from one Cause.\n 2. Connexion of Magnetic and Electric Polarity.\n 3. Amp\u00e8re's Theory.\n 4. Faraday's views.\n 5. Connexion of Electrical and Chemical Polarity.\n 6. Davy's and Faraday's views\n 7. Depend upon Ideas as well as Experiments.\n 8. Faraday's Anticipations.\n 9. Connexion of Chemical and Crystalline Polarities.\n 10. Connexion of Crystalline and Optical Polarities.\n 11. Connexion of Polarities in general.\n 12. Schelling's Speculations.\n 13. Hegel's vague notions.\n 14. Ideas must guide Experiment.\n\n\n\n\n{{1}}\nTHE\nPHILOSOPHY\nOF THE\nINDUCTIVE SCIENCES.\n\n\n\nINTRODUCTION.\n\n{{3}}\nINTRODUCTION.\n\n\nTHE PHILOSOPHY OF SCIENCE, if the phrase were to be\nunderstood in the comprehensive sense which most naturally\noffers itself to our thoughts, would imply nothing less than\na complete insight into the essence and conditions of all\nreal knowledge, and an exposition of the best methods for\nthe discovery of new truths. We must narrow and lower this\nconception, in order to mould it into a form in which we may\nmake it the immediate object of our labours with a good hope\nof success; yet still it may be a rational and useful\nundertaking, to endeavour to make some advance towards such\na Philosophy, even according to the most ample conception of\nit which we can form. The present work has been written with\na view of contributing, in some measure, however small it\nmay be, towards such an undertaking.\n\nBut in this, as in every attempt to advance beyond the\nposition which we at present occupy, our hope of success\nmust depend mainly upon our being able to profit, to the\nfullest extent, by the progress already made. We may best\nhope to understand the nature and conditions of real\nknowledge, by studying the nature and conditions of the most\ncertain and stable portions of knowledge which we already\npossess: and we are most likely to learn the best methods of\ndiscovering truth, by examining how truths, now universally\nrecognized, have really been discovered. Now there do exist\namong us doctrines of solid and acknowledged certainty, and\ntruths of which the discovery has been received with\nuniversal applause. These constitute what we commonly term\n_Sciences_; and of these bodies of exact and enduring\nknowledge, we have within our {4} reach so large and varied\na collection, that we may examine them, and the history of\ntheir formation, with a good prospect of deriving from the\nstudy such instruction as we seek. We may best hope to make\nsome progress towards the Philosophy of Science, by\nemploying ourselves upon THE PHILOSOPHY OF THE SCIENCES.\n\nThe _Sciences_ to which the name is most commonly and\nunhesitatingly given, are those which are concerned about\nthe material world; whether they deal with the celestial\nbodies, as the sun and stars, or the earth and its products,\nor the elements; whether they consider the differences which\nprevail among such objects, or their origin, or their mutual\noperation. And in all these Sciences it is familiarly\nunderstood and assumed, that their doctrines are obtained by\na common process of collecting general truths from\nparticular observed facts, which process is termed\n_Induction_. It is further assumed that both in these and in\nother provinces of knowledge, so long as this process is\nduly and legitimately performed, the results will be real\nsubstantial truth. And although this process, with the\nconditions under which it is legitimate, and the general\nlaws of the formation of Sciences, will hereafter be\nsubjects of discussion in this work, I shall at present so\nfar adopt the assumption of which I speak, as to give to the\nSciences from which our lessons are to be collected the name\nof _Inductive Sciences_. And thus it is that I am led to\ndesignate my work as THE PHILOSOPHY OF THE INDUCTIVE\nSCIENCES.\n\nThe views respecting the nature and progress of knowledge,\ntowards which we shall be directed by such a course of\ninquiry as I have pointed out, though derived from those\nportions of human knowledge which are more peculiarly and\ntechnically termed _Sciences_, will by no means be confined,\nin their bearing, to the domain of such Sciences as deal\nwith the material world, nor even to the whole range of\nSciences now existing. On the contrary, we shall be led to\nbelieve that the nature of truth is in all subjects the\nsame, and that its discovery involves, in all cases, the\nlike {5} conditions. On one subject of human speculation\nafter another, man's knowledge assumes that exact and\nsubstantial character which leads us to term it _Science_;\nand in all these cases, whether inert matter or living\nbodies, whether permanent relations or successive\noccurrences, be the subject of our attention, we can point\nout certain universal characters which belong to truth,\ncertain general laws which have regulated its progress among\nmen. And we naturally expect that, even when we extend our\nrange of speculation wider still, when we contemplate the\nworld within us as well as the world without us, when we\nconsider the thoughts and actions of men as well as the\nmotions and operations of unintelligent bodies, we shall\nstill find some general analogies which belong to the\nessence of truth, and run through the whole intellectual\nuniverse. Hence we have reason to trust that a just\nPhilosophy of the Sciences may throw light upon the nature\nand extent of our knowledge in every department of human\nspeculation. By considering what is the real import of our\nacquisitions, where they are certain and definite, we may\nlearn something respecting the difference between true\nknowledge and its precarious or illusory semblances; by\nexamining the steps by which such acquisitions have been\nmade, we may discover the conditions under which truth is to\nbe obtained; by tracing the boundary-line between our\nknowledge and our ignorance, we may ascertain in some\nmeasure the extent of the powers of man's understanding.\n\nBut it may be said, in such a design there is nothing new;\nthese are objects at which inquiring men have often before\naimed. To determine the difference between real and\nimaginary knowledge, the conditions under which we arrive at\ntruth, the range of the powers of the human mind, has been a\nfavourite employment of speculative men from the earliest to\nthe most recent times. To inquire into the original,\ncertainty, and compass of man's knowledge, the limits of his\ncapacity, the strength and weakness of his reason, has been\nthe professed purpose of many of the most conspicuous and\nvalued labours of the philosophers of {6} all periods up to\nour own day. It may appear, therefore, that there is little\nnecessity to add one more to these numerous essays; and\nlittle hope that any new attempt will make any very\nimportant addition to the stores of thought upon such\nquestions, which have been accumulated by the profoundest\nand acutest thinkers of all ages.\n\nTo this I reply, that without at all disparaging the value\nor importance of the labours of those who have previously\nwritten respecting the foundations and conditions of human\nknowledge, it may still be possible to add something to what\nthey have done. The writings of all great philosophers, up\nto our own time, form a series which is not yet terminated.\nThe books and systems of philosophy which have, each in its\nown time, won the admiration of men, and exercised a\npowerful influence upon their thoughts, have had each its\nown part and functions in the intellectual history of the\nworld; and other labours which shall succeed these may also\nhave their proper office and useful effect. We may not be\nable to do much, and yet still it may be in our power to\neffect something. Perhaps the very advances made by former\ninquirers may have made it possible for us, at present, to\nadvance still further. In the discovery of truth, in the\ndevelopment of man's mental powers and privileges, each\ngeneration has its assigned part; and it is for us to\nendeavour to perform our portion of this perpetual task of\nour species. Although the terms which describe our\nundertaking may be the same which have often been employed\nby previous writers to express their purpose, yet our\nposition is different from theirs, and thus the result may\nbe different too. We have, as they had, to run our\nappropriate course of speculation with the exertion of our\nbest powers; but our course lies in a more advanced part of\nthe great line along which Philosophy travels from age to\nage. However familiar and old, therefore, be the design of\nsuch a work as this, the execution may have, and if it be\nperformed in a manner suitable to the time, will have,\nsomething that is new and not unimportant. {7}\n\nIndeed, it appears to be absolutely necessary, in order to\ncheck the prevalence of grave and pernicious errour, that\nthe doctrines which are taught concerning the foundations of\nhuman knowledge and the powers of the human mind, should be\nfrom time to time revised and corrected or extended.\nErroneous and partial views are promulgated and accepted;\none portion of the truth is insisted upon to the undue\nexclusion of another; or principles true in themselves are\nexaggerated till they produce on men's minds the effect of\nfalsehood. When evils of this kind have grown to a serious\nheight, a _Reform_ is requisite. The faults of the existing\nsystems must be remedied by correcting what is wrong, and\nsupplying what is wanting. In such cases, all the merits and\nexcellencies of the labours of the preceding times do not\nsupersede the necessity of putting forth new views suited to\nthe emergency which has arrived. The new form which errour\nhas assumed makes it proper to endeavour to give a new and\ncorresponding form to truth. Thus the mere progress of time,\nand the natural growth of opinion from one stage to another,\nleads to the production of new systems and forms of\nphilosophy. It will be found, I think, that some of the\ndoctrines now most widely prevalent respecting the\nfoundations and nature of truth are of such a kind that a\nReform is needed. The present age seems, by many\nindications, to be called upon to seek a sounder Philosophy\nof Knowledge than is now current among us. To contribute\ntowards such a Philosophy is the object of the present work.\nThe work is, therefore, like all works which take into\naccount the most recent forms of speculative doctrine,\ninvested with a certain degree of novelty in its aspect and\nimport, by the mere time and circumstances of its\nappearance.\n\nBut, moreover, we can point out a very important peculiarity\nby which this work is, in its design, distinguished from\npreceding essays on like subjects; and this difference\nappears to be of such a kind as may well entitle us to\nexpect some substantial addition to our knowledge as the\nresult of our labours. The peculiarity {8} of which I speak\nhas already been announced;--it is this: that we purpose to\ncollect our doctrines concerning the nature of knowledge,\nand the best mode of acquiring it, from a contemplation of\nthe Structure and History of those Sciences (the Material\nSciences), which are universally recognized as the clearest\nand surest examples of knowledge and of discovery. It is by\nsurveying and studying the whole mass of such Sciences, and\nthe various steps of their progress, that we now hope to\napproach to the true Philosophy of Science.\n\nNow this, I venture to say, is a new method of pursuing the\nphilosophy of human knowledge. Those who have hitherto\nendeavoured to explain the nature of knowledge, and the\nprocess of discovery, have, it is true, often illustrated\ntheir views by adducing special examples of truths which\nthey conceived to be established, and by referring to the\nmode of their establishment. But these examples have, for\nthe most part, been taken at random, not selected according\nto any principle or system. Often they have involved\ndoctrines so precarious or so vague that they confused\nrather than elucidated the subject; and instead of a single\ndifficulty,--What is the nature of Knowledge? these attempts\nat illustration introduced two,--What was the true analysis\nof the Doctrines thus adduced? and,--Whether they might\nsafely be taken as types of real Knowledge?\n\nThis has usually been the case when there have been adduced,\nas standard examples of the formation of human knowledge,\ndoctrines belonging to supposed sciences other than the\nmaterial sciences; doctrines, for example, of Political\nEconomy, or Philology, or Morals, or the Philosophy of the\nFine Arts. I am very far from thinking that, in regard to\nsuch subjects, there are no important truths hitherto\nestablished: but it would seem that those truths which have\nbeen obtained in these provinces of knowledge, have not yet\nbeen fixed by means of distinct and permanent phraseology,\nand sanctioned by universal reception, and formed into a\nconnected system, and traced through the steps of their\ngradual discovery and establishment, so as to make {9} them\ninstructive examples of the nature and progress of truth in\ngeneral. Hereafter we trust to be able to show that the\nprogress of moral, and political, and philological, and\nother knowledge, is governed by the same laws as that of\nphysical science. But since, at present, the former class of\nsubjects are full of controversy, doubt, and obscurity,\nwhile the latter consist of undisputed truths clearly\nunderstood and expressed, it may be considered a wise\nprocedure to make the latter class of doctrines the basis of\nour speculations. And on the having taken this course, is,\nin a great measure, my hope founded, of obtaining valuable\ntruths which have escaped preceding inquirers.\n\nBut it may be said that many preceding writers on the nature\nand progress of knowledge have taken their examples\nabundantly from the Physical Sciences. It would be easy to\npoint out admirable works, which have appeared during the\npresent and former generations, in which instances of\ndiscovery, borrowed from the Physical Sciences, are\nintroduced in a manner most happily instructive. And to the\nworks in which this has been done, I gladly give my most\ncordial admiration. But at the same time I may venture to\nremark that there still remains a difference between my\ndesign and theirs: and that I use the Physical Sciences as\nexemplifications of the general progress of knowledge in a\nmanner very materially different from the course which is\nfollowed in works such as are now referred to. For the\nconclusions stated in the present work, respecting knowledge\nand discovery, are drawn from _a connected and systematic\nsurvey of the whole range of Physical Science and its\nHistory_; whereas, hitherto, philosophers have contented\nthemselves with adducing detached examples of scientific\ndoctrines, drawn from one or two departments of science. So\nlong as we select our examples in this arbitrary and limited\nmanner, we lose the best part of that philosophical\ninstruction, which the sciences are fitted to afford when we\nconsider them as all members of one series, and as governed\nby rules which are the same for all. Mathematical and\nchemical truths, physical and physiological doctrines, the\nsciences of {10} classification and of causation, must alike\nbe taken into our account, in order that we may learn what\nare the general characters of real knowledge. When our\nconclusions assume so comprehensive a shape that they apply\nto a range of subjects so vast and varied as these, we may\nfeel some confidence that they represent the genuine form of\nuniversal and permanent truth. But if our exemplification is\nof a narrower kind, it may easily cramp and disturb our\nphilosophy. We may, for instance, render our views of truth\nand its evidence so rigid and confined as to be quite\nworthless, by founding them too much on the contemplation of\nmathematical truth. We may overlook some of the most\nimportant steps in the general course of discovery, by\nfixing our attention too exclusively upon some one\nconspicuous group of discoveries, as, for instance, those of\nNewton. We may misunderstand the nature of physiological\ndiscoveries, by attempting to force an analogy between them\nand discoveries of mechanical laws, and by not attending to\nthe intermediate sciences which fill up the vast interval\nbetween these extreme terms in the series of material\nsciences. In these and in many other ways, a partial and\narbitrary reference to the material sciences in our inquiry\ninto human knowledge may mislead us; or at least may fail to\ngive us those wider views, and that deeper insight, which\nshould result from a systematic study of the whole range of\nsciences with this particular object.\n\nThe design of the following work, then, is to form a\nPhilosophy of Science, by analyzing the substance and\nexamining the progress of the existing body of the sciences.\nAs a preliminary to this undertaking, a survey of the\nhistory of the sciences was necessary. This, accordingly, I\nhave already performed; and the result of the labour thus\nundertaken has been laid before the public as a _History of\nthe Inductive Sciences_.\n\nIn that work I have endeavoured to trace the steps by which\nmen acquired each main portion of that knowledge on which\nthey now look with so much confidence and satisfaction. The\nevents which that History relates, the speculations and\ncontroversies {11} which are there described, and\ndiscussions of the same kind, far more extensive, which are\nthere omitted, must all be taken into our account at\npresent, as the prominent and standard examples of the\ncircumstances which attend the progress of knowledge. With\nso much of real historical fact before us, we may hope to\navoid such views of the processes of the human mind as are\ntoo partial and limited, or too vague and loose, or too\nabstract and unsubstantial, to represent fitly the real\nforms of discovery and of truth.\n\nOf former attempts, made with the same view of tracing the\nconditions of the progress of knowledge, that of Bacon is\nperhaps the most conspicuous: and his labours on this\nsubject were opened by his book on the _Advancement of\nLearning_, which contains, among other matter, a survey of\nthe then existing state of knowledge. But this review was\nundertaken rather with the object of ascertaining in what\nquarters future advances were to be hoped for, than of\nlearning by what means they were to be made. His examination\nof the domain of human knowledge was conducted rather with\nthe view of discovering what remained undone, than of\nfinding out how so much had been done. Bacon's survey was\nmade for the purpose of tracing the boundaries, rather than\nof detecting the principles of knowledge. 'I will now\nattempt,' he says[1\\I], 'to make a general and faithful\nperambulation of learning, with an inquiry what parts\nthereof lie fresh and waste, and not improved and converted\nby the industry of man; to the end that such a plot made and\nrecorded to memory, may both minister light to any public\ndesignation, and also serve to excite voluntary endeavours.'\nNor will it be foreign to our scheme also hereafter to\nexamine with a like purpose the frontier-line of man's\nintellectual estate. But the object of our perambulation in\nthe first place, is not so much to determine the extent of\nthe field, as the sources of its fertility. We would learn\nby what plan and rules {12} of culture, conspiring with the\nnative forces of the bounteous soil, those rich harvests\nhave been produced which fill our garners. Bacon's maxims,\non the other hand, respecting the mode in which he conceived\nthat knowledge was thenceforth to be cultivated, have little\nreference to the failures, still less to the successes,\nwhich are recorded in his Review of the learning of his\ntime. His precepts are connected with his historical views\nin a slight and unessential manner. His Philosophy of the\nSciences is not collected from the Sciences which are\nnoticed in his survey. Nor, in truth, could this, at the\ntime when he wrote, have easily been otherwise. At that\nperiod, scarce any branch of physics existed as a science,\nexcept Astronomy. The rules which Bacon gives for the\nconduct of scientific researches are obtained, as it were,\nby divination, from the contemplation of subjects with\nregard to which no sciences as yet were. His instances of\nsteps rightly or wrongly made in this path, are in a great\nmeasure cases of his own devising. He could not have\nexemplified his Aphorisms by references to treatises then\nextant, on the laws of nature; for the constant burden of\nhis exhortation is, that men up to his time had almost\nuniversally followed an erroneous course. And however we may\nadmire the sagacity with which he pointed the way along a\nbetter path, we have this great advantage over him;--that we\ncan interrogate the many travellers who since his time have\njourneyed on this road. At the present day, when we have\nunder our notice so many sciences, of such wide extent, so\nwell established; a Philosophy of the Sciences ought, it\nmust seem, to be founded, not upon conjecture, but upon an\nexamination of many instances;--should not consist of a few\nvague and unconnected maxims, difficult and doubtful in\ntheir application, but should form a system of which every\npart has been repeatedly confirmed and verified.\n\n[Note 1\\I: _Advancement of Learning_, b. i. p. 74.]\n\nThis accordingly it is the purpose of the present work to\nattempt. But I may further observe, that as my hope of\nmaking any progress in this undertaking is {13} founded upon\nthe design of keeping constantly in view the whole result of\nthe past history and present condition of science, I have\nalso been led to draw my lessons from my examples in a\nmanner more systematic and regular, as appears to me, than\nhas been done by preceding writers. Bacon, as I have just\nsaid, was led to his maxims for the promotion of knowledge\nby the sagacity of his own mind, with little or no aid from\nprevious examples. Succeeding philosophers may often have\ngathered useful instruction from the instances of scientific\ntruths and discoveries which they adduced, but their\nconclusions were drawn from their instances casually and\narbitrarily. They took for their moral any which the story\nmight suggest. But such a proceeding as this cannot suffice\nfor us, whose aim is to obtain a consistent body of\nphilosophy from a contemplation of the whole of Science and\nits History. For our purpose it is necessary to resolve\nscientific truths into their conditions and ingredients, in\norder that we may see in what manner each of these has been\nand is to be provided, in the cases which we may have to\nconsider. This accordingly is necessarily the first part of\nour task:--_to analyse Scientific Truth into its Elements_.\nThis attempt will occupy the earlier portion of the present\nwork; and will necessarily be somewhat long, and perhaps, in\nmany parts, abstruse and uninviting. The risk of such an\ninconvenience is inevitable; for the inquiry brings before\nus many of the most dark and entangled questions in which\nmen have at any time busied themselves. And even if these\ncan now be made clearer and plainer than of yore, still they\ncan be made so only by means of mental discipline and mental\neffort. Moreover this analysis of scientific truth into its\nelements contains much, both in its principles and in its\nresults, different from the doctrines most generally\nprevalent among us in recent times: but on that very account\nthis analysis is an essential part of the doctrines which I\nhave now to lay before the reader: and I must therefore\ncrave his indulgence towards any portion of it which may\nappear to him obscure or repulsive. {14}\n\nThere is another circumstance which may tend to make the\npresent work less pleasing than others on the same subject,\nin the nature of the examples of human knowledge to which I\nconfine myself; all my instances being, as I have said,\ntaken from the material sciences. For the truths belonging\nto these sciences are, for the most part, neither so\nfamiliar nor so interesting to the bulk of readers as those\ndoctrines which belong to some other subjects. Every general\nproposition concerning politics or morals at once stirs up\nan interest in men's bosoms, which makes them listen with\ncuriosity to the attempts to trace it to its origin and\nfoundation. Every rule of art or language brings before the\nmind of cultivated men subjects of familiar and agreeable\nthought, and is dwelt upon with pleasure for its own sake,\nas well as on account of the philosophical lessons which it\nmay convey. But the curiosity which regards the truths of\nphysics or chemistry, or even of physiology or astronomy, is\nof a more limited and less animated kind. Hence, in the mode\nof inquiry which I have prescribed to myself, the examples\nwhich I have to adduce will not amuse and relieve the\nreader's mind as much as they might do, if I could allow\nmyself to collect them from the whole field of human\nknowledge. They will have in them nothing to engage his\nfancy, or to warm his heart. I am compelled to detain the\nlistener in the chilly air of the external world, in order\nthat we may have the advantage of full daylight.\n\nBut although I cannot avoid this inconvenience, so far as it\nis one, I hope it will be recollected how great are the\nadvantages which we obtain by this restriction. We are thus\nenabled to draw all our conclusions from doctrines which are\nuniversally allowed to be eminently certain, clear, and\ndefinite. The portions of knowledge to which I refer are\nwell known, and well established among men. Their names are\nfamiliar, their assertions uncontested. Astronomy and\nGeology, Mechanics and Chemistry, Optics and Acoustics,\nBotany and Physiology, are each recognized as large and\nsubstantial collections of undoubted truths. Men are {15}\nwont to dwell with pride and triumph on the acquisitions of\nknowledge which have been made in each of these provinces;\nand to speak with confidence of the certainty of their\nresults. And all can easily learn in what repositories these\ntreasures of human knowledge are to be found. When,\ntherefore, we begin our inquiry from such examples, we\nproceed upon a solid foundation. With such a clear ground of\nconfidence, we shall not be met with general assertions of\nthe vagueness and uncertainty of human knowledge; with the\nquestion, What truth is, and How we are to recognize it;\nwith complaints concerning the hopelessness and\nunprofitableness of such researches. We have, at least, a\ndefinite problem before us. We have to examine the structure\nand scheme, not of a shapeless mass of incoherent materials,\nof which we doubt whether it be a ruin or a natural\nwilderness, but of a fair and lofty palace, still erect and\ntenanted, where hundreds of different apartments belong to a\ncommon plan, where every generation adds something to the\nextent and magnificence of the pile. The certainty and the\nconstant progress of science are things so unquestioned,\nthat we are at least engaged in an intelligible inquiry,\nwhen we are examining the grounds and nature of that\ncertainty, the causes and laws of that progress.\n\nTo this inquiry, then, we now proceed. And in entering upon\nthis task, however our plan or our principles may differ\nfrom those of the eminent philosophers who have endeavoured,\nin our own or in former times, to illustrate or enforce the\nphilosophy of science, we most willingly acknowledge them as\nin many things our leaders and teachers. Each reform must\ninvolve its own peculiar principles, and the result of our\nattempts, so far as they lead to a result, must be, in some\nrespects, different from those of former works. But we may\nstill share with the great writers who have treated this\nsubject before us, their spirit of hope and trust, their\nreverence for the dignity of the subject, their belief in\nthe vast powers and boundless destiny of man. And we may\nonce more venture to use the {16} words of hopeful\nexhortation, with which the greatest of those who have\ntrodden this path encouraged himself and his followers when\nhe set out upon his way.\n\n'Concerning ourselves we speak not; but as touching the\nmatter which we have in hand, this we ask;--that men deem it\nnot to be the setting up an Opinion, but the performing of a\nWork: and that they receive this as a certainty; that we are\nnot laying the foundations of any sect or doctrine, but of\nthe profit and dignity of mankind. Furthermore, that being\nwell disposed to what shall advantage themselves, and\nputting off factions and prejudices, they take common\ncounsel with us, to the end that being by these our aids and\nappliances freed and defended from wanderings and\nimpediments, they may lend their hands also to the labours\nwhich remain to be performed: and yet further, that they be\nof good hope; neither imagine to themselves this our Reform\nas something of infinite dimension, and beyond the grasp of\nmortal man, when in truth it is the end and true limit of\ninfinite errour; and is by no means unmindful of the\ncondition of mortality and humanity, not confiding that such\na thing can be carried to its perfect close in the space of\none single age, but assigning it as a task to a succession\nof generations.'\n\n[The Philosophy of the Inductive Sciences, according to our\nview, must be founded upon the History of such Sciences;\nwhich history we have attempted in a former work. The events\nof that history may be described generally as the rise of\nTheories out of Facts. But besides this, which we may term\nthe _external_ history of Theories, there is an internal\nhistory of Theories, namely, the series of steps by which\nthe human mind becomes capable of forming each Theory. Hence\nto complete the History of the Sciences as derived from\nFacts, we require a history of the Ideas by which such\nderivation has been made possible: and thus, the _First\nPart_ of our Philosophy must be a _History of Scientific\nIdeas_;--a labour no less historical than our former work,\nand concerned with the same events; but which has been\npurposely kept separate during the {17} composition, in\norder that it might be afterwards presented in a more\nsystematic form, which I have here attempted to do.\n\nScientific Ideas are the Conditions of the derivation of\nSciences from Facts: but can any method or methods be given\nby which such a Derivation can be ensured, or at least,\naided? Many such methods have been proposed; of which the\nmost celebrated is the _Novum Organon_ of Bacon, of which\nthe title was intended to imply that its scope goes much\nbeyond the _Organon_ of Aristotle. With the experience of\nthe formation of Science which the world has had since\nBacon's time, it does not appear presumptuous to suppose\nthat we can now improve or correct his methods; nor to term\nsuch an attempt _Novum Organon Renovatum_.\n\nThe Philosophy of the Inductive Sciences, then, contains\nthese two parts, _The History of Scientific Ideas_, and the\n_Novum Organon Renovatum_.]\n\n\n\n\n{{19}}\nTHE\nPHILOSOPHY\nOF THE\nINDUCTIVE SCIENCES.\n\n\nPART I.\n\nHISTORY OF SCIENTIFIC IDEAS.\n\n\n[We have just spoken of _Theories_ and _Facts_, of _Ideas_\nand _Facts_, and of _Inductive_ Sciences, which imply the\nopposition of _Induction_ and _Deduction_. The explanation\nof these antitheses must be the starting point of our\nPhilosophy.]\n\n\n[Knowledge grows, and] through the ages one increasing purpose runs,\nAnd the thoughts of men are widen'd with the process of the Suns.\n\n\n\n\nBOOK I.\n\n\nOF IDEAS IN GENERAL.\n\n\nQu\u00e6 adhuc inventa sunt in Scientiis, ea hujusmodi sunt ut\nNotionibus Vulgaribus fere subjaceant: ut vero ad interiora\net remotiora Natur\u00e6 penetretur, necesse est ut tam NOTIONES\nquam AXIOMATA magis cert\u00e2 et munit\u00e2 vi\u00e2 a particularibus\nabstrahantur; atque omnino melior et certior intellect\u00fbs\nadoperatio in usum veniat.\n\nBACON, _Nov. Org._, Lib. 1. Aphor. xviii.\n\n\n{{23}}\nBOOK I.\n\n\nOF IDEAS IN GENERAL.\n\n\nCHAPTER I.\n\nOF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY.\n\n\n_Sect._ 1.--_Thoughts and Things._\n\nIN order that we may do something towards determining the\nnature and conditions of human knowledge, (which I have\nalready stated as the purpose of this work,) I shall have to\nrefer to an antithesis or opposition, which is familiar and\ngenerally recognized, and in which the distinction of the\nthings opposed to each other is commonly considered very\nclear and plain. I shall have to attempt to make this\nopposition sharper and stronger than it is usually\nconceived, and yet to shew that the distinction is far from\nbeing so clear and definite as it is usually assumed to be:\nI shall have to point the contrast, yet shew that the things\nwhich are contrasted cannot be separated:--I must explain\nthat the antithesis is constant and essential, but yet that\nthere is no fixed and permanent line dividing its members. I\nmay thus appear, in different parts of my discussion, to be\nproceeding in opposite directions, but I hope that the\nreader who gives me a patient attention will see that both\nsteps lead to the point of view to which I wish to lead him.\n\nThe antithesis or opposition of which I speak is denoted,\nwith various modifications, by various pairs of terms: I\nshall endeavour to shew the connexion of these different\nmodes of expression, and I will begin with that form which\nis the simplest and most idiomatic. {24}\n\nThe simplest and most idiomatic expression of the antithesis\nto which I refer is that in which we oppose to each other\nTHINGS and THOUGHTS. The opposition is familiar and plain.\nOur thoughts are something which belongs to ourselves;\nsomething which takes place within us; they are what we\nthink; they are actions of our minds. Things, on the\ncontrary, are something different from ourselves and\nindependent of us; something which is without us; they\n_are_; we see them, touch them, and thus know that they\nexist; but we do not make them by seeing or touching them,\nas we make our _Thoughts_ by thinking them; we are passive,\nand _Things_ act upon our organs of perception.\n\nNow what I wish especially to remark is this: that in all\nhuman KNOWLEDGE both Thoughts and Things are concerned. In\nevery part of my knowledge there must be some _thing_ about\nwhich I know, and an internal act of _me_ who know. Thus, to\ntake simple yet definite parts of our knowledge, if I know\nthat a solar year consists of 365 days, or a lunar month of\n30 days, I know something about the sun or the moon; namely,\nthat those objects perform certain revolutions and go\nthrough certain changes, in those numbers of days; but I\ncount such numbers and conceive such revolutions and changes\nby acts of my own thoughts. And both these elements of my\nknowledge are indispensable. If there were not such external\nThings as the sun and the moon I could not have any\nknowledge of the progress of time as marked by them. And\nhowever regular were the motions of the sun and moon, if I\ncould not count their appearances and combine their changes\ninto a cycle, or if I could not understand this when done by\nother men, I could not know anything about a year or a\nmonth. In the former case I might be conceived as a human\nbeing, possessing the human powers of thinking and\nreckoning, but kept in a dark world with nothing to mark the\nprogress of existence. The latter is the case of brute\nanimals, which see the sun and moon, but do not know how\nmany days make a month or a year, because they have not\nhuman powers of thinking and reckoning. {25}\n\nThe two elements which are essential to our knowledge in the\nabove cases, are necessary to human knowledge in all cases.\nIn all cases, Knowledge implies a combination of Thoughts\nand Things. Without this combination, it would not be\nKnowledge. Without Thoughts, there could be no connexion;\nwithout Things, there could be no reality. Thoughts and\nThings are so intimately combined in our Knowledge, that we\ndo not look upon them as distinct. One single act of the\nmind involves them both; and their contrast disappears in\ntheir union.\n\nBut though Knowledge requires the union of these two\nelements, Philosophy requires the separation of them, in\norder that the nature and structure of Knowledge may be\nseen. Therefore I begin by considering this separation. And\nI now proceed to speak of another way of looking at the\nantithesis of which I have spoken; and which I may, for the\nreasons which I have just mentioned, call the FUNDAMENTAL\nANTITHESIS OF PHILOSOPHY.\n\n\n_Sect._ 2.--_Necessary and Experiential Truths._\n\nMOST persons are familiar with the distinction of\n_necessary_ and _contingent_ truths. The former kind are\nTruths which cannot but be true; as that 19 and 11 make\n30;--that parallelograms upon the same base and between the\nsame parallels are equal;--that all the angles in the same\nsegment of a circle are equal. The latter are Truths which\n_it happens_ (_contingit_) are true; but which, for anything\nwhich we can see, might have been otherwise; as that a lunar\nmonth contains 30 days, or that the stars revolve in circles\nround the pole. The latter kind of Truths are learnt by\nexperience, and hence we may call them _Truths of\nExperience_, or, for the sake of convenience, _Experiential_\nTruths, in contrast with Necessary Truths.\n\nGeometrical propositions are the most manifest examples of\nNecessary Truths. All persons who have read and understood\nthe elements of geometry, know that the propositions above\nstated (that parallelograms {26} upon the same base and\nbetween the same parallels are equal; that all the angles in\nthe same segment of a circle are equal,) are necessarily\ntrue; not only they are true, but they _must be_ true. The\nmeaning of the terms being understood, and the proof being\ngone through, the truth of the propositions must be assented\nto. We learn these propositions to be true by demonstrations\ndeduced from definitions and axioms; and when we have thus\nlearnt them, we see that they could not be otherwise. In the\nsame manner, the truths which concern numbers are necessary\ntruths: 19 and 11 not only _do_ make 30, but _must_ make\nthat number, and cannot make anything else. In the same\nmanner, it is a necessary truth that half the sum of two\nnumbers added to half their difference is equal to the\ngreater number.\n\nIt is easy to find examples of Experiential Truths;--\npropositions which we know to be true, but know by\nexperience only. We know, in this way, that salt will\ndissolve in water; that plants cannot live without light;--\nin short, we know in this way all that we do know in\nchemistry, physiology, and the material sciences in general.\nI take the _Sciences_ as my examples of human knowledge,\nrather than the common truths of daily life, or moral or\npolitical truths; because, though the latter are more\ngenerally interesting, the former are much more definite and\ncertain, and therefore better starting-points for our\nspeculations, as I have already said. And we may take\nelementary astronomical truths as the most familiar examples\nof Experiential Truths in the domain of science.\n\nWith these examples, the distinction of Necessary and\nExperiential Truths is, I hope, clear. The former kind, we\nsee to be true by thinking about them, and see that they\ncould not be otherwise. The latter kind, men could never\nhave discovered to be true without looking at them; and\nhaving so discovered them, still no one will pretend to say\nthey might not have been otherwise. For aught we can see,\nthe astronomical truths which express the motions and\nperiods of the sun, moon and stars, might have been\notherwise. If we had been placed in another part of the\nsolar system, our {27} experiential truths respecting days,\nyears, and the motions of the heavenly bodies, would have\nbeen other than they are, as we know from astronomy itself.\n\nIt is evident that this distinction of Necessary and\nExperiential Truths involves the same antithesis which we\nhave already considered;--the antithesis of Thoughts and\nThings. Necessary Truths are derived from our own Thoughts:\nExperiential truths are derived from our observation of\nThings about us. The opposition of Necessary and\nExperiential Truths is another aspect of the Fundamental\nAntithesis of Philosophy.\n\n\n_Sect._ 3.--_Deduction and Induction._\n\nI HAVE already stated that geometrical truths are\nestablished by demonstrations _deduced_ from definitions and\naxioms. The term _Deduction_ is specially applied to such a\ncourse of demonstration of truths from definitions and\naxioms. In the case of the parallelograms upon the same base\nand between the same parallels, we prove certain triangles\nto be equal, by supposing them placed so that their two\nbases have the same extremities; and hence, referring to an\nAxiom respecting straight lines, we infer that the bases\ncoincide. We combine these equal triangles with other equal\nspaces, and in this way make up both the one and the other\nof the parallelograms, in such a manner as to shew that they\nare equal. In this manner, going on step by step, deducing\nthe equality of the triangles from the axiom, and the\nequality of the parallelograms from that of the triangles,\nwe travel to the conclusion. And this process of successive\ndeduction is the scheme of all geometrical proof. We begin\nwith Definitions of the notions which we reason about, and\nwith Axioms, or self-evident truths, respecting these\nnotions; and we get, by reasoning from these, other truths\nwhich are demonstratively evident; and from these truths\nagain, others of the same kind, and so on. We begin with our\nown Thoughts, which supply us with Axioms to start from; and\nwe reason from these, till we come to propositions {28}\nwhich are applicable to the Things about us; as for\ninstance, the propositions respecting circles and spheres\napplicable to the motions of the heavenly bodies. This is\n_Deduction_, or _Deductive Reasoning_.\n\nExperiential truths are acquired in a very different way. In\norder to obtain such truths, we begin with Things. In order\nto learn how many days there are in a year, or in a lunar\nmonth, we must begin by observing the sun and the moon. We\nmust observe their changes day by day, and try to make the\ncycle of change fit into some notion of number which we\nsupply from our own Thoughts. We shall find that a cycle of\n30 days nearly will fit the changes of phase of the\nmoon;--that a cycle of 365 days nearly will fit the changes\nof daily motion of the sun. Or, to go on to experiential\ntruths of which the discovery comes within the limits of the\nhistory of science--we shall find (as Hipparchus found) that\nthe unequal motion of the sun among the stars, such as\nobservation shews it to be, may be fitly represented by the\nnotion of an _eccentric_;--a circle in which the sun has an\nequable annual motion, the spectator not being in the center\nof the circle. Again, in the same manner, at a later period,\nKepler started from more exact observations of the sun, and\ncompared them with a supposed motion in a certain ellipse;\nand was able to shew that, not a circle about an eccentric\npoint, but an ellipse, supplied the mode of conception which\ntruly agreed with the motion of the sun about the earth; or\nrather, as Copernicus had already shewn, of the earth about\nthe sun. In such cases, in which truths are obtained by\nbeginning from observation of external things and by finding\nsome notion with which the Things, as observed, agree, the\ntruths are said to be obtained by _Induction_. The process\nis an _Inductive Process_.\n\nThe contrast of the Deductive and Inductive process is\nobvious. In the former, we proceed at each step from general\ntruths to particular applications of them; in the latter,\nfrom particular observations to a general truth which\nincludes them. In the former case we may be said to reason\n_downwards_, in the latter case, {29} _upwards_; for general\nnotions are conceived as standing above particulars.\nNecessary truths are proved, like arithmetical sums, by\nadding together the portions of which they consist. An\ninductive truth is proved, like the guess which answers a\nriddle, by its agreeing with the facts described.\nDemonstration is irresistible in its effect on the belief,\nbut does not produce surprize, because all the steps to the\nconclusion are exhibited, before we arrive at the\nconclusion. Inductive inference is not demonstrative, but it\nis often more striking than demonstrative reasoning, because\nthe intermediate links between the particulars and the\ninference are not shewn. Deductive truths are the results of\nrelations among our own Thoughts. Inductive truths are\nrelations which we discern among existing Things; and thus,\nthis opposition of Deduction and Induction is again an\naspect of the Fundamental Antithesis already spoken of.\n\n\n_Sect._ 4.--_Theories and Facts._\n\nGENERAL experiential Truths, such as we have just spoken of,\nare called _Theories_, and the particular observations from\nwhich they are collected, and which they include and\nexplain, are called _Facts_. Thus Hipparchus's doctrine,\nthat the sun moves in an eccentric about the earth, is _his\nTheory_ of the Sun, or the _Eccentric Theory_. The doctrine\nof Kepler, that the Earth moves in an Ellipse about the Sun,\nis _Kepler's Theory_ of the Earth, the Elliptical Theory.\nNewton's doctrine that this elliptical motion of the Earth\nabout the Sun is produced and governed by the Sun's\nattraction upon the Earth, is the _Newtonian_ theory, the\n_Theory of Attraction_. Each of these Theories was accepted,\nbecause it included, connected and explained the _Facts_;\nthe Facts being, in the two former cases, the motions of the\nSun as observed; and in the other case, the elliptical\nmotion of the Earth as known by Kepler's Theory. This\nantithesis of _Theory_ and _Fact_ is included in what has\njust been said of Inductive Propositions. A Theory is an\nInductive Proposition, and the Facts {30} are the particular\nobservations from which, as I have said, such Propositions\nare inferred by Induction. The Antithesis of Theory and Fact\nimplies the fundamental Antithesis of Thoughts and Things;\nfor a Theory (that is, a true Theory) may be described as a\nThought which is contemplated distinct from Things and seen\nto agree with them; while a Fact is a combination of our\nThoughts with Things in so complete agreement that we do not\nregard them as separate.\n\nThus the antithesis of Theory and Fact involves the\nantithesis of Thoughts and Things, but is not identical with\nit. Facts involve Thoughts, for we know Facts only by\nthinking about them. The Fact that the year consists of 365\ndays; the Fact that the month consists of 30 days, cannot be\nknown to us, except we have the Thoughts of Time, Number and\nRecurrence. But these Thoughts are so familiar, that we have\nthe fact in our mind as a simple Thing without attending to\nthe Thought which it involves. When we mould our Thoughts\ninto a Theory, we consider the thought as distinct from the\nFacts; but yet, though distinct, not independent of them;\nfor it is a true Theory, only by including and agreeing with\nthe Facts.\n\n\n_Sect._ 5.--_Ideas and Sensations._\n\nWE have just seen that the antithesis of Theory and Fact,\nalthough it involves the antithesis of Thoughts and Things,\nis not identical with it. There are other modes of\nexpression also, which involve the same Fundamental\nAntithesis, more or less modified. Of these, the pair of\nwords which in their relations appear to separate the\nmembers of the antithesis most distinctly are _Ideas_ and\n_Sensations_. We see and hear and touch external things, and\nthus perceive them by our senses; but in perceiving them, we\nconnect the impressions of sense according to relations of\nspace, time, number, likeness, cause, &c. Now some at least\nof these kinds of connexion, as space, time, number, may be\ncontemplated distinct from the things to which they are\napplied; and so contemplated, I term them _Ideas_. And {31}\nthe other element, the impressions upon our senses which\nthey connect, are called _Sensations_.\n\nI term space, time, cause, &c., _Ideas_, because they are\ngeneral relations among our sensations, apprehended by an\nact of the mind, not by the senses simply. These relations\ninvolve something beyond what the senses alone could\nfurnish. By the sense of sight we see various shades and\ncolours and shapes before us, but the _outlines_ by which\nthey are separated into distinct objects of definite forms,\nare the work of the mind itself. And again, when we conceive\nvisible things, not only as surfaces of a certain form, but\nas _solid bodies_, placed at various distances in space, we\nagain exert an act of the mind upon them. When we see a body\nmove, we see it move in a path or _orbit_, but this orbit is\nnot itself seen; it is constructed by the mind. In like\nmanner when we see the motions of a needle towards a magnet,\nwe do not _see_ the attraction or force which produces the\neffects; but we infer the force, by having in our minds the\nIdea of Cause. Such acts of thought, such _Ideas_, enter\ninto our perceptions of external things.\n\nBut though our perceptions of external things involve some\nact of the mind, they must involve something else besides an\nact of the mind. If we must exercise an act of thought in\norder to see force exerted, or orbits described by bodies in\nmotion, or even in order to see bodies existing in space,\nand to distinguish one kind of object from another, still\nthe act of thought alone does not make the Bodies. There\nmust be something besides, _on which_ the thought is\nexerted. A colour, a form, a sound, are not produced by the\nmind, however they may be moulded, combined, and interpreted\nby our mental acts. A philosophical poet has spoken of\n All the world\n Of eye and ear, both what they half create,\n And what perceive.\nBut it is clear, that though they _half_ create, they do not\nwholly create: there must be an external world of colour and\nsound to give impressions to the eye and ear, as well as internal\npowers by which we perceive {32} what is offered to our organs.\nThe mind is in some way passive as well as active: there are\nobjects without as well as faculties within;--Sensations,\nas well as acts of Thought.\n\nIndeed this is so far generally acknowledged, that according\nto common apprehension, the mind is passive _rather_ than\nactive in acquiring the knowledge which it receives\nconcerning the material world. Its sensations are generally\nconsidered more distinct than its operations. The world\nwithout is held to be more clearly real than the faculties\nwithin. That there is something different from ourselves,\nsomething external to us, something independent of us,\nsomething which no act of our minds can make or can destroy,\nis held by all men to be at least as evident, as that our\nminds can exert any effectual process in modifying and\nappreciating the impressions made upon them. Most persons\nare more likely to doubt whether the mind be always actively\napplying Ideas to the objects which it perceives, than\nwhether it perceive them passively by means of Sensations.\n\nBut yet a little consideration will show us that an activity\nof the mind, and an activity according to certain Ideas, is\nrequisite in all our knowledge of external objects. We see\nobjects, of various solid forms, and at various distances\nfrom us. But we do not thus perceive them by sensation\nalone. Our visual impressions cannot, of themselves, convey\nto us a knowledge of solid form, or of distance from us.\nSuch knowledge is inferred from what we see:--inferred by\nconceiving the objects as existing in space, and by applying\nto them the Idea of Space. Again:--day after day passes,\ntill they make up a year: but we do not know that the days\nare 365, except we count them; and thus apply to them our\nIdea of Number. Again:--we see a needle drawn to a magnet:\nbut, in truth, the _drawing_ is what we cannot see. We see\nthe needle move, and infer the attraction, by applying to\nthe fact our Idea of Force, as the cause of motion.\nAgain:--we see two trees of different kinds; but we cannot\nknow that they are so, except by applying to them our Idea\nof the resemblance {33} and difference which makes kinds.\nAnd thus Ideas, as well as Sensations, necessarily enter\ninto all our knowledge of objects: and these two words\nexpress, perhaps more exactly than any of the pairs before\nmentioned, that Fundamental Antithesis, in the union of\nwhich, as I have said, all knowledge consists.\n\n\n_Sect._ 6.--_Reflexion and Sensation._\n\nIT will hereafter be my business to show what the Ideas are,\nwhich thus enter into our knowledge; and how each Idea has\nbeen, as a matter of historical fact, introduced into the\nScience to which it especially belongs. But before I proceed\nto do this, I will notice some other terms, besides the\nphrases already noticed, which have a reference, more or\nless direct, to the Fundamental Antithesis of Ideas and\nSensations. I will mention some of these, in order that if\nthey should come under the reader's notice, he may not be\nperplexed as to their bearing upon the view here presented\nto him.\n\nThe celebrated doctrine of Locke, that all our 'Ideas,'\n(that is, in his use of the word, all our objects of\nthinking,) come from Sensation or Reflexion, will naturally\noccur to the reader as connected with the antithesis of\nwhich I have been speaking. But there is a great difference\nbetween Locke's account of Sensation and Reflexion, and our\nview of Sensation and Ideas. He is speaking of the origin of\nour knowledge;--we, of its nature and composition. He is\ncontent to say that all the knowledge which we do not\nreceive directly by Sensation, we obtain by Reflex Acts of\nthe mind, which make up his Reflexion. But we hold that\nthere is no Sensation without an act of the mind, and that\nthe mind's activity is not only reflexly exerted upon\nitself, but directly upon objects, so as to perceive in them\nconnexions and relations which are not Sensations. He is\ncontent to put together, under the name of Reflexion,\neverything in our knowledge which is not Sensation: we are\nto attempt to analyze all that is not Sensation; not only to\nsay it consists of Ideas, but {34} to point out what those\nIdeas are, and to show the mode in which each of them enters\ninto our knowledge. His purpose was, to prove that there are\nno Ideas, except the reflex acts of the mind: our endeavour\nwill be to show that the acts of the mind, both direct and\nreflex, are governed by certain Laws, which may be\nconveniently termed Ideas. His procedure was, to deny that\nany knowledge could be derived from the mind alone: our\ncourse will be, to show that in every part of our most\ncertain and exact knowledge, those who have added to our\nknowledge in every age have referred to principles which the\nmind itself supplies. I do not say that my view is contrary\nto his: but it is altogether different from his. If I grant\nthat all our knowledge comes from Sensation and Reflexion,\nstill my task then is only begun; for I want further to\ndetermine, in each science, what portion comes, not from\nmere Sensation, but from those Ideas by the aid of which\neither Sensation or Reflexion can lead to Science.\n\nLocke's use of the word 'idea' is, as the reader will\nperceive, different from ours. He uses the word, as he says,\nwhich 'serves best to stand for whatsoever is the object of\nthe understanding when a man thinks.' 'I have used it,' he\nadds, 'to express whatever is meant by _phantasm_, _notion_,\n_species_, or whatever it is to which the mind can be\nemployed about in thinking.' It might be shown that this\nseparation of the _mind itself_ from the ideal _objects_\nabout which it is employed in thinking, may lead to very\nerroneous results. But it may suffice to observe that we use\nthe word _Ideas_, in the manner already explained, to\nexpress that element, supplied by the mind itself, which\nmust be combined with Sensation in order to produce\nknowledge. For us, Ideas are not Objects of Thought, but\nrather Laws of Thought. Ideas are not synonymous with\nNotions; they are Principles which give to our Notions\nwhatever they contain of truth. But our use of the term\n_Idea_ will be more fully explained hereafter. {35}\n\n\n_Sect._ 7.--_Subjective and Objective._\n\nTHE Fundamental Antithesis of Philosophy of which I have to\nspeak has been brought into great prominence in the writings\nof modern German philosophers, and has conspicuously formed\nthe basis of their systems. They have indicated this\nantithesis by the terms _subjective_ and _objective_.\nAccording to the technical language of old writers, a thing\nand its qualities are described as _subject_ and\n_attributes_; and thus a man's faculties and acts are\nattributes of which he is the _subject_. The mind is the\n_subject_ in which ideas inhere. Moreover, the man's\nfaculties and acts are employed upon external _objects_; and\nfrom objects all his sensations arise. Hence the part of a\nman's knowledge which belongs to his own mind, is\n_subjective_: that which flows in upon him from the world\nexternal to him, is _objective_. And as in man's\ncontemplation of nature, there is always some act of thought\nwhich depends upon himself, and some matter of thought which\nis independent of him, there is, in every part of his\nknowledge, a subjective and an objective element. The\ncombination of the two elements, the subjective or ideal,\nand the objective or observed, is necessary, in order to\ngive us any insight into the laws of nature. But different\npersons, according to their mental habits and constitution,\nmay be inclined to dwell by preference upon the one or the\nother of these two elements. It may perhaps interest the\nreader to see this difference of intellectual character\nillustrated in two eminent men of genius of modern times,\nG\u00f6the and Schiller.\n\nG\u00f6the himself gives us the account to which I refer, in his\nhistory of the progress of his speculations concerning the\nMetamorphosis of Plants; a mode of viewing their structure\nby which he explained, in a very striking and beautiful\nmanner, the relations of the different parts of a plant to\neach other; as has been narrated in the _History of the\nInductive Sciences_. G\u00f6the felt a delight in the passive\ncontemplation of nature, unmingled with the desire of\nreasoning and theorizing; a delight such as naturally\nbelongs to those poets who {36} merely embody the images\nwhich a fertile genius suggests, and do not mix with these\npictures, judgments and reflexions of their own. Schiller,\non the other hand, both by his own strong feeling of the\nvalue of a moral purpose in poetry, and by his adoption of a\nsystem of metaphysics in which the subjective element was\nmade very prominent, was well disposed to recognize fully\nthe authority of ideas over external impressions.\n\nG\u00f6the for a time felt a degree of estrangement towards\nSchiller, arising from this contrariety in their views and\ncharacters. But on one occasion they fell into discussion on\nthe study of natural history; and G\u00f6the endeavoured to\nimpress upon his companion his persuasion that nature was to\nbe considered, not as composed of detached and incoherent\nparts, but as active and alive, and unfolding herself in\neach portion, in virtue of principles which pervade the\nwhole. Schiller objected that no such view of the objects of\nnatural history had been pointed out by observation, the\nonly guide which the natural historians recommended; and was\ndisposed on this account to think the whole of their study\nnarrow and shallow. 'Upon this,' says G\u00f6the, 'I expounded to\nhim, in as lively a way as I could, the metamorphosis of\nplants, drawing on paper for him, as I proceeded, a diagram\nto represent that general form of a plant which shows itself\nin so many and so various transformations. Schiller attended\nand understood; and, accepting the explanation, he said,\n\"This is not observation, but an idea.\" I replied,' adds\nG\u00f6the, 'with some degree of irritation; for the point which\nseparated us was most luminously marked by this expression:\nbut I smothered my vexation, and merely said, \"I was happy\nto find that I had got ideas without knowing it; nay, that I\nsaw them before my eyes.\"' G\u00f6the then goes on to say, that\nhe had been grieved to the very soul by maxims promulgated\nby Schiller, that no observed fact ever could correspond\nwith an idea. Since he himself loved best to wander in the\ndomain of external observation, he had been led to look with\nrepugnance and hostility upon anything which professed to\ndepend upon ideas. 'Yet,' he {37} observes, 'it occurred to\nme that if my Observation was identical with his Idea, there\nmust be some common ground on which we might meet.' They\nwent on with their mutual explanations, and became intimate\nand lasting friends. 'And thus,' adds the poet, by means of\nthat mighty and interminable controversy between _object_\nand _subject_, we two concluded an alliance which remained\nunbroken, and produced much benefit to ourselves and others.'\n\nThe general diagram of a plant, of which G\u00f6the here speaks,\nmust have been a combination of lines and marks expressing\nthe relations of position and equivalence among the elements\nof vegetable forms, by which so many of their resemblances\nand differences may be explained. Such a symbol is not an\nIdea in that general sense in which we propose to use the\nterm, but is a particular modification of the general Ideas\nof symmetry, developement, and the like; and we shall\nhereafter see, according to the phraseology which we shall\nexplain in the next chapter, how such a diagram might\nexpress the _ideal conception_ of a plant.\n\nThe antithesis of _subjective_ and _objective_ is very\nfamiliar in the philosophical literature of Germany and\nFrance; nor is it uncommon in any age of our own literature.\nBut though efforts have recently been made to give currency\namong us to this phraseology, it has not been cordially\nreceived, and has been much complained of as not of obvious\nmeaning. Nor is the complaint without ground: for when we\nregard the mind as the _subject_ in which ideas inhere, it\nbecomes for us an _object_, and the antithesis vanishes. We\nare not so much accustomed to use _subject_ in this sense,\nas to make it a proper contrast to _object_. The combination\n'_ideal_ and _objective_,' would more readily convey to a\nmodern reader the opposition which is intended between the\nideas of the mind itself, and the objects which it\ncontemplates around it.\n\nTo the antitheses already noticed--Thoughts and Things;\nNecessary and Experiential Truths; Deduction and Induction;\nTheory and Fact; Ideas and Sensations; Reflexion and\nSensation; Subjective and {38} Objective; we may add others,\nby which distinctions depending more or less upon the\nfundamental antithesis have been denoted. Thus we speak of\nthe _internal_ and _external_ sources of our knowledge; of\nthe world _within_ and the world _without_ us; of _Man_ and\n_Nature_. Some of the more recent metaphysical writers of\nGermany have divided the universe into the _Me_ and _Not-me_\n(Ich and Nicht-ich). Upon such phraseology we may observe,\nthat to have the fundamental antithesis of which we speak\nreally understood, is of the highest consequence to\nphilosophy, but that little appears to be gained by\nexpressing it in any novel manner. The most weighty part of\nthe philosopher's task is to analyze the operations of the\nmind; and in this task, it can aid us but little to call it,\ninstead of the _mind_, the _subject_, or the _me_.\n\n\n_Sect._ 8.--_Matter and Form._\n\nTHERE are some other ways of expressing, or rather of\nillustrating, the fundamental antithesis, which I may\nbriefly notice. The antithesis has been at different times\npresented by means of various images. One of the most\nancient of these, and one which is still very instructive,\nis that which speaks of Sensations as the _Matter_, and\nIdeas as the _Form_, of our knowledge; just as ivory is the\nmatter, and a cube the form, of a die. This comparison has\nthe advantage of showing that two elements of an antithesis\nwhich cannot be separated in fact, may yet be advantageously\nseparated in our reasonings. For Matter and Form cannot by\nany means be detached from each other. All matter must have\nsome form; all form must be the form of some material thing.\nIf the ivory be not a cube, it must have a spherical or some\nother form. And the cube, in order to be a cube, must be of\nsome material;--if not of ivory, of wood, or stone, for\ninstance, A figure without matter is merely a geometrical\nconception;--a modification of the idea of space. Matter\nwithout figure is a mere abstract term;--a supposed union of\ncertain sensible qualities which, so insulated {39} from\nothers, cannot exist. Yet the distinction of Matter and Form\nis real; and, as a subject of contemplation, clear and\nplain. Nor is the distinction by any means useless. The\nspeculations which treat of the two subjects, Matter and\nFigure, are very different. Matter is the subject of the\nsciences of Mechanics and Chemistry; Figure, of Geometry.\nThese two classes of Sciences have quite different sets of\nprinciples. If we refuse to consider the Matter and the Form\nof bodies separately, because we cannot exhibit Matter and\nForm separately, we shut the door to all philosophy on such\nsubjects. In like manner, though Sensations and Ideas are\nnecessarily united in all our knowledge, they can be\nconsidered as distinct; and this distinction is the basis of\nall philosophy concerning knowledge.\n\nThis illustration of the relation of Ideas and Sensations\nmay enable us to estimate a doctrine which has been put\nforwards at various times. In a certain school of\nspeculators there has existed a disposition to derive all\nour Ideas from our Sensations, the term _Idea_, being, in\nthis school, used in its wider sense, so as to include all\nmodifications and limitations of our Fundamental Ideas. The\ndoctrines of this school have been summarily expressed by\nsaying that 'Every Idea is a transformed Sensation.' Now,\neven supposing this assertion to be exactly true, we easily\nsee, from what has been said, how little we are likely to\nanswer the ends of philosophy by putting forward such a\nmaxim as one of primary importance. For we might say, in\nlike manner, that every statue is but a transformed block of\nmarble, or every edifice but a collection of transformed\nstones. But what would these assertions avail us, if our\nobject were to trace the rules of art by which beautiful\nstatues were formed, or great works of architecture erected?\nThe question naturally occurs, What is the nature, the\nprinciple, the law of this Transformation? In what faculty\nresides the transforming power? What train of ideas of\nbeauty, and symmetry, and stability, in the mind of the\nstatuary or the architect, has produced those great works\nwhich {40} mankind look upon as among their most valuable\npossessions;--the Apollo of the Belvidere, the Parthenon,\nthe Cathedral of Cologne? When this is what we want to know,\nhow are we helped by learning that the Apollo is of Parian\nmarble, or the Cathedral of basaltic stone? We must know\nmuch more than this, in order to acquire any insight into\nthe principles of statuary or of architecture. In like\nmanner, in order that we may make any progress in the\nphilosophy of knowledge, which is our purpose, we must\nendeavour to learn something further respecting ideas than\nthat they are transformed sensations, even if they were this.\n\nBut, in reality, the assertion that our ideas are\ntransformed sensations, is erroneous as well as frivolous.\nFor it conveys, and is intended to convey, the opinion that\nour sensations have one form which properly belongs to them;\nand that, in order to become ideas, they are converted into\nsome other form. But the truth is, that our sensations, of\nthemselves, without some act of the mind, such as involves\nwhat we have termed an Idea, have no form. We cannot see one\nobject without the idea of space; we cannot see two without\nthe idea of resemblance or difference; and space and\ndifference are not sensations. Thus, if we are to employ the\nmetaphor of Matter and Form, which is implied in the\nexpression to which I have referred, our sensations, from\ntheir first reception, have their Form not _changed_, but\n_given_ by our Ideas. Without the relations of thought which\nwe here term _Ideas_, the sensations are matter without\nform. Matter without form cannot exist: and in like manner\nsensations cannot become perceptions of objects, without\nsome formative power of the mind. By the very act of being\nreceived as perceptions, they have a formative power\nexercised upon them, the operation of which might be\nexpressed, by speaking of them, not as _transformed_, but\nsimply as _formed_;--as invested with form, instead of being\nthe mere formless material of perception. The word _inform_,\naccording to its Latin etymology, at first implied this\nprocess by which matter is {41} invested with form. Thus\nVirgil[1\\1] speaks of the thunderbolt as _informed_ by the\nhands of Brontes, and Steropes, and Pyracmon. And Dryden\nintroduces the word in another place:--\n Let others better mould the running mass\n Of metals, or _inform_ the breathing brass.\nEven in this use of the word, the form is something superior\nto the brute manner, and gives it a new significance and\npurpose. And hence the term is again used to denote the\neffect produced by an intelligent principle of a still\nhigher kind:--\n . . . . He _informed_\n This ill-shaped body with a daring soul.\nAnd finally even the soul itself, in its original condition,\nis looked upon as matter, when viewed with reference to\neducation and knowledge, by which it is afterwards moulded;\nand hence these are, in our language, termed _information_.\nIf we confine ourselves to the first of these three uses of\nthe term, we may correct the erroneous opinion of which we\nhave just been speaking, and retain the metaphor by which it\nis expressed, by saying, that ideas are not _transformed_,\nbut _informed_ sensations.\n\n[Note 1\\1: Ferrum exercebant vasto Cyclopes in Antro\nBrontesque Steropesque et nudus membra Pyracmon;\nHis informatum manibus, jam parte polita\nFulmen erat.--_\u00c6n._ viii. 424.]\n\n\n_Sect._ 9.--_Man the Interpreter of Nature._\n\nTHERE is another image by which writers have represented the\nacts of thought through which knowledge is obtained from the\nobservation of the external world. Nature is the Book, and\nMan is the _Interpreter_. The facts of the external world\nare marks, in which man discovers a meaning, and so reads\nthem. Man is the Interpreter of Nature, and Science is the\nright Interpretation. And this image also is, in many\nrespects, {42} instructive. It exhibits to us the necessity\nof both elements;--the marks which man has to look at, and\nthe knowledge of the alphabet and language which he must\npossess and apply before he can find any meaning in what he\nsees. Moreover this image presents to us, as the ideal\nelement, an activity of the mind of that very kind which we\nwish to point out. Indeed the illustration is rather an\nexample than a comparison of the composition of our\nknowledge. The letters and symbols which are presented to\nthe Interpreter are really objects of sensation: the notion\nof letters as signs of words, the notion of connexions among\nwords by which they have meaning, really are among our\nIdeas;--_Signs_ and _Meaning_ are Ideas, supplied by the\nmind, and added to all that sensation can disclose in any\ncollection of visible marks. The Sciences are not\nfiguratively, but really, Interpretations of Nature. But\nthis image, whether taken as example or comparison, may\nserve to show both the opposite character of the two\nelements of knowledge, and their necessary combination, in\norder that there may be knowledge.\n\nThis illustration may also serve to explain another point in\nthe conditions of human knowledge which we shall have to\nnotice:--namely, the very different degrees in which, in\ndifferent cases, we are conscious of the mental act by which\nour sensations are converted into knowledge. For the same\ndifference occurs in reading an inscription. If the\ninscription were entire and plain, in a language with which\nwe were familiar, we should be unconscious of any mental act\nin reading it. We should seem to collect its meaning by the\nsight alone. But if we had to decipher an ancient\ninscription, of which only imperfect marks remained, with a\nfew entire letters among them, we should probably make\nseveral suppositions as to the mode of reading it, before we\nfound any mode which was quite successful; and thus, our\nguesses, being separate from the observed facts, and at\nfirst not fully in agreement with them, we should be clearly\naware that the conjectured meaning, on the one hand, and the\nobserved marks on the other, were distinct things, though\nthese {43} two things would become united as elements of one\nact of knowledge when we had hit upon the right conjecture.\n\n\n_Sect._ 10.--_The Fundamental Antithesis inseparable._\n\nTHE illustration just referred to, as well as other ways of\nconsidering the subject, may help us to get over a\ndifficulty which at first sight appears perplexing. We have\nspoken of the common opposition of _Theory_ and _Fact_ as\nimportant, and as involving what we have called the\nFundamental Antithesis of Philosophy. But after all, it may\nbe asked, Is this distinction of Theory and Fact really\ntenable? Is it not often difficult to say whether a special\npart of our knowledge is a Fact or a Theory? Is it a Fact or\na Theory that the stars revolve round the pole? Is it a Fact\nor a Theory that the earth is a globe revolving on its axis?\nIs it a Fact or a Theory that the earth travels in an\nellipse round the sun? Is it a Fact or a Theory that the sun\nattracts the earth? Is it a Fact or a Theory that the\nloadstone attracts the needle? In all these cases, probably\nsome persons would answer one way, and some persons the\nother. There are many persons by whom the doctrine of the\nglobular form of the earth, the doctrine of the earth's\nelliptical orbit, the doctrine of the sun's attraction on\nthe earth, would be called _theories_, even if they allowed\nthem to be true theories. But yet if each of these\npropositions be true, is it not a _fact_? And even with\nregard to the simpler facts, as the motion of the stars\nround the pole, although this may be a Fact to one who has\nwatched and measured the motions of the stars, one who has\nnot done this, and who has only carelessly looked at these\nstars from time to time, may naturally speak of the circles\nwhich the astronomer makes them describe as Theories. It\nwould seem, then, that we cannot in such cases expect\ngeneral assent, if we say, _This is a Fact and not a\nTheory_, or _This is a Theory and not a Fact_. And the same\nis true in a vast range of cases. It would seem, therefore,\nthat we cannot rest any reasoning upon this distinction of\nTheory {44} and Fact; and we cannot avoid asking whether\nthere is any real distinction in this antithesis, and if so,\nwhat it is.\n\nTo this I reply: the distinction between Theory (that is,\ntrue Theory) and Fact, is this: that in Theory the Ideas are\nconsidered as distinct from the Facts: in Facts, though\nIdeas may be involved, they are not, in our apprehension,\nseparated from the sensations. In a Fact, the Ideas are\napplied so readily and familiarly, and incorporated with the\nsensations so entirely, that we do not see _them_, we see\n_through them_. A person who carefully notes the motion of a\nstar all night, sees the circle which it describes, as he\nsees the star, though the circle is, really, a result of his\nown Ideas. A person who has in his mind the measures of\ndifferent lines and countries on the earth's surface, and\nwho can put them, together into one conception, finds that\nthey can make no figure but a globular one: to him, the\nearth's globular form is a Fact, as much as the square form\nof his chamber. A person to whom the grounds of believing\nthe earth to travel round the sun are as familiar as the\ngrounds for believing the movements of the mail-coaches in\nthis country, looks upon the former event as a Fact, just as\nhe looks upon the latter events as Facts. And a person who,\nknowing the Fact of the earth's annual motion, refers it\ndistinctly to its mechanical cause, conceives the sun's\nattraction as a Fact, just as he conceives as a Fact, the\naction of the wind which turns the sails of a mill. He\ncannot _see_ the force in either case; he supplies it out of\nhis own Ideas. And thus, a true Theory is a Fact; a Fact is\na familiar Theory. That which is a Fact under one aspect, is\na Theory under another. The most recondite Theories when\nfirmly established are Facts: the simplest Facts involve\nsomething of the nature of Theory. Theory and Fact\ncorrespond, in a certain degree, with Ideas and Sensations,\nas to the nature of their opposition. But the Facts are\nFacts, so far as the Ideas have been combined with the\nSensations and absorbed in them: the Theories are Theories,\nso far as the Ideas are kept distinct from the Sensations,\nand so far as it is {45} considered still a question whether\nthose can be made to agree with these.\n\nWe may, as I have said, illustrate this matter by\nconsidering man as _interpreting_ the phenomena which he\nsees. He often interprets without being aware that he does\nso. Thus when we see the needle move towards the magnet, we\nassert that the magnet exercises an attractive force on the\nneedle. But it is only by an interpretative act of our own\nminds that we ascribe this motion to attraction. That, in\nthis case, a force is exerted--something of the nature of\nthe pull which we could apply by our own volition--is our\ninterpretation of the phenomena; although we may be\nconscious of the act of interpretation, and may then regard\nthe attraction as a Fact.\n\nNor is it in such cases only that we interpret phenomena in\nour own way, without being conscious of what we do. We see a\ntree at a distance, and judge it to be a chestnut or a lime;\nyet this is only an inference from the colour or form of the\nmass according to preconceived classifications of our own.\nOur lives are full of such unconscious interpretations. The\nfarmer recognizes a good or a bad soil; the artist a picture\nof a favourite master; the geologist a rock of a known\nlocality, as we recognize the faces and voices of our\nfriends; that is, by judgments formed on what we see and\nhear; but judgments in which we do not analyze the steps, or\ndistinguish the inference from the appearance. And in these\nmixtures of observation and inference, we speak of the\njudgment thus formed, as a Fact directly observed.\n\nEven in the case in which our perceptions appear to be most\ndirect, and least to involve any interpretations of our\nown,--in the simple process of seeing,--who does not know\nhow much we, by an act of the mind, add to that which our\nsenses receive? Does any one fancy that he sees a solid\ncube? It is easy to show that the solidity of the figure,\nthe relative position of its faces and edges to each other,\nare inferences of the spectator; no more conveyed to his\nconviction by the eye alone, than they would be if he were\nlooking at {46} a painted representation of a cube. The\nscene of nature is a picture without depth of substance, no\nless than the scene of art; and in the one case as in the\nother, it is the mind which, by an act of its own, discovers\nthat colour and shape denote distance and solidity. Most men\nare unconscious of this perpetual habit of reading the\nlanguage of the external world, and translating as they\nread. The draughtsman, indeed, is compelled, for his\npurposes, to return back in thought from the solid bodies\nwhich he has inferred, to the shapes of surface which he\nreally sees. He knows that there is a mask of theory over\nthe whole face of nature, if it be _theory_ to infer more\nthan we _see_. But other men, unaware of this masquerade,\nhold it to be a fact that they see cubes and spheres,\nspacious apartments and winding avenues. And these things\nare facts to them, because they are unconscious of the\nmental operation by which they have penetrated nature's\ndisguise.\n\nAnd thus, we still have an intelligible distinction of Fact\nand Theory, if we consider Theory as a conscious, and Fact\nas an unconscious inference, from the phenomena which are\npresented to our senses.\n\nBut still, Theory and Fact, Inference and Perception,\nReasoning and Observation, are antitheses in none of which\ncan we separate the two members by any fixed and definite line.\n\nEven the simplest terms by which the antithesis is expressed\ncannot be separated. Ideas and Sensations, Thoughts and\nThings, Subject and Object, cannot in any case be applied\nabsolutely and exclusively. Our Sensations require Ideas to\nbind them together, namely, Ideas of space, time, number,\nand the like. If not so bound together, Sensations do not\ngive us any apprehension of Things or Objects. All Things,\nall Objects, must exist in space and in time--must be one or\nmany. Now space, time, number, are not Sensations or Things.\nThey are something different from, and opposed to Sensations\nand Things. We have termed them Ideas. It may be said they\nare _Relations_ of Things, or of Sensations. But granting\nthis form of expression, still a _Relation_ is not a Thing\nor a {47} Sensation; and therefore we must still have\nanother and opposite element, along with our Sensations. And\nyet, though we have thus these two elements in every act of\nperception, we cannot designate any portion of the act as\nabsolutely and exclusively belonging to one of the elements.\nPerception involves Sensation, along with Ideas of time,\nspace, and the like; or, if any one prefers the expression,\nwe may say, Perception involves Sensations along with the\napprehension of Relations. Perception is Sensation, along\nwith such Ideas as make Sensation into an apprehension of\nThings or Objects.\n\nAnd as Perception of Objects implies Ideas,--as Observation\nimplies Reasoning;--so, on the other hand, Ideas cannot\nexist where Sensation has not been; Reasoning cannot go on\nwhen there has not been previous Observation. This is\nevident from the necessary order of developement of the\nhuman faculties. Sensation necessarily exists from the first\nmoments of our existence, and is constantly at work.\nObservation begins before we can suppose the existence of\nany Reasoning which is not involved in Observation. Hence,\nat whatever period we consider our Ideas, we must consider\nthem as having been already engaged in connecting our\nSensations, and as having been modified by this employment.\nBy being so employed, our Ideas are unfolded and defined;\nand such developement and definition cannot be separated\nfrom the Ideas themselves. We cannot conceive space, without\nboundaries or forms; now Forms involve Sensations. We cannot\nconceive time, without events which mark the course of time;\nbut events involve Sensations. We cannot conceive number,\nwithout conceiving things which are numbered; and Things\nimply sensations. And the forms, things, events, which are\nthus implied in our Ideas, having been the objects of\nSensation constantly in every part of our life, have\nmodified, unfolded, and fixed our Ideas, to an extent which\nwe cannot estimate, but which we must suppose to be\nessential to the processes which at present go on in our\nminds. We cannot say that Objects create Ideas; for to\nperceive Objects we must already have Ideas. But we may {48}\nsay, that Objects and the constant Perception of Objects\nhave so far modified our Ideas, that we cannot, even in\nthought, separate our Ideas from the perception of Objects.\n\nWe cannot say of any Ideas, as of the Idea of space, or\ntime, or number, that they are absolutely and exclusively\nIdeas. We cannot conceive what space, or time, or number,\nwould be in our minds, if we had never perceived any Thing\nor Things in space or time. We cannot conceive ourselves in\nsuch a condition as never to have perceived any Thing or\nThings in space or time. But, on the other hand, just as\nlittle can we conceive ourselves becoming acquainted with\nspace and time or numbers as objects of Sensation. We cannot\nreason without having the operations of our minds affected\nby previous Sensations; but we cannot conceive Reasoning to\nbe merely a series of Sensations. In order to be used in\nReasoning, Sensation must become Observation; and, as we\nhave seen, Observation already involves Reasoning. In order\nto be connected by our Ideas, Sensations must be Things or\nObjects, and Things or Objects already include Ideas. And\nthus, none of the terms by which the fundamental antithesis\nis expressed can be absolutely and exclusively applied.\n\nI will make a remark suggested by the views which have thus\nbeen presented. Since, as we have just seen, none of the\nterms which express the fundamental antithesis can be\napplied absolutely and exclusively, the absolute application\nof the antithesis in any particular case can never be a\nconclusive or immoveable principle. This remark is the more\nnecessary to be borne in mind, as the terms of this\nantithesis are often used in a vehement and peremptory\nmanner. Thus we are often told that such a thing is _a\nFact_; A FACT and not a Theory, with all the emphasis which,\nin speaking or writing, tone or italics or capitals can\ngive. We see from what has been said, that when this is\nurged, before we can estimate the truth, or the value of the\nassertion, we must ask to whom is it a Fact? what habits of\nthought, what previous information, what Ideas does it\nimply, to conceive the Fact as a Fact? {49} Does not the\napprehension of the Fact imply assumptions which may with\nequal justice be called Theory, and which are perhaps false\nTheory? in which case, the Fact is no Fact. Did not the\nancients assert it as a Fact, that the earth stood still,\nand the stars moved? and can any Fact have stronger apparent\nevidence to justify persons in asserting it emphatically\nthan this had?\n\nThese remarks are by no means urged in order to show that no\nFact can be certainly known to be true; but only, to show\nthat no Fact can be certainly shown to be a Fact, merely by\ncalling it a Fact, however emphatically. There is by no\nmeans any ground of general skepticism with regard to truth,\ninvolved in the doctrine of the necessary combination of two\nelements in all our knowledge. On the contrary, Ideas are\nrequisite to the essence, and Things to the reality of our\nknowledge in every case. The proportions of Geometry and\nArithmetic are examples of knowledge respecting our Ideas of\nspace and number, with regard to which there is no room for\ndoubt. The doctrines of Astronomy are examples of truths not\nless certain respecting the Facts of the external world.\n\n\n_Sect._ 11.--_Successive Generalization._\n\nIN the preceding pages we have been led to the doctrine,\nthat though, in the Antithesis of Theory and Fact, there is\ninvolved an essential opposition; namely the opposition of\nthe thoughts within us and the phenomena without us; yet\nthat we cannot distinguish and define the members of this\nantithesis separately. Theories become Facts, by becoming\ncertain and familiar: and thus, as our knowledge becomes\nmore sure and more extensive, we are constantly transferring\nto the class of facts, opinions which were at first regarded\nas theories.\n\nNow we have further to remark, that in the progress of human\nknowledge respecting any branch of speculation, there may be\nseveral such steps in succession, each depending upon and\nincluding the preceding. {50} The theoretical views which\none generation of discoverers establishes, become the facts\nfrom which the next generation advances to new theories. As\nmen rise from the particular to the general, so, in the same\nmanner, they rise from what is general to what is more\ngeneral. Each induction supplies the materials of fresh\ninductions; each generalization, with all that it embraces\nin its circle, may be found to be but one of many circles,\ncomprehended within the circuit of some wider\ngeneralization.\n\nThis remark has already been made, and illustrated, in the\n_History of the Inductive Sciences_[2\\1]; and, in truth, the\nwhole of the history of science is full of suggestions and\nexemplifications of this course of things. It may be\nconvenient, however, to select a few instances which may\nfurther explain and confirm this view of the progress of\nscientific knowledge.\n\n[Note 2\\1: _Hist. Inductive Sciences_, b. vii. c. ii. sect. 5.]\n\nThe most conspicuous instance of this succession is to be\nfound in that science which has been progressive from the\nbeginning of the world to our own times, and which exhibits\nby far the richest collection of successive discoveries: I\nmean Astronomy. It is easy to see that each of these\nsuccessive discoveries depended on those antecedently made,\nand that in each, the truths which were the highest point of\nthe knowledge of one age were the fundamental basis of the\nefforts of the age which came next. Thus we find, in the\ndays of Greek discovery, Hipparchus and Ptolemy combining\nand explaining the particular _facts_ of the motion of the\nsun, moon, and planets, by means of the _theory_ of\nepicycles and eccentrics;--a highly important step, which\ngave an intelligible connexion and rule to the motions of\neach of these luminaries. When these cycles and epicycles,\nthus truly representing the apparent motions of the heavenly\nbodies, had accumulated to an inconvenient amount, by the\ndiscovery of many inequalities in the observed motions,\nCopernicus showed that their effects might all be more\nsimply included, by making the sun the center of motion of\nthe planets, instead of {51} the earth. But in this new\nview, he still retained the epicycles and eccentrics which\ngoverned the motion of each body. Tycho Brahe's\nobservations, and Kepler's calculations, showed that,\nbesides the vast number of facts which the epicyclical\ntheory could account for, there were some which it would not\nexactly include, and Kepler was led to the persuasion that\nthe planets move in ellipses. But this view of motion was at\nfirst conceived by Kepler as a modification of the\nconception of epicycles. On one occasion he blames himself\nfor not sooner seeing that such a modification was possible.\n'What an absurdity on my part!' he cries[3\\1]; 'as if\nlibration in the diameter of the epicycle might not come to\nthe same thing as motion in the ellipse.' But again;\nKepler's _laws_ of the elliptical motion of the planets were\nestablished; and these laws immediately became the _facts_\non which the mathematicians had to found their mechanical\ntheories. From these facts, Newton, as we have related,\nproved that the central force of the sun retains the planets\nin their orbits, according to the law of the inverse square\nof the distance. The same _law_ was shown to prevail in the\ngravitation of the earth. It was shown, too, by induction\nfrom the motions of Jupiter and Saturn, that the planets\nattract each other; by calculations from the figure of the\nearth, that the parts of the earth attract each other; and,\nby considering the course of the tides, that the sun and\nmoon attract the waters of the ocean. And all these curious\ndiscoveries being established as _facts_, the subject was\nready for another step of generalization. By an unparalleled\nrapidity in the progress of discovery in this case, not only\nwere all the inductions which we have first mentioned made\nby one individual, but the new advance, the higher flight,\nthe closing victory, fell to the lot of the same\nextraordinary person.\n\n[Note 3\\1: _Hist. Inductive Sciences_, b. v. c. iv. sect. 3.]\n\nThe attraction of the sun upon the planets, of the moon upon\nthe earth, of the planets on each other, of the parts of the\nearth on themselves, of the sun and {52} moon upon the\nocean;--all these truths, each of itself a great discovery,\nwere included by Newton in the higher _generalization_, of\nthe universal gravitation of matter, by which each particle\nis drawn to every other according to the law of the inverse\nsquare: and thus this long advance from discovery to\ndiscovery, from truths to truths, each justly admired when\nnew, and then rightly used as old, was closed in a worthy\nand consistent manner, by a truth which is the most worthy\nadmiration, because it includes all the researches of\npreceding ages of Astronomy.\n\nWe may take another example of a succession of this kind\nfrom the history of a science, which, though it has made\nwonderful advances, has not yet reached its goal, as\nphysical astronomy appears to have done, but seems to have\nbefore it a long prospect of future progress. I now refer to\nChemistry, in which I shall try to point out how the\npreceding discoveries afforded the materials of the\nsucceeding; although this subordination and connexion is, in\nthis case, less familiar to men's minds than in Astronomy,\nand is, perhaps, more difficult to present in a clear and\ndefinite shape. Sylvius saw, in the facts which occur, when\nan acid and an alkali are brought together, the evidence\nthat they neutralize each other. But cases of\nneutralization, and acidification, and many other effects of\nmixture of the ingredients of bodies, being thus viewed as\n_facts_, had an aspect of unity and law given them by\nGeoffroy and Bergman[4\\1], who introduced the _conception_\nof the Chemical Affinity or Elective Attraction, by which\ncertain elements select other elements, as if by preference.\nThat combustion, whether a chemical union or a chemical\nseparation of ingredients, is of the same nature with\nacidification, was the doctrine of Beccher and Stahl, and\nwas soon established as a truth which must form a part of\nevery succeeding physical theory. That the rules of affinity\nand chemical composition may include gaseous elements, was\nestablished by Black and Cavendish. And all these truths,\nthus brought to light by {53} chemical\ndiscoverers,--affinity, the identity of acidification and\ncombustion, the importance of gaseous elements,--along with\nall the facts respecting the weight of ingredients and\ncompounds which the balance disclosed,--were taken up,\nconnected, and included as _particulars_ in the oxygen\n_theory_ of Lavoisier. Again, the results of this theory,\nand the quantity of the several ingredients which entered\ninto each compound--(such results, for the most part, being\nnow no longer mere theoretical speculations, but recognized\nfacts)--were the _particulars_ from which Dalton derived\nthat wide law of chemical combination which we term the\nAtomic _Theory_. And this law, soon generally accepted among\nchemists, is already in its turn become one of the _facts_\nincluded in Faraday's _Theory_ of the identity of Chemical\nAffinity and Electric Attraction.\n\n[Note 4\\1: _Hist. Inductive Sciences_, b. xiv. c. iii.]\n\nIt is unnecessary to give further exemplifications of this\nconstant ascent from one step to a higher; this perpetual\nconversion of true theories into the materials of other and\nwider theories. It will hereafter be our business to\nexhibit, in a more full and formal manner, the mode in which\nthis principle determines the whole scheme and structure of\nall the most exact sciences. And thus, beginning with the\nfacts of sense, we gradually climb to the highest forms of\nhuman knowledge, and obtain from experience and observation\na vast collection of the most wide and elevated truths.\n\nThere are, however, truths of a very different kind, to\nwhich we must turn our attention, in order to pursue our\nresearches respecting the nature and grounds of our\nknowledge. But before we do this, we must notice one more\nfeature in that progress of science which we have already in\npart described.\n\n\n\n{{54}}\nCHAPTER II.\n\nOF TECHNICAL TERMS.\n\n\n1. IT has already been stated that we gather knowledge from\nthe external world, when we are able to apply, to the facts\nwhich we observe, some ideal conception, which gives unity\nand connexion to multiplied and separate perceptions. We\nhave also shown that our conceptions, thus verified by\nfacts, may themselves be united and connected by a new bond\nof the same nature; and that man may thus have to pursue his\nway from truth to truth through a long progression of\ndiscoveries, each resting on the preceding, and rising above it.\n\nEach of these steps, in succession, is recorded, fixed, and\nmade available, by some peculiar form of words; and such\nwords, thus rendered precise in their meaning, and\nappropriated to the service of science, we may call\n_Technical Terms_. It is in a great measure by inventing\nsuch Terms that men not only best express the discoveries\nthey have made, but also enable their followers to become so\nfamiliar with these discoveries, and to possess them so\nthoroughly, that they can readily use them in advancing to\nulterior generalizations.\n\nMost of our ideal conceptions are described by exact and\nconstant words or phrases, such as those of which we here\nspeak. We have already had occasion to employ many of these.\nThus we have had instances of technical Terms expressing\ngeometrical conceptions, as _Ellipsis_, _Radius Vector_,\n_Axis_, _Plane_, the Proportion of the _Inverse Square_, and\nthe like. Other Terms have described mechanical conceptions,\nas _Accelerating Force_ and _Attraction_. Again, chemistry\nexhibits (as do all sciences) a series of Terms which mark\nthe steps of our {55} progress. The views of the first real\nfounders of the science are recorded by the Terms which are\nstill in use, _Neutral Salts_, _Affinity_, and the like. The\nestablishment of Dalton's theory has produced the use of the\nword _Atom_ in a peculiar sense, or of some other word, as\n_Proportion_, in a sense equally technical. And Mr. Faraday\nhas found it necessary, in order to expound his\nelectro-chemical theory, to introduce such terms as _Anode_\nand _Cathode_, _An\u00efon_ and _Cath\u00efon_.\n\n2. I need not adduce any further examples, for my object at\npresent is only to point out the use and influence of such\nlanguage: its rules and principles I shall hereafter try, in\nsome measure, to fix. But what we have here to remark is,\nthe extraordinary degree in which the progress of science is\nfacilitated, by thus investing each new discovery with a\ncompendious and steady form of expression. These terms soon\nbecome part of the current language of all who take an\ninterest in speculation. However strange they may sound at\nfirst, they soon grow familiar in our ears, and are used\nwithout any effort, or any recollection of the difficulty\nthey once involved. They become as common as the phrases\nwhich express our most frequent feelings and interests,\nwhile yet they have incomparably more precision than belongs\nto any terms which express feelings; and they carry with\nthem, in their import, the results of deep and laborious\ntrains of research. They convey the mental treasures of one\nperiod to the generations that follow; and laden with this,\ntheir precious freight, they sail safely across gulfs of\ntime in which empires have suffered shipwreck, and the\nlanguages of common life have sunk into oblivion. We have\nstill in constant circulation among us the Terms which\nbelong to the geometry, the astronomy, the zoology, the\nmedicine of the Greeks, and the algebra and chemistry of the\nArabians. And we can in an instant, by means of a few words,\ncall to our own recollection, or convey to the apprehension\nof another person, phenomena and relations of phenomena in\noptics, mineralogy, chemistry, which are so complex and\nabstruse, that it might seem to require the utmost subtlety\nof the human mind to {56} grasp them, even if that were made\nthe sole object of its efforts. By this remarkable effect of\nTechnical Language, we have the results of all the labours\nof past times not only always accessible, but so prepared\nthat we may (provided we are careful in the use of our\ninstrument) employ what is really useful and efficacious for\nthe purpose of further success, without being in any way\nimpeded or perplexed by the length and weight of the chain\nof past connexions which we drag along with us.\n\nBy such means,--by the use of the Inductive Process, and by\nthe aid of Technical Terms,--man has been constantly\nadvancing in the path of scientific truth. In a succeeding\npart of this work we shall endeavour to trace the general\nrules of this advance, and to lay down the maxims by which\nit may be most successfully guided and forwarded. But in\norder that we may do this to the best advantage, we must\npursue still further the analysis of knowledge into its\nelements; and this will be our employment in the first part\nof the work.\n\n\n\n{{57}}\nCHAPTER III.\n\nOF NECESSARY TRUTHS.\n\n\n1. EVERY advance in human knowledge consists, as we have\nseen, in adapting new ideal conceptions to ascertained\nfacts, and thus in superinducing the Form upon the Matter,\nthe active upon the passive processes of our minds. Every\nsuch step introduces into our knowledge an additional\nportion of the ideal element, and of those relations which\nflow from the nature of Ideas. It is, therefore, important\nfor our purpose to examine more closely this element, and to\nlearn what the relations are which may thus come to form\npart of our knowledge. An inquiry into those Ideas which\nform the foundations of our sciences;--into the reality,\nindependence, extent, and principal heads of the knowledge\nwhich we thus acquire; is a task on which we must now enter,\nand which will employ us for several of the succeeding Books.\n\nIn this inquiry our object will be to pass in review all the\nmost important Fundamental Ideas which our sciences involve;\nand to prove more distinctly in reference to each, what we\nhave already asserted with regard to all, that there are\neverywhere involved in our knowledge acts of the mind as\nwell as impressions of sense; and that our knowledge\nderives, from these acts, a generality, certainty, and\nevidence which the senses could in no degree have supplied.\nBut before I proceed to do this in particular cases, I will\ngive some account of the argument in its general form.\n\nWe have already considered the separation of our knowledge\ninto its two elements,--Impressions of Sense and Ideas,--as\nevidently indicated by this; that all knowledge possesses\ncharacters which neither of these {58} elements alone could\nbestow. Without our ideas, our sensations could have no\nconnexion; without external impressions, our ideas would\nhave no reality; and thus both ingredients of our knowledge\nmust exist.\n\n2. There is another mode in which the distinction of the two\nelements of knowledge appears, as I have already said (c. i.\nsect. 2): namely in the distinction of _necessary_, and\n_contingent_ or _experiential_, truths. For of these two\nclasses of truths, the difference arises from this;--that\nthe one class derives its nature from the one, and the other\nfrom the other, of the two elements of knowledge. I have\nalready stated briefly the difference of these two kinds of\ntruths:--namely, that the former are truths which, we see,\nmust be true:--the latter are true, but so far as we can\nsee, might be otherwise. The former are true necessarily and\nuniversally: the latter are learnt from experience and\nlimited by experience. Now with regard to the former kind of\ntruths, I wish to show that the universality and necessity\nwhich distinguish them can by no means be derived from\nexperience; that these characters do in reality flow from\nthe ideas which these truths involve; and that when the\nnecessity of the truth is exhibited in the way of logical\ndemonstration, it is found to depend upon certain\nfundamental principles, (Definitions and Axioms,) which may\nthus be considered as expressing, in some measure, the\nessential characters of our ideas. These fundamental\nprinciples I shall afterwards proceed to discuss and to\nexhibit in each of the principal departments of science.\n\nI shall begin by considering Necessary Truths more fully\nthan I have yet done. As I have already said, necessary\ntruths are those in which we not only learn, that the\nproposition _is_ true, but see that it _must be_ true; in\nwhich the negation of the truth is not only false, but\nimpossible; in which we cannot, even by an effort of\nimagination, or in a supposition, conceive the reverse of\nthat which is asserted.\n\n3. That there are such truths cannot be doubted. We may\ntake, for example, all relations of number. Three and Two\nadded together make Five. We cannot {59} conceive it to be\notherwise. We cannot, by any freak of thought, imagine Three\nand Two to make Seven.\n\nIt may be said that this assertion merely expresses what we\nmean by our words; that it is a matter of definition; that\nthe proposition is an identical one.\n\nBut this is by no means so. The definition of Five is not\nThree and Two, but Four and One. How does it appear that\nThree and Two is the same number as Four and One? It is\nevident that it is so; but _why_ is it evident?--not because\nthe proposition is identical; for if that were the reason,\nall numerical propositions must be evident for the same\nreason. If it be a matter of definition that 3 and 2 make 5,\nit must be a matter of definition that 39 and 27 make 66.\nBut who will say that the definition of 66 is 39 and 27? Yet\nthe magnitude of the numbers can make no difference in the\nground of the truth. How do we know that the product of 13\nand 17 is 4 less than the product of 15 and 15? We see that\nit is so, if we perform certain operations by the rules of\narithmetic; but how do we know the truth of the rules of\narithmetic? If we divide 123375 by 987 according to the\nprocess taught us at school, how are we assured that the\nresult is correct, and that the number 125 thus obtained is\nreally the number of times one number is contained in the\nother?\n\nThe correctness of the rule, it may be replied, can be\nrigorously demonstrated. It can be shown that the process\nmust inevitably give the true quotient.\n\nCertainly this can be shown to be the case. And precisely\nbecause it _can_ be shown that the result must be true, we\nhave here an example of a necessary truth; and this truth,\nit appears, is not _therefore_ necessary because it is\nitself evidently identical, however it may be possible to\nprove it by reducing it to evidently identical propositions.\nAnd the same is the case with all other numerical\npropositions; for, as we have said, the nature of all of\nthem is the same.\n\nHere, then, we have instances of truths which are not only\ntrue, but demonstrably and necessarily true. Now such truths\nare, in this respect at least, altogether {60} different\nfrom truths, which, however certain they may be, are learnt\nto be so only by the evidence of observation, interpreted,\nas observation must be interpreted, by our own mental\nfaculties. There is no difficulty in finding examples of\nthese merely observed truths. We find that sugar dissolves\nin water, and forms a transparent fluid, but no one will say\nthat we can see any reason beforehand why the result _must_\nbe so. We find that all animals which chew the cud have also\nthe divided hoof; but could any one have predicted that this\nwould be universally the case? or supposing the truth of the\nrule to be known, can any one say that he cannot conceive\nthe facts as occurring otherwise? Water expands when it\ncrystallizes, some other substances contract in the same\ncircumstances; but can any one know that this will be so\notherwise than by observation? We have here propositions\n_rigorously_ true, (we will assume,) but can any one say\nthey are _necessarily_ true? These, and the great mass of\nthe doctrines established by induction, are actual, but so\nfar as we can see, accidental laws; results determined by\nsome unknown selection, not demonstrable consequences of the\nessence of things, inevitable and perceived to be\ninevitable. According to the phraseology which has been\nfrequently used by philosophical writers, they are\n_contingent_, not necessary truths.\n\nIt is requisite to insist upon this opposition, because no\ninsight can be obtained into the true nature of knowledge,\nand the mode of arriving at it, by any one who does not\nclearly appreciate the distinction. The separation of truths\nwhich are learnt by observation, and truths which can be\nseen to be true by a pure act of thought, is one of the\nfirst and most essential steps in our examination of the\nnature of truth, and the mode of its discovery. If any one\ndoes not clearly comprehend this distinction of necessary\nand contingent truths, he will not be able to go along with\nus in our researches into the foundations of human\nknowledge; nor, indeed, to pursue with success any\nspeculation on the subject. But, in fact, this distinction\nis one that can hardly fail to be at once understood. It\n{61} is insisted upon by almost all the best modern, as well\nas ancient, metaphysicians[5\\1], as of primary importance.\nAnd if any person does not fully apprehend, at first, the\ndifferent kinds of truth thus pointed out, let him study, to\nsome extent, those sciences which have necessary truth for\ntheir subject, as geometry, or the properties of numbers, so\nas to obtain a familiar acquaintance with such truth; and he\nwill then hardly fail to see how different the evidence of\nthe propositions which occur in these sciences, is from the\nevidence of the facts which are merely learnt from\nexperience. That the year goes through its course in 365\ndays, can only be known by observation of the sun or stars:\nthat 365 days is 52 weeks and a day, it requires no\nexperience, but only a little thought to perceive. That bees\nbuild their cells in the form of hexagons, we cannot know\nwithout looking at them; that regular hexagons may be\narranged so as to fill space, may be proved with the utmost\nrigour, even if there were not in existence such a thing as\na material hexagon.\n\n[Note 5\\1: Aristotle, Dr Whately, Dugald Stewart, &c.]\n\n4. As I have already said, one mode in which we may express\nthe difference of necessary truths and truths of experience,\nis, that necessary truths are those of which we cannot\ndistinctly conceive the contrary. We can very readily\nconceive the contrary of experiential truths. We can\nconceive the stars moving about the pole or across the sky\nin any kind of curves with any velocities; we can conceive\nthe moon always appearing during the whole month as a\nluminous disk, as she might do if her light were inherent\nand not borrowed. But we cannot conceive one of the\nparallelograms on the same base and between the same\nparallels larger than the other; for we find that, if we\nattempt to do this, when we separate the parallelograms into\nparts, we have to conceive one triangle larger than another,\nboth having all their parts equal; which we cannot conceive\nat all, if we conceive the triangles distinctly. We make\nthis impossibility more clear by conceiving {62} the\ntriangles to be placed so that two sides of the one coincide\nwith two sides of the other; and it is then seen, that in\norder to conceive the triangles unequal, we must conceive\nthe two bases which have the same extremities both ways, to\nbe different lines, though both straight lines. This it is\nimpossible to conceive: we assent to the impossibility as an\naxiom, when it is expressed by saying, that two straight\nlines cannot inclose a space; and thus we cannot distinctly\nconceive the contrary of the proposition just mentioned\nrespecting parallelograms.\n\nBut it is necessary, in applying this distinction, to bear\nin mind the terms of it;--that we cannot _distinctly_\nconceive the contrary of a necessary truth. For in a certain\nloose, indistinct way, persons conceive the contrary of\nnecessary geometrical truths, when they erroneously conceive\nfalse propositions to be true. Thus, Hobbes erroneously held\nthat he had discovered a means of geometrically 'doubling\nthe cube,' as it is called, that is, finding two mean\nproportionals between two given lines; a problem which\ncannot be solved by plane geometry. Hobbes not only proposed\na construction for this purpose, but obstinately maintained\nthat it was right, when it had been proved to be wrong. But\nthen, the discussion showed how indistinct the geometrical\nconceptions of Hobbes were; for when his critics had proved\nthat one of the lines in his diagram would not meet the\nother in the point which his reasoning supposed, but in\nanother point near to it; he maintained, in reply, that one\nof these points was large enough to include the other, so\nthat they might be considered as the same point. Such a mode\nof conceiving the opposite of a geometrical truth, forms no\nexception to the assertion, that this opposite cannot be\ndistinctly conceived.\n\nIn like manner, the indistinct conceptions of children and\nof rude savages do not invalidate the distinction of\nnecessary and experiential truths. Children and savages make\nmistakes even with regard to numbers; and might easily\nhappen to assert that 27 and 38 are equal to 63 or 64. But\nsuch mistakes cannot {63} make arithmetical truths cease to\nbe necessary truths. When any person conceives these numbers\nand their addition distinctly, by resolving them into parts,\nor in any other way, he sees that their sum is necessarily\n65. If, on the ground of the possibility of children and\nsavages conceiving something different, it be held that this\nis not a necessary truth, it must be held on the same\nground, that it is not a necessary truth that 7 and 4 are\nequal to 11; for children and savages might be found so\nunfamiliar with numbers as not to reject the assertion that\n7 and 4 are 10, or even that 4 and 3 are 6, or 8. But I\nsuppose that no persons would on such grounds hold that\nthese arithmetical truths are truths known only by\nexperience.\n\n5. I have taken examples of necessary truths from the\nproperties of number and space; but such truths exist no\nless in other subjects, although the discipline of thought\nwhich is requisite to perceive them distinctly, may not be\nso usual among men with regard to the sciences of mechanics\nand hydrostatics, as it is with regard to the sciences of\ngeometry and arithmetic. Yet every one may perceive that\nthere are such truths in mechanics. If I press the table\nwith my hand, the table presses my hand with an equal force:\nhere is a self-evident and necessary truth. In any machine,\nconstructed in whatever manner to increase the force which I\ncan exert, it is certain that what I gain in force I must\nlose in the velocity which I communicate. This is not a\ncontingent truth, borrowed from and limited by observation;\nfor a man of sound mechanical views applies it with like\nconfidence, however novel be the construction of the\nmachine. When I come to speak of the ideas which are\ninvolved in our mechanical knowledge, I may, perhaps, be\nable to bring more clearly into view the necessary truth of\ngeneral propositions on such subjects. That reaction is\nequal and opposite to action, is as necessarily true as that\ntwo straight lines cannot inclose a space; it is as\nimpossible theoretically to make a perpetual motion by mere\nmechanism as to make the diagonal of a square commensurable\nwith the side. {64}\n\n6. Necessary truths must be _universal_ truths. If any\nproperty belong to a right-angled triangle _necessarily_, it\nmust belong to _all_ right-angled triangles. And it shall be\nproved in the following Chapter, that truths possessing\nthese two characters, of Necessity and Universality, cannot\npossibly be the mere results of experience.\n\n[Necessary truths are not considered as a portion of the\n_Inductive_ Sciences. They are Deductions from our Ideas.\nThus the necessary truths which constitute the Science of\nGeometry are Deductions from our Idea of Space: the\nnecessary truths which constitute the Science of Arithmetic\nare Deductions from our notions of Number; which perhaps\ninvolves necessarily the Idea of Time. But though we do not\ncall those Sciences _Inductive_ which involve properties of\nSpace, Number and Time alone, the properties of Space, Time\nand Number enter in many very important ways into the\nInductive Sciences; and therefore the Ideas of Space, Time\nand Number require to be considered in the first place. And\nmoreover the examination of these Ideas is an essential step\ntowards the examination of other Ideas: and the conditions\nof the possibility and certainty of truth, which are\nexemplified in Geometry and Arithmetic, open to us important\nviews respecting the conditions of the possibility and\ncertainty of all Scientific Truth. We shall therefore in the\nnext Book examine the Ideas on which the Pure Sciences,\nGeometry and Arithmetic, are founded. But we must first say\na little more of Ideas in general.]\n\n\n\n{{65}}\nCHAPTER IV.\n\nOF EXPERIENCE.\n\n\n1. I HERE employ the term Experience in a more definite and\nlimited sense than that which it possesses in common usage;\nfor I restrict it to matters belonging to the domain of\nscience. In such cases, the knowledge which we acquire, by\nmeans of experience, is of a clear and precise nature; and\nthe passions and feelings and interests, which make the\nlessons of experience in practical matters so difficult to\nread aright, no longer disturb and confuse us. We may,\ntherefore, hope, by attending to such cases, to learn what\nefficacy experience really has, in the discovery of truth.\n\nThat from _experience_ (including intentional experience, or\n_observation_,) we obtain much knowledge which is highly\nimportant, and which could not be procured from any other\nsource, is abundantly clear. We have already taken several\nexamples of such knowledge. We know by experience that\nanimals which ruminate are cloven-hoofed; and we know this\nin no other manner. We know, in like manner, that all the\nplanets and their satellites revolve round the sun from west\nto east. It has been found by experience that all meteoric\nstones contain chrome. Many similar portions of our\nknowledge might be mentioned.\n\nNow what we have here to remark is this;--that in no case\ncan experience prove a proposition to be _necessarily_ or\n_universally_ true. However many instances we may have\nobserved of the truth of a proposition, yet if it be known\nmerely by observation, there is nothing to assure us that\nthe next case shall not be an exception to the rule. If it\nbe strictly true that every ruminant animal yet known has\ncloven hoofs, we {66} still cannot be sure that some\ncreature will not hereafter be discovered which has the\nfirst of these attributes without having the other. When the\nplanets and their satellites, as far as Saturn, had been all\nfound to move round the sun in one direction, it was still\npossible that there might be other such bodies not obeying\nthis rule; and, accordingly, when the satellites of Uranus\nwere detected, they appeared to offer an exception of this\nkind. Even in the mathematical sciences, we have examples of\nsuch rules suggested by experience, and also of their\nprecariousness. However far they may have been tested, we\ncannot depend upon their correctness, except we see some\nreason for the rule. For instance, various rules have been\ngiven, for the purpose of pointing out _prime numbers_; that\nis, those which cannot be divided by any other number. We\nmay try, as an example of such a rule, this one--any odd\npower of the number two, diminished by one. Thus the third\npower of two, diminished by one, is seven; the fifth power,\ndiminished by one, is thirty-one; the seventh power so\ndiminished is one hundred and twenty-seven. All these are\nprime numbers: and we might be led to suppose that the rule\nis universal. But the next example shows us the\nfallaciousness of such a belief. The ninth power of two,\ndiminished by one, is five hundred and eleven, which is not\na prime, being divisible by seven.\n\nExperience must always consist of a limited number of\nobservations. And, however numerous these may be, they can\nshow nothing with regard to the infinite number of cases in\nwhich the experiment has not been made. Experience being\nthus unable to prove a fact to be universal, is, as will\nreadily be seen, still more incapable of proving a truth to\nbe necessary. Experience cannot, indeed, offer the smallest\nground for the necessity of a proposition. She can observe\nand record what has happened; but she cannot find, in any\ncase, or in any accumulation of cases, any reason for what\nmust happen. She may see objects side by side; but she\ncannot see a reason why they must ever be side by side. She\nfinds certain events to occur in succession; but the\nsuccession supplies, in its occurrence, no {67} reason for\nits recurrence. She contemplates external objects; but she\ncannot detect any internal bond, which indissolubly connects\nthe future with the past, the possible with the real. To\nlearn a proposition by experience, and to see it to be\nnecessarily true, are two altogether different processes of\nthought.\n\n2. But it may be said, that we do learn by means of\nobservation and experience many universal truths; indeed,\nall the general truths of which science consists. Is not the\ndoctrine of universal gravitation learnt by experience? Are\nnot the laws of motion, the properties of light, the general\nprinciples of chemistry, so learnt? How, with these examples\nbefore us, can we say that experience teaches no universal\ntruths?\n\nTo this we reply, that these truths can only be known to be\ngeneral, not universal, if they depend upon experience\nalone. Experience cannot bestow that universality which she\nherself cannot have, and that necessity of which she has no\ncomprehension. If these doctrines _are_ universally true,\nthis universality flows from the _ideas_ which we apply to\nour experience, and which are, as we have seen, the real\nsources of necessary truth. How far these ideas can\ncommunicate their universality and necessity to the results\nof experience, it will hereafter be our business to\nconsider. It will then appear, that when the mind collects\nfrom observation truths of a wide and comprehensive kind,\nwhich approach to the simplicity and universality of the\ntruths of pure science; she gives them this character by\nthrowing upon them the light of her own Fundamental Ideas.\n\nBut the truths which we discover by observation of the\nexternal world, even when most strikingly simple and\nuniversal, are not necessary truths. Is the doctrine of\nuniversal gravitation necessarily true? It was doubted by\nClairaut (so far as it refers to the moon), when the\nprogression of the apogee in fact appeared to be twice as\ngreat as the theory admitted. It has been doubted, even more\nrecently, with respect to the planets, their mutual\nperturbations appearing to indicate a deviation from the\nlaw. It is doubted still, by some {68} persons, with respect\nto the double stars. But suppose all these doubts to be\nbanished, and the law to be universal; is it then proved to\nbe necessary? Manifestly not: the very existence of these\ndoubts proves that it is not so. For the doubts were\ndissipated by reference to observation and calculation, not\nby reasoning on the nature of the law. Clairaut's difficulty\nwas removed by a more exact calculation of the effect of the\nsun's force on the motion of the apogee. The suggestion of\nBessel, that the intensity of gravitation might be different\nfor different planets, was found to be unnecessary, when\nProfessor Airy gave a more accurate determination of the\nmass of Jupiter. And the question whether the extension of\nthe law of the inverse square to the double stars be true,\n(one of the most remarkable questions now before the\nscientific world,) must be answered, not by any speculations\nconcerning what the laws of attraction must necessarily be,\nbut by carefully determining the actual laws of the motion\nof these curious objects, by means of the observations such\nas those which Sir John Herschel has collected for that\npurpose, by his unexampled survey of both hemispheres of the\nsky. And since the extent of this truth is thus to be\ndetermined by reference to observed facts, it is clear that\nno mere accumulation of them can make its universality\ncertain, or its necessity apparent.\n\nThus no knowledge of the necessity of any truths can result\nfrom the observation of what really happens. This being\nclearly understood, we are led to an important inquiry.\n\nThe characters of universality and necessity in the truths\nwhich form part of our knowledge, can never be derived from\nexperience, by which so large a part of our knowledge is\nobtained. But since, as we have seen, we really do possess a\nlarge body of truths which are necessary, and because\nnecessary, therefore universal, the question still recurs,\nfrom what source these characters of universality and\nnecessity are derived.\n\nThe answer to this question we will attempt to give in the\nnext chapter.\n\n\n\n{{69}}\nCHAPTER V.\n\nOF THE GROUNDS OF NECESSARY TRUTHS.\n\n\n1. TO the question just stated, I reply, that the necessity\nand universality of the truths which form a part of our\nknowledge, are derived from the _Fundamental Ideas_ which\nthose truths involve. These ideas entirely shape and\ncircumscribe our knowledge; they regulate the active\noperations of our minds, without which our passive\nsensations do not become knowledge. They govern these\noperations, according to rules which are not only fixed and\npermanent, but which may be expressed in plain and definite\nterms; and these rules, when thus expressed, may be made the\nbasis of demonstrations by which the necessary relations\nimparted to our knowledge by our Ideas may be traced to\ntheir consequences in the most remote ramifications of\nscientific truth.\n\nThese enunciations of the necessary and evident conditions\nimposed upon our knowledge by the Fundamental Ideas which it\ninvolves, are termed _Axioms_. Thus the Axioms of Geometry\nexpress the necessary conditions which result from the Idea\nof Space; the Axioms of Mechanics express the necessary\nconditions which flow from the Ideas of Force and Motion;\nand so on.\n\n2. It will be the office of several of the succeeding Books\nof this work to establish and illustrate in detail what I\nhave thus stated in general terms. I shall there pass in\nreview many of the most important fundamental ideas on which\nthe existing body of our science depends; and I shall\nendeavour to show, for each such idea in succession, that\nknowledge involves an active as well as a passive element;\nthat it is not possible without an act of the mind,\nregulated by certain {70} laws. I shall further attempt to\nenumerate some of the principal fundamental relations which\neach idea thus introduces into our thoughts, and to express\nthem by means of definitions and axioms, and other suitable\nforms.\n\nI will only add a remark or two to illustrate further this\nview of the ideal grounds of our knowledge.\n\n3. To persons familiar with any of the demonstrative\nsciences, it will be apparent that if we state all the\nDefinitions and Axioms which are employed in the\ndemonstrations, we state the whole basis on which those\nreasonings rest. For the whole process of demonstrative or\ndeductive reasoning in any science, (as in geometry, for\ninstance,) consists entirely in combining some of these\nfirst principles so as to obtain the simplest propositions\nof the science; then combining these so as to obtain other\npropositions of greater complexity; and so on, till we\nadvance to the most recondite demonstrable truths; these\nlast, however intricate and unexpected, still involving no\nprinciples except the original definitions and axioms. Thus,\nby combining the Definition of a triangle, and the\nDefinitions of equal lines and equal angles, namely, that\nthey are such as when applied to each other, coincide, with\nthe Axiom respecting straight lines (that two such lines\ncannot inclose a space,) we demonstrate the equality of\ntriangles, under certain assumed conditions. Again, by\ncombining this result with the Definition of parallelograms,\nand with the Axiom that if equals be taken from equals the\nwholes are equal, we prove the equality of parallelograms\nbetween the same parallels and upon the same base. From this\nproposition, again, we prove the equality of the square on\nthe hypotenuse of a triangle to the squares on the two sides\ncontaining the right angle. But in all this there is nothing\ncontained which is not rigorously the result of our\ngeometrical Definitions and Axioms. All the rest of our\ntreatises of geometry consists only of terms and phrases of\nreasoning, the object of which is to connect those first\nprinciples, and to exhibit the effects of their combination\nin the shape of demonstration. {71}\n\n4. This combination of first principles takes place\naccording to the forms and rules of _Logic_. All the steps\nof the demonstration may be stated in the shape in which\nlogicians are accustomed to exhibit processes of reasoning\nin order to show their conclusiveness, that is, in\n_Syllogisms_. Thus our geometrical reasonings might be\nresolved into such steps as the following:--\nAll straight lines drawn from the centre of a circle to its\ncircumference are equal:\nBut the straight lines AB, AC, are drawn from the centre of\na circle to its circumference:\nTherefore the straight lines AB, AC, are equal.\n\nEach step of geometrical, and all other demonstrative\nreasoning, may be resolved into three such clauses as these;\nand these three clauses are termed respectively, the _major\npremiss_, the _minor premiss_, and the _conclusion_; or,\nmore briefly, the _major_, the _minor_, and the\n_**conclusion_.\n\nThe principle which justifies the reasoning when exhibited\nin this syllogistic form, is this:--that a truth which can\nbe asserted as generally, or rather as universally true, can\nbe asserted as true also in each particular case. The\n_minor_ only asserts a certain particular case to be an\nexample of such conditions as are spoken of in the _major_;\nand hence the conclusion, which is true of the major by\nsupposition, is true of the minor by consequence; and thus\nwe proceed from syllogism to syllogism, in each one\nemploying some general truth in some particular instance.\nAny proof which occurs in geometry, or any other science of\ndemonstration, may thus be reduced to a series of processes,\nin each of which we pass from some general proposition to\nthe narrower and more special propositions which it\nincludes. And this process of deriving truths by the mere\ncombination of general principles, applied in particular\nhypothetical cases, is called _deduction_; being opposed to\n_induction_, in which, as we have seen (chap. i. sect. 3), a\nnew general principle is introduced at every step.\n\n5. Now we have to remark that, this being so, however far we\nfollow such deductive reasoning, we can {72} never have, in\nour conclusion any truth which is not virtually included in\nthe original principles from which the reasoning started.\nFor since at any step we merely take out of a general\nproposition something included in it, while at the preceding\nstep we have taken this general proposition out of one more\ngeneral, and so on perpetually, it is manifest that our last\nresult was really included in the principle or principles\nwith which we began. I say _principles_, because, although\nour logical conclusion can only exhibit the legitimate issue\nof our first principles, it may, nevertheless, contain the\nresult of the combination of several such principles, and\nmay thus assume a great degree of complexity, and may appear\nso far removed from the parent truths, as to betray at first\nsight hardly any relationship with them. Thus the\nproposition which has already been quoted respecting the\nsquares on the sides of a right-angled triangle, contains\nthe results of many elementary principles; as, the\ndefinitions of parallels, triangle, and square; the axioms\nrespecting straight lines, and respecting parallels; and,\nperhaps, others. The conclusion is complicated by containing\nthe effects of the combination of all these elements; but it\ncontains nothing, and can contain nothing, but such elements\nand their combinations.\n\nThis doctrine, that logical reasoning produces no new\ntruths, but only unfolds and brings into view those truths\nwhich were, in effect, contained in the first principles of\nthe reasoning, is assented to by almost all who, in modern\ntimes, have attended to the science of logic. Such a view is\nadmitted both by those who defend, and by those who\ndepreciate the value of logic. 'Whatever is established by\nreasoning, must have been contained and virtually asserted\nin the premises[6\\1].' 'The only truth which such\npropositions can possess consists in conformity to the\noriginal principles.'\n\n[Note 6\\1: Whately's _Logic_, pp. 237, 238.]\n\nIn this manner the whole substance of our geometry is\nreduced to the Definitions and Axioms which we employ in our\nelementary reasonings; and in like {73} manner we reduce the\ndemonstrative truths of any other science to the definitions\nand axioms which we there employ.\n\n6. But in reference to this subject, it has sometimes been\nsaid that demonstrative sciences do in reality depend upon\nDefinitions only; and that no additional kind of principle,\nsuch as we have supposed Axioms to be, is absolutely\nrequired. It has been asserted that in geometry, for\nexample, the source of the necessary truth of our\npropositions is this, that they depend upon definitions\nalone, and consequently merely state the identity of the\nsame thing under different aspects.\n\nThat in the sciences which admit of demonstration, as\ngeometry, mechanics, and the like, Axioms as well as\nDefinitions are needed, in order to express the grounds of\nour necessary convictions, must be shown hereafter by an\nexamination of each of these sciences in particular. But\nthat the propositions of these sciences, those of geometry\nfor example, do not merely assert the identity of the same\nthing, will, I think, be generally allowed, if we consider\nthe assertions which we are enabled to make. When we declare\nthat 'a straight line is the shortest distance between two\npoints,' is this merely an identical proposition? the\ndefinition of a straight line in another form? Not so: the\ndefinition of a straight line involves the notion of form\nonly, and does not contain anything about magnitude;\nconsequently, it cannot contain anything equivalent to\n'shortest.' Thus the propositions of geometry are not merely\nidentical propositions; nor have we in their general\ncharacter anything to countenance the assertion, that they\nare the results of definitions alone. And when we come to\nexamine this and other sciences more closely, we shall find\nthat axioms, such as are usually in our treatises made the\nfundamental principles of our demonstrations, neither have\never been, nor can be, dispensed with. Axioms, as well as\nDefinitions, are in all cases requisite, in order properly\nto exhibit the grounds of necessary truth.\n\n7. Thus the real logical basis of every body of demonstrated\ntruths are the Definitions and Axioms {74} which are the\nfirst principles of the reasonings. But when we are arrived\nat this point, the question further occurs, what is the\nground of the truth of these Axioms? It is not the logical,\nbut the philosophical, not the formal, but the real\nfoundation of necessary truth, which we are seeking. Hence\nthis inquiry necessarily comes before us, What is the ground\nof the Axioms of Geometry, of Mechanics, and of any other\ndemonstrable science?\n\nThe answer which we are led to give, by the view which we\nhave taken of the nature of knowledge, has already been\nstated. The ground of the axioms belonging to each science\nis the _Idea_ which the axiom involves. The ground of the\nAxioms of Geometry is the _Idea of Space_: the ground of the\nAxioms of Mechanics is the _Idea of Force_, of _Action_ and\n_Reaction_, and the like. And hence these Ideas are\nFundamental Ideas; and since they are thus the foundations,\nnot only of demonstration but of truth, an examination into\ntheir real import and nature is of the greatest consequence\nto our purpose.\n\n8. Not only the Axioms, but the definitions which form the\nbasis of our reasonings, depend upon our Fundamental Ideas.\nAnd the Definitions are not arbitrary definitions, but are\ndetermined by a necessity no less rigorous than the Axioms\nthemselves. We could not think of geometrical truths without\nconceiving a circle; and we could not reason concerning such\ntruths without defining a circle in some mode equivalent to\nthat which is commonly adopted. The Definitions of\nparallels, of right angles, and the like, are quite as\nnecessarily prescribed by the nature of the case, as the\nAxioms which these Definitions bring with them. Indeed we\nmay substitute one of these kinds of principles for another.\nWe cannot always put a Definition in the place of an Axiom;\nbut we may always find an Axiom which shall take the place\nof a Definition. If we assume a proper Axiom respecting\nstraight lines, we need no Definition of a straight line.\nBut in whatever shape the principle appear, as Definition or\nas Axiom, it has about it nothing casual or {75} arbitrary,\nbut is determined to be what it is, as to its import, by the\nmost rigorous necessity, growing out of the Idea of Space.\n\n9. These principles,--Definitions, and Axioms,--thus\nexhibiting the primary developments of a fundamental idea,\ndo in fact express the idea, so far as its expression in\nwords forms part of our science. They are different views of\nthe same body of truth; and though each principle, by\nitself, exhibits only one aspect of this body, taken\ntogether they convey a sufficient conception of it for our\npurposes. The Idea itself cannot be fixed in words; but\nthese various lines of truth proceeding from it, suggest\nsufficiently to a fitly-prepared mind, the place where the\nidea resides, its nature, and its efficacy.\n\nIt is true that these principles,--our elementary\nDefinitions and Axioms,--even taken all together, express\nthe Idea incompletely. Thus the Definitions and Axioms of\nGeometry, as they are stated in our elementary works, do not\nfully express the Idea of Space as it exists in our minds.\nFor, in addition to these, other Axioms, independent of\nthese, and no less evident, can be stated; and are in fact\nstated when we come to the Higher Geometry. Such, for\ninstance, is the Axiom of Archimedes--that a curve line\nwhich joins two points is less than a broken line which\njoins the same points and includes the curve. And thus the\nIdea is disclosed but not fully revealed, imparted but not\ntransfused, by the use we make of it in science. When we\nhave taken from the fountain so much as serves our purpose,\nthere still remains behind a deep well of truth, which we\nhave not exhausted, and which we may easily believe to be\ninexhaustible.\n\n\n\n{{76}}\nCHAPTER VI.\n\nTHE FUNDAMENTAL IDEAS ARE NOT DERIVED FROM EXPERIENCE.\n\n\n1. BY the course of speculation contained in the last three\nChapters, we are again led to the conclusion which we have\nalready stated, that our knowledge contains an ideal\nelement, and that this element is not derived from\nexperience. For we have seen that there are propositions\nwhich are known to be necessarily true; and that such\nknowledge is not, and cannot be, obtained by mere\nobservation of actual facts. It has been shown, also, that\nthese necessary truths are the results of certain\nfundamental ideas, such as those of space, number, and the\nlike. Hence it follows inevitably that these ideas and\nothers of the same kind are not derived from experience. For\nthese ideas possess a power of infusing into their\ndevelopments that very necessity which experience can in no\nway bestow. This power they do not borrow from the external\nworld, but possess by their own nature. Thus we unfold out\nof the Idea of Space the propositions of geometry, which are\nplainly truths of the most rigorous necessity and\nuniversality. But if the idea of space were merely collected\nfrom observation of the external world, it could never\nenable or entitle us to assert such propositions: it could\nnever authorize us to say that not merely some lines, but\n_all_ lines, not only have, but _must_ have, those\nproperties which geometry teaches. Geometry in every\nproposition speaks a language which experience never dares\nto utter; and indeed of which she but half comprehends the\nmeaning. Experience sees that the assertions are true, but\nshe sees not how profound and absolute is their truth. {77}\nShe unhesitatingly assents to the laws which geometry\ndelivers, but she does not pretend to see the origin of\ntheir obligation. She is always ready to acknowledge the\nsway of pure scientific principles as a matter of fact, but\nshe does not dream of offering her opinion on their\nauthority as a matter of right; still less can she justly\nclaim to be herself the source of that authority.\n\nDavid Hume asserted[7\\1], that we are incapable of seeing in\nany of the appearances which the world presents anything of\nnecessary connexion; and hence he inferred that our\nknowledge cannot extend to any such connexion. It will be\nseen from what we have said that we assent to his remark as\nto the fact, but we differ from him altogether in the\nconsequence to be drawn from it. Our inference from Hume's\nobservation is, not the truth of his conclusion, but the\nfalsehood of his premises;--not that, therefore, we can know\nnothing of natural connexion, but that, therefore, we have\nsome other source of knowledge than experience:--not, that\nwe can have no idea of connexion or causation, because, in\nhis language, it cannot be the copy of an impression; but\nthat since we have such an idea, our ideas are not the\ncopies of our impressions.\n\n[Note 7\\1: _Essays_, vol. ii. p. 70.]\n\nSince it thus appears that our fundamental ideas are not\nacquired from the external world by our senses, but have\nsome separate and independent origin, it is important for us\nto examine their nature and properties, as they exist in\nthemselves; and this it will be our business to do through a\nportion of the following pages. But it may be proper first\nto notice one or two objections which may possibly occur to\nsome readers.\n\n2. It may be said that without the use of our senses, of\nsight and touch, for instance, we should never have any idea\nof space; that this idea, therefore, may properly be said to\nbe derived from those senses. And to this I reply, by\nreferring to a parallel instance. Without light we should\nhave no perception of visible {78} figure; yet the power of\nperceiving visible figure cannot be said to be derived from\nthe light, but resides in the structure of the eye. If we\nhad never seen objects in the light, we should be quite\nunaware that we possessed a power of vision; yet we should\nnot possess it the less on that account. If we had never\nexercised the senses of sight and touch (if we can conceive\nsuch a state of human existence) we know not that we should\nbe conscious of an idea of space. But the light reveals to\nus at the same time the existence of external objects and\nour own power of seeing. And in a very similar manner, the\nexercise of our senses discloses to us, at the same time,\nthe external world, and our own ideas of space, time, and\nother conditions, without which the external world can\nneither be observed nor conceived. That light is necessary\nto vision, does not, in any degree, supersede the importance\nof a separate examination of the laws of our visual powers,\nif we would understand the nature of our own bodily\nfaculties and the extent of the information they can give\nus. In like manner, the fact that intercourse with the\nexternal world is necessary for the conscious employment of\nour ideas, does not make it the less essential for us to\nexamine those ideas in their most intimate structure, in\norder that we may understand the grounds and limits of our\nknowledge. Even before we see a single object, we have a\nfaculty of vision; and in like manner, if we can suppose a\nman who has never contemplated an object in space or time,\nwe must still assume him to have the faculties of\nentertaining the ideas of space and time, which faculties\nare called into play on the very first occasion of the use\nof the senses.\n\n3. In answer to such remarks as the above, it has sometimes\nbeen said that to assume separate faculties in the mind for\nso many different processes of thought, is to give a mere\nverbal explanation, since we learn nothing concerning our\nidea of space by being told that we have a faculty of\nforming such an idea. It has been said that this course of\nexplanation leads to an endless multiplication of elements\nin man's nature, without any advantage to our knowledge of\nhis true {79} constitution. We may, it is said, assert man\nto have a faculty of walking, of standing, of breathing, of\nspeaking; but what, it is asked, is gained by such\nassertions? To this I reply, that we undoubtedly have such\nfaculties as those just named; that it is by no means\nunimportant to consider them; and that the main question in\nsuch cases is, whether they are separate and independent\nfaculties, or complex and derivative ones; and, if the\nlatter be the case, what are the simple and original\nfaculties by the combination of which the others are\nproduced. In walking, standing, breathing, for instance, a\ngreat part of the operation can be reduced to one single\nfaculty; the voluntary exercise of our muscles. But in\nbreathing this does not appear to be the whole of the\nprocess. The operation is, in part at least, involuntary;\nand it has been held that there is a certain sympathetic\naction of the nerves, in addition to the voluntary agency\nwhich they transmit, which is essential to the function. To\ndetermine whether or no this sympathetic faculty is real and\ndistinct, and if so, what are its laws and limits, is\ncertainly a highly philosophical inquiry, and well deserving\nthe attention which has been bestowed upon it by eminent\nphysiologists. And just of the same nature are the inquiries\nwith respect to man's intellectual constitution, on which we\npropose to enter. For instance, man has a faculty of\napprehending time, and a faculty of reckoning numbers: are\nthese distinct, or is one faculty derived from the other? To\nanalyze the various combinations of our ideas and\nobservations into the original faculties which they involve;\nto show that these faculties are original, and not capable\nof further analysis: to point out the characters which mark\nthese faculties and lead to the most important features of\nour knowledge;--these are the kind of researches on which we\nhave now to enter, and these, we trust, will be found to be\nfar from idle or useless parts of our plan. If we succeed in\nsuch attempts, it will appear that it is by no means a\nfrivolous or superfluous step to distinguish separate\nfaculties in the mind. If we do not learn much by being told\nthat we have a faculty {80} of forming the idea of space, we\nat least, by such a commencement, circumscribe a certain\nportion of the field of our investigations, which, we shall\nafterwards endeavour to show, requires and rewards a special\nexamination. And though we shall thus have to separate the\ndomain of our philosophy into many provinces, these are, as\nwe trust it will appear, neither arbitrarily assigned, nor\nvague in their limits, nor infinite in number.\n\n\n\n{{81}}\nCHAPTER VII.\n\nOF THE PHILOSOPHY OF THE SCIENCES.\n\n\nWE proceed, in the ensuing Books, to the closer examination\nof a considerable number of those Fundamental Ideas on which\nthe sciences, hitherto most successfully cultivated, are\nfounded. In this task, our objects will be to explain and\nanalyze such Ideas so as to bring into view the Definitions\nand Axioms, or other forms, in which we may clothe the\nconditions to which our speculative knowledge is subjected.\nI shall also try to prove, for some of these Ideas in\nparticular, what has been already urged respecting them in\ngeneral, that they are not derived from observation, but\nnecessarily impose their conditions upon that knowledge of\nwhich observation supplies the materials. I shall further,\nin some cases, endeavour to trace the history of these Ideas\nas they have successively come into notice in the progress\nof science; the gradual development by which they have\narrived at their due purity and clearness; and, as a\nnecessary part of such a history, I shall give a view of\nsome of the principal controversies which have taken place\nwith regard to each portion of knowledge.\n\nAn exposition and discussion of the Fundamental Ideas of\neach Science may, with great propriety, be termed the\nPHILOSOPHY OF such SCIENCE. These ideas contain in\nthemselves the elements of those truths which the science\ndiscovers and enunciates; and in the progress of the\nsciences, both in the world at large and in the mind of each\nindividual student, the most important steps consist in\napprehending these ideas clearly, and in bringing them into\naccordance with the observed facts. I shall, therefore, in a\nseries of Books, {82} treat of the _Philosophy of the Pure\nSciences_, the _Philosophy of the Mechanical Sciences_, the\n_Philosophy of Chemistry_, and the like, and shall analyze\nand examine the ideas which these sciences respectively\ninvolve.\n\nIn this undertaking, inevitably somewhat long, and involving\nmany deep and subtle discussions, I shall take, as a chart\nof the country before me, by which my course is to be\nguided, the scheme of the sciences which I was led to form\nby travelling over the history of each in order[8\\1]. Each\nof the sciences of which I then narrated the progress,\ndepends upon several of the Fundamental Ideas of which I\nhave to speak: some of these Ideas are peculiar to one field\nof speculation, others are common to more. A previous\nenumeration of Ideas thus collected may serve both to show\nthe course and limits of this part of our plan, and the\nvariety of interest which it offers.\n\n[Note 8\\1: _History of the Inductive Sciences._]\n\nI shall, then, successively, have to speak Of the Ideas\nwhich are the foundation of Geometry and Arithmetic, (and\nwhich also regulate all sciences depending upon these, as\nAstronomy and Mechanics;) namely, the Ideas of _Space_,\n_Time_, and _Number_ (Book II.):\n\nOf the Ideas on which the Mechanical Sciences (as Mechanics,\nHydrostatics, Physical Astronomy) more peculiarly rest; the\nideas of _Force_ and _Matter_, or rather the idea of\n_Cause_, which is the basis of these (Book III.):\n\nOf the Ideas which the Secondary Mechanical Sciences\n(Acoustics, Optics, and Thermotics) involve; namely, the\nIdeas of the _Externality_ of objects, and of the _Media_ by\nwhich we perceive their qualities (Book IV.):\n\nOf the Ideas which are the basis of Mechanico-chemical and\nChemical Science; _Polarity_, _Chemical Affinity_, and\n_Substance_; and the Idea of _Symmetry_, a necessary part of\nthe Philosophy of Crystallography (Books V. VI.):\n\nOf the Ideas on which the Classificatory Sciences proceed\n(Mineralogy, Botany, and Zoology); namely, {83} the Ideas of\n_Resemblance_, and of its gradations, and of _Natural\nAffinity_ (Books VII. VIII.):\n\nFinally, of those Ideas on which the Physiological Sciences\nare founded; the Ideas of separate Vital Powers, such as\n_Assimilation_ and _Irritability_; and the Idea of _Final\nCause_ (Book IX.):\n\nWe have, besides these, the Pal\u00e6tiological Sciences, which\nproceed mainly on the conception of _Historical Causation_\n(Book X.):\n\nIt is plain that when we have proceeded so far as this, we\nhave advanced to the verge of those speculations which have\nto do with mind as well as body. The extension of our\nphilosophy to such a field, if it can be justly so extended,\nwill be one of the most important results of our researches;\nbut on that very account we must fully study the lessons\nwhich we learn in those fields of speculation where our\ndoctrines are most secure, before we venture into a region\nwhere our principles will appear to be more precarious, and\nwhere they are inevitably less precise.\n\nWe now proceed to the examination of the above Ideas, and to\nsuch essays towards the philosophy of each Science as this\ncourse of investigation may suggest.\n\n\n\n{{85}}\nBOOK II.\n\n\nTHE\nPHILOSOPHY\nOF THE\nPURE SCIENCES.\n\n\n\n\nThe way in which we are led to regard human knowledge is\nlike the way in which Copernicus was led to regard the\nheavens. When the explanation of the celestial motions could\nnot be made to go right so long as he assumed that all the\nhost of stars turns round the spectator, he tried whether it\nwould not answer better if he made the spectator turn, and\nleft the stars at rest. We may make a similar trial in\nMetaphysics, as to our way of looking at objects. If our\nview of them must be governed altogether by the properties\nof the objects themselves, I see not how man can know\nanything about them _\u00e0 priori_. But if the thing, as an\nobject of the senses, is regulated by the constitution of\nour power of knowing, I can very readily represent to myself\nthis possibility.\n\nKANT, _Kritik d. R. V. Pref._\n\n\n{{87}}\nBOOK II.\n\nTHE PHILOSOPHY OF THE PURE SCIENCES.\n\n\n[The principal question discussed in the last Book was this\n(see chaps. V. and VI.): How are _necessary_ and _universal_\ntruths possible? And the answer then given was: that the\nnecessity and universality of truths are derived from the\n_Fundamental Ideas_ which they involve. And we proceed in\nthis Book to exemplify this doctrine in the case of the\ntruths of Geometry and Arithmetic, which derive their\nnecessity and universality from the Fundamental Ideas of\nSpace, and Time, or Number.\n\nThe question thus examined is that which Kant undertook to\ndeal with in his celebrated work, _Kritik der reinen\nVernunft_ (_Examination of the Pure Reason_): and our\nsolution of the Problem, so far as the Ideas of Space and\nTime are concerned, agrees in the main with his. The\narguments contained in chapters II. and **VII. of this Book,\nare the leading arguments respecting Space and Time, in\nKant's _Kritik_. Kant, however, instead of calling Space and\nTime _Ideas_, calls them the necessary _Forms_ of our\nexperience, as I have stated in the text.\n\nBut though I have adopted Kant's arguments as to Space and\nTime, all that follows in the succeeding Books, with regard\nto other Ideas, has no resemblance to any doctrines of Kant\nor his school (with the exception, perhaps, of some of the\nviews on the Idea of _Cause_). The nature and character of\nthe other Scientific Ideas which I have examined, in the\nsucceeding Books, have been established by an analysis of\nthe history of the several Sciences to which those Ideas are\nessential, and an examination of the writings of the\nprincipal discoverers in those Sciences.]\n\n\n\n{{88}}\nCHAPTER I.\n\nOF THE PURE SCIENCES.\n\n\n1. ALL external objects and events which we can contemplate\nare viewed as having relations of Space, Time, and Number;\nand are subject to the general conditions which these Ideas\nimpose, as well as to the particular laws which belong to\neach class of objects and occurrences. The special laws of\nnature, considered under the various aspects which\nconstitute the different sciences, are obtained by a mixed\nreference to Experience and to the Fundamental Ideas of each\nscience. But besides the sciences thus formed by the aid of\nspecial experience, the conditions which flow from those\nmore comprehensive ideas first mentioned, Space, Time, and\nNumber, constitute a body of science, applicable to objects\nand changes of all kinds, and deduced without recurrence\nbeing had to any observation in particular. These sciences,\nthus unfolded out of ideas alone, unmixed with any reference\nto the phenomena of matter, are hence termed _Pure_\nSciences. The principal sciences of this class are Geometry,\nTheoretical Arithmetic, and Algebra considered in its most\ngeneral sense, as the investigation of the relations of\nspace and number by means of general symbols.\n\n2. These Pure Sciences were not included in our survey of\nthe history of the sciences, because they are not\n_inductive_ sciences. Their progress has not consisted in\ncollecting laws from phenomena, true theories from observed\nfacts, and more general from more limited laws; but in\ntracing the consequences of the ideas themselves, and in\ndetecting the most general and intimate analogies and\nconnexions which prevail {89} among such conceptions as are\nderivable from the ideas. These sciences have no principles\nbesides definitions and axioms, and no process of proof but\n_deduction_; this process, however, assuming here a most\nremarkable character; and exhibiting a combination of\nsimplicity and complexity, of rigour and generality, quite\nunparalleled in other subjects.\n\n3. The universality of the truths, and the rigour of the\ndemonstrations of these pure sciences, attracted attention\nin the earliest times; and it was perceived that they\noffered an exercise and a discipline of the intellectual\nfaculties, in a form peculiarly free from admixture of\nextraneous elements. They were strenuously cultivated by the\nGreeks, both with a view to such a discipline, and from the\nlove of speculative truth which prevailed among that people:\nand the name _mathematics_, by which they are designated,\nindicates this their character of _disciplinal_ studies.\n\n4. As has already been said, the ideas which these sciences\ninvolve extend to all the objects and changes which we\nobserve in the external world; and hence the consideration\nof mathematical relations forms a large portion of many of\nthe sciences which treat of the phenomena and laws of\nexternal nature, as Astronomy, Optics, and Mechanics. Such\nsciences are hence often termed _Mixed Mathematics_, the\nrelations of space and number being, in these branches of\nknowledge, combined with principles collected from special\nobservation; while Geometry, Algebra, and the like subjects,\nwhich involve no result of experience, are called _Pure\nMathematics_.\n\n5. Space, time, and number, may be conceived as _forms_ by\nwhich the knowledge derived from our sensations is moulded,\nand which are independent of the differences in the _matter_\nof our knowledge, arising from the sensations themselves.\nHence the sciences which have these ideas for their subject\nmay be termed _Formal Sciences_. In this point of view, they\nare distinguished from sciences in which, besides these mere\nformal laws by which appearances are corrected, we endeavour\nto apply to the phenomena the idea of cause, {90} or some of\nthe other ideas which penetrate further into the principles\nof nature. We have thus, in the History, distinguished\nFormal Astronomy and Formal Optics from Physical Astronomy\nand Physical Optics.\n\nWe now proceed to our examination of the Ideas which\nconstitute the foundation of these formal or pure\nmathematical sciences, beginning with the Idea of Space.\n\n\n\n{{91}}\nCHAPTER II.\n\nOF THE IDEA OF SPACE.\n\n\n1. BY speaking of space as an Idea, I intend to imply, as\nhas already been stated, that the apprehension of objects as\nexisting in space, and of the relations of position, &c.,\nprevailing among them, is not a consequence of experience,\nbut a result of a peculiar constitution and activity of the\nmind, which is independent of all experience in its origin,\nthough constantly combined with experience in its exercise.\n\nThat the idea of space is thus independent of experience,\nhas already been pointed out in speaking of ideas in\ngeneral: but it may be useful to illustrate the doctrine\nfurther in this particular case.\n\nI assert, then, that space is not a notion obtained by\nexperience. Experience gives us information concerning\nthings without us: but our apprehending them _as_ without\nus, takes for granted their existence in space. Experience\nacquaints us what are the form, position, magnitude of\nparticular objects: but that they have form, position,\nmagnitude, presupposes that they are in space. We cannot\nderive from appearances, by the way of observation, the\nhabit of representing things to ourselves as in space; for\nno single act of observation is possible any otherwise than\nby beginning with such a representation, and conceiving\nobjects as already existing in space.\n\n2. That our mode of representing space to ourselves is not\nderived from experience, is clear also from this: that\nthrough this mode of representation we arrive at\npropositions which are rigorously universal and necessary.\nPropositions of such a kind could not possibly be obtained\nfrom experience; for experience can {92} only teach us by a\nlimited number of examples, and therefore can never securely\nestablish a universal proposition: and again, experience can\nonly inform us that anything is so, and can never prove that\nit must be so. That two sides of a triangle are greater than\nthe third is a universal and necessary geometrical truth: it\nis true of all triangles; it is true in such a way that the\ncontrary cannot be conceived. Experience could not prove\nsuch a proposition. And experience has not proved it; for\nperhaps no man ever made the trial as a means of removing\ndoubts: and no trial could, in fact, add in the smallest\ndegree to the certainty of this truth. To seek for proof of\ngeometrical propositions by an appeal to observation proves\nnothing in reality, except that the person who has recourse\nto such grounds has no due apprehension of the nature of\ngeometrical demonstration. We have heard of persons who\nconvinced themselves by measurement that the geometrical\nrule respecting the squares on the sides of a right-angled\ntriangle was true: but these were persons whose minds had\nbeen engrossed by practical habits, and in whom the\nspeculative development of the idea of space had been\nstifled by other employments. The practical trial of the\nrule may illustrate, but cannot prove it. The rule will of\ncourse be confirmed by such trial, because what is true in\ngeneral is true in particular: but the rule cannot be proved\nfrom any number of trials, for no accumulation of particular\ncases makes up a universal case. To all persons who can see\nthe force of any proof, the geometrical rule above referred\nto is as evident, and its evidence as independent of\nexperience, as the assertion that sixteen and nine make\ntwenty-five. At the same time, the truth of the geometrical\nrule is quite independent of numerical truths, and results\nfrom the relations of space alone. This could not be if our\napprehension of the relations of space were the fruit of\nexperience: for experience has no element from which such\ntruth and such proof could arise.\n\n3. Thus the existence of necessary truths, such as those of\ngeometry, proves that the idea of space from {93} which they\nflow is not derived from experience. Such truths are\ninconceivable on the supposition of their being collected\nfrom observation; for the impressions of sense include no\nevidence of necessity. But we can readily understand the\nnecessary character of such truths, if we conceive that\nthere are certain necessary conditions under which alone the\nmind receives the impressions of sense. Since these\nconditions reside in the constitution of the mind, and apply\nto every perception of an object to which the mind can\nattain, we easily see that their rules must include, not\nonly all that has been, but all that can be, matter of\nexperience. Our sensations can each convey no information\nexcept about itself; each can contain no trace of another\nadditional sensation; and thus no relation and connexion\nbetween two sensations can be given by the sensations\nthemselves. But the mode in which the mind perceives these\nimpressions as objects, may and will introduce necessary\nrelations among them: and thus by conceiving the idea of\nspace to be a condition of perception in the mind, we can\nconceive the existence of necessary truths, which apply to\nall perceived objects.\n\n4. If we consider the impressions of sense as the mere\nmaterials of our experience, such materials may be\naccumulated in any quantity and in any order. But if we\nsuppose that this matter has a certain form given it, in the\nact of being accepted by the mind, we can understand how it\nis that these materials are subject to inevitable\nrules;--how nothing can be perceived exempt from the\nrelations which belong to such a form. And since there are\nsuch truths applicable to our experience, and arising from\nthe nature of space, we may thus consider space as a _form_\nwhich the materials given by experience necessarily assume\nin the mind; as an arrangement derived from the perceiving\nmind, and not from the sensations alone.\n\n5. Thus this phrase,--that space is a _form_ belonging to\nour perceptive power,--may be employed to express that we\ncannot perceive objects as in space, without an operation of\nthe mind as well as of the senses--without active as well as\npassive faculties. This phrase, however, {94} is not\nnecessary to the exposition of our doctrines. Whether we\ncall the conception of space a Condition of perception, a\nForm of perception, or an Idea, or by any other term, it is\nsomething originally inherent in the mind perceiving, and\nnot in the objects perceived. And it is because the\napprehension of all objects is thus subjected to certain\nmental conditions, forms or ideas, that our knowledge\ninvolves certain inviolable relations and necessary truths.\nThe principles of such truths, so far as they regard space,\nare derived from the idea of space, and we must endeavour to\nexhibit such principles in their general form. But before we\ndo this, we may notice some of the conditions which belong,\nnot to our Ideas in general, but to this Idea of Space in\nparticular.\n\n\n\n{{95}}\nCHAPTER III.\n\nOF SOME PECULIARITIES OF THE IDEA OF SPACE.\n\n\n1. SOME of the Ideas which we shall have to examine involve\nconceptions of certain relations of objects, as the idea of\nCause and of Likeness; and may appear to be suggested by\nexperience, enabling us to _abstract_ this general relation\nfrom particular cases. But it will be seen that Space is not\nsuch a general conception of a relation. For we do not speak\nof _Spaces_ as we speak of Causes and Likenesses, but of\nSpace. And when we speak of _spaces_, we understand by the\nexpression, parts of one and the same identical\neverywhere-extended Space. We conceive a universal Space;\nwhich is not made up of these partial spaces as its\ncomponent parts, for it would remain if these were taken\naway; and these cannot be conceived without presupposing\nabsolute space. Absolute Space is essentially one; and the\ncomplication which exists in it, and the conception of\nvarious spaces, depends merely upon boundaries. Space must,\ntherefore, be, as we have said, not a general conception\nabstracted from particulars, but a universal mode of\nrepresentation, altogether independent of experience.\n\n2. Space is infinite. We represent it to ourselves as an\ninfinitely great magnitude. Such an idea as that of Likeness\nor Cause, is, no doubt, found in an infinite number of\nparticular cases, and so far includes these cases. But these\nideas do not include an infinite number of cases as parts of\nan infinite whole. When we say that all bodies and partial\nspaces exist _in_ infinite space, we use an expression which\nis not applied in the same sense to any cases except those\nof Space and Time. {96}\n\n3. What is here said may appear to be a denial of the real\nexistence of space. It must be observed, however, that we do\nnot deny, but distinctly assert, the existence of space as a\nreal and necessary condition of all objects perceived; and\nthat we not only allow that objects are seen external to us,\nbut we found upon the fact of their being so seen, our view\nof the nature of space. If, however, it be said that we deny\nthe reality of space as an object or thing, this is true.\nNor does it appear easy to maintain that space exists as a\nthing, when it is considered that this thing is infinite in\nall its dimensions; and, moreover, that it is a thing,\nwhich, being nothing in itself, exists only that other\nthings may exist in it. And those who maintain the real\nexistence of space, must also maintain the real existence of\ntime in the same sense. Now two infinite things, thus really\nexisting, and yet existing only as other things exist in\nthem, are notions so extravagant that we are driven to some\nother mode of explaining the state of the matter.\n\n4. Thus space is not an object of which we perceive the\nproperties, but a form of our perception; not a thing which\naffects our senses, but an idea to which we conform the\nimpressions of sense. And its peculiarities appear to depend\nupon this, that it is not only a form of sensation, but of\n_intuition_; that in reference to space, we not only\nperceive but _contemplate_ objects. We see objects in space,\nside by side, exterior to each other; space, and objects in\nso far as they occupy space, have parts exterior to other\nparts; and have the whole thus made up by the juxtaposition\nof parts. This mode of apprehension belongs only to the\nideas of space and time. Space and Time are made up of\nparts, but Cause and Likeness are not apprehended as made up\nof parts. And the term _intuition_ (in its rigorous sense)\nis applicable only to that mode of contemplation in which we\nthus look at objects as made up of parts, and apprehend the\nrelations of those parts at the same time and by the same\nact by which we apprehend the objects themselves.\n\n5. As we have said, space limited by _boundaries_ {97} gives\nrise to various conceptions which we have often to consider.\nThus limited, space assumes _form_ or _figure_; and the\nvariety of conceptions thus brought under our notice is\ninfinite. We have every possible form of line, straight\nline, and curve; and of curves an endless number;--circles,\nparabolas, hyperbolas, spirals, helices. We have plane\nsurfaces of various shapes,--parallelograms, polygons,\nellipses; and we have solid figures,--cubes, cones,\ncylinders, spheres, spheroids, and so on. All these have\ntheir various properties, depending on the relations of\ntheir boundaries; and the investigation of their properties\nforms the business of the science of Geometry.\n\n6. Space has three dimensions, or directions in which it may\nbe measured; it cannot have more or fewer. The simplest\nmeasurement is that of a straight line, which has length\nalone. A surface has both length and breadth: and solid\nspace has length, breadth, and thickness or depth. The\norigin of such a difference of dimensions will be seen if we\nreflect that each portion of space has a boundary, and is\nextended both _in_ the direction in which its boundary\nextends, and also in a direction _from_ its boundary; for\notherwise it would not be a boundary. A point has no\ndimensions. A line has but one dimension,--the distance from\nits boundary, or its _length_. A plane, bounded by a\nstraight line, has the dimension which belongs to this line,\nand also has another dimension arising from the distance of\nits parts from this boundary line; and this may be called\n_breadth_. A solid, bounded by a plane, has the dimensions\nwhich this plane has; and has also a third dimension, which\nwe may call _height_ or _depth_, as we consider the solid\nextended above or below the plane; or _thickness_, if we\nomit all consideration of up and down. And no space can have\nany dimensions which are not resoluble into these three.\n\nWe may now proceed to consider the mode in which the idea of\nspace is employed in the formation of Geometry.\n\n\n\n{{98}}\nCHAPTER IV.\n\nOF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE.\n\n\n1. THE relations of space have been apprehended with\npeculiar distinctness and clearness from the very first\nunfolding of man's speculative powers. This was a\nconsequence of the circumstance which we have just noticed,\nthat the simplest of these relations, and those on which the\nothers depend, are seen by intuition. Hence, as soon as men\nwere led to speculate concerning the relations of space,\nthey assumed just principles, and obtained true results. It\nis said that the science of _geometry_ had its origin in\nEgypt, before the dawn of the Greek philosophy: but the\nknowledge of the early Egyptians (exclusive of their\nmythology) appears to have been purely practical; and,\nprobably, their geometry consisted only in some maxims of\n_land-measuring_, which is what the term implies. The Greeks\nof the time of Plato, had, however, not only possessed\nthemselves of many of the most remarkable elementary\ntheorems of the science; but had, in several instances,\nreached the boundary of the science in its elementary form;\nas when they proposed to themselves the problems of doubling\nthe cube and squaring the circle.\n\nBut the deduction of these theorems by a systematic process,\nand the primary exhibition of the simplest principles\ninvolved in the idea of space, which such a deduction\nrequires, did not take place, so far as we are aware, till a\nperiod somewhat later. The _Elements of Geometry_ of Euclid,\nin which this task was performed, are to this day the\nstandard work on the subject: the author of this work taught\nmathematics with great applause at Alexandria, in the reign\nof Ptolemy Lagus, {99} about 280 years before Christ. The\nprinciples which Euclid makes the basis of his system have\nbeen very little simplified since his time; and all the\nessays and controversies which bear upon these principles,\nhave had a reference to the form in which they are stated by him.\n\n2. _Definitions._--The first principles of Euclid's geometry\nare, as the first principles of any system of geometry must\nbe, definitions and axioms respecting the various ideal\nconceptions which he introduces; as straight lines, parallel\nlines, angles, circles, and the like. But it is to be\nobserved that these definitions and axioms are very far from\nbeing arbitrary hypotheses and assumptions. They have their\norigin in the idea of space, and are merely modes of\nexhibiting that idea in such a manner as to make it afford\ngrounds of deductive reasoning. The axioms are necessary\nconsequences of the conceptions respecting which they are\nasserted; and the definitions are no less necessary\nlimitations of conceptions; not requisite in order to arrive\nat this or that consequence; but necessary in order that it\nmay be possible to draw any consequences, and to establish\nany general truths.\n\nFor example, if we rest the end of one straight staff upon\nthe middle of another straight staff, and move the first\nstaff into various positions, we, by so doing, alter the\nangles which the first staff makes with the other to the\nright hand and to the left. But if we place the staff in\nthat special position in which these two angles are equal,\neach of them is a right angle, according to Euclid; and this\nis the _definition_ of a right angle, except that Euclid\nemploys the abstract conception of straight lines, instead\nof speaking, as we have done, of staves. But this selection\nof the case in which the two angles are equal is not a mere\nact of caprice; as it might have been if he had selected a\ncase in which these angles are unequal in any proportion.\nFor the consequences which can be drawn concerning the cases\nof unequal angles, do not lead to general truths, without\nsome reference to that peculiar case in which the angles are\nequal: and thus it becomes necessary to {100} single out and\ndefine that special case, marking it by a special phrase.\nAnd this definition not only gives complete and distinct\nknowledge what a right angle is, to any one who can form the\nconception of an angle in general; but also supplies a\nprinciple from which all the properties of right angles may\nbe deduced.\n\n3. _Axioms._--With regard to other conceptions also, as\ncircles, squares, and the like, it is possible to lay down\ndefinitions which are a sufficient basis for our reasoning,\nso far as such figures are concerned. But, besides these\ndefinitions, it has been found necessary to introduce\ncertain axioms among the fundamental principles of geometry.\nThese are of the simplest character; for instance, that two\nstraight lines cannot cut each other in more than one point,\nand an axiom concerning parallel lines. Like the\ndefinitions, these axioms flow from the Idea of Space, and\npresent that idea under various aspects. They are different\nfrom the definitions; nor can the definitions be made to\ntake the place of the axioms in the reasoning by which\nelementary geometrical properties are established. For\nexample, the definition of parallel straight lines is, that\nthey are such as, however far continued, can never meet:\nbut, in order to reason concerning such lines, we must\nfurther adopt some axiom respecting them: for example, we\nmay very conveniently take this axiom; that two straight\nlines which cut one another are not both of them parallel to\na third straight line[1\\2]. The definition and the axiom are\nseen to be inseparably connected by our intuition of the\nproperties of space; but the axiom cannot be proved from the\ndefinition, by any rigorous deductive demonstration. And if\nwe were to take any other definition of two parallel\nstraight lines, (as that they are both perpendicular to a\nthird straight line,) we should still, at some point or\nother of our progress, fall in with the same difficulty of\ndemonstratively establishing their properties without some\nfurther assumption.\n\n[Note 1\\2: This axiom is simpler and more convenient than\nthat of Euclid. It is employed by the late Professor\nPlayfair in his _Geometry_.]\n\n{101} 4. Thus the elementary properties of figures, which\nare the basis of our geometry, are necessary results of our\nIdea of Space; and are connected with each other by the\nnature of that idea, and not merely by our hypotheses and\nconstructions. Definitions and axioms must be combined, in\norder to express this idea so far as the purposes of\ndemonstrative reasoning require. These verbal enunciations\nof the results of the idea cannot be made to depend on each\nother by logical consequence; but have a mutual dependence\nof a more intimate kind, which words cannot fully convey. It\nis not possible to resolve these truths into certain\n_hypotheses_, of which all the rest shall be the necessary\nlogical consequence. The necessity is not hypothetical, but\nintuitive. The axioms require not to be granted, but to be\nseen. If any one were to assent to them without seeing them\nto be true, his assent would be of no avail for purposes of\nreasoning: for he would be also unable to see in what cases\nthey might be applied. The clear possession of the Idea of\nSpace is the first requisite for all geometrical reasoning;\nand this clearness of idea may be tested by examining\nwhether the axioms offer themselves to the mind as evident.\n\n5. The necessity of ideas added to sensations, in order to\nproduce knowledge, has often been overlooked or denied in\nmodern times. The ground of necessary truth which ideas\nsupply being thus lost, it was conceived that there still\nremained a ground of necessity in definitions;--that we\nmight have necessary truths, by asserting especially what\nthe definition implicitly involved in general. It was held,\nalso, that this was the case in geometry:--that all the\nproperties of a circle, for instance, were implicitly\ncontained in the definition of a circle. That this alone is\nnot the ground of the necessity of the truths which regard\nthe circle,--that we could not in this way unfold a\ndefinition into proportions, without possessing an intuition\nof the relations to which the definition led,--has already\nbeen shown. But the insufficiency of the above account of\nthe grounds of necessary geometrical truth appeared in\nanother way also. It was found impossible to lay {102} down\na system of definitions out of which alone the whole of\ngeometrical truth could be evolved. It was found that axioms\ncould not be superseded. No definition of a straight line\ncould be given which rendered the axiom concerning straight\nlines superfluous. And thus it appeared that the source of\ngeometrical truths was not definition alone; and we find in\nthis result a confirmation of the doctrine which we are here\nurging, that this source of truth is to be found in the form\nor conditions of our perception;--in the idea which we\nunavoidably combine with the impressions of sense;--in the\nactivity, and not in the passivity of the mind[2\\2].\n\n[Note 2\\2: I formerly stated views similar to these in some\n'Remarks' appended to a work which I termed _The Mechanical\nEuclid_, published in 1837. These Remarks, so far as they\nbear upon the question here discussed, were noticed and\ncontroverted in No. 135 of the _Edinburgh Review_. As an\nexamination of the reviewer's objections may serve further\nto illustrate the subject, I shall annex to this chapter an\nanswer to the article to which I have referred.]\n\n6. This will appear further when we come to consider the\nmode in which we exercise our observation upon the relations\nof space. But we may, in the first place, make a remark\nwhich tends to show the connexion between our conception of\na straight line, and the axiom which is made the foundation\nof our reasonings concerning space. The axiom is this;--that\ntwo straight lines, which have both their ends joined,\ncannot have the intervening parts separated so as to inclose\na space. The necessity of this axiom is of exactly the same\nkind as the necessity of the definition of a right angle, of\nwhich we have already spoken. For as the line standing on\nanother makes _right angles_ when it makes the angles on the\ntwo sides of it equal; so a line is a _straight line_ when\nit makes the two portions of space, on the two sides of it,\nsimilar. And as there is only a single position of the line\nfirst mentioned, which can make the angles equal, so there\nis only a single form of a line which can make the spaces\nnear the line similar on one side and on the other: and\n{103} therefore there cannot be two straight lines, such as\nthe axiom describes, which, between the same limits, give\ntwo different boundaries to space thus separated. And thus\nwe see a reason for the axiom. Perhaps this view may be\nfurther elucidated if we take a leaf of paper, double it,\nand crease the folded edge. We shall thus obtain a straight\nline at the folded edge; and this line divides the surface\nof the paper, as it was originally spread out, into two\nsimilar spaces. And that these spaces are similar so far as\nthe fold which separates them is concerned, appears from\nthis;--that these two parts coincide when the paper is\ndoubled. And thus a fold in a sheet of paper at the same\ntime illustrates the definition of a straight line according\nto the above view, and confirms the axiom that two such\nlines cannot inclose a space.\n\nIf the separation of the two parts of space were made by any\nother than a straight line; if, for instance, the paper were\ncut by a concave line; then, on turning one of the parts\nover, it is easy to see that the edge of one part being\nconcave one way, and the edge of the other part concave the\nother way, these two lines would enclose a space. And each\nof them would divide the whole space into two portions which\nwere not similar; for one portion would have a concave edge,\nand the other a convex edge. Between any two points, there\nmight be innumerable lines drawn, some, convex one way, and\nsome, convex the other way; but the straight line is the\nline which is not convex either one way or the other; it is\nthe single medium standard from which the others may deviate\nin opposite directions.\n\nSuch considerations as these show sufficiently that the\nsingleness of the straight line which connects any two\npoints is a result of our fundamental conceptions of space.\nBut yet the above conceptions of the similar form of the two\nparts of space on the two sides of a line, and of the form\nof a line which is intermediate among all other forms, are\nof so vague a nature, that they cannot fitly be made the\nbasis of our elementary geometry; and they are far more\nconveniently replaced, as they have been in almost all\ntreatises of {104} geometry, by the axiom, that two straight\nlines cannot inclose a space.\n\n7. But we may remark that, in what precedes, we have\nconsidered space only under one of its aspects:--as a plane.\nThe sheet of paper which we assumed in order to illustrate\nthe nature of a straight line, was supposed to be perfectly\n_plane_ or _flat_: for otherwise, by folding it, we might\nobtain a line not straight. Now this assumption of a plane\nappears to take for granted that very conception of a\nstraight line which the sheet was employed to illustrate;\nfor the definition of a plane given in the Elements of\nGeometry is, that it is a surface on which lie all straight\nlines drawn from one point of the surface to another. And\nthus the explanation above given of the nature of a straight\nline,--that it divides a plane space into similar portions\non each side,--appears to be imperfect or nugatory.\n\nTo this we reply, that the explanation must be rendered\ncomplete and valid by deriving the conception of a plane\nfrom considerations of the same kind as those which we\nemployed for a straight line. Any portion of solid space may\nbe divided into two portions by surfaces passing through any\ngiven line or boundaries. And these surfaces may be convex\neither on one side or on the other, and they admit of\ninnumerable changes from being convex on one side to being\nconvex on the other in any degree. So long as the surface is\nconvex either way, the two portions of space which it\nseparates are not similar, one having a convex and the other\na concave boundary. But there is a certain intermediate\nposition of the surface, in which position the two portions\nof space which it divides have their boundaries exactly\nsimilar. In this position, the surface is neither convex nor\nconcave, but plane. And thus a plane surface is determined\nby this condition--of its being that single surface which is\nthe intermediate form among all convex and concave surfaces\nby which solid space can be divided,--and of its separating\nsuch space into two portions, of which the boundaries,\nthough they are the same surface in two opposite positions,\nare exactly similar. {105}\n\nThus a plane is the simplest and most symmetrical boundary\nby which a solid can be divided; and a straight line is the\nsimplest and most symmetrical boundary by which a plane can\nbe separated. These conceptions are obtained by considering\nthe boundaries of an interminable space, capable of\nimaginary division in every direction. And as a limited\nspace may be separated into two parts by a plane, and a\nplane again separated into two parts by a straight line, so\na line is divided into two portions by a point, which is the\ncommon boundary of the two portions; the end of the one and\nthe beginning of the other portion having itself no\nmagnitude, form, or parts.\n\n8. The geometrical properties of planes and solids are\ndeducible from the first principles of the Elements, without\nany new axioms; the definition of a plane above\nquoted,--that all straight lines joining its points lie in\nthe plane,--being a sufficient basis for all reasoning upon\nthese subjects. And thus, the views which we have presented\nof the nature of space being verbally expressed by means of\ncertain definitions and axioms, become the groundwork of a\nlong series of deductive reasoning, by which is established\na very large and curious collection of truths, namely, the\nwhole science of Elementary Plane and Solid Geometry.\n\nThis science is one of indispensable use and constant\nreference, for every student of the laws of nature; for the\nrelations of space and number are the _alphabet_ in which\nthose laws are written. But besides the interest and\nimportance of this kind which geometry possesses, it has a\ngreat and peculiar value for all who wish to understand the\nfoundations of human knowledge, and the methods by which it\nis acquired. For the student of geometry acquires, with a\ndegree of insight and clearness which the unmathematical\nreader can but feebly imagine, a conviction that there are\nnecessary truths, many of them of a very complex and\nstriking character; and that a few of the most simple and\nself-evident truths which it is possible for the mind of man\nto apprehend, may, by systematic deduction, lead to the most\nremote and unexpected results. {106}\n\nIn pursuing such philosophical researches as that in which\nwe are now engaged, it is of great advantage to the\nspeculator to have cultivated to some extent the study of\ngeometry; since by this study he may become fully aware of\nsuch features in human knowledge as those which we have\nmentioned. By the aid of the lesson thus learned from the\ncontemplation of geometrical truths, we have been\nendeavouriug to establish those further doctrines;--that\nthese truths are but different aspects of the same\nFundamental Idea, and that the grounds of the necessity\nwhich these truths possess reside in the Idea from which\nthey flow, this Idea not being a derivative result of\nexperience, but its primary rule. When the reader has\nobtained a clear and satisfactory view of these doctrines,\nso far as they are applicable to our knowledge concerning\nspace, he has, we may trust, overcome the main difficulty\nwhich will occur in following the course of the speculations\nnow presented to him. He is then prepared to go forwards\nwith us; to see over how wide a field the same doctrines are\napplicable: and how rich and various a harvest of knowledge\nsprings from these seemingly scanty principles.\n\nBut before we quit the subject now under our consideration,\nwe shall endeavour to answer some objections which have been\nmade to the views here presented; and shall attempt to\nillustrate further the active powers which we have ascribed\nto the mind.\n\n\n\n{{107}}\nCHAPTER V.\n\nOF SOME OBJECTIONS WHICH HAVE BEEN MADE TO THE DOCTRINES\nSTATED IN THE PREVIOUS CHAPTER.[3\\2]\n\n\n[Note 3\\2: In order to render the present chapter more\nintelligible, it may be proper to state briefly the\narguments which gave occasion to the review. After noticing\nStewart's assertions, that the certainty of mathematical\nreasoning arises from its depending upon definitions, and\nthat mathematical truth is hypothetical; I urged,--that no\none has yet been able to construct a system of mathematical\ntruths by the aid of definitions alone; that a definition\nwould not be admissible or applicable except it agreed with\na distinct conception in the mind; that the definitions\nwhich we employ in mathematics are not arbitrary or\nhypothetical, but necessary definitions; that if Stewart had\ntaken as his examples of axioms the peculiar geometrical\naxioms, his assertions would have been obviously erroneous;\nand that the real foundation of the truths of mathematics is\nthe Idea of Space, which may be expressed (for purposes of\ndemonstration) partly by definitions and partly by axioms.]\n\nTHE _Edinburgh Review_, No. cxxxv., contains a critique on a\nwork termed _The Mechanical Euclid_, in which opinions were\ndelivered to nearly the same effect as some of those stated\nin the last chapter, and hereafter in Chapter xi. Although I\nbelieve that there are no arguments used by the reviewer to\nwhich the answers will not suggest themselves in the mind of\nany one who has read with attention what has been said in\nthe preceding chapters (except, perhaps, one or two remarks\nwhich have reference to mechanical ideas), it may serve to\nillustrate the subject if I reply to the objections\ndirectly, taking them as the reviewer has stated them.\n\nI. I had dissented from Stewart's assertion that\nmathematical truth is hypothetical, or depends upon\narbitrary definitions; since we understand by an {108}\nhypothesis a supposition, not only which we may make, but\nmay abstain from making, or may replace by a different\nsupposition; whereas the definitions and hypotheses of\ngeometry are necessarily such as they are, and cannot be\naltered or excluded. The reviewer (p. 84) informs us that he\nunderstands Stewart, when he speaks of hypotheses and\ndefinitions being the foundation of geometry, to speak of\nthe hypothesis that real objects correspond to our\ngeometrical definitions. '_If_ a crystal be an exact\nhexahedron, the geometrical properties of the hexahedron may\nbe predicated of that crystal.' To this I reply,--that such\nhypotheses as this are the grounds of our applications of\ngeometrical truths to real objects, but can in no way be\nsaid to be the foundation of the truths themselves;--that I\ndo not think that the sense which the reviewer gives was\nStewart's meaning;--but that if it was, this view of the use\nof mathematics does not at all affect the question which\nboth he and I proposed to discuss, which was, the ground of\nmathematical certainty. I may add, that whether a crystal be\nan exact hexahedron, is a matter of observation and\nmeasurement, not of definition. I think the reader can have\nno difficulty in seeing how little my doctrine is affected\nby the connexion on which the reviewer thus insists. I have\nasserted that the proposition which affirms the square on\nthe diagonal of a rectangle to be equal to the squares on\ntwo sides, does not rest upon arbitrary hypotheses; the\nobjector answers, that the proposition that the square on\nthe diagonal _of this page_ is equal to the squares on the\nsides, depends upon the arbitrary hypothesis that the page\nis a rectangle. Even if this fact were a matter of arbitrary\nhypothesis, what could it have to do with the general\ngeometrical proposition? How could a single fact, observed\nor hypothetical, affect a universal and necessary truth,\nwhich would be equally true if the fact were false? If there\nbe nothing arbitrary or hypothetical in geometry till we\ncome to such steps in its application, it is plain that the\ntruths themselves are not hypothetical; which is the\nquestion for us to decide. {109}\n\n2. The reviewer then (p. 85) considers the doctrine that\naxioms as well as definitions are the foundations of\ngeometry; and here he strangely narrows and confuses the\ndiscussion by making himself the advocate of Stewart,\ninstead of arguing the question itself. I had asserted that\nsome axioms are necessary as the foundations of mathematical\nreasoning, in addition to the definitions. If Stewart did\nnot intend to discuss this question, I had no concern with\nwhat he had said about axioms. But I had every reason to\nbelieve that this was the question which Stewart did intend\nto discuss. I conceive there is no doubt that he intended to\ngive an opinion upon the grounds of mathematical reasoning\nin general. For he begins his discussions (_Elements_, vol.\nii. p. 38) by contesting Reid's opinion on this subject,\nwhich is stated generally; and he refers again to the same\nsubject, asserting in general terms, that the first\nprinciples of mathematics are not axioms but definitions.\nIf, then, afterwards, he made his proof narrower than his\nassertion;--if having declared that no axioms are necessary,\nhe afterwards limited himself to showing that seven out of\ntwelve of Euclid's axioms are barren truisms, it was no\nconcern of mine to contest this assertion, which left my\nthesis untouched. I had asserted that the proper geometrical\naxioms (that two straight lines cannot inclose a space, and\nthe axiom about parallel lines) are indispensable in\ngeometry. What account the reviewer gives of these axioms we\nshall soon see; but if Stewart allowed them to be axioms\nnecessary to geometrical reasoning, he overturned his own\nassertion as to the foundations of such reasoning; and if he\nsaid nothing decisive about these axioms, which are the\npoints on which the battle must turn, he left his assertion\naltogether unproved; nor was it necessary for me to pursue\nthe war into a barren and unimportant corner, when the\nmetropolis was surrendered. The reviewer's exultation that I\nhave not contested the first seven axioms is an amusing\nexample of the self-complacent zeal of advocacy.\n\n3. But let us turn to the material point,--the proper\ngeometrical axioms. What is the reviewer's account of {110}\nthese? Which side of the alternative does he adopt? Do they\ndepend upon the definitions, and is he prepared to show the\ndependence? Or are they superfluous, and can he erect the\nstructure of geometry without their aid? One of these two\ncourses, it would seem, he must take. For we both begin by\nasserting the excellence of geometry as an example of\ndemonstrated truth. It is precisely this attribute which\ngives an interest to our present inquiry. How, then, does\nthe reviewer explain this excellence on his views? How does\nhe reckon the foundation courses of the edifice which we\nagree in considering as a perfect example of intellectual\nbuilding?\n\nI presume I may take, as his answer to this question, his\nhypothetical statement of what Stewart would have said (p.\n87), on the supposition that there had been, among the\nfoundations of geometry, self-evident indemonstrable truths:\nalthough it is certainly strange that the reviewer should\nnot venture to make up his mind as to the truth or falsehood\nof this supposition. If there were such truths they would\nbe, he says, 'legitimate filiations' of the definitions.\nThey would be involved in the definitions. And again he\nspeaks of the foundation of the geometrical doctrine of\nparallels as a flaw, and as a truth which requires, but has\nnot received demonstration. And yet again, he tells us that\neach of these supposed axioms (Euclid's twelfth, for\ninstance) is 'merely an indication of the point at which\ngeometry fails to perform that which it undertakes to\nperform' (p. 91); and that in reality her truths are not yet\ndemonstrated. The amount of this is, that the geometrical\naxioms are to be held to be _legitimate filiations_ of the\ndefinitions, because though certainly true, they cannot be\nproved from the definitions; that they are involved in the\ndefinitions, although they cannot be evolved out of them;\nand that rather than admit that they have any other origin\nthan the definitions, we are to proclaim that geometry has\nfailed to perform what she undertakes to perform.\n\nTo this I reply--that I cannot understand what is meant by\n'legitimate filiations' of principles, if the {111} phrase\ndo not mean consequences of such principles established by\nrigorous and formal demonstrations;--that the reviewer, if\nhe claims any real signification for his phrase, must\nsubstantiate the meaning of it by such a demonstration; he\nmust establish his 'legitimate filiation' by a genealogical\ntable in a satisfactory form. When this cannot be done, to\nassert, notwithstanding, that the propositions are involved\nin the definitions, is a mere begging the question; and to\nexcuse this defect by saying that geometry fails to perform\nwhat she has promised, is to calumniate the character of\nthat science which we profess to make our standard, rather\nthan abandon an arbitrary and unproved assertion respecting\nthe real grounds of her excellence. I add, further, that if\nthe doctrine of parallel lines, or any other geometrical\ndoctrine of which we see the truth, with the most perfect\ninsight of its necessity, have not hitherto received\ndemonstration to the satisfaction of any school of\nreasoners, the defect must arise from their erroneous views\nof the nature of demonstrations, and the grounds of\nmathematical certainty.\n\n4. I conceive, then, that the reviewer has failed altogether\nto disprove the doctrine that the axioms of geometry are\nnecessary as a part of the foundations of the science. I had\nasserted further that these axioms supply what the\ndefinitions leave deficient; and that they, along with\ndefinitions, serve to present the idea of space under such\naspects that we can reason logically concerning it. To this\nthe reviewer opposes (p. 96) the common opinion that a\nperfect definition is a complete explanation of a name, and\nthat the test of its perfection is, that we may substitute\nthe definition for the name wherever it occurs. I reply,\nthat my doctrine, that a definition expresses a part, but\nnot the whole, of the essential characters of an idea, is\ncertainly at variance with an opinion sometimes maintained,\nthat a definition merely explains a word, and should explain\nit so fully that it may always replace it. The error of this\ncommon opinion may, I think, be shown from considerations\nsuch as these;--that if {112} we undertake to explain one\nword by several, we may be called upon, on the same ground,\nto explain each of these several by others, and that in this\nway we can reach no limit nor resting-place;--that in point\nof fact, it is not found to lead to clearness, but to\nobscurity, when in the discussion of general principles, we\nthus substitute definitions for single terms;--that even if\nthis be done, we cannot reason without conceiving what the\nterms mean;--and that, in doing this, the relations of our\nconceptions, and not the arbitrary equivalence of two forms\nof expression, are the foundations of our reasoning.\n\n5. The reviewer conceives that some of the so-called axioms\nare really definitions. The axiom, that 'magnitudes which\ncoincide with each other, that is, which fill the same\nspace, are equal,' is a definition of geometrical\n_equality_: the axiom, that 'the whole is greater than its\npart,' is a definition of _whole_ and _part_. But surely\nthere are very serious objections to this view. It would\nseem more natural to say, if the former axiom is a\ndefinition of the word _equal_, that the latter is a\ndefinition of the word _greater_. And how can one short\nphrase define two terms? If I say, 'the heat of summer is\ngreater than the heat of winter,' does this assertion define\nanything, though the proposition is perfectly intelligible\nand distinct? I think, then, that this attempt to reduce\nthese axioms to definitions is quite untenable.\n\n6. I have stated that a definition can be of no use, except\nwe can conceive the possibility and truth of the property\nconnected with it; and that if we do conceive this, we may\nrightly begin our reasonings by stating the property as an\naxiom; which Euclid does, in the case of straight lines and\nof parallels. The reviewer inquires (p. 92), whether I am\nprepared to extend this doctrine to the case of circles, for\nwhich the reasoning is usually rested upon the\ndefinition;--whether I would replace this definition by an\naxiom, asserting the possibility of such a circle. To this I\nmight reply, that it is not at all incumbent upon me to\nassent to such a change; for I have all along stated that it\nis indifferent {113} whether the fundamental properties from\nwhich we reason be exhibited as definitions or as axioms,\nprovided the necessity be clearly seen. But I am ready to\ndeclare that I think the form of our geometry would be not\nat all the worse, if, instead of the usual definition of a\ncircle,--'that it is a figure contained by one line, which\nis called the circumference, and which is such, that all\nstraight lines drawn from a certain point within the\ncircumference are equal to one another,'--we were to\nsubstitute an axiom and a definition, as follows:--\n_Axiom_. If a line be drawn so as to be at every point\nequally distant from a certain point, this line will return\ninto itself or will be _one_ line including a space.\n_Definition_. The space is called a _circle_, the line the\n_circumference_, and the point the _center_.\n\nAnd this being done, it would be true, as the reviewer\nremarks, that geometry cannot stir _one_ step without\nresting on an axiom. And I do not at all hesitate to say,\nthat the above axiom, expressed or understood, is no less\nnecessary than the definition, and is tacitly assumed in\nevery proposition into which circles enter.\n\n7. I have, I think, now disposed of the principal objections\nwhich bear upon the proper axioms of geometry. The\nprinciples which are stated as the first seven axioms of\nEuclid's _Elements_, need not, as I have said, be here\ndiscussed. They are principles which refer, not to Space in\nparticular, but to Quantity in general: such, for instance,\nas these; 'If equals be added to equals the wholes are\nequal;'--'If equals be taken from equals the remainders are\nequal.' But I will make an observation or two upon them\nbefore I proceed.\n\nBoth Locke and Stewart have spoken of these axioms as barren\ntruisms: as propositions from which it is not possible to\ndeduce a single inference: and the reviewer asserts that\nthey are not first principles, but laws of thought (p. 88).\nTo this last expression I am {114} willing to assent; but I\nwould add, that not only these, but all the principles which\nexpress the fundamental conditions of our knowledge, may\nwith equal propriety be termed laws of thought; for these\nprinciples depend upon our ideas, and regulate the active\noperations of the mind, by which coherence and connexion are\ngiven to its passive impressions. But the assertion that no\nconclusions can be drawn from simple axioms, or laws of\nhuman thought, which regard quantity, is by no means true.\nThe whole of arithmetic,--for instance, the rules for the\nmultiplication and division of large numbers, the rule for\nfinding a common measure, and, in short, a vast body of\ntheory respecting numbers,--rests upon no other foundation\nthan such axioms as have been just noticed, that if equals\nbe added to equals the wholes will be equal. And even when\nLocke's assertion, that from these axioms no truths can be\ndeduced, is modified by Stewart and the reviewer, and\nlimited to _geometrical_ truths, it is hardly tenable\n(although, in fact, it matters little to our argument\nwhether it is or no). For the greater part of the Seventh\nBook of Euclid's _Elements_, (on Commensurable and\nIncommensurable Quantities,) and the Fifth Book, (on\nProportion,) depend upon these axioms, with the addition\nonly of the definition or axiom (for it may be stated either\nway) which expresses the idea of proportionality in numbers.\nSo that the attempt to disprove the necessity and use of\naxioms, as principles of reasoning, fails even when we take\nthose instances which the opponents consider as the more\nmanifestly favourable to their doctrine.\n\n8. But perhaps the question may have already suggested\nitself to the reader's mind, of what use can it be formally\nto state such principles as these, (for example, that if\nequals be added to equals the wholes are equal,) since,\nwhether stated or no, they will be assumed in our reasoning?\nAnd how can such principles be said to be necessary, when\nour proof proceeds equally well without any reference to\nthem? And the answer is, that it is precisely because these\nare the {115} common principles of reasoning, which we\nnaturally employ without specially contemplating them, that\nthey require to be separated from the other steps and\nformally stated, when we _analyse_ the demonstrations which\nwe have obtained. In every mental process many principles\nare combined and abbreviated, and thus in some measure\nconcealed and obscured. In analysing these processes, the\ncombination must be resolved, and the abbreviation expanded,\nand thus the appearance is presented of a pedantic and\nsuperfluous formality. But that which is superfluous for\nproof, is necessary for the analysis of proof. In order to\nexhibit the conditions of demonstration distinctly, they\nmust be exhibited formally. In the same manner, in\ndemonstration we do not usually express every step in the\nform of a syllogism, but we see the grounds of the\nconclusiveness of a demonstration, by resolving it into\nsyllogisms. Neither axioms nor syllogisms are necessary for\nconviction; but they are necessary to display the conditions\nunder which conviction becomes inevitable. The application\nof a single one of the axioms just spoken of is so minute a\nstep in the proof, that it appears pedantic to give it a\nmarked place; but the very essence of demonstration consists\nin this, that it is composed of an indissoluble succession\nof such minute steps. The admirable circumstance is, that by\nthe accumulation of such apparently imperceptible advances,\nwe can in the end make so vast and so sure a progress. The\ncompleteness of the analysis of our knowledge appears in the\nsmallness of the elements into which it is thus resolved.\nThe minuteness of any of these elements of truth, of axioms\nfor instance, does not prevent their being as essential as\nothers which are more obvious. And any attempt to assume one\nkind of element only, when the course of our analysis brings\nbefore us two or more kinds, is altogether unphilosophical.\nAxioms and definitions are the proximate constituent\nprinciples of our demonstrations; and the intimate bond\nwhich connects together a definition and an axiom on the\nsame subject is not truly expressed {116} by asserting the\nlatter to be derived from the former. This bond of connexion\nexists in the mind of the reasoner, in his conception of\n_that_ to which both definition and axiom refer, and\nconsequently in the general Fundamental Idea of which that\nconception is a modification.\n\n\n\n{{117}}\nCHAPTER VI.\n\nOF THE PERCEPTION OF SPACE.\n\n\n1. ACCORDING to the views above explained, certain of the\nimpressions of our senses convey to us the perception of\nobjects as existing in space; inasmuch as by the\nconstitution of our minds we cannot receive those\nimpressions otherwise than in a certain form, involving such\na manner of existence. But the question deserves to be\nasked, _What_ are the impressions of sense by which we thus\nbecome acquainted with space and its relations? And as we\nhave seen that this idea of space implies an act of the mind\nas well as an impression on the sense, what manifestations\ndo we find of this activity of the mind, in our observation\nof the external world?\n\nIt is evident that sight and touch are the senses by which\nthe relations of space are perceived, principally or\nentirely. It does not appear that an odour, or a feeling of\nwarmth or cold, would, independently of experience, suggest\nto us the conception of a space surrounding us. But when we\n_see_ objects, we see that they are extended and occupy\nspace; when we _touch_ them, we feel that they are in a\nspace in which we also are. We have before our eyes any\nobject, for instance, a board covered with geometrical\ndiagrams; and we distinctly perceive, by vision, those lines\nof which the relations are the subjects of our mathematical\nreasoning. Again, we see before us a solid object, a cubical\nbox for instance; we see that it is within reach; we stretch\nout the hand and perceive by the touch that it has sides,\nedges, corners, which we had already perceived by vision. {118}\n\n2. Probably most persons do not generally apprehend that\nthere is any material difference in these two cases;--that\nthere are any different acts of mind concerned in perceiving\nby sight a mathematical diagram upon paper, and a solid cube\nlying on a table. Yet it is not difficult to show that, in\nthe latter case at least, the perception of the shape of the\nobject is not immediate. A very little attention teaches us\nthat there is an act of judgment as well as a mere\nimpression of sense requisite, in order that we may see any\nsolid object. For there is no visible appearance which is\ninseparably connected with solidity. If a picture of a cube\nbe rightly drawn, in perspective and skilfully shaded, the\nimpression upon the sense is the same as if it were a real\ncube. The picture may be mistaken for a solid object. But it\nis clear that, in this case, the solidity is given to the\nobject by an act of mental judgment. All that is seen is\noutline and shade, figures and colours on a flat board. The\nsolid angles and edges, the relation of the faces of the\nfigure by which they form a cube, are matters of inference.\nThis, which is evident in the case of the pictured cube, is\ntrue in all vision whatever. We see a scene before us on\nwhich are various figures and colours, but the eye cannot\nsee more. It sees length and breadth, but no third\ndimension. In order to know that there are solids, we must\ninfer as well as see. And this we do readily and constantly;\nso familiarly, indeed, that we do not perceive the\noperation. Yet we may detect this latent process in many\nways; for instance, by attending to cases in which the habit\nof drawing such inferences misleads us. Most persons have\nexperienced this delusion in looking at a scene in a\ntheatre, and especially that kind of scene which is called a\n_diorama_, when the interior of a building is represented.\nIn these cases, the perspective representations of the\nvarious members of the architecture and decoration impress\nus almost irresistibly with the conviction that we have\nbefore us a space of great extent and complex form, instead\nof a flat painted canvass. Here, at least, the space is our\nown creation; but yet here, it is {119} manifestly created\nby the same act of thought as if we were really in the\npalace or the cathedral of which the halls and aisles thus\nseem to inclose us. And the act by which we thus create\nspace of three dimensions out of visible extent of length\nand breadth, is constantly and imperceptibly going on. We\nare perpetually interpreting in this manner the language of\nthe visible world. From the appearances of things which we\ndirectly see, we are constantly inferring that which we\ncannot directly see,--their distance from us, and the\nposition of their parts.\n\n3. The characters which we thus interpret are various. They\nare, for instance, the visible forms, colours, and shades of\nthe parts, understood according to the maxims of\nperspective; (for of perspective every one has a practical\nknowledge, as every one has of grammar;) the effort by which\nwe fix both our eyes on the same object, and adjust each eye\nto distinct vision; and the like. The right interpretation\nof the information which such circumstances give us\nrespecting the true forms and distances of things, is\ngradually learned; the lesson being begun in our earliest\ninfancy, and inculcated upon us every hour during which we\nuse our eyes. The completeness with which the lesson is\nmastered is truly admirable; for we forget that our\nconclusion is obtained indirectly, and mistake a judgment on\nevidence for an intuitive perception. We see the breadth of\nthe street, as clearly and readily as we see the house on\nthe other side of it; and we see the house to be square,\nhowever obliquely it be presented to us. This, however, by\nno means throws any doubt or difficulty on the doctrine that\nin all these cases we do interpret and infer. The rapidity\nof the process, and the unconsciousness of the effort, are\nnot more remarkable in this case than they are when we\nunderstand the meaning of the speech which we hear, or of\nthe book which we read. In these latter cases we merely hear\nnoises or see black marks; but we make, out of these\nelements, thought and feeling, without being aware of the\nact by which we do so. And by an exactly similar process we\nsee a variously-coloured {120} expanse, and collect from it\na space occupied by solid objects. In both cases the act of\ninterpretation is become so habitual that we can hardly stop\nshort at the mere impression of sense.\n\n4. But yet there are various ways in which we may satisfy\nourselves that these two parts of the process of seeing\nobjects are distinct. To separate these operations is\nprecisely the task which the artist has to execute, in\nmaking a drawing of what he sees. He has to recover the\nconsciousness of his real and genuine sensations, and to\ndiscern the lines of objects as they appear. This at first\nhe finds difficult; for he is tempted to draw what he knows\nof the forms of visible objects, and not what he sees: but\nas he improves in his art, he learns to put on paper what he\nsees only, separated from what he infers, in order that thus\nthe inference, and with it a conception like that of the\nreality, may be left to the spectator. And thus the natural\nprocess of vision is the habit of seeing that which cannot\nbe seen; and the difficulty of the art of drawing consists\nin learning not to see more than is visible.\n\n5. But again; even in the simplest drawing we exhibit\nsomething which we do not see. However slight is our\nrepresentation of objects, it contains something which we\ncreate for ourselves. For we draw an _outline_. Now an\noutline has no existence in nature. There are no visible\nlines presented to the eye by a group of figures. We\nseparate each figure from the rest, and the boundary by\nwhich we do this is the outline of the figure; and the like\nmay be said of each member of every figure. A painter of our\nown times has made this remark in a work upon his art[4\\2]:\n'The effect which natural objects produce upon our sense of\nvision is that of a number of parts, or distinct masses of\nform and colour, and not of lines. But when we endeavour to\nrepresent by painting the objects which are before us, or\nwhich invention supplies to our minds, {121} the first and\nthe simplest means we resort to is this picture, by which we\nseparate the form of each object from those that surround\nit, marking its boundary, the extreme extent of its\ndimensions in every direction, as impressed on our vision:\nand this is termed drawing its outline.'\n\n[Note 4\\2: Phillips _On Painting._]\n\n6. Again, there are other ways in which we see clear\nmanifestations of the act of thought by which we assign to\nthe parts of objects their relations in space, the\nimpressions of sense being merely subservient to this act.\nIf we look at a medal through a glass which inverts it, we\nsee the figures upon it become concave depressions instead\nof projecting convexities; for the light which illuminates\nthe nearer side of the convexity will be transferred to the\nopposite side by the apparent inversion of the medal, and\nwill thus imply a hollow in which the side nearest the light\ngathers the shade. Here our decision as to which part is\nnearest to us, has reference to the side from which the\nlight comes. In other cases the decision is more\nspontaneous. If we draw black outlines, such as represent\nthe edges of a cube seen in perspective, certain of the\nlines will cross each other; and we may make this cube\nappear to assume two different positions, by determining in\nour own mind that the lines which belong to one end of the\ncube shall be understood to be before or to be behind those\nwhich they cross. Here an act of the will, operating upon\nthe same sensible image, gives us two cubes, occupying two\nentirely different positions. Again, many persons may have\nobserved that when a windmill in motion at a distance from\nus, (so that the outline of the sails only is seen,) stands\nobliquely to the eye, we may, by an effort of thought, make\nthe obliquity assume one or the other of two positions; and\nas we do this, the sails, which in one instance appear to\nturn from right to left, in the other case turn from left to\nright. A person a little familiar with this mental effort,\ncan invert the motion as often as he pleases, so long as the\nconditions of form and light do not offer a manifest\ncontradiction to either position. {122}.\n\nThus we have these abundant and various manifestations of\nthe activity of the mind, in the process by which we collect\nfrom vision the relations of solid space of three\ndimensions. But we must further make some remarks on the\nprocess by which we perceive mere visible figure; and also,\non the mode in which we perceive the relations of space by\nthe touch; and first, of the latter subject.\n\n7. The opinion above illustrated, that our sight does not\ngive us a direct knowledge of the relations of solid space,\nand that this knowledge is acquired only by an inference of\nthe mind, was first clearly taught by the celebrated Bishop\nBerkeley[5\\2], and is a doctrine now generally assented to\nby metaphysical speculators.\n\n[Note 5\\2: _Theory of Vision._]\n\nBut does the sense of _touch_ give us directly a knowledge\nof space? This is a question which has attracted\nconsiderable notice in recent times; and new light has been\nthrown upon it in a degree which is very remarkable, when we\nconsider that the philosophy of perception has been a\nprominent subject of inquiry from the earliest times. Two\nphilosophers, advancing to this inquiry from different\nsides, the one a metaphysician, the other a physiologist,\nhave independently arrived at the conviction that the long\ncurrent opinion, according to which we acquire a knowledge\nof space by the sense of touch, is erroneous. And the\ndoctrine which they teach instead of the ancient errour, has\na very important bearing upon the principle which we are\nendeavouring to establish,--that our knowledge of space and\nits properties is derived rather from the active operations\nthan from the passive impressions of the percipient mind.\n\nUndoubtedly the persuasion that we acquire a knowledge of\nform by the touch is very obviously suggested by our common\nhabits. If we wish to know the form of any body in the dark,\nor to correct the impressions conveyed by sight, when we\nsuspect them to be false, we have only, it seems to us, at\nleast at first, to stretch forth the hand and touch the\nobject; and we learn its {123} shape with, no chance of\nerrour. In these cases, form appears to be as immediate a\nperception of the sense of touch, as colour is of the sense\nof sight.\n\n8. But is this perception really the result of the passive\nsense of touch merely? Against such an opinion Dr. Brown,\nthe metaphysician of whom I speak, urges[6\\2] that the\nfeeling of touch alone, when any object is applied to the\nhand, or any other part of the body, can no more convey the\nconception of form or extension, than the sensation of an\nodour or a taste can do, except we have already some\nknowledge of the relative position of the parts of our\nbodies; that is, except we are already in possession of an\nidea of space, and have, in our minds, referred our limbs to\ntheir positions; which is to suppose the conception of form\nalready acquired.\n\n[Note 6\\2: _Lectures_, Vol. i. p. 459, (1824).]\n\n9. By what faculty then do we originally acquire our\nconceptions of the relations of position? Brown answers by\nthe _muscular sense_; that is, by the conscious exertions of\nthe various muscles by which we move our limbs. When we feel\nout the form and position of bodies by the hand, our\nknowledge is acquired, not by the mere touch of the body,\nbut by perceiving the course the fingers must take in order\nto follow the surface of the body, or to pass from one body\nto another. We are conscious of the slightest of the\nvolitions by which we thus feel out form and place; we know\nwhether we move the finger to the right or left, up or down,\nto us or from us, through a large or a small space; and all\nthese conscious acts are bound together and regulated in our\nminds by an idea of an extended space in which they are\nperformed. That this idea of space is not borrowed from the\nsight, and transferred to the muscular feelings by habit, is\nevident. For a man born blind can feel out his way with his\nstaff, and has his conceptions of position determined by the\nconditions of space, no less than one who has the use of his\neyes. And the muscular consciousness which reveals to us the\nposition of objects and parts of objects, {124} when we feel\nthem out by means of the hand, shows itself in a thousand\nother ways, and in all our limbs: for our habits of\nstanding, walking, and all other attitudes and motions, are\nregulated by our feeling of our position and that of\nsurrounding objects. And thus, we cannot touch any object\nwithout learning something respecting its position; not that\nthe sense of touch directly conveys such knowledge; but we\nhave already learnt, from the muscular sense, constantly\nexercised, the position of the limb which the object thus\ntouches.\n\n10. The justice of this distinction will, I think, be\nassented to by all persons who attend steadily to the\nprocess itself, and might be maintained by many forcible\nreasons. Perhaps one of the most striking evidences in its\nfavour is that, as I have already intimated, it is the\nopinion to which another distinguished philosopher, Sir\nCharles Bell, has been led, reasoning entirely upon\nphysiological principles. From his researches it resulted\nthat besides the nerves which convey the impulse of the will\nfrom the brain to the muscle, by which every motion of our\nlimbs is produced, there is another set of nerves which\ncarry back to the brain a sense of the condition of the\nmuscle, and thus regulate its activity; and give us the\nconsciousness of our position and relation to surrounding\nobjects. The motion of the hand and fingers, or the\nconsciousness of this motion, must be combined with the\nsense of touch properly so called, in order to make an inlet\nto the knowledge of such relations. This consciousness of\nmuscular exertion, which he has called a sixth sense[7\\2],\nis our guide, Sir C. Bell shows, in the common practical\ngovernment of our motions; and he states that having given\nthis explanation of perception as a physiological doctrine,\nhe had afterwards with satisfaction seen it confirmed by Dr.\nBrown's speculations.\n\n[Note 7\\2: _Bridgewater Treatise_, p. 195. _Phil. Trans._\n1826, Pt. ii. p. 167.]\n\n11. Thus it appears that our consciousness of the relations\nof space is inseparably and fundamentally connected with our\nown actions in space. We perceive {125} only while we act;\nour sensations require to be interpreted by our volitions.\nThe apprehension of extension and figure is far from being a\nprocess in which we are inert and passive. We draw lines\nwith our fingers; we construct surfaces by curving our\nhands; we generate spaces by the motion of our arms. When\nthe geometer bids us form lines, or surfaces, or solids by\nmotion, he intends his injunction to be taken as\nhypothetical only; we need only conceive such motions. But\nyet this hypothesis represents truly the origin of our\nknowledge; we perceive spaces by motion at first, as we\nconceive spaces by motion afterwards:--or if not always by\nactual motion, at least by potential. If we perceive the\nlength of a staff by holding its two ends in our two hands\nwithout running the finger along it, this is because by\nhabitual motion we have already acquired a measure of the\ndistance of our hands in any attitude of which we are\nconscious. Even in the simplest case, our perceptions are\nderived not from the touch, but from the sixth sense; and\nthis sixth sense at least, whatever may be the case with the\nother five, implies an active mind along with the passive sense.\n\n12. Upon attentive consideration, it will be clear that a\nlarge portion of the perceptions respecting space which\nappear at first to be obtained by sight alone, are, in fact,\nacquired by means of this sixth sense. Thus we consider the\nvisible sky as a single surface surrounding us and returning\ninto itself, and thus forming a hemisphere. But such a mode\nof conceiving an object of vision could never have occurred\nto us, if we had not been able to turn our heads, to follow\nthis surface, to pursue it till we find it returning into\nitself. And when we have done this, we necessarily present\nit to ourselves as a concave inclosure within which we are.\nThe sense of sight alone, without the power of muscular\nmotion, could not have led us to view the sky as a vault or\nhemisphere. Under such circumstances, we should have\nperceived only what was presented to the eye in one\nposition; and if different appearances had been presented in\nsuccession, we could {126} not have connected them as parts\nof the same picture, for want of any perception of their\nrelative position. They would have been so many detached and\nincoherent visual sensations. The muscular sense connects\ntheir parts into a whole, making them to be only different\nportions of one universal scene[8\\2].\n\n[Note 8\\2: It has been objected to this view that we might\nobtain a conception of the sky as a hemisphere, by being\nourselves turned round, (as on a music-stool, for instance,)\nand thus seeing in succession all parts of the sky. But this\nassertion I conceive to be erroneous. By being thus turned\nround, we should see a number of pictures which we should\nput together as parts of a plane picture; and when we came\nround to the original point, we should have no possible\nmeans of deciding that it was the _same_ point: it would\nappear only as a _repetition_ of the picture. That sight, of\nitself, can give us only a plane picture, the doctrine of\nBerkeley, appears to be indisputable; and, no less so, the\ndoctrine that it is the consciousness of our own action in\nspace which puts together these pictures so that they cover\nthe surface of a solid body. We can see length and breadth\nwith our eyes, but we must thrust out our arm towards the\nflat surface, in order that we may, in our thoughts, combine\na third dimension with the other two.]\n\n13. These considerations point out the fallacy of a very\ncurious representation made by Dr. Reid, of the convictions\nto which man would be led, if he possessed vision without\nthe sense of touch. To illustrate this subject, Reid uses\nthe fiction of a nation whom he terms the _Idomenians_, who\nhave no sense except that of sight. He describes their\nnotions of the relations of space as being entirely\ndifferent from ours. The axioms of their geometry are quite\ncontradictory to our axioms. For example, it is held to be\nself-evident among them that two straight lines which\nintersect each other once, must intersect a second time;\nthat the three angles of any triangle are _greater_ than two\nright angles; and the like. These paradoxes are obtained by\ntracing the relations of lines on the surface of a concave\nsphere, which surrounds the spectator, and on which all\nvisible appearances may be supposed to be presented to him.\nBut from what is said above it appears that the notion of\nsuch a sphere, and such a connexion of visible objects which\nare seen in different {127} directions, cannot be arrived at\nby sight alone. When the spectator combines in his\nconception the relations of long-drawn lines and large\nfigures, as he sees them by turning his head to the right\nand to the left, upwards and downwards, he ceases to be an\nIdomenian. And thus our conceptions of the properties of\nspace, derived through the exercise of one mode of\nperception, are not at variance with those obtained in\nanother way; but all such conceptions, however produced or\nsuggested, are in harmony with each other; being, as has\nalready been said, only different aspects of the same idea.\n\n14. If our perceptions of the position of objects around us\ndo not depend on the sense of vision alone, but on the\nmuscular feeling brought into play when we turn our head, it\nwill obviously follow that the same is true when we turn the\neye instead of the head. And thus we may learn the form of\nobjects, not by looking at them with a fixed gaze, but by\nfollowing the boundary of them with the eye. While the head\nis held perfectly still, the eye can rove along the outlines\nof visible objects, scrutinize each point in succession, and\nleap from one point to another; each such act being\naccompanied by a muscular consciousness which makes us aware\nof the direction in which the look is travelling. And we may\nthus gather information concerning the figures and places\nwhich we trace out with the visual ray, as the blind man\nlearns the forms of things which he traces out with his\nstaff, being conscious of the motions of his hand.\n\n15. This view of the mode in which the eye perceives\nposition, which is thus supported by the analogy of other\nmembers employed for the same purpose, is further confirmed\nby Sir Charles Bell by physiological reasons. He teaches us\nthat[9\\2] when an object is seen we employ two senses: there\nis an impression on the retina; but we receive also the idea\nof position or relation in space, which it is not the office\nof the retina to give, by our consciousness of the efforts\nof the voluntary {128} muscles of the eye: and he has traced\nin detail the course of the nerves by which these muscles\nconvey their information. The constant _searching_ motion of\nthe eye, as he terms it[10\\2], is the means by which we\nbecome aware of the position of objects about us.\n\n[Note 9\\2: _Phil. Trans._ 1823. On the Motions of the Eye.]\n\n[Note 10\\2: _Bridgewater Treatise_, p. 282. I have adopted,\nin writing the above, the views and expressions of Sir\nCharles Bell. The essential part of the doctrine there\npresented is, that the eye constantly makes efforts to turn,\nso that the image of an object to which our attention is\ndrawn, shall fall upon a certain particular point of the\nretina; and that when the image falls upon any other point,\nthe eye turns away from this oblique into the direct\nposition. Other writers have maintained that the eye thus\nturns not because the point on which the image falls in\ndirect vision is the most _sensible_ point, but that it is\nthe point of _greatest distinctness_ of vision. They urge\nthat a small star, which disappears when the eye is turned\nfull upon it, may often be seen by looking a little away\nfrom it: and hence, they infer that the parts of the retina\nremoved from the spot of direct vision, are more sensible\nthan it is. The facts are very curious, however they be\nexplained, but they do not disturb the doctrine delivered in\nthe text.]\n\n16. It is not to our present purpose to follow the\nphysiology of this subject; but we may notice that Sir C.\nBell has examined the special circumstances which belong to\nthis operation of the eye. We learn from him that the\nparticular point of the eye which thus traces the forms of\nvisible objects is a part of the retina which has been\ntermed the _sensible spot_; being that part which is _most\ndistinctly_ sensible to the impressions of light and colour.\nThis part, indeed, is not a spot of definite size and form,\nfor it appears that proceeding from a certain point of the\nretina, the distinct sensibility diminishes on every side by\ndegrees. And the searching motion of the eye arises from the\ndesire which we instinctively feel of receiving upon the\nsensible spot the image of the object to which the attention\nis directed. We are uneasy and impatient till the eye is\nturned so that this is effected. And as our attention is\ntransferred from point to point of the scene before us, the\neye, and this point of the eye in particular, travel along\nwith the thoughts; and the muscular sense, which tells us of\nthese movements of the organ of {129} vision, conveys to us\na knowledge of the forms and places which we thus\nsuccessively survey.\n\n17. How much of activity there is in the process by which we\nperceive the outlines of objects appears further from the\nlanguage by which we describe their forms. We apply to them\nnot merely adjectives of form, but verbs of motion. An\nabrupt hill _starts_ out of the plain; a beautiful figure\nhas a _gliding_ outline. We have\n The windy summit, wild and high,\n Roughly _rushing_ on the sky.\nThese terms express the course of the eye as it follows the\nlines by which such forms are bounded and marked. In like\nmanner another modern poet[11\\2] says of Soracte, that it\n From out the plain\n _Heaves_ like a long-swept wave about to break,\n And on the curl _hangs pausing_.\n\n[Note 11\\2: Byron, _Ch. Har._ vi. st. 75.]\n\nThus the muscular sense, which is inseparably connected with\nan act originating in our own mind, not only gives us all\nthat portion of our perceptions of space in which we use the\nsense of touch, but also, at least in a great measure,\nanother large portion of such perceptions, in which we\nemploy the sense of sight. As we have before seen that our\n_knowledge_ of solid space and its properties is not\nconceivable in any other way than as the result of a mental\nact, governed by conditions depending on its own nature; so\nit now appears that our _perceptions_ of visible figure are\nnot obtained without an act performed under the same\nconditions. The sensations of touch and sight are\nsubordinated to an idea which is the basis of our\nspeculative knowledge concerning space and its relations;\nand this same idea is disclosed to our consciousness by its\npractically regulating our intercourse with the external world.\n\nBy considerations such as have been adduced and referred to,\nit is proved beyond doubt, that in a great {130} number of\ncases our knowledge of form and position is acquired from\nthe muscular sense, and not from sight directly:--for\ninstance, in all cases in which we have before us objects so\nlarge and prospects so extensive that we cannot see the\nwhole of them in one position of the eye[12\\2].\n\n[Note 12\\2: The expression in the first edition was 'large\nobjects and extensive spaces.' In the text as now given, I\nstate a definite size and extent, within which the sight by\nitself can judge of position and figure.\n\nThe doctrine, that we require the assistance of the muscular\nsense to enable us to perceive space of three dimensions, is\nnot at all inconsistent with this other doctrine, that\nwithin the space which is seen by the fixed eye, we perceive\nthe relative positions of points directly by vision, and\nthat, consequently, we have a perception of _visible\nfigure_.\n\nSir Charles Bell has said, (_Phil. Trans._ 1823, p. 181,)\n'It appears to me that the utmost ingenuity will be at a\nloss to devise an explanation of that power by which the eye\nbecomes acquainted with the position and relation of\nobjects, if the sense of muscular activity be excluded which\naccompanies the motion of the eyeball.' But surely we should\nhave no difficulty in perceiving the relation of the sides\nand angles of a small triangle, placed before the eye, even\nif the muscles of the eyeball were severed. This subject is\nresumed b. iv. c. ii. sect. 11.]\n\nWe now quit the consideration of the properties of Space,\nand consider the Idea of Time.\n\n\n\n{{131}}\nCHAPTER VII.\n\nOF THE IDEA OF TIME.\n\n\n1. RESPECTING the Idea of Time, we may make several of the\nsame remarks which we made concerning the idea of space, in\norder to show that it is not borrowed from experience, but\nis a bond of connexion among the impressions of sense,\nderived from a peculiar activity of the mind, and forming a\nfoundation both of our experience and of our speculative\nknowledge.\n\nTime is not a notion obtained by experience. Experience,\nthat is, the impressions of sense and our consciousness of\nour thoughts, gives us various perceptions; and different\nsuccessive perceptions considered together exemplify the\nnotion of change. But this very connexion of different\nperceptions,--this successiveness,--presupposes that the\nperceptions exist _in time_. That things happen either\ntogether, or one after the other, is intelligible only by\nassuming time as the condition under which they are\npresented to us.\n\nThus time is a necessary condition in the presentation of\nall occurrences to our minds. We cannot conceive this\ncondition to be taken away. We can conceive time to go on\nwhile nothing happens in it; but we cannot conceive anything\nto happen while time does not go on.\n\nIt is clear from this that time is not an impression derived\nfrom experience, in the same manner in which we derive from\nexperience our information concerning the objects which\nexist, and the occurrences which take place in time. The\nobjects of experience can easily be conceived to be, or not\nto be:--to be absent as well as present. Time always is, and\nalways is {132} present, and even in our thoughts we cannot\nform the contrary supposition.\n\n2. Thus time is something distinct from the _matter_ or\nsubstance of our experience, and may be considered as a\nnecessary _form_ which that matter (the experience of\nchange) must assume, in order to be an object of\ncontemplation to the mind. Time is one of the necessary\nconditions under which we apprehend the information which\nour senses and consciousness give us. By considering time as\na form which belongs to our power of apprehending\noccurrences and changes, and under which alone all such\nexperience can be accepted by the mind, we explain the\nnecessity, which we find to exist, of conceiving all such\nchanges as happening in time; and we thus see that time is\nnot a property perceived as existing in objects, or as\nconveyed to us by our senses; but a condition impressed upon\nour knowledge by the constitution of the mind itself;\ninvolving an act of thought as well as an impression of sense.\n\n3. We showed that space is an idea of the mind, or form of\nour perceiving power, independent of experience, by pointing\nout that we possess necessary and universal truths\nconcerning the relations of space, which could never be\ngiven by means of experience; but of which the necessity is\nreadily conceivable, if we suppose them to have for their\nbasis the constitution of the mind. There exist also\nrespecting number, many truths absolutely necessary,\nentirely independent of experience and anterior to it; and\nso far as the conception of number depends upon the idea of\ntime, the same argument might be used to show that the idea\nof time is not derived from experience, but is a result of\nthe native activity of the mind: but we shall defer all\nviews of this kind till we come to the consideration of Number.\n\n4. Some persons have supposed that we obtain the notion of\ntime from the perception of motion. But it is clear that the\nperception of motion, that is, change of place, presupposes\nthe conception of time, and is not capable of being\npresented to the mind in any other {133} way. If we\ncontemplate the same body as being in different places at\ndifferent times, and connect these observations, we have the\nconception of motion, which thus presupposes the necessary\nconditions that existence in time implies. And thus we see\nthat it is possible there should be necessary truths\nconcerning all Motion, and consequently, concerning those\nmotions which are the objects of experience; but that the\nsource of this necessity is the Ideas of Time and Space,\nwhich, being universal conditions of knowledge residing in\nthe mind, afford a foundation for necessary truths.\n\n\n\n{{134}}\nCHAPTER VIII.\n\nOF SOME PECULIARITIES OF THE IDEA OF TIME.\n\n\n1. THE Idea of Time, like the Idea of Space, offers to our\nnotice some characters which do not belong to our\nfundamental ideas generally, but which are deserving of\nremark. These characters are, in some respects, closely\nsimilar with regard to Time and to Space, while, in other\nrespects, the peculiarities of these two ideas are widely\ndifferent. We shall point out some of these characters.\n\nTime is not a general _abstract_ notion collected from\nexperience; as, for example, a certain general conception of\nthe relations of things. For we do not consider particular\n_times_ as examples of Time in general, (as we consider\nparticular causes to be examples of Cause,) but we conceive\nall particular times to be parts of a single and endless\nTime. This continually-flowing and endless time is what\noffers itself to us when we contemplate any series of\noccurrences. All actual and possible times exist as Parts,\nin this original and general Time. And since all particular\ntimes are considered as derivable from time in general, it\nis manifest that the notion of time in general cannot be\nderived from the notions of particular times. The notion of\ntime in general is therefore not a general conception\ngathered from experience.\n\n2. Time is infinite. Since all actual and possible times\nexist in the general course of time, this general time must\nbe infinite. All limitation merely divides, and does not\nterminate, the extent of absolute time. Time has no\nbeginning and no end; but the beginning and the end of every\nother existence takes place in it.\n\n3. Time, like space, is not only a form of perception, but\nof _intuition_. We contemplate events as {135} taking place\n_in_ time. We consider its parts as added to one another,\nand events as filling a larger or smaller extent of such\nparts. The time which any event takes up is the sum of all\nsuch parts, and the relation of the same to time is fully\nunderstood when we can clearly see what portions of time it\noccupies, and what it does not. Thus the relation of known\noccurrences to time is perceived by intuition; and time is a\nform of intuition of the external world.\n\n4. Time is conceived as a quantity of one dimension; it has\ngreat analogy with a line, but none at all with a surface or\nsolid. Time may be considered as consisting of a series of\ninstants, which are before and after one another; and they\nhave no other relation than this, of _before_ and _after_.\nJust the same would be the case with a series of points\ntaken along a line; each would be after those on one side of\nit, and before those on another. Indeed the analogy between\ntime, and space of one dimension, is so close, that the same\nterms are applied to both ideas, and we hardly know to which\nthey originally belong. Times and lines are alike called\n_long_ and _short_; we speak of the _beginning_ and _end_ of\na line; of a _point_ of time, and of the _limits_ of a\nportion of duration.\n\n5. But, as has been said, there is nothing in time which\ncorresponds to more than one dimension in space, and hence\nnothing which has any obvious analogy with figure. Time\nresembles a line indefinitely extended both ways; all\npartial times are portions of this line; and no mode of\nconceiving time suggests to us a line making any angle with\nthe original line, or any other combination which might give\nrise to figures of any kind. The analogy between time and\nspace, which in many circumstances is so clear, here\ndisappears altogether. Spaces of two and of three\ndimensions, planes and solids, have nothing to which we can\ncompare them in the conceptions arising out of time.\n\n6. As figure is a conception solely appropriate to space,\nthere is also a conception which peculiarly belongs to time,\nnamely, the conception of recurrence of times similarly\nmarked; or, as it may be termed, {136} _rhythm_, using this\nword in a general sense. The term rhythm is most commonly\nused to designate the recurrence of times marked by the\nsyllables of a verse, or the notes of a melody: but it is\neasy to see that the general conception of such a recurrence\ndoes not depend on the mode in which it is impressed upon\nthe sense. The forms of such recurrence are innumerable.\nThus in such a line as\n Qu\u00e1druped\u00e1nte putr\u00e9m sonit\u00fa quatit \u00fangula c\u00e1mpum,\nwe have alternately one long or forcible syllable, and two\nshort or light ones, recurring over and over. In like manner\nin our own language, in the line\n At the cl\u00f3se of the d\u00e1y when the h\u00e1mlet is still,\nwe have two light and one strong syllable repeated four\ntimes over. Such repetition is the essence of versification.\nThe same kind of rhythm is one of the main elements of\nmusic, with this difference only, that in music the forcible\nsyllables are made so for the purposes of rhythm by their\nlength only or principally; for example, if either of the\nabove lines were imitated by a melody in the most simple and\nobvious manner, each strong syllable would occupy exactly\ntwice as much time as two of the weaker ones. Something very\nanalogous to such rhythm may be traced in other parts of\npoetry and art, which we need not here dwell upon. But in\nreference to our present subject, we may remark that by the\nintroduction of such rhythm, the flow of time, which appears\notherwise so perfectly simple and homogeneous, admits of an\ninfinite number of varied yet regular modes of progress. All\nthe kinds of versification which occur in all languages, and\nthe still more varied forms of recurrence of notes of\ndifferent lengths, which are heard in all the varied strains\nof melodies, are only examples of such modifications, or\nconfigurations as we may call them, of time. They involve\nrelations of various portions of time, as figures involve\nrelations of various portions of space. But yet the analogy\nbetween rhythm and figure is by no means very close; for in\nrhythm we have relations of quantity alone in the parts of\ntime, whereas in figure we have {137} relations not only of\nquantity, but of a kind altogether different,--namely, of\nposition. On the other hand, a _repetition_ of similar\nelements, which does not necessarily occur in figures, is\nquite essential in order to impress upon us that measured\nprogress of time of which we here speak. And thus the ideas\nof time and space have each its peculiar and exclusive\nrelations; position and figure belonging only to space,\nwhile repetition and rhythm are appropriate to time.\n\n7. One of the simplest forms of recurrence is _alternation_,\nas when we have alternate strong and slight syllables. For\ninstance,--\n Aw\u00e1ke, ar\u00edse, or b\u00e9 for \u00e9ver f\u00e1ll'n.\nOr without any subordination, as when we reckon numbers, and\ncall them in succession, _odd_, _even_, _odd_, _even_.\n\n8. But the simplest of all forms of recurrence is that which\nhas no variety;--in which a series of units, each considered\nas exactly similar to the rest, succeed each other; as\n_one_, _one_, _one_, and so on. In this case, however, we\nare led to consider each unit with reference to all that\nhave preceded; and thus the series _one_, _one_, _one_, and\nso forth, becomes _one_, _two_, _three_, _four_, _five_, and\nso on; a series with which all are familiar, and which may\nbe continued without limit.\n\nWe thus collect from that repetition of which time admits,\nthe conception of _Number_.\n\n9. The relations of position and figure are the subject of\nthe science of geometry; and are, as we have already said,\ntraced into a very remarkable and extensive body of truths,\nwhich rests for its foundations on axioms involved in the\nIdea of Space. There is, in like manner, a science of great\ncomplexity and extent, which has its foundation in the Idea\nof Time. But this science, as it is usually pursued, applies\nonly to the conception of Number, which is, as we have said,\nthe simplest result of repetition. This science is\n_Theoretical Arithmetic_, or the speculative doctrine of the\nproperties and relations of numbers; and we must say a few\nwords concerning the principles which it is requisite to\nassume as the basis of this science.\n\n\n\n{{138}}\nCHAPTER IX.\n\nOF THE AXIOMS WHICH RELATE TO NUMBER.\n\n\n1. THE foundations of our speculative knowledge of the\nrelations and properties of Number, as well as of Space, are\ncontained in the mode in which we represent to ourselves the\nmagnitudes which are the subjects of our reasonings. To\nexpress these foundations in axioms in the case of number,\nis a matter requiring some consideration, for the same\nreason as in the case of geometry; that is, because these\naxioms are principles which we assume as true, without being\naware that we have made any assumption; and we cannot,\nwithout careful scrutiny, determine when we have stated, in\nthe form of axioms, all that is necessary for the formation\nof the science, and no more than is necessary. We will,\nhowever, attempt to detect the principles which really must\nform the basis of theoretical arithmetic.\n\n2. Why is it that three and two are equal to four and one?\nBecause if we look at five things of any kind, we see that\nit is so. The five are four and one; they are also three and\ntwo. The truth of our assertion is involved in our being\nable to conceive the number five at all. We perceive this\ntruth by _intuition_, for we cannot see, or imagine we see,\nfive things, without perceiving also that the assertion\nabove stated is true.\n\nBut how do we state in words this fundamental principle of\nthe doctrine of numbers? Let us consider a very simple case.\nIf we wish to show that seven and two are equal to four and\nfive, we say that seven are four and three, _therefore_\nseven and two are four and three and two; and because three\nand two are {139} five, this is four and five. Mathematical\nreasoners justify the first inference (marked by the\nconjunctive word _therefore_), by saying that \"When equals\nare added to equals the wholes are equal,\" and that thus,\nsince seven is equal to three and four, if we add two to\nboth, seven and two are equal to four and three and two.\n\n3. Such _axioms_ as this, that when equals are added to\nequals the wholes are equal, are, in fact, expressions of\nthe general condition of intuition, by which a whole is\ncontemplated as made up of parts, and as identical with the\naggregate of the parts. And a yet more general form in which\nwe might more adequately express this condition of intuition\nwould be this; that 'Two magnitudes are equal when they can\nbe divided into parts which are equal, each to each.' Thus\nin the above example, seven and two are equal to four and\nfive, because each of the two sums can be divided into the\nparts, four, three, and two.\n\n4. In all these cases, a person who had never seen such\naxioms enunciated in a verbal form would employ the same\nreasoning as a practised mathematician, in order to satisfy\nhimself that the proposition was true. The steps of the\nreasoning, being seen to be true by intuition, would carry\nan entire conviction, whether or not the argument were made\nverbally complete. Hence the axioms may appear superfluous,\nand on this account such axioms have often been spoken\ncontemptuously of, as empty and barren assertions. In fact,\nhowever, although they cannot supply the deficiency of the\nclear intuition of number and space in the reasoner himself,\nand although when he possesses such a faculty, he will\nreason rightly if he have never heard of such axioms, they\nstill have their place properly at the beginning of our\ntreatises on the science of quantity; since they express, as\nsimply as words can express, those conditions of the\nintuition of magnitudes on which all reasoning concerning\nquantity must be based; and are necessary when we want, not\nonly to see the truth of the elementary reasonings on these\nsubjects, but to put such reasonings in a formal and logical\nshape. {140}\n\n5. We have considered the above-mentioned axioms as the\nbasis of all arithmetical operations of the nature of\n_addition_. But it is easily seen that the same principle\nmay be carried into other cases; as for instance,\n_multiplication_, which is merely a repeated addition, and\nadmits of the same kind of evidence. Thus five times three\nare equal to three times five; why is this? If we arrange\nfifteen things in five rows of three, it is seen by looking,\nor by imaginary looking, which is _intuition_, that they may\nalso be taken as three rows of five. And thus the principle\nthat those wholes are equal which can be resolved into the\nsame partial magnitudes, is immediately applicable in this\nas in the other case.\n\n6. We may proceed to higher numbers, and may find ourselves\nobliged to use artificial nomenclature and notation in order\nto represent and reckon them; but the reasoning in these\ncases also is still the same. And the usual artifice by\nwhich our reasoning in such instances is assisted is, that\nthe number which is the root of our scale of notation (which\nis _ten_ in our usual system), is alternately separated into\nparts and treated as a single thing. Thus 47 and 35 are 82;\nfor 47 is four tens and seven; 35 is three tens and five;\nwhence 47 and 35 are seven tens and twelve; that is, 7 tens,\n1 ten, and 2; which is 8 tens and 2, or 82. The like\nreasoning is applicable in other cases. And since the most\nremote and complex properties of numbers are obtained by a\nprolongation of a course of reasoning exactly similar to\nthat by which we thus establish the most elementary\npropositions, we have, in the principles just noticed, the\nfoundation of the whole of Theoretical Arithmetic.\n\n\n\n{{141}}\nCHAPTER X.\n\nOF THE PERCEPTION OF TIME AND NUMBER.\n\n\n1. OUR perception of the passage of time involves a series\nof acts of memory. This is easily seen and assented to, when\nlarge intervals of time and a complex train of occurrences\nare concerned. But since memory is requisite in order to\napprehend time in such cases, we cannot doubt that the same\nfaculty must be concerned in the shortest and simplest cases\nof succession; for it will hardly be maintained that the\nprocess by which we contemplate the progress of time is\ndifferent, when small, and when large intervals are\nconcerned. If memory be absolutely requisite to connect two\nevents which begin and end a day, and to perceive a tract of\ntime between them, it must be equally indispensable to\nconnect the beginning and end of a minute, or a second;\nthough in this case the effort may be smaller, and\nconsequently more easily overlooked. In common cases, we are\nunconscious of the act of thought by which we recollect the\npreceding instant, though we perceive the effort when we\nrecollect some distant event. And this is analogous to what\nhappens in other instances. Thus, we walk without being\nconscious of the volitions by which we move our muscles;\nbut, in order to leap, a distinct and manifest exertion of\nthe same muscles is necessary. Yet no one will doubt that we\nwalk as well as leap by an act of the will exerted through\nthe muscles; and in like manner, our consciousness of small\nas well as large intervals of time involves something of the\nnature of an act of memory.\n\n2. But this constant and almost imperceptible kind of\nmemory, by which we connect the beginning and {142} end of\neach instant as it passes, may very fitly be distinguished\nin common cases from manifest acts of recollection, although\nit may be difficult or impossible to separate the two\noperations in general. This perpetual and latent kind of\nmemory may be termed a _sense of successiveness_; and must\nbe considered as an internal sense by which we perceive\nourselves existing in time, much in the same way as by our\nexternal and muscular sense we perceive ourselves existing\nin space. And both our internal thoughts and feelings, and\nthe events which take place around us, are apprehended as\nobjects of this internal sense, and thus as taking place in\ntime.\n\n3. In the same manner in which our interpretation of the\nnotices of the muscular sense implies the power of moving\nour limbs, and of touching at will this object or that; our\napprehension of the relations of time, by means of the\ninternal sense of successiveness, implies a power of\nrecalling what has past, and of retaining what is passing.\nWe are able to seize the occurrences which have just taken\nplace, and to hold them fast in our minds so as mentally to\nmeasure their distance in time from occurrences now present.\nAnd thus, this sense of successiveness, like the muscular\nsense with which we have compared it, implies activity of\nthe mind itself, and is not a sense passively receiving\nimpressions.\n\n4. The conception of _Number_ appears to require the\nexercise of the same sense of succession. At first sight,\nindeed, we seem to apprehend Number without any act of\nmemory, or any reference to time: for example, we look at a\nhorse, and see that his legs are four; and this we seem to\ndo at once, without reckoning them. But it is not difficult\nto see that this seeming instantaneousness of the perception\nof small numbers is an illusion. This resembles the many\nother cases in which we perform short and easy acts so\nrapidly and familiarly that we are unconscious of them; as\nin the acts of seeing, and of articulating our words. And\nthis is the more manifest, since we begin our acquaintance\nwith number by counting even the {143} smallest numbers.\nChildren and very rude savages must use an effort to reckon\neven their five fingers, and find a difficulty in going\nfurther. And persons have been known who were able by habit,\nor by a peculiar natural aptitude, to count by dozens as\nrapidly as common persons can by units. We may conclude,\ntherefore, that when we appear to catch a small number by a\nsingle glance of the eye, we do in fact count the units of\nit in a regular, though very brief succession. To count\nrequires an act of memory. Of this we are sensible when we\ncount very slowly, as when we reckon the strokes of a\nchurch-clock; for in such a case we may forget in the\nintervals of the strokes, and _miscount_. Now it will not be\ndoubted that the nature of the process in counting is the\nsame whether we count fast or slow. There is no definite\nspeed of reckoning at which the faculties which it requires\nare changed; and therefore memory, which is requisite in\nsome cases, must be so in all[13\\2].\n\n[Note 13\\2: I have considered Number as involving the\nexercise of the sense of succession, because I cannot draw\nany line between those cases of large numbers, in which, the\nprocess of counting being performed, there is a manifest\napprehension of succession; and those cases of small\nnumbers, in which we seem to see the number at one glance.\nBut if any one holds Number to be apprehended by a direct\nact of intuition, as Space and Time are, this view will not\ndisturb the other doctrines delivered in the text.]\n\nThe act of counting, (_one_, _two_, _three_, and so on,) is\nthe foundation of all our knowledge of number. The intuition\nof the relations of number involves this act of counting;\nfor, as we have just seen, the conception of number cannot\nbe obtained in any other way. And thus the whole of\ntheoretical arithmetic depends upon an act of the mind, and\nupon the conditions which the exercise of that act implies.\nThese have been already explained in the last chapter.\n\n5. But if the apprehension of number be accompanied by an\nact of the mind, the apprehension of _rhythm_ is so still\nmore clearly. All the forms of versification and the\n_measures_ of melodies are the creations of man, who thus\nrealizes in words and sounds the {144} forms of recurrence\nwhich rise within his own mind. When we hear in a quiet\nscene any rapidly-repeated sound, as those made by the\nhammer of the smith or the saw of the carpenter, every one\nknows how insensibly we throw these noises into a rhythmical\nform in our own apprehension. We do this even without any\nsuggestion from the sounds themselves. For instance, if the\nbeats of a clock or watch be ever so exactly alike, we still\nreckon them alternately tick-_tack_, tick-_tack_. That this\nis the case, may be proved by taking a watch or clock of\nsuch a construction that the returning swing of the pendulum\nis silent, and in which therefore all the beats are\nrigorously alike: we shall find ourselves still reckoning\nits sounds as tick-_tack_. In this instance it is manifest\nthat the rhythm is entirely of our own making. In melodies,\nalso, and in verses in which the rhythm is complex, obscure\nand difficult, we perceive something is required on our\npart; for we are often incapable of contributing our share,\nand thus lose the sense of the measure altogether. And when\nwe consider such cases, and attend to what passes within us\nwhen we catch the measure, even of the simplest and\nbest-known air, we shall no longer doubt that an act of our\nown thoughts is requisite in such cases, as well as\nimpressions on the sense. And thus the conception of this\npeculiar modification of time, which we have called\n_rhythm_, like all the other views which we have taken of\nthe subject, shows that we must, in order to form such\nconceptions, supply a certain idea by our own thoughts, as\nwell as merely receive by senses, whether external or\ninternal, the impressions of appearances and collections of\nappearances.\n\n\n\n{{145}}\nNOTE TO CHAPTER X.\n\n\nI HAVE in the last ten chapters described Space, Time, and\nNumber by various expressions, all intended to point out\ntheir office as exemplifying the Ideal Element of human\nknowledge. I have called them _Fundamental Ideas_; _Forms of\nPerception_; _Forms of Intuition_; and perhaps other names.\nI might add yet other phrases. I might say that the\nproperties of Space, Time, and Number are _Laws of the\nMind's Activity_ in apprehending what is. For the mind\ncannot apprehend any thing or event except conformably to\nthe properties of space, time, and number. It is not only\nthat it _does_ not, but it _can_ not: and this impossibility\nshows that the law is a law of the mind, and not of objects\nextraneous to the mind.\n\nIt is usual for some of those who reject the doctrines here\npresented to say that the axioms of geometry, and of other\nsciences, are obtained by Induction from facts constantly\npresented by experience. But I do not see how Induction can\nprove that a proposition _must_ be true. The only\nintelligible usage of the word _Induction_ appears to me to\nbe, that in which it is applied to a proposition which,\nbeing separable from the facts in our apprehension, and\nbeing compared with them, is seen to agree with them. But in\nthe cases now spoken of, the proposition is not separable\nfrom the facts. We cannot infer by induction that two\nstraight lines cannot inclose a space, because we cannot\ncontemplate special cases of two lines inclosing a space, in\nwhich it remains to be determined whether or not the\nproposition, that both are straight, is true.\n\nI do not deny that the activity of the mind by which it\nperceives objects and events as related according to the\nlaws of space, time, and number, is awakened and developed\nby being constantly exercised; and that we cannot imagine a\nstage of human existence in which the powers have not been\nawakened and {146} developed by such exercise. In this way,\nexperience and observation are necessary conditions and\nprerequisites of our apprehension of geometrical (and other)\naxioms. We cannot see the truth of these axioms without some\nexperience, because we cannot see any thing, or be human\nbeings, without some experience. This might be expressed by\nsaying that such truths are acquired necessarily _in the\ncourse of_ all experience; but I think it is very\nundesirable to apply, to such a case, the word _Induction_,\nof which it is so important to us to keep the scientific\nmeaning free from confusion. Induction cannot give\ndemonstrative proofs, as I have already stated in Book 1. C.\ni. sect. 3, and therefore cannot be the ground of necessary\ntruths.\n\nAnother expression which may be used to describe the\nFundamental Ideas here spoken of is suggested by the\nlanguage of a very profound and acute Review of the former\nedition. The Reviewer holds that we pass from special\nexperiences to universal truths in virtue of 'the inductive\npropensity--the irresistible impulse of the mind to\ngeneralize _ad infinitum_.' I have already given reasons why\nI cannot adopt the former expression; but I do not see why\nspace, time, number, cause, and the rest, may not be termed\n_different forms_ of the _impulse of the mind to\ngeneralize_. But if we put together all the Fundamental\nIdeas as results of the Generalizing Impulse, we must still\nseparate them as different modes of action of that Impulse,\nshowing themselves in various characteristic ways in the\naxioms and modes of reasoning which belong to different\nsciences. The Generalizing Impulse in one case proceeds\naccording to the Idea of Space; in another, according to the\nIdea of Mechanical Cause; and so in other subjects.\n\n\n\n{{147}}\nCHAPTER XI.\n\nOF MATHEMATICAL REASONING.\n\n\n1. _Discursive Reasoning._--WE have thus seen that our\nnotions of space, time, and their modifications, necessarily\ninvolve a certain activity of the mind; and that the\nconditions of this activity form the foundations of those\nsciences which have the relations of space, time, and\nnumber, for their object. Upon the fundamental principles\nthus established, the various sciences which are included in\nthe term _Pure Mathematics_, (Geometry, Algebra,\nTrigonometry, Conic Sections, and the rest of the Higher\nGeometry, the Differential Calculus, and the like,) are\nbuilt up by a series of reasonings. These reasonings are\nsubject to the rules of Logic, as we have already remarked;\nnor is it necessary here to dwell long on the nature and\nrules of such processes. But we may here notice that such\nprocesses are termed _discursive_, in opposition to the\noperations by which we acquire our fundamental principles,\nwhich are, as we have seen, _intuitive_. This opposition was\nformerly very familiar to our writers; as Milton,--\n . . . Thus the soul reason receives,\n Discursive or intuitive.--_Paradise Lost_, v. 438.\nFor in such reasonings we obtain our conclusions, not by\nlooking at our conceptions steadily in one view, which is\n_intuition_, but by passing from one view to another, like\nthose who run from place to place (_discursus_). Thus a\nstraight line may be at the same time a side of a triangle\nand a radius of a circle: and in the first proposition of\nEuclid a line is considered, first in one of these\nrelations, and then in the other, and thus the sides of a\ncertain triangle are proved to be equal. And by this\n'discourse of reason,' as by our older {148} writers it was\ntermed, we set forth from those axioms which we perceive by\nintuition, travel securely over a vast and varied region,\nand become possessed of a copious store of mathematical\ntruths.\n\n2. _Technical Terms of Reasoning._--The reasoning of\nmathematics, thus proceeding from a few simple principles to\nmany truths, is conducted according to the rules of Logic.\nIf it be necessary, mathematical proofs may be reduced to\nlogical forms, and expressed in Syllogisms, consisting of\nmajor, minor, and conclusion. But in most cases the\nsyllogism is of that kind which is called by logical writers\nan _Enthymeme_; a word which implies something existing in\nthe thoughts only, and which designates a syllogism in which\none of the premises is understood, and not expressed. Thus\nwe say in a mathematical proof, 'because the point C is the\ncenter of the circle AB, AC is equal to BC;' not stating the\n_major_,--that all lines drawn from the center of a circle\nto the circumference are equal; or introducing it only by a\ntransient reference to the definition of a circle. But the\nenthymeme is so constantly used in all habitual forms of\nreasoning, that it does not occur to us as being anything\npeculiar in mathematical works.\n\nThe propositions which are proved to be generally true are\ntermed _Theorems_: but when anything is required to be done,\nas to draw a line or a circle under given conditions, this\nproposition is a _Problem_. A theorem requires\ndemonstration; a problem, solution. And for both purposes\nthe mathematician usually makes a _Construction_. He directs\nus to draw certain lines, circles, or other curves, on which\nis to be founded his demonstration that his theorem is true,\nor that his problem is solved. Sometimes, too, he\nestablishes some _Lemma_, or preparatory proposition, before\nhe proceeds to his main task; and often he deduces from his\ndemonstration some conclusion in addition to that which was\nthe professed object of his proposition; and this is termed\na _Corollary_.\n\nThese technical terms are noted here, not as being very\nimportant, but in order that they may not sound {149}\nstrange and unintelligible if we should have occasion to use\nsome of them. There is, however, one technical distinction\nmore peculiar, and more important.\n\n3. _Geometrical Analysis and Synthesis._--In geometrical\nreasoning such as we have described, we introduce at every\nstep some new consideration; and it is by combining all\nthese considerations, that we arrive at the conclusion, that\nis, the demonstration of the proposition. Each step tends to\nthe final result, by exhibiting some part of the figure\nunder a new relation. To what we have already proved, is\nadded something more; and hence this process is called\n_Synthesis_, or _putting together_. The proof flows on,\nreceiving at every turn new contributions from different\nquarters; like a river fed and augmented by many tributary\nstreams. And each of these tributaries flows from some\ndefinition or axiom as its fountain, or is itself formed by\nthe union of smaller rivulets which have sources of this\nkind. In descending along its course, the synthetical proof\ngathers all these accessions into one common trunk, the\nproposition finally proved.\n\nBut we may proceed in a different manner. We may begin from\nthe formed river, and ascend to its sources. We may take the\nproposition of which we require a proof, and may examine\nwhat the supposition of its truth implies. If this be true,\nthen something else may be seen to be true; and from this,\nsomething else, and so on. We may often, in this way,\ndiscover of what simpler propositions our theorem or\nsolution is compounded, and may resolve these in succession,\ntill we come to some proposition which is obvious. This is\ngeometrical _Analysis_. Having succeeded in this analytical\nprocess, we may invert it; and may descend again from the\nsimple and known propositions, to the proof of a theorem, or\nthe solution of a problem, which was our starting-place.\n\nThis process resembles, as we have said, tracing a river to\nits sources. As we ascend the stream, we perpetually meet\nwith bifurcations; and some sagacity is needed to enable us\nto see which, in each case, is the main stream: but if we\nproceed in our research, we {150} exhaust the unexplored\nvalleys, and finally obtain a clear knowledge of the place\nwhence the waters flow. _Analytical_ is sometimes confounded\nwith _symbolical_ reasoning, on which subject we shall make\na remark in the next chapter. The object of that chapter is\nto notice certain other fundamental principles and ideas,\nnot included in those hitherto spoken of, which we find\nthrown in our way as we proceed in our mathematical\nspeculations. It would detain us too long, and involve us in\nsubtle and technical disquisitions, to examine fully the\ngrounds of these principles; but the Mathematics hold so\nimportant a place in relation to the inductive sciences,\nthat I shall briefly notice the leading ideas which the\nulterior progress of the subject involves.\n\n\n\n{{151}}\nCHAPTER XII.\n\nOF THE FOUNDATIONS OF THE HIGHER MATHEMATICS.\n\n\n1. _The Idea of a Limit._--THE general truths concerning\nrelations of space which depend upon the axioms and\ndefinitions contained in Euclid's _Elements_, and which\ninvolve only properties of straight lines and circles, are\ntermed Elementary Geometry: all beyond this belongs to the\nHigher Geometry. To this latter province appertain, for\nexample, all propositions respecting the lengths of any\nportions of curve lines; for these cannot be obtained by\nmeans of the principles of the Elements alone. Here then we\nmust ask to what other principles the geometer has recourse,\nand from what source these are drawn. Is there any origin of\ngeometrical truth which we have not yet explored?\n\nThe _Idea of a Limit_ supplies a new mode of establishing\nmathematical truths. Thus with regard to the length of any\nportion of a curve, a problem which we have just mentioned;\na curve is not made up of straight lines, and therefore we\ncannot by means of any of the doctrines of elementary\ngeometry measure the length of any curve. But we may make up\na figure nearly resembling any curve by putting together\nmany short straight lines, just as a polygonal building of\nvery many sides may nearly resemble a circular room. And in\norder to approach nearer and nearer to the curve, we may\nmake the sides more and more small, more and more numerous.\nWe may then possibly find some mode of measurement, some\nrelation of these small lines to other lines, which is not\ndisturbed by the multiplication of the sides, however far it\nbe carried. And thus, we may do what is equivalent to\nmeasuring the curve itself; for by multiplying the {152}\nsides we may approach more and more closely to the curve\ntill no appreciable difference remains. The curve line is\nthe _Limit_ of the polygon; and in this process we proceed\non the _Axiom_, that 'What is true up to the Limit is true\nat the Limit.'\n\nThis mode of conceiving mathematical magnitudes is of wide\nextent and use; for every curve may be considered as the\nlimit of some polygon; every varied magnitude, as the limit\nof some aggregate of simpler forms; and thus the relations\nof the elementary figures enable us to advance to the\nproperties of the most complex cases.\n\nA Limit is a peculiar and fundamental conception, the use of\nwhich in proving the propositions of the Higher Geometry\ncannot be superseded by any combination of other hypotheses\nand definitions[14\\2]. The axiom just noticed, that what is\ntrue up to the limit is true at the limit, is involved in\nthe very conception of a Limit: and this principle, with its\nconsequences, leads to all the results which form the\nsubject of the higher mathematics, whether proved by the\nconsideration of evanescent triangles, by the processes of\nthe Differential Calculus, or in any other way.\n\n[Note 14\\2: This assertion cannot be fully proved and\nillustrated without a reference to mathematical reasonings\nwhich would not be generally intelligible. I have shown the\ntruth of the assertion in my _Thoughts on the Study of\nMathematics_, annexed to the _Principles of English\nUniversity Education_. The proof is of this kind:--The\nultimate equality of an arc of a curve and the corresponding\nperiphery of a polygon, when the sides of the polygon are\nindefinitely increased in number, is _evident_. But this\ntruth cannot be proved from any other axiom. For if we take\nthe supposed axiom, that a curve is always less than the\nincluding broken line, this is not true, except with a\ncondition; and in tracing the import of this condition, we\nfind its necessity becomes evident only when we introduce a\nreference to a Limit. And the same is the case if we attempt\nto supersede the notion of a Limit in proving any other\nsimple and evident proposition in which that notion is\ninvolved. Therefore these evident truths are _self_-evident,\n_in virtue of the Idea of a Limit_.]\n\nThe ancients did not expressly introduce this conception of\na Limit into their mathematical reasonings; although in the\napplication of what is termed the {153} _Method of\nExhaustions_, (in which they show how to _exhaust_ the\n_difference_ between a polygon and a curve, or the like,)\nthey were in fact proceeding upon an obscure apprehension of\nprinciples equivalent to those of the Method of Limits. Yet\nthe necessary fundamental principle not having, in their\ntime, been clearly developed, their reasonings were both\nneedlessly intricate and imperfectly satisfactory. Moreover\nthey were led to put in the place of axioms, assumptions\nwhich were by no means self-evident; as when Archimedes\nassumed, for the basis of his measure of the circumference\nof the circle, the proposition that a circular arc is\nnecessarily less than two lines which inclose it, joining\nits extremities. The reasonings of the older mathematicians,\nwhich professed to proceed upon such assumptions, led to\ntrue results in reality, only because they were guided by a\nlatent reference to the limiting case of such assumptions.\nAnd this latent employment of the conception of a Limit,\nreappeared in various forms during the early period of\nmodern mathematics; as for example, in the _Method of\nIndivisibles_ of Cavalleri, and the _Characteristic\nTriangle_ of Barrow; till at last, Newton distinctly\nreferred such reasonings to the conception of a Limit, and\nestablished the fundamental principles and processes which\nthat conception introduces, with a distinctness and\nexactness which required little improvement to make it as\nunimpeachable as the demonstrations of geometry. And when\nsuch processes as Newton thus deduced from the conception of\na Limit, are represented by means of general algebraical\nsymbols instead of geometrical diagrams, we have then before\nus the _Method of Fluxions_, or the _Differential Calculus_;\na mode of treating mathematical problems justly considered\nas the principal weapon by which the splendid triumphs of\nmodern mathematics have been achieved.\n\n2. _The Use of General Symbols._--The employment of\nalgebraical symbols, of which we have just spoken, has been\nanother of the main instruments to which the successes of\nmodern mathematics are owing. And here again the processes\nby which we obtain our {154} results depend for their\nevidence upon a fundamental conception,--the conception of\n_arbitrary symbols_ as the _Signs_ of quantity and its\nrelations; and upon a corresponding axiom, that 'The\ninterpretation of such symbols must be perfectly general.'\nIn this case, as in the last, it was only by degrees that\nmathematicians were led to a just apprehension of the\ngrounds of their reasoning. For symbols were at first used\nonly to represent numbers considered with regard to their\nnumerical properties; and thus the science of Algebra was\nformed. But it was found, even in cases belonging to common\nalgebra, that the symbols often admitted of an\ninterpretation which went beyond the limits of the problem,\nand which yet was not unmeaning, since it pointed out a\nquestion closely analogous to the question proposed. This\nwas the case, for example, when the answer was a _negative\nquantity_; for when Descartes had introduced the mode of\nrepresenting curves by means of algebraical relations among\nthe symbols of the _co-ordinates_, or distances of each of\ntheir points from fixed lines, it was found that negative\nquantities must be dealt with as not less truly significant\nthan positive ones. And as the researches of mathematicians\nproceeded, other cases also were found, in which the\nsymbols, although destitute of meaning according to the\noriginal conventions of their institution, still pointed out\ntruths which could be verified in other ways; as in the\ncases in which what are called _impossible quantities_\noccur. Such processes may usually be confirmed upon other\nprinciples, and the truth in question may be established by\nmeans of a demonstration in which no such seeming fallacies\ndefeat the reasoning. But it has also been shown in many\nsuch cases, that the process in which some of the steps\nappear to be without real meaning, does in fact involve a\nvalid proof of the proposition. And what we have here to\nremark is, that this is not true accidentally or partially\nonly, but that the results of systematic symbolical\nreasoning must _always_ express general truths, by their\nnature; and do not, for their justification, require each of\nthe steps of the process to represent {155} some definite\noperation upon quantity. _The absolute universality of the\ninterpretation of symbols_ is the fundamental principle of\ntheir use. This has been shown very ably by Dr. Peacock in\nhis _Algebra_. He has there illustrated, in a variety of\nways, this principle: that 'If general symbols express an\nidentity when they are supposed to be of any special nature,\nthey must also express an identity when they are general in\ntheir nature.' And thus, this universality of symbols is a\nprinciple in addition to those we have already noticed; and\nis a principle of the greatest importance in the formation\nof mathematical science, according to the wide generality\nwhich such science has in modern times assumed.\n\n3. _Connexion of Symbols and Analysis._--Since in our\nsymbolical reasoning our symbols thus reason for us, we do\nnot necessarily here, as in geometrical reasoning, go on\nadding carefully one known truth to another, till we reach\nthe desired result. On the contrary, if we have a theorem to\nprove or a problem to solve which can be brought under the\ndomain of our symbols, we may at once state the given but\nunproved truth, or the given combination of unknown\nquantities, in its symbolical form. After this first\nprocess, we may then proceed to trace, by means of our\nsymbols, what other truth is involved in the one just\nstated, or what the unknown symbols must signify; resolving\nstep by step the symbolical assertion with which we began,\ninto others more fitted for our purpose. The former process\nis a kind of _synthesis_, the latter is termed _analysis_.\nAnd although symbolical reasoning does not necessarily imply\nsuch analysis; yet the connexion is so familiar, that the\nterm _analysis_ is frequently used to designate symbolical\nreasoning.\n\n\n\n{{156}}\nCHAPTER XIII.\n\nTHE DOCTRINE OF MOTION.\n\n\n1. _Pure Mechanism._--THE doctrine of Motion, of which we\nhave here to speak, is that in which motion is considered\nquite independently of its cause, force; for all\nconsideration of force belongs to a class of ideas entirely\ndifferent from those with which we are here concerned. In\nthis view it may be termed the _pure_ doctrine of motion,\nsince it has to do solely with space and time, which are the\nsubjects of pure mathematics. (See c. i. of this book.)\nAlthough the doctrine of motion in connexion with force,\nwhich is the subject of mechanics, is by far the most\nimportant form in which the consideration of motion enters\ninto the formation of our sciences, the Pure Doctrine of\nMotion, which treats of space, time, and velocity, might be\nfollowed out so as to give rise to a very considerable and\ncurious body of science. Such a science is the science of\nMechanism, independent of force, and considered as the\nsolution of a problem which may be thus enunciated: 'To\ncommunicate any given motion from a first mover to a given\nbody.' The science which should have for its object to solve\nall the various cases into which this problem would ramify,\nmight be termed _Pure Mechanism_, in contradistinction to\n_Mechanics Proper_, or _Machinery_, in which Force is taken\ninto consideration. The greater part of the machines which\nhave been constructed for use in manufactures have been\npractical solutions of some of the cases of this problem. We\nhave also important contributions to such a science in the\nworks of Mathematicians; for example, the various\ninvestigations and demonstrations which have been published\nrespecting the form of the Teeth {157} of Wheels, and Mr.\nBabbage's memoir[15\\2] on the Language of Machinery. There\nare also several works which contain collections of the\nmechanical contrivances which have been invented for the\npurpose of transmitting and modifying motion, and these\nworks may be considered as treatises on the science of Pure\nMechanism. But this science has not yet been reduced to the\nsystematic simplicity which is desirable, nor indeed\ngenerally recognized as a separate science. It has been\nconfounded, under the common name of _Mechanics_, with the\nother **science, Mechanics Proper, or Machinery, which\nconsiders the effect of _force_ transmitted by Mechanism\nfrom one part of a material combination to another. For\nexample, the _Mechanical Powers_, as they are usually\ntermed, (the Lever, the Wheel and Axle, the Inclined Plane,\nthe Wedge, and the Screw,) have almost always been treated\nwith reference to the relation between the _Power_ and the\n_Weight_, and not primarily as a mode of changing the\nvelocity and kind of the motion. The science of pure motion\nhas not generally been separated from the science of motion\nviewed with reference to its causes.\n\n[Note 15\\2: _On a Method of expressing by Signs the action\nof Machinery._ _Phil. Trans._ 1826, p. 250.]\n\nRecently, indeed, the necessity of such a separation has\nbeen seen by those who have taken a philosophical view of\nscience. Thus this necessity has been urged by M. Amp\u00e8re, in\nhis _Essai sur la Philosophie des Sciences_ (1834): 'Long,'\nhe says, (p. 50,) 'before I employed myself upon the present\nwork, I had remarked that it is usual to omit, in the\nbeginning of all books treating of sciences which regard\nmotion and force, certain considerations which, duly\ndeveloped, must constitute a special science: of which\nscience certain parts have been treated of, either in\nmemoirs or in special works; such, for example, as that of\nCarnot upon Motion considered Geometrically, and the essay\nof Lanz and Betancourt upon the Composition of Machines.' He\nthen proceeds to describe this science nearly as we have\n{158} done, and proposes to term it _Kinematics_\n(_Cin\u00e9matique_), from \u03ba\u03af\u03bd\u03b7\u03bc\u03b1, motion.\n\n2. _Formal Astronomy._--I shall not attempt here further to\ndevelop the form which such a science must assume. But I may\nnotice one very large province which belongs to it. When men\nhad ascertained the apparent motions of the sun, moon, and\nstars, to a moderate degree of regularity and accuracy, they\ntried to conceive in their minds some mechanism by which\nthese motions might be produced; and thus they in fact\nproposed to themselves a very extensive problem in\n_Kinematics_. This, indeed, was the view originally\nentertained of the nature of the science of astronomy. Thus\nPlato in the seventh Book of his _Republic_[16\\2], speaks of\nastronomy as the doctrine of the motion of solids, meaning\nthereby, spheres. And the same was a proper description of\nthe science till the time of Kepler, and even later: for\nKepler endeavoured in vain to conjoin with the knowledge of\nthe motions of the heavenly bodies, those true mechanical\nconceptions which converted formal into physical\nastronomy[17\\2].\n\n[Note 16\\2: P. 528.]\n\n[Note 17\\2: _Hist. Induc. Sc._ ii. 130.]\n\nThe astronomy of the ancients admitted none but uniform\ncircular motions, and could therefore be completely\ncultivated by the aid of their elementary geometry. But the\npure science of motion might be extended to all motions,\nhowever varied as to the speed or the path of the moving\nbody. In this form it must depend upon the doctrine of\nlimits; and the fundamental principle of its reasonings\nwould be this: That velocity is measured by the Limit of the\n_space_ described, considered with reference to the _time_\nin which it is described. I shall not further pursue this\nsubject; and in order to complete what I have to say\nrespecting the Pure Sciences, I have only a few words to add\nrespecting their bearing on Inductive Science in general.\n\n\n\n{{159}}\nCHAPTER XIV.\n\nOF THE APPLICATION OF MATHEMATICS TO THE INDUCTIVE SCIENCES.\n\n\n1. ALL objects in the world which can be made the subjects\nof our contemplation are subordinate to the conditions of\nSpace, Time, and Number; and on this account, the doctrines\nof pure mathematics have most numerous and extensive\napplications in every department of our investigations of\nnature. And there is a peculiarity in these Ideas, which has\ncaused the mathematical sciences to be, in all cases, the\nfirst successful efforts of the awakening speculative powers\nof nations at the commencement of their intellectual\nprogress. Conceptions derived from these Ideas are, from the\nvery first, perfectly precise and clear, so as to be fit\nelements of scientific truths. This is not the case with the\nother conceptions which form the subjects of scientific\ninquiries. The conception of _statical force_, for instance,\nwas never presented in a distinct form till the works of\nArchimedes appeared: the conception of _accelerating force_\nwas confused, in the mind of Kepler and his contemporaries,\nand only became clear enough for purposes of sound\nscientific reasoning in the succeeding century: the just\nconception of chemical _composition_ of elements gradually,\nin modern times, emerged from the erroneous and vague\nnotions of the ancients. If we take works published on such\nsubjects before the epoch when the foundations of the true\nscience were laid, we find the knowledge not only small, but\nworthless. The writers did not see any evidence in what we\nnow consider as the axioms of the science; nor any\ninconsistency where we now see self-contradiction. But this\nwas never the case with speculations concerning {160} space\nand number. From their first rise, these were true as far as\nthey went. The Geometry and Arithmetic of the Greeks and\nIndians, even in their first and most scanty form, contained\nnone but true propositions. Men's intuitions upon these\nsubjects never allowed them to slide into error and\nconfusion; and the truths to which they were led by the\nfirst efforts of their faculties, so employed, form part of\nthe present stock of our mathematical knowledge.\n\n2. But we are here not so much concerned with mathematics in\ntheir pure form, as with their application to the phenomena\nand laws of nature. And here also the very earliest history\nof civilization presents to us some of the most remarkable\nexamples of man's success in his attempts to attain to\nscience. Space and time, position and motion, govern all\nvisible objects; but by far the most conspicuous examples of\nthe relations which arise out of such elements, are\ndisplayed by the ever-moving luminaries of the sky, which\nmeasure days, and months, and years, by their motions, and\nman's place on the earth by their position. Hence the\nsciences of space and number were from the first cultivated\nwith peculiar reference to Astronomy. I have elsewhere[18\\2]\nquoted Plato's remark,--that it is absurd to call the\nscience of the relations of space _geometry_, the measure of\nthe earth, since its most important office is to be found in\nits application to the heavens. And on other occasions also\nit appears how strongly he, who may be considered as the\nrepresentative of the scientific and speculative tendencies\nof his time and country, had been impressed with the\nconviction, that the formation of a science of the celestial\nmotions must depend entirely upon the progress of\nmathematics. In the Epilogue to the Dialogue on the\nLaws[19\\2], he declares mathematical knowledge to be the\nfirst and main requisite for the astronomer, and describes\nthe portions of it which he holds necessary for astronomical\nspeculators to cultivate. These seem to be, Plane Geometry,\nTheoretical Arithmetic, the Application of Arithmetic {161}\nto planes and to solids, and finally the doctrine of\nHarmonics. Indeed the bias of Plato appears to be rather to\nconsider mathematics as the essence of the science of\nastronomy, than as its instrument; and he seems disposed, in\nthis as in other things, to disparage observation, and to\naspire after a science founded upon demonstration alone. 'An\nastronomer,' he says in the same place, 'must not be like\nHesiod and persons of that kind, whose astronomy consists in\nnoting the settings and risings of the stars; but he must be\none who understands the revolutions of the celestial\nspheres, each performing its proper cycle.'\n\n[Note 18\\2: _Hist. Ind. Sc._ b. iii. c. ii.]\n\n[Note 19\\2: _Epinomis_, p. 990.]\n\nA large portion of the mathematics of the Greeks, so long as\ntheir scientific activity continued, was directed towards\nAstronomy. Besides many curious propositions of plane and\nsolid Geometry, to which their astronomers were led, their\nArithmetic, though very inconvenient in its fundamental\nassumptions (as being sexagesimal not decimal), was\ncultivated to a great extent; and the science of\nTrigonometry, in which problems concerning the relations of\nspace were resolved by means of tables of numerical results\npreviously obtained, was created. Menelaus of Alexandria\nwrote six Books on Chords, probably containing methods of\ncalculating Tables of these quantities; such Tables were\nfamiliarly used by the later Greek astronomers. The same\nauthor also wrote three Books on Spherical Trigonometry,\nwhich are still extant.\n\n3. The Greeks, however, in the first vigour of their pursuit\nof mathematical truth, at the time of Plato and soon after,\nhad by no means confined themselves to those propositions\nwhich had a visible bearing on the phenomena of nature; but\nhad followed out many beautiful trains of research,\nconcerning various kinds of figures, for the sake of their\nbeauty alone; as for instance in their doctrine of Conic\nSections, of which curves they had discovered all the\nprincipal properties. But it is curious to remark, that\nthese investigations, thus pursued at first as mere matters\nof curiosity and intellectual gratification, were destined,\ntwo thousand years later, to play a very important part in\n{162} establishing that system of the celestial motions\nwhich succeeded the Platonic scheme of cycles and epicycles.\nIf the properties of the conic sections had not been\ndemonstrated by the Greeks, and thus rendered familiar to\nthe mathematicians of succeeding ages, Kepler would probably\nnot have been able to discover those laws respecting the\norbits and motions of the planets which were the occasion of\nthe greatest revolution that ever happened in the history of\nscience.\n\n4. The Arabians, who, as I have elsewhere said, added little\nof their own to the stores of science which they received\nfrom the Greeks, did however make some very important\ncontributions in those portions of pure mathematics which\nare subservient to astronomy. Their adoption of the Indian\nmode of computation by means of the Ten Digits, 1, 2, 3, 4,\n5, 6, 7, 8, 9, 0, and by the method of Local Values, instead\nof the cumbrous sexagesimal arithmetic of the Greeks, was an\nimprovement by which the convenience and facility of\nnumerical calculations were immeasurably augmented. The\nArabians also rendered several of the processes of\ntrigonometry much more commodious, by using the Sine of an\narc instead of the Chord; an improvement which Albategnius\nappears to claim for himself[20\\2]; and by employing also\nthe Tangents of arcs, or, as they called them[21\\2],\n_upright shadows_.\n\n[Note 20\\2: Delambre, _Ast., M. A._, p. 12.]\n\n[Note 21\\2: _Ibid._ p. 17.]\n\n5. The constant application of mathematical knowledge to the\nresearches of Astronomy, and the mutual influence of each\nscience on the progress of the other, has been still more\nconspicuous in modern times. Newton's Method of Prime and\nUltimate Ratios, which we have already noticed as the first\ncorrect exposition of the doctrine of a Limit, is stated in\na series of Lemmas, or preparatory theorems, prefixed to his\n_Treatise on the System of the World_. Both the properties\nof curve lines and the doctrines concerning force and\nmotion, which he had to establish, required that the common\nmathematical processes should be methodized and extended. If\nNewton had not been a most {163} expert and inventive\nmathematician, as well as a profound and philosophical\nthinker, he could never have made any one of those vast\nstrides in discovery of which the rapid succession in his\nwork strikes us with wonder[22\\2]. And if we see that the\ngreat task begun by him, goes on more slowly in the hands of\nhis immediate successors, and lingers a little before its\nfull completion, we perceive that this arises, in a great\nmeasure, from the defect of the mathematical methods then\nused. Newton's synthetical modes of investigation, as we\nhave elsewhere observed, were an instrument[23\\2], powerful\nindeed in his mighty hand, but too ponderous for other\npersons to employ with effect. The countrymen of Newton\nclung to it the longest, out of veneration for their master;\nand English cultivators of physical astronomy were, on that\nvery account, left behind the progress of mathematical\nscience in France and Germany, by a wide interval, which\nthey have only recently recovered. On the Continent, the\nadvantages offered by a familiar use of symbols, and by\nattention to their symmetry and other relations, were\naccepted without reserve. In this manner the Differential\nCalculus of Leibnitz, which was in its origin and\nsignification identical with the Method of Fluxions of\nNewton, soon surpassed its rival in the extent and\ngenerality of its application to problems. This Calculus was\napplied to the science of mechanics, to which it, along with\nthe symmetrical use of co-ordinates, gave a new form; for it\nwas soon seen that the most difficult problems might in\ngeneral be reduced to finding integrals, which is the\nreciprocal process of that by which differentials are found;\nso that all difficulties of physical astronomy were reduced\nto difficulties of symbolical calculation, these, indeed,\nbeing often sufficiently stubborn. Clairaut, Euler, and\nD'Alembert employed the increased resources of mathematical\nscience upon the Theory of the Moon, and other questions\nrelative to the system of the world; and thus began to\npursue such inquiries in the course in which mathematicians\n{164} are still labouring up to the present day. This course\nwas not without its checks and perplexities. We have\nelsewhere quoted[24\\2] Clairaut's expression when he had\nobtained the very complex differential equations which\ncontain the solution of the problem of the moon's motion:\n'Now integrate them who can!' But in no very long time they\nwere integrated, at least approximately; and the methods of\napproximation have since then been improved; so that now,\nwith a due expenditure of labour, they may be carried to any\nextent which is thought desirable. If the methods of\nastronomical observation should hereafter reach a higher\ndegree of exactness than they now profess, so that\nirregularities in the motions of the sun, moon, and planets,\nshall be detected which at present escape us, the\nmathematical part of the theory of universal gravitation is\nin such a condition that it can soon be brought into\ncomparison with the newly-observed facts. Indeed at present\nthe mathematical theory is in advance of such observations.\nIt can venture to suggest what may afterwards be detected,\nas well as to explain what has already been observed. This\nhas happened recently; for Professor Airy has calculated the\nlaw and amount of an inequality depending upon the mutual\nattraction of the Earth and Venus; of which inequality (so\nsmall is it,) it remains to be determined whether its effect\ncan be traced in the series of astronomical observations.\n\n[Note 22\\2: _Hist. Ind. Sc._ b. vii. c. ii.]\n\n[Note 23\\2: _Ibid._ p. 175.]\n\n[Note 24\\2: _Hist. Ind. Sc._ b. vi. c. vi. sect. 7.]\n\n6. As the influence of mathematics upon the progress of\nastronomy is thus seen in the cases in which theory and\nobservation confirm each other, so this influence appears in\nanother way, in the very few cases in which the facts have\nnot been fully reduced to an agreement with theory. The most\nconspicuous case of this kind is the state of our knowledge\nof the Tides. This is a portion of astronomy: for the\nNewtonian theory asserts these curious phenomena to be the\nresult of the attraction of the sun and moon. Nor can there\nbe any doubt that this is true, as a general statement; yet\nthe subject is up to the present time a blot {165} on the\nperfection of the theory of universal gravitation; for we\nare very far from being able in this, as in the other parts\nof astronomy, to show that theory will exactly account for\nthe time, and magnitude, and all other circumstances of the\nphenomenon at every place on the earth's surface. And what\nis the portion of our mathematics which is connected with\nthis solitary signal defect in astronomy? It is the\nmathematics of the Motion of Fluids; a portion in which\nextremely little progress has been made, and in which all\nthe more general problems of the subject have hitherto\nremained entirely insoluble. The attempts of the greatest\nmathematicians, Newton, Maclaurin, Bernoulli, Clairaut,\nLaplace, to master such questions, all involve some\ngratuitous assumption, which is introduced because the\nproblem cannot otherwise be mathematically dealt with: these\nassumptions confessedly render the result defective, and how\ndefective, it is hard to say. And it was probably precisely\nthe absence of a theory which could be reasonably expected\nto agree with the observations, which made Observations of\nthis very curious phenomenon, the Tides, to be so much\nneglected as till very recently they were. Of late years\nsuch observations have been pursued, and their results have\nbeen resolved into empirical laws, so that the rules of the\nphenomena have been ascertained, although the dependence of\nthese rules upon the lunar and solar forces has not been\nshown. Here then we have a portion of our knowledge relating\nto facts undoubtedly dependent upon universal gravitation,\nin which Observation has outstripped Theory in her progress,\nand is compelled to wait till her usual companion overtakes\nher. This is a position of which Mathematical Theory has\nusually been very impatient, and we may expect that she will\nbe no less so in the present instance.\n\n7. It would be easy to show from the history of other\nsciences, for example, Mechanics and Optics, how essential\nthe cultivation of pure mathematics has been to their\nprogress. The parabola was already familiar among\nmathematicians when Galileo discovered that it was the\ntheoretical path of a Projectile; and the {166} extension\nand generalization of the Laws of Motion could never have\nbeen effected, unless the Differential and Integral Calculus\nhad been at hand, ready to trace the results of every\nhypothesis which could be made. D'Alembert's mode of\nexpressing the Third Law of Motion in its most general\nform[25\\2], if it did not prove the law, at least reduced\nthe application of it to analytical processes which could be\nperformed in most of those cases in which they were needed.\nIn many instances the demands of mechanical science\nsuggested the extension of the methods of pure analysis. The\nproblem of Vibrating Strings gave rise to the Calculus of\nPartial Differences, which was still further stimulated by\nits application to the motions of fluids and other\nmechanical problems. And we have in the writings of Lagrange\nand Laplace other instances equally remarkable of new\nanalytical methods, to which mechanical problems, and\nespecially cosmical problems, have given occasion.\n\n[Note 25\\2: _Hist. Ind. Sc._ b. vi. c. vi. sect. 7.]\n\n8. The progress of Optics as a science has, in like manner,\nbeen throughout dependent upon the progress of pure\nmathematics. The first rise of Geometry was followed by some\nadvances, slight ones no doubt, in the doctrine of\nReflection and in Perspective. The law of Refraction was\ntraced to its consequences by means of Trigonometry, which\nindeed was requisite to express the law in a simple form.\nThe steps made in Optical science by Descartes, Newton,\nEuler, and Huyghens, required the geometrical skill which\nthose philosophers possessed. And if Young and Fresnel had\nnot been, each in his peculiar way, persons of eminent\nmathematical endowments, they would not have been able to\nbring the Theory of Undulations and Interferences into a\ncondition in which it could be tested by experiments. We may\nsee how unexpectedly recondite parts of pure mathematics may\nbear upon physical science, by calling to mind a\ncircumstance already noticed in the History of\nScience[26\\2];--that Fresnel obtained one of the {167} most\ncurious confirmations of the theory (the laws of Circular\nPolarization by reflection) through an interpretation of an\nalgebraical expression, which, according to the original\nconventional meaning of the symbols, involved an impossible\nquantity. We have already remarked, that in virtue of the\nprinciple of the generality of symbolical language, such an\ninterpretation may often point out some real and important\nanalogy.\n\n[Note 26\\2: _Hist. Ind. Sc._ b. ix. c. xiii. sect. 2.]\n\n9. From this rapid sketch it may be seen how important an\noffice in promoting the progress of the physical sciences\nbelongs to mathematics. Indeed in the progress of many\nsciences, every step has been so intimately connected with\nsome advance in mathematics, that we can hardly be surprised\nif some persons have considered mathematical reasoning to be\nthe most essential part of such sciences; and have\noverlooked the other elements which enter into their\nformation. How erroneous this view is we shall best see by\nturning our attention to the other Ideas besides those of\nspace, number, and motion, which enter into some of the most\nconspicuous and admired portions of what is termed exact\nscience; and by showing that the clear and distinct\ndevelopment of such Ideas is quite as necessary to the\nprogress of exact and real knowledge as an acquaintance with\narithmetic and geometry.\n\n\n\n\n{{169}}\nBOOK III.\n\n\nTHE\nPHILOSOPHY\nOF THE\nMECHANICAL SCIENCES.\n\n\n\n\nIT is only because we subject trains of phenomena, that is,\nall change whatever, to the law of causality--to the\nrelation of cause and effect--that experience or empirical\nknowledge becomes possible.\n\nKANT, _Kr. d. R. V._ 11 Th. 1 Abth. 11 Buch. 2 Haupt.\n\nQuicquid premit vel trahit alterum, tantundem ab eo premitur\nvel trahitur ... Si corpus aliquod in corpus aliud impingens\nmotum ejus vi su\u00e2 quomodocunque mutaverit, idem quoque\nvicissim in motu proprio eandem mutationem in partem\ncontrariam vi alterius (ob \u00e6qualitatem pressionis, mutu\u00e6)\nsubibit ... Obtinet etiam h\u00e6c Lex in attractionibus.\n\nNEWTON, _Princip._ ad init.\n\n\n\n{{171}}\nBOOK III.\n\n\nTHE PHILOSOPHY OF THE MECHANICAL SCIENCES.\n\n\nCHAPTER I.\n\nOF THE MECHANICAL SCIENCES.\n\n\nIN the History of the Sciences, that class of which we here\nspeak occupies a conspicuous and important place; coming\ninto notice immediately after those parts of Astronomy which\nrequire for their cultivation merely the ideas of space,\ntime, motion, and number. It appears from our History, that\ncertain truths concerning the _equilibrium_ of bodies were\nestablished by Archimedes;--that, after a long interval of\ninactivity, his principles were extended and pursued further\nin modern times:--and that to these doctrines concerning\nequilibrium and the forces which produce it, (which\nconstitute the science _Statics_,) were added many other\ndoctrines concerning the _motions_ of bodies, considered\nalso as produced by forces, and thus the science of\n_Dynamics_ was produced. The assemblage of these sciences\ncomposes the province of _Mechanics_. Moreover, philosophers\nhave laboured to make out the laws of the equilibrium of\n_fluid_ as well as solid bodies; and hence has arisen the\nscience of _Hydrostatics_. And the doctrines of Mechanics\nhave been found to have a most remarkable bearing upon the\nmotions of the heavenly bodies; with reference to which,\nindeed, they were at first principally studied. The\nexplanation of those cosmical facts by means of mechanical\n{172} principles and their consequences, forms the science\nof _Physical Astronomy_. These are the principal examples of\nmechanical science; although some other portions of Physics,\nas Magnetism and Electrodynamics, introduce mechanical\ndoctrines very largely into their speculations.\n\nNow in all these sciences we have to consider _Forces_. In\nall mechanical reasonings forces enter, either as producing\nmotion, or as prevented from doing so by other forces. Thus\nforce, in its most general sense, is the _cause_ of motion,\nor of tendency to motion; and in order to discover the\nprinciples on which the mechanical sciences truly rest, we\nmust examine the nature and origin of our knowledge of Causes.\n\nIn these sciences, however, we have not to deal with Cause\nin its more general acceptation, in which it applies to all\nkinds of agency, material or immaterial;--to the influence\nof thought and will, as well as of bodily pressure and\nattractive force. Our business at present is only with such\ncauses as immediately operate upon matter. We shall\nnevertheless, in the first place, consider the nature of\nCause in its most general form; and afterwards narrow our\nspeculations so as to direct them specially to the\nmechanical sciences.\n\n\n\n{{173}}\nCHAPTER II.\n\nOF THE IDEA OF CAUSE.\n\n\n1. WE see in the world around us a constant succession of\ncauses and effects connected with each other. The laws of\nthis connexion we learn in a great measure from experience,\nby observation of the occurrences which present themselves\nto our notice, succeeding one another. But in doing this,\nand in attending to this succession of appearances, of which\nwe are aware by means of our senses, we supply from our own\nminds the Idea of Cause. This Idea, as we have already shown\nwith respect to other Ideas, is not derived from experience,\nbut has its origin in the mind itself;--is introduced into\nour experience by the active, and not by the passive part of\nour nature.\n\nBy Cause we mean some quality, power, or efficacy, by which\na state of things produces a succeeding state. Thus the\nmotion of bodies from rest is produced by a cause which we\ncall _Force_: and in the particular case in which bodies\nfall to the earth, this force is termed _Gravity_. In these\ncases, the Conceptions of Force and Gravity receive their\nmeaning from the Idea of Cause which they involve: for Force\nis conceived as the Cause of Motion. That this Idea of Cause\nis not derived from experience, we prove (as in former\ncases) by this consideration: that we can make assertions,\ninvolving this idea, which are rigorously necessary and\nuniversal; whereas knowledge derived from experience can\nonly be true as far as experience goes, and can never\ncontain in itself any evidence whatever of its necessity. We\nassert that 'Every event must have a cause:' and this\nproposition we know to be true, not only probably, and\ngenerally, and as far as we can see: {174} but we cannot\nsuppose it to be false in any single instance. We are as\ncertain of it as of the truths of arithmetic or geometry. We\ncannot doubt that it must apply to all events past and\nfuture, in every part of the universe, just as truly as to\nthose occurrences which we have ourselves observed. _What_\ncauses produce what effects;--what is the cause of any\nparticular event;--what will be the effect of any peculiar\nprocess;--these are points on which experience may enlighten\nus. Observation and experience may be requisite, to enable\nus to judge respecting such matters. But that every event\nhas _some_ cause, Experience cannot prove any more than she\ncan disprove. She can add nothing to the evidence of the\ntruth, however often she may exemplify it. This doctrine,\nthen, cannot have been acquired by her teaching; and the\nIdea of Cause, which the doctrine involves, and on which it\ndepends, cannot have come into our minds from the region of\nobservation.\n\n2. That we do, in fact, apply the Idea of Cause in a more\nextensive manner than could be justified, if it were derived\nfrom experience only, is easily shown. For from the\nprinciple that everything must have a cause, we not only\nreason concerning the succession of the events which occur\nin the progress of the world, and which form the course of\nexperience; but we infer that the world itself must have a\ncause;--that the chain of events connected by common\ncausation, must have a First Cause of a nature different\nfrom the events themselves. This we are entitled to do, if\nour Idea of Cause be independent of, and superior to,\nexperience: but if we have no Idea of Cause except such as\nwe gather from experience, this reasoning is altogether\nbaseless and unmeaning.\n\n3. Again; by the use of our powers of observation, we are\naware of a succession of appearances and events. But none of\nour senses or powers of external observation can detect in\nthese appearances the power or quality which we call Cause.\nCause is that which connects one event with another; but no\nsense or perception discloses to us, or can disclose, any\nconnexion {175} among the events which we observe. We see\nthat one occurrence follows another, but we can never see\nanything which shows that one occurrence _must_ follow\nanother. We have already noticed[1\\3], that this truth has\nbeen urged by metaphysicians in modern times, and generally\nassented to by those who examine carefully the connexion of\ntheir own thoughts. The arguments are, indeed, obvious\nenough. One ball strikes another and causes it to move\nforwards. But by what compulsion? Where is the necessity? If\nthe mind can see any circumstance in this case which makes\nthe result inevitable, let this circumstance be pointed out.\nBut, in fact, there is no such discoverable necessity; for\nwe can conceive this event not to take place at all. The\nstruck ball may stand still, for aught we can see. 'But the\nlaws of motion will not allow it to do so.' Doubtless they\nwill not. But the laws of motion are learnt from experience,\nand therefore can prove no necessity. Why should not the\nlaws of motion be other than they are? Are they necessarily\ntrue? That they are necessarily such as do actually regulate\nthe impact of bodies, is at least no obvious truth; and\ntherefore this necessity cannot be, in common minds, the\nground of connecting the impact of one ball with the motion\nof another. And assuredly, if this fail, no other ground of\nsuch necessary connexion can be shown. In this case, then,\nthe events are not seen to be necessarily connected. But if\nthis case, where one ball moves another by impulse, be not\nan instance of events exhibiting a necessary connexion, we\nshall look in vain for any example of such a connexion.\nThere is, then, no case in which events can be observed to\nbe necessarily connected: our idea of causation, which\nimplies that the event is necessarily connected with the\ncause, cannot be derived from observation.\n\n[Note 1\\3: Book 3. chap. ii.]\n\n4. But it may be said, we have not any such Idea of Cause,\nimplying necessary connexion with effect, and a quality by\nwhich this connexion is produced. {176} We see nothing but\nthe succession of events; and by _cause_ we mean nothing but\na certain succession of events;--namely, a constant,\nunvarying succession. Cause and effect are only two events\nof which the second invariably follows the first. We delude\nourselves when we imagine that our idea of causation\ninvolves anything more.\n\nTo this I reply by asking, what then is the meaning of the\nmaxim above quoted, and allowed by all to be universally and\nnecessarily true, that every event must have a cause? Let us\nput this maxim into the language of the explanation just\nnoticed; and it becomes this:--'Every event must have a\ncertain other event invariably preceding it.' But why must\nit? Where is the necessity? Why must like events always be\npreceded by like, except so far as other events interfere?\nThat there is such a necessity, no one can doubt. All will\nallow that if a stone ascend because it is thrown upwards in\none case, a stone which ascends in another case has also\nbeen thrown upwards, or has undergone some equivalent\noperation. All will allow that in this sense, every kind of\nevent must have some other specific kind of event preceding\nit. But this turn of men's thoughts shows that they see in\nevents a connexion which is not mere succession. They see in\ncause and effect, not merely what does, often or always,\nprecede and follow, but what _must_ precede and follow. The\nevents are not only conjoined, they are connected. The cause\nis more than the prelude, the effect is more than the\nsequel, of the fact. The cause is conceived not as a mere\noccasion; it is a power, an efficacy, which has a real\noperation.\n\n5. Thus we have drawn from the maxim, that Every Effect must\nhave a Cause, arguments to show that we have an Idea of\nCause which is not borrowed from experience, and which\ninvolves more than mere succession. Similar arguments might\nbe derived from any other maxims of universal and necessary\nvalidity, which we can obtain concerning Cause: as, for\nexample, the maxims that Causes are measured by their\nEffects, and that Reaction is equal and opposite to {177}\nAction. These maxims we shall soon have to examine; but we\nmay observe here, that the necessary truth which belongs to\nthem, shows that they, and the Ideas which they involve, are\nnot the mere fruits of observation; while their meaning,\nincluding, as it does, something quite different from the\nmere conception of succession of events, proves that such a\nconception is far from containing the whole import and\nsignification of our Idea of Cause.\n\nThe progress of the opinions of philosophers on the points\ndiscussed in this chapter, has been one of the most\nremarkable parts of the history of Metaphysics in modern\ntimes: and I shall therefore briefly notice some of its\nfeatures.\n\n\n\n{{178}}\nCHAPTER III.\n\nMODERN OPINIONS RESPECTING THE IDEA OF CAUSE.\n\n\n1. TOWARDS the end of the seventeenth century there existed\nin the minds of many of the most vigorous and active\nspeculators of the European literary world, a strong\ntendency to ascribe the whole of our Knowledge to the\nteaching of Experience. This tendency, with its\nconsequences, including among them the reaction which was\nproduced when the tenet had been pushed to a length\nmanifestly absurd, has exercised a very powerful influence\nupon the progress of metaphysical doctrines up to the\npresent time. I proceed to notice some of the most prominent\nof the opinions which have thus obtained prevalence among\nphilosophers, so far as the Idea of Cause is concerned.\n\nLocke was one of the metaphysicians who produced the\ngreatest effect in diffusing this opinion, of the exclusive\ndependence of our knowledge upon experience. Agreeably to\nthis general system, he taught[2\\3] that our ideas of Cause\nand Effect are got from observation of the things about us.\nYet notwithstanding this tenet of his, he endeavoured still\nto employ these ideas in reasoning on subjects which are far\nbeyond all limits of experience: for he professed to prove,\nfrom our idea of Causation, the existence of the Deity[3\\3].\n\n[Note 2\\3: _Essay on the Human Understanding_, b. ii. c. xxvi.]\n\n[Note 3\\3: B. iv. c. x.]\n\nHume noticed this obvious inconsistency; but declared\nhimself unable to discover any remedy for a defect so fatal\nto the most important parts of our knowledge. He could see,\nin our belief of the succession of cause and effect, nothing\nbut the habit of associating in our minds what had often\nbeen {179} associated in our experience. He therefore\nmaintained that we could not, with logical propriety, extend\nour belief of such a succession to cases entirely distinct\nfrom all those of which our experience consisted. We see, he\nsaid, an actual _conjunction_ of two events; but we can in\nno way detect a necessary _connexion_; and therefore we have\nno means of inferring cause from effect, or effect from\ncause[4\\3]. The only way in which we recognize Cause and\nEffect in the field of our experience, is as an unfailing\nSequence: we look in vain for anything which can assure us\nof an infallible Consequence. And since experience is the\nonly source of our knowledge, we cannot with any justice\nassert that the world in which we live must necessarily have\nhad a cause.\n\n[Note 4\\3: Hume's _Phil. of the Human Mind_, vol. i. p.\n94.]\n\n2. This doctrine, taken in conjunction with the known\nskepticism of its author on religious points, produced a\nconsiderable fermentation in the speculative world. The\nsolution of the difficulty thus thrown before philosophers,\nwas by no means obvious. It was vain to endeavour to find in\nexperience any other property of a Cause, than a constant\nsequence of the effect. Yet it was equally vain to try to\npersuade men that they had no idea of Cause; or even to\nshake their belief in the cogency of the familiar arguments\nconcerning the necessity of an original cause of all that is\nand happens. Accordingly these hostile and apparently\nirreconcilable doctrines,--the indispensable necessity of a\ncause of every event, and the impossibility of our knowing\nsuch a necessity,--were at last allowed to encamp side by\nside. Reid, Beattie, and others, formed one party, who\nshowed how widely and constantly the idea of a cause\npervades all the processes of the human mind: while another\nsect, including Brown, and apparently Stewart, maintained\nthat this idea is always capable of being resolved into a\nconstant sequence; and these latter reasoners tried to\nobviate the dangerous and shocking inferences which some\npersons might try to draw from their opinion, by declaring\nthe {180} maxim that \"Every event must have a cause,\" to be\nan instinctive law of belief, or a fundamental principle of\nthe human mind[5\\3].\n\n[Note 5\\3: Stewart's _Active Powers_, vol. i. p. 347.\nBrowne's _Lectures_, vol. i. p. 115.]\n\n3. While this series of discussions was going on in Britain,\na great metaphysical genius in Germany was unravelling the\nperplexity in another way. Kant's speculations originated,\nas he informs us, in the trains of thought to which Hume's\nwritings gave rise; and the _Kritik der Reinen Vernunft_, or\n_Examination of the Pure Reason_, was published in 1787,\nwith the view of showing the true nature of our knowledge.\n\nKant's solution of the difficulties just mentioned differs\nmaterially from that above stated. According to Brown[6\\3],\nsuccession observed and cause inferred,--the memory of past\nconjunctions of events and the belief of similar future\nconjunctions,--are facts, independent, so far as we can\ndiscover, but inseparably combined by a law of our mental\nnature. According to Kant, causality is an inseparable\ncondition of our experience: a connexion in events is\nrequisite to our apprehending them _as_ events. Future\noccurrences must be connected by causation as the past have\nbeen, because we cannot think of past, present, and future,\nwithout such connexion. We cannot fix the mind upon\noccurrences, without including these occurrences in a series\nof causes and effects. The relation of Causation is a\ncondition under which we think of events, as the relations\nof space are a condition under which we see objects.\n\n[Note 6\\3: _Lectures_, vol. i. p. 114.]\n\n4. On a subject so abstruse, it is not easy to make our\ndistinctions very clear. Some of Brown's illustrations\nappear to approach very near to the doctrine of Kant. Thus\nhe says[7\\3], 'The _form_ of bodies is the relation of their\nelements to each other in space,--the _power_ of bodies is\ntheir relation to each other in time.' Yet notwithstanding\nsuch approximations in expression, the Kantian doctrine\nappears to be different from {181} the views of Stewart and\nBrown, as commonly understood. According to the Scotch\nphilosophers, the cause and the effect are two things,\nconnected in our minds by a law of our nature. But this view\nrequires us to suppose that we can conceive the law to be\nabsent, and the course of events to be unconnected. If we\ncan understand what is the special force of this law, we\nmust be able to imagine what the case would be if the law\nwere non-existing. We must be able to conceive a mind which\ndoes not connect effects with causes. The Kantian doctrine,\non the other hand, teaches that we cannot imagine events\nliberated from the connexion of cause and effect: this\nconnexion is a condition of our conceiving any real\noccurrences: we cannot think of a real sequence of things,\nexcept as involving the operation of causes. In the Scotch\nsystem, the past and the future are in their nature\nindependent, but bound together by a rule; in the German\nsystem, they share in a common nature and mutual relation,\nby the act of thought which makes them past and future. In\nthe former doctrine cause is a tie which binds; in the\nlatter it is a character which pervades and shapes events.\nThe Scotch metaphysicians only assert the _universality_ of\nthe relation; the German attempts further to explain its\n_necessity_.\n\n[Note 7\\3: _Lectures_, vol. i. p. 127.]\n\nThis being the state of the case, such illustrations as that\nof Dr. Brown quoted above, in which he represents _cause_ as\na relation of the same kind with _form_, do not appear\nexactly to fit his opinions. Can the relations of figure be\nproperly said to be connected with each other by a law of\nour nature, or a tendency of our mental constitution? Can we\nascribe it to a law of our thoughts, that we believe the\nthree angles of a triangle to be equal to two right angles?\nIf so, we must give the same reason for our belief that two\nstraight lines cannot inclose a space; or that three and two\nare five. But will any one refer us to an ultimate law of\nour constitution for the belief that three and two are five?\nDo we not see that they are so, as plainly as we see that\nthey are three and two? Can we imagine laws of our\nconstitution abolished, so that three and two shall {182}\nmake something different from five;--so that an inclosed\nspace shall lie between two straight lines;--so that the\nthree angles of a plane triangle shall be greater than two\nright angles? We cannot conceive this. If the numbers _are_\nthree and two; if the lines _are_ straight; if the triangle\n_is_ a rectilinear triangle, the consequences are\ninevitable. We cannot even imagine the contrary. We do not\nwant a law to direct that things should be what they are.\nThe relation, then, of cause and effect, being of the same\nkind as the necessary relations of figure and number, is not\nproperly spoken of as established in our minds by a special\nlaw of our constitution: for we reject that loose and\ninappropriate phraseology which speaks of the relations of\nfigure and number as 'determined by laws of belief.'\n\n5. In the present work, we accept and adopt, as the basis of\nour inquiry concerning our knowledge, the existence of\nnecessary truths concerning causes, as there exist necessary\ntruths concerning figure and number. We find such truths\nuniversally established and assented to among the\ncultivators of science, and among speculative men in\ngeneral. All mechanicians agree that reaction is equal and\nopposite to action, both when one body presses another, and\nwhen one body communicates motion to another. All reasoners\njoin in the assertion, not only that every observed change\nof motion has had a cause, but that every change of motion\nmust have a cause. Here we have certain portions of\nsubstantial and undoubted knowledge. Now the essential point\nin the view which we must take of the idea of cause is\nthis,--that our view must be such as to form a solid basis\nfor our knowledge. We have, in the Mechanical Sciences,\ncertain universal and necessary truths on the subject of\ncauses. Now any view which refers our belief in causation to\nmere experience or habit, cannot explain the possibility of\nsuch necessary truths, since experience and habit can never\nlead to a perception of necessary connexion. But a view\nwhich teaches us to acknowledge axioms concerning cause, as\nwe acknowledge axioms {183} concerning space, will lead us\nto look upon the science of mechanics as equally certain and\nuniversal with the science of geometry; and will thus\nmaterially affect our judgment concerning the nature and\nclaims of our scientific knowledge.\n\nAxioms concerning Cause, or concerning Force, which as we\nshall see, is a modification of Cause, will flow from an\nIdea of Cause, just as axioms concerning space and number\nflow from the ideas of space and number or time. And thus\nthe propositions which constitute the science of Mechanics\nprove that we possess an idea of cause, in the same sense in\nwhich the propositions of geometry and arithmetic prove our\npossession of the ideas of space and of time or number.\n\n6. The idea of cause, like the ideas of space and time, is a\npart of the _active_ powers of the mind. The relation of\ncause and effect is a relation or condition under which\nevents are apprehended, which relation is not given by\nobservation, but supplied by the mind itself. According to\nthe views which explain our apprehension of cause by\nreference to habit, or to a supposed law of our mental\nnature, causal connexion is a consequence of agencies which\nthe mind passively obeys; but according to the view to which\nwe are led, this connexion is a result of faculties which\nthe mind actively exercises. And thus the relation of cause\nand effect is a condition of our apprehending successive\nevents, a part of the mind's constant and universal\nactivity, a source of necessary truths; or, to sum all this\nin one phrase, a Fundamental Idea.\n\n\n\n{{184}}\nCHAPTER IV.\n\nOF THE AXIOMS WHICH RELATE TO THE IDEA OF CAUSE.\n\n\n1. _Causes are abstract Conceptions._--WE have now to\nexpress, as well as we can, the fundamental character of\nthat Idea of Cause of which we have just proved the\nexistence. This may be done, at least for purposes of\nreasoning, in this as in former instances, by means of\naxioms. I shall state the principal axioms which belong to\nthis subject, referring the reader to his own thoughts for\nthe axiomatic evidence which belongs to them.\n\nBut I must first observe, that in order to express general\nand abstract truths concerning cause and effect, these\nterms, _cause_ and _effect_, must be understood in a general\nand abstract manner. When one event gives rise to another,\nthe first _event_ is, in common language, often called the\ncause, and the second the effect. Thus the meeting of two\nbilliard-balls may be said to be the cause of one of them\nturning aside out of the path in which it was moving. For\nour present purposes, however, we must not apply the term\ncause to such occurrences as this meeting and turning, but\nto a certain conception, _force_, abstracted from all such\nspecial events, and considered as a quality or property by\nwhich one body affects the motion of the other. And in like\nmanner in other cases, cause is to be conceived as some\nabstract quality, power, or efficacy, by which change is\nproduced; a quality not identical with the events, but\ndisclosed by means of them. Not only is this abstract mode\nof conceiving force and cause useful in expressing the\nfundamental principles of science; but it supplies us with\nthe only mode by which such principles can be {185} stated\nin a general manner, and made to lead to substantial truth\nand real knowledge.\n\nUnderstanding _cause_, therefore, in this sense, we proceed\nto our Axioms.\n\n2. First Axiom. _Nothing can take place without a Cause._\n\nEvery event, of whatever kind, must have a cause in the\nsense of the term which we have just indicated; and that it\nmust, is a universal and necessary proposition to which we\nirresistibly assent as soon as it is understood. We believe\neach appearance to come into existence,--we conceive every\nchange to take place,--not only with something preceding it,\nbut something by which it is made to be what it is. An\neffect without a cause;--an event without a preceding\ncondition involving the efficacy by which the event is\nproduced;--are suppositions which we cannot for a moment\nadmit. That the connexion of effect with cause is universal\nand necessary, is a universal and constant conviction of\nmankind. It persists in the minds of all men, undisturbed by\nall the assaults of sophistry and skepticism; and, as we\nhave seen in the last chapter, remains unshaken, even when\nits foundations seem to be ruined. This axiom expresses, to\na certain extent, our Idea of Cause; and when that idea is\nclearly apprehended, the axiom requires no proof, and indeed\nadmits of none which makes it more evident. That\nnotwithstanding its simplicity, it is of use in our\nspeculations, we shall hereafter see; but in the first\nplace, we must consider the other axioms belonging to this\nsubject.\n\n3. Second Axiom. _Effects are proportional to their Causes,\nand Causes are measured by their Effects._\n\nWe have already said that _cause_ is that quality or power,\nin the circumstances of each case, by which the effect is\nproduced; and this power, an abstract property of the\ncondition of things to which it belongs, can in no way fall\ndirectly under the cognizance of the senses. Cause, of\nwhatever kind, is not apprehended as including objects and\nevents which share its nature by being co-extensive with\ncertain portions of it, as space and time are. It cannot\ntherefore, like them, be {186} measured by repetition of its\nown parts, as space is measured by repetition of inches, and\ntime by repetition of minutes. Causes may be greater or\nless; as, for instance, the force of a man is greater than\nthe force of a child. But how much is the one greater than\nthe other? How are we to compare the abstract conception,\nforce, in such cases as these?\n\nTo this, the obvious and only answer is, that we must\ncompare causes by means of their effects;--that we must\ncompare force by something which force can do. The child can\nlift one fagot; the man can lift ten such fagots: we have\nhere a means of comparison. And whether or not the rule is\nto be applied in this manner, that is, by the number of\nthings operated on, (a question which we shall have to\nconsider hereafter,) it is clear that this form of rule,\nnamely, a reference to some effect or other as our measure,\nis the right, because the only possible form. The cause\ndetermines the effect. The cause being the same, the effect\nmust be the same. The connexion of the two is governed by a\nfixed and inviolable rule. It admits of no ambiguity. Every\ndegree of intensity in the cause has some peculiar\nmodification of the effect corresponding to it. Hence the\neffect is an unfailing index of the amount of the cause; and\nif it be a measurable effect, gives a measure of the cause.\nWe can have no other measure; but we need no other, for this\nis exact, sufficient and complete.\n\nIt may be said, that various effects are produced by the\nsame cause. The sun's heat melts wax and expands\nquicksilver. The force of gravity causes bodies to move\ndownwards if they are free, and to press down upon their\nsupports if they are supported. Which of the effects is to\nbe taken as the measure of heat, or of gravity, in these\ncases? To this we reply, that if we had merely different\nstates of the same cause to compare, any of the effects\nmight be taken. The sun's heat on different days might be\nmeasured by the expansion of quicksilver, or by the quantity\nof wax melted. The force of gravity, if it were different at\ndifferent places, might be measured by the spaces through\nwhich a given weight would bend an elastic {187} support, or\nby the spaces through which a body would fall in a given\ntime. All these measures are consistent with the general\ncharacter of our idea of cause.\n\n4. _Limitation of the Second Axiom._--But there may be\ncircumstances in the nature of the case which may further\ndetermine the kind of effect which we must take for the\nmeasure of the cause. For example, if causes are conceived\nto be of such a nature as to be capable of addition, the\neffects taken as their measure must conform to this\ncondition. This is the case with mechanical causes. The\nweights of two bodies are the causes of the pressure which\nthey exert downwards; and these weights are capable of\naddition. The weight of the two is the sum of the weight of\neach. We are therefore not at liberty to say that weights\nshall be measured by the spaces through which they bend a\ncertain elastic support, except we have first ascertained\nthat the whole weight bends it through a space equal to the\nsum of the inflections produced by the separate weights.\nWithout this precaution, we might obtain inconsistent\nresults. Two weights, each of the magnitude 3 as measured by\ntheir effects, might, if we took the inflections of a spring\nfor the effects, be together equal to 5 or to 7 by the same\nkind of measurement. For the inflection produced by two\nweights of 3 might, for aught we can see beforehand, be more\nor less than twice as great as the inflection produced by\none weight of 3. That forces are capable of addition, is a\ncondition which limits, and, as we shall see, in some cases\nrigorously fixes, the kind of effects which are to be taken\nas their measures.\n\nCauses which are thus capable of addition are to be measured\nby the repeated addition of equal quantities. Two such\ncauses are _equal_ to each other when they produce exactly\nthe same effect. So far our axiom is applied directly. But\nthese two causes can be _added_ together; and being thus\nadded, they are _double_ of one of them; and the cause\ncomposed by addition of _three_ such, is _three_ times as\ngreat as the first; and so on for any measure whatever. By\nthis means, and by this {188} means only, we have a complete\nand consistent measure of those causes which are so\nconceived as to be subject to this condition of being added\nand multiplied.\n\nCauses are, in the present chapter, to be understood in the\nwidest sense of the term; and the axiom now under our\nconsideration applies to them, whenever they are of such a\nnature as to admit of any measure at all. But the cases\nwhich we have more particularly in view are _mechanical_\ncauses, the causes of the motion and of the equilibrium of\nbodies. In these cases, forces are conceived as capable of\naddition; and what has been said of the measure of causes in\nsuch cases, applies peculiarly to mechanical forces. Two\nweights, placed together, may be considered as a single\nweight, equal to the _sum_ of the two. Two pressures,\npushing a body in the same direction at the same point, are\nidentical in all respects with some single pressure, their\n_sum_, pushing in like manner; and this is true whether or\nnot they put the body in motion. In the cases of mechanical\nforces, therefore, we take some certain effect, velocity\ngenerated or weight supported, which may fix the _unit_ of\nforce; and we then measure all other forces by the\nsuccessive repetition of this unit, as we measure all spaces\nby the successive repetition of our unit of lineal measure.\n\nBut these steps in the formation of the science of Mechanics\nwill be further explained, when we come to follow our axioms\nconcerning cause into their application in that science. At\npresent we have, perhaps, sufficiently explained the axiom\nthat causes are measured by their effects, and we now\nproceed to a third axiom, also of great importance.\n\n5. Third Axiom. _Reaction is equal and opposite to Action._\n\nIn the case of mechanical forces, the action of a cause\noften takes place by an operation of one body upon another;\nand in this case, the action is always and inevitably\naccompanied by an _opposite_ action. If I press a stone with\nmy hand, the stone presses my hand in return. If one ball\nstrike another and put it in motion, the second ball\ndiminishes the motion of {189} the first. In these cases the\noperation is mutual; the Action is accompanied by a\nReaction. And in all such cases the Reaction is a force of\nexactly the same nature as the Action, exerted in an\nopposite direction. A pressure exerted upon a body at rest\nis resisted and balanced by another pressure; when the\npressure of one body puts another in motion, the body,\nthough it yields to the force, nevertheless exerts upon the\npressing body a force like that which it suffers.\n\nNow the axiom asserts further, that this Reaction is\n_equal_, as well as opposite, to the Action. For the\nReaction is an effect of the Action, and is determined by\nit. And since the two, Action and Reaction, are forces of\nthe same nature, each may be considered as cause and as\neffect; and they must, therefore, determine each other by a\ncommon rule. But this consideration leads necessarily to\ntheir equality: for since the rule is mutual, if we could\nfor an instant suppose the Reaction to be less than the\nAction, we must, by the same rule, suppose the Action to be\nless than the Reaction. And thus Action and Reaction, in\nevery such case, are rigorously equal to each other.\n\nIt is easily seen that this axiom is not a proposition which\nis, or can be, proved by experience; but that its truth is\nanterior to special observation, and depends on our\nconception of Action and Reaction. Like our other axioms,\nthis has its source in an Idea; namely, the Idea of Cause,\nunder that particular condition in which cause and effect\nare mutual. The necessary and universal truth which we\ncannot help ascribing to the axiom, shows that it is not\nderived from the stores of experience, which can never\ncontain truths of this character. Accordingly, it was\nasserted with equal confidence and generality by those who\ndid not refer to experience for their principles, and by\nthose who did. Leonicus Tom\u00e6us, a commentator of Aristotle,\nwhose work was published in 1552, and therefore at a period\nwhen no right opinions concerning mechanical reaction were\ncurrent, at least in his school, says, in his remarks on the\nAuthor's Questions concerning the communication of motion,\nthat 'Reaction is equal and {190} contrary to Action.' The\nsame principle was taken for granted by all parties, in all\nthe controversies concerning the proper measure of force, of\nwhich we shall have to speak: and would be rigorously true,\nas a law of motion, whichever of the rival interpretations\nof the measure of the term 'Action' we were to take.\n\n6. _Extent of the Third Axiom._--It may naturally be asked\nwhether this third Axiom respecting causation extends to any\nother cases than those of mechanical action, since the\nnotion of Cause in general has certainly a much wider\nextent. For instance, when a hot body heats a cold one, is\nthere necessarily an equal reaction of the second body upon\nthe first? Does the snowball cool the boy's hand exactly as\nmuch as the hand heats the snow? To this we reply, that, in\nevery case in which one body acts upon another by its\nphysical qualities, there must be some reaction. No body can\naffect another without being itself also affected. But in\nany physical change the _action_ exerted is an abstract term\nwhich may be variously understood. The hot hand may _melt_ a\ncool body, or may _warm_ it: which kind of effect is to be\ntaken as action? This remains to be determined by other\nconsiderations.\n\nIn all cases of physical change produced by one body in\nanother, it is generally possible to assume such a meaning\nof action, that the reaction shall be of the same nature as\nthe action; and when this is done, the third axiom of\ncausation, that reaction is equal to action, is universally\ntrue. Thus if a hot body heat a cold one, the change may be\nconceived as the transfer of a certain substance, _heat_ or\n_caloric_, from the first body to the second. On this\nsupposition, the first body _loses_ just as much heat as the\nother _gains_; action and reaction are equal. But if the\nreaction be of a different kind to the action we can no\nlonger apply the axiom. If a hot body _melt_ a cold one, the\nlatter _cools_ the former: here, then, is reaction; but so\nlong as the action and reaction are stated in this form, we\ncannot assert any equality between them.\n\nIn treating of the secondary mechanical sciences, we {191}\nshall see further in what way we may conceive the physical\naction of one body upon another, so that the same axioms\nwhich are the basis of the science of Mechanics shall apply\nto changes not at first sight manifestly mechanical.\n\nThe three axioms of causation which we have now stated are\nthe fundamental maxims of all reasoning concerning causes as\nto their quantities; and it will be shown in the sequel that\nthese axioms form the basis of the science of Mechanics,\ndetermining its form, extent, and certainty. We must,\nhowever, in the first place, consider how we acquire those\nconceptions upon which the axioms now established are to be\nemployed.\n\n[2d Ed.] [The Axiom that _Reaction is equal and opposite to\nAction_, may appear to be at variance with a maxim\nconcerning Cause which is commonly current; namely, that the\n'Cause precedes Effect, and Effect follows Cause.' For it\nmay be said, if _A_, the Action, and _R_, the Reaction, can\nbe considered as mutually the cause of each other, _A_ must\nprecede _R_, and yet must follow it, which is impossible.\nBut to this I reply, that in those cases of direct Causation\nto which the maxim applies, the Cause and Effect are not\nsuccessive, but simultaneous. If I press against some\nobstacle, the obstacle resists and returns the pressure at\nthe instant it is exerted, not after any interval of time,\nhowever small. The common maxim, that the effect follows the\ncause, has arisen from the practice of considering, as\nexamples of cause and effect, not instantaneous forces or\ncauses, and the instantaneous changes which they produce;\nbut taking, instead of this latter, the _cumulative_ effects\nproduced in the course of time, and compared with like\nresults occurring without the action of the cause. Thus, if\nwe alter the length of a clock-pendulum, this change\nproduces, as its effect, a subsequent change of rate in the\nclock: because the rate is measured by the accumulated\neffects of the pendulum's gravity, before and after the\nchange. But the pendulum produces its mechanical effect upon\nthe escapement, at the moment of its contact, and each wheel\nupon the next, at the moment of _its_ contact. As has {192}\nbeen said in a Review of this work, 'The time lost in cases\nof indirect physical causation is consumed in the movements\nwhich take place among the parts of the mechanism in action,\nby which the active forces so transformed into momentum are\ntransported over intervals of space to new points of action,\nthe motion of matter in such cases being regarded as a mere\ncarrier of force.' (_Quarterly Rev._ No. cxxxv. p. 212.)\n\nThis subject I have further treated in the _Memoirs of the\nCambridge Philosophical Society_, vol. vii. part iii.] [In\nthis Third Edition I add this discussion.]\n\n_Discussion of the Question:--Are Cause and Effect\nsuccessive or simultaneous?_\n\nI HAVE at various times laid before this Society\ndissertations on the metaphysical grounds and elements of\nour knowledge, and especially on the foundations of the\nscience of mechanics. As these speculations have not failed\nto excite some attention, both here and elsewhere, I am\ntempted to bring forward in the same manner some additional\ndisquisitions of the same kind. Indeed, the immediate\noccasion of the present memoir is of itself an evidence that\nsuch subjects are not supposed to be without their interest\nfor the general reader; for I am led to the views and\nreasonings which I am now about to lay before the Society,\nby some remarks in one of our most popular Reviews, (_The\nQuarterly Review_, Article on the _History_ and _Philosophy\nof the Inductive Sciences_, June 1841). A writer of singular\nacuteness and comprehensiveness of view has there made\nremarks upon the doctrines which I had delivered in the\n_Philosophy of the Inductive Sciences_, which remarks appear\nto me in the highest degree instructive and philosophical. I\nam not, however, going here to discuss fully the doctrines\ncontained in this critique. With respect to its general\ntendency, I will only observe, that the author does not\naccept, in the form in which I had given it, the account of\nthe origin and ground of necessary and universal truths. I\nhad stated that our knowledge is derived from Sensations and\nIdeas; and that Ideas, which are the conditions of\nperception, such as _space_, _time_, _likeness_, _cause_,\nmake universal and necessary knowledge possible; whereas, if\nknowledge were derived from Sensation alone, it could not\nhave those characters. I have moreover {193} enumerated a\nlong series of Fundamental Ideas as the bases of a\ncorresponding series of sciences, of which sciences I have\nshown also, by an historical survey, that they claim to\npossess universal truths, and have their claims allowed. I\nhave gone further: for I have stated the Axioms which flow\nfrom these Fundamental Ideas, and which are the logical\ngrounds of necessity and universality in the truths of each\nscience, when the science is presented in the form of a\ndemonstrated system. The Reviewer does not assent to this\ndoctrine, nor to the argument by which it is supported;\nnamely, that Experience cannot lead to universal truths,\nexcept by means of a universal Idea supplied by the mind,\nand infused into the particular facts which observation\nministers. He considers that the existence of universal\ntruths in our knowledge may be explained otherwise. He holds\nthat it is a sufficient account of the matter to say that we\npass from special experience to universal truth in virtue of\n'the inductive propensity--the irresistible impulse of the\nmind to generalize _ad infinitum_.' I shall not here dwell\nupon very strong reasons which may be assigned, as I\nconceive, for not accepting this as a full and satisfactory\nexplanation of the difficulty. Instead of doing so, I shall\nhere content myself with remarking, that even if we adopt\nthe Reviewer's expressions, we must still contend that there\nare _different forms_ of the _impulse of the mind to\ngeneralize_, corresponding to each of the Fundamental Ideas\nof our system. These Fundamental Ideas, if they be nothing\nelse, must at least be accepted as a classification of the\nmodes of action of the Inductive Propensity,--as so many\ndifferent paths and tendencies of the Generalizing Impulse:\nand the Axioms which I have stated as the express results of\nthe Fundamental Ideas, and as the steps by which those Ideas\nmake universal truths possible, are still no less worthy of\nnotice, if they are stated as the results of our\nGeneralizing Impulse; and as the steps by which that\nImpulse, in its many various forms, makes universal truths\npossible. The Generalizing Impulse in that operation by\nwhich it leads us to the Axioms of Geometry, and to those of\nMechanics, takes very different courses; and these courses\nmay well deserve to be separately studied. And perhaps, even\nif we accept this view of the philosophy of our knowledge,\nno simpler or clearer way can be found of describing and\ndistinguishing these fundamentally different operations of\nthe Inductive Propensity, than by saying, {194} that in the\none case it proceeds according to the Idea of Space, in\nanother according to the Idea of Mechanical Cause; and the\nlike phraseology may be employed for all the other cases.\n\nThis then being understood, my present object is to consider\nsome very remarkable, and, as appears to me, novel views of\nthe Idea of Cause which the Reviewer propounds. And these\nmay be best brought under our discussion by considering them\nas an attempt to solve the question, Whether, according to\nour fundamental apprehensions of the relation of Cause and\nEffect, effect follows cause in the order of time, or is\nsimultaneous with it.\n\nAt first sight, this question may seem to be completely\ndecided by our fundamental convictions respecting cause and\neffect, and by the axioms which have been propounded by\nalmost all writers, and have obtained universal currency\namong reasoners on this subject. That the cause must precede\nthe effect,--that the effect must follow the cause,--are, it\nmight seem, self-evident truths, assumed and assented to by\nall persons in all reasonings in which those notions occur.\nSuch a doctrine is commonly asserted in general terms, and\nseems to be verified in all the applications of the idea of\ncause. A heavy body produces motion by its weight; the\nmotion produced is subsequent in time to the pressure which\nthe weight exerts. In a machine, bodies push or strike each\nother, and so produce a series of motions; each motion, in\nthis case, is the result of the motions and configurations\nwhich have preceded it. The whole series of such motions\nemploys time; and this time is filled up and measured by the\nseries of causes and effects, the effects being, in their\nturn, causes of other effects. This is the common mode of\napprehending the universal course of events, in which the\nchain of causation, and the progress of time, are\ncontemplated as each the necessary condition and\naccompaniment of the other.\n\nBut this, the Critic remarks, is not true in _direct_\ncausation. 'If the antecedence and consequence in question\nbe understood as the interposition of an interval of time,\nhowever small, between the action of the cause and the\nproduction of the effect, we regard it as inadmissible. In\nthe production of motion by force, for instance, though the\neffect be cumulative with continued exertion of the cause,\nyet each elementary or individual action is, to our\napprehension, _instanter_ accompanied with its corresponding\nincrement of momentum in the body moved. In all dynamical\n{195} reasonings no one has ever thought of interposing an\ninstant of time between the action and its resulting\nmomentum; nor does it appear necessary.' This is so evident,\nthat it appears strange it should have the air of novelty;\nyet, so far as I am aware, the matter has never before been\nput in the same point of view. But this being the case, the\nquestion occurs, how it is that time _seems_ to be employed\nin the progress from cause to effect? How is it that the\nopinion of the effect being subsequent to the cause has\ngenerally obtained? And to this the Critic's answer is\nobvious:--it is so in cases of indirect or of _cumulative_\neffect. If a ball _A_ strikes another, _B_, and puts it in\nmotion, and _B_ strikes _C_, and puts it in motion, _A_'s\nimpact may be considered as the cause, though not the direct\ncause, of _C_'s motion. Now time, namely the time of _B_'s\nmotion after it is struck by _A_, and before it strikes _C_,\nintervenes between _A_'s impact and the beginning of _C_'s\nmotion: that is, between the cause and its effect. In this\nsense, the effect is subsequent to the cause. Again, if a\nbody be put in motion by a series of impulses acting at\nfinite intervals of time, all in the same direction, the\nmotion at the end of all these intervals is the effect of\nall the impulses, and exists after they have all acted. It\nis the accumulated effect, and subsequent to each separate\naction of the cause. But in this case, each impulse produces\nits effect instantaneously, and the time is employed, not in\nthe transition from any cause to its effect, but in the\nintervals between the action of the several causes, during\nwhich intervals the body goes on with the velocity already\ncommunicated to it. In each impulse, force produces motion:\nand the motion goes on till a new change takes place, by the\nsame kind of action. The force may be said, in the language\nemployed by the Critic, to be transformed into momentum; and\nin the successive impulses, successive portions of force are\nthus transformed; while in the intervening intervals, the\nforce thus transformed into momentum is carried by the body\nfrom one place to another, where a new change awaits it.\n'The cause is absorbed and transformed into effect, and\ntherein treasured up.' Hence, as the Writer says, 'The time\nlost in cases of indirect physical causation is that\nconsumed in the movements which take place among the parts\nof the mechanism set in action, by which the active forces\nso transformed into mechanism are transported over intervals\nof space to new points of action, the motion of matter in\nsuch cases being {196} regarded as a mere carrier of\nforce':--and when force is directly counteracted by force,\ntheir mutual destruction must be conceived, as the Reviewer\nsays, to be instantaneous. We can therefore hardly resist\nhis conclusion, that men have been misled in assuming\nsequence as a feature in the relation of cause and effect;\nand we may readily assent to his suggestion, that sequence,\nwhen observed, is to be held as a sure indication of\nindirect action, accompanied with a movement of parts.\n\nBut yet if we turn for a moment to other kinds of causation,\nwe seem to be compelled at every step to recognize the truth\nof the usual maxim upon this subject, that effects are\nsubsequent to causes. Is not poison, taken at a certain\nmoment, the cause of disorder and death which follow at a\n_subsequent_ period? Is not a man's early prudence often the\ncause of his prosperity in _later_ life, and his folly,\nthough for a moment it may produce gratification, _finally_\nthe cause of his ruin? And even in the case of mechanism,\nif, in a clock which goes rightly, we alter the length of\nthe pendulum, is not this alteration the cause of an\nalteration which _afterwards_ takes place in the rate of the\nclock's going? Are not all these, and innumerable other\ncases, instances in which the usual notion of the effect\nfollowing the cause is verified? and are they not\nirreconcileable with the new doctrine of cause and effect\nbeing simultaneous?\n\nIn order to disentangle this apparent confusion, let us\nfirst consider the case last mentioned, of a clock, in which\nsome alteration is made which affects the rate of going.\n\nSo long as the parts of the clock remain unaltered, its rate\nwill remain unaltered; and any part which is considered as\ncapable of alteration, may be considered as, if we please,\nthe cause of the unaltered rate, by being itself unaltered.\nBut we do not usually introduce the positive idea of cause,\nto correspond with this negation of change. If we speak of\nthe rate as unaltered, we may also say that it is so because\nthere is _no cause_ of alteration. The steady rate is the\nindication of the absence of any cause of alteration; and\nthe rate of going measures the progress of time, in a state\nof things in which causes of change are thus excluded. If an\nalteration takes place in any part of the clock, once for\nall, the rate is altered; but the new rate is steady as the\nold rate was, and, like it, measures the uniform progress of\ntime. But the difference between the new rate and the old is\noccasioned by {197} the difference of the parts of the\nclock; and the new rate may very properly be said to be\ncaused by the change of the parts, and to be subsequent to\nit: for it does prevail after the change, and does not\nprevail before.\n\nBut how is this view to be reconciled with the one just\nquoted from the Reviewer, and, as it appeared,\nsatisfactorily proved by him; according to which all\nmechanical effects are simultaneous with their causes, and\nnot subsequent to them? We have here the two views in close\ncontact, and in seeming opposition.\n\nIn the going of a clock, the parts are in motion; and these\nmotions are determined by forces arising from the form and\nconnexion of the parts of the mechanism. Each of the forces\nthus exerted at any instant produces its effect at the same\ninstant; and thus, so far as the term _cause_ refers to such\ninstantaneous forces, the cause and the effect are\nsimultaneous. But if such instantaneous forces act at\nsuccessive intervals of time, the motion during each\ninterval is unaltered, and by its uniform progress measures\nthe progress of time. And thus the motion of the machine\nconsists of a series of intervals, during each of which the\nmotion is uniform, and measures the time; separated from\neach other by a series of changes, at each of which the\nchange measures the instantaneous force, and is simultaneous\nwith it. And if, in this case, we suppose, at any point of\ntime, the instantaneous forces to cease, the succession of\nthem being terminated, from that point of time the motion\nwould be uniform. And since the rate of the motion in each\ninterval of time is determined by the instantaneous force\nwhich last acted and by the preceding motion, the rate of\nthe motion in each interval of time is determined by all the\npreceding instantaneous forces. Hence, when the series of\ninstantaneous forces stops, the rate at which the motion\ngoes on permanently, from that point of time, is determined\nby the antecedent series of such forces, which series may be\nconsidered as an aggregate cause; and hence it appears, that\nthe _permanent_ effect is determined by the _aggregate_\ncause; and in this sense the effect is subsequent to the\ncause.\n\nThus we obtain, in this case, a solution of the difficulty\nwhich is placed before us. The instantaneous effect or\nchange is simultaneous with the instantaneous force or cause\nby which it is {198} produced. But if we consider a series\nof such instantaneous forces as a single aggregate cause,\nand the final condition as a permanent effect of this cause,\nthe effect is subsequent to the cause. In this case, the\ncause is immediately succeeded by the effect. The cause acts\nin time: the effect goes on in time. The times occupied by\nthe cause and by the effect succeed each other, the one\nending at the point of time at which the other begins. But\nthe time which the cause occupies is really composed of a\nseries of instants of uniform motion interposed between\ninstantaneous forces; and during the time that this series\nof causes is going on, to make up the aggregate cause, a\nseries of effects is going on to make up the final effect.\nThere is a progressive cause and a progressive effect which\ngo on together, and occupy the same finite time; and this\nsimultaneous progression is composed of all the simultaneous\ninstantaneous steps of cause and effect. The aggregate cause\nis the sum of the progression of causes; the final effect is\nthe last term of the progression of effects. At each step,\nas the Reviewer says, cause is transformed into effect; and\nit is treasured up in the results during the intermediate\nintervals; and the time occupied is not the time which\nintervenes between cause and effect at each step, but the\ntime which intervenes between these transformations.\n\nI have supposed forces to act at distinct instants, and to\ncease to act in the intervals between; and then, the\naggregate of such intervals to make up a finite time, during\nwhich an aggregate force acts. But if the action of the\nforce be rigorously continuous, it will easily be seen that\nall the consequences as to cause and effect will be the\nsame; the discontinuous action being merely the usual\nartifice by which, in mathematical reasonings, we obtain\nresults respecting continuous changes. It will still be\ntrue, that the uniform motion which takes place after a\ncontinuous force has acted, is the effect subsequent to the\ncause; while the change which takes place at any instant by\nthe action of the force, is the instantaneous effect\nsimultaneous with the cause.\n\nIt may be objected, that this solution does not appear\nimmediately to apply: for the motion of a clock is not\nuniform during any portion of the time. The parts move by\nintervals of varied motion and of rest; or by oscillations\nbackwards and forwards; and the succession of forces which\nacts during any {199} oscillation, or any cycle of motion,\nis repeated during the succeeding oscillation or cycle, and\nso on indefinitely; and if an alteration be made in the\nparts, it is not a change once for all, but recurs in its\noperation in every cycle of the motion.\n\nBut it will be found that this circumstance does not prevent\nthe same explanation from being still applicable with a\nslight modification. Instead of uniform motion in the\nintervals of causation, we shall have to speak of _steady\ngoing_: and instead of considering all the forces which\naffect the motion as causes of change of uniform motion, we\nshall have to speak of changes in the parts of the mechanism\nas causes of _change of rate of going_. With this\nmodification, it will still be true, that any instantaneous\ncause produces its instantaneous effect simultaneously,\nwhile the permanent effect is subsequent to the change which\nis its cause. The steady going of the clock is assumed as a\nnormal condition, in which it measures the progress of time;\nand in this assumption, the notion of cause and effect is\nnot brought into view. But a steady rate thus denoting the\nmean passage of time, a change in the rate indicates a cause\nof change. The _change of rate_, as an instantaneous\n_transition_ from one rate to another, is _simultaneous_\nwith the change in the parts. But then the _changed rate_ as\na continued _condition_ in which, no new change supervening,\nthe rate again measures the progress of time, is\n_subsequent_ to the change of parts, for it begins when that\nends, and continues when the progress of that has ceased.\n\nIf, however, this be a satisfactory solution of the\ndifficulty in the case of mechanism, how shall we apply the\nsame views to the other cases? Growth, the effect of food,\nis subsequent to the act of taking food; disorder, the\neffect of poison, is subsequent to the introduction of\npoison into the system. Can we say that the animal would\ncontinue unchanged if it were not to take food; and that\nfood is the cause of a change, namely, of growth? This is\nmanifestly false; for if the animal were not to take food,\nit would soon perish. But the analogy of the former case, of\nthe clock, will enable us to avoid this perplexity. As we\nassumed a steady rate of going in the clock to be the\nmeasure of time when we considered the effect of mechanism,\nso we assume a steady rate of action in the animal functions\nto be the measure of the progress of time when we consider\nthe causes which act upon the {200} development and health\nof animals. Digestion, and of course nutrition, are a part\nof this normal condition; they are involved in the steady\ngoing of the animal mechanism, and we must suppose these\nfunctions to go regularly on, in order that the animal may\npreserve its character of animal. Food and digestion may be\nconsidered as causes of the continued existence of the\nanimal, in the same way in which the form of the parts of a\nclock is the cause of the steady going of a clock. And when\nwe come to consider causes of change, this kind of\ncausation, which produces a normal condition of things,\nmerely measuring the flow of time, is left out of our\naccount. We can conceive an uniform condition of animal\nexistence, the animal neither growing nor wasting. This\nbeing taken as the normal condition, any deviation from this\ncondition indicates a cause, and is taken as the evidence\nand measure of the cause of change. And thus, in a growing\nanimal, the food partly keeps the animal in continued animal\nexistence, and partly, and in addition to this, causes its\ngrowth. Food, in the former view, is always circulating in\nthe system, and is supposed to be uniformly administered;\nthe cycles of nutrition being merged in the notion of\nuniform existence, as the oscillations of the pendulum in a\nclock are merged in the notion of uniform going; and the\nelementary steps of nutrition which are, in this view,\nsupposed to take place at each instant, produce their\ninstantaneous effect, for they are requisite in the cycle of\nanimal processes which goes on from instant to instant. But\non the other hand, in considering growth, we compare the\nstate of an animal with a preceding state, and consider the\nnutriment taken in the intervening time as the cause of the\nchange: hence this nutriment, as an aggregate, is considered\nas the cause of growth of the animal; and in this view the\neffect is subsequent to the cause. But yet here, as in the\ncase of mechanism, the progressive effect is simultaneous,\nstep by step, with the progressive cause. There is a series\nof operations; as for instance, intussusception, digestion,\nassimilation, growth: each of these is a progressive\noperation; and in the progress of each operation, the steps\nof the effect and the instantaneous forces are simultaneous.\nBut the end of one operation is the beginning of the next,\nor at least in part, and hence we have time occupied by the\nsuccession. The end of intussusception is the beginning of\ndigestion, the end of digestion the beginning of\nassimilation, {201} and so on. These aggregate effects\nsucceed each other; and hence growth is subsequent to the\ntaking of food; though each instantaneous force of animal\nlife, no less than of mechanism, produces an effect\nsimultaneous with its action. Each of these separate\noperations is an aggregate operation, and occupies time; and\neach aggregate effect is a condition of the action of the\ncause in the next operation.\n\nAgain; if an animal in a permanent condition, neither waxing\nnor wasting, may be taken as the normal state in which the\nfunctions of life measure time, in order that we may\nconsider growth as an effect, to be referred to food as\ncause; we may, for other purposes, consider, as the normal\ncondition, an animal waxing and then wasting, according to\nthe usual law of animal life: and we must take this, the\nhealthy progress of an animal, as our normal condition, if\nwe have to consider causes which produce disease. If we have\nto refer the morbid condition of an animal to the influence\nof poison, for example, we must consider how far the\ncondition deviates from what it would have been if the\npoison had not been taken into the frame. The usual progress\nof the animal functions including its growth, is the measure\nof time; the deviation from this usual progress is the\nindication of cause; and the effect of the poison is\nsubsequent to the cause, because the poison acts through the\ncycle of the animal functions just mentioned, which occupies\ntime; and because the taking the poison into the system, not\nany subsequent action of the animal forces in the system, is\nconsidered as the event which we must contemplate as a\ncause. To resume the analogy of the clock: the rate of the\nclock is altered by altering the parts; but this alteration\nitself may occupy time; as if we alter the rate of a clock\nby applying a drop of acid, which gradually eats off a part\nof the pendulum, the corrosion, as an aggregate effect,\noccupies time; and the rates before and after the change are\nseparated by this time. But the application of the drop is\nthe cause; and thus, in this case the final effect is\nsubsequent to the cause, though here, as in the case of\nmechanism, the instantaneous forces always produce a\nsimultaneous effect.\n\nThus we have in every case a _uniform_ state, or a state\nwhich is considered as uniform, or at least _normal_; and\nwhich is taken as the indication and measure of _time_; and\nwe have also _change_, {202} which is contemplated as a\ndeviation from uniformity, and is taken as the indication\nand measure of _cause_. The uniform state may be one which\nnever exists, being purely imaginary; as the case in which\nno forces act; and the case in which animal functions go on\npermanently, the animal neither growing nor wasting. The\nnormal state may also be a state in which change is\nconstantly taking place, as, in fact, even a state of motion\nis a state of change; such states also are, in a further\nsense, that of a clock going by starts, and that of an\nanimal constantly growing: in these cases the changes are\nall merged in a wider view of uniformity, so that these are\ntaken as the normal states. And in all these cases,\nsuccessive changes which take place are separated by\nintervals of time, measured by the normal progress; and each\nchange is produced by some _simultaneous_ instantaneous\ncause. But taking the cause in a larger sense, we group\nthese instantaneous causes, and perhaps omit in our\ncontemplation some of the intervening intervals; and thus\nassign the cause to a _preceding_, and the effect to a\n_succeeding_ time.\n\nI may observe further, as a corollary from what has been\nsaid, that the measure of time is different, when we\nconsider different kinds of causation; and in each case, is\n_homogeneous_ with the changes which causation effects. In\nthe consideration of mechanical causes, we measure time by\nmechanical changes;--by uniform motion, or uniform\nsuccession of cycles of motion; by the rotation of a wheel,\nor the oscillation of a pendulum. But if we have to consider\nphysiological changes, the progress of time is\nphysiologically measured;--by the normal progress of vital\noperations; by the circulation, digestion or development of\nthe organized body; by the pulse, or by the growth. These\ndifferent measures of time give to time, so far as it is\nexhibited by facts and events, a different character in the\ndifferent cases. Phenomenal time has a different nature and\nessence according to the kind of the changes which we\nconsider, and which gives us our sole phenomenal indication\nof cause.\n\nI fear that I am travelling into matters too abstruse and\nmetaphysical for the occasion: but before I conclude, I will\npresent one other aspect of the subject.\n\nIn stating the difficulty, I referred to cases of moral as\nwell as physical causation; as when prudence produces\nprosperity, or {203} when folly produces ruin. It may be\nasked, whether we are here to apply the same\nexplanation;--whether we are to assume a normal condition of\nhuman existence, in which neither prudence nor folly are\ndisplayed, neither prosperity nor adversity\nproduced;--whether we are to conceive the progress of such a\nstate to measure the progress of time, and deviations from\nit to denote causes of the kind mentioned. It may be asked\nfurther, whether, if we do make this supposition, we can\nresolve the influence of such causes as prudence or\nimprudence into instantaneous acts, which produce their\neffects immediately: and which occupy time only by being\nseparated by intervals of the inactive normal moral\ncondition. To this I must here reply, that the discussion of\nsuch questions would carry me too far, and would involve\nspeculations not included within the acknowledged domain of\nthis Society, from which I therefore abstain. But I may say,\nbefore quitting the subject, that I do not think the\nsuppositions above suggested are untenable; and that in\norder to include moral causation under the maxims of\ncausation in general, we must necessarily make some such\nhypothesis. The peculiarity of that kind of causation which\nthe will and the character exert, and which is exerted upon\nthe will and the character, would make this case far more\ncomplex and difficult than those already considered; but, at\nthe same time, would offer us the means of explaining what\nmay seem harsh, in the above analogy. For instance, we\nshould have to assume such a maxim as this: that in moral\ncausation, time is not to be measured by the flow of\nmechanical or physiological events;--not by the clock, or by\nthe pulse. Moral causation has its own clock, its own pulse,\nin the progress of man's moral being; and by this measure of\ntime is the relation of moral cause and effect to be\ndefined.\n\nThat in estimating moral causation, the progress of time is\nnecessarily estimated by moral changes, and not by\nmachinery,--by the progress of events, and not by the going\nof the clock,--is a truth familiar as a practical maxim to\nall who give their thoughts to dramatic or narrative\nfictions. Who feels any thing incongruous or extravagantly\nhurried in the progress of events in that great exhibition\nof moral causation, the tragedy of Othello? If we were asked\nwhat time those vast and terrible {204} and complex changes\nof the being and feelings of the characters occupy, we\nshould say, that, measured on its own scale, the event is of\ngreat extent;--that the transaction is of considerable\nmagnitude in all ways. But if, with previous critics, we\nlook into the progress of time by the day and the hour--what\nis the measure of this history? Forty-eight hours.\n\n\n\n{{205}}\nCHAPTER V.\n\nOF THE ORIGIN OF OUR CONCEPTIONS OF FORCE AND MATTER.\n\n\n1. _Force._--WHEN the faculties of observation and thought\nare developed in man, the idea of causation is applied to\nthose changes which we see and feel in the state of rest and\nmotion of bodies around us. And when our abstract\nconceptions are thus formed and named, we adopt the term\n_Force_, and use it to denote that property which is the\ncause of motion produced, changed, or prevented. This\nconception is, it would seem, mainly and primarily suggested\nby our consciousness of the exertions by which we put bodies\nin motion. The Latin and Greek words for _Force_, Vis, \u03dc\u1f76\u03c2,\nwere probably, like all abstract terms, derived at first\nfrom some sensible object. The original meaning of the Greek\nword was a _muscle_ or _tendon_. Its first application as an\nabstract term is accordingly to muscular force:\n\n \u0394\u03b5\u03cd\u03c4\u03b5\u03c1\u03bf\u03c2 \u03b1\u1f56\u03c4' \u0391\u1f34\u03b1\u03c2 \u03c0\u03bf\u03bb\u1f7a \u03bc\u03b5\u03af\u03b6\u03bf\u03bd\u03b1 \u03bb\u1fb6\u03b1\u03bd \u1f00\u03b5\u03af\u03c1\u03b1\u03c2\n \u1f26\u03ba' \u1f10\u03c0\u03b9\u03b4\u03b9\u03bd\u03ae\u03c3\u03b1\u03c2, \u1f10\u03c0\u03ad\u03c1\u03b5\u03b9\u03c3\u03b5 \u03b4\u1f72 \u03dc\u00ce\u0342\u039d' \u1f00\u03c0\u03ad\u03bb\u03b5\u03b8\u03c1\u03bf\u03bd.\n\n Then Ajax a far heavier stone upheaved,\n He whirled it, and impressing Force intense\n Upon the mass, dismist it.\n\nThe property by which bodies affect each other's motions,\nwas naturally likened to that energy which we exert upon\nthem with similar effect: and thus the labouring horse, the\nrushing torrent, the descending weight, the elastic bow,\nwere said to exert force. {206} Homer[8\\3] speaks of the\n_force_ of the river, \u03dc\u1f76\u03c2 \u03c0\u03bf\u03c4\u03b1\u03bc\u03bf\u1fd6\u03bf; and Hesiod[9\\3] of the\n_force_ of the north wind, \u03dc\u1f76\u03c2 \u1f00\u03bd\u03ad\u03bc\u03bf\u03c5 \u03b2\u03bf\u03c1\u03ad\u03b1\u03bf.\n\n[Note 8\\3: _Il._ xxi.]\n\n[Note 9\\3: _Op. et D._]\n\nThus man's general notion of force was probably first\nsuggested by his muscular exertions, that is, by an act\ndepending upon that muscular sense, to which, as we have\nalready seen, the perception of space is mainly due. And\nthis being the case, it will be easily understood that the\n_Direction_ of the force thus exerted is perceived by the\nmuscular sense, at the same time that the force itself is\nperceived; and that the direction of any other force is\nunderstood by comparison with force which man must exert to\nproduce the same effect, in the same manner as force itself\nis so understood.\n\nThis abstract notion of Force long remained in a very vague\nand obscure condition, as may be seen by referring to the\nHistory for the failures of attempts at a science of force\nand motion, made by the ancients and their commentators in\nthe middle ages. By degrees, in modern times, we see the\nscientific faculty revive. The conception of Force becomes\nso far distinct and precise that it can be reasoned upon in\na consistent manner, with demonstrated consequences; and a\ngenuine science of Mechanics comes into existence. The\nfoundations of this science are to be found in the Axioms\nconcerning causation which we have already stated; these\naxioms being interpreted and fixed in their application by a\nconstant reference to observed facts, as we shall show. But\nwe must, in the first place, consider further those primary\nprocesses of observation by which we acquire the first\nmaterials of thought on such subjects.\n\n2. _Matter._--The conception of Force, as we have said,\narises with our consciousness of our own muscular exertions.\nBut we cannot imagine such exertions without also imagining\nsome bodily substance against which they are exercised. If\nwe press, we press something: if we thrust or throw, there\nmust be something {207} to resist the thrust or to receive\nthe impulse. Without body, muscular force cannot be exerted,\nand force in general is not conceivable.\n\nThus Force cannot exist without _Body_ on which it acts. The\ntwo conceptions, Force and Matter, are co-existent and\ncorrelative. Force implies resistance; and the force is\neffective only when the resistance is called into play. If\nwe grasp a stone, we have no hold of it till the closing of\nthe hand is resisted by the solid texture of the stone. If\nwe push open a gate, we must surmount the opposition which\nit exerts while turning on its hinges. However slight the\nresistance be, there must be some resistance, or there would\nbe no force. If we imagine a state of things in which\nobjects do not resist our touch, they must also cease to be\ninfluenced by our strength. Such a state of things we\nsometimes imagine in our dreams; and such are the poetical\npictures of the regions inhabited by disembodied spirits. In\nthese, the figures which appear are conspicuous to the eye,\nbut impalpable like shadow or smoke; and as they do not\nresist the corporeal impressions, so neither do they obey\nthem. The spectator tries in vain to strike or to grasp\nthem.\n\n Et ni docta comes tenues sine corpore vitas\n Admoneat volitare cav\u00e2 sub imagine form\u00e6,\n Irruat ac frustra ferro diverberet umbras.\n\n The Sibyl warns him that there round him fly\n Bodiless things, but substance to the eye;\n Else had he pierced those shapes with life-like face,\n And smitten, fierce, the unresisting space.\n\n Neque illum\n Prensantem nequicquam umbras et multa volentem\n Dicere, preterea vidit.\n\n He grasps her form, and clutches but the shade.\n\nSuch may be the circumstances of the unreal world of dreams,\nor of poetical fancies approaching to dreams: for in these\nworlds our imaginary perceptions are bound by no rigid\nconditions of force and reaction. In {208} such cases, the\nmind casts off the empire of the idea of cause, as it casts\noff even the still more familiar sway of the ideas of space\nand time. But the character of the material world in which\nwe live when awake is, that we have at every instant and at\nevery place, force operating on matter and matter resisting\nforce.\n\n3. _Solidity._--From our consciousness of muscular exertion,\nwe derive, as we have seen, the conception of force, and\nwith that also the conception of matter. We have already\nshown, in a former chapter, that the same part of our frame,\nthe muscular system, is the organ by which we perceive\nextension and the relations of space. Thus the same organ\ngives us the perception of body as resisting force, and as\noccupying space; and by combining these conditions we have\nthe conception of _solid_ extended bodies. In reality, this\nresistance is inevitably presented to our notice in the very\nfacts from which we collect the notion of extension. For the\naction of the hand and arm by which we follow the forms of\nobjects, implies that we apply our fingers to their surface;\nand we are stopped there by the resistance which the body\noffers. This resistance is precisely that which is requisite\nin order to make us conscious of cur muscular effort[10\\3].\nNeither touch, nor any other mere passive sensation, could\nproduce the perception of extent, as we have already urged:\nnor could the muscular sense lead to such a perception,\nexcept the extension of the muscles were felt to be\nresisted. And thus the perception of resistance enters the\nmind along with the perception of extended bodies. All the\nobjects with which we have to do are not only extended but\nsolid.\n\n[Note 10\\3: Brown's _Lectures_, i. 466.]\n\nThis sense of the term _solidity_, (the general property of\nall matter,) is different to that in which we oppose\n_solidity_ to _fluidity_. We may avoid ambiguity by opposing\n_rigid_ to _fluid_ bodies. By solid bodies, as we now speak\nof them, we mean only such as resist the pressure which we\nexert, so long as their parts continue in their places. By\nfluid bodies, we mean those {209} whose parts are, by a\nslight pressure, removed out of their places. A drop of\nwater ceases to prevent the contact of our two hands, not by\nceasing to have solidity in this sense, but by being thrust\nout of the way. If it could remain in its place, it could\nnot cease to exercise its resistance to our pressure, except\nby ceasing to be matter altogether.\n\nThe perception of solidity, like the perception of\nextension, implies an act of the mind, as well as an\nimpression of the senses: as the perception of extension\nimplies the idea of space, so the perception of solidity\nimplies the idea of action and reaction. That an Idea is\ninvolved in our knowledge on this subject, appears, as in\nother instances, from this consideration, that the\nconvictions of persons, even of those who allow of no ground\nof knowledge but experience, do in fact go far beyond the\npossible limits of experience. Thus Locke says[11\\3], that\n'the bodies which we daily handle hinder by an\n_insurmountable_ force the approach of the parts of our\nhands that press them.' Now it is manifest that our\nobservation can never go to this length. By our senses we\ncan only perceive that bodies resist the greatest actual\nforces that we exert upon them. But our conception of force\ncarries us further: and since, so long as the body is there\nto receive the action of the force, it must suffer the whole\nof that action, and must react as much as it suffers: it is\ntherefore true, that so long as the body remains there, the\nforce which is exerted upon it can never surmount the\nresistance which the body exercises. And thus this doctrine,\nthat bodies resist the intrusion of other bodies by an\ninsurmountable force, is, in fact, a consequence of the\naxiom that the reaction is always equal to the action.\n\n[Note 11\\3: _Essay_, b. ii. c. 4.]\n\n4. _Inertia._--But this principle of the equality of action\nand reaction appears also in another way. Not only when we\nexert force upon bodies at rest, but when, by our exertions,\nwe put them in motion, they react. If we set a large stone\nin motion, the stone {210} resists; for the operation\nrequires an effort. By increasing the effort, we can\nincrease the effect, that is, the motion produced; but the\nresistance still remains. And the greater the stone moved,\nthe greater is the effort requisite to move it. There is, in\nevery case, a resistance to motion, which shows itself, not\nin preventing the motion, but in a reciprocal force, exerted\nbackwards upon the agent by which the motion is produced.\nAnd this resistance resides in each portion of matter, for\nit is increased as we add one portion of matter to another.\nWe can push a light boat rapidly through the water; but we\nmay go on increasing its freight, till we are barely able to\nstir it. This property of matter, then, by which it resists\nthe reception of motion, or rather by which it reacts and\nrequires an adequate force in order that any motion may\nresult, is called its inertness, or _inertia_. That matter\nhas such a property, is a conviction flowing from that idea\nof a reaction equal and opposite to the action, which the\nconception of all force involves. By what laws this inertia\ndepends on the magnitude, form, and material of the body,\nmust be the subject of our consideration hereafter. But that\nmatter has this inertia, in virtue of which, as the matter\nis greater, the velocity which the same effort can\ncommunicate to it is less, is a principle inseparable from\nthe notion of matter itself.\n\nHermann says that Kepler first introduced this 'most\nsignificant' _inertia_. Whether it is to be found in earlier\nwriters I know not; Kepler certainly does use it familiarly\nin those attempts to assign physical reasons for the motions\nof the planets which were among the main occasions of the\ndiscovery of the true laws of mechanics. He assumes the\nslowness of the motions of the planets to increase, (other\ncauses remaining the same,) as the inertia increases; and\nthough, even in this assumption, there is an errour\ninvolved, (if we adopt that interpretation of the term\n_inertia_ to which subsequent researches led,) the\nintroduction of such a word was one step in determining and\nexpressing those laws of motion which depend on the\nfundamental principle of the equality of action and\nreaction. {211}\n\n5. We have thus seen, I trust in a satisfactory manner, the\norigin of our conceptions of Force, Matter, Solidity, and\nInertness. It has appeared that the organ by which we obtain\nsuch conceptions is that very muscular frame, which is the\nmain instrument of our perceptions of space; but that,\nbesides bodily sensations, these ideal conceptions, like all\nthe others which we have hitherto considered, involve also\nan habitual activity of the mind, giving to our sensations a\nmeaning which they could not otherwise possess. And among\nthe ideas thus brought into play, is an idea of action with\nan equal and opposite reaction, which forms a foundation for\nuniversal truths to be hereafter established respecting the\nconceptions thus obtained.\n\nWe must now endeavour to trace in what manner these\nfundamental principles and conceptions are unfolded by means\nof observation and reasoning, till they become an extensive\nyet indisputable science.\n\n\n\n{{212}}\nCHAPTER VI.\n\nOF THE ESTABLISHMENT OF THE PRINCIPLES OF STATICS.\n\n\n1. _Object of the Chapter._--IN the present and the\nsucceeding chapters we have to show how the general axioms\nof Causation enable us to construct the science of\nMechanics. We have to consider these axioms as moulding\nthemselves, in the first place, into certain fundamental\nmechanical principles, which are of evident and necessary\ntruth in virtue of their dependence upon the general axioms\nof Causation; and thus as forming a foundation for the whole\nstructure of the science;--a system of truths no less\nnecessary than the fundamental principles, because derived\nfrom these by rigorous demonstration.\n\nThis account of the construction of the science of\nMechanics, however generally treated, cannot be otherwise\nthan technical in its details, and will probably be\nimperfectly understood by any one not acquainted with\nMechanics as a mathematical science.\n\nI cannot omit this portion of my survey without rendering my\nwork incomplete; but I may remark that the main purpose of\nit is to prove, in a more particular manner, what I have\nalready declared in general, that there are, in Mechanics no\nless than in Geometry, fundamental principles of axiomatic\nevidence and necessity;--that these principles derive their\naxiomatic character from the Idea which they involve,\nnamely, the Idea of Cause;--and that through the combination\nof principles of this kind, the whole science of Mechanics,\nincluding its most complex and remote results, exists as a\nbody of solid and universal truths. {213}\n\n2. _Statics and Dynamics._--We must first turn our attention\nto a technical distinction of Mechanics into two portions,\naccording as the forces about which we reason produce rest,\nor motion; the former portion is termed _Statics_, the\nlatter _Dynamics_. If a stone fall, or a weight put a\nmachine in motion, the problem belongs to Dynamics; but if\nthe stone rest upon the ground, or a weight be merely\nsupported by a machine, without being raised higher, the\nquestion is one of Statics.\n\n3. _Equilibrium._--In Statics, forces _balance_ each other,\nor keep each other _in equilibrium_. And forces which\ndirectly balance each other, or keep each other in\nequilibrium, are necessarily and manifestly equal. If we see\ntwo boys pull at two ends of a rope so that neither of them\nin the smallest degree prevails over the other, we have a\ncase in which two forces are in equilibrium. The two forces\nare evidently equal, and are a statical exemplification of\naction and reaction, such as are spoken of in the third\naxiom concerning causes. Now the same exemplification occurs\nin every case of equilibrium. No point or body can be kept\nat rest except in virtue of opposing forces acting upon it;\nand these forces must always be equal in their opposite\neffect. When a stone lies on the floor, the weight of the\nstone downwards is opposed and balanced by an equal pressure\nof the floor upwards. If the stone rests on a slope, its\ntendency to slide is counteracted by some equal and opposite\nforce, arising, it may be, from the resistance which the\nsloping ground opposes to any motion along its surface.\nEvery case of rest is a case of equilibrium: every case of\nequilibrium is a case of equal and opposite forces.\n\nThe most complex frame-work on which weights are supported,\nas the roof of a building, or the cordage of a machine, are\nstill examples of equilibrium. In such cases we may have\nmany forces all combining to balance each other; and the\nequilibrium will depend on various conditions of direction\nand magnitude among the forces. And in order to understand\nwhat are these conditions, we must ask, in the first place,\nwhat {214} we understand by the magnitude of such\nforces;--what is the measure of statical forces.\n\n4. _Measure of Statical Forces._--At first we might expect,\nperhaps, that since statical forces come under the general\nnotion of Cause, the mode of measuring them would be derived\nfrom the second axiom of Causation, that causes are measured\nby their effects. But we find that the application of this\naxiom is controlled by the limitation which we noticed,\nafter stating that axiom; namely, the condition that the\ncauses shall be capable of addition. Further, as we have\nseen, a statical force produces no other effect than this,\nthat it balances some other statical force; and hence the\nmeasure of statical forces is necessarily dependent upon\ntheir balancing, that is, upon the equality of action and\nreaction.\n\nThat _statical forces are capable of addition_ is involved\nin our conception of such forces. When two men pull at a\nrope in the same direction, the forces which they exert are\nadded together. When two heavy bodies are put into a basket\nsuspended by a string, their weights are added, and the sum\nis supported by the string.\n\nCombining these considerations, it will appear that the\nmeasure of statical forces is necessarily given at once by\nthe fundamental principle of the equality of action and\nreaction. Since two opposite forces which balance each other\nare equal, each force is measured by that which it balances;\nand since forces are capable of addition, a force of any\nmagnitude is measured by adding together a proper number of\nsuch equal forces. Thus a heavy body which, appended to some\ncertain elastic branch of a tree, would bend it down through\none inch, may be taken as a unit of weight. Then if we\nremove this first body, and find a second heavy body which\nwill also bend the branch through the same space, this is\nalso a unit of weight; and in like manner we might go on to\na third and a fourth equal body; and adding together the\ntwo, or the three, or the four heavy bodies, we have a force\ntwice, or three times, or four times the unit of weight. And\nwith {215} such a collection of heavy bodies, or _weights_,\nwe can readily measure all other forces; for the same\nprinciple of the equality of action and reaction leads at\nonce to this maxim, that any statical force is measured by\nthe weight which it would support.\n\nAs has been said, it might at first have been supposed that\nwe should have to apply, in this case, the axiom that causes\nare measured by their effects in another manner; that thus,\nif that body were a unit of weight which bent the bough of a\ntree through one inch, _that_ body would be _two_ units\nwhich bent it through _two_ inches, and so on. But, as we\nhave already stated, the measures of weight must be subject\nto this condition, that they are susceptible of being added:\nand therefore we cannot take the deflexion of the bough for\nour measure, till we have ascertained, that which experience\nalone can teach us, that under the burden of two equal\nweights, the deflexion will be twice as great as it is with\none weight, which is not true, or at least is neither\nobviously nor necessarily true. In this, as in all other\ncases, although causes must be measured by their effects, we\nlearn from experience only how the effects are to be\ninterpreted, so as to give a true and consistent measure.\n\nWith regard, however, to the measure of statical force, and\nof weight, no difficulty really occurred to philosophers\nfrom the time when they first began to speculate on such\nsubjects; for it was easily seen that if we take any uniform\nmaterial, as wood, or stone, or iron, portions of this which\nare geometrically equal, must also be equal in statical\neffect; since this was implied in the very hypothesis of a\nuniform material And a body ten times as large as another of\nthe same substance, will be of ten times the weight. But\nbefore men could establish by reasoning the conditions under\nwhich weights would be in equilibrium, some other principles\nwere needed in addition to the mere measure of forces. The\nprinciples introduced for this purpose still resulted from\nthe conception of equal action and reaction; but it required\nno small clearness of thought to select them rightly, and to\nemploy them {216} successfully. This, however, was done, to\na certain extent, by the Greeks; and the treatise of\nArchimedes _On the Center of Gravity_, is founded on\nprinciples which may still be considered as the genuine\nbasis of statical reasoning. I shall make a few remarks on\nthe most important principle among those which Archimedes\nthus employs.\n\n5. _The Center of Gravity._--The most important of the\nprinciples which enter into the demonstration of Archimedes\nis this: that \"Every body has a center of gravity;\" meaning\nby the center of gravity, a point at which the whole matter\nof the body may be supposed to be collected, to all intents\nand purposes of statical reasoning. This principle has been\nput in various forms by succeeding writers: for instance, it\nhas been thought sufficient to assume a case much simpler\nthan the general one; and to assert that two _equal_ bodies\nhave their center of gravity in the point midway between\nthem. It is to be observed, that this assertion not only\nimplies that the two bodies will _balance_ upon a support\nplaced at that midway point, but also, that they will\nexercise, upon such a support, a _pressure equal to their\nsum_; for this point being the center of gravity, the whole\nmatter of the two bodies may be conceived to be collected\nthere, and therefore the whole weight will press there. And\nthus the principle in question amounts to this, that _when\ntwo equal heavy bodies are supported on the middle point\nbetween them, the pressure upon the support is equal to the\nsum of the weights of the bodies_.\n\nA clear understanding of the nature and grounds of this\nprinciple is of great consequence: for in it we have the\nfoundation of a large portion of the science of Mechanics.\nAnd if this principle can be shown to be necessarily true,\nin virtue of our Fundamental Ideas, we can hardly doubt that\nthere exist many other truths of the same kind, and that no\nsound view of the evidence and extent of human knowledge can\nbe obtained, so long as we mistake the nature of these, its\nfirst principles. {217}\n\nThe above principle, that the pressure on the support is\nequal to the sum of the bodies supported, is often stated as\nan axiom in the outset of books on Mechanics. And this\nappears to be the true place and character of this\nprinciple, in accordance with the reasonings which we have\nalready urged. The axiom depends upon our conception of\naction and reaction. That the two weights are supported,\nimplies that the supporting force must be equal to the force\nor weight supported.\n\nIn order further to show the foundation of this principle,\nwe may ask the question:--If it be not an axiom, deriving\nits truth from the fundamental conception of equal action\nand reaction, which equilibrium always implies, what is the\norigin of its certainty? The principle is never for an\ninstant denied or questioned: it is taken for granted, even\nbefore it is stated. No one will doubt that it is not only\ntrue, but true with the same rigour and universality as the\naxioms of Geometry. Will it be said, that it is borrowed\nfrom experience? Experience could never prove a principle to\nbe universally and rigorously true. Moreover, when from\nexperience we prove a proposition to possess great exactness\nand generality, we approach by degrees to this proof: the\nconviction becomes stronger, the truth more secure, as we\naccumulate trials. But nothing of this kind is the case in\nthe instance before us. There is no gradation from less to\ngreater certainty;--no hesitation which precedes confidence.\nFrom the first, we know that the axiom is exactly and\ncertainly true. In order to be convinced of it, we do not\nrequire many trials, but merely a clear understanding of the\nassertion itself.\n\nBut in fact, not only are trials not necessary to the proof,\nbut they do not strengthen it. Probably no one ever made a\ntrial for the purpose of showing that the pressure upon the\nsupport is equal to the sum of the two weights. Certainly no\nperson with clear mechanical conceptions ever wanted such a\ntrial to convince him of the truth; or thought the truth\nclearer after the trial had been made. If to such a person,\nan {218} experiment were shown which seemed to contradict\nthe principle, his conclusion would be, not that the\nprinciple was doubtful, but that the apparatus was out of\norder. Nothing can be less like collecting truth from\nexperience than this.\n\nWe maintain, then, that this equality of mechanical action\nand reaction, is one of the principles which do not flow\nfrom, but regulate our experience. To this principle, the\nfacts which we observe must conform; and we cannot help\ninterpreting them in such a manner that they shall be\nexemplifications of the principle. A mechanical pressure not\naccompanied by an equal and opposite pressure, can no more\nbe given by experience, than two unequal right angles. With\nthe supposition of such inequalities, space ceases to be\nspace, force ceases to be force, matter ceases to be matter.\nAnd this equality of action and reaction, considered in the\ncase in which two bodies are connected so as to act on a\nsingle support, leads to the axiom which we have stated\nabove, and which is one of the main foundations of the\nscience of Mechanics.\n\n[2d ed.] [To the doctrine that mechanical principles, such\nas the one here under consideration (that the pressure on\nthe point of support is equal to the sum of the weights),\nare derived from our Ideas, and do not flow from but\nregulate our experience, objections are naturally made by\nthose who assert all our knowledge to be derived from\nexperience. How, they ask, can we know the properties of\npressures, levers and the like, except from experience? What\nbut experience can possibly inform us that a force applied\ntransversely to a lever will have any tendency to turn the\nlever on its center? This cannot be, except we suppose in\nthe lever tenacity, rigidity and the like, which are\nqualities known only by experience. And it is obvious that\nthis line of argument might be carried on through the whole\nsubject.\n\nMy answer to this objection is a remark of the same kind as\none which I have made respecting the Ideas of Space, Time,\nand Number, in the last Book. The mind, in apprehending\nevents as causes {219} and effects, is governed by Laws of\nits own Activity; and these Laws govern the results of the\nmind's action; and make these results conform to the Axioms\nof Causation. But this activity of the mind is awakened and\ndeveloped by being exercised; and in dealing with the\nexamples of cause and effect here spoken of, (namely,\npressure and resistance, force and motion,) the mind's\nactivity is necessarily governed also by the bodily powers\nof perception and action. We are human beings only in so far\nas we have existed in space and time; and of our human\nfaculties, developed by our existence in space and time,\nspace and time are necessary conditions. In like manner, we\nare human beings only in so far as we have bodies, and\nbodily organs; and our bodies necessarily imply material\nobjects external to us. And hence our human faculties,\ndeveloped by our bodily existence in a material world, have\nthe conditions of matter for their necessary Laws. I have\nalready said (chap. v.) that our conception of Force arises\nwith our consciousness of our own muscular exertions;--that\nForce cannot be conceived without Resistance to exercise\nitself upon;--and that this resistance is supplied by\nMatter. And thus the conception of Matter, and of the most\ngeneral modes in which Matter receives, resists, and\ntransmits force, are parts of our constitution which, though\nawakened and unfolded by our being in a material world, are\nnot distinguishable from the original structure of the mind.\nI do not ascribe to the mind _innate_ Ideas--Ideas which it\nwould have, even if it had no intercourse with the world of\nspace, time, and matter; because we cannot imagine a mind in\nsuch a state. But I attempt to point out and classify those\nConditions of all Experience, to which the intercourse of\nall minds with the material world has necessarily given rise\nin all. Truths _thus_ necessarily acquired in the course of\nall experience, cannot be said to be learnt _from\nexperience_, in the same sense in which particular facts, at\ndefinite times, are learnt from experience--learnt by some\npersons and not by others--learnt with more or less of\ncertainty. These latter _special truths of_ {220}\n_experience_ will be very important subjects of our\nconsideration; but our whole chance of discussing them with\nany profit depends upon our keeping them distinct from the\n_necessary and universal conditions of experience_. Here, as\neverywhere, we must keep in view the fundamental antithesis\nof Ideas and Facts.]\n\n6. _Oblique Forces._--By the aid of the above axiom and a\nfew others, the Greeks made some progress in the science of\nStatics. But after a short advance, they arrived at another\ndifficulty, that of Oblique Forces, which they never\novercame; and which no mathematician mastered till modern\ntimes. The unpublished manuscripts of Leonardo da Vinci,\nwritten in the fifteenth century, and the works of Stevinus\nand Galileo, in the sixteenth, are the places in which we\nfind the first solid grounds of reasoning on the subject of\nforces acting obliquely to each other. And from that period,\nmathematicians, having thus become possessed of all the\nmechanical principles which are requisite in problems\nrespecting equilibrium, soon framed a complete science of\nStatics. Succeeding writers presented this science in forms\nvariously modified; for it was found, in Mechanics as in\nGeometry, that various propositions might be taken as the\nstarting points; and that the collection of truths which it\nwas the mechanician's business to include in his course,\nmight thus be traversed by various routes, each path\noffering a series of satisfactory demonstrations. The\nfundamental conceptions of force and resistance, like those\nof space and number, could be contemplated under different\naspects, each of which might be made the basis of axioms, or\nof principles employed as axioms. Hence the grounds of the\ntruth of Statics may be stated in various ways; and it would\nbe a task of some length to examine all these completely,\nand to trace them to their Fundamental Ideas. This I shall\nnot undertake here to do; but the philosophical importance\nof the subject makes it proper to offer a few remarks on\nsome of the main principles involved in the different modes\nof presenting Statics as a rigorously demonstrated science.\n{221}\n\n7. _A Force may be supposed to act at any Point of its\nDirection._--It has been stated in the history of\nMechanics[12\\3], that Leonardo da Vinci and Galileo obtained\nthe true measure of the effect of oblique forces, by\nreasonings which were, in substance, the same. The principle\nof these reasonings is that expressed at the head of this\nparagraph; and when we have a little accustomed ourselves to\ncontemplate our conceptions of force, and its action on\nmatter, in an abstract manner, we shall have no difficulty\nin assenting to the principle in this general form. But it\nmay, perhaps, be more obvious at first in a special case.\n\n[Note 12\\3: _Hist. Ind. Sc._ b. vi. c. i. sect. 2.]\n\nIf we suppose a wheel, moveable about its axis, and carrying\nwith it in its motion a weight, (as, for example, one of the\nwheels by means of which the large bells of a church are\nrung,) this weight may be supported by means of a rope (not\npassing along the circumference of the wheel, as is usual in\nthe case of bells,) but fastened to one of the spokes of the\nwheel. Now the principle which is enunciated above asserts,\nthat if the rope pass in a straight line across several of\nthe spokes of the wheel, it makes no difference in the\nmechanical effect of the force applied, for the purpose of\nputting the bell in motion, to _which_ of these spokes the\nrope is _fastened_. In each case, the fastening of the rope\nto the wheel merely serves to enable the force to produce\nmotion about the center; and so long as the force acts in\nthe same line, the effect is the same, at whatever point of\nthe rope the line of action finishes.\n\nThis axiom very readily aids us in estimating the effect of\noblique forces. For when a force acts on one of the arms of\na lever at any oblique angle, we suppose another arm\nprojecting from the center of motion, like another spoke of\nthe same wheel, so situated that it is perpendicular to the\nforce. This arm we may, with Leonardo, call the _virtual\nlever_; for, by the axiom, we may suppose the force to act\nwhere the line of its direction meets this arm; and thus we\nreduce the case {222} to that in which the force acts\nperpendicularly on the arm.\n\nThe ground of this axiom is, that matter, in Statics, is\nnecessarily conceived as _transmitting_ force. That force\ncan be transmitted from one place to another, by means of\nmatter;--that we can push with a rod, pull with a rope,--are\nsuppositions implied in our conceptions of force and matter.\nMatter is, as we have said, that which receives the\nimpression of force, and the modes just mentioned, are the\nsimplest ways in which that impression operates. And since,\nin any of these cases, the force might be resisted by a\nreaction equal to the force itself, the reaction in each\ncase would be equal, and, therefore, the action in each case\nis necessarily equal; and thus the forces must be\ntransmitted, from one point to another, without increase or\ndiminution.\n\nThis property of matter, of transmitting the action of\nforce, is of various kinds. We have the coherence of a rope\nwhich enables us to pull, and the rigidity of a staff, which\nenables us to push with it in the direction of its length;\nand again, the same staff has a rigidity of another kind, in\nvirtue of which we can use it as a lever; that is, a\nrigidity to resist flexure, and to transmit the force which\nturns a body round a fulcrum. There is, further, the\nrigidity by which a solid body resists _twisting_. Of these\nkinds of rigidity, the first is that to which our axiom\nrefers; but in order to complete the list of the elementary\nprinciples of Statics, we ought also to lay down axioms\nrespecting the other kinds of rigidity[13\\3]. These,\nhowever, I shall not here state, as they do not involve any\nnew principle. Like the one just considered, they form part\nof our fundamental conception of matter; they are not the\nresults of any experience, but are the hypotheses to which\nwe are irresistibly led, when we would liberate our\nreasonings concerning force and matter from a dependence on\nthe special results of experience. We cannot even {223}\nconceive (that is, if we have any clear mechanical\nconceptions at all) the force exerted by the point of a\nstaff and resisting the force which we steadily impress on\nthe head of it, to be different from the impressed force.\n\n[Note 13\\3: Such axioms are given in a little work (_The\nMechanical Euclid_) which I published on the Elements of\nMechanics.]\n\n8. _Forces may have equivalent Forces substituted for them.\nThe Parallelogram of Forces._--It has already been observed,\nthat in order to prove the doctrines of Statics, we may take\nvarious principles as our starting points, and may still\nfind a course of demonstration by which the leading\npropositions belonging to the subject may be established.\nThus, instead of beginning our reasonings, as in the last\nsection we supposed them to commence, with the case in which\nforces act upon different points of the same body in the\nsame line of force, and counteract each other in virtue of\nthe intervening matter by which the effect of force is\ntransferred from one point to another; we may suppose\ndifferent forces to act at the same point, and may thus\ncommence our reasonings with a case in which we have to\ncontemplate force, without having to take into our account\nthe resistance or rigidity of matter. Two statical forces,\nthus acting at a mathematical point, are equivalent, in all\nrespects, to some single force acting at the same point; and\nwould be kept in equilibrium by a force equal and opposite\nto that single force. And the rule by which the single force\nis derived from the two, is commonly termed _the\nparallelogram of forces_; the proposition being this,--That\nif the two forces be represented in magnitude and direction\nby the two sides of a parallelogram, the resulting force\nwill be represented in the same manner by the diagonal of\nthe parallelogram. This proposition has very frequently been\nmade, by modern writers, the commencement of the science of\nMechanics: a position for which, by its simplicity, it is\nwell suited; although, in order to deduce from it the other\nelementary propositions of the science, as, for instance,\nthose respecting the lever, we require the axiom stated in\nthe last section.\n\n9. _The Parallelogram of Forces is a necessary Truth._--In\nthe series of discussions in which we are {224} here\nengaged, our main business is to ascertain the nature and\ngrounds of the certainty of scientific truths. We have,\ntherefore, to ask whether this proposition, the\nparallelogram of forces, be a necessary truth; and if so, on\nwhat grounds its necessity ultimately rests. We shall find\nthat this, like the other fundamental doctrines of Statics,\njustly claim a demonstrative certainty. Daniel Bernoulli, in\n1726, gave the first proof of this important proposition on\npure statical principles; and thus, as he says[14\\3],\n'proved that statical theorems are not less necessarily true\nthan geometrical are.' If we examine this proof of\nBernoulli, in order to discover what are the principles on\nwhich it rests, we shall find that the reasoning employs in\nits progress such axioms as this;--That if from forces which\nare in equilibrium at a point be taken away other forces\nwhich are in equilibrium at the same point, the remainder\nwill be in equilibrium; and generally;--That if forces can\nbe resolved into other equivalent forces, these may be\nseparated, grouped, and recombined, in any new manner, and\nthe result will still be identical with what it was at\nfirst. Thus in Bernoulli's proof, the two forces to be\ncompounded are represented by P and Q; P is resolved into\ntwo other forces, X and U; and Q into two others, Y and V,\nunder certain conditions. It is then assumed that these\nforces may be grouped into the pairs X, Y, and U, V: and\nwhen it has been shown that X and Y are in equilibrium, they\nmay, by what has been said, be removed, and the forces, P,\nQ, are equivalent to U, V; which, being in the same\ndirection by the course of the construction, have a result\nequal to their sum.\n\n[Note 14\\3: _Comm. Petrop._ vol. i.]\n\nIt is clear that the principles here assumed are genuine\naxioms, depending upon our conception of the nature of\nequivalence of forces, and upon their being capable of\naddition and composition. If the forces, P, Q, be\n_equivalent_ to forces X, U, Y, V, they are equivalent to\nthese forces added and compounded in any order; just as a\ngeometrical figure is, by our conception of {225} space,\nequivalent to its parts added together in any order. The\napprehension of forces as having magnitude, as made up of\nparts, as capable of composition, leads to such axioms in\nStatics, in the same manner as the like apprehension of\nspace leads to the axioms of Geometry. And thus the truths\nof Statics, resting upon such foundations, are independent\nof experience in the same manner in which geometrical truths\nare so.\n\nThe proof of the parallelogram of forces thus given by\nDaniel Bernoulli, as it was the first, is also one of the\nmost simple proofs of that proposition which have been\ndevised up to the present day. Many other demonstrations,\nhowever, have been given of the same proposition. Jacobi, a\nGerman mathematician, has collected and examined eighteen of\nthese[15\\3]. They all depend either upon such principles as\nhave just been stated; That forces may in every way be\nreplaced by those which are equivalent to them;--or else\nupon those previously stated, the doctrine of the lever, and\nthe transfer of a force from one point to another of its\ndirection. In either case, they are necessary results of our\nstatical conceptions, independent of any observed laws of\nmotion, and indeed, of the conception of actual motion\naltogether.\n\n[Note 15\\3: These are by the following mathematicians; D.\nBernoulli (1726); Lambert (1771); Scarella (1756); Venini\n(1764); Araldi (1806); Wachter (1815); Kaestner; Marini;\nEytelwein; Salimbeni; Duchayla; two different proofs by\nFoncenex (1760); three by D'Alembert; and those of Laplace\nand M. Poisson.]\n\nThere is another class of alleged proofs of the\nparallelogram of forces, which involve the consideration of\nthe motion produced by the forces. But such reasonings are,\nin fact, altogether irrelevant to the subject of Statics. In\nthat science, forces are not measured by the motion which\nthey produce, but by the forces which they will balance, as\nwe have already seen. The combination of two forces employed\nin producing motion in the same body, either simultaneously\nor successively, {226} belongs to that part of Mechanics\nwhich has motion for its subject, and is to be considered in\ntreating of the laws of motion. The composition of motion,\n(as when a man moves in a ship while the ship moves through\nthe water,) has constantly been confounded with the\ncomposition of force. But though it has been done by very\neminent mathematicians, it is quite necessary for us to keep\nthe two subjects distinct, in order to see the real nature\nof the evidence of truth in either case. The conditions of\nequilibrium of two forces on a lever, or of three forces at\na point, can be established without any reference whatever\nto any motions which the forces might, under _other_\ncircumstances, produce. And because this can be done, to do\nso is the only scientific procedure. To prove such\npropositions by any other course, would be to support truth\nby extraneous and inconclusive reasons; which would be\nforeign to our purpose, since we seek not only knowledge,\nbut the grounds of our knowledge.\n\n10. _The Center of gravity seeks the lowest place._--The\nprinciples which we have already mentioned afford a\nsufficient basis for the science of Statics in its most\nextensive and varied applications; and the conditions of\nequilibrium of the most complex combinations of machinery\nmay be deduced from these principles with a rigour not\ninferior to that of geometry. But in some of the more\ncomplex cases, the results of long trains of reasoning may\nbe foreseen, in virtue of certain maxims which appear to us\nself-evident, although it may not be easy to trace the exact\ndependence of these maxims upon our fundamental conceptions\nof force and matter. Of this nature is the maxim now\nstated;--That in any combination of matter any how\nsupported, the Center of Gravity will descend into the\nlowest position which the connexion of the parts allows it\nto assume by descending. It is easily seen that this maxim\ncarries to a much greater extent the principle which the\nGreek mathematicians assumed, that every body has a Center\nof Gravity, that is, a point in which, if the whole matter\nof the body be collected, the effect will remain unchanged.\nFor the Greeks asserted this of a {227} single rigid mass\nonly; whereas, in the maxim now under our notice, it is\nasserted of any masses, connected by strings, rods, joints,\nor in any manner. We have already seen that more modern\nwriters on mechanics, desirous of assuming as fundamental no\nwider principles than are absolutely necessary, have not\nadopted the Greek axiom in all its generality, but have only\nasserted that two _equal_ weights have a center of gravity\nmidway between them. Yet the principle that every body,\nhowever irregular, has a center of gravity, and will be\nsupported if that center is supported, and not otherwise, is\nso far evident, that it might be employed as a fundamental\ntruth, if we could not resolve it into any simpler truths:\nand, historically speaking, it was assumed as evident by the\nGreeks. In like manner the still wider principle, that a\ncollection of bodies, as, for instance, a flexible chain\nhanging upon one or more supports, has a center of gravity;\nand that this point will descend to the lowest possible\nsituation, as a single body would do, has been adopted at\nvarious periods in the history of mechanics; and especially\nat conjunctures when mathematical philosophers have had new\nand difficult problems to contend with. For in almost every\ninstance it has only been by repeated struggles that\nphilosophers have reduced the solution of such problems to a\nclear dependence upon the most simple axioms.\n\n11. _Stevinus's Proof for Oblique Forces._--We have an\nexample of this mode of dealing with problems, in Stevinus's\nmode of reasoning concerning the Inclined Plane; which, as\nwe have stated in the History of Mechanics, was the first\ncorrect published solution of that problem. Stevinus\nsupposes a loop of chain, or a loop of string loaded with a\nseries of equal balls at equal distances, to hang over the\nInclined Plane; and his reasoning proceeds upon this\nassumption,--That such a loop so hanging will find a certain\nposition in which it will rest: for otherwise, says\nhe[16\\3], its motion must go on for ever, which is absurd.\nIt may be asked how {228} this absurdity of a perpetual\nmotion appears; and it will perhaps be added, that although\nthe impossibility of a machine with such a condition may be\nproved as a remote result of mechanical principles, this\nimpossibility can hardly be itself recognized as a\nself-evident truth. But to this we may reply, that the\nimpossibility is really evident in the case contemplated by\nStevinus; for we cannot conceive a loop of chain to go on\nthrough all eternity, sliding round and round upon its\nsupport, by the effect of its own weight. And the ground of\nour conviction that this cannot be, seems to be this\nconsideration; that when the chain moves by the effect of\nits weight, we consider its motion as the result of an\neffort to reach some certain position, in which it can rest;\njust as a single ball in a bowl moves till it comes to rest\nat the lowest point of the bowl. Such an effect of weight in\nthe chain, we may represent to ourselves by conceiving all\nthe matter of the chain to be collected in one single point,\nand this single heavy point to hang from the support in some\nway or other, so as fitly to represent the mode of support\nof the chain. In whatever manner this heavy point (the\ncenter of gravity of the chain) be supported and controlled\nin its movements, there will still be some position of rest\nwhich it will seek and find. And thus there will be some\ncorresponding position of rest for the chain; and the\ninterminable shifting from one position to another, with no\ndisposition to rest in any position, cannot exist.\n\n[Note 16\\3: Stevin. _Statique_, livre i. prop. 19.]\n\nThus the demonstration of the property of the Inclined Plane\nby Stevinus, depends upon a principle which, though far from\nbeing the simplest of those to which the case can be\nreduced, is still both true and evident: and the evidence of\nthis principle, depending upon the assumption of a center of\ngravity, is of the same nature as the evidence of the Greek\nstatical demonstrations, the earliest real advances in the science.\n\n12. _Principle of Virtual Velocities._--We have referred\nabove to an assertion often made, that we may, from the\nsimple principles of Mechanics, demonstrate the\nimpossibility of a perpetual motion. In reality, {229}\nhowever, the simplest proof of that impossibility, in a\nmachine acted upon by weight only, arises from the very\nmaxim above stated, that the center of gravity seeks and\nfinds the lowest place; or from some similar proposition.\nFor if, as is done by many writers, we profess to prove the\nimpossibility of a perpetual motion by means of that\nproposition which includes the conditions of equilibrium,\nand is called the _Principle of Virtual Velocities_[17\\3],\nwe are under the necessity of first proving in a general\nmanner that principle. And if this be done by a mere\nenumeration of cases, (as by taking those five cases which\nare called the _Mechanical Powers_,) there may remain some\ndoubts whether the enumeration of possible mechanical\ncombinations be complete. Accordingly, some writers have\nattempted independent and general proofs of the Principle of\nVirtual Velocities; and these proofs rest upon assumptions\nof the same nature as that now under notice. This is, for\nexample, the case with Lagrange's proof, which depends upon\nwhat he calls the _Principle of Pulleys_. For this principle\nis,--That a weight any how supported, as by a string passing\nround any number of pulleys any how placed, will be at rest\nthen only, when it cannot get lower by any small motion of\nthe pulleys. And thus the maxim that a weight will descend\nif it can, is assumed as the basis of this proof.\n\n[Note 17\\3: See _Hist. Ind Sc._ b. vi. c. ii. sect. 4.]\n\nThere is, as we have said, no need to assume such principles\nas these for the foundation of our mechanical science. But\nit is, on various accounts, useful to direct our attention\nto those cases in which truths, apprehended at first in a\ncomplex and derivative form, have afterwards been reduced to\ntheir simpler elements;--in which, also, sagacious and\ninventive men have fixed upon those truths as self-evident,\nwhich now appear to us only certain in virtue of\ndemonstration. In these cases we can hardly doubt that such\nmen were led to assert the doctrines which they discovered,\nnot by any capricious conjecture of arbitrary selection, but\nby having a keener and deeper insight than other persons\n{230} into the relations which were the object of their\ncontemplation; and in the science now spoken of, they were\nled to their assumptions by possessing clearly and\ndistinctly the conceptions of mechanical cause and\neffect,--action and reaction,--force, and the nature of its\noperation.\n\n13. _Fluids press Equally in all Directions._--The doctrines\nwhich concern the equilibrium of fluids depend on principles\nno less certain and simple than those which refer to the\nequilibrium of solid bodies; and the Greeks, who, as we have\nseen, obtained a clear view of some of the principles of\nStatics, also made a beginning in the kindred subject of\nHydrostatics. We still possess a treatise of Archimedes _On\nFloating Bodies_, which contains correct solutions of\nseveral problems belonging to this subject, and of some\nwhich are by no means easy. In this treatise, the\nfundamental assumption is of this kind: 'Let it be assumed\nthat the nature of a fluid is such, that the parts which are\nless pressed yield to those which are more pressed.' In this\nassumption or axiom it is implied that a pressure exerted\nupon a fluid in one direction produces a pressure in another\ndirection; thus, the weight of the fluid which arises from a\ndownward force produces a lateral pressure against the sides\nof the containing vessel. Not only does the pressure thus\ndiverge from its original direction into all other\ndirections, but the pressure is in all directions exactly\nequal, an equal extent of the fluid being taken. This\nprinciple, which was involved in the reasoning of\nArchimedes, is still to the present day the basis of all\nhydrostatical treatises, and is expressed, as above, by\nsaying that _fluids press equally in all directions_.\n\nConcerning this, as concerning previously-noticed\nprinciples, we have to ask whether it can rightly be said to\nbe derived from experience. And to this the answer must\nstill be, as in the former cases, that the proposition is\nnot one borrowed from experience in any usual or exact sense\nof the phrase. I will endeavour to illustrate this. There\nare many elementary propositions in physics, our knowledge\nof which {231} indisputably depends upon experience; and in\nthese cases there is no difficulty in seeing the evidence of\nthis dependence. In such cases, the _experiments_ which\nprove the law are prominently stated in treatises upon the\nsubject: they are given with exact measures, and with an\naccount of the means by which errours were avoided: the\nexperiments of more recent times have either rendered more\ncertain the law originally asserted, or have pointed out\nsome correction of it as requisite: and the names, both of\nthe discoverers of the law and of its subsequent reformers,\nare well known. For instance, the proposition that 'The\nelastic force of air varies as the density,' was first\nproved by Boyle, by means of operations of which the detail\nis given in his _Defence_ of his _Pneumatical\nExperiments_[18\\3]; and by **Mariotte in his _Trait\u00e9 de\nl'\u00c9quilibre des Liquides_, from whom it has generally been\ntermed Mariotte's law. After being confirmed by many other\nexperimenters, this law was suspected to be slightly\ninaccurate, and a commission of the French Academy of\nSciences was appointed, consisting of several distinguished\nphilosophers[19\\3], to ascertain the truth or falsehood of\nthis suspicion. The result of their investigations appeared\nto be, that the law is exact, as nearly as the inevitable\ninaccuracies of machinery and measures will allow us to\njudge. Here we have an example of a law which is of the\nsimplest kind and form; and which yet is not allowed to rest\nupon its simplicity or apparent probability, but is\nrigorously tested by experience. In this case, the\nassertion, that the law depends upon experience, contains a\nreference to plain and notorious passages in the history of\nscience.\n\n[Note 18\\3: Shaw's _Boyle_, Vol. ii. p. 671.]\n\n[Note 19\\3: The members were Prony, Arago, Amp\u00e8re, Girard,\nand Dulong. The experiments were extended to a pressure of\ntwenty-seven atmospheres; and in no instance did the\ndifference between the observed and calculated elasticity\namount to one-hundredth of the whole; nor did the difference\nappear to increase with the increase of pressure.--Fechner,\n_Repertorium_, i. 110.]\n\nNow with regard to the principle that fluids press equally\nin all directions, the case is altogether different. {232}\nIt is, indeed, often asserted in works on hydrostatics, that\nthe principle is collected from experience, and sometimes a\nfew experiments are described as exhibiting its effect; but\nthese are such as to illustrate and explain, rather than to\nprove, the truth of the principle: they are never related to\nhave been made with that exactness of precaution and\nmeasurement, or that frequency of repetition, which are\nnecessary to establish a purely experimental truth. Nor did\nsuch experiments occur as important steps in the history of\nscience. It does not appear that Archimedes thought\nexperiment necessary to confirm the truth of the law as he\nemployed it: on the contrary, he states it in exactly the\nsame shape as the axioms which he employs in statics, and\neven in geometry; namely, as an assumption. Nor does any\nintelligent student of the subject find any difficulty in\nassenting to this fundamental principle of hydrostatics as\nsoon as it is propounded to him. Experiment was not\nrequisite for its discovery; experiment is not necessary for\nits proof at present; and we may add, that experiment,\nthough it may make the proposition the more readily\nintelligible, can add nothing to our conviction of its truth\nwhen it is once understood.\n\n14. _Foundation of the above Axiom._--But it will naturally\nbe asked, What then is the ground of our conviction of this\ndoctrine of the equal pressure of a fluid in all directions?\nAnd to this I reply, that the reasons of this conviction are\ninvolved in our idea of a fluid, which is considered as\nmatter, and therefore as capable of receiving, resisting,\nand transmitting force according to the general conception\nof matter; and which is also considered as matter which has\nits parts perfectly moveable among one another. For it\nfollows from these suppositions, that if the fluid be\nconfined, a pressure which thrusts in one side of the\ncontaining vessel, may cause any other side to bulge\noutwards, if there be a part of the surface which has not\nstrength to resist this pressure from within. And that this\npressure, when thus transferred into a direction different\nfrom the original one, is not altered in intensity, {233}\ndepends upon this consideration; that any difference in the\ntwo pressures would be considered as a defect of _perfect_\nfluidity, since the fluidity would be still more complete,\nif this entire and undiminished transmission of pressure in\nall directions were supposed. If, for instance, the lateral\npressure were less than the vertical, this could be\nconceived no other way than as indicating some rigidity or\nadhesion of the parts of the fluid. When the fluidity is\nperfect, the two pressures which act in the two different\nparts of the fluid exactly balance each other: they are the\naction and the reaction; and must hence be equal by the same\nnecessity as two directly opposite forces in statics.\n\nBut it may be urged, that even if we grant that this\nconception of a perfect fluid, as a body which has its parts\nperfectly moveable among each other, leads us necessarily to\nthe principle of the equality of hydrostatic pressure in all\ndirections, still this conception itself is obtained from\nexperience, or suggested by observation. And to this we may\nreply, that the conception of a fluid, as contemplated in\nmechanical theory, cannot be said to be derived from\nexperience, except in the same manner as the conception of a\nsolid and rigid body may be said to be acquired by\nexperience. For if we imagine a vessel full of small, smooth\nspherical balls, such a collection of balls would approach\nto the nature of a fluid, in having its parts moveable among\neach other; and would approach to perfect fluidity, as the\nballs became smoother and smaller. And such a collection of\nballs would also possess the statical properties of a fluid;\nfor it would transmit pressure out of a vertical into a\nlateral (or any other) direction, in the same manner as a\nfluid would do. And thus a collection of solid bodies has\nthe same property which a fluid has; and the science of\nHydrostatics borrows from experience no principles beyond\nthose which are involved in the science of Statics\nrespecting solids. And since in this latter portion of\nscience, as we have already seen, none of the principles\ndepend for their evidence upon any special experience, the\ndoctrines of Hydrostatics also are not {234} proved by\nexperience, but have a necessary truth borrowed from the\nrelations of our ideas.\n\nIt is hardly to be expected that the above reasoning will,\nat first sight, produce conviction in the mind of the\nreader, except he have, to a certain extent, acquainted\nhimself with the elementary doctrines of the science of\nHydrostatics as usually delivered; and have followed, with\nclear and steady apprehension, some of the trains of\nreasoning by which the pressures of fluids are determined;\nas, for instance, the explanation of what is called _the\nHydrostatic Paradox_. The necessity of such a discipline in\norder that the reader may enter fully into this part of our\nspeculations, naturally renders them less popular; but this\ndisadvantage is inevitable in our plan. We cannot expect to\nthrow light upon philosophy by means of the advances which\nhave been made in the mathematical and physical sciences,\nexcept we really understand the doctrines which have been\nfirmly established in those sciences. This preparation for\nphilosophizing may be somewhat laborious; but such labour is\nnecessary if we would pursue speculative truth with all the\nadvantages which the present condition of human knowledge\nplaces within our reach.\n\nWe may add, that the consequences to which we are directed\nby the preceding opinions, are of very great importance in\ntheir bearing upon our general views respecting human\nknowledge. I trust to be able to show, that some important\ndistinctions are illustrated, some perplexing paradoxes\nsolved, and some large anticipations of the future extension\nof our knowledge suggested, by means of the conclusions to\nwhich the preceding discussions have conducted us. But\nbefore I proceed to these general topics, I must consider\nthe foundations of some of the remaining portions of the\nscience of Mechanics.\n\n\n\n{{235}}\nCHAPTER VII.\n\nOF THE ESTABLISHMENT OF THE PRINCIPLES OF DYNAMICS.\n\n\n1. IN the History of Mechanics, I have traced the steps by\nwhich the three Laws of Motion and the other principles of\nmechanics were discovered, established, and extended to the\nwidest generality of form and application. We have, in these\nlaws, examples of principles which were, historically\nspeaking, obtained by reference to experience. Bearing in\nmind the object and the result of the preceding discussions,\nwe cannot but turn with much interest to examine these\nportions of science; to inquire whether there be any real\ndifference in the grounds and nature between the knowledge\nthus obtained, and those truths which we have already\ncontemplated; and which, as we have seen, contain their own\nevidence, and do not require proof from experiment.\n\n2. _The First Law of Motion._--The first law of motion is,\nthat _When a body moves not acted upon by any force, it will\ngo on perpetually in a straight line, and with a uniform\nvelocity._ Now what is the real ground of our assent to this\nproposition? That it is not at first sight a self-evident\ntruth, appears to be clear; since from the time of Aristotle\nto that of Galileo the opposite assertion was held to be\ntrue; and it was believed that all bodies in motion had, by\ntheir own nature, a constant tendency to move more and more\nslowly, so as to stop at last. This belief, indeed, is\nprobably even now entertained by most persons, till their\nattention is fixed upon the arguments by which the first law\nof motion is established. It is, however, not difficult to\nlead any person of a speculative habit {236} of thought to\nsee that the retardation which constantly takes place in the\nmotion of all bodies when left to themselves, is, in\nreality, the effect of extraneous forces which destroy the\nvelocity. A top ceases to spin because the friction against\nthe ground and the resistance of the air gradually diminish\nits motion, and not because its motion has any internal\nprinciple of decay or fatigue. This may be shown, and was,\nin fact, shown by Hooke before the Royal Society, at the\ntime when the laws of motion were still under discussion, by\nmeans of experiments in which the weight of the top is\nincreased, and the resistance to motion offered by its\nsupport, is diminished; for by such contrivances its motion\nis made to continue much longer than it would otherwise do.\nAnd by experiments of this nature, although we can never\nremove the whole of the external impediments to continued\nmotion, and although, consequently, there will always be\nsome retardation; and an end of the motion of a body left to\nitself, however long it may be delayed, must at last come;\nyet we can establish a conviction that if all resistance\ncould be removed, there would be no diminution of velocity,\nand thus the motion would go on for ever.\n\nIf we call to mind the axioms which we formerly stated, as\ncontaining the most important conditions involved in the\nidea of Cause, it will be seen that our conviction in this\ncase depends upon the first axiom of Causation, that nothing\ncan happen without a cause. Every change in the velocity of\nthe moving body must have a cause; and if the change can, in\nany manner, be referred to the presence of other bodies,\nthese are said to exert _force_ upon the moving body: and\nthe conception of force is thus evolved from the general\nidea of cause. _Force is any cause which has motion, or\nchange of motion, for its effect_; and thus, all the change\nof velocity of a body which can be referred to extraneous\nbodies,--as the air which surrounds it, or the support on\nwhich it rests,--is considered as the effect of forces; and\nthis consideration is looked upon as explaining the\ndifference between the motion which really takes places in\nthe experiment, and that motion {237} which, as the law\nasserts, would take place if the body were not acted on by\nany forces.\n\nThus the truth of the first law of motion depends upon the\naxiom that no change can take place without a cause; and\nfollows from the definition of force, if we suppose that\nthere can be none but an _external_ cause of change. But in\norder to establish the law, it was necessary further to be\nassured that there is no _internal_ cause of change of\nvelocity belonging to all matter whatever, and operating in\nsuch a manner that the mere progress of time is sufficient\nto produce a diminution of velocity in all moving bodies. It\nappears from the history of mechanical science, that this\nlatter step required a reference to observation and\nexperiment; and that the first law of motion is so far,\nhistorically at least, dependent upon our experience.\n\nBut notwithstanding this historical evidence of the need\nwhich we have of a reference to observed facts, in order to\nplace this first law of motion out of doubt, it has been\nmaintained by very eminent mathematicians and philosophers,\nthat the law is, in truth, evident of itself, and does not\nreally rest upon experimental proof. Such, for example, is\nthe opinion of d'Alembert[20\\3], who offers what is called\nan _\u00e0 priori_ proof of this law; that is, a demonstration\nderived from our ideas alone. When a body is put in motion,\neither, he says, the cause which puts it in motion at first,\nsuffices to make it move one foot, or the continued action\nof the cause during this foot is requisite for the motion.\nIn the first case, the same reason which made the body\nproceed to the end of the first foot will hold for its going\non through a second, a third, a fourth foot, and so on for\nany number. In the second case, the same reason which made\nthe force continue to act during the first foot, will hold\nfor its acting, and therefore for the body moving during\neach succeeding foot. And thus the body, once beginning to\nmove, must go on moving for ever.\n\n[Note 20\\3: _Dynamique._]\n\n{238} It is obvious that we might reply to this argument,\nthat the reasons for the body proceeding during each\nsucceeding foot may not necessarily be all the same; for\namong these reasons may be the time which has elapsed; and\nthus the velocity may undergo a change as the time proceeds:\nand we require observation to inform us that it does not do so.\n\nProfessor Playfair has presented nearly the same argument,\nalthough in a different and more mathematical form[21\\3]. If\nthe velocity change, says he, it must change according to\nsome expression of calculation depending upon the time, or,\nin mathematical language, must be a _function_ of the time.\nIf the velocity diminish as the time increases, this may be\nexpressed by stating the velocity in each case as a certain\nnumber, from which another quantity, or _term_, increasing\nas the time increases, is subtracted. But, Playfair adds,\nthere is no condition involved in the nature of the case, by\nwhich the _coefficients_, or numbers which are to be\nemployed, along with the number representing the time, in\ncalculating this second term, can be determined to be of one\nmagnitude rather than of any other. Therefore he infers\nthere can be no such coefficients, and that the velocity is\nin each case equal to some constant number, independent of\nthe time; and is therefore the same for all times.\n\n[Note 21\\3: _Outlines of Natural Philosophy_, p. 26.]\n\nIn reply to this we may observe, that the circumstance of\n_our not seeing_ in the nature of the case anything which\ndetermines for us the coefficients above spoken of, cannot\nprove that they have not some certain value _in nature_. We\ndo not see in the nature of the case anything which should\ndetermine a body to fall sixteen feet in a second of time,\nrather than one foot or one hundred feet: yet in fact the\nspace thus run through by falling bodies is determined to a\ncertain magnitude. It would be easy to assign a mathematical\nexpression for the velocity of a body, implying that\none-hundredth of the velocity, or any other {239} fraction,\nis lost in each second[22\\3]: and where is the absurdity of\nsupposing such an expression really to represent the\nvelocity?\n\n[Note 22\\3: This would be the case, if, _t_ being the\nnumber of seconds elapsed, and _C_ some constant quantity,\nthe velocity were expressed by this mathematical formula,\n_C_(99/100)^_t_.]\n\nMost modern writers on mechanics have embraced the opposite\nopinion, and have ascribed our knowledge of this first law\nof motion to experience. Thus M. Poisson, one of the most\neminent of the mathematicians who have written on this\nsubject, says[23\\3], \"We cannot affirm _\u00e0 priori_ that the\nvelocity communicated to a body will not become slower and\nslower of itself, and end by being entirely extinguished. It\nis only by experience and induction that this question can\nbe decided.\"\n\n[Note 23\\3: Poisson, _Dynamique_, ed. 2, art. 113.]\n\nYet it cannot be denied that there is much force in those\narguments by which it is attempted to show that the First\nLaw of Motion, such as we find it, is more consonant to our\nconceptions than any other would be. The Law, as it exists,\nis the most simple that we can conceive. Instead of having\nto determine by experiments what is the law of the natural\nchange of velocity, we find the Law to be that it does not\nchange at all. To a certain extent, the Law depends upon the\nevident axiom, that no change can take place without a\ncause. But the question further occurs, whether the mere\nlapse of time may not be a cause of change of velocity. In\norder to ensure this, we have recourse to experiment; and\nthe result is that time alone does not produce any such\nchange. In addition to the conditions of change which we\ncollect from our own Ideas, we ask of Experience what other\nconditions and circumstances she has to offer; and the\nanswer is, that she can point out none; When we have removed\nthe alterations which external causes, in our very\nconception of them, occasion, there are no longer any\nalterations. Instead of having to guide ourselves {240} by\nexperience, we learn that on this subject she has nothing to\ntell us. Instead of having to take into account a number of\ncircumstances, we find that we have only to reject all\ncircumstances. The velocity of a body remains unaltered by\ntime alone, of whatever kind the body itself be.\n\nBut the doctrine that time alone is not a cause of change of\nvelocity in any body is further recommended to us by this\nconsideration;--that time is conceived by us not as a cause,\nbut only as a condition of other causes producing their\neffects. Causes operate in time; but it is only when the\ncause exists, that the lapse of time can give rise to\nalterations. When therefore all external causes of change of\nvelocity are supposed to be removed, the velocity must\ncontinue identical with itself, whatever the time which\nelapses. An eternity of negation can produce no positive\nresult.\n\nThus, though the discovery of the First Law of Motion was\nmade, historically speaking, by means of experiment, we have\nnow attained a point of view in which we see that it might\nhave been certainly known to be true independently of\nexperience. This law in its ultimate form, when completely\nsimplified and steadily contemplated, assumes the character\nof a self-evident truth. We shall find the same process to\ntake place in other instances. And this feature in the\nprogress of science will hereafter be found to suggest very\nimportant views with regard both to the nature and prospects\nof our knowledge.\n\n3. _Gravity is a Uniform Force._--We shall find observations\nof the same kind offering themselves in a manner more or\nless obvious, with regard to the other principles of\nDynamics. The determination of the laws according to which\nbodies fall downwards by the common action of gravity, has\nalready been noticed in the History of Mechanics[24\\3], as\none of the earliest positive advances in the doctrine of\nmotion. These laws were first rightly stated by Galileo, and\n{241} established by reasoning and by experiment, not\nwithout dissent and controversy. The amount of these\ndoctrines is this: That gravity is a uniform accelerating\nforce; such a _uniform force_ having this for its character,\nthat it _makes the velocity increase in exact proportion to\nthe time of motion_. The relation which the spaces described\nby the body bear to the times in which they are described,\nis obtained by mathematical deduction from this definition\nof the force.\n\n[Note 24\\3: _Hist. Ind. Sc._ b. vi. c. ii. sect. 2.]\n\nThe clear Definition of a uniform accelerating force, and\nthe Proposition that gravity is such a force, were\nco-ordinate and contemporary steps in this discovery. In\ndefining accelerating force, reference, tacit or express,\nwas necessarily made to the second of the general axioms\nrespecting causation,--That causes are measured by their\neffects. Force, in the cases now under our notice, is\nconceived to be, as we have already stated, (p. 236,) any\ncause which, acting from without, changes the motion of a\nbody. It must, therefore, in this acceptation, be measured\nby the magnitude of the changes which are produced. But in\nwhat manner the changes of motion are to be employed as the\nmeasures of force, is learnt from observation of the facts\nwhich we see taking place in the world. Experience\n_interprets_ the axiom of causation, from which otherwise we\ncould not deduce any real knowledge. We may assume, in\nvirtue of our general conceptions of force, that under the\nsame circumstances, a greater change of motion implies a\ngreater force producing it; but what are we to expect when\nthe circumstances change? The weight of a body makes it fall\nfrom rest at first, and causes it to move more quickly as it\ndescends lower. We may express this by saying, that gravity,\nthe universal force which makes all terrestrial bodies fall\nwhen not supported, by its continuous action first _gives_\nvelocity to the body when it has none, and afterwards _adds_\nvelocity to that which the body already has. But how is the\nvelocity added proportioned to the velocity which already\nexists? Force acting on a body at rest, and on a body in\nmotion, appears under very different {242} conditions;--how\nare the effects related? Let the force be conceived to be in\nboth cases the same, since force is conceived to depend upon\nthe extraneous bodies, and not upon the condition of the\nmoving mass itself. But the force being the same, the\neffects may still be different. It is at first sight\nconceivable that the body, acted upon by the same gravity,\nmay receive a less addition of velocity when it is already\nmoving in the direction in which this gravity impels it; for\nif we ourselves push a body forwards, we can produce little\nadditional effect upon it when it is already moving rapidly\naway from us. May it not be true, in like manner, that\nalthough gravity be always the same force, its effect\ndepends upon the velocity which the body under its influence\nalready possesses?\n\nObservation and reasoning combined, as we have said, enabled\nGalileo to answer these questions. He asserted and proved\nthat we may consistently and properly measure a force by the\nvelocity which is by it generated in a body, in some certain\ntime, as one second; and further, that if we adopt this\nmeasure, gravity will be a force of the same value under all\ncircumstances of the body which it affects; since it\nappeared that, in fact, a falling body does receive equal\nincrements of velocity in equal times from first to last.\n\nIf it be asked whether we could have known, anterior to, or\nindependent of, experiment, that gravity is a uniform force\nin the sense thus imposed upon the term; it appears clear\nthat we must reply, that we could not have attained to such\nknowledge, since other laws of the motion of bodies\ndownwards are easily conceivable, and nothing but\nobservation could inform us that one of these laws does not\nprevail in fact. Indeed, we may add, that the assertion that\nthe force of gravity is uniform, is so far from being\nself-evident, that it is not even true; for gravity varies\naccording to the distance from the center of the earth; and\nalthough this variation is so small as to be, in the case of\nfalling bodies, imperceptible, it negatives the rigorous\nuniformity of the force as completely, though {243} not to\nthe same extent, as if the weight of a body diminished in a\nmarked degree, when it was carried from the lower to the\nupper room of a house. It cannot, then, be a truth\nindependent of experience, that gravity is uniform.\n\nYet, in fact, the assertion that gravity is uniform was\nassented to, not only before it was proved, but even before\nit was clearly understood. It was readily granted by all,\nthat bodies which fall freely are _uniformly_ accelerated;\nbut while some held the opinion just stated, that uniformly\naccelerated motion is that in which the velocity increases\nin proportion to the _time_, others maintained, that _that_\nis uniformly accelerated motion, in which the velocity\nincreases in proportion to the _space_; so that, for\nexample, a body in falling vertically through twenty feet\nshould acquire twice as great a velocity as one which falls\nthrough ten feet.\n\nThese two opinions are both put forward by the interlocutors\nof Galileo's Dialogue on this subject[25\\3]. And the latter\nsupposition is rejected, the author showing, not that it is\ninconsistent with experience, but that it is impossible in\nitself: inasmuch as it would inevitably lead to the\nconclusion, that the fall through a large and a small\nvertical space would occupy exactly the same time.\n\n[Note 25\\3: _Dialogo_, iii. p. 95.]\n\nIndeed, Galileo assumes his definition of uniformly\naccelerated motion as one which is sufficiently recommended\nby its own simplicity. 'If we attend carefully,' he says,\n'we shall find that no mode of increase of velocity is more\nsimple than that which adds equal increments in equal times.\nWhich we may easily understand if we consider the close\naffinity of time and motion: for as the uniformity of motion\nis defined by the equality of spaces described in equal\ntimes, so we may conceive the uniformity of acceleration to\nexist when equal velocities are added in equal times.'\n\nGalileo's mode of supporting his opinion, that bodies\nfalling by the action of gravity are thus uniformly {244}\naccelerated, consists, in the first place, in adducing the\nmaxim that nature always employs the most simple\nmeans[26\\3]. But he is far from considering this a decisive\nargument. 'I,' says one of his speakers, 'as it would be\nvery unreasonable in me to gainsay this or any other\ndefinition which any author may please to make, since they\nare all arbitrary, may still, without offence, doubt whether\nsuch a definition, conceived and admitted in the abstract,\nfits, agrees, and is verified in that kind of accelerated\nmotion which bodies have when they descend naturally.'\n\n[Note 26\\3: _Dialogo_, iii. p. 91.]\n\nThe experimental proof that bodies, when they fall\ndownwards, are uniformly accelerated, is (by Galileo)\nderived from the inclined plane; and therefore assumes the\nproposition, that if such uniform acceleration prevail in\nvertical motion, it will also hold when a body is compelled\nto describe an oblique rectilinear path. This proposition\nmay be shown to be true, if (assuming by anticipation the\nThird Law of Motion, of which we shall shortly have to\nspeak,) we introduce the conception of a uniform statical\nforce as the cause of uniform acceleration. For the force on\nthe inclined plane bears a constant proportion to the\nvertical force, and this proportion is known from statical\nconsiderations. But in the work of which we are speaking,\nGalileo does not introduce this abstract conception of force\nas the foundation of his doctrines. Instead of this, he\nproposes, as a postulate sufficiently evident to be made the\nbasis of his reasonings, That bodies which descend down\ninclined planes of different inclinations, but of the same\nvertical height, all acquire the same velocity[27\\3]. But\nwhen this postulate has been propounded by one of the\npersons of the dialogue, another interlocutor says, 'You\ndiscourse very probably; but besides this likelihood, I wish\nto augment the probability so far, that it shall be almost\nas complete as a necessary demonstration.' He then proceeds\nto describe a very ingenious and simple experiment, which\nshows that when a body is made to swing upwards at the end\nof {245} a string, it attains to the same height, whatever\nis the path it follows, so long as it starts from the lowest\npoint with the same velocity. And thus Galileo's postulate\nis experimentally confirmed, so far as the force of gravity\ncan be taken as an example of the forces which the postulate\ncontemplates: and conversely, gravity is proved to be a\nuniform force, so far as it can be considered clear that the\npostulate is true of uniform forces.\n\n[Note 276\\3: _Dialogo_, iii. p. 36.]\n\nWhen we have introduced the conception and definition of\naccelerating force, Galileo's postulate, that bodies\ndescending down inclined planes of the same vertical height,\nacquire the same velocity, may, by a few steps of reasoning,\nbe demonstrated to be true of uniform forces: and thus the\nproof that gravity, either in vertical or oblique motion, is\na uniform force, is confirmed by the experiment above\nmentioned; as it also is, on like grounds, by many other\nexperiments, made upon inclined planes and pendulums.\n\nThus the propriety of Galileo's conception of a uniform\nforce, and the doctrine that gravity is a uniform force,\nwere confirmed by the same reasonings and experiments. We\nmay make here two remarks; _First_, that the conception,\nwhen established and rightly stated, appears so simple as\nhardly to require experimental proof; a remark which we have\nalready made with regard to the First Law of Motion: and\n_Second_, that the discovery of the real law of nature was\nmade by assuming propositions which, without further proof,\nwe should consider as very precarious, and as far less\nobvious, as well as less evident, than the law of nature in\nits simple form.\n\n4. _The Second Law of Motion._--When a body, instead of\nfalling downwards from rest, is thrown in any direction, it\ndescribes a curve line, till its motion is stopped. In this,\nand in all other cases in which a body describes a curved\npath in free space, its motion is determined by the Second\nLaw of Motion. The law, in its general form, is as\nfollows:--When a body is thus cast forth and acted upon by a\nforce in a direction {246} transverse to its motion, the\nresult is, That _there is combined with the motion with\nwhich the body is thrown, another motion, exactly the same\nas that which the same force would have communicated to a\nbody at rest_.\n\nIt will readily be understood that the basis of this law is\nthe axiom already stated, that effects are measured by their\ncauses. In virtue of this axiom, the effect of gravity\nacting upon a body in a direction transverse to its motion,\nmust measure the accelerative or deflective force of gravity\nunder those circumstances. If this effect vary with the\nvarying velocity and direction of the body thus acted upon,\nthe deflective force of gravity also will vary with those\ncircumstances. The more simple supposition is, that the\ndeflective force of gravity is the same, whatever be the\nvelocity and direction of the body which is subjected to its\ninfluence: and this is the supposition which we find to be\nverified by facts. For example, a ball let fall from the top\nof a ship's upright mast, when she is sailing steadily\nforward, will fall at the foot of the mast, just as if it\nwere let fall while the ship were at rest; thus showing that\nthe motion which gravity gives to the ball is compounded\nwith the horizontal motion which the ball shares with the\nship from the first. This general and simple conception of\nmotions as _compounded_ with one another, represents, it is\nproved, the manner in which the motion produced by gravity\nmodifies any other motion which the body may previously have had.\n\nThe discussions which terminated in the general reception of\nthis Second Law of Motion among mechanical writers, were\nmuch mixed up with the arguments for and against the\nCopernican system, which system represented the earth as\nrevolving upon its axis. For the obvious argument against\nthis system was, that if each point of the earth's surface\nwere thus in motion from west to east, a stone dropt from\nthe top of a tower would be left behind, the tower moving\naway from it: and the answer was, that by this law of\nmotion, the stone would have the earth's motion impressed\nupon it, as well as that motion which would {247} arise from\nits gravity to the earth; and that the motion of the stone\nrelative to the tower would thus be the same as if both\nearth and tower were at rest. Galileo further urged, as a\npresumption in favour of the opinion that the two\nmotions,--the circular motion arising from the rotation of\nthe earth, and the downward motion arising from the gravity\nof the stone, would be compounded in the way we have\ndescribed, (neither of them disturbing or diminishing the\nother,)--that the first motion was in its own nature not\nliable to any change or diminution[28\\3], as we learn from\nthe First Law of Motion. Nor was the subject lightly\ndismissed. The experiment of the stone let fall from the top\nof the mast was made in various forms by Gassendi; and in\nhis Epistle, _De Motu impresso a Motore translato_, the rule\nnow in question is supported by reference to these\nexperiments. In this manner, the general truth, the Second\nLaw of Motion, was established completely and beyond\ndispute.\n\n[Note 28\\3: _Dialogo_, ii. p. 114.]\n\nBut when this law had been proved to be true in a general\nsense, with such accuracy as rude experiments, like those of\nGalileo and Gassendi, would admit, it still remained to be\nascertained (supposing our knowledge of the law to be the\nresult of experience alone,) whether it were true with that\nprecise and rigorous exactness which more refined modes of\nexperimenting could test. We so willingly believe in the\nsimplicity of laws of nature, that the rigorous accuracy of\nsuch a law, known to be at least approximately true, was\ntaken for granted, till some ground for suspecting the\ncontrary should appear. Yet calculations have not been\nwanting which might confirm the law as true to the last\ndegree of accuracy. Laplace relates (_Syst. du Monde_, livre\niv. chap. 16,) that at one time he had conceived it possible\nthat the effect of gravity upon the moon might be slightly\nmodified by the moon's direction and velocity; and that in\nthis way an explanation might be found for the moon's\n_acceleration_ (a deviation of her observed from her\ncalculated place, which long {248} perplexed\nmathematicians). But it was after some time discovered that\nthis feature in the moon's motion arose from another cause;\nand the second law of motion was confirmed as true in the\nmost rigorous sense.\n\nThus we see that although there were arguments which might\nbe urged in favour of this law, founded upon the necessary\nrelations of ideas, men became convinced of its truth only\nwhen it was verified and confirmed by actual experiment. But\nyet in this case again, as in the former ones, when the law\nhad been established beyond doubt or question, men were very\nready to believe that it was not a mere result of\nobservation,--that the truth which it contained was not\nderived from experience,--that it might have been assumed as\ntrue in virtue of reasonings anterior to experience,--and\nthat experiments served only to make the law more plain and\nintelligible, as visible diagrams in geometry serve to\nillustrate geometrical truths; our knowledge not being (they\ndeemed) in mechanics, any more than in geometry, borrowed\nfrom the senses. It was thought by many to be self-evident,\nthat the effect of a force in any direction cannot be\nincreased or diminished by any motion transverse to the\ndirection of the force which the body may have at the same\ntime: or, to express it otherwise, that if the motion of the\nbody be compounded of a horizontal and vertical motion, the\nvertical motion alone will be affected by the vertical\nforce. This principle, indeed, not only has appeared evident\nto many persons, but even at the present day is assumed as\nan axiom by many of the most eminent mathematicians. It is,\nfor example, so employed in the _M\u00e9canique C\u00e9leste_ of\nLaplace, which may be looked upon as the standard of\nmathematical mechanics in our time; and in the _M\u00e9canique\nAnalytique_ of Lagrange, the most consummate example which\nhas appeared of subtilty of thought on such subjects, as\nwell as of power of mathematical generalization[29\\3]. And\n{249} thus we have here another example of that circumstance\nwhich we have already noticed in speaking of the First Law\nof Motion, (Art. 2 of this chapter,) and of the Law that\nGravity is a uniform Force, (Art. 3); namely, that the law,\nthough historically established by experiments, appears,\nwhen once discovered and reduced to its most simple and\ngeneral form, to be self-evident. I am the more desirous of\ndrawing attention to this feature in various portions of the\nhistory of science, inasmuch as it will be found to lead to\nsome very extensive and important views, hereafter to be\nconsidered.\n\n[Note 29\\3: I may observe that the rule that we may\n_compound_ motions, as the Law supposes, is involved in the\nstep of _resolving_ them; which is done in the passage to\nwhich I refer. (_M\u00e9c. Analyt._ ptie. i. sect. i. art. 3. p.\n225.) 'Si on con\u00e7oit que le mouvement d'un corps et les\nforces qui le sollicitent soient _decompos\u00e9es_ suivant trois\nlignes droites perpendiculaires entre elles, on pourra\nconsid\u00e9rer s\u00e9par\u00e9ment les mouvemens et les forces relatives\n\u00e0 chacun de ces trois directions. Car \u00e0 cause de la\nperpendicularit\u00e9 des directions il est visible que chacun de\nces mouvemens partiels peut \u00eatre regard\u00e9 comme ind\u00e9pendant\ndes deux autres, et qu'il ne peut recevoir d'alt\u00e9ration que\nde la part de la force qui agit dans la direction de ce\nmouvement; l'on peut conclure que ces trois mouvemens\ndoivent suivre, chacun en particulier, les lois des\nmouvemens rectilignes acc\u00e9l\u00e9r\u00e9s ou retard\u00e9s par les forces\ndonn\u00e9es.' Laplace makes the same assumption in effect,\n(_M\u00e9c. C\u00e9l._ p. i. liv. i. art. 7), by resolving the forces\nwhich act upon a point in three rectangular directions, and\nreasoning separately concerning each direction. But in his\nmode of treating the subject is involved a principle which\nbelongs to the Third Law of Motion, namely, the doctrine\nthat the velocity is as the force, of which we shall have to\nspeak elsewhere.]\n\n5. _The Third Law of Motion._--We have, in the definition of\nAccelerating Force, a measure of Forces, so far as they are\nconcerned in producing motion. We had before, in speaking of\nthe principles of statics, defined the measure of Forces or\nPressures, so far as they are employed in producing\nequilibrium. But these two aspects of Force are closely\nconnected; and we require a law which shall lay down the\nrule of their connexion. By the same kind of muscular\nexertion by which we can support a heavy stone, we can also\nput it in motion. The question then occurs, how is the rate\nand manner of its motion determined? The answer to this\nquestion is contained in the Third Law {250} of Motion, and\nit is to this effect: that the _Momentum_ which any pressure\nproduces in the mass in a given time is proportional to the\npressure. By _Momentum_ is meant the product of the numbers\nwhich express the velocity and the mass of the body: and\nhence, if the mass of the body be the same in the instances\nwhich we compare, the rule is,--That _the velocity is as the\nforce which produces it_; and this is one of the simplest\nways of expressing the Third Law of Motion.\n\nIn agreement with our general plan, we have to ask, What is\nthe ground of this rule? What is the simplest and most\nsatisfactory form to which we can reduce the proof of it?\nOr, to take an instance; if a double pressure be exerted\nagainst a given mass, so disposed as to be capable of\nmotion, why must it produce twice the velocity in the same time?\n\nTo answer this question, suppose the double pressure to be\nresolved into two single pressures: one of these will\nproduce a certain velocity; and the question is, why an\nequal pressure, acting upon the same mass, will produce an\nequal velocity _in addition_ to the former? Or, stating the\nmatter otherwise, the question is, why each of the two\nforces will produce its separate effect, unaltered by the\nsimultaneous action of the other force?\n\nThis statement of the case makes it seem to approach very\nnear to such cases as are included in the Second Law of\nMotion, and therefore it might appear that this Third Law\nhas no grounds distinct from the Second. But it must be\nrecollected that the word _force_ has a different meaning in\nthis case and in that; in this place it signifies\n_pressure_; in the statement of the Second Law its import\nwas _accelerative_ or _deflective force_, measured by the\nvelocity or deflexion generated. And thus the Third Law of\nMotion, so far as our reasonings yet go, appears to rest on\na foundation different from the Second.\n\nAccordingly, that part of the Third Law of Motion which we\nare now considering, that the velocity generated is as the\nforce, was obtained, in fact, by a separate train of\nresearch. The first exemplification of this {251} law which\nwas studied by mathematicians, was the motion of bodies upon\ninclined planes: for the force which urges a body down an\ninclined plane is known by statics, and hence the velocity\nof its descent was to be determined. Galileo\noriginally[30\\3] in his attempts to solve this problem of\nthe descent of a body down an inclined plane, did not\nproceed from the principle which we have stated, (the\ndetermination of the force which acts down the inclined\nplane from statical considerations,) obvious as it may seem;\nbut assumed, as we have already seen, a proposition\napparently far more precarious;--namely, that a body sliding\ndown a smooth inclined plane acquires always the same\nvelocity, so long as the _vertical_ height fallen through is\nthe same. And this conjecture (for at first it was nothing\nmore than a conjecture) he confirmed by an ingenious\nexperiment; in which bodies acquired or lost the same\nvelocity by descending or ascending through the same height,\nalthough their paths were different in other respects.\n\n[Note 30\\3: _Dial. della Sc. Nuov._ iii. p. 96. See _Hist.\nInd. Sci._ b. vi. c. ii. sect. 5.]\n\nThis was the form in which the doctrine of the motion of\nbodies down inclined planes was at first presented in\nGalileo's _Dialogues_ on the Science of Motion. But his\ndisciple Viviani was dissatisfied with the assumption thus\nintroduced; and in succeeding editions of the _Dialogues_,\nthe apparent chasm in the reasoning was much narrowed, by\nmaking the proof depend upon a principle nearly identical\nwith the third law of motion as we have just stated it. In\nthe proof thus added, 'We are agreed,' says the\ninterlocutor[31\\3], 'that in a moving body the impetus,\nenergy, momentum, or propension to motion, is as great as is\nthe force or least resistance which suffices to sustain it;'\nand the impetus or momentum, in the course of the proof,\nbeing taken to be as the velocity produced in a given time,\nit is manifest that the principle so stated amounts to this;\nthat the velocity produced is as the statical force. And\nthus this law of motion appears, {252} in the school of\nGalileo, to have been suggested and established at first by\nexperiment, but afterwards confirmed and demonstrated by _\u00e0\npriori_ considerations.\n\n[Note 31\\3: _Dialogo_, p. 104.]\n\nWe see, in the above reasoning, a number of abstract terms\nintroduced which are not, at first at least, very distinctly\ndefined, as _impetus_, _momentum_, &c. Of these, _momentum_\nhas been selected, to express that quantity which, in a\nmoving body, measures the statical force impressed upon the\nbody. This quantity is, as we have just seen, proportional\nto the velocity in a given body. It is also, in different\nbodies, proportional to the mass of the body. This part of\nthe third law of motion follows from our conception of\nmatter in general as consisting of parts capable of\naddition. A double pressure must be required to produce the\nsame velocity in a double mass; for if the mass be halved,\neach half will require an equal pressure; and the addition,\nboth of the pressures and of the masses, will take place\nwithout disturbing the effects.\n\nThe measure of the quantity of matter of a body considered\nas affecting the velocity which pressure produces in the\nbody, is termed its _inertia_, as we have already stated (c.\nv.). Inertia is the property by which a large mass of matter\nrequires a greater force than a small mass, to give it an\nequal velocity. It belongs to each portion of matter; and\nportions of inertia are added whenever portions of matter\nare added. Hence _inertia is as the quantity of matter_;\nwhich is only another way of expressing this third law of\nmotion, so far as quantity of matter is concerned.\n\nBut how do we know the quantity of matter of a body? We may\nreply, that we take the weight as the measure of the\nquantity of matter: but we may then be again asked, how it\nappears that the weight is proportional to the inertia;\nwhich it must be, in order that the quantity of matter may\nbe proportional to both one and the other. We answer, that\nthis appears to be true experimentally, because all bodies\nfall with equal velocities by gravity, when the known causes\nof difference are removed. The observations of falling {253}\nbodies, indeed, are not susceptible of much exactness: but\nexperiments leading to the same result, and capable of great\nprecision, were made upon pendulums by Newton; as he relates\nin his _Principia_, Book III. prop. 6. They all agreed, he\nsays, with perfect accuracy: and thus the weight and the\ninertia are proportional in all cases, and therefore each\nproportional to the quantity of matter as measured by the other.\n\nThe conception of inertia, as we have already seen in\nchapter V., involves the notion of action and reaction; and\nthus the laws which involve inertia depend upon the idea of\nmutual causation. The rule, that the velocity is as the\nforce, depends upon the principle of causation, that the\neffect is proportional to the cause; the effect being here\nso estimated as to be consistent both with the other laws of\nmotion and with experiment.\n\nBut here, as in other cases, the question occurs again; Is\nexperiment really requisite for the proof of this law? If we\nlook to authorities, we shall be not a little embarrassed to\ndecide. D'Alembert is against the necessity of experimental\nproof. 'Why,' says he[32\\3], 'should we have recourse to\nthis principle employed, at the present day, by everybody,\nthat the force is proportional to the velocity? ... a\nprinciple resting solely upon this vague and obscure axiom,\nthat the effect is proportional to the cause. We shall not\nexamine here,' he adds, 'if this principle is necessarily\ntrue; we shall only avow that the proofs which have hitherto\nbeen adduced do not appear to us unexceptionable: nor shall\nwe, with some geometers, adopt it as a purely contingent\ntruth; which would be to ruin the certainty of mechanics,\nand to reduce it to be nothing more than an experimental\nscience. We shall content ourselves with observing,' he\nproceeds, 'that certain or doubtful, clear or obscure, it is\nuseless in mechanics, and consequently ought to be banished\nfrom the science.' Though D'Alembert rejects the third law\nof motion in this form, he accepts one of {254} equivalent\nimport, which appears to him to possess axiomatic certainty;\nand this procedure is in consistence with the course which\nhe takes, of claiming for the science of mechanics more than\nmere experimental truth. On the contrary, Laplace considers\nthis third law as established by experiment. 'Is the force,'\nhe says'[33\\3], 'proportioned to the velocity? This,' he\nreplies, 'we cannot know _\u00e0 priori_, seeing that we are in\nignorance of the nature of moving force: we must therefore,\nfor this purpose, recur to experience; for all which is not\na necessary consequence of the few data we have respecting\nthe nature of things, is, for us, only a result of\nobservation.' And again he says[34\\3], 'Here, then, we have\ntwo laws of motion,--the law of inertia [the first law of\nmotion], and the law of the force proportional to the\nvelocity,--which are given by observation. They are the most\nnatural and the most simple laws which we can imagine, and\nwithout doubt they flow from the very nature of matter; but\nthis nature being unknown, they are, for us, only observed\nfacts: the only ones, however, which Mechanics borrows from\nexperience.'\n\n[Note 32\\3: _Dynamique_, Pref. p. x.]\n\n[Note 33\\3: _M\u00e9c. C\u00e9l._ p. 15.]\n\n[Note 34\\3: p. 18.]\n\nIt will appear, I think, from the views given in this and\nseveral other parts of the present work, that we cannot with\njustice say that we have very 'few data respecting the\nnature of things,' in speculating concerning the laws of the\nuniverse; since all the consequences which flow from the\nrelations of our fundamental ideas, necessarily regulate our\nknowledge of things, so far as we have any such knowledge.\nNor can we say that the nature of matter is unknown to us,\nin any sense in which we can conceive knowledge as possible.\nThe nature of matter is no more unknown than the nature of\nspace or of number. In our conception of matter, as of space\nand of number, are involved certain relations, which are the\nnecessary groundwork of our knowledge; and anything which is\nindependent of these relations, is not unknown, but\ninconceivable. {255}\n\nIt must be already clear to the reader, from the phraseology\nemployed by these two eminent mathematicians, that the\nquestion respecting the formation of the third law of motion\ncan only be solved by a careful consideration of what we\nmean by observation and experience, nature and matter. But\nit will probably be generally allowed, that, taking into\naccount the explanations already offered of the necessary\nconditions of experience and of the conception of inertia,\nthis law of motion, that the inertia is as the quantity of\nmatter, is almost or altogether self-evident.\n\n6. _Action and Reaction are Equal in Moving Bodies._--When\nwe have to consider bodies as acting upon one another, and\ninfluencing each other's motions, the third law of motion is\nstill applied; but along with this, we also employ the\ngeneral principle that action and reaction are equal and\nopposite. Action and reaction are here to be understood as\nmomentum produced and destroyed, according to the measure of\naction established by the Third Law of Motion: and the cases\nin which this principle is thus employed form so large a\nportion of those in which the third law of motion is used,\nthat some writers (Newton at the head of them) have\nstated the equality of action and reaction as the third law\nof motion.\n\nThe third law of motion being once established, the equality\nof action and reaction, in the sense of momentum gained and\nlost, necessarily follows. Thus, if a weight hanging by a\nstring over the edge of a smooth level table draw another\nweight along the table, the hanging weight moves more slowly\nthan it would do if not so connected, and thus loses\nvelocity by the connexion; while the other weight gains by\nthe connexion all the velocity which it has, for if left to\nitself it would rest. And the pressures which restrain the\ndescent of the first body and accelerate the motion of the\nsecond, are equal at all instants of time, for each of these\npressures is the tension of the string: and hence, by the\nthird law of motion, the momentum gained by the one body,\nand the momentum lost by the other in virtue of the action\nof this string, are equal. And similar {256} reasoning may\nbe employed in any other case where bodies are connected.\n\nThe case where one body does not push or draw, but _strikes_\nanother, appeared at first to mechanical reasoners to be of\na different nature from the others; but a little\nconsideration was sufficient to show that a blow is, in\nfact, only a short and violent pressure; and that,\ntherefore, the general rule of the equality of momentum lost\nand gained applies to this as well as to the other cases.\n\nThus, in order to determine the case of the direct action of\nbodies upon one another, we require no new law of motion.\nThe equality of action and reaction, which enters\nnecessarily into every conception of mechanical operation,\ncombined with the measure of action as given by the third\nlaw of motion, enables us to trace the consequences of every\ncase, whether of pressure or of impact.\n\n7. _D'Alembert's Principle._--But what will be the result\nwhen bodies do not act directly upon each other, but are\n_indirectly_ connected in any way by levers, strings,\npulleys, or in any other manner, so that one part of the\nsystem has a mechanical advantage over another? The result\nmust still be determined by the principle that action and\nreaction balance each other. The action and reaction, being\npressures in one sense, must balance each other by the laws\nof statics, for these laws determine the equilibrium of\npressure. Now action and reaction, according to their\nmeasures in the Third Law of Motion, are momentum gained and\nlost, when the action is direct; and except the indirect\naction introduce some modification of the law, they must\nhave the same measure still. But, in fact, we cannot well\nconceive any modification of the law to take place in this\ncase; for direct action is only one (the ultimate) case of\nindirect action. Thus if two heavy bodies act at different\npoints of a lever, the action of each on the other is\nindirect; but if the two points come together, the action\nbecomes direct. Hence the rule must be that which we have\nalready stated; for if the rule were false for indirect\naction, it would {257} also be false for direct action, for\nwhich case we have shown it to be true. And thus we obtain\nthe general principle, that in any system of bodies which\nact on each other, action and reaction, estimated by\nmomentum gained and lost, balance each other according to\nthe laws of equilibrium. This principle, which is so general\nas to supply a key to the solution of all possible\nmechanical problems, is commonly called _D'Alembert's\nPrinciple_. The experimental proofs which convinced men of\nthe truth of the Third Law of Motion were, many or most of\nthem, proofs of the law in this extended sense. And thus the\nproof of D'Alembert's Principle, both from the idea of\nmechanical action and from experience, is included in the\nproof of the law already stated.\n\n8. _Connexion of Dynamical and Statical Principles._--The\nprinciple of equilibrium of D'Alembert just stated, is the\nlaw which he would substitute for the Third Law of Motion;\nand he would thus remove the necessity for an independent\nproof of that law. In like manner, the Second Law of Motion\nis by some writers derived from the principle of the\ncomposition of statical forces; and they would thus\nsupersede the necessity of a reference to experiment in that\ncase. Laplace takes this course, and thus, as we have seen,\nrests only the First and Third Law of Motion upon\nexperience. Newton, on the other hand, recognizes the same\nconnexion of propositions, but for a different purpose; for\nhe derives the composition of statical forces from the\nSecond Law of Motion.\n\nThe close connexion of these three principles, the\ncomposition of (statical) forces, the composition of\n(accelerating) forces with velocities, and the measure of\n(moving) forces by velocities, cannot be denied; yet it\nappears to be by no means easy to supersede the necessity of\nindependent proofs of the last two of these principles. Both\nmay be proved or illustrated by experiment: and the\nexperiments which prove the one are different from those\nwhich establish the other. For example, it appears by easy\ncalculations, that when we apply our principles to the\noscillations of a pendulum, {258} the Second Law is proved\nby the fact, that the oscillations take place at the same\nrate in an east and west, and in a north and south\ndirection: under the same circumstances, the Third Law is\nproved by our finding that the time of a small oscillation\nis proportional to the square root of the length of a\npendulum; and similar differences might be pointed out in\nother experiments, as to their bearing upon the one law or\nthe other.\n\n9. _Mechanical Principles become gradually more simple and\nmore evident._--I will again point out in general two\ncircumstances which I have already noticed in particular\ncases of the laws of motion.--Truths are often at first\nassumed in a form which is far from being the most obvious\nor simple;--and truths once discovered are gradually\nsimplified, so as to assume the appearance of self-evident\ntruths.\n\nThe former circumstance is exemplified in several of the\ninstances which we have had to consider. The assumption,\nthat a perpetual motion is impossible, preceded the\nknowledge of the first law of motion. The assumed equality\nof the velocities acquired down two inclined planes of the\nsame height, was afterwards reduced to the third law of\nmotion by Galileo himself. In the History[35\\3], we have\nnoted Huyghens's assumption of the equality of the actual\ndescent and potential ascent of the center of gravity: this\nwas afterwards reduced by Herman and the Bernoullis, to the\nstatical equivalence of the solicitations of gravity and the\nvicarious solicitations of the effective forces which act on\neach point; and finally to the principle of D'Alembert,\nwhich asserts that the motions gained and lost balance each\nother.\n\n[Note 35\\3: B. vi. c. v. sect. 2.]\n\nThis early assertion of principles which now appear neither\nobvious nor self-evident, is not to be considered as a\ngroundless assumption on the part of the discoverers by whom\nit was made. On the contrary, it is evidence of the deep\nsagacity and clear thought which were {259} requisite in\norder to make such discoveries. For these results are really\nrigorous consequences of the laws of motion in their\nsimplest form: and the evidence of them was probably\npresent, though undeveloped, in the minds of the\ndiscoverers. We are told of geometrical students, who, by a\npeculiar aptitude of mind, perceived the evidence of some of\nthe more advanced propositions of geometry without going\nthrough the introductory steps. We must suppose a similar\naptitude for mechanical reasonings, which, existing in the\nminds of Stevinus, Galileo, Newton, and Huyghens, led them\nto make those assumptions which finally resolved themselves\ninto the laws of motion.\n\nWe may observe further, that the simplicity and evidence\nwhich the laws of mechanics have at length assumed, are much\nfavoured by the usage of words among the best writers on\nsuch subjects. Terms which originally, and before the laws\nof motion were fully known, were used in a very vague and\nfluctuating sense, were afterwards limited and rendered\nprecise, so that assertions which at first appear identical\npropositions become distinct and important principles. Thus\n_force_, _motion_, _momentum_, are terms which were\nemployed, though in a loose manner, from the very outset of\nmechanical speculation. And so long as these words retained\nthe vagueness of common language, it would have been a\nuseless and barren truism to say that 'the momentum is\nproportional to the force,' or that 'a body loses as much\nmotion as it communicates to another.' But when 'momentum'\nand 'quantity of motion' are defined to mean the product of\nmass and velocity, these two propositions immediately become\ndistinct statements of the third law of motion and its\nconsequences. In like manner, the assertion that 'gravity is\na uniform force' was assented to, before it was settled what\na uniform force was; but this assertion only became\nsignificant and useful when that point had been properly\ndetermined. The statement that 'when different motions are\ncommunicated to the same body their effects are {260}\ncompounded,' becomes the second law of motion, when we\ndefine what composition of motions is. And the same process\nmay be observed in other cases.\n\nAnd thus we see how well the form which science ultimately\nassumes is adapted to simplify knowledge. The definitions\nwhich are adopted, and the terms which become current in\nprecise senses, produce a complete harmony between the\nmatter and the form of our knowledge; so that truths which\nwere at first unexpected and recondite, became familiar\nphrases, and after a few generations sound, even to common\nears, like identical propositions.\n\n10. _Controversy of the Measure of Force._--In the History\nof Mechanics[36\\3], we have given an account of the\ncontroversy which, for some time, occupied the\nmathematicians of Europe, whether the forces of bodies in\nmotion should be reckoned proportional to the velocity, or\nto the square of the velocity. We need not here recall the\nevents of this dispute; but we may remark, that its history,\nas a metaphysical controversy, is remarkable in this\nrespect, that it has been finally and completely settled;\nfor it is now agreed among mathematicians that both sides\nwere right, and that the results of mechanical action may be\nexpressed with equal correctness by means of _momentum_ and\nof _vis viva_. It is, in one sense, as D'Alembert has\nsaid[37\\3], a dispute about words; but we are not to infer\nthat, on that account, it was frivolous or useless; for such\ndisputes are one principal means of reducing the principles\nof our {261} knowledge to their utmost simplicity and\nclearness. The terms which are employed in the science of\nmechanics are now liberated for ever, in the minds of\nmathematicians, from that ambiguity which was the\nbattleground in the war of the _vis viva_.\n\n[Note 36\\3: B. vi. c. v. sect. 2.]\n\n[Note 37\\3: D'Alembert has also remarked (_Dynamique_, Pref.\nxxi.) that this controversy 'shows how little justice and\nprecision there is in the pretended axiom that causes are\nproportional to their effects.' But this reflection is by no\nmeans well founded. For since both measures are true, it\nappears that causes may be _justly_ measured by their\neffects, even when very different kinds of effects are\ntaken. That the axiom does not point out one _precise_\nmeasure, till illustrated by experience or by other\nconsiderations, we grant: but the same thing occurs in the\napplication of other axioms also.]\n\nBut we may observe that the real reason of this controversy\nwas exactly that tendency which we have been noticing;--the\ndisposition of man to assume in his speculations certain\ngeneral propositions as true, and to fix the sense of terms\nso that they shall fall in with this truth. It was agreed,\non all hands, that in the mutual action of bodies the same\nquantity of force is always preserved; and the question was,\nby which of the two measures this rule could best be\nverified. We see, therefore, that the dispute was not\nconcerning a definition merely, but concerning a definition\ncombined with a general proposition. Such a question may be\nreadily conceived to have been by no means unimportant; and\nwe may remark, in passing, that such controversies, although\nthey are commonly afterwards stigmatized as quarrels about\nwords and definitions, are, in reality, events of\nconsiderable consequence in the history of science; since\nthey dissipate all ambiguity and vagueness in the use of\nterms, and bring into view the conditions under which the\nfundamental principles of our knowledge can be most clearly\nand simply presented.\n\nIt is worth our while to pause for a moment on the prospect\nthat we have thus obtained, of the advance of knowledge, as\nexemplified in the history of Mechanics. The general\ntransformation of our views from vague to definite, from\ncomplex to simple, from unexpected discoveries to\nself-evident truths, from seeming contradictions to\nidentical propositions, is very remarkable, but it is by no\nmeans peculiar to our subject. The same circumstances, more\nor less prominent, more or less developed, appear in the\nhistory of other sciences, according to the point of advance\nwhich each has reached. They bear upon very important\ndoctrines respecting the prospects, the {262} limits, and\nthe very nature of our knowledge. And though these doctrines\nrequire to be considered with reference to the whole body of\nscience, yet the peculiar manner in which they are\nillustrated by the survey of the history of Mechanics, on\nwhich we have just been engaged, appears to make this a\nconvenient place for introducing them to the reader.\n\n\n\n{{263}}\nCHAPTER VIII.\n\nOF THE PARADOX OF UNIVERSAL PROPOSITIONS OBTAINED FROM\nEXPERIENCE.\n\n\n1. IT was formerly stated[38\\3] that experience cannot\nestablish any universal or necessary truths. The number of\ntrials which we can make of any proposition is necessarily\nlimited, and observation alone cannot give us any ground of\nextending the inference to untried cases. Observed facts\nhave no visible bond of necessary connexion, and no exercise\nof our senses can enable us to discover such connexion. We\ncan never acquire from a mere observation of facts, the\nright to assert that a proposition is true in all cases, and\nthat it could not be otherwise than we find it to be.\n\n[Note 38\\3: B. i. c. iv. Of Experience]\n\nYet, as we have just seen in the history of the laws of\nmotion, we may go on collecting our knowledge from\nobservation, and enlarging and simplifying it, till it\napproaches or attains to complete universality and seeming\nnecessity. Whether the laws of motion, as we now know them,\ncan be rigorously traced to an absolute necessity in the\nnature of things, we have not ventured absolutely to\npronounce. But we have seen that some of the most acute and\nprofound mathematicians have believed that, for these laws\nof motion, or some of them, there was such a demonstrable\nnecessity compelling them to be such as they are, and no\nother. Most of those who have carefully studied the\nprinciples of Mechanics will allow that some at least of the\nprimary laws of motion approach very near to this character\nof necessary truth; and will confess that it would be\ndifficult to imagine any other consistent {264} scheme of\nfundamental principles. And almost all mathematicians will\nallow to these laws an absolute universality; so that we may\napply them without scruple or misgiving, in cases the most\nremote from those to which our experience has extended. What\nastronomer would fear to refer to the known laws of motion,\nin reasoning concerning the double stars; although these\nobjects are at an immeasurably remote distance from that\nsolar system which has been the only field of our\nobservation of mechanical facts? What philosopher, in\nspeculating respecting a magnetic fluid, or a luminiferous\nether, would hesitate to apply to it the mechanical\nprinciples which are applicable to fluids of known\nmechanical properties? When we assert that the quantity of\nmotion in the world cannot be increased or diminished by the\nmutual actions of bodies, does not every mathematician feel\nconvinced that it would be an unphilosophical restriction to\nlimit this proposition to such modes of action as we have tried?\n\nYet no one can doubt that, in historical fact, these laws\nwere collected from experience. That such is the case, is no\nmatter of conjecture. We know the time, the persons, the\ncircumstances, belonging to each step of each discovery. I\nhave, in the History, given an account of these discoveries;\nand in the previous chapters of the present work, I have\nfurther examined the nature and the import of the principles\nwhich were thus brought to light.\n\nHere, then, is an apparent contradiction. Experience, it\nwould seem, has done that which we had proved that she\ncannot do. She has led men to propositions, universal at\nleast, and to principles which appear to some persons\nnecessary. What is the explanation of this contradiction,\nthe solution of this paradox? Is it true that Experience can\nreveal to us universal and necessary truths? Does she\npossess some secret virtue, some unsuspected power, by which\nshe can detect connexions and consequences which we have\ndeclared to be out of her sphere? Can she see more than mere\nappearances, and observe more than mere facts? Can {265} she\npenetrate, in some way, to the nature of things?--descend\nbelow the surface of phenomena to their causes and origins,\nso as to be able to say what can and what can not be;--what\noccurrences are partial, and what universal? If this be so,\nwe have indeed mistaken her character and powers; and the\nwhole course of our reasoning becomes precarious and\nobscure. But, then, when we return upon our path we cannot\nfind the point at which we deviated, we cannot detect the\nfalse step in our deduction. It still seems that by\nexperience, strictly so called, we cannot discover necessary\nand universal truths. Our senses can give us no evidence of\na necessary connexion in phenomena. Our observation must be\nlimited, and cannot testify concerning anything which is\nbeyond its limits. A general view of our faculties appears\nto prove it to be impossible that men should do what the\nhistory of the science of mechanics shows that they have done.\n\n2. But in order to try to solve this Paradox, let us again\nrefer to the History of Mechanics. In the cases belonging to\nthat science, in which propositions of the most\nunquestionable universality, and most approaching to the\ncharacter of necessary truths, (as, for instance, the laws\nof motion,) have been arrived at, what is the source of the\naxiomatic character which the propositions thus assume? The\nanswer to this question will, we may hope, throw some light\non the perplexity in which we appear to be involved.\n\nNow the answer to this inquiry is, that the laws of motion\nborrow their axiomatic character from their being merely\n_interpretations_ of the Axioms of Causation. Those axioms,\nbeing exhibitions of the Idea of Cause under various\naspects, are of the most rigorous universality and\nnecessity. And so far as the laws of motion are\nexemplifications of those axioms, these laws must be no less\nuniversal and necessary. How these axioms are to be\nunderstood;--in what sense _cause_ and _effect_, _action_\nand _reaction_, are to be taken, experience and observation\ndid, in fact, teach inquirers on this subject; and without\nthis teaching, the laws of motion could never have been\ndistinctly known. If two forces {266} act together, each\nmust produce its effect, by the axiom of causation; and,\ntherefore, the effects of the separate forces must be\n_compounded_. But a long course of discussion and experiment\nmust instruct men of what kind this _composition_ of forces\nis. Again; action and reaction must be equal; but much\nthought and some trial were needed to show what _action_ and\n_reaction_ are. Those metaphysicians who enunciated Laws of\nmotion without reference to experience, propounded only such\nlaws as were vague and inapplicable. But yet these persons\nmanifested the indestructible conviction, belonging to man's\nspeculative nature, that there exist Laws of motion, that\nis, universal formul\u00e6, connecting the causes and effects\nwhen motion takes place. Those mechanicians, again, who,\nobserved facts involving equilibrium and motion, and stated\nsome narrow rules, without attempting to ascend to any\nuniversal and simple principle, obtained laws no less barren\nand useless than the metaphysicians; for they could not tell\nin what new cases, or whether in any, their laws would be\nverified;--they needed a more general rule, to show them the\nlimits of the rule they had discovered. They went wrong in\neach attempt to solve a new problem, because their\ninterpretation of the terms of the axioms, though true,\nperhaps, in certain cases, was not right in general.\n\nThus Pappus erred in attempting to interpret as a case of\nthe lever, the problem of supporting a weight upon an\ninclined plane; thus Aristotle erred in interpreting the\ndoctrine that the weight of bodies is the cause of their\nfall; thus Kepler erred in interpreting the rule that the\nvelocity of bodies depends upon the force; thus\nBernoulli[39\\3] erred in interpreting the equality of action\nand reaction upon a lever in motion. In each of these\ninstances, true doctrines, already established, (whether by\nexperiment or otherwise,) were erroneously applied. And the\nerror was corrected by further reflection, which pointed out\nthat another mode of interpretation was requisite, in order\nthat the axiom {267} which, was appealed to in each case\nmight retain its force in the most general sense. And in the\nreasonings which avoided or corrected such errors, and which\nled to substantial general truths, the object of the\nspeculator always was to give to the acknowledged maxims\nwhich the Idea of Cause suggested, such a signification as\nshould be consistent with their universal validity. The rule\nwas not accepted as particular at the outset, and afterwards\ngeneralized more and more widely; but from the very first,\nthe universality of the rule was assumed, and the question\nwas, how it should be understood so as to be universally\ntrue. At every stage of speculation, the law was regarded as\na general law. This was not an aspect which it gradually\nacquired, by the accumulating contributions of experience,\nbut a feature of its original and native character. _What_\nshould happen universally, experience might be needed to\nshow: but that what happened should happen _universally_,\nwas implied in the nature of knowledge. The universality of\nthe laws of motion was not gathered from experience, however\nmuch the laws themselves might be so.\n\n[Note 39\\3: _Hist. Ind. Sc._ b. vi. c. v. sect. 2.]\n\n3. Thus we obtain the solution of our Paradox, so far as the\ncase before us is concerned. The laws of motion borrow their\n_form_ from the Idea of Causation, though their _matter_ may\nbe given by experience: and hence they possess a\nuniversality which experience cannot give. They are\ncertainly and universally valid; and the only question for\nobservation to decide is, how they are to be understood.\nThey are like general mathematical formul\u00e6, which are known\nto be true, even while we are ignorant what are the unknown\nquantities which they involve. It must be allowed, on the\nother hand, that so long as these formul\u00e6 are not\ninterpreted by a real study of nature, they are not only\nuseless but prejudicial; filling men's minds with vague\ngeneral terms, empty maxims, and unintelligible\nabstractions, which they mistake for knowledge. Of such\nperversion of the speculative propensities of man's nature,\nthe world has seen too much in all ages. Yet we must not, on\nthat account, despise these forms of {268} truth, since\nwithout them, no general knowledge is possible. Without\ngeneral terms, and maxims, and abstractions, we can have no\nscience, no speculation; hardly, indeed, consistent thought\nor the exercise of reason. The course of real knowledge is,\nto obtain from thought and experience the right\ninterpretation of our general terms, the real import of our\nmaxims, the true generalizations which our abstractions\ninvolve.\n\n4. If it be asked, How Experience is able to teach us to\ninterpret aright the general terms which the Axioms of\nCausation involve;--whence she derives the light which she\nis to throw on these general notions; the answer is\nobvious;--namely, that the relations of causation are the\n_conditions_ of Experience;--that the general notions are\n_exemplified_ in the particular cases of which she takes\ncognizance. The events which take place about us, and which\nare the objects of our observation, we cannot conceive\notherwise than as subject to the laws of cause and effect.\nEvery event must have a cause;--Every effect must be\ndetermined by its cause;--these maxims are true of the\nphenomena which form the materials of our experience. It is\nprecisely to them, that these truths apply. It is in the\nworld which we have before our eyes, that these propositions\nare universally verified; and it is therefore by the\nobservation of what we see, that we must learn how these\npropositions are to be understood. Every fact, every\nexperiment, is an example of these statements; and it is\ntherefore by attention to and familiarity with facts and\nexperiments, that we learn the signification of the\nexpressions in which the statements are made; just as in any\nother case we learn the import of language by observing the\nmanner in which it is applied in known cases. Experience is\nthe interpreter of nature; it being understood that she is\nto make her interpretation in that comprehensive phraseology\nwhich is the genuine language of science.\n\n5. We may return for an instant to the objection, that\nexperience cannot give us general truths, since, after any\nnumber of trials confirming a rule, we may for aught we can\nforesee, have one which violates the {269} rule. When we\nhave seen a thousand stones fall to the ground, we may see\none which does not fall under the same apparent\ncircumstances. How then, it is asked, can experience teach\nus that _all_ stones, rigorously speaking, will fall if\nunsupported? And to this we reply, that it is not true that\nwe can conceive one stone to be suspended in the air, while\na thousand others fall, without believing some peculiar\ncause to support it; and that, therefore, such a supposition\nforms no exception to the law, that gravity is a force by\nwhich _all_ bodies are urged downwards. Undoubtedly we can\nconceive a body, when dropt or thrown, to move in a line\nquite different from other bodies: thus a certain\nmissile[40\\3] used by the natives of Australia, and lately\nbrought to this country, when thrown from the hand in a\nproper manner, describes a curve, and returns to the place\nfrom whence it was thrown. But did any one, therefore, even\nfor an instant suppose that the laws of motion are different\nfor this and for other bodies? On the contrary, was not\nevery person of a speculative turn immediately led to\ninquire how it was that the known causes which modify\nmotion, the resistance of the air and the other causes,\nproduced in this instance so peculiar an effect? And if the\nmotion had been still more unaccountable, it would not have\noccasioned any uncertainty whether it were consistent with\nthe agency of gravity and the laws of motion. If a body\nsuddenly alter its direction, or move in any other\nunexpected manner, we never doubt that there is a cause of\nthe change. We may continue quite ignorant of the nature of\nthis cause, but this ignorance never occasions a moment's\ndoubt that the cause exists and is exactly suited to the\neffect. And thus experience can prove or discover to us\ngeneral rules, but she can never prove that general rules do\nnot exist. Anomalies, exceptions, unexplained phenomena, may\nremind us that we have much still to learn, but they can\nnever make us suppose that truths are not universal. We may\nobserve facts that show us we have not fully {270}\nunderstood the meaning of our general laws, but we can never\nfind facts which show our laws to have no meaning. Our\nexperience is bound in by the limits of cause and effect,\nand can give us no information concerning any region where\nthat relation does not prevail. The whole series of external\noccurrences and objects, through all time and space, exists\nonly, and is conceived only, as subject to this relation;\nand therefore we endeavour in vain to imagine to ourselves\nwhen and where and how exceptions to this relation may\noccur. The assumption of the connexion of cause and effect\nis essential to our experience, as the recognition of the\nmaxims which express this connexion is essential to our\nknowledge.\n\n[Note 40\\3: Called the Bo-me-rang.]\n\n6. I have thus endeavoured to explain in some measure how,\nat least in the field of our mechanical knowledge,\nexperience can discover universal truths, though she cannot\ngive them their universality; and how such truths, though\nborrowing their form from our ideas, cannot be understood\nexcept by the actual study of external nature. And thus with\nregard to the laws of motion, and other fundamental\nprinciples of Mechanics, the analysis of our ideas and the\nhistory of the progress of the science well illustrate each\nother.\n\nIf the paradox of the discovery of universal truths by\nexperience be thus solved in one instance, a much wider\nquestion offers itself to us;--How far the difficulty, and\nhow far the solution, are applicable to other subjects. It\nis easy to see that this question involves most grave and\nextensive doctrines with regard to the whole compass of\nhuman knowledge: and the views to which we have been led in\nthe present Book of this work are, we trust, fitted to throw\nmuch light upon the general aspect of the subject. But after\ndiscussions so abstract, and perhaps obscure, as those in\nwhich we have been engaged for some chapters, I willingly\npostpone to a future occasion an investigation which may\nperhaps appear to most readers more recondite and difficult\nstill. And we have, in fact, many other special fields of\nknowledge to survey, before we are led by the order of our\nsubject, to {271} those general questions and doctrines,\nthose antitheses brought into view and again resolved, which\na view of the whole territory of human knowledge suggests,\nand by which the nature and conditions of knowledge are\nexhibited.\n\nBefore we quit the subject of mechanical science we shall\nmake a few remarks on another doctrine which forms part of\nthe established truths of the science, namely, the doctrine\nof universal gravitation.\n\n\n\n{{272}}\nCHAPTER IX.\n\nOF THE ESTABLISHMENT OF THE LAW OF UNIVERSAL GRAVITATION.\n\n\nTHE doctrine of universal gravitation is a feature of so\nmuch importance in the history of science that we shall not\npass it by without a few remarks on the nature and evidence\nof the doctrine.\n\n1. To a certain extent the doctrine of the attraction of\nbodies according to the law of the inverse square of the\ndistance, exhibits in its progress among men the same\ngeneral features which we have noticed in the history of the\nlaws of motion. This doctrine was maintained _\u00e0 priori_ on\nthe ground of its simplicity, and was asserted positively,\neven before it was clearly understood:--notwithstanding this\nanticipation, its establishment on the ground of facts was a\ntask of vast labour and sagacity:--when it had been so\nestablished in a general way, there occurred at later\nperiods, an occasional suspicion that it might be\napproximately true only:--these suspicions led to further\nresearches, which showed the rule to be rigorously\nexact:--and at present there are mathematicians who\nmaintain, not only that it is true, but that it is a\nnecessary property of matter. A very few words on each of\nthese points will suffice.\n\n2. I have shown in the _History of Science_[41\\3], that the\nattraction of the sun according to the inverse square of the\ndistance, had been divined by Bullialdus, Hooke, Halley, and\nothers, before it was proved by Newton. Probably the reason\nwhich suggested this conjecture was, that gravity might be\nconsidered {273} as a sort of emanation; and that thus, like\nlight or any other effect diffused from a center, it must\nfollow the law just stated, the efficacy of the force being\nweakened in receding from the center, exactly in proportion\nto the space through which it is diffused. It cannot be\ndenied that such a view appears to be strongly recommended\nby analogy.\n\n[Note 41\\3: B. vii. c. i.]\n\nWhen it had been proved by Newton that the planets were\nreally retained in their elliptical orbits by a central\nforce, his calculations also showed that the above-stated\n_law_ of the force must be at least very approximately\ncorrect, since otherwise the aphelia of the orbits could not\nbe so nearly at rest as they were. Yet when it seemed as if\nthe motion of the moon's apogee could not be accounted for\nwithout some new supposition, the _\u00e0 priori_ argument in\nfavour of the inverse square did not prevent Clairaut from\ntrying the hypothesis of a small term added to that which\nexpressed the ancient law: but when, in order to test the\naccuracy of this hypothesis, the calculation of the motion\nof the moon's apogee was pushed to a greater degree of\nexactness than had been obtained before, it was found that\nthe new term vanished of itself; and that the inverse square\nnow accounted for the whole of the motion. And thus, as in\nthe case of the second law of motion, the most scrupulous\nexamination terminated in showing the simplest rule to be\nrigorously true.\n\n3. Similar events occurred in the history of another part of\nthe law of gravitation: namely, that the attraction is\nproportional to the quantity of matter attracted. This part\nof the law may also be thus stated, That the weight of\nbodies arising from gravity is proportional to their\ninertia; and thus, that the _accelerating force_ on all\nbodies under the same circumstances is the same. Newton made\nexperiments which proved this with regard to terrestrial\nbodies; for he found that, at the end of equal strings,\nballs of all substances, gold, silver, lead, glass, wood,\n&c., oscillated in equal times[42\\3]. But a few years ago,\ndoubts {274} arose among the German astronomers whether this\nlaw was rigorously true with regard to the planetary bodies.\nSome calculations appeared to prove, that the attraction of\nJupiter as shown by the perturbations which he produces in\nthe small planets Juno, Vesta, and Pallas, was different\nfrom the attraction which he exerts on his own satellites.\nNor did there appear to these philosophers anything\ninconceivable in the supposition that the attraction of a\nplanet might be thus _elective_. But when Mr. Airy obtained\na more exact determination of the mass of Jupiter, as\nindicated by his effect on his satellites, it was found that\nthis suspicion was unfounded; and that there was, in this\ncase, no exception to the universality of the rule, that\nthis cosmical attraction is in the proportion of the\nattracted mass.\n\n[Note 42\\3: _Prin._ lib. iii. prop. 6.]\n\n4. Again: when it had thus been shown that a mutual\nattraction of parts, according to the law above mentioned,\nprevailed throughout the extent of the solar system, it\nmight still be doubted whether the same law extended to\nother regions of the universe. It might have been perhaps\nimagined that each fixed star had its peculiar law of force.\nBut the examination of the motions of double stars about\neach other, by the two Herschels and others, appears to show\nthat these bodies describe ellipses as the planets do; and\nthus extends the law of the inverse squares to parts of the\nuniverse immeasurably distant from the whole solar system.\n\n5. Since every doubt which has been raised with regard to\nthe universality and accuracy of the law of gravitation, has\nthus ended in confirming the rule, it is not surprizing that\nmen's minds should have returned with additional force to\nthose views which had at first represented the law as a\nnecessary truth, capable of being established by reason\nalone. When it had been proved by Newton that gravity is\nreally a _universal_ attribute of matter as far as we can\nlearn, his pupils were not content without maintaining it to\nbe an _essential_ quality. This is the doctrine held by\nCotes in the preface to the second edition of the\n_Principia_ (1712): {275} 'Gravity,' he says, 'is a primary\nquality of bodies, as extension, mobility, and\nimpenetrability are.' But Newton himself by no means went so\nfar. In his second Letter to Bentley (1693), he says, 'You\nsometimes speak of gravity as essential and inherent to\nmatter; pray do not ascribe that notion to me. The cause of\ngravity,' he adds, 'I do not pretend to know, and would take\nmore time to consider of it.'\n\nCotes maintains his opinion by urging, that we learn by\n_experience_ that all bodies possess gravity, and that we do\nnot learn in any other way that they are extended, moveable,\nor solid. But we have already seen, that the ideas of space,\ntime, and reaction, on which depend extension, mobility, and\nsolidity, are not results, but conditions, of experience. We\ncannot conceive a body except as extended; we cannot\nconceive it to exert mechanical action except with some kind\nof solidity. But so far as our conceptions of body have\nhitherto been developed, we find no difficulty in conceiving\ntwo bodies which do not attract each other.\n\n6. Newton lays down, in the second edition of the\n_Principia_, this 'Rule of Philosophizing' (book iii.); that\n'The qualities of bodies which cannot be made more or less\nintense, and which belong to all bodies on which we are able\nto make experiments, are to be held to be qualities of all\nbodies in general.' And this Rule is cited in the sixth\nProposition of the Third Book of the _Principia_, (Cor. 2,)\nin order to prove that gravity, proportional to the quantity\nof matter, may be asserted to be a quality of all bodies\nuniversally. But we may remark that a Rule of\nPhilosophizing, itself of precarious authority, cannot\nauthorize us in ascribing universality to an empirical\nresult. Geometrical and statical properties are seen to be\nnecessary, and _therefore_ universal: but Newton appears\ndisposed to assert a like universality of gravity, quite\nunconnected with any necessity. It would be a very\ninadequate statement, indeed a false representation, of\nstatical truth, if we were to say, that because every body\nwhich has hitherto been tried _has been found_ to have a\ncenter of gravity, we venture to assert that all bodies\nwhatever {276} have a center of gravity. And if we are ever\nable to assert the absolute universality of the law of\ngravitation, we shall have to rest this truth upon the\nclearer development of our ideas of matter and force; not\nupon a Rule of Philosophizing, which, till otherwise proved,\nmust be a mere rule of prudence, and which the opponent may\nrefuse to admit.\n\n7. Other persons, instead of asserting gravity to be in its\nown nature essential to matter, have made hypotheses\nconcerning some mechanism or other, by which this mutual\nattraction of bodies is produced[43\\3]. Thus the Cartesians\nascribed to a vortex the tendency of bodies to a center;\nNewton himself seems to have been disposed to refer this\ntendency to the elasticity of an ether; Le Sage propounded a\ncurious hypothesis, in which this attraction is accounted\nfor by the impulse of infinite streams of particles flowing\nconstantly through the universe in all directions. In these\nspeculations, the force of gravity is resolved into the\npressure or impulse of solids or fluids. On the other hand,\nhypotheses have been propounded, in which the solidity, and\nother physical qualities of bodies, have been explained by\nrepresenting the bodies as a collection of points, from\nwhich points, repulsive, as well as attractive, forces\nemanate. This view of the constitution of bodies was\nmaintained and developed by Boscovich, and is hence termed\n'Boscovich's Theory:' and the discussion of it will more\nproperly come under our review at a future period, when we\nspeak of the question whether bodies are made up of atoms.\nBut we may observe, that Newton himself appears to have\ninclined, as his followers certainly did, to this mode of\ncontemplating the physical properties of bodies. In his\nPreface to the _Principia_, after speaking of the central\nforces which are exhibited in cosmical phenomena, he says:\n'Would that we could derive the other phenomena of Nature\nfrom mechanical principles by the same mode of reasoning.\nFor many things move me {277} so that I suspect all these\nphenomena may depend upon certain forces, by which the\nparticles of bodies, through causes not yet known, are\neither impelled to each other and cohere according to\nregular figures, or are repelled and recede from each other:\nwhich forces being unknown, philosophers have hitherto made\ntheir attempts upon nature in vain.'\n\n[Note 43\\3: See Vince, _Observations on the Hypothesis\nrespecting Gravitation_, and the Critique of that work,\n_Edinb. Rev._ vol. xiii.]\n\n8. But both these hypotheses;--that by which cohesion and\nsolidity are reduced to attractive and repulsive forces, and\nthat by which attraction is reduced to the impulse and\npressure of media;--are hitherto merely modes of\nrepresenting mechanical laws of nature; and cannot, either\nof them, be asserted as possessing any evident truth or\nperemptory authority to the exclusion of the other. This\nconsideration may enable us to estimate the real weight of\nthe difficulty felt in assenting to the mutual attraction of\nbodies not in contact with each other; for it is often urged\nthat this attraction of bodies at a distance is an absurd\nsupposition.\n\nThe doctrine is often thus stigmatized, both by popular and\nby learned writers. It was long received as a maxim in\nphilosophy (as Monboddo informs us[44\\3]), that a body\ncannot act _where_ it is not, any more than _when_ it is\nnot. But to this we reply, that time is a necessary\ncondition of our conception of causation, in a different\nmanner from space. The action of force can only be conceived\nas taking place in a succession of moments, in each of which\ncause and effect immediately succeed each other: and thus\nthe interval of time between a cause and its remote effect\nis filled up by a continuous succession of events connected\nby the same chain of causation. But in space, there is no\nsuch visible necessity of continuity; the action and\nreaction may take place at a distance from each other; all\nthat is necessary being that they be equal and opposite.\n\n[Note 44\\3: _Ancient Metaphysics_, vol. ii. p. 175.]\n\nUndoubtedly the existence of attraction is rendered more\nacceptable to common apprehension by supposing {278} some\nintermediate machinery,--a cord, or rod, or fluid,--by which\nthe forces may be conveyed from one point to another. But\nsuch images are rather fitted to satisfy those prejudices\nwhich arise from the earlier application of our ideas of\nforce, than to exhibit the real nature of those ideas. If we\nsuppose two bodies to pull each other by means of a rod or\ncord, we only suppose, in addition to those equal and\nopposite forces acting upon the two bodies, (which forces\nare alone essential to mutual attraction) a certain power of\nresisting transverse pressure at every point of the\nintermediate line: which additional supposition is entirely\nuseless, and quite unconnected with the essential conditions\nof the case. When the Newtonians were accused of introducing\ninto philosophy an unknown cause which they termed\n_attraction_, they justly replied that they knew as much\nrespecting attraction as their opponents did about impulse.\nIn each case we have a knowledge of the conception in\nquestion so far as we clearly apprehend it under the\nconditions of those axioms of mechanical causation which\nform the basis of our science on such subjects.\n\nHaving thus examined the degree of certainty and generality\nto which our knowledge of the law of universal gravitation\nhas been carried, by the progress of mechanical discovery\nand speculation up to the present time, we might proceed to\nthe other branches of science, and examine in like manner\ntheir grounds and conditions. But before we do this, it will\nbe worth our while to attend for a moment to the effect\nwhich the progress of mechanical ideas among mathematicians\nand mechanical philosophers has produced upon the minds of\nother persons, who share only in an indirect and derivative\nmanner in the influence of science.\n\n\n\n{{279}}\nCHAPTER X.\n\nOF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS.\n\n\n1. WE have seen how the progress of knowledge upon the\nsubject of motion and force has produced, in the course of\nthe world's history, a great change in the minds of acute\nand speculative men; so that such persons can now reason\nwith perfect steadiness and precision upon subjects on\nwhich, at first, their thoughts were vague and confused; and\ncan apprehend, as truths of complete certainty and evidence,\nlaws which it required great labour and time to discover.\nThis _complete_ development and clear manifestation of\nmechanical ideas has taken place only among mathematicians\nand philosophers. But yet a progress of thought upon such\nsubjects,--an advance from the obscure to the clear, and\nfrom errour to truth,--may be traced in the world at large,\nand among those who have not directly cultivated the exact\nsciences. This diffused and collateral influence of science\nmanifests itself, although in a wavering and fluctuating\nmanner, by various indications, at various periods of\nliterary history. The opinions and reasonings which are put\nforth upon mechanical subjects, and above all, the adoption,\ninto common language, of terms and phrases belonging to the\nprevalent mechanical systems, exhibit to us the most\nprofound discoveries and speculations of philosophers in\ntheir effect upon more common and familiar trains of\nthought. This effect is by no means unimportant, and we\nshall point out some examples of such indications as we have\nmentioned.\n\n2. The discoveries of the ancients in speculative mechanics\nwere, as we have seen, very scanty; and {280} hardly\nextended their influence to the unmathematical world. Yet\nthe familiar use of the term 'center of gravity' preserved\nand suggested the most important part of what the Greeks had\nto teach. The other phrases which they employed, as\n_momentum_, _energy_, _virtue_, _force_, and the like, never\nhad any exact meaning, even among mathematicians; and\ntherefore never, in the ancient world, became the means of\nsuggesting just habits of thought. I have pointed out, in\nthe History of Science, several circumstances which appear\nto denote the general confusion of ideas which prevailed\nupon mechanical subjects during the times of the Roman\nempire. I have there taken as one of the examples of this\nconfusion, the fable narrated by Pliny and others concerning\nthe echine\u00efs, a small fish, which was said to stop a ship\nmerely by sticking to it[45\\3]. This story was adduced as\nbetraying the absence of any steady apprehension of the\nequality of action and reaction; since the fish, except it\nhad some immoveable obstacle to hold by, must be pulled\nforward by the ship, as much as it pulled the ship backward.\nIf the writers who speak of this wonder had shown any\nperception of the necessity of a reaction, either produced\nby the rapid motion of the fish's fins in the water, or in\nany other way, they would not be chargeable with this\nconfusion of thought; but from their expressions it is, I\nthink, evident that they saw no such necessity[46\\3]. Their\nidea of mechanical action was not sufficiently distinct to\nenable them to see the absurdity of {281} supposing an\nintense pressure with no obstacle for it to exert itself\nagainst.\n\n[Note 45\\3: _Hist. Ind. Sc._ b. iv. c. i. sect. 2.]\n\n[Note 46\\3: See Prof. Powell, _On the Nature and Evidence of\nthe Laws of Motion_. _Reports of the Ashmolean Society_.\nOxford. 1837. Professor Powell has made an objection to my\nuse of this instance of confusion of thought; the remark in\nthe text seems to me to justify what I said in the History.\nAs an evidence that the fish was not supposed to produce its\neffect by its muscular power acting on the water, we may\ntake what Pliny says, _Nat. Hist._ xxxii. 1, 'Domat mundi\nrabiem, nullo suo labore; non retinendo, aut alio modo quam\nadh\u00e6rendo:' and also what he states in another place (ix.\n41), that when it is preserved in pickle, it may be used in\nrecovering gold which has fallen into a deep well. All this\nimplies adhesion alone, with no conception of reaction.]\n\n3. We may trace, in more modern times also, indications of a\ngeneral ignorance of mechanical truths. Thus the phrase of\nshooting at an object 'point-blank,' implies the belief that\na cannon-ball describes a path of which the first portion is\na straight line. This errour was corrected by the true\nmechanical principles which Galileo and his followers\nbrought to light; but these principles made their way to\npopular notice, principally in consequence of their\napplication to the motions of the solar system, and to the\ncontroversies which took place respecting those motions.\nThus by far the most powerful argument against the reception\nof the Copernican system of the universe, was that of those\nwho asked, Why a stone dropt from a tower was not left\nbehind by the motion of the earth? The answer to this\nquestion, now universally familiar, involves a reference to\nthe true doctrine of the composition of motions. Again;\nKepler's persevering and strenuous attempts[47\\3] to frame a\nphysical theory of the universe were frustrated by his\nignorance of the first law of motion, which informs us that\na body will retain its velocity without any maintaining\nforce. He proceeded upon the supposition that the sun's\nforce was requisite to _keep up_ the motion of the planets,\nas well as to deflect and modify it; and he was thus led to\na system which represented the sun as carrying round the\nplanets in their orbits by means of a _vortex_, produced by\nhis revolution. The same neglect of the laws of motion\npresided in the formation of Descartes' system of vortices.\nAlthough Descartes had enunciated in words the laws of\nmotion, he and his followers showed that they had not the\npractical habit of referring to these mechanical principles;\nand dared not trust the planets to move in free space\nwithout some surrounding machinery to support them[48\\3].\n\n[Note 47\\3: _Hist. Ind. Sc._ b. v. c. iv. and b. vii. c. i.]\n\n[Note 48\\3: I have, in the History, applied to Descartes the\ncharacter which Bacon gives to Aristotle, 'Audax simul et\npavidus:' though he was bold enough to enunciate the laws of\nmotion without knowing them aright, he had not the courage\nto leave the planets to describe their orbits by the agency\nof those laws, without the machinery of contact.]\n\n{282} 4. When at last mathematicians, following Newton, had\nventured to consider the motion of each planet as a\nmechanical problem not different in its nature from the\nmotion of a stone cast from the hand; and when the solution\nof this problem and its immense consequences had become\nmatters of general notoriety and interest; the new views\nintroduced, as is usual, new terms, which soon became\nextensively current. We meet with such phrases as 'flying\noff in the tangent,' and 'deflexion from the tangent;' with\nantitheses between 'centripetal' and 'centrifugal force,' or\nbetween 'projectile' and 'central force.' 'Centers of\nforce,' 'disturbing forces,' 'perturbations,' and\n'perturbations of higher orders,' are not unfrequently\nspoken of: and the expression 'to gravitate,' and the term\n'universal gravitation,' acquired a permanent place in the\nlanguage.\n\nYet for a long time, and even up to the present day, we find\nmany indications that false and confused apprehensions on\nsuch subjects are by no means extirpated. Arguments are\nurged against the mechanical system of the universe,\nimplying in the opponents an absence of all clear mechanical\nnotions. Many of this class of writers retrograde to\nKepler's point of view. This is, for example, the case with\nLord Monboddo, who, arguing on the assumption that force is\nrequisite to maintain, as well as to deflect motion,\nproduced a series of attacks upon the Newtonian philosophy;\nwhich he inserted in his _Ancient Metaphysics_, published in\n1779 and the succeeding years. This writer (like Kepler),\nmeasures force by the velocity which the body _has_[49\\3],\nnot by that which it _gains_. Such a use of language would\nprevent our obtaining any laws of motion at all.\nAccordingly, the author, in the very next page to that which\nI have just quoted, abandons this measure of force, and, in\ncurvilinear motion, measures {283} force by 'the fall from\nthe extremity of the arc.' Again; in his objections to the\nreceived theory, he denies that curvilinear motion is\ncompounded, although his own mode of considering such motion\nassumes this composition in the only way in which it was\never intended by mathematicians. Many more instances might\nbe adduced to show that a want of cultivation of the\nmechanical ideas rendered this philosopher incapable of\njudging of a mechanical system.\n\n[Note 49\\3: _Anc. Met._ vol. ii. b. v. c. vi. p. 413.]\n\nThe following extract from the _Ancient Metaphysics_, may be\nsufficient to show the value of the author's criticism on\nthe subjects of which we are now speaking. His object is to\nprove that there do not exist a centripetal and a\ncentrifugal force in the case of elliptical motion. 'Let any\nman move in a circular or elliptical line described to him;\nand he will find no tendency in himself either to the center\nor from it, much less both. If indeed he attempt to make the\nmotion with great velocity, or if he do it carelessly and\ninattentively, he may go out of the line, either towards the\ncenter or from it: but this is to be ascribed, not to the\nnature of the motion, but to our infirmity; or perhaps to\nthe animal form, which is more fitted for progressive motion\nin a right line than for any kind of curvilinear motion. But\nthis is not the case with a sphere or spheroid, which is\nequally adapted to motion in all directions[50\\3].' We need\nhardly remind the reader that the manner in which a man\nrunning round a small circle, finds it necessary to lean\ninwards, in order that there may be a centripetal\ninclination to counteract the centrifugal force, is a\nstandard example of our mechanical doctrines; and this fact\n(quite familiar in practice as well as theory) is in direct\ncontradiction of Lord Monboddo's assertion.\n\n[Note 50\\3: _Anc. Met._ vol. i. b. ii. c. 19, p. 264.]\n\n5. A similar absence of distinct mechanical thought appears\nin some of the most celebrated metaphysicians of Germany. I\nhave elsewhere noted[51\\3] the opinion expressed by Hegel,\nthat the glory which belongs to {284} Kepler has been\nunjustly transferred to Newton; and I have suggested, as the\nexplanation of this mode of thinking, that Hegel himself, in\nthe knowledge of mechanical truth, had not advanced beyond\nKepler's point of view. Persons who possess conceptions of\nspace and number, but who have not learnt to deal with ideas\nof force and causation, may see more value in the\ndiscoveries of Kepler than in those of Newton. Another\nexemplification of this state of mind may be found in\nProfessor Schelling's speculations; for instance, in his\n_Lectures on the Method of Academical Study_. In the twelfth\nLecture, on the study of Physics and Chemistry, he says, (p.\n266,) 'What the mathematical natural philosophy has done for\nthe knowledge of the laws of the universe since the time\nthat they were discovered by his (Kepler's) godlike genius,\nis, as is well known, this: it has attempted a construction\nof those laws which, according to its foundations, is\naltogether empirical. We may assume it as a general rule,\nthat in any proposed construction, that which is not a pure\ngeneral form cannot have any scientific import or truth. The\nfoundation from which the centrifugal motion of the bodies\nof the world is derived, is no necessary form, it is an\nempirical fact. The Newtonian attractive force, even if it\nbe a necessary assumption for a merely reflective view of\nthe subject, is still of no significance for the Reason,\nwhich recognizes only absolute relations. The grounds of the\nKeplerian laws can be derived, without any empirical\nappendage, purely from the doctrine of Ideas, and of the two\nUnities, which are in themselves one Unity, and in virtue of\nwhich each being, while it is absolute in itself, is at the\nsame time in the absolute, and reciprocally.'\n\n[Note 51\\3: _Hist. Ind. Sc._ b. vii. c. ii. sect. 5.]\n\nIt will be observed, that in this passage our mechanical\nlaws are objected to because they are not necessary results\nof our ideas; which, however, as we have seen, according to\nthe opinion of some eminent mechanical philosophers, they\nare. But to assume this evident necessity as a condition of\nevery advance in science, is to mistake the last, perhaps\nunattainable step, for the first, which lies before our\nfeet. And, {285} without inquiring further about 'the\nDoctrine of the two Unities,' or the manner in which from\nthat doctrine we may deduce the Keplerian laws, we may be\nwell convinced that such a doctrine cannot supply any\nsufficient reason to induce us to quit the inductive path by\nwhich all scientific truth up to the present time has been\nacquired.\n\n6. But without going to schools of philosophy opposed to the\nInductive School, we may find many loose and vague habits of\nthinking on mechanical subjects among the common classes of\nreaders and reasoners. And there are some familiar modes of\nemploying the phraseology of mechanical science, which are,\nin a certain degree, chargeable with inaccuracy, and may\nproduce or perpetuate confusion. Among such cases we may\nmention the way in which the centripetal and centrifugal\nforces, and also the projectile and central forces of the\nplanets, are often compared or opposed. Such antitheses\nsometimes proceed upon the false notion that the two members\nof these pairs of forces are of the same kind: whereas on\nthe contrary the _projectile_ force is a hypothetical\nimpulsive force which may, at some former period, have\ncaused the motion to begin; while the _central_ force is an\nactual force, which must act continuously and during the\nwhole time of the motion, in order that the motion may go on\nin the curve. In the same manner the _centrifugal_ force is\nnot a distinct force in a strict sense, but only a certain\nresult of the first law of motion, measured by the portion\nof _centripetal_ force which counteracts it. Comparisons of\nquantities so heterogeneous imply confusion of thought, and\noften suggest baseless speculations and imagined reforms of\nthe received opinions.\n\n7. I might point out other terms and maxims, in addition to\nthose already mentioned, which, though formerly employed in\na loose and vague manner, are now accurately understood and\nemployed by all just thinkers; and thus secure and diffuse a\nright understanding of mechanical truths. Such are\n_momentum_, _inertia_, _quantity of matter_, _quantity of\nmotion_; that _force is proportional to its effects_; that\n_action and_ {286} _reaction are equal_; that _what is\ngained in force by machinery is lost in time_; that _the\nquantity of motion in the world cannot be either increased\nor diminished_. When the expression of the truth thus\nbecomes easy and simple, clear and convincing, the meanings\ngiven to words and phrases by discoverers glide into the\nhabitual texture of men's reasonings, and the effect of the\nestablishment of true mechanical principles is felt far from\nthe school of the mechanician. If these terms and maxims are\nunderstood with tolerable clearness, they carry the\ninfluence of truth to those who have no direct access to its\nsources. Many an extravagant project in practical machinery,\nand many a wild hypothesis in speculative physics, has been\nrepressed by the general currency of such maxims as we have\njust quoted.\n\n8. Indeed so familiar and evident are the elementary truths\nof mechanics when expressed in this simple form, that they\nare received as truisms; and men are disposed to look back\nwith surprise and scorn at the speculations which were\ncarried on in neglect of them. The most superficial reasoner\nof modern times thinks himself entitled to speak with\ncontempt and ridicule of Kepler's hypothesis concerning the\nphysical causes of the celestial motions: and gives himself\ncredit for intellectual superiority, because he sees, as\nself-evident, what such a man could not discover at all. It\nis well for such a person to recollect, that the real cause\nof his superior insight is not the pre-eminence of his\nfaculties, but the successful labours of those who have\npreceded him. The language which he has learnt to use\nunconsciously, has been adapted to, and moulded on,\nascertained truths. When he talks familiarly of\n\"accelerating forces\" and \"deflexions from the tangent,\" he\nis assuming that which Kepler did not know, and which it\ncost Galileo and his disciples so much labour and thought to\nestablish. Language is often called an instrument of\nthought; but it is also the nutriment of thought; or rather,\nit is the atmosphere in which thought lives: a medium\nessential to the activity of our speculative power, although\ninvisible {287} and imperceptible in its operation; and an\nelement modifying, by its qualities and changes, the growth\nand complexion of the faculties which it feeds. In this way\nthe influence of preceding discoveries upon subsequent ones,\nof the past upon the present, is most penetrating and\nuniversal, though most subtle and difficult to trace. The\nmost familiar words and phrases are connected by\nimperceptible ties with the reasonings and discoveries of\nformer men and distant times. Their knowledge is an\ninseparable part of ours; the present generation inherits\nand uses the scientific wealth of all the past. And this is\nthe fortune, not only of the great and rich in the\nintellectual world: of those who have the key to the ancient\nstorehouses, and who have accumulated treasures of their\nown;--but the humblest inquirer, while he puts his\nreasonings into words, benefits by the labours of the\ngreatest discoverers. When he counts his little wealth, he\nfinds that he has in his hands coins which bear the image\nand superscription of ancient and modern intellectual\ndynasties; and that in virtue of this possession,\nacquisitions are in his power, solid knowledge within his\nreach, which none could ever have attained to, if it were\nnot that the gold of truth, once dug out of the mine,\ncirculates more and more widely among mankind.\n\n9. Having so fully examined, in the preceding instances, the\nnature of the progress of thought which science implies,\nboth among the peculiar cultivators of science, and in that\nwider world of general culture which receives only an\nindirect influence from scientific discoveries, we shall not\nfind it necessary to go into the same extent of detail with\nregard to the other provinces of human knowledge. In the\ncase of the Mechanical Sciences, we have endeavoured to\nshow, not only that Ideas are requisite in order to form\ninto a science the Facts which nature offers to us, but that\nwe can advance, almost or quite, to a complete\nidentification of the Facts with the Ideas. In the sciences\nto which we now proceed, we shall not seek to fill up the\nchasm by which Facts and Ideas are separated; but we shall\nendeavour to detect the Ideas which our {288} knowledge\ninvolves, to show how essential these are; and in some\nrespects to trace the mode in which they have been gradually\ndeveloped among men.\n\n10. The motions of the heavenly bodies, their laws, their\ncauses, are among the subjects of the first division of the\nMechanical Sciences; and of these sciences we formerly\nsketched the history, and have now endeavoured to exhibit\nthe philosophy. If we were to take any other class of\nmotions, _their_ laws and causes might give rise to sciences\nwhich would be mechanical sciences in exactly the same sense\nin which Physical Astronomy is so. The phenomena of magnets,\nof electrical bodies, of galvanical apparatus, seem to form\nobvious materials for such sciences; and if they were so\ntreated, the philosophy of such branches of knowledge would\nnaturally come under our consideration at this point of our\nprogress.\n\nBut on looking more attentively at the sciences of\nElectricity, Magnetism, and Galvanism, we discover cogent\nreasons for transferring them to another part of our\narrangement; we find it advisable to associate them with\nChemistry, and to discuss their principles when we can\nconnect them with the principles of chemical science. For\nthough the first steps and narrower generalizations of these\nsciences depend upon mechanical ideas, the highest laws and\nwidest generalizations which we can reach respecting them,\ninvolve chemical relations. The progress of these portions\nof knowledge is in some respects opposite to the progress of\nPhysical Astronomy. In this, we begin with phenomena which\nappear to indicate peculiar and various qualities in the\nbodies which we consider, (namely, the heavenly bodies,) and\nwe find in the end that all these qualities resolve\nthemselves into one common mechanical property, which exists\nalike in all bodies and parts of bodies. On the contrary, in\nstudying magnetical and electrical laws, we appear at first\nto have a single extensive phenomenon, attraction and\nrepulsion: but in our attempts to generalize this\nphenomenon, we find that it is governed by conditions\ndepending upon something quite separate from the bodies\nthemselves, upon {289} the presence and distribution of\npeculiar and transitory agencies; and, so far as we can\ndiscover, the general laws of these agencies are of a\n_chemical_ nature, and are brought into action by peculiar\nproperties of special substances. In cosmical phenomena,\neverything, in proportion as it is referred to mechanical\nprinciples, tends to simplicity,--to permanent uniform\nforces,--to one common, positive, property. In magnetical\nand electrical appearances, on the contrary, the application\nof mechanical principles leads only to a new complexity,\nwhich requires a new explanation; and this explanation\ninvolves changeable and various forces,--gradations and\noppositions of qualities. The doctrine of the universal\ngravitation of matter is a simple and ultimate truth, in\nwhich the mind can acquiesce and repose. We rank gravity\namong the mechanical attributes of matter, and we see no\nnecessity to derive it from any ulterior properties. Gravity\nbelongs to matter, independent of any conditions. But the\n_conditions_ of magnetic or electrical activity require\ninvestigation as much as the _laws_ of their action. Of\nthese conditions no mere mechanical explanation can be\ngiven; we are compelled to take along with us chemical\nproperties and relations also: and thus magnetism,\nelectricity, galvanism, are _mechanico-chemical sciences_.\n\n11. Before considering these, therefore, I shall treat of\nwhat I shall call _Secondary Mechanical Sciences_; by which\nexpression I mean the sciences depending upon certain\nqualities which our senses discover to us in\nbodies;--_Optics_, which has visible phenomena for its\nsubject; _Acoustics_, the science of hearing; the doctrine\nof _Heat_, a quality which our touch recognizes: to this\nlast science I shall take the liberty of sometimes giving\nthe name _Thermotics_, analogous to the names of the other\ntwo. If our knowledge of the phenomena of Smell and Taste\nhad been successfully cultivated and systematized, the\npresent part of our work would be the place for the\nphilosophical discussion of those sensations as the subjects\nof science.\n\nThe branches of knowledge thus grouped in one class involve\ncommon Fundamental Ideas, from which {290} their principles\nare derived in a mode analogous, at least in a certain\ndegree, to the mode in which the principles of the\nmechanical sciences are derived from the fundamental ideas\nof causation and reaction. We proceed now to consider these\nFundamental Ideas, their nature, development, and\nconsequences.\n\n\n\n\n{{291}}\nBOOK IV.\n\n\nTHE\nPHILOSOPHY\nOF THE\nSECONDARY\nMECHANICAL SCIENCES.\n\n\n\n\n\u03a0\u03ac\u03c3\u03c7\u03bf\u03bd\u03c4\u03bf\u03c2 \u03b3\u03ac\u03c1 \u03c4\u03b9 \u03c4\u03bf\u1fe6 \u03b1\u1f30\u03c3\u03b8\u03b7\u03c4\u03b9\u03ba\u03bf\u1fe6 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c4\u1f78 \u1f41\u03c1\u1fb6\u03bd\u00b7 \u1f51\u03c0' \u03b1\u1f50\u03c4\u03bf\u1fe6\n\u03bc\u1f72\u03bd \u03bf\u1f56\u03bd \u03c4\u03bf\u1fe6 \u1f41\u03c1\u03c9\u03bc\u03ad\u03bd\u03bf\u03c5 \u03c7\u03c1\u03ce\u03bc\u03b1\u03c4\u03bf\u03c2 \u1f00\u03b4\u03cd\u03bd\u03b1\u03c4\u03bf\u03bd\u00b7 \u03bb\u03b5\u03af\u03c0\u03b5\u03c4\u03b1\u03b9 \u03b4\u1f74 \u1f51\u03c0\u1f78 _\u03c4\u03bf\u1fe6\n\u03bc\u03b5\u03c4\u03b1\u03be\u03cd_, \u1f65\u03c3\u03c4' \u1f00\u03bd\u03b1\u03b3\u03ba\u03b1\u1fd6\u03cc\u03bd \u03c4\u03b9 \u03b5\u1f36\u03bd\u03b1\u03b9 _\u03bc\u03b5\u03c4\u03b1\u03be\u03cd_\u00b7 \u03ba\u03b5\u03bd\u03bf\u1fe6 \u03b4\u1f72\n\u03b3\u03b5\u03bd\u03bf\u03bc\u03ad\u03bd\u03bf\u03c5 \u03bf\u1f50\u03c7 \u1f45\u03c4\u03b9 \u1f00\u03ba\u03c1\u03b9\u03b2\u1ff6\u03c2, \u1f00\u03bb\u03bb' \u1f45\u03bb\u03c9\u03c2 \u03bf\u1f50\u03b8\u1f72\u03bd \u1f40\u03c6\u03b8\u03ae\u03c3\u03b5\u03c4\u03b1\u03b9. \u03b4\u03b9' \u1f23\u03bd\n\u03bc\u1f72\u03bd \u03bf\u1f56\u03bd \u03b1\u1f30\u03c4\u03af\u03b1\u03bd \u03c4\u1f78 \u03c7\u03c1\u1ff6\u03bc\u03b1 \u1f00\u03bd\u03b1\u03b3\u03ba\u03b1\u1fd6\u03bf\u03bd \u1f10\u03bd \u03c6\u03c9\u03c4\u1f76 \u1f41\u03c1\u1fb6\u03c3\u03b8\u03b1\u03b9, \u03b5\u1f34\u03c1\u03b7\u03c4\u03b1\u03b9.\n\u03c0\u1fe6\u03c1 \u03b4\u1f72 \u1f10\u03bd \u1f00\u03bc\u03c6\u03bf\u1fd6\u03bd \u1f41\u03c1\u1fb6\u03c4\u03b1\u03b9, \u03ba\u03b1\u1f76 \u1f10\u03bd \u03c3\u03ba\u03cc\u03c4\u03b5\u03b9 \u03ba\u03b1\u1f76 \u1f10\u03bd \u03c6\u03c9\u03c4\u03af, \u03ba\u03b1\u1f76\n\u03c4\u03bf\u1fe6\u03c4\u03bf _\u1f10\u03be \u1f00\u03bd\u03ac\u03b3\u03ba\u03b7\u03c2_\u00b7 \u03c4\u1f78 \u03b3\u1f70\u03c1 \u03b4\u03b9\u03b1\u03c6\u03b1\u03bd\u1f72\u03c2 \u1f51\u03c0\u1f78 \u03c4\u03bf\u03cd\u03c4\u03bf\u03c5 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9\n\u03b4\u03b9\u03b1\u03c6\u03b1\u03bd\u03ad\u03c2. \u1f41 \u03b4' \u03b1\u1f50\u03c4\u1f78\u03c2 \u03bb\u03cc\u03b3\u03bf\u03c2 \u03ba\u03b1\u1f76 \u03c0\u03b5\u03c1\u1f76 \u03c8\u03cc\u03c6\u03bf\u03c5 \u03ba\u03b1\u1f76 \u1f40\u03c3\u03bc\u1fc6\u03c2 \u1f10\u03c3\u03c4\u03b9\u03bd\u00b7\n\u03bf\u1f50\u03b8\u1f72\u03bd \u03b3\u1f70\u03c1 \u03b1\u1f50\u03c4\u1ff6\u03bd \u1f01\u03c0\u03c4\u03cc\u03bc\u03b5\u03bd\u03bf\u03bd \u03c4\u03bf\u1fe6 \u03b1\u1f30\u03c3\u03b8\u03b7\u03c4\u03b7\u03c1\u03af\u03bf\u03c5 \u03c0\u03bf\u03b9\u03b5\u1fd6 \u03c4\u1f74\u03bd\n\u03b1\u1f34\u03c3\u03b8\u03b7\u03c3\u03b9\u03bd, \u1f00\u03bb\u03bb' \u1f51\u03c0\u1f78 \u03bc\u1f72\u03bd \u1f40\u03c3\u03bc\u1fc6\u03c2 \u03ba\u03b1\u1f76 \u03c8\u03cc\u03c6\u03bf\u03c5 _\u03c4\u1f78 \u03bc\u03b5\u03c4\u03b1\u03be\u1f7a_ \u03ba\u03b9\u03bd\u03b5\u1fd6\u03c4\u03b1\u03b9,\n\u1f51\u03c0\u1f78 \u03b4\u1f72 \u03c4\u03bf\u03cd\u03c4\u03bf\u03c5 \u03c4\u1ff6\u03bd \u03b1\u1f30\u03c3\u03b8\u03b7\u03c4\u03b7\u03c1\u03af\u03c9\u03bd \u1f11\u03ba\u03ac\u03c4\u03b5\u03c1\u03bf\u03bd\u00b7 \u1f45\u03c4\u03b1\u03bd \u03b4' \u1f10\u03c0' \u03b1\u1f50\u03c4\u03cc \u03c4\u03b9\u03c2\n\u1f10\u03c0\u03b9\u03b8\u1fc7 \u03c4\u1f78 \u03b1\u1f30\u03c3\u03b8\u03b7\u03c4\u03ae\u03c1\u03b9\u03bf\u03bd \u03c4\u1f78 \u03c8\u03bf\u03c6\u03bf\u1fe6\u03bd \u1f22 \u03c4\u1f78 \u1f44\u03b6\u03bf\u03bd, \u03bf\u1f50\u03b4\u03b5\u03bc\u03af\u03b1\u03bd \u03b1\u1f34\u03c3\u03b8\u03b7\u03c3\u03b9\u03bd\n\u03c0\u03bf\u03b9\u03ae\u03c3\u03b5\u03b9.\n\nARISTOT. _De Anima_, II. 7.\n\n\n\n{{293}} BOOK IV.\n\n\nTHE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES.\n\n\nCHAPTER I.\n\nOF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED.\n\n\n1. _Of Primary and Secondary Qualities._--IN the same way in\nwhich the mechanical sciences depend upon the Idea of Cause,\nand have their principles regulated by the development of\nthat Idea, it will be found that the sciences which have for\ntheir subject Sound, Light, and Heat, depend for _their_\nprinciples upon the Fundamental Idea of Media by means of\nwhich we perceive those qualities. Like the idea of cause,\nthis idea of a medium is unavoidably employed, more or less\ndistinctly, in the common, unscientific operations of the\nunderstanding; and is recognized as an express principle in\nthe earliest speculative essays of man. But here also, as in\nthe case of the mechanical sciences, the development of the\nidea, and the establishment of the scientific truths which\ndepend upon it, was the business of a succeeding period, and\nwas only executed by means of long and laborious researches,\nconducted with a constant reference to experiment and\nobservation.\n\nAmong the most prominent manifestations of the influence of\nthe idea of a medium of which we have now to speak, is the\ndistinction of the qualities of bodies into _primary_, and\n_secondary_ qualities. This distinction has {294} been\nconstantly spoken of in modern times: yet it has often been\na subject of discussion among metaphysicians whether there\nbe really such a distinction, and what the true difference\nis. Locke states it thus[1\\4]: Original or Primary qualities\nof bodies are 'such as are utterly inseparable from the body\nin what estate soever it may be,--such as sense constantly\nfinds in every particle of matter which has bulk enough to\nbe perceived, and the mind finds inseparable from every\nparticle of matter, though less than to make itself singly\nperceived by our senses:' and he enumerates them as\nsolidity, extension, figure, motion or rest, and number.\nSecondary qualities, on the other hand, are such 'which in\ntruth are nothing in the objects themselves, but powers to\nproduce various sensations in us by their primary qualities,\n_i.e._ by the bulk, figure, texture, and motion of their\ninsensible parts, as colours, sounds, tastes, &c.'\n\n[Note 1\\4: _Essay_, b. ii. ch. viii. s. 9, 10.]\n\nDr. Reid[2\\4], reconsidering this subject, puts the\ndifference in another way. There is, he says, a real\nfoundation for the distinction of Primary and Secondary\nqualities, and it is this: 'That our senses give us a direct\nand distinct notion of the primary qualities, and inform us\nwhat they are in themselves; but of the secondary qualities,\nour senses give us only a relative and obscure notion. They\ninform us only that they are qualities that affect us in a\ncertain manner, that is, produce in us a certain sensation;\nbut as to what they are in themselves, our senses leave us\nin the dark.'\n\n[Note 2\\4: _Essays_, b. ii. c. xvii.]\n\nDr. Brown[3\\4] states the distinction somewhat otherwise. We\ngive the name of Matter, he observes, to that which has\nextension and resistance: these, therefore, are Primary\nqualities of matter, because they compose our definition of\nit. All other qualities are Secondary, since they are\nascribed to bodies only because we find them associated with\nthe primary qualities which form our notion of those bodies.\n\n[Note 3\\4: _Lectures_, ii. 12.]\n\n{295} It is not necessary to criticize very strictly these\nvarious distinctions. If it were, it would be easy to find\nobjections to them. Thus Locke, it may be observed, does not\npoint out any _reason_ for believing that his secondary\nqualities are produced by the primary. How are we to learn\nthat the colour of a rose arises from the bulk, figure,\ntexture, and motion of its particles? Certainly our senses\ndo not teach us this; and in what other way, on Locke's\nprinciples, can we learn it? Reid's statement is not more\nfree from the same objection. How does it appear that our\nnotion of Warmth is relative to our own sensations more than\nour notion of Solidity? And if we take Brown's account, we\nmay still ask whether our selection of certain qualities to\nform our idea and definition of Matter be arbitrary and\nwithout reason? If it be, how can it make a real\ndistinction? if it be not, what is the reason?\n\nI do not press these objections, because I believe that any\nof the above accounts of the distinction of Primary and\nSecondary qualities is right in the main, however imperfect\nit may be. The difference between such qualities as\nExtension and Solidity on the one hand, and Colour or\nFragrance on the other, is assented to by all, with a\nconviction so firm and indestructible, that there must be\nsome fundamental principle at the bottom of the belief,\nhowever difficult it may be to clothe the principle in\nwords. That successive efforts to express the real nature of\nthe difference were made by men so clear-sighted and acute\nas those whom I have quoted, even if none of them are\nsatisfactory, shows how strong and how deeply-seated is the\nperception of truth which impels us to such attempts.\n\nThe most obvious mode of stating the difference of Primary\nand Secondary qualities, as it naturally offers itself to\nspeculative minds, appears to be that employed by Locke,\nslightly modified. Certain of the qualities of bodies, as\ntheir bulk, figure, and motion, are perceived immediately in\nthe bodies themselves. Certain other qualities as sound,\ncolour, heat, are {296} perceived by means of some medium.\nOur conviction that this is the case is spontaneous and\nirresistible; and this difference of qualities immediately\nand mediately perceived is the distinction of Primary and\nSecondary qualities. We proceed further to examine this\nconviction.\n\n2. _The Idea of Externality._--In reasoning concerning the\nSecondary Qualities of bodies, we are led to assume the\nbodies to be external to us, and to be perceived by means of\nsome Medium intermediate between us and them. These\nassumptions are fundamental conditions of perception,\ninseparable from perception even in thought.\n\nThat objects are _external_ to us, that they are _without_\nus, that they have _outness_, is as clear as it is that\nthese words have any meaning at all. This conviction is,\nindeed, involved in the exercise of that faculty by which we\nperceive all things as existing in space; for by this\nfaculty we place ourselves and other objects in one common\nspace, and thus they are exterior to us. It may be remarked\nthat this apprehension of objects as external to us,\nalthough it assumes the idea of space, is far from being\nimplied in the idea of space. The objects which we\ncontemplate are considered as existing in space, and by that\nmeans become invested with certain mutual relations of\nposition; but when we consider them as existing without\n_us_, we make the additional step of supposing _ourselves_\nand the objects to exist in one common space. The question\nrespecting the Ideal Theory of Berkeley has been mixed up\nwith the recognition of this condition of the externality of\nobjects. That philosopher maintained, as is well known, that\nthe perceptible qualities of bodies have no existence except\nin a perceiving mind. This system has often been understood\nas if he had imagined the world to be a kind of optical\nillusion, like the images which we see when we shut our\neyes, appearing to be without us, though they are only in\nour organs; and thus this Ideal System has been opposed to a\nbelief in an external world. In truth, however, no such\nopposition exists. The Ideal System is an attempt to explain\nthe {297} mental process of perception, and to get over the\ndifficulty of mind being affected by matter. But the author\nof that system did not deny that objects were perceived\nunder the conditions of space and mechanical\ncausation;--that they were _external_ and _material_ so far\nas those words describe perceptible qualities. Berkeley's\nsystem, however visionary or erroneous, did not prevent his\nentertaining views as just, concerning optics or acoustics,\nas if he had held any other doctrine of the nature of\nperception.\n\nBut when Berkeley's theory was understood as a denial of the\nexistence of objects without us, how was it answered? If we\nexamine the answers which are given by Reid and other\nphilosophers to this hypothesis, it will be found that they\namount to this: that objects _are_ without us, since we\n_perceive_ that they are so; that we perceive them to be\nexternal, by the same act by which we perceive them to be\nobjects. And thus, in this stage of philosophical inquiry,\nthe externality of objects is recognized as one of the\ninevitable conditions of our perception of them; and hence\nthe Idea of Externality is adopted as one of the necessary\nfoundations of all reasoning concerning all objects\nwhatever.\n\n3. _Sensation by a Medium._--Objects, as we have just seen,\nare necessarily apprehended as _without_ us; and in general,\nas removed from us by a great or small distance. Yet they\naffect our bodily senses; and this leads us irresistibly to\nthe conviction that they are perceived by means of something\nintermediate. Vision, or hearing, or smell, or the warmth of\na fire, must be communicated to us by some Medium of\nSensation. This unavoidable belief appears in all attempts,\nthe earliest and the latest alike, to speculate upon such\nsubjects. Thus, for instance, Aristotle says[4\\4], 'Seeing\ntakes place in virtue of some action which the sentient\norgan suffers: now it cannot suffer action from the colour\nof the object directly: the only remaining possible case\nthen is, that it is acted upon by an {298} intervening\nMedium; there must then be an intervening Medium.' 'And the\nsame may be said,' he adds, 'concerning sounding and odorous\nbodies; for these do not produce sensation by touching the\nsentient organ, but the intervening Medium is acted on by\nthe sound or the smell, and the proper organ, by the Medium\n... In sound the Medium is air; in smell we have no name for\nit.' In the sense of taste, the necessity of a Medium is not\nat first so obviously seen, because the object tasted is\nbrought into contact with the organ; but a little attention\nconvinces us that the taste of a solid body can only be\nperceived when it is conveyed in some liquid vehicle. Till\nthe fruit is crushed, and till its juices are pressed out,\nwe do not distinguish its flavour. In the case of heat, it\nis still more clear that we are compelled to suppose some\ninvisible fluid, or other means of communication, between\nthe distant body which warms us and ourselves.\n\n[Note 4\\4: \u03a0\u03b5\u03c1\u1f76 \u03a8\u03c5\u03c7\u1fc6\u03c2. ii. 7. See the motto to this Book.]\n\nIt may appear to some persons that the assumption of an\nintermedium between the object perceived and the sentient\norgan results from the principles which form the basis of\nour mechanical reasonings,--that every change must have a\ncause, and that bodies can act upon each other only by\ncontact. It cannot be denied that this principle does offer\nitself very naturally as the ground of our belief in media\nof sensation; and it appears to be referred to for this\npurpose by Aristotle in the passage quoted above. But yet we\ncannot but ask, Does the principle, that matter produces its\neffect by contact only, manifestly apply here? When we so\napply it, we include _sensation_ among the _effects_ which\nmaterial contact produces;--a case so different from any\nmerely mechanical effect, that the principle, so employed,\nappears to acquire a new signification. May we not, then,\nrather say that we have here a new axiom,--That sensation\nimplies a material cause immediately acting on the\norgan,--than a new application of our former\nproposition,--That all mechanical change implies contact?\n\nThe solution of this doubt is not of any material\nconsequence to our reasonings; for whatever be the {299}\nground of the assumption, it is certain that we do assume\nthe existence of media by which the sensations of sight,\nhearing, and the like, are produced; and it will be seen\nshortly that principles inseparably connected with this\nassumption are the basis of the sciences now before us.\n\nThis assumption makes its appearance in the physical\ndoctrines of all the schools of philosophy. It is exhibited\nperhaps most prominently in the tenets of the Epicureans,\nwho were materialists, and extended to all kinds of\ncausation the axiom of the existence of a corporeal\nmechanism by which alone the effect is produced. Thus,\naccording to them, vision is produced by certain images or\nmaterial films which flow from the object, strike upon the\neyes, and so become sensible. This opinion is urged with\ngreat detail and earnestness by Lucretius, the poetical\nexpositor of the Epicurean creed among the Romans. His\nfundamental conviction of the necessity of a material medium\nis obviously the basis of his reasoning, though he attempts\nto show the existence of such a medium by facts. Thus he\nargues[5\\4], that by shouting loud we make the throat sore;\nwhich shows, he says, that the voice must be material, so\nthat it can hurt the passage in coming out.\n Haud igitur dubium est quin voces verbaque constent\n Corporeis e principiis ut l\u00e6dere possint.\n\n[Note 5\\4: _De Rerum Natur\u00e2_, Lib. iv. 529.]\n\n4. _The Process of Perception of Secondary Qualities._--The\nlikenesses or representatives of objects by which they\naffect our senses were called by some writers _species_, or\n_sensible species_, a term which continued in use till the\nrevival of science. It may be observed that the conception\nof these _species_ as films cast off from the object, and\nretaining its shape, was different, as we have seen, from\nthe view which Aristotle took, though it has sometimes been\ncalled the Peripatetic doctrine[6\\4]. We may add that the\nexpression was latterly applied to express the supposition\nof an emanation of any kind, and implied little {300} more\nthan that supposition of a Medium of which we are now\nspeaking. Thus Bacon, after reviewing the phenomena of\nsound, says[7\\4], 'Videntur motus soni fieri per _species\nspirituales_: ita enim loquendum donec certius quippiam\ninveniatur.'\n\n[Note 6\\4: Brown, vol. ii. p. 98.]\n\n[Note 7\\4: _Hist. Son. et Aud._ vol. ix. p. 87.]\n\nThough the fundamental principles of several sciences depend\nupon the assumption of a Medium of Perception, these\nprinciples do not at all depend upon any special view of the\nProcess of our perceptions. The mechanism of that process is\na curious subject of consideration; but it belongs to\nphysiology, more properly than either to metaphysics, or to\nthose branches of physics of which we are now speaking. The\ngeneral nature of the process is the same for all the\nsenses. The object affects the appropriate intermedium; the\nmedium, through the proper organ, the eye, the ear, the\nnose, affects the nerves of the particular sense; and, by\nthese, in some way, the sensation is conveyed to the mind,\nBut to treat the _impression_ upon the nerves as the _act_\nof sensation which we have to consider, would be to mistake\nour object, which is not the constitution of the human body,\nbut of the human mind. It would be to mistake one link of\nthe chain for the power which holds the end of the chain. No\nanatomical analysis of the corporeal conditions of vision,\nor hearing, or feeling warm, is necessary to the sciences of\nOptics, or Acoustics, or Thermotics.\n\nNot only is this physiological research an extraneous part\nof our subject, but a partial pursuit of such a research may\nmislead the inquirer. We perceive objects _by means of_\ncertain media, and _by means of_ certain impressions on the\nnerves: but we cannot with propriety say that we perceive\neither the media or the impressions on the nerves. What\nperson in the act of seeing is conscious of the little\ncoloured spaces on the retina? or of the motions of the\nbones of the auditory apparatus whilst he is hearing?\nSurely, no one. This may appear obvious enough, and yet a\nwriter of no common acuteness, Dr. Brown, has put forth\nseveral {301} very strange opinions, all resting upon the\ndoctrine that the coloured spaces on the retina are the\n_objects_ which we perceive; and there are some supposed\ndifficulties and paradoxes on the same subject which have\nbecome quite celebrated (as upright vision with inverted\nimages), arising from the same confusion of thought.\n\nAs the consideration of the difficulties which have arisen\nrespecting the Philosophy of Perception may serve still\nfurther to illustrate the principles on which we necessarily\nreason respecting the secondary qualities of bodies, I shall\nhere devote a few pages to that subject.\n\n\n\n{{302}}\nCHAPTER II.\n\nON PECULIARITIES IN THE PERCEPTIONS OF THE DIFFERENT SENSES.\n\n\n1. WE cannot doubt that we perceive all secondary qualities\nby means of immediate impressions made, through the proper\nmedium of sensation, upon our organs. Hence all the senses\nare sometimes vaguely spoken of as modifications of the\nsense of feeling. It will, however, be seen, on reflection,\nthat this mode of speaking identifies in words things which\nin our conceptions have nothing in common. No impression on\nthe organs of touch can be conceived as having any\nresemblance to colour or smell. No effort, no ingenuity, can\nenable us to describe the impressions of one sense in terms\nborrowed from another.\n\nThe senses have, however, each its peculiar powers, and\nthese powers may be in some respects compared, so as to show\ntheir leading resemblances and differences, and the\ncharacteristic privileges and laws of each. This is what we\nshall do as briefly as possible.\n\n\nSECT. I.--_Prerogatives of Sight._\n\nTHE sight distinguishes colours, as the hearing\ndistinguishes tones; the sight estimates degrees of\nbrightness, the ear, degrees of loudness; but with several\nresemblances, there are most remarkable differences between\nthese two senses.\n\n2. _Position._--The sight has this peculiar prerogative,\nthat it apprehends the _place_ of its objects directly and\nprimarily. We see _where_ an object is at the same instant\nthat we see what it is. If we see two objects, we see their\nrelative position. We cannot help {303} perceiving that one\nis above or below, to the right or to the left of the other,\nif we perceive them at all.\n\nThere is nothing corresponding to this in sound. When we\nhear a noise, we do not necessarily assign a place to it. It\nmay easily happen that we cannot tell from which side a\nthunder-clap comes. And though we often can judge in what\ndirection a voice is heard, this is a matter of secondary\nimpression, and of inference from concomitant circumstances,\nnot a primary fact of sensation. The judgments which we form\nconcerning the position of sounding bodies are obtained by\nthe conscious or unconscious comparison of the impressions\nmade on the two ears, and on the bones of the head in\ngeneral; they are not inseparable conditions of hearing. We\nmay hear sounds, and be uncertain whether they are 'above,\naround, or underneath!' but the moment anything visible\nappears, however unexpected, we can say, 'see _where_ it\ncomes!'\n\nSince we can see the relative position of things, we can see\n_figure_, which is but the relative position of the\ndifferent parts of the boundary of the object. And thus the\nwhole visible world exhibits to us a scene of various\nshapes, coloured and shaded according to their form and\nposition, but each having relations of position to all the\nrest; and altogether, entirely filling up the whole range\nwhich the eye can command.\n\n3. _Distance._--The distance of objects from us is no matter\nof immediate perception, but is a judgment and inference\nformed from our sensations, in something of the same way as\nour judgment of position by the ear, though more precise.\nThat this is so, was most distinctly shown by Berkeley, in\nhis _New Theory of Vision_. The elements on which we form\nour judgment are, the effort by which we fix both eyes on\nthe same object, the effort by which we adjust each eye to\ndistinct vision, and the known forms, colours, and parts of\nobjects, as compared with their appearance. The right\ninterpretation of the information which these circumstances\ngive us respecting the true distances and forms of things,\nis gradually learnt by experience, the lesson being begun in\nour earliest infancy, and inculcated upon us every hour\nduring which we {304} use our eyes. The completeness with\nwhich the lesson is learnt is truly admirable; for we forget\nthat our conclusion is obtained indirectly, and mistake a\njudgment on evidence for an intuitive perception. This,\nhowever, is not more surprizing than the rapidity and\nunconsciousness of effort with which we understand the\nmeaning of the speech that we hear, or the book that we\nread. In both cases, the habit of interpretation is become\nas familiar as the act of perception. And this is the case\nwith regard to vision. We see the breadth of the street as\nclearly and readily as we see the house on the other side of\nit. We see the house to be square, however obliquely it be\npresented to us. Indeed the difficulty is, to recover the\nconsciousness of our real and original sensations;--to\ndiscover what is the _apparent_ relation of the lines which\nappear before us. As we have already said, (book ii. chap.\n6) in the common process of vision we suppose ourselves to\nsee that which cannot be seen; and when we would make a\npicture of an object, the difficulty is to represent what is\nvisible and no more.\n\nBut perfect as is our habit of interpreting what we\nperceive, we could not interpret if we did not perceive. If\nthe eye did not apprehend visible position, it could not\ninfer actual position, which is collected from visible\nposition as a consequence: if we did not see apparent\nfigure, we could not arrive at any opinion concerning real\nform. The perception of place, which is the prerogative of\nthe eye, is the basis of all its other superiority.\n\nThe precision with which the eye can judge of apparent\nposition is remarkable. If we had before us two stars\ndistant from each other by one-twentieth of the moon's\ndiameter, we could easily decide the apparent direction of\nthe one from the other, as above or below, to the right or\nleft. Yet eight millions of stars might be placed in the\nvisible hemisphere of the sky at such distances from each\nother; and thus the eye would recognize the relative\nposition in a portion of its range not greater than one\neight-millionth of the whole. Such is the accuracy of the\nsense of vision in this {305} respect; and, indeed, we might\nwith truth have stated it much higher. Our judgment of the\nposition of distant objects in a landscape depends upon\nfeatures far more minute than the magnitude we have here\ndescribed.\n\nAs our object is to point out principally the differences of\nthe senses, we do not dwell upon the delicacy with which we\ndistinguish tints and shades, but proceed to another sense.\n\n\nSECT. II.--_Prerogatives of Hearing._\n\nTHE sense of hearing has two remarkable prerogatives; it can\nperceive a definite and peculiar relation between certain\ntones, and it can clearly perceive two tones together; in\nboth these circumstances it is distinguished from vision,\nand from the other senses.\n\n4. _Musical intervals._--We perceive that two tones have, or\nhave not, certain definite relations to each other, which we\ncall _Concords_: one sound is a _Fifth_, an _Octave_, &c.,\nabove the other. And when this is the case, our perception\nof the relation is extremely precise. It is easy to perceive\nwhen a fifth is out of tune by one-twentieth of a tone; that\nis, by one-seventieth of itself. To this there is nothing\nanalogous in vision. Colours have certain vague relations to\none another; they look well together, by contrast or by\nresemblance; but this is an indefinite, and in most cases a\ncasual and variable feeling. The relation of _complementary_\ncolours to one another, as of red to green, is somewhat more\ndefinite; but still, has nothing of the exactness and\npeculiarity which belongs to a musical concord. In the case\nof the two sounds, there is an exact point at which the\nrelation obtains; when by altering one note we pass this\npoint, the concord does not gradually fade away, but\ninstantly becomes a discord; and if we go further still, we\nobtain another concord of quite a different character.\n\nWe learn from the theory of sound that concords occur when\nthe times of vibration of the notes have exact simple\nratios; an octave has these times as 1 to {306} 2; a fifth,\nas 2 to 3. According to the undulatory theory of light, such\nratios occur in colours, yet the eye is not affected by them\nin any peculiar way. The times of the undulations of certain\nred and certain violet rays are as 2 to 3, but we do not\nperceive any peculiar harmony or connexion between those\ncolours.\n\n5. _Chords._--Again, the ear has this prerogative, that it\ncan apprehend two notes together, yet distinct. If two\nnotes, distant by a fifth from each other, are sounded on\ntwo wind instruments, both they and their musical relation\nare clearly perceived. There is not a mixture, but a\nconcord, a musical interval. In colours, the case is\notherwise. If blue and yellow fall on the same spot, they\nform green; the colour is simple to the eye; it can no more\nbe decomposed by the vision than if it were the simple green\nof the prismatic spectrum: it is impossible for us, by\nsight, to tell whether it is so or not.\n\nThese are very remarkable differences of the two senses: two\ncolours can be compounded into an apparently simple one; two\nsounds cannot: colours pass into each other by gradations\nand intermediate tints; sounds pass from one concord to\nanother by no gradations: the most intolerable discord is\nthat which is near a concord. We shall hereafter see how\nthese differences affect the _scales_ of sound and of\ncolour.\n\n6. _Rhythm._--We might remark, that as we see objects in\n_space_, we hear sounds in _time_; and that we thus\nintroduce an arrangement among sounds which has several\nanalogies with the arrangement of objects in space. But the\nconception of time does not seem to be peculiarly connected\nwith the sense of hearing; a faculty of apprehending tone\nand time, or in musical phraseology _tune_ and _rhythm_, are\ncertainly very distinct. I shall not, therefore, here dwell\nupon such analogies.\n\nThe other Senses have not any peculiar prerogatives, at\nleast none which bear on the formation of science. I may,\nhowever, notice, in the feeling of heat, this circumstance;\nthat it presents us with two opposites, heat and cold, which\ngraduate into each other. This {307} is not quite peculiar,\nfor vision also exhibits to us white and black, which are\nclearly opposites, and which pass into each other by the\nshades of gray.\n\n\nSECT. III.--_The Paradoxes of Vision._\n\n7. _First Paradox of Vision. Upright Vision._--All our\nsenses appear to have this in common; That they act by means\nof organs, in which a bundle of nerves receives the\nimpression of the appropriate medium of the sense. In the\nconstruction of these organs there are great differences and\npeculiarities, corresponding, in part at least, to the\ndifferences in the information given. Moreover, in some\ncases, as we have noted in the case of audible position and\nvisible distance, that which seems to be a perception is\nreally a judgment founded on perceptions of which we are not\ndirectly aware. It will be seen, therefore, that with\nrespect to the peculiar powers of each sense, it may be\nasked;--whether they can be explained by the construction of\nthe peculiar organ;--whether they are acquired judgments and\nnot direct perceptions;--or whether they are inexplicable in\neither of these ways, and cannot, at present at least, be\nresolved into anything but conditions of the intellectual\nact of perception.\n\nTwo of these questions with regard to vision, have been much\ndiscussed by psychological writers: the cause of our seeing\nobjects upright by inverted images on the retina; and of our\nseeing single with two such images.\n\nPhysiologists have very completely explained the exquisitely\nbeautiful mechanism of the eye, considered as analogous to\nan optical instrument; and it is indisputable that by means\nof certain transparent lenses and humours, an inverted image\nof the objects which are looked at is formed upon the\n_retina_, or fine net-work of nerve, with which the back of\nthe eye is lined. We cannot doubt that the impression thus\nproduced on these nerves is essential to the act of vision;\nand so far as we consider the nerves {308} themselves to\nfeel or perceive by contact, we may say that they perceive\nthis image, or the affections of light which it indicates.\nBut we cannot with any propriety say that _we_ perceive, or\nthat our mind perceives, this image; for we are not\nconscious of it, and none but anatomists are aware of its\nexistence: we perceive _by means_ of it.\n\nA difficulty has been raised, and dwelt upon in a most\nunaccountable manner, arising from the neglect of this\nobvious distinction. It has been asked, how is it that we\nsee an object, a man for instance, upright, when the\nimmediate object of our sensation, the image of the man on\nour retina, is inverted? To this we must answer, that we see\nhim upright _because_ the image is inverted; that the\ninverted image is the necessary means of seeing an upright\nobject. This is granted, and where then is the difficulty?\nPerhaps it may be put thus: How is it that we do not judge\nthe man to be inverted, since the sensible image is so? To\nthis we may reply, that we have no notion of _upright_ or\ninverted, except that which is founded on experience, and\nthat all our experience, without exception, must have taught\nus that such a sensible image belongs to a man who is in an\nupright position. Indeed, the contrary judgment is not\nconceivable; a man is upright whose head is upwards and his\nfeet downwards. But what are the sensible images of\n_upwards_ and _downwards_? Whatever be our standard of up\nand down, the sensible representation of _up_ will be an\nimage moving on the retina towards the lower side, and the\nsensible representation of _down_ will be a motion towards\nthe upper side. The head of the man's image is towards the\nimage of the sky, its feet are towards the image of the\nground; how then should it appear otherwise than upright? Do\nwe expect that the whole world should appear inverted? Be it\nso: but if the whole be inverted, how is the relation of the\nparts altered? Do we expect that we should think our own\npersons in particular? This cannot be, for we look at them\nas we do at other objects. Do we expect that things should\nappear to fall {309} upwards? Surely not. For what do we\nknow of upwards, except that it is the direction in which\nbodies do _not_ fall? In short, the whole of this\ndifficulty, though it has in no small degree embarrassed\nmetaphysicians, appears to result from a very palpable\nconfusion of ideas; from an attempt at comparison of what\n_we_ see, with that which the retina feels, as if they were\nseparately presentable. It is a sufficient explanation to\nsay, that we do not see the image on the retina, but see by\n_means_ of it. The perplexity does not require much more\nskill to disentangle, than it does to see that a word\nwritten in _black_ ink, may signify _white_[8\\4].\n\n[Note 8\\4: The explanation of our seeing objects erect when\nthe image is inverted has been put very simply, by saying,\n'We _call_ that the _lower_ end of an object which is next\nthe ground.' The observer cannot look into his own eye; he\nknows _by experience_ what kind of image corresponds to a\nman in an upright position. The anatomist tells him that\nthis image is _inverted_: but this does not disturb the\nprocess of judging by experience. It does not appear why any\none should be perplexed at the notion of seeing objects\nerect by means of inverted images, rather than at the notion\nof seeing objects large by means of small images; or cubical\nand pyramidal, by means of images on a spherical surface; or\ngreen and red, by means of images on a black surface. Indeed\nsome persons have contrived to perplex themselves with these\nlatter questions, as well as the first.\n\nThe above explanation is not at all affected, as to its\nsubstance, if we adopt Sir David Brewster's expression, and\nsay that the _line of visible direction_ is a line passing\nthrough the center of the spherical surface of the retina,\nand therefore of course perpendicular to the surface. In\nspeaking of 'the inverted image,' it has always been\nsupposed to be determined by such lines; and though the\npoint where they intersect may not have been ascertained\nwith exactness by previous physiologists, the philosophical\nview of the matter was not in any degree vitiated by this\nimperfection.]\n\n8. _Second Paradox of Vision. Single Vision._--(1.) _Small\nor Distant Objects._--The other difficulty, why with two\nimages on the retina we see only one object, is of a much\nmore real and important kind. This effect is manifestly\nlimited by certain circumstances of a very precise nature;\nfor if we direct our eyes at an object which is very near\nthe eye, we see {310} all other objects double. The fact is\nnot, therefore, that we are incapable of receiving two\nimpressions from the two images, but that, under certain\nconditions, the two impressions form one. A little attention\nshows us that these conditions are, that with both eyes we\nshould look at the same object; and again, we find that to\nlook at an object with either eye, is to direct the eye so\nthat the image falls on or near a particular point about the\nmiddle of the retina. Thus these middle points in the two\nretinas correspond, and we see an image single when the two\nimages fall on the corresponding points.\n\nAgain, as each eye judges of position, and as the two eyes\njudge similarly, an object will be seen in the same place by\none eye and by the other, when the two images which it\nproduces are _similarly situated_ with regard to the\n_corresponding points_ of the retina[9\\4].\n\n[Note 9\\4: The explanation of single vision with two eyes\nmay be put in another form. Each eye judges immediately of\nthe relative position of all objects within the field of its\ndirect vision. Therefore when we look with both eyes at a\n_distant_ prospect (so distant that the distance between the\neyes is small in comparison) the two prospects, being\nsimilar collections of forms, will coincide altogether, if a\ncorresponding point in one and in the other coincide. If\nthis be the case, the two images of every object will fall\nupon corresponding points of the retina, and will appear\nsingle.\n\nIf the two prospects seen by the two eyes do not exactly\ncoincide, in consequence of nearness of the objects, or\ndistortion of the eyes, but if they nearly coincide, the\nstronger image of an object absorbs the weaker, and the\nobject is seen single; yet modified by the combination, as\nwill be seen when we speak of the single vision of near\nobjects. When the two images of an object are considerably\napart, we see it double.\n\nThis explanation is not different in substance from the one\ngiven in the text; but perhaps it is better to avoid the\nassertion that the law of corresponding points is 'a\ndistinct and original principle of our constitution,' as I\nhad stated in the first edition. The simpler mode of stating\nthe law of our constitution appears to be to say, that each\neye determines similarly the position of objects; and that\nwhen the positions of an object, as seen by the two eyes,\ncoincide (or nearly coincide) the object is seen single.]\n\nThis is the Law of Single Vision, at least so far as regards\nsmall objects; namely, objects so small that in\ncontemplating them we consider their position only, {311}\nand not their solid dimensions. Single vision in such cases\nis a result of the law of vision simply: and it is a mistake\nto call in, as some have done, the influence of habit and of\nacquired judgments, in order to determine the result in such\ncases.\n\nTo ascribe the apparent singleness of objects to the\nimpressions of vision corrected by the experience of\ntouch[10\\4], would be to assert that a person who had not\nbeen in the habit of handling what he saw, would see all\nobjects double; and also, to assert that a person beginning\nwith the double world which vision thus offers to him,\nwould, by the continued habit of handling objects, gradually\nand at last learn to see them single. But all the facts of\nthe case show such suppositions to be utterly fantastical.\nNo one can, in this case, go back from the habitual judgment\nof the singleness of objects, to the original and direct\nperception of their doubleness, as the draughtsman goes back\nfrom judgments to perception, in representing solid\ndistances and forms by means of perspective pictures. No one\ncan point out any case in which the habit is imperfectly\nformed; even children of the most tender age look at an\nobject with both eyes, and see it as one.\n\n[Note 10\\4: See Brown, vol. ii. p. 81.]\n\nIn cases when the eyes are distorted (in squinting), one eye\nonly is used, or if both are employed, there is double\nvision; and thus any derangement of the correspondence of\nmotion in the two eyes will produce double-sightedness.\n\nBrown is one of those[11\\4] who assert that two images\nsuggest a single object because we have _always found_ two\nimages to belong to a single object. He urges as an\nillustration, that the _two_ words 'he conquered,' by custom\nexcite exactly the same notion as the _one_ Latin word\n'vicit;' and thus that two visual images, by the effect of\nhabit, produce the same belief of a single object as one\ntactual impression. But in order to make this pretended\nillustration of any value, it ought to be true that when a\nperson has thoroughly learnt the Latin language, he can no\nlonger distinguish {312} any separate meaning in 'he' and in\n'conquered.' We can by no effort perceive the double\nsensation, when we look _at_ the object with the two eyes.\nThose who squint, learn by habit to see objects single: but\nthe habit which they acquire is that of attending to the\nimpressions of one eye only at once, not of combining the\ntwo impressions. It is obvious, that if each eye spreads\nbefore us the same visible scene, with the same objects and\nthe same relations of place, then, if one object in each\nscene coincide, the whole of the two visible impressions\nwill be coincident. And here the remarkable circumstance is,\nthat not only each eye judges for itself of the relations of\nposition which come within its field of view; but that there\nis a superior and more comprehensive faculty which combines\nand compares the two fields of view; which asserts or denies\ntheir coincidence; which contemplates, as in a relative\nposition to one another, these two visible worlds, in which\nall other relative position is given. This power of\nconfronting two sets of visible images and figured spaces\nbefore a purely intellectual tribunal, is one of the most\nremarkable circumstances in the sense of vision.\n\n[Note 11\\4: _Lectures_, vol. ii. p. 81.]\n\n9. (2.) _Near Objects._--We have hitherto spoken of the\nsingleness of objects whose images occupy corresponding\npositions on the retina of the two eyes. But here occurs a\ndifficulty. If an object of moderate size, a small thick\nbook for example, be held at a little distance from the\neyes, it produces an image on the retina of each eye; and\nthese two images are perspective representations of the book\nfrom different points of view, (the positions of the two\neyes,) and are therefore of different forms. Hence the two\nimages cannot occupy corresponding points of the retina\nthroughout their whole extent. If the central parts of the\ntwo images occupy corresponding points, the boundaries of\nthe two wall not correspond. How is it then consistent with\nthe law above stated that in this case the object appears\nsingle?\n\nIt may be observed, that the two images in such a case will\ndiffer most widely when the object is not a {313} mere\nsurface, but a solid. If a book, for example, be held with\none of its upright edges towards the face, the right eye\nwill see one side more directly than the left eye, and the\nleft eye will see another side more directly, and the\noutline of the two images upon the two retinas will exhibit\nthis difference. And it may be further observed, that this\ndifference in the images received by the two eyes, is a\nplain and demonstrative evidence of the solidity of the\nobject seen; since nothing but a solid object could (without\nsome special contrivance) produce these different forms of\nthe images in the two eyes.\n\nHence the absence of exact coincidence in the two images on\nthe retina is the necessary condition of the solidity of the\nobject seen, and must be one of the indications by means of\nwhich our vision apprehends an object as solid. And that\nthis is so, Mr. Wheatstone has proved experimentally, by\nmeans of some most ingenious and striking contrivances. He\nhas devised[12\\4] an instrument (the _stereoscope_) by which\ntwo images (drawn in outline) differing exactly as much as\nthe two images of a solid body seen near the face would\ndiffer, are conveyed, one to one eye, and the other to the\nother. And it is found that when this is effected, the\nobject which the images represent is not only seen single,\nbut is apprehended as solid with a clearness and reality of\nconviction quite distinct from any impression which a mere\nperspective representation can give.\n\n[Note 12\\4: _Phil. Trans._ 1839.]\n\nAt the same time it is found that the object is then only\napprehended as single when the two images are such as are\ncapable of being excited by one single object placed in\nsolid space, and seen by the two eyes. If the images differ\nmore or otherwise than this condition allows, the result is,\nthat both are seen, their lines crossing and interfering\nwith one another.\n\nIt may be observed, too, that if an object be of such large\nsize as not to be taken in by a single glance of the eyes,\nit is no longer apprehended as single by a direct act of\nperception; but its parts are looked at {314} separately and\nsuccessively, and the impressions thus obtained are put\ntogether by a succeeding act of the mind. Hence the objects\nwhich are directly seen as solid, will be of moderate size;\nin which case it is not difficult to show that the outlines\nof the two images will differ from each other only slightly.\n\nHence we are led to the following, as the Law of Single\nVision for _near_ objects:--When the two images in the two\neyes are situated (part for part) nearly, but not exactly,\nupon corresponding points, the object is apprehended as\nsingle, if the two images are such as are or would be given\nby a single solid object seen by the two eyes separately:\nand in this case the object is necessarily apprehended as solid.\n\nThis law of vision does not contradict that stated above for\ndistant objects: for when an object is removed to a\nconsiderable distance, the images in the two eyes coincide\nexactly, and the object is seen as single, though without\nany direct apprehension of its solidity. The first law is a\nspecial case of the second. Under the condition of _exactly_\ncorresponding points, we have the perception of singleness,\nbut no evidence of solidity. Under the condition of _nearly_\ncorresponding points, we may have the perception of\nsingleness, and with it, of solidity.\n\nWe have before noted it as an important feature in our\nvisual perception, that while we have two distinct\nimpressions upon the sense, which we can contemplate\nseparately and alternately, (the impressions on the two\neyes,) we have a higher perceptive faculty which can\nrecognize these two impressions, exactly similar to each\nother, as only two images of one and the same assemblage of\nobjects. But we now see that the faculty by which we\nperceive visible objects can do much more than this:--it can\nnot only unite two impressions, and recognize them as\nbelonging to one object in virtue of their coincidence, but\nit can also unite and identify them, even when they do not\nexactly coincide. It can correct and adjust their small\ndifference, so that they are both apprehended as\nrepresentations of the same figure. It can infer from them a\nreal form, not {315} agreeing with either of them; and a\nsolid space, which they are quite incapable of exemplifying.\nThe visual faculty decides whether or not the two ocular\nimages can be pictures of the same solid object, and if they\ncan, it undoubtingly and necessarily accepts them as being\nso. This faculty operates as if it had the power of calling\nbefore it all possible solid figures, and of ascertaining by\ntrial whether any of those will, at the same time, fit both\nthe outlines which are given by the sense. It assumes the\nreality of solid space, and, if it be possible, reconciles\nthe appearances with that reality. And thus an activity of\nthe mind of a very remarkable and peculiar kind is exercised\nin the most common act of seeing.\n\n10. It may be said that this doctrine, of such a visual\nfaculty as has been described, is very vague and obscure,\nsince we are not told what are its limits. It adjusts and\ncorrects figures which _nearly_ coincide, so as to identify\nthem. But _how_ nearly, it may be asked, must the figures\napproach each other, in order that this adjustment may be\npossible? What discrepance renders impossible the\nreconcilement of which we speak? Is it not impossible to\ngive a definite answer to these questions, and therefore\nimpossible to lay down definitely such laws of vision as we\nhave stated? To this I reply, that the indefiniteness thus\nobjected to us, is no new difficulty, but one with which\nphilosophers are familiar, and to which they are already\nreconciled. It is, in fact, no other than the indefiniteness\nof the limits of distinct vision. How near to the face must\nan object be brought, so that we shall cease to see it\ndistinctly? The distance, it will be answered, is\nindefinite: it is different for different persons; and for\nthe same person, it varies with the degree of effort,\nattention, and habit. But this indefiniteness is only the\nindefiniteness, in another form, of the deviation of the two\nocular images from one another: and in reply to the question\nconcerning them we must still say, as before, that in\ndoubtful cases, the power of apprehending an object as\nsingle, when this _can_ be done, will vary with effort,\nattention, and habit. The assumption {316} that the apparent\nobject exists as a real figure, in real space, is to be\nverified, if possible; but, in extreme cases, from the\nunfitness of the point of view, or from any other cause of\nvisual confusion or deception, the existence of a real\nobject corresponding to the appearance may be doubtful; as\nin any other kind of perception it may be doubtful whether\nour senses, under disadvantageous circumstances, give us\ntrue information. The vagueness of the limits, then, within\nwhich this visual faculty can be successfully exercised, is\nno valid argument against the existence of the faculty, or\nthe truth of the law which we have stated concerning its\naction.\n\n\nSECT. IV.--_The Perception of Visible Figure._\n\n11. _Visible Figure._--There is one tenet on the subject of\nvision which appears to me so extravagant and\nunphilosophical, that I should not have thought it necessary\nto notice it, if it had not been recently promulgated by a\nwriter of great acuteness in a book which has obtained, for\na metaphysical work, considerable circulation. I speak of\nBrown's opinion[13\\4] that we have no immediate perception\nof visible figure. I confess myself unable to comprehend\nfully the doctrine which he would substitute in the place of\nthe one commonly received. He states it thus[14\\4]: 'When\nthe simple affection of sight is blended with the ideas of\nsuggestion [those arising from touch, &c.] in what are\ntermed the acquired perceptions of vision, as, for example,\nin the perception of a sphere, it is colour only which is\nblended with the large convexity, and not a small coloured\nplane.' The doctrine which Brown asserts in this and similar\npassages, appears to be, that we do not by vision perceive\n_both_ colour and _figure_; but that the colour which we see\nis blended with the figure which we learn the existence of\nby other means, as by touch. But if this were possible when\nwe can call in other perceptions, how is it possible when we\ncannot or do not touch the object? {317} Why does the moon\nappear round, gibbous, or horned? What sense besides vision\nsuggests to us the idea of her figure? And even in objects\nwhich we can reach, what is that circumstance in the sense\nof vision which suggests to us that the colour belongs to\nthe sphere, except that we see the colour where we see the\nsphere? If we do not see figure, we do not see position; for\nfigure is the relative position of the parts of a boundary.\nIf we do not see position, why do we ascribe the yellow\ncolour to the sphere on our left, rather than to the cube on\nour right? We _associate_ the colour with the object, says\nDr. Brown; but if his opinion were true, we could not\nassociate two colours with two objects, for we could not\napprehend the colours as occupying two different places.\n\n[Note 13\\4: _Lectures_, vol. ii. p. 82.]\n\n[Note 14\\4: _Ib._ vol. ii. p. 90.]\n\nThe whole of Brown's reasoning on this subject is so\nirreconcilable with the first facts of vision, that it is\ndifficult to conceive how it could proceed from a person who\nhas reasoned with great acuteness concerning touch. In order\nto prove his assertion, he undertakes to examine the only\nreasons which, he says[15\\4], he can imagine for believing\nthe immediate perception of visible figure: (1) That it is\nabsolutely impossible, in our present sensations of sight,\nto separate colour from extension; and (2) That there are,\nin fact, figures on the retina corresponding to the apparent\nfigures of objects.\n\n[Note 15\\4: _Lectures_, vol. ii. p. 83.]\n\nOn the subject of the first reason, he says, that the figure\nwhich we perceive as associated with colour, is the real,\nand not the apparent figure. 'Is there,' he asks, 'the\nslightest consciousness of a perception of visible figure,\ncorresponding to the affected portion of the retina?' To\nwhich, though he seems to think an affirmative answer\nimpossible, we cannot hesitate to reply, that there is\nundoubtedly such a consciousness; that though obscured by\nbeing made the ground of habitual inference as to the real\nfigure, this consciousness is constantly referred to by the\ndraughtsman, and easily recalled by any one. We may separate\ncolour, he says {318} again[16\\4], from the figures on the\nretina, as we may separate it from length, breadth, and\nthickness, which we do not see. But this is altogether\nfalse: we cannot separate colour from length, breadth, and\nthickness, _in any other way_, than by transferring it to\nthe visible figure which we do see. He cannot, he allows,\nseparate the colour from the visible form of the trunk of a\nlarge oak; but just as little, he thinks, can he separate it\nfrom the convex mass of the trunk, which (it is allowed on\nall hands) he does not immediately see. But in this he is\nmistaken: for if he were to make a _picture_ of the oak, he\nwould separate the colour from the convex shape, which he\ndoes not imitate, but he could not separate it from the\nvisible figure, which he does imitate; and he would then\nperceive that the fact that he _has not_ an immediate\nperception of the convex form, is necessarily connected with\nthe fact that he _has_ an immediate perception of the\napparent figure; so far is the rejection of immediate\nperception in the former case from being a reason for\nrejecting it in the latter.\n\n[Note 16\\4: _Lectures_, vol. ii. p. 84.]\n\nAgain, with regard to the second argument. It does not, he\nsays, follow, that because a certain figured portion of the\nretina is affected by light, we should see such a figure;\nfor if a certain figured portion of the olfactory organ were\naffected by odours, we should not acquire by smell any\nperception of such figure[17\\4]. This is merely to say, that\nbecause we do not perceive position and figure by one sense,\nwe cannot do so by another sense. But this again is\naltogether erroneous. It is an office of our sight to inform\nus of position, and consequently of figure; for this\npurpose, the organ is so constructed that the position of\nthe object determines the position of the point of the\nretina affected. There is nothing of this kind in the organ\nof smell; objects in different positions and of different\nforms do not affect different parts of the olfactory nerve,\nor portions of different shape. Different objects, remote\nfrom each other, if perceived by smell, affect the same\n{319} part of the olfactory organs. This is all quite\nintelligible; for it is not the office of smell to inform us\nof position. Of what use or meaning would be the curious and\ncomplex structure of the eye, if it gave us only such vague\nand wandering notions of the colours and forms of the\nflowers in a garden, as we receive from their odours when we\nwalk among them blindfold? It is, as we have said, the\n_prerogative_ of vision to apprehend position: the places of\nobjects on the retina give this information. We do not\nsuppose that the affection of a certain shape of nervous\nexpanse will necessarily and in all cases give us the\nimpression of figure; but we know that in vision it does;\nand it is clear that if we did not acquire our acquaintance\nwith visible figure in this way, we could not acquire it in\nany way[18\\4].\n\n[Note 17\\4: _Ib._ p. 87.]\n\n[Note 18\\4: When Brown says further (p. 87), that we can\nindeed show the image in the dissected eye; but that 'it is\nnot in the dissected eye that vision takes place;' it is\ndifficult to see what his drift is. Does he doubt that there\nis an image formed in the living as completely as in the\ndissected eye?]\n\nThe whole of this strange mistake of Brown's appears to\narise from the fault already noticed;--that of considering\nthe image on the retina as the _object_ instead of the\n_means_ of vision. This indeed is what he says: 'the true\nobject of vision is not the distant body itself, but the\nlight that has reached the expansive termination of the\noptic nerve[19\\4].' Even if this were so, we do not see why\nwe should not perceive the position of the impression on\nthis expanded nerve. But as we have already said, the\nimpression on the nerve is the means of vision, and enables\nus to assign a place, or at least a direction, to the object\nfrom which the light proceeds, and thus makes vision\npossible. Brown, indeed, pursues his own peculiar view till\nhe involves the subject in utter confusion. Thus he\nsays[20\\4], 'According to the common theory [that figure can\nbe perceived by the eye,] a visible sphere is at once to my\nperception convex and plane; and if the sphere be a one, it\nis perceived at once to be a sphere of {320} many feet in\ndiameter, and a plane circular surface of the diameter of a\nquarter of an inch.' It is easy to deduce these and greater\nabsurdities, if we proceed on his strange and baseless\nsupposition that the object and the image on the retina are\n_both_ perceived. But who is conscious of the image on the\nretina in any other way than as he sees the object by means\nof it?\n\n[Note 19\\4: _Lectures_, vol. ii. p. 57.]\n\n[Note 20\\4: _Ib._ vol. ii. p. 89.]\n\nBrown seems to have imagined that he was analysing the\nperception of figure 'in the same manner in which Berkeley\nhad analyzed the perception of distance. He ought to have\nrecollected that such an undertaking, to be successful,\nrequired him to show _what_ elements he analyzed it _into_.\nBerkeley analyzed the perception of real figure into the\ninterpretation of visible figure according to certain rules\nwhich he distinctly stated. Brown analyzes the perception of\nvisible figure into no elements. Berkeley says, that we do\nnot directly perceive distance, but that we perceive\nsomething else, from which we infer distance, namely,\nvisible figure and colour, and our own efforts in seeing;\nBrown says, that we do not see figure, but infer it; what\nthen do we see, which we infer it from? To this he offers no\nanswer. He asserts the seeming perception of visible figure\nto be a result of 'association;'--of 'suggestion.' But what\nmeaning can we attach to this? Suggestion requires something\nwhich suggests; and not a hint is given what it is which\nsuggests position. Association implies two things\nassociated; what is the sensation which we associate with\nform? What is that visual perception which is not figure,\nand which we mistake for figure? What perception is it that\nsuggests a square to the eye? What impressions are those\nwhich have been associated with a visible triangle, so that\nthe revival of the impressions revives the notion of the\ntriangle? Brown has nowhere pointed out such perceptions and\nimpressions; nor indeed was it possible for him to do so;\nfor the only visual perceptions which he allows to remain,\nthose of colour, most assuredly do not suggest visible\nfigures by their differences; red is not associated with\nsquare rather than with round, or with round rather than\nsquare. On the contrary, the {321} eye, constructed in a\nvery complex and wonderful manner in order that it may give\nto us directly the perception of position as well as of\ncolour, has it for one of its prerogatives to give us this\ninformation; and the perception of the relative position of\neach part of the visible boundary of an object constitutes\nthe perception of its apparent figure; which faculty we\ncannot deny to the eye without rejecting the plain and\nconstant evidence of our senses, making the mechanism of the\neye unmeaning, confounding the object with the means of\nvision, and rendering the mental process of vision utterly\nunintelligible.\n\nHaving sufficiently discussed the processes of perception, I\nnow return to the consideration of the Ideas which these\nprocesses assume.\n\n\n\n{{322}}\nCHAPTER III.\n\nSUCCESSIVE ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE\nIDEA OF A MEDIUM.\n\n\n1. IN what precedes, we have shown by various considerations\nthat we necessarily and universally assume the perception of\nsecondary qualities to take place by means of a medium\ninterjacent between the object and the person perceiving.\nPerception is affected by various peculiarities, according\nto the nature of the quality perceived: but in all cases a\nmedium is equally essential to the process.\n\nThis principle, which, as we have seen, is accepted as\nevident by the common understanding of mankind, is confirmed\nby all additional reflection and discipline of the mind, and\nis the foundation of all the theories which have been\nproposed concerning the processes by which the perception\ntakes place, and concerning the modifications of the\nqualities thus perceived. The medium, and the mode in which\nthe impression is conveyed through the medium, seem to be\ndifferent for different qualities; but the existence of the\nmedium leads to certain necessary conditions or\nalternatives, which have successively made their appearance\nin science, in the course of the attempts of men to theorize\nconcerning the principal secondary qualities, sound, light,\nand heat. We must now point out some of the ways, at first\nimperfect and erroneous, in which the consequences of the\nfundamental assumption were traced.\n\n2. _Sound._--In all cases the medium of sensation, whatever\nit is, is supposed to produce the effect of conveying\nsecondary qualities to our perception by means of its\nprimary qualities. It was conceived to operate {323} by the\nsize, form, and motion of its parts. This is a fundamental\nprinciple of the class of sciences of which we have at\npresent to speak.\n\nIt was assumed from the first, as we have seen in the\npassage lately quoted from Aristotle[21\\4], that in the\nconveyance of _sound_, the medium of communication was the\nair. But although the first theorists were right so far,\nthat circumstance did not prevent their going entirely wrong\nwhen they had further to determine the nature of the\nprocess. It was conceived by Aristotle that the air acted\nafter the manner of a rigid body;--like a staff, which,\nreceiving an impulse at one end, transmits it to the other.\nNow this is altogether an erroneous view of the manner in\nwhich the air conveys the impulse by which sound is\nperceived. An approach was made to the true view of this\nprocess, by assimilating it to the diffusion of the little\ncircular waves which are produced on the surface of still\nwater when a stone is dropt into it. These little waves\nbegin from the point thus disturbed, and run outwards,\nexpanding on every side, in concentric circles, till they\nare lost. The propagation of sound through the air from the\npoint where it is produced, was compared by Vitruvius to\nthis diffusion of circular waves in water; and thus the\nnotion of a propagation of impulse by the _waves_ of a fluid\nwas introduced, in the place of the former notion of the\nimpulse of an unyielding body.\n\n[Note 21\\4: _Supr._ p. 297.]\n\nBut though, taking an enlarged view of the nature of the\nprogress of a wave, this is a just representation of the\nmotion of air in conveying sound, we cannot suppose that the\nprocess was, at the period of which we speak, rightly\nunderstood. For the waves of water were contemplated only as\naffecting the surface of the water; and as the air has no\nsurface, the communication must take place by means of an\ninternal motion, which can bear only a remote and obscure\nresemblance to the waves which we see. And even with regard\nto the waves of water, the mechanism by which they are {324}\nproduced and transferred was not at all understood; so that\nthe comparison employed by Vitruvius must be considered\nrather as a loose analogy than as an exact scientific\nexplanation.\n\nNo correct account of such motions was given, till the\nformation of the science of Mechanics in modern times had\nenabled philosophers to understand more distinctly the mode\nin which motion is propagated through a fluid, and to\ndiscern the forces which the process calls into play, so as\nto continue the motion once begun. Newton introduced into\nthis subject the exact and rigorous conception of an\n_Undulation_, which is the true key to the explanation of\nimpulses conveyed through a fluid.\n\nEven at the present day, the right apprehension of the\nnature of an Undulation transmitted through a fluid is found\nto be very difficult for all persons except those whose\nminds have been duly disciplined by mathematical studies.\nWhen we see a wave run along the surface of water, we are\napt to imagine at first that a portion of the fluid is\ntransferred bodily from one place to another. But with a\nlittle consideration we may easily satisfy ourselves that\nthis is not so: for if we look at a field of standing corn,\nwhen a breeze blows over it, we see waves like those of\nwater run along its surface. Yet it is clear that in this\ncase the separate stalks of corn only bend backwards and\nforwards, and no portion of the grain is really conveyed\nfrom one part of the field to the other. This is obvious\neven to popular apprehension. The poet speaks of\n . . . . The rye,\n That stoops its head when whirlwinds rave\n And springs again in eddying wave\n As each wild gust sweeps by.\nEach particle of the mass in succession has a small motion\nbackwards and forwards; and by this means a large ridge made\nby many such particles runs along the mass to any distance.\nThis is the true conception of an undulation in general.\n\nThus, when an Undulation is propagated in a fluid, it is not\n_matter_, but _form_, which is transmitted from {325} one\nplace to another. The particles along the line of each wave\nassume a certain arrangement, and this arrangement passes\nfrom one part to another, the particles changing their\nplaces only within narrow limits, so as to lend themselves\nsuccessively to the arrangements by which the successive\nwaves, and the intervals between the waves, are formed.\n\nWhen such an Undulation is propagated through air, the wave\nis composed, not, as in water, of particles which are higher\nthan the rest, but of particles which are closer to each\nother than the rest. The wave is not a ridge of elevation,\nbut a line of condensation; and as in water we have\nalternately elevated and depressed lines, we have in air\nlines alternately condensed and rarefied. And the motion of\nthe particles is not, as in water, up and down, in a\ndirection transverse to that of the wave which runs\nforwards; in the motion of an undulation through air the\nmotion of each particle is alternately forwards and\nbackwards, while the motion of the undulation is constantly\nforwards.\n\nThis precise and detailed account of the Undulatory Motion\nof air by which sound is transmitted was first given by\nNewton. He further attempted to determine the motions of the\nseparate particles, and to point out the force by which each\nparticle affects the next, so as to continue the progress of\nthe undulation once begun. The motions of each particle must\nbe oscillatory; he assumed the oscillations to be governed\nby the simplest law of oscillation which had come under the\nnotice of mathematicians, (that of small vibrations of a\npendulum;) and he proved that in this manner the forces\nwhich are called into play by the contraction and expansion\nof the parts of the elastic fluid are such as the\ncontinuance of the motion requires.\n\nNewton's proof of the exact law of Oscillatory Motion of the\na\u00ebrial particles was not considered satisfactory by\nsucceeding mathematicians; for it was found that the same\nresult, the development of forces adequate to continue the\nmotion, would follow if any other law of the motion were\nassumed. Cramer proved this by a sort of _parody_ on\nNewton's proof, in which, by the {326} alteration of a few\nphrases in this formula of demonstration, it was made to\nestablish an entirely different conclusion.\n\nBut the general conception of an Undulation as presented by\nNewton was, as from its manifest mechanical truth it could\nnot fail to be, accepted by all mathematicians; and in\nproportion as the methods of calculating the motions of\nfluids were further improved, the necessary consequences of\nthis conception, in the communication of sound through air,\nwere traced by unexceptionable reasoning. This was\nespecially done by Euler and Lagrange, whose memoirs on such\nmotions of fluids are some of the most admirable examples\nwhich exist, of refined mathematical methods applied to the\nsolution of difficult mechanical problems.\n\nBut the great step in the formation of the theory of sound\nwas undoubtedly that which we have noticed, the introduction\nof the Conception of an Undulation such as we have attempted\nto describe it:--a state, condition, or arrangement of the\nparticles of a fluid, which is transferred from one part of\nspace to another by means of small motions of the particles,\naltogether distinct from the movement of the Undulation\nitself. This is a conception which is not obvious to common\napprehension. It appears paradoxical at first sight to speak\nof a large _wave_ (as the tide-wave) running up a river at\nthe rate of twenty miles an hour, while the _stream_ of the\nriver is all the while flowing downwards. Yet this is a very\ncommon fact. And the conception of such a motion must be\nfully mastered by all who would reason rightly concerning\nthe mechanical transmission of impressions through a medium.\n\nWe have described the motion of sound as produced by small\nmotions of the particle forwards and backwards, while the\nwaves, or condensed and rarefied lines, move constantly\nforwards. It may be asked what right we have to suppose the\nmotion to be of this kind, since when sound is heard, no\nsuch motions of the particles of air can be observed, even\nby refined methods of observation. Thus Bacon declares\nhimself against the hypothesis of such a vibration, since,\nas he remarks, it {327} cannot be perceived in any visible\nimpression upon the flame of a candle. And to this we reply,\nthat the supposition of this Vibration is made in virtue of\na principle which is involved in the original assumption of\na medium; namely, That _a Medium, in conveying Secondary\nqualities, operates by means of its Primary qualities_, the\nbulk, figure, motion, and other mechanical properties of its\nparts. This is an Axiom belonging to the Idea of a Medium.\nIn virtue of this axiom it is demonstrable that the motion\nof the air, when any how disturbed, must be such as is\nsupposed in our acoustical reasonings. For the elasticity of\nthe parts of the air, called into play by its expansion and\ncontraction, lead, by a mechanical necessity, to such a\nmotion as we have described. We may add that, by proper\ncontrivances, this motion may be made perceptible in its\nvisible effects. Thus the theory of sound, as an impression\nconveyed through air, is established upon evident general\nprinciples, although the mathematical calculations which are\nrequisite to investigate its consequences are, some of them,\nof a very recondite kind.\n\n3. _Light._--The early attempts to explain Vision\nrepresented it as performed by means of material rays\nproceeding _from_ the eye, by the help of which the eye felt\nout the form and other visible qualities of an object, as a\nblind man might do with his staff. But this opinion could\nnot keep its ground long: for it did not even explain the\nfact that light is necessary to vision. Light, as a peculiar\nmedium, was next assumed as the machinery of vision; but the\nmode in which the impression was conveyed through the medium\nwas left undetermined, and no advance was made towards sound\ntheory, on that subject, by the ancients.\n\nIn modern times, when the prevalent philosophy began to\nassume a mechanical turn (as in the theories of Descartes),\nlight was conceived to be a material substance which is\nemitted from luminous bodies, and which is also conveyed\nfrom all bodies to the eye, so as to render them visible.\nThe various changes of direction by which the rays of light\nare affected, (reflection, {328} refraction, &c.,) Descartes\nexplained, by considering the particles of light as small\nglobules, which change their direction when they impinge\nupon other bodies, according to the laws of Mechanics.\nNewton, with a much more profound knowledge of Mechanics\nthan Descartes possessed, adopted, in the most mature of his\nspeculations, nearly the same view of the nature of light;\nand endeavoured to show that reflection, refraction, and\nother properties of light, might be explained as the effects\nwhich certain forces, emanating from the particles of\nbodies, produce upon the luminiferous globules.\n\nBut though some of the properties of light could thus be\naccounted for by the assumption of particles emitted from\nluminous bodies, and reflected or refracted by forces, other\nproperties came into view which would not admit of the same\nexplanation. The phenomena of _diffraction_ (the fringes\nwhich accompany shadows) could never be truly represented by\nsuch an hypothesis, in spite of many attempts which were\nmade. And the _colours of thin plates_, which show the rays\nof light to be affected by an alternation of two different\nconditions at small intervals along their length, led Newton\nhimself to incline, often and strongly, to some hypothesis\nof undulation. The _double refraction_ of Iceland spar, a\nphenomenon in itself very complex, could, it was found by\nHuyghens, be expressed with great simplicity by a certain\nhypothesis of undulations.\n\nTwo hypotheses of the nature of the luminiferous medium were\nthus brought under consideration; the one representing Light\nas Matter emitted from the luminous object, the other, as\nUndulations propagated through a fluid. These two hypotheses\nremained in presence of each other during the whole of the\nlast century, neither of them gaining any material advantage\nover the other, though the greater part of mathematicians,\nfollowing Newton, embraced the emission theory. But at the\nbeginning of the present century, an additional class of\nphenomena, those of the _interference_ of two rays of light,\nwere brought under {329} consideration by Dr. Young; and\nthese phenomena were strongly in favour of the undulatory\ntheory, while they were irreconcilable with the hypothesis\nof emission. If it had not been for the original bias of\nNewton and his school to the other side, there can be little\ndoubt that from this period light as well as sound would\nhave been supposed to be propagated by undulations; although\nin this case it was necessary to assume as the vehicle of\nsuch undulations a special medium or _ether_. Several points\nof the phenomena of vision no doubt remained unexplained by\nthe undulatory theory, as absorption, and the natural\ncolours of bodies; but such facts, though they did not\nconfirm, did not evidently contradict the theory of a\nLuminiferous Ether; and the facts which such a theory did\nexplain, it explained with singular happiness and accuracy.\n\nBut before this Undulatory Theory could be generally\naccepted, it was presented in an entirely new point of view\nby being combined with the facts of _polarization_. The\ngeneral idea of polarization must be illustrated hereafter;\nbut we may here remark that Young and Fresnel, who had\nadopted the undulatory theory, after being embarrassed for\nsome time by the new facts which were thus presented to\ntheir notice, at last saw that these facts might be\nexplained by conceiving the vibrations to be transverse to\nthe ray, the motions of the particles being not backwards\nand forwards in the line in which the impulse travels, but\nto the right and left of that line. This conception of\n_transverse vibrations_, though quite unforeseen, had\nnothing in it which was at all difficult to reconcile with\nthe general notion of an undulation. We have described an\nundulation, or wave, as a certain condition or arrangement\nof the particles of the fluid successively transferred from\none part of space to another: and it is easily conceivable\nthat this arrangement or wave may be produced by a lateral\ntransfer of the particles from their quiescent positions.\nThis conception of transverse vibrations being accepted, it\nwas found that the explanation of the phenomena of\npolarization and of those of interference led to the same\ntheory {330} with a correspondence truly wonderful; and this\ncoincidence in the views, collected from two quite distinct\nclasses of phenomena, was justly considered as an almost\ndemonstrative evidence of the truth of this undulatory\ntheory.\n\nIt remained to be considered whether the doctrine of\ntransverse vibrations in a fluid could be reconciled with\nthe principles of Mechanics. And it was found that by making\ncertain suppositions, in which no inherent improbability\nexisted, the hypothesis of transverse vibrations would\nexplain the laws, both of interference and of polarization\nof light, in air and in crystals of all kinds, with a\nsurprizing fertility and fidelity.\n\nThus the Undulatory Theory of Light, like the Undulatory\nTheory of Sound, is recommended by its conformity to the\nfundamental principle of the Secondary Mechanical Sciences,\nthat the medium must be supposed to transmit its peculiar\nimpulses according to the laws of Mechanics. Although no one\nhad previously dreamt of qualities being conveyed through a\nmedium by such a process, yet when it is once suggested as\nthe only mode of explaining some of the phenomena, there is\nnothing to prevent our accepting it entirely, as a\nsatisfactory theory for all the known laws of Light.\n\n4. _Heat._--With regard to Heat as with regard to Light, a\nfluid medium was necessarily assumed as the vehicle of the\nproperty. During the last century, this medium was supposed\nto be an emitted fluid. And many of the ascertained Laws of\nHeat, those which prevail with regard to its radiation more\nespecially, were well explained by this hypothesis[22\\4].\nOther effects of heat, however, as for instance _latent\nheat_[23\\4], and the change of _consistence_ of\nbodies[24\\4], were not satisfactorily brought into connexion\nwith the hypothesis; while {331} _conduction_[25\\4], which\nat first did not appear to result from the fundamental\nassumption, was to a certain extent explained as internal\nradiation.\n\n[Note 22\\4: See the Account of the Theory of Exchanges,\n_Hist. Ind. Sc._ b. x. c. i. sect. 2.]\n\n[Note 23\\4: _Ib._ c. ii. sect. 3.]\n\n[Note 24\\4: _Ib._ c. ii. sect. 2.]\n\n[Note 25\\4: _Ib._ c. i. sect. 7.]\n\nBut it was by no means clear that an Undulatory Theory of\nHeat might not be made to explain these phenomena equally\nwell. Several philosophers inclined to such a theory; and\nfinally, Amp\u00e8re showed that the doctrine that the heat of a\nbody consists in the undulations of its particles propagated\nby means of the undulations of a medium, might be so\nadjusted as to explain all which the theory of emission\ncould explain, and moreover to account for facts and laws\nwhich were out of the reach of that theory. About the same\ntime it was discovered by Prof. Forbes and M. Nobili that\nradiant heat is, under certain circumstances, polarized. Now\npolarization had been most satisfactorily explained by means\nof transverse undulations in the case of light; while all\nattempts to modify the emission theory so as to include\npolarization in it, had been found ineffectual. Hence this\ndiscovery was justly considered as lending great countenance\nto the opinion that Heat consists in the vibrations of its\nproper medium.\n\nBut what is this medium? Is it the same by which the\nimpressions of Light are conveyed? This is a difficult\nquestion; or rather it is one which we cannot at present\nhope to answer with certainty. No doubt the connexion\nbetween Light and Heat is so intimate and constant, that we\ncan hardly refrain from considering them as affections of\nthe same medium. But instead of attempting to erect our\nsystems on such loose and general views of connexion, it is\nrather the business of the philosophers of the present day\nto determine the laws of the operation of heat, and its real\nrelation to light, in order that we may afterwards be able\nto connect the theories of the two qualities. Perhaps in a\nmore advanced state of our knowledge we may be able to state\nit as an Axiom, that two Secondary Qualities, which are\nintimately connected in their causes and effects, must be\naffections of the same Medium. {332} But at present it does\nnot appear safe to proceed upon such a principle, although\nmany writers, in their speculations both concerning Light\nand Heat, and concerning other properties, have not\nhesitated to do so.\n\nSome other consequences follow from the Idea of a Medium\nwhich must be the subject of another chapter.\n\n\n\n{{333}}\nCHAPTER IV.\n\nOF THE MEASURE OF SECONDARY QUALITIES.\n\n\nSECT. I.--_Scales of Qualities in general._\n\nTHE ultimate object of our investigation in each of the\nSecondary Mechanical Sciences, is the nature of the\nprocesses by which the special impressions of sound, light,\nand heat, are conveyed, and the modifications of which these\nprocesses are susceptible. And of this investigation, as we\nhave seen, the necessary basis is the principle, that these\nimpressions are transmitted by means of a medium. But before\nwe arrive at this ultimate object, we may find it necessary\nto occupy ourselves with several intermediate objects:\nbefore we discover the _cause_, it may be necessary to\ndetermine the _laws_ of the phenomena. Even if we cannot\nimmediately ascertain the mechanism of light or heat, it may\nstill be interesting and important to arrange and measure\nthe effects which we observe.\n\nThe idea of a Medium affects our proceeding in this research\nalso. We cannot measure Secondary qualities in the same\nmanner in which we measure Primary qualities, by a mere\naddition of parts. There is this leading and remarkable\ndifference, that while both classes of qualities are\nsusceptible of changes of magnitude, primary qualities\nincrease by addition of _extension_, secondary, by\naugmentation of _intensity_. A space is doubled when another\nequal space is placed by its side; one weight joined to\nanother makes up the sum of the two. But when one degree of\nwarmth is combined with another, or one shade of red colour\nwith another, we cannot in like manner talk of the _sum_.\nThe component parts do not evidently retain their {334}\nseparate existence; we cannot separate a strong green colour\ninto two weaker ones, as we can separate a large force into\ntwo smaller. The increase is absorbed into the previous\namount, and is no longer in evidence as a part of the whole.\nAnd this is the difference which has given birth to the two\nwords _extended_, and _intense_. That is extended which has\n'partes extra partes,' parts outside of parts: that is\nintense which becomes stronger by some indirect and\nunapparent increase of agency, like the stretching of the\ninternal springs of a machine, as the term _intense_\nimplies. Extended magnitudes can at will be resolved into\nthe parts of which they were originally composed, or any\nother which the nature of their extension admits; their\nproportion is apparent; they are directly and at once\nsubject to the relations of number. Intensive magnitudes\ncannot be resolved into smaller magnitudes; we can see that\nthey differ, but we cannot tell in what proportion; we have\nno direct measure of their quantity. How many times hotter\nthan blood is boiling water? The answer cannot be given by\nthe aid of our feelings of heat alone.\n\nThe difference, as we have said, is connected with the\nfundamental principle that we do not perceive Secondary\nqualities directly, but through a Medium. We have no natural\napprehension of light, or sound, or heat, as they exist in\nthe bodies from which they proceed, but only as they affect\nour organs. We can only measure them, therefore, by some\n_Scale_ supplied by their effects. And thus while extended\nmagnitudes, as space, time, are measurable directly and of\nthemselves; intensive magnitudes, as brightness, loudness,\nheat, are measurable only by artificial means and\nconventional scales. Space, time, measure themselves: the\nrepetition of a smaller space, or time, while it composes a\nlarger one, measures it. But for light and heat we must have\nPhotometers and Thermometers, which measure something which\nis assumed to be an indication of the quality in question.\nIn the one case, the mode of applying the measure, and the\nmeaning of the number resulting, are seen by intuition; in\nthe {335} other, they are consequences of assumption and\nreasoning. In the one case, they are _Units_, of which the\nextension is made up; in the other, they are _Degrees_ by\nwhich the intensity ascends.\n\n2. When we discover any property in a sensible quality,\nwhich at once refers us to number or space, we readily take\nthis property as a measure; and thus we make a transition\nfrom quality to quantity. Thus Ptolemy in the third chapter\nof the First Book of his _Harmonics_ begins thus: 'As to the\ndifferences which exist in sounds both in _quality_ and in\n_quantity_, if we consider that difference which refers to\nthe acuteness and graveness, we cannot at once tell to which\nof the above two classes it belongs, till we have considered\nthe causes of such symptoms.' But at the end of the chapter,\nhaving satisfied himself that grave sounds result from the\nmagnitude of the string or pipe, other things being equal,\nhe infers, 'Thus the difference of acute and grave appears\nto be a difference of _quantity_.'\n\nIn the same manner, in order to form Secondary Mechanical\nSciences respecting any of the other properties of bodies,\nwe must reduce these properties to a dependence upon\nquantity, and thus make them subject to measurement. We\ncannot obtain any sciential truths respecting the comparison\nof sensible qualities, till we have discovered measures and\nscales of the qualities which we have to consider; and\naccordingly, some of the most important steps in such\nsciences have been the establishment of such measures and\nscales, and the invention of the requisite instruments.\n\nThe formation of the mathematical sciences which rest upon\nthe measures of the intensity of sensible qualities took\nplace mainly in the course of the last century. Perhaps we\nmay consider Lambert, a mathematician who resided in\nSwitzerland, and published about 1750, as the person who\nfirst clearly felt the importance of establishing such\nsciences. His Photometry, Pyrometry, and Hygrometry, are\nexamples of the systematic reduction of sensible qualities\n(light, heat, moisture) to modes of numerical measurement.\n{336}\n\nWe now proceed to speak of such modes of measurement with\nregard to the most obvious properties of bodies.\n\n\nSECT. II.--_The Musical Scale._\n\n3. THE establishment of the _Harmonic Canon_, that is, of a\nScale and Measure of the musical place of notes, in the\nrelation of _high_ and _low_, was the first step in the\nscience of Harmonics. The perception of the differences and\nrelations of musical sounds is the office of the sense of\nhearing; but these relations are fixed, and rendered\naccurately recognizable by artificial means. 'Indeed, in all\nthe senses,' as Ptolemy truly says in the opening of his\nHarmonics, 'the sense discovers what is approximately true,\nand receives accuracy from another quarter: the reason\nreceives the approximately-true from another quarter, and\ndiscovers the accurate truth.' We can have no measures of\nsensible qualities which do not ultimately refer to the\nsense;--whether they do this immediately, as when we refer\nColours to an assumed Standard; or mediately, as when we\nmeasure Heat by Expansion, having previously found by an\nappeal to sense that the expansion increases with the heat.\nSuch relations of sensible qualities cannot be described in\nwords, and can only be apprehended by their appropriate\nfaculty. The faculty by which the relations of sounds are\napprehended is a _musical ear_ in the largest acceptation of\nthe term. In this signification the faculty is nearly\nuniversal among men; for all persons have musical ears\nsufficiently delicate to understand and to imitate the\nmodulations corresponding to various emotions in speaking;\nwhich modulations depend upon the succession of acuter and\ngraver tones. These are the relations now spoken of, and\nthese are plainly perceived by persons who have very\nimperfect musical ears, according to the common use of the\nphrase. But the relations of tones which occur in speaking\nare somewhat indefinite; and in forming that musical scale\nwhich is the basis of our science upon the subject, we {337}\ntake the most definite and marked of such relations of\nnotes; such as occur, not in speaking but in singing. Those\nmusical relations of two sounds which we call the _octave_,\nthe _fifth_, the _fourth_, the _third_, are recognized after\na short familiarity with them. These _chords_ or _intervals_\nare perceived to have each a peculiar character, which\nseparates them from the relations of two sounds taken at\nrandom, and makes it easy to know them when sung or played\non an instrument; and for most persons, not difficult to\nsing the sounds in succession exactly, or nearly correct.\nThese musical relations, or _concords_, then, are the\ngroundwork of our musical series of sounds. But how are we\nto name these indescribable sensible characters? how to\nrefer, with unerring accuracy, to a type which exists only\nin our own perceptions? We must have for this purpose a\n_Scale_ and a _Standard_.\n\nThe Musical Scale is a series of eight notes, ascending by\ncertain steps from the first or key-note to the octave above\nit, each of the notes being fixed by such distinguishable\nmusical relations as we have spoken of above. We may call\nthese notes C, D, E, F, G, A, B, _c_; and we may then say\nthat G is determined by its being a fifth above C; D by its\nbeing a fourth below G; E by its being a third above C; and\nsimilarly of the rest. It will be recollected that the terms\na _fifth_, a _fourth_, a _third_, have hitherto been\nintroduced as expressing certain simple and indescribable\nmusical relations among sounds, which might have been\nindicated by any other names. Thus we might call the fifth\nthe _dominant_, and the fourth the _subdominant_, as is done\nin one part of musical science. But the names we have used,\nwhich are the common ones, are in fact derived from the\nnumber of notes which these intervals include in the scale\nobtained in the above manner. The notes, C, D, E, F, G,\nbeing five, the interval from C to G is a fifth, and so of\nthe rest. The fixation of this scale gave the means of\ndescribing exactly any note which occurs in the scale, and\nthe method is easily applicable to notes above and below\nthis range; for in a series of sounds higher or lower by an\noctave than {338} this standard series, the ear discovers a\nrecurrence of the same relations so exact, that a person may\nsometimes imagine he is producing the same notes as another\nwhen he is singing the same air an octave higher. Hence the\nnext eight notes may be conveniently denoted by a repetition\nof the same letters, as the first; thus, C, D, E, F, G, A,\nB, _c_, _d_, _e_, _f_, _g_, _a_, _b_; and it is easy to\ndevise a continuation of such cycles. And other admissible\nnotes are designated by a further modification of the\nstandard ones, as by making each note _flat_ or _sharp_;\nwhich modification it is not necessary here to consider,\nsince our object is only to show how a standard is\nattainable, and how it serves the ends of science.\n\nWe may observe, however, that the above is not an exact\naccount of the first, or early Greek scale; for that scale\nwas founded on a primary division of the interval of two\noctaves (the extreme range which it admitted) into five\n_tetrachords_, each tetrachord including the interval of a\nfourth. All the notes of this series had different names\nborrowed from this division[26\\4]; thus _mese_ was the\nmiddle or key-note; the note below it was _lichanos mes\u00f4n_,\nthe next below was _parypate mes\u00f4n_, the next lower, _hypate\nmes\u00f4n_. The fifth above _mese_ was _nete diazeugmen\u00f4n_, the\noctave was _nete hyperbol\u00e6\u00f4n_.\n\n[Note 26\\4: Burney's _History of Music_, vol. i. p. 28.]\n\n4. But supposing a complete system of such denominations\nestablished, how could it be with certainty and rigour\napplied? The human ear is fallible, the organs of voice\nimperfectly obedient; if this were not so, there would be no\nsuch thing as a _good_ ear or a _good_ voice. What means can\nbe devised of finding at will a _perfect_ concord, a fifth\nor a fourth? Or supposing such concords fixed by an\nacknowledged authority, how can they be referred to, and the\nauthority adduced? How can we enact a Standard of sounds?\n\nA Standard was discovered in the _Monochord_. A musical\nstring properly stretched, may be made to produce different\nnotes, in proportion as we intercept a longer or shorter\nportion, and make this portion {339} vibrate. The relation\nof the length of the strings which thus sound the two notes\nG and C is fixed and constant, and the same is true of all\nother notes. Hence the musical interval of any notes of\nwhich we know the places in the musical scale, may be\nreproduced by measuring the lengths of string which are\nknown to give them. If C be of the length 180, D is 160, E\nis 144, F is 135, G is 120; and thus the musical relations\nare reduced to numerical relations, and the monochord is a\ncomplete and perfect _Tonometer_.\n\nWe have here taken the length of the string as the measure\nof the tone: but we may observe that there is in us a\nnecessary tendency to assume that the ground of this measure\nis to be sought in some ulterior cause; and when we consider\nthe matter further, we find this cause in the frequency of\nthese vibrations of the string. The truth that the same note\nmust result from the same frequency of vibration is readily\nassented to on a slight suggestion of experience. Thus\nMersenne[27\\4], when he undertakes to determine the\nfrequency of vibrations of a given sound, says 'Supponendum\nest quoscunque nervos et quaslibet chordas unisonum\nfacientes eundem efficere numerum recursuum eodem vel equali\ntempore, quod perpetu\u00e2 constat experienti\u00e2.' And he proceeds\nto apply it to cases where experience could not verify this\nassertion, or at least had not verified it, as to that of pipes.\n\n[Note 27\\4: _Harmonia_, lib. ii. prop. 19.]\n\nThe pursuit of these numerical relations of tones forms the\nscience of Harmonics; of which here we do not pretend to\ngive an account, but only to show, how the invention of a\nScale and Nomenclature, a Standard and Measure of the tone\nof sounds, is its necessary basis. We will therefore now\nproceed to speak of another subject; _colour_.\n\n\nSECT. III.--_Scales of Colour._\n\n5. _The Prismatic Scale of Colour._--A SCALE of Colour must\ndepend originally upon differences {340} discernible by the\neye, as a scale of notes depends on differences perceived by\nthe ear. In one respect the difficulty is greater in the\ncase of the visible qualities, for there are no relations of\ncolour which the eye peculiarly singles out and\ndistinguishes, as the ear selects and distinguishes an\noctave or a fifth. Hence we are compelled to take an\narbitrary scale; and we have to find one which is fixed, and\nwhich includes a proper collection of colours. The\n_prismatic spectrum_, or coloured image produced when a\nsmall beam of light passes obliquely through any transparent\nsurface (as the surface of a prism of glass,) offers an\nobvious Standard as far as it is applicable. Accordingly\ncolours have, for various purposes, been designated by their\nplace in the spectrum, ever since the time of Newton; and we\nhave thus a means of referring to such colours as are\nincluded in the series _red_, _orange_, _yellow_, _green_,\n_blue_, _violet_, _indigo_, and the intermediate tints.\n\nBut this scale is not capable of numerical precision. If the\nspectrum could be exactly defined as to its extremities, and\nif these colours occupied always the same proportional part\nof it, we might describe any colour in the above series by\nthe measure of its position. But the fact is otherwise. The\nspectrum is too indefinite in its boundaries to afford any\ndistinct point from which we may commence our measures; and\nmoreover the spectra produced by different transparent\nbodies differ from each other. Newton had supposed that the\nspectrum and its parts were the same, so long as the\nrefraction was the same; but his successors discovered that,\nwith the same amount of refraction in different kinds of\nglass, there are different magnitudes of the spectrum; and\nwhat is still worse with reference to our present purpose,\nthat the spectra from different glasses have the colours\ndistributed in different proportions. In order, therefore,\nto make the spectrum the scale of colour, we must assume\nsome fixed substance; for instance, we may take water, and\nthus a series approaching to the colours of the _rainbow_\nwill be our standard. But we should still have an extreme\ndifficulty in applying such a rule. The distinctions of\n{341} colour which the terms of common language express, are\nnot used with perfect unanimity or with rigorous precision.\nWhat one person calls _bluish green_ another calls _greenish\nblue_. Nobody can say what is the precise boundary between\nred and orange. Thus the prismatic scale of colour was\nincapable of mathematical exactness, and this inconvenience\nwas felt up to our own times.\n\nBut this difficulty was removed by a curious discovery of\nWollaston and Fraunhofer; who found that there are, in the\nsolar spectrum, certain fine black Lines which occupy a\ndefinite place in the series of colours, and can be observed\nwith perfect precision. We have now no uncertainty as to\nwhat coloured light we are speaking of, when we describe it\nas that part of the spectrum in which Fraunhofer's Line C or\nD occurs. And thus, by this discovery, the prismatic\nspectrum of sunlight became, for certain purposes, an exact\n_Chromatometer_.\n\n6. _Newton's Scale of Colours._--Still, such a standard,\nthough definite, is arbitrary and seemingly anomalous. The\nlines A, B, C, D, &c., of Fraunhofer's spectrum are\ndistributed without any apparent order or law; and we do\nnot, in this way, obtain numerical measures, which is what,\nin all cases, we desire to have. Another discovery of\nNewton, however, gives us a spectrum containing the same\ncolours as the prismatic spectrum, but produced in another\nway, so that the colours have a numerical relation. I speak\nof the laws of the _Colours of Thin Plates_. The little\nrainbows which we sometimes see in the cracks of broken\nglass are governed by fixed and simple laws. The kind of\ncolour produced at any point depends on the thickness of the\nthin plate of air included in the fissure. If the thickness\nbe eight-millionths of an inch, the colour is orange, if\nfifteen-millionths of an inch, we have green, and so on; and\nthus these numbers, which succeed each other in a regular\norder from red to indigo, give a numerical measure of each\ncolour; which measure, when we pursue the subject, we find\nis one of the bases of all optical theory. The series of\ncolours obtained from plates of air of gradually increasing\nthickness is called {342} _Newton's Scale of Colours_; but\nwe may observe that this is not precisely what we are here\nspeaking of, a scale of _simple_ colours; it is a series\nproduced by certain combinations, resulting from the\nrepetition of the first spectrum, and is mainly useful as a\nstandard for similar phenomena, and not for colour in\ngeneral. The real scale of colour is to be found, as we have\nsaid, in the numbers which express the thickness of the\nproducing film;--in the length of a _fit_ in Newton's\nphraseology, or the length of an _undulation_ in the modern\ntheory.\n\n7. _Scales of Impure Colours._--The standards just spoken of\ninclude (mainly at least) only pure and simple colours; and\nhowever complete these standards may be for certain objects\nof the science of optics, they are insufficient for other\npurposes. They do not enable us to put in their place mixed\nand impure colours. And there is, in the case of colour, a\ndifficulty already noticed, which does not occur in the case\nof sound; two notes, when sounded together, are not\nnecessarily heard as one; they are recognized as still two,\nand as forming a concord or a discord. But two colours form\na single colour; and the eye cannot, in any way, distinguish\nbetween a green compound of blue and yellow, and the simple,\nundecomposable green of the spectrum. By composition of\nthree or more colours, innumerable new colours may be\ngenerated which form no part of the prismatic series; and by\nsuch compositions is woven the infinitely varied web of\ncolour which forms the clothing of nature. How are we to\nclassify and arrange all the possible colours of objects, so\nthat each shall have a place and name? How shall we find a\n_chromatometer_ for impure as well as for pure colour?\n\nThough no optical investigations have depended on a scale of\nimpure colours, such a scale has been wanted and invented\nfor other purposes; for instance, in order to identify and\ndescribe objects of natural history. Not to speak of earlier\nessays, we may notice Werner's Nomenclature of Colours,\ndevised for the purpose of describing minerals. This scale\nof colour was far superior to any which had previously been\npromulgated. {343} It was, indeed, arbitrary in the\nselection of its degrees, and in a great measure in their\narrangement; and the colours were described by the usual\nterms, though generally with some added distinction; as\n_blackish green_, _bluish green_, _apple-green_,\n_emerald-green_. But the great merit of the scale was its\ngiving a _fixed_ conventional meaning to these terms, so\nthat they lost much of their usual vagueness. Thus\n_apple-green_ did not mean the colour of any green apple\ncasually taken; but a certain definite colour which the\nstudent was to bear in mind, whether or not he had ever seen\nan apple of that exact hue. The words were not a\ndescription, but a _record_ of the colour: the memory was to\nretain a _sensation_, not a name.\n\nThe imperfection of the system (arising from its arbitrary\nform) was its incompleteness: however well it served for the\nreference of the colours which it did contain, it was\napplicable to no others; and thus though Werner's\nenumeration extended to more than a hundred colours, there\noccur in nature a still greater number which cannot be\nexactly described by means of it.\n\nIn such cases the unclassed colour is, by the Wernerians,\ndefined by stating it as intermediate between two others:\nthus we have an object described as _between emerald-green\nand grass-green_. The eye is capable of perceiving a\ngradation from one colour to another; such as may be\nproduced by a gradual mixture in various ways. And if we\nimage to ourselves such a mixture, we can compare with it a\ngiven colour. But in employing this method we have nothing\nto tell us in what part of the scale we must seek for an\napproximation to our unclassed colour. We have no rule for\ndiscovering where we are to look for the boundaries of the\ndefinition of a colour which the Wernerian series does not\nsupply. For it is not always between contiguous members of\nthe series that the undescribed colour is found. If we place\nemerald-green between apple-green and grass-green, we may\nyet have a colour intermediate between emerald-green and\nleek-green; and, in fact, the Wernerian series of colours is\ndestitute {344} of a principle of self-arrangement and\ngradation; and is thus necessarily and incurably imperfect.\n\n8. We should have a complete Scale of Colours, if we could\nform a series including all colours, and arranged so that\neach colour was intermediate in its tint between the\nadjacent terms of the series; for then, whether we took many\nor few of the steps of the series for our standard terms,\nthe rest could be supplied by the law of continuity; and any\ngiven colour would either correspond to one of the steps of\nour scale or fall between two intermediate ones. The\ninvention of a Chromatometer for Impure Colours, therefore,\nrequires that we should be able to form all possible colours\nby such intermediation in a systematic manner; that is, by\nthe mixture or combination of certain elementary colours\naccording to a simple rule: and we are led to ask whether\nsuch a process has been shown to be possible.\n\nThe colours of the prismatic spectrum obviously do form a\ncontinuous series; green is intermediate between its\nneighbours yellow and blue, orange between red and yellow;\nand if we suppose the two ends of the spectrum bent round to\nmeet each other, so that the arrangement of the colours may\nbe circular, the violet and indigo will find their\nappropriate place between the blue and red. And all the\ninterjacent tints of the spectrum, as well as the ones just\nnamed, will result from such an arrangement. Thus all the\n_pure_ colours are produced by combinations two and two of\nthree primary colours, Red, Yellow, and Blue: and the\nquestion suggests itself whether these three are not really\nthe only Primary Colours, and whether all the impure colours\ndo not arise from mixtures of the three in various\nproportions. There are various modes in which this\nsuggestion may be applied to the construction of a scale of\ncolours; but the simplest, and the one which appears really\nto verify the conjecture that all possible colours may be so\nexhibited, is the following. A certain combination of red,\nyellow, and blue, will produce black, or pure grey, and when\ndiluted, will give all the shades of grey which intervene\nbetween {345} black and white. By adding various shades of\ngrey, then, to pure colours, we may obtain all the possible\nternary combinations of red, yellow, and blue; and in this\nway it is found that we exhaust the range of colours. Thus\nthe circle of pure colours of which we have spoken may be\naccompanied by several other circles, in which these colours\nare tinged with a less or greater shade of grey; and in this\nmanner it is found that we have a perfect chromatometer;\nevery possible colour being exhibited either exactly or by\nmeans of approximate and contiguous limits. The arrangement\nof colours has been brought into this final and complete\nform by M. Merim\u00e9e, whose Chromatic Scale is published by M.\nMirbel in his _Elements of Botany_. We may observe that such\na standard affords us a numerical exponent for every colour\nby means of the proportions of the three primary colours\nwhich compose it; or, expressing the same result otherwise,\nby means of the pure colour which is involved, and the\nproportion of grey by which it is rendered impure. In such a\nscale the fundamental elements would be the precise tints of\nred, yellow, and blue which are found or assumed to be\nprimary; the numerical exponents of each colour would depend\nupon the arbitrary number of degrees which we interpose\nbetween each two primary colours; and between each pure\ncolour and absolute blackness. No such numerical scale has,\nhowever, as yet, obtained general acceptation[28\\4].\n\n[Note 28\\4: The reference to _Fraunhofer's Lines_, as a\nmeans of determining the place of a colour in the prismatic\nseries, has been objected to, because, as is asserted, the\ncolours which are in the neighbourhood of each line vary\nwith the position of the sun, state of the atmosphere and\nthe like. It is very evident that coloured light refracted\nby the prism will not give the same spectrum as white light.\nThe spectrum given by white light is of course the one here\nmeant. It is an usual practice of optical experimenters to\nrefer to the colours of such a spectrum, defining them by\nFraunhofer's Lines.\n\nI do not know whether it needs explanation that the 'first\nspectrum' in Newton's rings is a ring of the prismatic\ncolours.\n\nI have not had an opportunity of consulting Lambert's\n_Photometria, sive de mensura et gradibus luminis, colorum,\net umbr\u00e6_, published in 1760, nor Mayer's _Commentatio de\nAffinitate Colorum_, (1758), in which, I believe, he\ndescribes a chromatometer. The present work is not intended\nto be complete as a history; and I hope I have given\nsufficient historical detail to answer its philosophical\npurpose.]\n\n\n{346} SECT. IV.--_Scales of Light._\n\n9. _Photometer._--ANOTHER instrument much needed in optical\nresearches is a _Photometer_, a measure of the intensity of\nlight. In this case, also, the organ of sense, the eye, is\nthe ultimate judge; nor has any effect of light, as light,\nyet been discovered which we can substitute for such a\njudgment. All instruments, such as that of Leslie, which\nemploy the heating effect of light, or at least all that\nhave hitherto been proposed, are inadmissible as\nphotometers. But though the eye can judge of two surfaces\nilluminated by light of the same colour, and can determine\nwhen they are equally bright, or which is the brighter, the\neye can by no means decide at sight the proportion of\nillumination. How much in such judgments we are affected by\ncontrast, is easily seen when we consider how different is\nthe apparent brightness of the moon at mid-day and at\nmidnight, though the light which we receive from her is, in\nfact, the same at both periods. In order to apply a scale in\nthis case, we must take advantage of the known numerical\nrelations of light. We are certain that if all other\nillumination be excluded, two equal luminaries, under the\nsame circumstances, will produce an illumination twice as\ngreat as one does; and we can easily prove, from\nmathematical considerations, that if light be not enfeebled\nby the medium through which it passes, the illumination on a\ngiven surface will diminish as the square of the distance of\nthe luminary increases. If, therefore, we can by taking a\nfraction thus known of the illuminating effect of one\nluminary, make it equal to the total effect of another, of\nwhich equality the eye is a competent judge, we compare the\neffects of the two luminaries. In order to make this\ncomparison we may, with Rumford, look at the shadows of the\nsame object made by the two lights, {347} or with Ritchie,\nwe may view the brightness produced on two contiguous\nsurfaces, framing an apparatus so that the equality may be\nbrought about by proper adjustment; and thus a measure will\nbecome practicable. Or we may employ other methods as was\ndone by Wollaston[29\\4], who reduced the light of the sun by\nobserving it as reflected from a bright globule, and thus\nfound the light of the sun to be 10,000,000,000 times that\nof Sirius, the brightest fixed star. All these methods are\ninaccurate, even as methods of comparison; and do not offer\nany fixed or convenient numerical standard; but none better\nhave yet been devised[30\\4].\n\n[Note 29\\4: _Phil. Trans._ 1820, p. 19.]\n\n[Note 30\\4: Improved Photometers have been devised by\nProfessor Wheatstone, Professor Potter, and Professor\nSteinheil; but they depend upon principles similar to those\nmentioned in the text.]\n\n10. _Cyanometer._--As we thus measure the brightness of a\ncolourless light, we may measure the intensity of any\nparticular colour in the same way; that is, by applying a\nstandard exhibiting the gradations of the colour in question\ntill we find a shade which is seen to agree with the\nproposed object. Such an instrument we have in the\n_Cyanometer_, which was invented by Saussure for the purpose\nof measuring the intensity of the blue colour of the sky. We\nmay introduce into such an instrument a numerical scale, but\nthe numbers in such a scale will be altogether arbitrary.\n\n\nSECT. V.--_Scales of Heat._\n\n11. _Thermometers._--WHEN we proceed to the sensation of\nheat, and seek a measure of that quality, we find, at first\nsight, new difficulties. Our sensations of this kind are\nmore fluctuating than those of vision; for we know that the\nsame object may feel warm to one hand and cold to another at\nthe same instant, if the hands have been previously cooled\nand warmed respectively. Nor can we obtain here, as in the\ncase of light, self-evident numerical relations of the heat\ncommunicated in given circumstances; for we know that the\n{348} effect so produced will depend on the warmth of the\nbody to be heated, as well as on that of the source of heat;\nthe summer sun, which warms our bodies, will not augment the\nheat of a red-hot iron. The cause of the difference of these\ncases is, that bodies do not receive the whole of their\nheat, as they receive the whole of their light, from the\nimmediate influence of obvious external agents. There is no\nreadily-discovered absolute cold, corresponding to the\nabsolute darkness which we can easily produce or imagine.\nHence we should be greatly at a loss to devise a\n_Thermometer_, if we did not find an indirect effect of heat\nsufficiently constant and measurable to answer this purpose.\nWe discover, however, such an effect in the _expansion_ of\nbodies by the effect of heat.\n\n12. Many obvious phenomena show that air, under given\ncircumstances, expands by the effect of heat; the same is\nseen to be true of liquids, as of water, and spirit of wine;\nand the property is found to belong also to the metallic\nfluid, quicksilver. A more careful examination showed that\nthe increase of bulk in some of these bodies by increase of\nHeat was a fact of a nature sufficiently constant and\nregular to afford a means of measuring that previously\nintangible quality; and the Thermometer was invented. There\nwere, however, many difficulties to overcome, and many\npoints to settle, before this instrument was fit for the\npurposes of science.\n\nAn explanation of the way in which this was done necessarily\nincludes an important chapter of the history of Thermotics.\nWe must now, therefore, briefly notice historically the\nprogress of the Thermometer. The leading steps of this\nprogress, after the first invention of the instrument,\nwere--The establishment of _fixed points_ in the\nthermometric scale--The _comparison of the scales_ of\ndifferent substances--And the reconcilement of these\ndifferences by some method of interpreting them as\nindications of the absolute _quantity of heat_.\n\n13. It would occupy too much space to give in detail the\nhistory of the successive attempts by which {349} these\nsteps were effected. A thermometer is described by Bacon\nunder the title _Vitrum Calendare_; this was an air\nthermometer. Newton used a thermometer of linseed oil, and\nhe perceived that the first step requisite to give value to\nsuch an instrument was to fix its scale; accordingly he\nproposed his _Scala Graduum Caloris_[31\\4]. But when\nthermometers of different liquids were compared, it\nappeared, from their discrepancies, that this fixation of\nthe scale of heat was more difficult than had been supposed.\nIt was, however, effected. Newton had taken freezing water,\nor rather thawing snow, as the zero of his scale, which is\nreally a fixed point; Halley and Amontons discovered (in\n1693 and 1702) that the heat of boiling water is another\nfixed point; and Daniel Gabriel Fahrenheit, of Dantzig, by\ncarefully applying these two standard points, produced,\nabout 1714, thermometers, which were constantly consistent\nwith each other. This result was much admired at the time,\nand was, in fact, the solution of the problem just stated,\nthe _fixation of the scale of heat_.\n\n[Note 31\\4: _Phil. Trans._ 1701.]\n\n14. But the scale thus obtained is a conventional not a\nnatural scale. It depends upon the fluid employed for the\nthermometer. The progress of expansion from the heat of\nfreezing to that of boiling water is different for mercury,\noil, water, spirit of wine, air. A degree of heat which is\nhalf-way between these two standard points according to a\nmercurial thermometer, will be below the half-way point in a\nspirit thermometer, and above it in an air thermometer. Each\nliquid has its own _march_ in the course of its expansion.\nDeluc and others compared the marches of various liquids,\nand thus made what we may call a _concordance_ of\nthermometers of various kinds.\n\n15. Here the question further occurs: Is there not some\n_natural measure_ of the degrees of heat? It appears certain\nthat there must be such a measure, and that by means of it\nall the scales of different liquids must be reconciled. Yet\nthis does not seem to have occurred at once to men's minds.\nDeluc, in speaking {350} of the researches which we have\njust mentioned, says[32\\4], 'When I undertook these\nexperiments, it never once came into my thoughts that they\ncould conduct me with any probability to a table of real\ndegrees of heat. But hope grows with success, and desire\nwith hope.' Accordingly he pursued this inquiry for a long\ncourse of years.\n\n[Note 32\\4: _Modif. de l'Atmosph._ 1782, p. 303.]\n\nWhat are the principles by which we are to be guided to the\ntrue measure of heat? Here, as in all the sciences of this\nclass, we have the general principle, that the secondary\nquality, Heat, must be supposed to be perceived in some way\nby a material Medium or Fluid. If we take that which is,\nperhaps, the simplest form of this hypothesis, that the heat\ndepends upon the _quantity_ of this fluid, or _Caloric_,\nwhich is present, we shall find that we are led to\npropositions which may serve as a foundation for a natural\nmeasure of heat. The _Method of Mixtures_ is one example of\nsuch a result. If we mix together two pints of water, one\nhot and one cold, is it not manifest that the temperature of\nthe mixture must be midway between the two? Each of the two\nportions brings with it its own heat. The whole heat, or\ncaloric, of the mixture is the sum of the two; and the heat\nof each half must be the half of this sum, and therefore its\ntemperature must be intermediate between the temperatures of\nthe equal portions which were mixed. Deluc made experiments\nfounded upon this principle, and was led by them to conclude\nthat 'the dilatations of mercury follow an accelerated march\nfor successive equal augmentations of heat.'\n\nBut there are various circumstances which prevent this\nmethod of mixtures from being so satisfactory as at first\nsight it seems to promise to be. The different capacities\nfor heat of different substances, and even of the same\nsubstance at different temperatures, introduce much\ndifficulty into the experiments; and this path of inquiry\nhas not yet led to a satisfactory result. {351}\n\n16. Another mode of inquiring into the natural measure of\nheat is to seek it by researches on the _law of cooling_ of\nhot bodies. If we assume that the process of cooling of hot\nbodies consists in a certain material heat flying off, we\nmay, by means of certain probable hypotheses, determine\nmathematically the law according to which the temperature\ndecreases as time goes on; and we may assume _that_ to be\nthe true measure of temperature which gives to the\nexperimental law of cooling the most simple and probable\nform.\n\nIt appears evident from the most obvious conceptions which\nwe can form of the manner in which a body parts with its\nsuperabundant heat, that the hotter a body is, the faster it\ncools; though it is not clear without experiment, by what\nlaw the rate of cooling will depend upon the heat of the\nbody. Newton took for granted the most simple and seemingly\nnatural law of this dependence: he supposed the rate of\ncooling to be _proportional_ to the temperature, and from\nthis supposition he could deduce the temperature of a hot\niron, calculating from the original temperature and the time\nduring which it had been cooling. By calculation founded on\nsuch a basis, he graduated his thermometer.\n\n17. But a little further consideration showed that the rate\nof cooling of a hot body depended upon the temperature of\nthe surrounding bodies, as well as upon its own temperature.\nPrevost's _Theory of Exchanges_[33\\4] was propounded with a\nview of explaining this dependence, and was generally\naccepted. According to this theory, all bodies radiate heat\nto one another, and are thus constantly giving and receiving\nheat; and a body which is hotter than surrounding bodies,\ncools itself, and warms the surrounding, bodies, by an\nexchange of heat for heat, in which they are the gainers.\nHence if _\u03b8_ be the temperature of the bodies, or of the\nspace, by which the hot body is surrounded, and _\u03b8_ + _t_ the\ntemperature of the hot body, the rate of cooling will depend\n{352} upon the excess of the radiation for a temperature _\u03b8_ +\n_t_, above the radiation for a temperature _\u03b8_.\n\n[Note 33\\4: _Recherches sur la Chaleur_, 1791. _Hist. Ind.\nSc._ b. x. c. i. sect. 2.]\n\nAccordingly, in the admirable researches of MM. Dulong and\nPetit upon the cooling of bodies, it was assumed that the\nrate of cooling of the hot body was represented by the\nexcess of F(_\u03b8_ + _t_) above F(_\u03b8_); where F represented some\nmathematical _function_, that is, some expression obtained\nby arithmetical operations from the temperatures _\u03b8_ + _t_ and\n_\u03b8_; although what these operations are to be, was left\nundecided, and was in fact determined by the experiments.\nAnd the result of their investigations was, that the\nfunction is of this kind: when the temperature increases by\nequal intervals, the function increases in a continued\ngeometric proportion[34\\4]. This was, in fact, the same law\nwhich had been assumed by Newton and others, with this\ndifference, that _they_ had neglected the term which depends\nupon the temperature of the surrounding space.\n\n[Note 34\\4: The formula for the rate of cooling is _ma^(\u03b8 +\nt) - ma^\u03b8_, where the quantity _m_ depends upon the nature\nof the body, the state of its surface, and other\ncircumstances.--_Ann. Chim._ vii. 150.]\n\n18. This law falls in so well with the best conceptions we\ncan form of the mechanism of cooling upon the supposition of\na radiant fluid caloric, that it gives great probability to\nthe scale of temperature on which the simplicity of the\nresult depends. Now the temperatures in the formul\u00e6 just\nreferred to were expressed by means of the _air\nthermometer_. Hence MM. Dulong and Petit justly state, that\nwhile all different substances employed as thermometers give\ndifferent laws of thermotical phenomena, their own success\nin obtaining simple and general laws by means of the air\nthermometer, is a strong recommendation of that as the\n_natural scale of heat_. They add[35\\4], 'The well-known\nuniformity of the principal physical properties of all\ngases, and especially the perfect identity of their laws of\ndilatation by heat, [a very important discovery of {353}\nDalton and Gay Lussac[36\\4],] make it very probable that in\nthis class of bodies the disturbing causes have not the same\ninfluence as in solids and liquids; and consequently that\nthe changes of bulk produced by the action of heat are here\nin a more immediate dependence on the force which produces them.'\n\n[Note 35\\4: _Annales de Chimie_, vii. 153.]\n\n[Note 36\\4: _Hist. Ind. Sc._ b. x. c. ii. sect. 1.]\n\n19. Still we cannot consider this point as settled till we\nobtain a more complete theoretical insight into the nature\nof heat itself. If it be true that heat consists in the\nvibrations of a fluid, then, although, as Amp\u00e8re has\nshown[37\\4], the laws of radiation will, on mathematical\ngrounds, be the same as they are on the hypothesis of\nemission, we cannot consider the natural scale of heat as\ndetermined, till we have discovered some means of measuring\nthe caloriferous vibrations as we measure luminiferous\nvibrations. We shall only know what the quantity of heat is\nwhen we know what heat itself is;--when we have obtained a\ntheory which satisfactorily explains the manner in which the\nsubstance or medium of heat produces its effects. When we\nsee how radiation and conduction, dilatation and\nliquefaction, are all produced by mechanical changes of the\nsame fluid, we shall then see what the nature of that change\nis which dilatation really measures, and what relation it\nbears to any more proper standard of heat.\n\n[Note 37\\4: _Ib._ c. iv.]\n\nWe may add, that while our thermotical theory is still so\nimperfect as it is, all attempts to divine the true nature\nof the relation between light and heat are premature, and\nmust be in the highest degree insecure and visionary.\nSpeculations in which, from the general assumption of a\ncaloriferous and luminiferous medium, and from a few facts\narbitrarily selected and loosely analysed, a general theory\nof light and heat is asserted, are entirely foreign to the\ncourse of inductive science, and cannot lead to any stable\nand substantial truth.\n\n20. _Other Instruments for measuring Heat._--It does not\nbelong to our present purpose to speak of {354} instruments\nof which the object is to measure, not sensible qualities,\nbut some effect or modification of the cause by which such\nqualities are produced: such, for instance, are the\n_Calorimeter_, employed by Lavoisier and Laplace, in order\nto compare the _Specific Heat_ of different substances; and\nthe _Actinometer_, invented by Sir John Herschel, in order\nto determine the _effect of the Sun's Rays_ by means of the\nheat which they communicate in a given time; which effect\nis, as may readily be supposed, very different under\ndifferent circumstances of atmosphere and position. The laws\nof such effects may be valuable contributions to our\nknowledge of heat, but the interpretation of them must\ndepend on a previous knowledge of the relations which\ntemperature bears to heat, according to the views just\nexplained.\n\n\nSECT. VI.--_Scales of other Qualities._\n\n21. BEFORE quitting the subject of the measures of sensible\nqualities, we may observe that there are several other such\nqualities for which it would be necessary to have scales and\nmeans of measuring, in order to make any approach to science\non such subjects. This is true, for instance, of Tastes and\nSmells. Indeed some attempts have been made towards a\nclassification of the Tastes of sapid substances, but these\nhave not yet assumed any satisfactory or systematic\ncharacter; and I am not aware that any instrument has been\nsuggested for _measuring_ either the Flavour or the Odour of\nbodies which possess such qualities.\n\n22. _Quality of Sounds._--The same is true of that kind of\ndifference in sounds which is peculiarly termed their\n_Quality_; that character by which, for instance, the sound\nof a flute differs from that of a hautbois, when the note is\nthe same; or a woman's voice from a boy's.\n\n23. _Articulate Sounds._--There is also in sounds another\ndifference, of which the nature is still obscure, but in\nreducing which to rule, and consequently to measure, some\nprogress has nevertheless been made. {355} I speak of the\ndifferences of sound considered as _articulate_.\nClassifications of the sounds of the usual alphabets have\nbeen frequently proposed; for instance, that which arranges\nthe _Consonants_ in the following groups,:\n\nSharp. Flat. Sharp Aspirate. Flat Aspirate. Nasal.\n p b ph (_f_) bh (_v_) m\n k g (hard) kh gh ng\n t d th (sharp) th (flat) n\n s z sh zh\n\nIt is easily perceived that the relations of the sounds in\neach of these horizontal lines are analogous; and\naccordingly the rules of derivation and modification of\nwords in several languages proceed upon such analogies. In\nthe same manner the _Vowels_ may be arranged in an order\ndepending on their sound. But to make such arrangements\nfixed and indisputable, we ought to know the mechanism by\nwhich such modifications are caused. Instruments have been\ninvented by which some of these sounds can be imitated; and\nif such instruments could be made to produce the above\nseries of articulate sounds, by connected and regular\nprocesses, we should find, in the process, a _measure_ of\nthe sound produced. This has been in a great degree effected\nfor the Vowels by Professor Willis's artificial mode of\nimitating them. For he finds that if a musical reed be made\nto sound through a cylindrical pipe, we obtain by gradually\nlengthening the cylindrical pipe, the series of vowels I, E,\nA, O, U, with intermediate sounds[38\\4]. In this instrument,\nthen, the length of the pipe would determine the vowel, and\nmight be used numerically to express it. Such an instrument\nso employed would be a measure of vowel quality, and might\nbe called a _Phthongometer_.\n\n[Note 38\\4: _Camb. Trans._ vol. iii. p. 239.]\n\nOur business at present, however, is not with instruments\nwhich might be devised for measuring sensible qualities, but\nwith those which have been so used, and have thus been the\nbasis of the sciences in which {356} such qualities are\ntreated of; and this we have now done sufficiently for our\npresent purpose.\n\n24. There is another Idea which, though hitherto very\nvaguely entertained, has had considerable influence in the\nformation, both of the sciences spoken of in the present\nBook, and on others which will hereafter come under our\nnotice: namely, the Idea of Polarity. This Idea will be the\nsubject of the ensuing Book. And although this Idea forms a\npart of the basis of various other extensive portions of\nscience, as Optics and Chemistry, it occupies so peculiarly\nconspicuous a place in speculations belonging to what I have\ntermed the Mechanico-Chemical Sciences, (Magnetism and\nElectricity,) that I shall designate the discussion of the\nIdea of Polarity as the Philosophy of those Sciences.\n\n\n\n\n{{357}}\nBOOK V.\n\n\n\nTHE\nPHILOSOPHY\nOF THE\nMECHANICO-CHEMICAL SCIENCES.\n\n\n\n\nEn donnant \u00e0 ces c\u00f4t\u00e9s le nom de _poles_, j'appelerai\n_polarisation_ la modification qui donne \u00e0 la lumi\u00e8re des\npropri\u00e9t\u00e9s relatives \u00e0 ces poles. J'ai tard\u00e9 jusqu'\u00e0 pr\u00e9sent\n\u00e0 admettre ce terme dans la description des ph\u00e9nom\u00e8nes\nphysiques dont il est question; je n'ai pas os\u00e9 l'introduire\ndans les m\u00e9moires o\u00f9 j'ai publi\u00e9 mes derni\u00e8res exp\u00e9riences;\nmais les vari\u00e9t\u00e9s qu'offre ce nouveau ph\u00e9nom\u00e8ne, et la\ndifficult\u00e9 de les d\u00e9crire, me forcent \u00e0 admettre cette\nnouvelle expression, qui signifie simplement la modification\nque la lumi\u00e8re a subie en acqu\u00e9rant de nouvelles propri\u00e9t\u00e9s\nqui ne sont pas relatives \u00e0 la direction du rayon, mais\nseulement \u00e0 ses c\u00f4t\u00e9s consid\u00e9r\u00e9s \u00e0 angles droits et dans un\nplan perpendiculaire \u00e0 sa direction.\n\nMalus (1811), _M\u00e9m. de Inst._ tom. xi. p. 106.\n\n\n\n{{359}}\nBOOK V.\n\n\nTHE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES.\n\n\nCHAPTER I.\n\nATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA OF\nPOLARITY.\n\n\n1. IN some of the mechanical sciences, as Magnetism and\nOptics, the phenomena are found to depend upon position (the\nposition of the magnet, or of the ray of light,) in a\npeculiar alternate manner. This dependence, as it was first\napprehended, was represented by means of certain conceptions\nof space and force, as for instance by considering the two\n_Poles_ of a magnet. But in all such modes of representing\nthese alternations by the conceptions borrowed from other\nideas, a closer examination detected something superfluous\nand something defective; and in proportion as the view which\nphilosophers took of this relation was gradually purified\nfrom these incongruous elements, and was rendered more\ngeneral and abstract by the discovery of analogous\nproperties in new cases, it was perceived that the relation\ncould not be adequately apprehended without considering it\nas involving a peculiar and independent Idea, which we may\ndesignate by the term _Polarity_.\n\nWe shall trace some of the forms in which this Idea has\nmanifested itself in the history of science. In doing so we\nshall not begin, as in other Books of this work we have\ndone, by speaking of the notion as it is {360} employed in\ncommon use: for the relation of Polarity is of so abstract\nand technical a nature, that it is not employed, at least in\nany distinct and obvious manner, on any ordinary or\npractical occasions. The idea belongs peculiarly to the\nregion of speculation: in persons of common habits of\nthought it is probably almost or quite undeveloped; and even\nmost of those whose minds have been long occupied by\nscience, find a difficulty in apprehending it in its full\ngenerality and abstraction, and stript of all irrelevant\nhypothesis.\n\n2. _Magnetism._--The name and the notion of _Poles_ were\nfirst adopted in the case of a magnet. If we have two\nmagnets, their extremities attract and repel each other\nalternatively. If the first end of the one attract the first\nend of the other, it repels the second end, and conversely.\nIn order to express this rule conveniently, the two ends of\neach magnet are called the _north pole_ and the _south pole_\nrespectively, the denominations being borrowed from the\npoles of the earth and heavens. 'These poles,' as Gilbert\nsays[1\\5], 'regulate the motions of the celestial spheres\nand of the earth. In like manner the magnet has its poles, a\nnorthern and a southern one; certain and determined points\nconstituted by nature in the stone, the primary terms of its\nmotions and effects, the limits and governors of many\nactions and virtues.'\n\n[Note 1\\5: _De Magn._ lib. i. c. iii.]\n\nThe nature of the opposition of properties of which we speak\nmay be stated thus:\nThe North pole of one magnet attracts the South pole of another\nmagnet.\nThe North pole of one magnet _repels_ the North pole of another\nmagnet.\nThe South pole of one magnet repels the South pole of another\nmagnet.\nThe South pole of one magnet _attracts_ the North pole of\nanother magnet.\n\nIt will be observed that the contrariety of position which\nis indicated by putting the South pole for the North pole in\neither magnet, is accompanied by the {361} opposition of\nmechanical effect which is expressed by changing attraction\ninto repulsion and repulsion into attraction: and thus we\nhave the general feature of Polarity,--A contrast of\nproperties corresponding to a contrast of positions.\n\n3. _Electricity._--When the phenomena of Electricity came to\nbe studied, it appeared that they involved relations in some\nrespects Analogous to those of magnetism.\n\nTwo kinds of electricity were distinguished, the positive\nand the negative; and it appeared that two bodies electrized\npositively, or two electrized negatively, repelled each\nother, like two north or two south magnetic poles; while a\npositively and a negatively electrized body attracted each\nother, like the north and south poles of two magnets. In\nconductors of an oblong form, the electricity could easily\nbe made to distribute itself so that one end should be\npositively and one end negatively electrized; and then such\nconductors acted on each other exactly as magnets would do.\n\nBut in conductors, however electrized, there is no peculiar\npoint which can permanently be considered as the _pole_. The\ndistribution of electricity in the conductor depends upon\nexternal circumstances: and thus, although the phenomena\noffer the general character of _polarity_--alternative\nresults corresponding to alternative positions,--they cannot\nbe referred to poles. Some other mode of representing the\nforces must be adopted than that which makes them emanate\nfrom permanent points as in a magnet.\n\nThe phenomena of attraction and repulsion in electrized\nbodies were conveniently represented by means of the\nhypothesis of _two_ electric _fluids_, a positive and a\nnegative one, which were supposed to be distributed in the\nbodies. Of these fluids, it was supposed that each repelled\nits own parts and attracted those of the opposite fluid: and\nit was found that this hypothesis explained all the obvious\nlaws of electric action. Here then we have the phenomena of\npolarization explained by a new kind of machinery:--two\nopposite fluids {362} distributed in bodies, and supplying\nthem, so to speak, with their polar forces. This hypothesis\nnot only explains electrical attraction, but also the\nelectrical spark: namely, thus: when two bodies, of which\nthe neighbouring surfaces are charged with the two opposite\nfluids, approach near to each other, the mutual attraction\nof the fluids becomes more and more intense, till at last\nthe excess of fluid on the one body breaks through the air\nand rushes to the other body, in a form accompanied by light\nand noise. When this transfer has taken place, the\nattraction ceases, the positive and the negative fluid\nhaving neutralized each other. Their effort was to unite;\nand this union being effected, there is no longer any force\nin action. Bodies in their natural unexcited condition may\nbe considered as occupied by a combination of the two\nfluids: and hence we see how the production of either kind\nof electricity is necessarily accompanied with the\nproduction of an equivalent amount of the opposite kind.\n\n4. _Voltaic Electricity._--Such is the case in Franklinic\nelectricity,--that which is excited by the common electrical\nmachine. In studying Voltaic electricity, we are led to the\nconviction that the fluid which is in a condition of\nmomentary _equilibrium_ in electrized conductors, exists in\nthe state of a _Current_ in the voltaic circuit. And here we\nfind polar relations of a new kind existing among the\nforces. Two voltaic Currents _attract_ each other when they\nare moving in the _same_, and _repel_ each other when they\nare moving in _opposite_, directions.\n\nBut we find, in addition to these, other polar relations of\na more abstruse kind, and which the supposition of two\nfluids does not so readily explain. For instance, if such\nfluids existed, distinct from each other, it might be\nexpected that it would be possible to exhibit one of them\nseparate from the other. Yet in all the phenomena of\nelectromotive currents, we attempt in vain to obtain one\nkind of electricity separately. 'I have not,' says Mr.\nFaraday[2\\5], 'been able to find a {363} single fact which\ncould be adduced to prove the theory of two electricities\nrather than one, in electric currents; or, admitting the\nhypothesis of two electricities, have I been able to\nperceive the slightest grounds that one electricity can be\nmore powerful than the other, or that it can be present\nwithout the other, or that it can be varied or in the\nslightest degree affected without a corresponding variation\nin the other.' 'Thus,' he adds, 'the polar character of the\npowers is rigorous and complete.' Thus, we too may remark,\nall the superfluous and precarious parts gradually drop off\nfrom the hypothesis which we devise in order to represent\npolar phenomena; and the abstract notion of Polarity--of\nequal and opposite powers called into existence by a common\ncondition--remains unincumbered with extraneous machinery.\n\n[Note 2\\5: _Researches_, 516.]\n\n5. _Light._--Another very important example of the\napplication of the Idea of Polarity is that supplied by the\ndiscovery of the polarization of light. A ray of light may,\nby various processes, be modified, so that it has different\nproperties according to its different _sides_, although this\ndifference is not perceptible by any common effects. If, for\ninstance, a ray thus modified, pass perpendicularly through\na circular glass, and fall upon the eye, we may turn the\nglass round and round in its frame, and we shall make no\ndifference in the brightness of the spot which we see. But\nif, instead of a glass, we look through a longitudinal slice\nof tourmaline, the spot is alternately dark and bright as we\nturn the crystal through successive quadrants. Here we have\na contrast of Properties (dark and bright) corresponding to\na contrast of positions, (the position of a line east and\nwest being contrasted with the position north and south,)\nwhich, as we have said, is the general character of\nPolarity. It was with a view of expressing this character\nthat the term _Polarization_ was originally introduced.\nMalus was forced by his discoveries into the use of this\nexpression. 'We find,' he says, in 1811, 'that light\nacquires properties which are relative only to the sides of\nthe ray,--which are the same for the north and south sides\nof the ray, (using {364} the points of the compass for\ndescription's sake only,) and which are different when we go\nfrom the north and south to the east or to the west sides of\nthe ray. I shall give the name of _poles_ to these sides of\nthe ray, and shall call _polarization_ the modification\nwhich gives to light these properties relative to these\npoles. I have _put off_ hitherto the admission of this term\ninto the description of the physical phenomena with which we\nhave to do: I did not _dare_ to introduce it into the\nMemoirs in which I published my last observations: but the\nvariety of forms in which this new phenomenon appears, and\nthe difficulty of describing them, compel me to admit this\nnew expression; which signifies simply the modification\nwhich light has undergone in acquiring new properties which\nare not relative to the direction of the ray, but only to\nits sides considered at right angles to each other, and in a\nplane perpendicular to its direction.'\n\nThe theory which represents light as an emission of\nparticles was in vogue at the time when Malus published his\ndiscoveries; and some of his followers in optical research\nconceived that the phenomena which he thus described\nrendered it necessary to ascribe poles and an axis to each\nparticle of light. On this hypothesis, light would be\npolarized when the axes of all the particles were in the\nsame direction: and, making such a supposition, it may\neasily be conceived capable of transmission through a\ncrystal whose axis is parallel to that of the luminous\nparticles, and intransmissible when the axis of the crystal\nis in a position transverse to that of the particles.\n\nThe hypothesis of particles possessing _poles_ is a rude and\narbitrary assumption, in this as in other cases; but it\nserves to convey the general notion of polarity, which is\nthe essential feature of the phenomena. The term\n'polarization of light has sometimes been complained of in\nmodern times as hypothetical and obscure. But the real cause\nof obscurity was, that the Idea of Polarity was, till\nlately, very imperfectly developed in men's minds. As we\nhave seen, the general notion of Polarity,--opposite\nproperties in opposite {365} directions,--exactly describes\nthe character of the optical phenomena to which the term is\napplied.\n\nIt is to be recollected that in optics we never speak of the\n_poles_, but of the _plane of polarization_ of a ray. The\nword _sides_, which Newton and Malus have used, neither of\nthem appears to have been satisfied with; Newton, in\nemploying it, had recourse to the strange Gallicism of\nspeaking of the _coast_ of usual and of unusual refraction\nof a crystal.\n\nThe modern theory of optics represents the plane of\npolarization of light as depending, not on the position in\nwhich the axes of the luminiferous particles lie, but on the\n_direction_ of those _transverse vibrations_ in which light\nconsists. This theory is, as we have stated in the History,\nrecommended by an extraordinary series of successes in\naccounting for the phenomena. And this hypothesis of\ntransverse vibrations shows us another mechanical mode,\n(besides the hypothesis of particles with axes,) by which we\nmay represent the polarity of a ray. But we may remark that\nthe general notion of Polarity, as applied to light in such\ncases, would subsist, even if the undulatory theory were\nrejected. The idea is, as we have before said, independent\nof all hypothetical machinery.\n\nI need not here refer to the various ways in which light may\nbe polarized; as, for instance, by being reflected from the\nsurface of water, or of glass, at certain angles, by being\ntransmitted, through crystals, and in other ways. In all\ncases the modification produced, the polarization, is\nidentically the same property. Nor need I mention the\nvarious kinds of phenomena which appear as contrasts in the\nresult; for these are not merely light and dark, or white\nand black, but red and green, and generally, a colour and\nits _complementary_ colour, exhibited in many complex and\nvaried configurations. These multiplied modes in which\npolarized light presents itself add nothing to the original\nconception of Polarization: and I shall therefore pass on to\nanother subject.\n\n6. _Crystallization._--Bodies which are perfectly\ncrystallized exhibit the most complete regularity and {366}\nsymmetry of form; and this regularity not only appears in\ntheir outward shape, but pervades their whole texture, and\nmanifests itself in their cleavage, their transparency, and\nin the uniform and determinate optical properties which\nexist in every part, even in the smallest fragment of the\nmass. If we conceive crystals as composed of particles, we\nmust suppose these particles to be arranged in the most\nregular manner; for example, if we suppose each particle to\nhave an axis, we must suppose all these axes to be parallel;\nfor the direction of the axis of the particles is indicated\nby the physical and optical properties of the crystal, and\ntherefore this direction must be the same for every portion\nof the crystal. This parallelism of the axes of the\nparticles may be conceived to result from the circumstance\nof each particle having poles, the opposite poles attracting\neach other. In virtue of forces acting as this hypothesis\nassumes, a collection of small _magnetic_ particles would\narrange themselves in parallel positions; and such a\ncollection of magnetic particles offers a sort of image of a\ncrystal. Thus we are led to conceive the particles of\ncrystals as polarized, and as determined in their\ncrystalline positions by polar forces. This mode of\napprehending the constitution of crystals has been adopted\nby some of our most eminent philosophers. Thus Berzelius\nsays[3\\5], 'It is demonstrated, that the regular forms of\nbodies presuppose an effort of their atoms to touch each\nother by preference in certain points; that is, they are\nfounded upon a Polarity;'--he adds, 'a polarity which can be\nno other than an electric or magnetic polarity.' In this\nlatter clause we have the identity of different kinds of\npolarity asserted; a principle which we shall speak of in\nthe next chapter. But we may remark, that even without\ndwelling upon this connexion, any notion which we can form\nof the structure of Crystals necessarily involves the idea\nof Polarity. Whether this polarity necessarily requires us\nto believe crystals to be composed of Atoms which exert an\neffort to touch {367} each other in certain points by\npreference, is another question. And, in agreement with what\nhas been said respecting other kinds of polarity, we shall\nprobably find, on a more profound examination of the\nsubject, that while the Idea of Polarity is essential, the\nmachinery by which it is thus expressed is precarious and\nsuperfluous.\n\n[Note 3\\5: _Essay on the Theory of Chemical Properties_,\n1820, p. 113.]\n\n7. _Chemical Affinity._--We shall have, in the next Book, to\nspeak of Chemical Affinity at some length; but since the\nultimate views to which philosophers have been led, induce\nthem to consider the forces of Affinity as Polar Forces, we\nmust enumerate these among the examples of Polarity. In\nchemical processes, opposites tend to unite, and to\nneutralize each other by their union. Thus an _acid_ or an\n_alkali_ combine with vehemence, and form a compound, a\nneutral salt, which is neither acid nor alkaline.\n\nThis conception of contrariety and mutual neutralization,\ninvolves the Idea of Polarity. In the conception as\nentertained by the earlier chemists, the Idea enters very\nobscurely: but in the attempts which have more recently been\nmade to connect this relation (of acid and base), with other\nrelations, the chemical elements have been conceived as\ncomposed of particles which possess poles; _like_ poles\nrepelling, and _unlike_ attracting each other, as they do in\nmagnetic and electric phenomena. This is, however, a rude\nand arbitrary way of expressing Polarity, and, as may be\neasily shown, involves many difficulties which do not belong\nto the Idea itself. Mr. Faraday, who has been led by his\nresearches to a conviction of the polar nature of the forces\nof chemical affinity, has expressed their character in a\nmore general manner, and without any of the machinery of\nparticles indued with poles. According to his view, chemical\nsynthesis and analysis must always be conceived as taking\nplace in virtue of equal and opposite forces, by which the\nparticles are united or separated. These forces, by the very\ncircumstance of their being polar, may be transferred from\npoint to point. For if we conceive a string of particles,\nand if the positive force of the first particle {368} be\nliberated and brought into action, its negative force also\nmust be set free: this negative force neutralizes the\npositive force of the next particle, and therefore the\nnegative force of this particle (before employed in\nneutralizing its positive force) is set free: this is in the\nsame way transferred to the next particle, and so on. And\nthus we have a positive force active at one extremity of a\nline of particles, corresponding to a negative force at the\nother extremity, all the intermediate particles reciprocally\nneutralizing each other's action. This conception of the\ntransfer of chemical action was indeed at an earlier period\nintroduced by Grotthus[4\\5], and confirmed by Davy. But in\nMr. Faraday's hands we see it divested of all that is\nsuperfluous, and spoken of, not as a line of particles, but\nas 'an axis of power, having [at every point] contrary\nforces, exactly equal, in opposite directions.'\n\n[Note 4\\5: DUMAS, _Le\u00e7ons sur la Philosophie Chimique_, p. 401.]\n\n8. _General Remarks._--Thus, as we see, the notion of\nPolarity is applicable to many large classes of phenomena.\nYet the Idea in a distinct and general form is only of late\ngrowth among philosophers. It has gradually been abstracted\nand refined from many extraneous hypotheses which were at\nfirst supposed to be essential to it. We have noticed some\nof these hypotheses;--as the poles of a _body_; the poles of\nthe _particles_ of a fluid; _two_ opposite fluids; a single\nfluid in _excess_ and _defect_; transverse _vibrations_. To\nthese others might be added. Thus Dr. Prout[5\\5] assumes\nthat the polarity of molecules results from their _rotation_\non their axes, the opposite motions of contiguous molecules\nbeing the cause of opposite (positive and negative)\npolarities.\n\n[Note 5\\5: _Bridgewater Treatise_, p. 559.]\n\nBut none of these hypotheses can be proved by the fact of\nPolarity alone; and they have been in succession rejected\nwhen they had been assumed on that ground. Thus Davy, in\n1826, speaking of chemical forces says[6\\5], 'In assuming\nthe idea of two ethereal, subtile, elastic {369} fluids,\nattractive of the particles of each other, and repulsive as\nto their own particles, capable of combining in different\nproportions with bodies, and according to their proportions\ngiving them their specific qualities and rendering them\nequivalent masses, it would be natural to refer the action\nof the poles to the repulsions of the substances combined\nwith the excess of one fluid, and the attractions of those\nunited to the excess of the other fluid; and a history of\nthe phenomena, not unsatisfactory to the reason, might in\nthis way be made out. But as it is possible likewise to take\nan entirely different view of the subject, on the idea of\nthe dependence of the results upon the primary attractive\npowers of the parts of the combination on a single subtile\nfluid, I shall not enter into any discussion on this obscure\npart of the theory.' Which of these theories will best\nrepresent the case, will depend upon the consideration of\nother facts, in combination with the polar phenomena, as we\nsee in the history of optical theory. In like manner Mr.\nFaraday proved by experiment[7\\5] the errour of all theories\nwhich ascribe electro-chemical decomposition to the\nattraction of the poles of the voltaic battery.\n\n[Note 6\\5: _Phil. Tr._ 1826, p. 415.]\n\n[Note 7\\5: _Researches_, p. 495, &c.]\n\nIn order that they may distinctly image to themselves the\nIdea of Polarity, men clothe it in some of the forms of\nmachinery above spoken of; yet every new attempt shows them\nthe unnecessary difficulties in which they thus involve\nthemselves. But on the other hand it is difficult to\napprehend this Idea divested of all machinery; and to\nentertain it in such a form that it shall apply at the same\ntime to magnetism and electricity, galvanism and chemistry,\ncrystalline structure and light. The Idea of _Polarity_\nbecomes most pure and genuine, when we entirely reject the\nconception of _Poles_, as Faraday has taught us to do in\nconsidering electro-chemical decomposition; but it is only\nby degrees and by effort that we can reach this point of\nabstraction and generality. {370}\n\n9. There is one other remark which we may here make. It was\na maxim commonly received in the ancient schools of\nphilosophy, that 'Like attracts Like:' but as we have seen,\nthe universal maxim of Polar Phenomena is, that Like\n_repels_ Like, and attracts Unlike. The north pole attracts\nthe south pole, the positive fluid attracts the negative\nfluid; opposite elements rush together; opposite motions\nreduce each other to rest. The permanent and stable course\nof things is that which results from the balance and\nneutralization of contrary tendencies. Nature is constantly\nlabouring after repose by the effect of such tendencies; and\nso far as Polar Forces enter into her economy, she seeks\nharmony by means of discord, and unity by opposition.\n\nAlthough the Idea of Polarity is as yet somewhat vague and\nobscure, even in the minds of the cultivators of physical\nscience, it has nevertheless given birth to some general\nprinciples which have been accepted as evident, and have had\ngreat influence on the progress of science. These we shall\nnow consider.\n\n\n\n{{371}}\nCHAPTER II.\n\nOF THE CONNEXION OF POLARITIES.\n\n\n1. IT has appeared in the preceding chapter that in cases in\nwhich the phenomena suggest to us the idea of Polarity, we\nare also led to assume some material machinery as the mode\nin which the polar forces are exerted. We assume, for\ninstance, globular particles which possess poles, or the\nvibrations of a fluid, or two fluids attracting each other;\nin every case, in short, some hypothesis by which the\nexistence and operation of the Polarity is embodied in\ngeometrical and mechanical properties of a medium; nor is it\npossible for us to avoid proceeding upon the conviction that\nsome such hypothesis must be true; although the nature of\nthe connexion between the mechanism and the phenomena must\nstill be indefinite and arbitrary.\n\nBut since each class of Polar Phenomena is thus referred to\nan ulterior cause, of which we know no more than that it has\na polar character, it follows that _different_ Polarities\nmay result from the _same_ cause manifesting its polar\ncharacter under different aspects. Taking, for example, the\nhypothesis of globular particles, if electricity result from\nan action dependent upon the _poles_ of each globule,\nmagnetism may depend upon an action in the _equator_ of each\nglobule; or taking the supposition of transverse vibrations,\nif polarized light result directly from such _vibrations_,\ncrystallization may have reference to the _axes_ of the\nelasticity of the _medium_ by which the vibrations are\nrendered transverse,--so far as the polar character only of\nthe phenomena is to be accounted for. I say this _may_ be\nso, _in so far_ only as the polar character of the phenomena\nis concerned; for whether the relation of {372} electricity\nto magnetism, or of crystalline forces to light, can really\nbe explained by such hypotheses, remains to be determined by\nthe facts themselves. But since the first necessary feature\nof the hypothesis is, that it shall give polarity, and since\nan hypothesis which does this, may, by its mathematical\nrelations, give polarities of different kinds and in\ndifferent directions, any two co-existent kinds of polarity\nmay result from the same cause, manifesting itself in\nvarious manners.\n\nThe conclusion to which we are led by these general\nconsiderations is, that two co-existing classes of polar\nphenomena _may_ be effects of the same cause. But those who\nhave studied such phenomena more deeply and attentively\nhave, in most or in all cases, arrived at the conviction\nthat the various kinds of Polarity in such cases _must_ be\nconnected and fundamentally identical. As this conviction\nhas exercised a great influence, both upon the discoveries\nof new facts and upon the theoretical speculations of modern\nphilosophers, and has been put forward by some writers as a\nuniversal principle of science, I will consider some of the\ncases in which it has been thus applied.\n\n2. _Connexion of Magnetic and Electric Polarity._--The polar\nphenomena of electricity and magnetism are clearly analogous\nin their laws: and obvious facts showed at an early period\nthat there was some connexion between the two agencies.\nAttempts were made to establish an evident and definite\nrelation between the two kinds of force, which attempts\nproceeded upon the principle now under\nconsideration;--namely, that in such cases, the two kinds of\nPolarity must be connected. Professor \u0152rsted, of Copenhagen,\nwas one of those who made many trials founded upon this\nconviction: yet all these were long unsuccessful. At length,\nin 1820, he discovered that a galvanic current, passing at\nright angles near to a magnetic needle, exercises upon it a\npowerful deflecting force. The connexion once detected\nbetween magnetism and galvanism was soon recognized as\nconstant and universal. It was represented in different\nhypothetical modes by different persons; some considering\nthe galvanic {373} current as the primitive axis, and the\nmagnet as constituted of galvanic currents passing round it\nat right angles to the magnetic axis; while others conceived\nthe magnetic axis as the primitive one, and the electric\ncurrent as implying a magnetic current round the wire. So\nfar as many of the general relations of these two kinds of\nforce were concerned, either mode of representation served\nto express them; and thus the assumption that the two\nPolarities, the magnetic and the electric, were\nfundamentally identical, was verified, so far as the\nphenomena of magnetic attraction, and the like, were\nconcerned.\n\nI need not here mention how this was further confirmed by\nthe experiments in which, by means of the forces thus\nbrought into view, a galvanic wire was made to revolve round\na magnet, and a magnet round a galvanic wire;--in which\nartificial magnets were constructed of coils of galvanic\nwire;--and finally, in which the galvanic spark was obtained\nfrom the magnet. The identity which sagacious speculators\nhad divined even before it was discovered, and which they\nhad seen to be universal as soon as it was brought to light,\nwas completely manifested in every imaginable form.\n\nThe relation of the electric and magnetic Polarities was\nfound to be, that they were _transverse_ to each other, and\nthis relation exhibited under various conditions of form and\nposition of the apparatus, gave rise to very curious and\nunexpected perplexities. The degree of complication which\nthis relation may occasion, may be judged of from the number\nof constructions and modes of conception offered by \u0152rsted,\nWollaston, Faraday, and others, for the purpose of framing a\ntechnical memory of the results. The magnetic polarity gives\nus the north and south poles of the needle; the electric\npolarity makes the current positive and negative; and these\npairs of opposites are connected by relations of situation,\nas above and below, right and left; and give rise to the\nresulting motion of the needle one way or the other. {374}\n\n3. Amp\u00e8re, by framing his hypotheses of the action of\nvoltaic currents and the constitution of magnets, reduced\nall these technical rules to rigorous deductions from one\ngeneral principle. And thus the vague and obscure persuasion\nthat there _must_ be _some_ connexion between Electricity\nand Magnetism, so long an idle and barren conjecture, was\nunfolded into a complete theory, according to which magnetic\nand electromotive actions are only two different\nmanifestations of the same forces; and all the\nabove-mentioned complex relations of polarities are reduced\nto one single polarity, that of the electro-dynamic current.\n\n4. As the Idea of Polarity was thus firmly established and\nclearly developed, it became an instrument of reasoning.\nThus it led Amp\u00e8re to maintain that the original or\nelementary forces in electro-dynamic action could not be as\nM. Biot thought they were, a statical _couple_, but must be\ndirectly opposite to each other. The same idea enabled Mr.\nFaraday to carry on with confidence such reasonings as the\nfollowing[8\\5]: 'No other known power has like direction\nwith that exerted between an electric current and a magnetic\npole; it is tangential, while all other forces acting at a\ndistance are direct. Hence if a magnetic pole on one side of\na revolving plate follow its course by reason of its\nobedience to the tangential force exerted upon it by the\nvery current of electricity which it has itself caused; a\nsimilar pole on the other side of the plate should\nimmediately set it free from this force; for the currents\nwhich have to be formed by the two poles are in contrary\ndirections.' And in Article 1114 of his _Researches_, the\nsame eminent philosopher infers that if electricity and\nmagnetism are considered as the results of a peculiar agent\nor condition, exerted in determinate directions\nperpendicular to each other, one must be by some means\nconvertible into the other; and this he was afterwards able\nto prove to be the case in fact.\n\n[Note 8\\5: _Researches_, 244.]\n\n{375} Thus the principle that the Co-existent Polarities of\nmagnetism and electricity are connected and fundamentally\nidentical, is not only true, but is far from being either\nvague or barren. It has been a fertile source both of\ntheories which have, at present, a very great probability,\nand of the discovery of new and striking facts. We proceed\nto consider other similar cases.\n\n5. _Connexion of Electrical and Chemical Polarities._--The\ndoctrine that the chemical forces by which the elements of\nbodies are held together or separated, are identical with\nthe polar forces of electricity, is a great discovery of\nmodern times; so great and so recent, indeed, that probably\nmen of science in general have hardly yet obtained a clear\nview and firm hold of this truth. This doctrine is now,\nhowever, entirely established in the minds of the most\nprofound and philosophical chemists of our time. The\ncomplete development and confirmation of this as of other\ngreat truths, was preceded by more vague and confused\nopinions gradually tending to this point; and the progress\nof thought and of research was impelled and guided, in this\nas in similar cases, by the persuasion that these\nco-existent polarities could not fail to be closely\nconnected with each other. While the ultimate and exact\ntheory to which previous incomplete and transitory theories\ntended is still so new and so unfamiliar, it must needs be a\nmatter of difficulty and responsibility for a common reader\nto describe the steps by which truth has advanced from point\nto point. I shall, therefore, in doing this, guide myself\nmainly by the historical sketches of the progress of this\ngreat theory, which, fortunately for us, have been given us\nby the two philosophers who have played by far the most\nimportant parts in the discovery, Davy and Faraday.\n\nIt will be observed that we are concerned here with the\nprogress of theory, and not of experiment, except so far as\nit is confirmatory of theory. In Davy's Memoir[9\\5] of 1826,\non the Relations of Electrical and {376} Chemical Changes,\nhe gives the historical details to which I have alluded.\nAlready in 1802 he had conjectured that all chemical\ndecompositions might be polar. In 1806 he attempted to\nconfirm this conjecture, and succeeded, to his own\nsatisfaction, in establishing[10\\5] that the combinations\nand decompositions by electricity were referable to the law\nof electrical attractions and repulsions; and advanced the\nhypothesis (as he calls it), that chemical and electrical\nattractions were produced by the same cause, acting in one\ncase on particles, in the other on masses. This hypothesis\nwas most strikingly confirmed by the author's being able to\nuse electrical agency as a more powerful means of chemical\ndecomposition than any which had yet been applied.\n'Believing,' he adds, 'that our philosophical systems are\nexceedingly imperfect, I never attached much importance to\nthis hypothesis; but having formed it after a copious\ninduction of facts, and having gained by the application of\nit a number of practical results, and considering myself as\nmuch the author of it as I was of the decomposition of the\nalkalies, and having developed it in an elementary work as\nfar as the present state of chemistry seemed to allow, I\nhave never,' he says, 'criticised or examined the manner in\nwhich different authors have adopted or explained it,\ncontented, if in the hands of others, it assisted the\narrangements of chemistry or mineralogy, or became an\ninstrument of discovery.' When the doctrine had found an\nextensive acceptance among chemists, attempts were made to\nshow that it had been asserted by earlier writers: and\nthough Davy justly denies all value to these pretended\nanticipations, they serve to show, however dimly, the\nworking of that conviction of the Connexion of Co-existent\nProperties which all along presided in men's minds during\nthis course of investigation. 'Ritter and Winterl have been\nquoted,' Davy says[11\\5], 'among other persons, as having\nimagined or anticipated the relation between electrical\npowers and chemical affinities before the discovery of the\npile {377} of Volta. But whoever will read with attention\nRitter's \"Evidence that Galvanic action exists in organised\nnature,\" and **Winterl's _Prolusiones ad Chemiam s\u00e6culi decimi\nnoni_, will find nothing to justify this opinion.' He then\nrefers to the Queries of Newton at the end of his Optics.\n'These,' he says, 'contain more grand and speculative views\nthat might be brought to bear upon this question than any\nfound in the works of modern electricians; but it is very\nunjust to the experimentalists who by the laborious\napplication of new instruments, have discovered novel facts\nand analogies, to refer them to any such suppositions as\nthat all attractions, chemical, electrical, magnetical, and\ngravitative, may depend upon the same cause.' It is\nperfectly true, that such vague opinions, though arising\nfrom that tendency to generalize which is the essence of\nscience, are of no value except so far as they are both\nrendered intelligible, and confirmed by experimental\nresearch.\n\n[Note 9\\5: _Phil. Trans._ 1826, p. 383.]\n\n[Note 10\\5: _Phil. Trans._ 1826, p. 389.]\n\n[Note 11\\5: _Ibid._ p. 384.]\n\nThe phenomena of chemical decomposition by means of the\nvoltaic pile, however, led other persons to views very\nsimilar to those of Davy. Thus Grotthus in 1805[12\\5]\npublished an hypothesis of the same kind. 'The pile of\nVolta,' he says, 'is an electrical magnet, of which each\nelement, that is, each pair of plates, has a positive and a\nnegative pole. The consideration of this polarity suggested\nto me the idea that a similar polarity may come into play\nbetween the elementary particles of water when acted upon by\nthe same electrical agent; and I avow that this thought was\nfor me a flash of light.'\n\n[Note 12\\5: _Ann. Chim._ lxviii. 54.]\n\n6. The thought, however, though thus brought into being, was\nvery far from being as yet freed from vagueness,\nsuperfluities, and errours. I have elsewhere noticed[13\\5]\nFaraday's remark on Davy's celebrated Memoir of 1806; that\n'the mode of action by which the effects take place is\nstated very generally, so generally, indeed, that probably a\ndozen precise schemes of electro-chemical action might be\ndrawn up, differing {378} essentially from each other, yet\nall agreeing with the statement there given.' When Davy and\nothers proceeded to give a little more definiteness and\nprecision to the statement of their views, they soon\nintroduced into the theory features which it was afterwards\nfound necessary to abandon. Thus[14\\5] both Davy, Grotthus,\nRiffault, and Chompr\u00e9, ascribed electrical decomposition to\nthe action of the _poles_, and some of them even pretended\nto assign the proportion in which the force of the pole\ndiminishes as the distance from it increases. Faraday, as I\nhave already stated, showed that the polarity must be\nconsidered as residing not only in what had till then been\ncalled the _poles_, but at every point of the circuit. He\nascribed[15\\5] electro-chemical decomposition to internal\nforces, residing in the _particles_ of the matter under\ndecomposition, not to external forces, exerted by the poles.\nHence he shortly afterwards[16\\5] proposed to reject the\nword _poles_ altogether, and to employ instead, the term\n_electrode_, meaning the doors or passages (of whatever\nsurface formed) by which the decomposed elements pass out.\nWhat have been called the _positive_ and _negative_ poles he\nfurther termed the _Anode_ and _Cathode_; and he introduced\nsome other changes in nomenclature connected with these. He\nthen, as I have related in the History[17\\5], invented the\nVolta-electrometer, which enabled him to measure the\nquantity of voltaic action, and this he found to be\nidentical with the quantity of chemical affinity; and he was\nthus led to the clearest view of the truth towards which he\nand his predecessors had so long been travelling, that\nelectrical and chemical forces are identical[18\\5].\n\n[Note 13\\5: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 1.]\n\n[Note 14\\5: See Faraday's Historical Sketch, _Researches_,\n481-492.]\n\n[Note 15\\5: Art. 524.]\n\n[Note 16\\5: In 1834. Eleventh Series of Researches. Art. 662.]\n\n[Note 17\\5: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 2.]\n\n[Note 18\\5: Arts. 915, 916, 917.]\n\n7. It will, perhaps, be said that this beautiful train of\ndiscovery was entirely due to experiment, and not to any _\u00e0\npriori_ conviction that co-existent polarities {379} must be\nconnected. I trust I have sufficiently stated that such an\n_\u00e0 priori_ principle could not be proved, nor even\nunderstood, without a most laborious and enlightened use of\nexperiment; but yet I think that the doctrine, when once\nfully unfolded, exhibited clearly, and established as true,\ntakes possession of the mind with a more entire conviction\nof its certainty and universality, in virtue of the\nprinciple we are now considering. When the theory has\nassumed so simple a form, it appears to derive immense\nprobability (to say the least) from its simplicity. Like the\nlaws of motion, when stated in its most general form, it\nappears to carry with it its own evidence. And thus this\ngreat theory borrows something of its character from the\nIdeas which it involves, as well as from the Experiments by\nwhich it was established.\n\n8. We may find in many of Mr. Faraday's subsequent\nreasonings, clear evidence that this idea of the Connexion\nof Polarities, as now developed, is not limited in its\napplication to facts already known experimentally, but, like\nother ideas, determines the philosopher's researches into\nthe unknown, and gives us the _form_ of knowledge even\nbefore we possess the _matter_. Thus, he says, in his\nThirteenth Series[19\\5], 'I have long sought, and still\nseek, for an effect or condition which shall be to statical\nelectricity what magnetic force is to current electricity;\nfor as the lines of discharge are associated with a certain\ntransverse effect, so it appeared to me impossible but that\nthe lines of tension or of inductive action, which of\nnecessity precede the discharge, should also have their\ncorrespondent transverse condition or effect.' Other similar\npassages might be found.\n\n[Note 19\\5: Art. 1658.]\n\nI will now consider another case to which we may apply the\nPrinciple of Connected Polarities.\n\n9. _Connexion of Chemical and Crystalline Polarities._--The\nclose connexion between the Chemical Affinity and the\nCrystalline Attraction of elements cannot be overlooked.\nBodies never crystallize but when their elements combine\nchemically; and solid bodies which {380} combine, when they\ndo it most completely and exactly, also crystallize. The\nforces which _hold together_ the elements of a crystal of\nalum are the same forces which make it a _crystal_. There is\nno distinguishing between the two sets of forces.\n\nBoth _chemical_ and _crystalline_ forces are _polar_, as we\nstated in the last chapter; but the polarity in the two\ncases is of a different kind. The polarity of chemical\nforces is then put in the most distinct form, when it is\nidentified with electrical polarity; the polarity of the\nparticles of crystals has reference to their geometrical\nform. And it is clear that these two kinds of polarity must\nbe connected. Accordingly, Berzelius expressly asserts[20\\5]\nthe necessary identity of these two polarities. 'The regular\nforms of bodies suppose a polarity which _can be_ no other\nthan an electric or magnetic polarity.' This being so\nseemingly inevitable, we might expect to find the electric\nforces manifesting some relation to the definite directions\nof crystalline forms. Mr. Faraday tried, but in vain, to\ndetect some such relation. He attempted to ascertain[21\\5]\nwhether a cube of rock crystal transmitted the electrical\nforce of tension with different intensity along and across\nthe axis of the crystal. In the first specimen there seemed\nto be some difference; but in other experiments, made both\nwith rock crystal and with calc spar, this difference\ndisappeared. Although therefore we may venture to assert\nthat there must be some very close connexion between\nelectrical and crystalline forces, we are, as yet, quite\nignorant what the nature of the connexion is, and in what\nkind of phenomena it will manifest itself.\n\n[Note 20\\5: _Essay on Chemical Prop._ 113.]\n\n[Note 21\\5: _Researches_. Art. 1689.]\n\n10. _Connexion of Crystalline and Optical\nPolarities._--Crystals present to us _optical_ phenomena\nwhich have a manifestly polar character. The double\nrefraction, both of uniaxal and of biaxal crystals, is\nalways accompanied with opposite polarization of the two\nrays; and in this and in other ways light is polarized in\ndirections dependent upon the axes of the crystalline form,\nthat is, on the directions of the polarities of the {381}\ncrystalline particles. The identity of these two kinds of\npolarity (crystalline and optical) is too obvious to need\ninsisting on; and it is not necessary for us here to decide\nby what hypothesis this identity may most properly be\nrepresented. We may hereafter perhaps find ourselves\njustified in considering the crystalline forces as\ndetermining the _elasticity_ of the luminiferous ether to be\ndifferent in _different directions_ within the crystal, and\nthus as determining the refraction and polarization of the\nlight which the crystal transmits. But at present we merely\nnote this case as an additional example of the manifest\nconnexion and fundamental identity of two co-existent\npolarities.\n\n11. _Connexion of Polarities in general._--Thus we find that\nthe Connexion of different kinds of Polarities, magnetic,\nelectric, chemical, crystalline, and optical, is certain as\na truth of experimental science. We have attempted to show\nfurther that in the minds of several of the most eminent\ndiscoverers and philosophers, such a conviction is something\nmore than a mere empirical result: it is a principle which\nhas regulated their researches while it was still but\nobscurely seen and imperfectly unfolded, and has given to\ntheir theories a character of generality and self-evidence\nwhich experience alone cannot bestow.\n\nIt will, perhaps, be said that these doctrines,--that\nscientific researches may usefully be directed by principles\nin themselves vague and obscure;--that theories may have an\nevidence superior to and anterior to experience;--are\ndoctrines in the highest degree dangerous, and utterly at\nvariance with the soundest maxims of modern times respecting\nthe cultivation of science.\n\nIn the justice and wisdom of this caution I entirely agree:\nand although I have shown that this principle of the\n_Connexion of Polarities_, rightly interpreted and\nestablished in each case by experiment, involves profound\nand comprehensive truths; I think it no less important to\nremark that, at least in the present stage of our knowledge,\nwe can make no use of this principle without taking care, at\nevery step, to determine by {382} clear and decisive\nexperiments, its proper meaning and application. All\nendeavours to proceed otherwise have led, and must lead, to\nignorance and confusion. Attempts to deduce from our bare\nIdea of Polarity, and our fundamental convictions respecting\nthe connexion of polarities, theories concerning the forces\nwhich really exist in nature, can hardly have any other\nresult than to bewilder men's minds, and to misdirect their\nefforts.\n\nSo far, indeed, as this persuasion of a connexion among\napparently different kinds of agencies, impels men, engaged\nin the pursuit of knowledge, to collect observations, to\nmultiply, repeat, and vary experiments, and to contemplate\nthe result of these in all aspects and relations, it may be\nan occasion of the most important discoveries. Accordingly\nwe find that the great laws of phenomena which govern the\nmotions of the planets about the sun, were first discovered\nby Kepler, in consequence of his scrutinizing the recorded\nobservations with an intense conviction of the existence of\ngeometrical and arithmetical harmonies in the solar system.\nPerhaps we may consider the discovery of the connexion of\nmagnetism and electricity by Professor \u0152rsted in 1820, as an\nexample somewhat of the same kind; for he also was a\nbeliever in certain comprehensive but undefined relations\namong the properties of bodies; and in consequence of such\nviews entertained great admiration for the _Prologue to the\nChemistry of the Nineteenth Century_, of Winterl, already\nmentioned. M. \u0152rsted, in 1803, published a summary of this\nwork; and in so doing, praised the views of Winterl as far\nmore profound and comprehensive than those of Lavoisier.\nSoon afterwards a Review of this publication appeared in\nFrance[22\\5], in which it was spoken of as a work only fit\nfor the dark ages, and as the indication of a sect which had\nfor some time 'ravaged Germany,' and inundated that country\nwith extravagant and unintelligible mysticism. It was,\ntherefore, a kind of triumph to M. \u0152rsted to be, after {383}\nsome years' labour, the author of one of the most remarkable\nand fertile physical discoveries of his time.\n\n[Note 22\\5: _Ann. Chim._, Tom. 1. (1804), p. 191.]\n\n12. It was not indeed without some reason that certain of\nthe German philosophers were accused of dealing in doctrines\nvast and profound in their aspect, but, in reality,\nindefinite, ambiguous, and inapplicable. And the most\nprominent of such doctrines had reference to the principle\nnow under our consideration; they represented the properties\nof bodies as consisting in certain polarities, and professed\nto deduce, from the very nature of things, with little or no\nreference to experiment, the existence and connexion of\nthese polarities. Thus Schelling, in his _Ideas towards a\nPhilosophy of Nature_, published in 1803, says[23\\5],\n'Magnetism is the universal act of investing Multiplicity\nwith Unity; but the universal form of the reduction of\nMultiplicity to Unity is the Line, pure Longitudinal\nExtension: hence Magnetism is determination of pure\nLongitudinal Extension; and as this manifests itself by\nabsolute Cohesion, Magnetism is the determination of\nabsolute Cohesion.' And as Magnetism was, by such reasoning,\nconceived to be proved as a universal property of matter,\nSchelling asserted it to be a confirmation of his views when\nit was discovered that other bodies besides iron are\nmagnetic. In like manner he used such expressions as the\nfollowing[24\\5]: 'The threefold character of the Universal,\nthe Particular, and the Indifference of the two,--as\nexpressed in their Identity, is Magnetism, as expressed in\ntheir Difference, is Electricity, and as expressed in the\nTotality, is Chemical Process. Thus these forms are only one\nform; and the Chemical Process is a mere transfer of the\nthree Points of Magnetism into the Triangle of Chemistry.'\n\n[Note 23\\5: P. 223.]\n\n[Note 24\\5: P. 486.]\n\nIt was very natural that the chemists should refuse to\nacknowledge, in this fanciful and vague language,\n(delivered, however, it is to be recollected, in 1803,) an\nanticipation of Davy's doctrine of the identity of\nelectrical and chemical forces, or of \u0152rsted's {384}\nelectro-magnetic agency. Yet it was perhaps no less natural\nthat the author of such assertions should look upon every\ngreat step in the electro-chemical theory as an illustration\nof his own doctrines. Accordingly we find Schelling\nwelcoming, with a due sense of their importance, the\ndiscoveries of Faraday. When he heard of the experiment in\nwhich electricity was produced from common magnetism, he\nfastened with enthusiasm upon the discovery, even before he\nknew any of its details, and proclaimed it at a public\nmeeting of a scientific body[25\\5] as one of the most\nimportant advances of modern science. We have (he thus\nreasoned) three effects of polar forces;--Electro-chemical\nDecomposition, Electrical Action, Magnetism. Volta and Davy\nhad confirmed experimentally the identity of the two former\nagencies: \u0152rsted showed that a closed voltaic circuit\nacquired magnetic properties: but in order to exhibit the\nidentity of electric and magnetic action it was requisite\nthat electric forces should be extricated from magnetic.\nThis great step Faraday, he remarked, had made, in producing\nthe electric spark by means of magnets.\n\n[Note 25\\5: Ueber Faraday's _Neueste Entdeckung_. M\u00fcnchen. 1832.]\n\n13. Although conjectures and assertions of the kind thus put\nforth by Schelling involve a persuasion of the pervading\ninfluence and connexion of polarities, which persuasion has\nalready been confirmed in many instances, they involve this\nprinciple in a manner so vague and ambiguous that it can\nrarely, in such a form, be of any use or value. Such views\nof polarity can never teach us in what cases we are and in\nwhat we are not expected to find polar relations; and indeed\ntend rather to diffuse error and confusion, than to promote\nknowledge. Accordingly we cannot be surprized to find such\ndoctrines put forward by their authors as an evidence of the\nsmall value and small necessity of experimental science.\nThis is done by the celebrated metaphysician Hegel, in his\n_Encyclop\u00e6dia_[26\\5]. 'Since,' {385} says he, 'the plane of\nincidence and of reflection in simple reflection is the same\nplane, when a second reflector is introduced which further\ndistributes the illumination reflected from the first, the\nposition of the first plane with respect to the second\nplane, containing the direction of the first reflection and\nof the second, has its influence upon the position,\nillumination or darkening of the object as it appears by the\nsecond reflection. This influence must be the strongest when\nthe two planes are what we must call _negatively_ related to\neach other:--that is, when they are at right angles.' 'But,'\nhe adds, 'when men infer (as Malus has done) from the\nmodification which is produced by this situation, in the\nillumination of the reflection, that the molecules of light\nin themselves, that is, on their different sides, possess\ndifferent physical energies; and when on this foundation,\nalong with the phenomena of entoptical colours therewith\nconnected, a wide labyrinth of the most complex theory is\nerected; we have then one of the most remarkable examples of\nthe _inferences_ of physics from experiment.' If Hegel's\nreasoning prove anything, it must prove that polarization\nalways accompanies reflection under such circumstances as he\ndescribes: yet all physical philosophers know that in the\ncase of metals, in which the reflection is most complete,\nlight is not completely polarized at any angle; and that in\nother substances the polarization depends upon various\ncircumstances which show how idle and inapplicable is the\naccount which he thus gives of the property. His\nself-complacent remark about the inferences of physics from\nexperiment, is intended to recommend by comparison his own\nmethod of considering the nature of 'things in themselves;'\na mode of obtaining physical truth which had been more than\nexhausted by Aristotle, and out of which no new attempts\nhave extracted anything of value since his time.\n\n[Note 26\\5: Sec. 278.]\n\n14. Thus the general conclusion to which we are led on this\nsubject, is, that the persuasion of the existence and\nConnexion or Identity of various Polarities in nature,\nalthough very naturally admitted, and in many {386} cases\ninterpreted and confirmed by observed facts, is of itself,\nso far as we at present possess it, a very insecure guide to\nscientific doctrines. When it is allowed to dictate our\ntheories, instead of animating and extending our\nexperimental researches, it leads only to errour, confusion,\nobscurity, and mysticism.\n\nThis Fifth Book, on the subject of Polarities, is a short\none compared with most of the others. This arises in a great\nmeasure from the circumstance that the Idea of Polarity has\nonly recently been apprehended and applied, with any great\ndegree of clearness, among physical philosophers; and is\neven yet probably entertained in an obscure and ambiguous\nmanner by most experimental inquirers. I have been desirous\nof not attempting to bring forward any doctrines upon the\nsubject, except such as have been fully illustrated and\nexemplified by the acknowledged progress of the physical\nsciences. If I had been willing to discuss the various\nspeculations which have been published respecting the\nuniversal prevalence of Polarities in the universe, and\ntheir results in every province of nature, I might easily\nhave presented this subject in a more extended form; but\nthis would not have been consistent with my plan of tracing\nthe influence of scientific Ideas only so far as they have\nreally aided in disclosing and developing scientific truths.\nAnd as the influence of this Idea is clearly distinguishable\nboth from those which precede and those which follow, in the\ncharacter of the sciences to which it gives rise, and as it\nappears likely to be hereafter of great extent and\nconsequence, it seemed better to treat of it in a separate\nBook, although of a brevity disproportioned to the rest.\n\n\n\n\nEND OF VOL. I.\n\n\n\nCambridge: Printed at the University Press.\n\n\n\n\nHISTORY\nOF\nSCIENTIFIC IDEAS.\n\n\n\nVOLUME II.\n\n\n\n\nCambridge;\nPRINTED BY C. J. CLAY, M.A.\nAT THE UNIVERSITY PRESS.\n\n\n\nHISTORY\nOF\nSCIENTIFIC IDEAS.\n\nBY WILLIAM WHEWELL, D.D.,\nMASTER OF TRINITY COLLEGE, CAMBRIDGE, AND\nCORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.\n\n\n\nBEING THE FIRST PART OF THE PHILOSOPHY\nOF THE INDUCTIVE SCIENCES.\n\n\n\n_THE THIRD EDITION._\n\nIN TWO VOLUMES.\n\n\n\u039b\u0391\u039c\u03a0\u0391\u0394I\u0391 \u0395\u03a7\u039f\u039d\u03a4\u0395\u03a3 \u0394I\u0391\u0394\u03a9\u03a3\u039f\u03a5\u03a3I\u039d \u0391\u039b\u039b\u0397\u039b\u039fI\u03a3\n\n\nVOLUME II.\n\n\n\nLONDON:\nJOHN W. PARKER AND SON, WEST STRAND.\n1858.\n\n\nCONTENTS\nOF\nTHE SECOND VOLUME.\n\n\nBOOK VI.\n\nTHE PHILOSOPHY OF CHEMISTRY.\n\n PAGE\nCHAP. I. ATTEMPTS TO CONCEIVE ELEMENTARY COMPOSITION 3\n\n _Art._ 1. Fundamental Ideas of Chemistry.\n 2. Elements.\n 3. Do Compounds resemble their Elements?\n 4. The Three Principles.\n 5. A Modern Errour.\n 6. Are Compounds determined by the Figure of Elements?\n 7. Crystalline Form depends on Figure of Elements.\n 8. Are Compounds determined by Mechanical Attraction\n of Elements?\n 9. Newton's followers.\n 10. Imperfection of their Hypotheses.\n\nCHAP. II. ESTABLISHMENT AND DEVELOPMENT OF THE IDEA OF\n CHEMICAL AFFINITY 15\n\n _Art._ 1. Early Chemists.\n 2. Chemical Affinity.\n 3. Affinity or Attraction?\n 4. Affinity preferable.\n 5. Analysis is possible.\n{vi}\n 6. Affinity is Elective.\n 7. Controversy on this.\n 8. Affinity is Definite.\n 9. Are these Principles necessarily true?\n 10. Composition determines Properties.\n 11. Comparison on this subject.\n 12. Composition determines Crystalline Form.\n\nCHAP. III. OF THE IDEA OF SUBSTANCE 29\n\n _Art._ 1. Indestructibility of Substance.\n 2. The Idea of Substance.\n 3. Locke's Denial of Substance.\n 4. Is all Substance heavy?\n Note on Sir W. Hamilton's objections 37\n\nCHAP. IV. APPLICATION OF THE IDEA OF SUBSTANCE IN CHEMISTRY 39\n\n _Art._ 1. A Body is Equal to its Elements.\n 2. Lavoisier.\n 3. Are there Imponderable Elements?\n 4. Faraday's views.\n 5. Composition of Water.\n 6. Heat in Chemistry.\n\nCHAP. V. THE ATOMIC THEORY 48\n\n _Art._ 1. The Theory on Chemical Grounds.\n 2. Hypothesis of Atoms.\n 3. Its Chemical Difficulties.\n 4. Grounds of the Atomic Doctrine.\n 5. Ancient Atomists.\n 6. Francis Bacon.\n 7. Modern Atomists.\n 8. Arguments for and against.\n 9. Boscovich's Theory.\n 10. Molecular Hypothesis.\n 11. Poisson's Inference.\n 12. Wollaston's Argument.\n 13. Properties are Permanent.\n{vii}\nBOOK VII.\n\nTHE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY.\n\nCHAP. I. EXPLICATION OF THE IDEA OF SYMMETRY 67\n\n _Art._ 1. Symmetry, what.\n 2. Kinds of Symmetry.\n 3. Examples in Nature.\n 4. Vegetables and Animals.\n 5. Symmetry a Fundamental Idea.\n 6. Result of Symmetry.\n\nCHAP. II. APPLICATION OF THE IDEA OF SYMMETRY TO CRYSTALS 75\n\n _Art._ 1. 'Fundamental Forms.'\n 2. Their use.\n 3. 'Systems of Crystallization.'\n 4. Cleavage.\n 5. Other Properties.\n\nCHAP. III. SPECULATIONS FOUNDED UPON THE SYMMETRY OF CRYSTALS 80\n\n _Art._ 1. Integrant Molecules.\n 2. Difficulties of the Theory.\n 3. Merit of the Theory.\n 4. Wollaston's Hypothesis.\n 5. Maxim for such Hypotheses.\n 6. Dalton's Hypothesis.\n 7. Amp\u00e8re's Hypothesis.\n 8. Difficulty of such Hypotheses.\n 9. Isomorphism.\n{viii}\nBOOK VIII.\n\nPHILOSOPHY OF THE CLASSIFICATORY SCIENCES.\n\nCHAP. I. THE IDEA OF LIKENESS AS GOVERNING THE USE OF\n COMMON NAMES 95\n\n _Art._ 1. Object of the Chapter.\n 2. Unity of the Individual.\n 3. Condition of Unity.\n 4. Kinds.\n 5. Not made by Definitions.\n 6. Condition of the Use of Terms.\n 7. Terms may have different Uses.\n 8. Gradation of Kinds.\n 9. Characters of Kinds.\n 10. Difficulty of Definitions.\n 11. 'The Five Words.'\n\nCHAP. II. THE METHODS OF NATURAL HISTORY, AS REGULATED\n BY THE IDEA OF LIKENESS 108\n\n_Sect._ I. _Natural History in General._\n _Art._ 1. Idea of Likeness in Natural History.\n 2. Condition of its Use.\n\n_Sect._ II. _Terminology._\n _Art._ 3. Meaning of the word.\n\n_Sect._ III. _The Plan of the System._\n _Art._ 4. Its Meaning.\n 5. Latent Reference to Natural Affinity.\n 6. Natural Classes.\n 7. Artificial Classes.\n 8. Are Genera Natural?\n 9. Natural History and Mathematics.\n 10. Natural Groups given by Type, not by Definition.\n 11. Physiography.\n 12. Artificial and Natural Systems.\n{ix}\n_Sect._ IV. _Methods of framing Natural Systems._\n _Art._ 13. Method of Blind Trial.\n 14. Method of General Comparison.\n\n_Sect._ V. _Gradation of Groups._\n _Art._ 15. Series of Subdivisions.\n 16. What is a Species?\n 17. The _words_ 'Species' and 'Genus.'\n 18. Varieties. Races.\n\n_Sect._ VI. _Nomenclature._\n _Art._ 19. Binary Nomenclature.\n\n_Sect._ VII. _Diagnosis._\n _Art._ 20. Characteristick and Systematick.\n\nCHAP. III. APPLICATION OF THE NATURAL HISTORY METHOD\n TO MINERALOGY 138\n\n _Art._ 1. Mohs's System.\n 2. His 'Characteristick.'\n 3. Mineral _Species_ not yet well fixed.\n 4. _Orders_ of Minerals.\n 5. Nomenclature of Minerals.\n 6. M. Necker's 'R\u00e8gne Mineral.'\n 7. Inconvenience of taking a Chemical Basis of\n Mineral Systems.\n 8. Relation of Natural History and Chemistry.\n 9. What is a Mineralogical Individual?\n 10. A well-formed Crystal is an Individual.\n 11. Not the Integrant Molecules,\n 12. Nor the Cleavage Forms.\n 13. Compound Crystals are not Individuals.\n 14. Crystalline Forms are sufficiently complete for\n this.\n 15. Including aggregate Masses.\n 16. Do Artificial Crystals belong to Mineralogy?\n 17. The Mineralogical Individual extends as far as\n the same Crystalline Axes extend.\n 18. Artificial Crystals do belong to Mineralogy:\n{x}\n 19. Cannot be excluded.\n 20. Species to be determined by the Crystalline Power.\n 21. Secondary Derivative Forms are Varieties:\n 22. Are not Species, as M. Necker holds.\n\nCHAP. IV. OF THE IDEA OF NATURAL AFFINITY 159\n\n _Art._ 1. The Idea of Affinity\n 2. Is not to be made out by Arbitrary Rules.\n 3. Functions of Living things are many,\n 4. But all lead to the same arrangement.\n 5. This is Cuvier's principle:\n 6. And Decandolle's.\n 7. Is this applicable to Inorganic Bodies?\n 8. Yes; by the agreement of Physical and\n Chemical Arrangement.\n\n\nBOOK IX.\n\nTHE PHILOSOPHY OF BIOLOGY.\n\nCHAP. 1. ANALOGY OF BIOLOGY WITH OTHER SCIENCES. 169\n\n _Art._ 1. Biology involves the Idea of Life.\n 2. This Idea to be historically traced.\n 3. The Idea at first expressed by means of other\n Ideas.\n 4. Mystical, Mechanical, Chemical, and Vital\n Fluid Hypotheses.\n\nCHAP. II. SUCCESSIVE BIOLOGICAL HYPOTHESES 174\n\n_Sect._ I. _The Mystical School._\n\n_Sect._ II. _The Iatrochemical School._\n\n_Sect._ III. _The Iatromathematical School._\n\n_Sect._ IV. _The Vital Fluid School._\n\n_Sect._ V. _The Psychical School._\n{xi}\n\nCHAP. III. ATTEMPTS TO ANALYSE THE IDEA OF LIFE 195\n\n _Art._ 1. Definitions of Life,\n 2. By Stahl, Humboldt, Kant.\n 3. Definition of Organization by Kant.\n 4. Life is a System of Functions.\n 5. Bichat. _Sum_ of Functions.\n 6. Use of Definition.\n 7. Cuvier's view.\n 8. Classifications of Functions.\n 9. Vital, Natural, and Animal Functions.\n 10. Bichat. Organic and Animal Life.\n 11. Use of this Classification.\n\nCHAP. IV. ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES,\n AND FIRST, OF ASSIMILATION AND SECRETION 203\n\n_Sect._ I. _Course of Biological Research._\n _Art._ 1. Observation and New Conceptions.\n\n_Sect._ II. _Attempts to form a distinct Conception\n of Assimilation and Secretion._\n _Art._ 2. The Ancients.\n 3. Buffon. Interior Mould.\n 4. Defect of this view.\n 5. Cuvier. Life a Vortex.\n 6. Defect of this view.\n 7. Schelling. Matter and Form.\n 8. Life a constant Form of circulating Matter, &c.\n\n_Sect._ III. _Attempts to conceive the Forces of\n Assimilation and Secretion._\n _Art._ 9. Assimilation is a Vital Force.\n 10. The name 'Assimilation.'\n 11. Several processes involved in Assimilation.\n 12. _Absorption_. Endosmose.\n 13. Absorption involves a Vital Force.\n 14. _Secretion_. Glands.\n 15. Motions of Vital Fluids.\n{xii}\n_Sect._ IV. _Attempts to conceive the Process of Generation._\n _Art._ 16. 'Reproduction' figuratively used for Generation.\n 17. Nutrition different from\n 18. Generation.\n 19. Generations successively included.\n 20. Pre-existence of Germs.\n 21. Difficulty of this view.\n 22. Communication of Vital Forces.\n 23. Close similarity of Nutrition and Generation.\n 24. The Identity of the two Processes exemplified.\n\nCHAP. V. ATTEMPTS TO FORM IDEAS OF SEPARATE VITAL\n FORCES, _continued_.--VOLUNTARY MOTION. 222\n\n _Art._ 1. Voluntary Motion one of the animal Functions.\n 2. Progressive knowledge of it.\n 3. Nervous Fluid not electric.\n 4. Irritability. Glisson.\n 5. Haller.\n 6. Contractility.\n 7. Organic Sensibility and Contractility not separable.\n 8. Improperly described by Bichat.\n 9. Brown.\n 10. Contractility a peculiar Power.\n 11. Cuvier's view.\n 12. Elementary contractile Action.\n 13. Strength of Muscular Fibre.\n 14. Sensations become Perceptions\n 15. By means of Ideas;\n 16. And lead to Muscular Actions.\n 17. Volition comes between Perception and Action.\n 18. Transition to Psychology,\n 19. A center is introduced.\n 20. The central consciousness may be obscure.\n 21. Reflex Muscular Action.\n 22. Instinct.\n 23. Difficulty of conceiving Instinct.\n 24. Instinct opposed to Insight.\n{xiii}\n\nCHAP. VI. OF THE IDEA OF FINAL CAUSES 239\n\n _Art._ 1. Organization. Parts are Ends and Means.\n 2. Not merely mutually dependent.\n 3. Not merely mutually Cause and Effect.\n 4. Notion of _End_ not derived from Facts.\n 5. This notion has regulated Physiology.\n 6. Notion of Design comes from within.\n 7. Design not understood by Savages.\n 8. Design opposed to Morphology.\n 9. Impression of Design when fresh.\n 10. Acknowledgement of an End by adverse Physiologists.\n 11. This included in the Notion of Disease.\n 12. It belongs to organized Creatures only.\n 13. The term Final _Cause_.\n 14. Law and Design.\n 15. Final Causes and Morphology.\n 16. Expressions of physiological Ends.\n 17. The Conditions of Existence.\n 18. The asserted presumption of Teleology.\n 19. Final Causes in other subjects.\n 20. Transition to Pal\u00e6tiology.\n\n\nBOOK X.\n\nTHE PHILOSOPHY OF PAL\u00c6TIOLOGY.\n\nCHAP. I. OF PAL\u00c6TIOLOGICAL SCIENCES IN GENERAL. 257\n\n _Art._ 1. Description of Pal\u00e6tiology.\n 2. Its Members.\n 3. Other Members.\n 4. Connexion of the whole subject.\n 5. We shall take Material Sciences only;\n 6. But these are connected with others.\n\nCHAP. II. OF THE THREE MEMBERS OF A PAL\u00c6TIOLOGICAL SCIENCE 263\n\n _Art._ 1. Divisions of such Sciences.\n 2. The Study of Causes.\n 3. \u00c6tiology.\n{xiv}\n 4. Phenomenology requires Classification. Phenomenal\n Geology.\n 5. Phenomenal Uranology.\n 6. Phenomenal Geography of Plants and Animals.\n 7. Phenomenal Glossology.\n 8. The Study of Phenomena leads to Theory.\n 9. No sound Theory without \u00c6tiology.\n 10. Causes in Pal\u00e6tiology.\n 11. Various kinds of Cause.\n 12. Hypothetical Order of Pal\u00e6tiological Causes.\n 13. Mode of Cultivating \u00c6tiology:--In Geology:\n 14. In the Geography of Plants and Animals:\n 15. In Languages.\n 16. Construction of Theories.\n 17. No sound Pal\u00e6tiological Theory yet extant.\n\nCHAP. III. OF THE DOCTRINE OF CATASTROPHES AND THE\n DOCTRINE OF UNIFORMITY 284\n\n _Art._ 1. Doctrine of Catastrophes.\n 2. Doctrine of Uniformity.\n 3. Is Uniformity probable _a priori_?\n 4. Cycle of Uniformity indefinite.\n 5. Uniformitarian Arguments are Negative only.\n 6. Uniformity in the Organic World.\n 7. Origin of the present Organic World.\n 8. Nebular Origin of the Solar System.\n 9. Origin of Languages.\n 10. No Natural Origin discoverable.\n\nCHAP. IV. OF THE RELATION OF TRADITION TO PAL\u00c6TIOLOGY 297\n\n _Art._ 1. Importance of Tradition.\n 2. Connexion of Tradition and Science.\n 3. Natural and Providential History of the World.\n 4. The Sacred Narrative.\n 5. Difficulties in interpreting the Sacred Narrative.\n 6. Such Difficulties inevitable.\n 7. Science tells us nothing concerning Creation.\n{xv}\n 8. Scientific views, when familiar, do not disturb\n the authority of Scripture.\n 9. When should Old Interpretations be given up?\n 10. In what Spirit should the Change be accepted?\n 11. In what Spirit should the Change be urged?\n 12. Duty of Mutual forbearance.\n 13. Case of Galileo.\n\nCHAP. V. OF THE CONCEPTION OF A FIRST CAUSE 316\n\n _Art._ 1. The Origin of things is not naturally discoverable;\n 2. Yet has always been sought after.\n 3. There must be a First Cause.\n 4. This is an Axiom.\n 5. Involved in the proof of a Deity.\n 6. The mind is not satisfied without it.\n 7. The Whole Course of Nature must have a Cause.\n 8. Necessary Existence of God.\n 9. Forms of the Proof.\n 10. Idea of a First Cause is Necessary.\n 11. Conception of a First Cause.\n 12. The First Cause in all Sciences is the same.\n 13. We are thus led to Moral Subjects.\n\n Conclusion of this History.\n\n\n\n\n{{1}}\nBOOK VI.\n\n\nTHE\nPHILOSOPHY\nOF\nCHEMISTRY.\n\n\n\n\nA PHILOSOPHER was asked:--How much does smoke weigh? He\nanswered: Subtract from the weight of the fuel the weight of\nthe ashes, and thou hast the weight of the smoke. Thus he\nassumed as incontrovertible that, even in the fire, the\nSubstance does not perish, only its Form undergoes a change.\nIn like manner the proposition, _Nothing can come of\nNothing_ was only another consequence of the Principle of\nPermanence, or rather of the Principle of the Enduring\nExistence of the same subject with different appearances.\n\nKant, _Kritik d. r. Vern._\n\n\n\n{{3}}\nBOOK VI.\n\n\nTHE PHILOSOPHY OF CHEMISTRY.\n\n\nCHAPTER I.\n\nATTEMPTS TO CONCEIVE ELEMENTARY COMPOSITION.\n\n\n1. WE have now to bring into view, if possible, the Ideas\nand General Principles which are involved in Chemistry,--the\nscience of the composition of bodies. For in this as in\nother parts of human knowledge, we shall find that there are\ncertain Ideas, deeply seated in the mind, though shaped and\nunfolded by external observation, which are necessary\nconditions of the existence of such a science. These Ideas\nit is, which impel man to such a knowledge of the\nComposition of bodies, which give _meaning_ to _facts_\nexhibiting this composition, and _universality_ to _special_\ntruths discovered by experience. These are the Ideas of\n_Element_ and of _Substance_.\n\nUnlike the Idea of Polarity, of which we treated in the last\nBook, these Ideas have been current in men's minds from very\nearly times, and formed the subject of some of the first\nspeculations of philosophers. It happened however, as might\nhave been expected, that in the first attempts they were not\nclearly distinguished from other notions, and were\napprehended and applied in an obscure and confused manner.\nWe cannot better exhibit the peculiar character and meaning\nof these Ideas than by tracing the form which they have\nassumed {4} and the efficacy which they have exerted in\nthese successive essays. This, therefore, I shall endeavour\nto do, beginning with the Idea of Element.\n\n2. That bodies are composed or made up of certain parts,\nelements, or principles, is a conception which has existed\nin men's minds from the beginning of the first attempts at\nspeculative knowledge. The doctrine of the Four Elements,\nEarth, Air, Fire and Water, of which all things in the\nuniverse were supposed to be constituted, is one of the\nearliest forms in which this conception was systematized;\nand this doctrine is stated by various authors to have\nexisted as early as the times of the ancient Egyptians[1\\6].\nThe words usually employed by Greek writers to express these\nelements are \u1f00\u03c1\u03c7\u1f74 a _principle_ or _beginning_, and\n\u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u1fd6\u03bf\u03bd, which probably meant a _letter_ (of a word)\nbefore it meant an _element_ of a compound. For the\nresolution of a word into its letters is undoubtedly a\nremarkable instance of a successful analysis performed at an\nearly stage of man's history; and might very naturally\nsupply a metaphor to denote the analysis of substances into\ntheir intimate parts, when men began to contemplate such an\nanalysis as a subject of speculation. The Latin word\n_elementum_ itself, though by its form it appears to be a\nderivative abstract term, comes from some root now obsolete;\nprobably[2\\6] from a word signifying _to grow_ or _spring up_.\n\n[Note 1\\6: Gilbert's _Phys._ 1. i. c. iii.]\n\n[Note 2\\6: Vossius _in voce_. \"Conjecto esse ab antiqua voco\n_eleo_ pro _oleo_, id est _cresco_: a qua signiflcatione\nproles, _suboles_, _adolescens_: ut ab _juratum_,\n_juramentum_; ab _adjutum_, _adjumentum_: sic ab _eletum_,\n_elementum_: quia inde omnia crescunt ac nascuntur.\"]\n\nThe mode in which elements form the compound bodies and\ndetermine their properties was at first, as might be\nexpected, vaguely and variously conceived. It will, I trust,\nhereafter be made clear to the reader that the relation of\nthe elements to the compound involves a peculiar and\nappropriate Fundamental Idea, not susceptible of being\ncorrectly represented by any comparison or combination of\nother ideas, and guiding us to clear and definite results\nonly when it is illustrated {5} and nourished by an abundant\nsupply of experimental facts. But at first the peculiar and\nspecial notion which is required in a just conception of the\nconstitution of bodies was neither discerned nor suspected;\nand up to a very late period in the history of chemistry,\nmen went on attempting to apprehend the constitution of\nbodies more clearly by substituting for this obscure and\nrecondite idea of Elementary Composition, some other idea\nmore obvious, more luminous, and more familiar, such as the\nideas of Resemblance, Position, and mechanical Force. We\nshall briefly speak of some of these attempts, and of the\nerrours which were thus introduced into speculations on the\nrelations of elements and compounds.\n\n3. _Compounds assumed to resemble their Elements._--The\nfirst notion was that compounds derive their qualities from\ntheir elements by _resemblance_:--they are hot in virtue of\na hot element, heavy in virtue of a heavy element, and so\non. In this way the doctrine of the _four elements_ was\nframed; for every body is either hot or cold, moist or dry;\nand by combining these qualities in all possible ways, men\ndevised four elementary substances, as has been stated in\nthe History[3\\6].\n\n[Note 3\\6: _Hist. Ind. Sc._ b. i. c. ii. sec. 2.]\n\nThis assumption of the derivation of the qualities of bodies\nfrom similar qualities in the elements was, as we shall see,\naltogether baseless and unphilosophical, yet it prevailed\nlong and universally. It was the foundation of medicine for\na long period, both in Europe and Asia; disorders being\ndivided into hot, cold, and the like; and remedies being\narranged according to similar distinctions. Many readers\nwill recollect, perhaps, the story[4\\6] of the indignation\nwhich the Persian physicians felt towards the European, when\nhe undertook to cure the ill effects of cucumber upon the\npatient, by means of mercurial medicine: for cucumber, which\nis cold, could not be counteracted, they maintained, by\nmercury, which in their classification is cold also. Similar\nviews of the operation of medicines might {6} easily be\ntraced in our own country. A moment's reflection may\nconvince us that when drugs of any kind are subjected to the\nchemistry of the human stomach and thus made to operate on\nthe human frame, it is utterly impossible to form the most\nremote conjecture what the result will be, from any such\nvague notions of their qualities as the common use of our\nsenses can give. And in like manner the common operations of\nchemistry give rise, in almost every instance, to products\nwhich bear no resemblance to the materials employed. The\nresults of the furnace, the alembic, the mixture, frequently\nhave no visible likeness to the ingredients operated upon.\nIron becomes steel by the addition of a little charcoal; but\nwhat visible trace of the charcoal is presented by the metal\nthus modified? The most beautiful colours are given to glass\nand earthenware by minute portions of the ores of black or\ndingy metals, as iron and manganese. The worker in metal,\nthe painter, the dyer, the vintner, the brewer, all the\nartisans in short who deal with practical chemistry, are\nable to teach the speculative chemist that it is an utter\nmistake to expect that the qualities of the elements shall\nbe still discoverable, in an unaltered form, in the\ncompound. This first rude notion of an element, that it\ndetermines the properties of bodies _by resemblance_, must\nbe utterly rejected and abandoned before we can make any\nadvance towards a true apprehension of the constitution of\nbodies.\n\n[Note 4\\6: See _Hadji Baba_.]\n\n4. This step accordingly was made, when the hypothesis of\nthe four elements was given up, and the doctrine of the\n_three Principles_, Salt, Sulphur, and Mercury, was\nsubstituted in its place. For in making this change, as I\nhave remarked in the History[5\\6], the real advance was the\nacknowledgment of the changes, produced by the chemist's\noperations, as results to be accounted for by the union and\nseparation of substantial elements, however great the\nchanges, and however unlike the product might be to the\nmaterials. And this step once made, chemists went on\nconstantly {7} advancing towards a truer view of the nature\nof an element, and consequently, towards a more satisfactory\ntheory of chemical operations.\n\n[Note 5\\6: _Hist. Ind. Sc._ b. iv. c. 1.]\n\n5. Yet we may, I think, note one instance, even in the works\nof eminent modern chemists, in which this maxim, that we\nhave no right to expect any resemblance between the elements\nand the compound, is lost sight of. I speak of certain\nclassifications of mineral substances. Berzelius, in his\nSystem of Mineral Arrangement, places _sulphur_ next to the\n_sulphurets_. But surely this is an errour, involving the\nancient assumption of the resemblance of elements and\ncompounds; as if we were to expect the sulphurets to bear a\nresemblance to sulphur. All classifications are intended to\nbring together things resembling each other: the sulphurets\nof metals have certain general resemblances to each other\nwhich make them a tolerably distinct, well determined, class\nof bodies. But sulphur has no resemblances with these, and\nno analogies with them, either in physical or even in\nchemical properties. It is a simple body; and both its\nresemblances and its analogies direct us to place it along\nwith other simple bodies, (selenium, and phosphorus,) which,\nunited with metals, produce compounds not very different\nfrom the sulphurets. Sulphur cannot be, nor approach to\nbeing, a sulphuret; we must not confound what it _is_ with\nwhat it _makes_. Sulphur has its proper influence in\ndetermining the properties of the compound into which it\nenters; but it does not do this according to resemblance of\nqualities, or according to any principle which properly\nleads to propinquity in classification.\n\n6. _Compounds assumed to be determined by the Figure of\nElements._--I pass over the fanciful modes of representing\nchemical changes which were employed by the Alchemists; for\nthese strange inventions did little in leading men towards a\njuster view of the relations of elements to compounds. I\nproceed for an instant to the attempt to substitute another\nobvious conception for the still obscure notion of\nelementary composition. It was imagined that all the\nproperties of bodies and their mutual operations might be\n{8} accounted for by supposing them constituted of\n_particles_ of various _forms_, round or angular, pointed or\nhooked, straight or spiral. This is a very ancient\nhypothesis, and a favourite one with many casual speculators\nin all ages. Thus Lucretius undertakes to explain why wine\npasses rapidly through a sieve and oil slowly, by telling us\nthat the latter substance has its particles either larger\nthan those of the other, or more hooked and interwoven\ntogether. And he accounts for the difference of sweet and\nbitter by supposing the particles in the former case to be\nround and smooth, in the latter sharp and jagged[6\\6].\nSimilar assumptions prevailed in modern times on the revival\nof the mechanical philosophy, and constitute a large part of\nthe physical schemes of Descartes and Gassendi. They were\nalso adopted to a considerable extent by the chemists. Acids\nwere without hesitation assumed to consist of sharp pointed\nparticles; which, 'I hope,' Lemery says[7\\6], 'no one will\ndispute, seeing every one's experience does demonstrate it:\nhe needs but taste an acid to be satisfied of it, for it\npricks the tongue like anything keen and finely cut.' Such\nan assumption is not only altogether gratuitous and useless,\nbut appears to be founded in some degree upon a confusion in\nthe metaphorical and literal use of such words as _keen_ and\n_sharp_. The assumption once made, it was easy to\naccommodate it, in a manner equally arbitrary, to other\nfacts. 'A demonstrative and convincing proof that an acid\ndoes consist of pointed parts is, that not only all acid\nsalts do crystallize into edges, but all dissolutions of\ndifferent things, caused by acid liquors, do assume this\nfigure in their crystallization. These crystals consist of\npoints differing both in length and bigness one from\nanother, and this diversity must be attributed to the keener\nor blunter edges of the different sorts of acids: and so\nlikewise this difference of the points in subtilty is the\ncause that one acid can penetrate and dissolve with one sort\nof _mixt_, that another can't rarify at all: Thus _vinegar_\ndissolves _lead_, {9} which _aqua fortis_ can't: _aqua\nfortis_ dissolves _quicksilver_, which _vinegar_ will not\ntouch; _aqua regalis_ dissolves _gold_, whenas _aqua fortis_\ncannot meddle with it; on the contrary, _aqua fortis_\ndissolves _silver_, but can do nothing with gold, and so of\nthe rest.'\n\n[Note 6\\6: _De Rerum Natura_, ii. 390 sqq.]\n\n[Note 7\\6: _Chemistry_, p. 25.]\n\nThe leading fact of the vehement combination and complete\nunion of acid and alkali readily suggested a fit form for\nthe particles of the latter class of substances. 'This\neffect,' Lemery adds, 'may make us reasonably conjecture\nthat an alkali is a terrestrious and solid matter whose\nforms are figured after such a manner that the acid points\nentering in do strike and divide whatever opposes their\nmotion.' And in a like spirit are the speculations in Dr.\nMead's _Mechanical Account of Poisons_ (1745). Thus he\nexplains the poisonous effect of _corrosive sublimate_ of\nmercury by saying[8\\6] that the particles of the salt are a\nkind of lamell\u00e6 or blades to which the mercury gives an\nadditional weight. If resublimed with three-fourths the\nquantity of mercury, it loses its corrosiveness, (becoming\n_calomel_,) which arises from this, that in sublimation 'the\ncrystalline blades are divided every time more and more by\nthe force of the fire:' and 'the broken pieces of the\ncrystals uniting into little masses of differing figures\nfrom their former make, those cutting points are now so much\nsmaller that they cannot make wounds deep enough to be\nequally mischievous and deadly: and therefore do only\nvellicate and twitch the sensible membranes of the stomach.'\n\n[Note 8\\6: P. 199.]\n\n7. Among all this very fanciful and gratuitous assumption we\nmay notice one true principle clearly introduced, namely,\nthat the suppositions which we make respecting the forms of\nthe elementary particles of bodies and their mode of\ncombination must be such as to explain the facts of\ncrystallization, as well as of mere chemical change. This\nprinciple we shall hereafter have occasion to insist upon\nfurther.\n\nI now proceed to consider a more refined form of assumption\nrespecting the constitution of bodies, yet {10} still one in\nwhich a vain attempt is made to substitute for the peculiar\nidea of chemical composition a more familiar mechanical\nconception.\n\n8. _Compounds assumed to be determined by the Mechanical\nAttraction of the Elements._--When, in consequence of the\ninvestigations and discoveries of Newton and his\npredecessors, the conception of mechanical force had become\nclear and familiar, so far as the action of external forces\nupon a body was concerned, it was very natural that the\nmathematicians who had pursued this train of speculation\nshould attempt to apply the same conception to that mutual\naction of the internal parts of a body by which they are\nheld together. Newton himself had pointed the way to this\nattempt. In the Preface to the _Principia_, after speaking\nof what he has done in calculating the effects of forces\nupon the planets, satellites, &e., he adds, 'Would it were\npermitted us to deduce the other phenomena of nature from\nmechanical principles by the same kind of reasoning. For\nmany things move me to suspect that all these phenomena\ndepend upon certain forces, by which the particles of\nbodies, through causes not yet known, are either urged\ntowards each other, and cohere according to regular figures,\nor are repelled and recede from each other; which forces\nbeing unknown, philosophers have hitherto made their\nattempts upon nature in vain.' The same thought is at a\nlater period followed out further in one of the Queries at\nthe end of the Opticks[9\\6]. 'Have not the small particles\nof bodies certain Powers, Virtues, or Forces, by which they\nact at a distance, not only upon the rays of light for\nreflecting, refracting and inflecting them, but also upon\none another for producing a great part of the phenomena of\nnature?' And a little further on he proceeds to apply this\nexpressly to chemical changes. 'When Salt of Tartar runs\n_per deliquium_ [or as we now express it, deliquesces] is\nnot this done by an _attraction_ between the particles of\nthe Salt of Tartar and the particles of the water which\nfloat in the air in {11} the form of vapours? And why does\nnot common salt, or saltpetre, or vitriol, run _per\ndeliquium_, but for want of such an attraction? or why does\nnot Salt of Tartar draw more water out of the air than in a\ncertain proportion to its quantity, but for want of an\nattractive force after it is saturated with water?' He goes\non to put a great number of similar cases, all tending to\nthe same point, that chemical combinations cannot be\nconceived in any other way than as an attraction of\nparticles.\n\n[Note 9\\6: Query 31.]\n\n9. Succeeding speculators in his school attempted to follow\nout this view. Dr. Frend, of Christ Church, in 1710,\npublished his _Pr\u00e6lectiones Chymic\u00e6, in quibus omne fere\nOperationes Chymic\u00e6 ad vera Principia ex ipsius Natur\u00e6\nLegibus rediguntur. Oxonii habit\u00e6_. This book is dedicated\nto Newton, and in the dedication, the promise of advantage\nto chemistry from the influence of the Newtonian discoveries\nis spoken of somewhat largely,--much more largely, indeed,\nthan has yet been justified by the sequel. After declaring\nin strong terms that the only prospect of improving science\nconsists in following the footsteps of Newton, the author\nadds, 'That force of attraction, of which you first so\nsuccessfully traced the influence in the heavenly bodies,\noperates in the most minute corpuscles, as you long ago\nhinted in your _Principia_, and have lately plainly shown in\nyour _Opticks_; and this force we are only just beginning to\nperceive and to study. Under these circumstances I have been\ndesirous of trying what is the result of this view in\nchemistry.' The work opens formally enough, with a statement\nof general mechanical principles, of which the most peculiar\nare these:--'That there exists an attractive force by which\nparticles when at very small distances from each other, are\ndrawn together;--that this force is different, according to\nthe different figure and density of the particles;--that the\nforce may be greater on one side of a particle than on the\nother;--that the force by which particles cohere together\narises from attraction, and is variously modified according\nto the quantity of contacts.' But these principles are not\n{12} applied in any definite manner to the explanation of\nspecific phenomena. He attempts, indeed, the question of\nspecial solvents[10\\6]. Why does _aqua fortis_ dissolve\nsilver and not gold, while _aqua regia_ dissolves gold and\nnot silver? which, he says, is the most difficult question\nin chemistry, and which is certainly a fundamental question\nin the formation of chemical theory. He solves it by certain\nassumptions respecting the forces of attraction of the\nparticles, and also the diameter of the particles of the\nacids and the pores of the metals, all which suppositions\nare gratuitous.\n\n[Note 10\\6: P. 54.]\n\n10. We may observe further, that by speaking, as I have\nstated that he does, of the figure of particles, he mixes\ntogether the assumption of the last section with the one\nwhich we are considering in this. This combination is very\nunphilosophical, or, to say the least, very insufficient,\nsince it makes a new hypothesis necessary. If a body be\ncomposed of cubical particles, held together by their mutual\nattraction, by what force are the parts of each cube held\ntogether? In order to understand their structure, we are\nobliged again to assume a cohesive force of the second\norder, binding together the particles of each particle. And\ntherefore Newton himself says[11\\6], very justly, 'The parts\nof all homogeneal hard bodies which fully touch each other,\nstick together very strongly: and for explaining how this\nis, some have invented hooked atoms, _which is begging the\nquestion_.' For (he means to imply,) how do the parts of the\nhook stick together?\n\n[Note 11\\6: _Opticks_, p. 364.]\n\nThe same remark is applicable to all hypotheses in which\nparticles of a complex structure are assumed as the\nconstituents of bodies: for while we suppose bodies and\ntheir known properties to result from the mutual actions of\nthese particles, we are compelled to suppose the parts of\neach particle to be held together by forces still more\ndifficult to conceive, since they are disclosed only by the\nproperties of these particles, which as yet are unknown. Yet\nNewton himself has not abstained from such hypotheses: thus\nhe says[12\\6], 'A particle of {13} a salt may be compared to\na chaos, being dense, hard, dry, and earthy in the center,\nand moist and watery in the circumference.'\n\n[Note 12\\6: _Opticks_, p. 362.]\n\nSince Newton's time the use of the term _attraction_, as\nexpressing the cause of the union of the chemical elements\nof bodies, has been familiarly continued; and has, no doubt,\nbeen accompanied in the minds of many persons with an\nobscure notion that chemical attraction is, in some way, a\nkind of mechanical attraction of the particles of bodies.\nYet the doctrine that _chemical_ 'attraction' and\n_mechanical_ attraction are forces of the same kind has\nnever, so far as I am aware, been worked out into a system\nof chemical theory; nor even applied with any distinctness\nas an explanation of any particular chemical phenomena. Any\nsuch attempt, indeed, could only tend to bring more clearly\ninto view the entire inadequacy of such a mode of\nexplanation. For the leading phenomena of chemistry are all\nof such a nature that no mechanical combination can serve to\nexpress them, without an immense accumulation of additional\nhypotheses. If we take as our problem the changes of colour,\ntransparency, texture, taste, odour, produced by small\nchanges in the ingredients, how can we expect to give a\nmechanical account of these, till we can give a mechanical\naccount of colour, transparency, texture, taste, odour,\nthemselves? And if our mechanical hypothesis of the\nelementary constitution of bodies does not explain _such_\nphenomena as those changes, what can it explain, or what can\nbe the value of it? I do not here insist upon a remark which\nwill afterwards come before us, that even crystalline form,\na phenomenon of a far more obviously mechanical nature than\nthose just alluded to, has never yet been in any degree\nexplained by such assumptions as this, that bodies consist\nof elementary particles exerting forces of the same nature\nas the central forces which we contemplate in Mechanics.\n\nWhen therefore Newton asks, 'When some stones, as spar of\nlead, dissolved in proper menstruums, become salts, do not\nthese things show that salts are dry earth and watery acid\nunited by _attraction_?' we may {14} answer, that this mode\nof expression appears to be intended to identify chemical\ncombination with mechanical attraction;--that there would be\nno objection to any such identification, if we could, in\nthat way, explain, or even classify well, a collection of\nchemical facts; but that this has never yet been done by the\nhelp of such expressions. Till some advance of this kind can\nbe pointed out, we must necessarily consider the power which\nproduces chemical combination as a peculiar principle, a\nspecial relation of the elements, not rightly expressed in\nmechanical terms. And we now proceed to consider this\nrelation under the name by which it is most familiarly\nknown.\n\n\n\n{{15}}\nCHAPTER II.\n\nESTABLISHMENT AND DEVELOPMENT OF THE IDEA OF CHEMICAL\nAFFINITY.\n\n\n1. THE earlier chemists did not commonly involve themselves\nin the confusion into which the mechanical philosophers ran,\nof comparing chemical to mechanical forces. Their attention\nwas engaged, and their ideas were moulded, by their own\npursuits. They saw that the connexion of elements and\ncompounds with which they had to deal, was a peculiar\nrelation which must be studied directly; and which must be\nunderstood, if understood at all, in itself, and not by\ncomparison with a different class of relations. At different\nperiods of the progress of chemistry, the conception of this\nrelation, still vague and obscure, was expressed in various\nmanners; and at last this conception was clothed in\ntolerably consistent phraseology, and the principles which\nit involved were, by the united force of thought and\nexperiment, brought into view.\n\n2. The power by which the elements of bodies combine\nchemically, being, as we have seen, a peculiar agency,\ndifferent from mere mechanical connexion or attraction, it\nis desirable to have it designated by a distinct and\npeculiar name; and the term _Affinity_ has been employed for\nthat purpose by most modern chemists. The word 'affinity' in\ncommon language means, sometimes resemblance, and sometimes\nrelationship and ties of family. It is from the latter sense\nthat the metaphor is borrowed when we speak of 'chemical\naffinity.' By the employment of this term we do not indicate\na resemblance, but a disposition to unite. Using the word in\na common unscientific manner, we might say that chlorine,\nbromine, and iodine, have a great {16} _natural affinity_\nwith each other, for there are considerable resemblances and\nanalogies among them; but these bodies have very little\n_chemical_ Affinity for each other. The use of the word in\nthe _former_ sense, of resemblance, can be traced in earlier\nchemists; but the word does not appear to have acquired its\npeculiar chemical meaning till after Boerhaave's time.\nBoerhaave, however, is the writer in whom we first find a\ndue apprehension of the peculiarity and importance of the\nIdea which it now expresses. When we make a chemical\nsolution[13\\6], he says, not only are the particles of the\ndissolved body separated from each other, but they are\nclosely united to the particles of the solvent. When _aqua\nregia_ dissolves gold, do you not see, he says to his\nhearers, that there must be between each particle of the\nsolvent and of the metal, a mutual virtue by which each\nloves, unites with, and holds the other (_amat_, _unit_,\n_retinet_)? The opinion previously prevalent had been that\nthe solvent merely separates the parts of the body\ndissolved: and most philosophers had conceived this\nseparation as performed by mechanical operations of the\nparticles, resembling, for instance, the operation of wedges\nbreaking up a block of timber. But Boerhaave forcibly and\nearnestly points out the insufficiency of the conception.\nThis, he says, does not account for what we see. We have not\nonly a separation, but a new combination. There is a force\nby which the particles of the solvent associate to\nthemselves the parts dissolved, not a force by which they\nrepel and dissever them. We are here to imagine not\nmechanical action, not violent impulse, not antipathy, but\nlove, at least if love be the desire of uniting. (Non igitur\nhic etiam actiones mechanic\u00e6, non propulsiones violent\u00e6, non\ninimiciti\u00e6 cogitand\u00e6, sed amiciti\u00e6, si amor dicendus copul\u00e6\ncupido.) The novelty of this view is evidenced by the mode\nin which he apologizes for introducing it. 'Fateor, paradoxa\nh\u00e6c assertio.' To Boerhaave, therefore, (especially\nconsidering his great influence as a teacher of chemistry,)\nwe may {17} assign the merit of first diffusing a proper\nview of Chemical Affinity as a peculiar force, the origin of\nalmost all chemical changes and operations.\n\n[Note 13\\6: _Elementa Chemi\u00e6_, Lugd. Bat. 1732, p. 677.]\n\n3. To Boerhaave is usually assigned also the credit of\nintroducing the _word_ 'Affinity' among chemists; but I do\nnot find that the word is often used by him in this sense;\nperhaps not at all[14\\6]. But however this may be, the term\nis, on many accounts, well worthy to be preserved, as I\nshall endeavour to show. Other terms were used in the same\nsense during the early part of the eighteenth century. Thus\nwhen Geoffroy, in 1718, laid before the Academy of Paris his\nTables of Affinities, which perhaps did more than any other\nevent to fix the Idea of Affinity, he termed them 'Tables of\nthe Relations of Bodies;' '_Tables des Rapports_:' speaking\nhowever, also, of their 'disposition to unite,' and using\nother phrases of the same import.\n\n[Note 14\\6: See Dumas, _Le\u00e7ons de Phil. Chim._ p. 364. Rees'\n_Cyclop\u00e6dia_, Art. Chemistry. In the passage of Boerhaave to\nwhich I refer above, _affinitas_ is rather opposed to, than\nidentified with, chemical combination. When, he says, the\nparts of the body to be dissolved are dissevered by the\nsolvent, why do they remain united to the particles of the\nsolvent, and why do not rather both the particles of the\nsolvent and of the dissolved body collect into homogeneous\nbodies by their _affinity_? 'denuo se affinitate su\u00e6 natur\u00e6\ncolligant in corpora homogenea?' And the answer is, because\nthey possess another force which counteracts this affinity\nof homogeneous particles, and makes compounds of different\nelements. Affinity, in chemistry, now means the tendency of\n_different_ kinds of matter to unite: but it appears, as I\nhave said, to have acquired this sense since Boerhaave's time.]\n\nThe term _attraction_, having been recommended by Newton as\na fit word to designate the force which produces chemical\ncombination, continued in great favour in England, where the\nNewtonian philosophy was looked upon as applicable to every\nbranch of science. In France, on the contrary, where\nDescartes still reigned triumphant, 'attraction,' the\nwatch-word of the enemy, was a sound never uttered but with\ndislike and suspicion. In 1718 (in the notice of Geoffroy's\nTable,) the Secretary of the Academy, after pointing out\nsome of the peculiar circumstances of chemical {18}\ncombinations, says, 'Sympathies and attractions would suit\nwell here, if there were such things,' 'Les sympathies, les\nattractions conviendroient bien ici, si elles \u00e9taient\nquelque chose.' And at a later period, in 1731, having to\nwrite the _\u00e9loge_ of Geoffroy after his death, he says, 'He\ngave, in 1718, a singular system, and a Table of\n_Affinities_, or Relations of the different substances in\nchemistry. These affinities gave an easiness to some\npersons, who feared that they were _attractions in\ndisguise_, and all the more dangerous in consequence of the\nseductive forms which clever people have contrived to give\nthem. It was found in the sequel that this scruple might be\ngot over.'\n\nThis is the earliest published instance, so far as I am\naware, in which the word 'Affinity' is distinctly used for\nthe cause of chemical composition; and taking into account\nthe circumstances, the word appears to have been adopted in\nFrance in order to avoid the word _attraction_, which had\nthe taint of Newtonianism. Accordingly we find the word\n_affinit\u00e9_ employed in the works of French chemists from\nthis time. Thus, in the _Transactions of the French Academy_\nfor 1746, in a paper of Macquer's upon Arsenic, he\nsays[15\\6], 'On peut facilement rendre raison de ces\nphenom\u00e8nes par le moyen des affinit\u00e9s que les diff\u00e9rens\nsubstances qui entrent dans ces combinaisons, ont les uns\navec les autres:' and he proceeds to explain the facts by\nreference to Geoffroy's Table. And in Macquer's _Elements of\nChemistry_, which appeared a few years later, the 'Affinity\nof Composition' is treated of as a leading part of the\nsubject, much in the same way as has been practised in such\nbooks up to the present time. From this period, the word\nappears to have become familiar to all European chemists in\nthe sense of which we are now speaking. Thus, in the year\n1758, the Academy of Sciences at Rouen offered a prize for\nthe best dissertation on Affinity. The prize was shared\nbetween M. Limbourg of Theux, near Liege, and M. Le Sage\n{19} of Geneva[16\\6]. About the same time other persons\n(Manherr[17\\6], Nicolai[18\\6], and others) wrote on the same\nsubject, employing the same name.\n\n[Note 15\\6: _A. P._ 1746, p. 201.]\n\n[Note 16\\6: Thomson's _Chemistry_, iii. 10. Limbourg's\nDissertation was published at Liege, in 1761; and Le Sage's\nat Geneva.]\n\n[Note 17\\6: _Dissertatio de Affinitate Corporum_. Vindob. 1762.]\n\n[Note 18\\6: _Progr._ I. II. _de Affinitate Corporum Chimica_.\nJen. 1775, 1776.]\n\nNevertheless, in 1775, the Swedish chemist Bergman, pursuing\nstill further this subject of Chemical Affinities, and the\nexpression of them by means of Tables, returned again to the\nold Newtonian term; and designated the disposition of a body\nto combine with one rather than another of two others as\n_Elective Attraction_. And as his work on _Elective\nAttractions_ had great circulation and great influence, this\nphrase has obtained a footing by the side of _Affinity_, and\nboth one and the other are now in common use among chemists.\n\n4. I have said above that the term _Affinity_ is worthy of\nbeing retained as a technical term. If we use the word\n_attraction_ in this case, we identify or compare chemical\nwith mechanical attraction; from which identification and\ncomparison, as I have already remarked, no one has yet been\nable to extract the means of expressing any single\nscientific truth. If such an identification or comparison be\nnot intended, the use of the same word in two different\nsenses can only lead to confusion; and the proper course,\nrecommended by all the best analogies of scientific history,\nis to adopt a peculiar term for that peculiar relation on\nwhich chemical composition depends. The word _Affinity_,\neven if it were not rigorously proper according to its\ncommon meaning, still, being simple, familiar, and well\nestablished in this very usage, is much to be preferred\nbefore any other.\n\nBut further, there are some analogies drawn from the common\nmeaning of this word, which appear to recommend it as\nsuitable for the office which it has to discharge. For\ncommon mechanical attractions and {20} repulsions, the\nforces by which one body considered as a _whole_ acts upon\nanother external to it, are, as we have said, to be\ndistinguished from those more intimate ties by which the\n_parts_ of each body are held together. Now this difference\nis implied, if we compare the former relations, the\nattractions and repulsions, to alliances and wars between\nStates, and the latter, the internal union of particles, to\nthose bonds of affinity which connect the citizens of the\nsame state with one another, and especially to the ties of\nFamily. We have seen that Boerhaave compares the union of\ntwo elements of a compound to their marriage; 'we must\nallow,' says an eminent chemist of our own time[19\\6], 'that\nthere is some truth in this poetical comparison.' It\ncontains this truth,--that the two become one to most\nintents and purposes, and that the Unit thus formed (the\nFamily) is not a mere juxtaposition of the component parts.\nAnd thus the Idea of Affinity as the peculiar principle of\nchemical composition, is established among chemists, and\ndesignated by a familiar and appropriate name.\n\n[Note 19\\6: Dumas, _Le\u00e7ons de Phil. Chim._ p. 363.]\n\n5. _Analysis is possible._--We must, however, endeavour to\nobtain a further insight into this Idea, thus fixed and\nnamed. We must endeavour to extricate, if not from the Idea\nitself, from the processes by which it has obtained\nacceptation and currency among chemists, some principles\nwhich may define its application, some additional\nspecialities in the relations which it implies. This we\nshall proceed to do.\n\nThe Idea of Affinity, as already explained, implies a\ndisposition to combine. But this combination is to be\nunderstood as admitting also of a possibility of separation.\nSynthesis implies Analysis as conceivable: or to recur to\nthe image which we have already used, Divorce is possible\nwhen the Marriage has taken place.\n\nThat there is this possibility, is a conviction implied in\nall the researches of chemists, ever since the true notion\nof composition began to predominate in their investigations.\nOne of the first persons who clearly {21} expressed this\nconviction was Mayow, an English physician, who published\nhis _Medico-Physical Tracts_ in 1674. The first of them _De\nSale-Nitro et Spiritu Nitro-Aerio_, contains a clear\nenunciation of this principle. After showing how, in the\ncombinations of opposite elements, as acid and alkali, their\nproperties entirely disappear, and a new substance is formed\nnot at all resembling either of the ingredients, he\nadds[20\\6], 'Although these salts thus mixed appear to be\ndestroyed it is still possible for them to be separated from\neach other, with their powers still entire.' He proceeds to\nexemplify this, and illustrates it by the same image which I\nhave already alluded to: 'Salia acida a salibus\nvolatilibus discedunt, ut cum sale fixo tartari, tanquam\n_sponso_ magis idoneo, _conjugium_ strictius ineunt.' This\nidea of a synthesis which left a complete analysis still\npossible, was opposed to a notion previously current, that\nwhen two heterogeneous bodies united together and formed a\nthird body, the two constituents were entirely destroyed,\nand the result formed out of their ruins[21\\6]. And this\nconception of Synthesis and Analysis, as processes which are\npossible successively and alternately, and each of which\nsupposes the possibility of the other, has been the\nfundamental and regulative principle of the operations and\nspeculations of analytical chemistry from the time of Mayow\nto the present day.\n\n[Note 20\\6: Cap. xiv. p. 233.]\n\n[Note 21\\6: Thomson's _Chemistry_, iii. 8.]\n\n6. _Affinity is Elective._--When the idea of chemical\naffinity, or disposition to unite, was brought into view by\nthe experiments and reasonings of chemists, they found it\nnecessary to consider this disposition as _elective_;--each\nelement _chose_ one rather than another of the elements\nwhich were presented to it, and quitted its union with one\nto unite with another which it preferred. This has already\nappeared in the passage just quoted from Mayow. He adds in\nthe same strain, 'I have no doubt that fixed salts choose\none acid rather than another, in order that they may\ncoalesce with it {22} in a more intimate union.'--'Nullus\ndubito salia fixa acidum unum pr\u00e6 aliis _eligere_, ut cum\neodem arctiore unione coalescant.' The same thought is\nexpressed and exemplified by other chemists: they notice\ninnumerable cases in which, when an ingredient is combined\nwith a liquid, if a new substance be immersed which has a\ngreater affinity for the liquid, the liquid combines with\nthe new substance by election, and the former **ingredient\nis _precipitated_. Thus Stahl says[22\\6], 'In spirit of\nnitre dissolve silver; put in copper and the silver is\nthrown down; put in iron and the copper goes down; put in\nzinc, the iron precipitates; put in volatile alkali, the\nzinc is separated; put in fixed alkali, the volatile quits\nits hold.'--As may be seen in this example, we have in such\ncases, not only a preference, but a long gradation of\npreferences. The spirit of nitre will combine with silver,\nbut it prefers copper; prefers iron more; zinc still more;\nvolatile alkali yet more; fixed alkali the most.\n\n[Note 22\\6: _Zymotechnia_, 1697, p. 117.]\n\nThe same thing was proved to obtain with regard to each\nelement; and when this was ascertained, it became the object\nof chemists to express these degrees of preference, by lists\nin which substances were arranged according to their\ndisposition to unite with another substance. In this manner\nwas formed Geoffroy's Table of Affinities (1718), which we\nhave already mentioned. This Table was further improved by\nother writers, as Gellert (1751) and Limbourg (1761).\nFinally Bergman improved these Tables still further, taking\ninto account not only the order of affinities of each\nelement for others, but the _sum_ of the tendencies to unite\nof each two elements, which sum, he held, determined the\nresulting combination when several elements were in contact\nwith each other.\n\n7. As we have stated in the History[23\\6], when the doctrine\nof elective affinities had assumed this very definite and\nsystematic form, it was assailed by Berthollet, who\nmaintained, in his _Essai de Statique_ {23} _Chimique_,\n(1803,) that chemical affinities are _not_ elective:--that,\nwhen various elements are brought together, their\ncombinations do not depend upon the kind of elements alone,\nbut upon the quantity of each which is present, that which\nis most abundant always entering most largely into the\nresulting compounds. It may seem strange that it should be\npossible, at so late a period of the science, to throw doubt\nupon a doctrine which had presided over and directed its\nprogress so long. Proust answered Berthollet, and again\nmaintained that chemical affinity is elective. I have, in\nthe History, given the judgment of Berzelius upon this\ncontroversy. 'Berthollet,' he says, 'defended himself with\nan acuteness which makes the reader hesitate in his\njudgment; but the great mass of facts finally decided the\npoint in favour of Proust.' I may here add the opinion\npronounced upon this subject by Dr. Turner[24\\6]: 'Bergman\nerred in supposing the result of the chemical action to be\nin every case owing to elective affinity [for this power is\nmodified in its effects by various circumstances]: but\nBerthollet ran into the opposite extreme in declaring that\nthe effects formerly ascribed to that power are never\nproduced by it. That chemical attraction is exerted between\ndifferent bodies with different degrees of energy, is, I\napprehend, indisputable.' And he then proceeds to give many\ninstances of differences in affinity which cannot be\naccounted for by the operation of any modifying causes.\nStill more recently, M. Dumas has taken a review of this\ncontroversy; and, speaking with enthusiasm of the work of\nBerthollet, as one which had been of inestimable service to\nhimself in his early study of chemistry, he appears at first\ndisposed to award to him the victory in this dispute. But\nhis final verdict leaves undamaged the general principle now\nunder our consideration, that chemical affinity is elective.\n'For my own part,' he says[25\\6], 'I willingly admit the\nnotions of Berthollet when we have to do with acids or {24}\nwith bases, of which the energy is nearly equal: but when\nbodies endued with very energetic affinities are in presence\nof other bodies of which the affinities are very feeble, I\npropose to adopt the following rule: In a solution,\neverything remaining dissolved, the strong affinities\nsatisfy themselves, leaving the weak affinities to arrange\nmatters with one another. The strong acids take the strong\nbases, and the weak acids can only unite with the weak\nbases. The known facts are perfectly in accordance with this\npractical rule.' It is obvious that this recognition of a\ndistinction between strong and weak affinities, which\noperates to such an extent as to determine entirely the\nresult, is a complete acknowledgement of the Elective nature\nof Affinity, as far as any person acquainted with chemical\noperations could contend for it. For it must be allowed by\nall, that solubility, and other collateral circumstances,\ninfluence the course of chemical combinations, since they\ndetermine whether or not there shall take place that contact\nof elements without which affinity cannot possibly operate.\n\n[Note 23\\6: _Hist. Ind. Sc._ b. xiv. c. iii.]\n\n[Note 24\\6: _Chemistry_, p. 199. 6th edition.]\n\n[Note 25\\6: _Le\u00e7ons de Philosophie Chimique_, p. 386.]\n\n8. _Affinity is Definite as to quantity._--In proportion as\nchemists obtained a clearer view of the products of the\nlaboratory as results of the composition of elements, they\nsaw more and more clearly that these results were definite;\nthat one element not only preferred to combine with another\nof a certain kind, but also would combine with it to a\ncertain extent and no further, thus giving to the result not\nan accidental and variable, but a fixed and constant\ncharacter. Thus salts being considered as the result of the\ncombination of two opposite principles, acid and alkali, and\nbeing termed _neutral_ when these principles exactly\nbalanced each other, Rouelle (who was Royal Professor at\nParis in 1742) admits of neutral salts with excess of acid,\nneutral salts with excess of base, and perfect neutral\nsalts. Beaume maintained[26\\6] against him that there were\nno salts except those perfectly neutral, the other classes\nbeing the results of mixture and imperfect {25} combination.\nBut this question was not adequately treated till chemists\nmade every experiment with the balance in their hands. When\nthis was done, they soon discovered that, in each neutral\nsalt, the proportional weights of the ingredients which\ncomposed it were always the same. This was ascertained by\nWenzel, whose _Doctrine of the Affinities of Bodies_\nappeared in 1777. He not only ascertained that the\nproportions of elements in neutral chemical compounds are\ndefinite, but also that they are reciprocal; that is, (to\nexpress his results in a manner now employed by chemists),\nthat if A, a certain weight of a certain acid, neutralize\n_m_, a certain weight of a certain base, and B, a certain\nweight of a certain other acid, neutralize _n_, a certain\nweight of a certain other base; the compound of A and _n_\nwill also be neutral; as also that of B and _m_. The same\nviews were again presented by Richter in 1792, in his\n_Principles of the Measure of Chemical Elements_. And along\nwith these facts, that of the combination of elements in\nmultiple proportions being also taken into account, the\nfoundations of the Atomic Theory were laid; and that Theory\nwas propounded in 1803 by Mr. Dalton. That theory, however,\nrests upon the Idea of Substance, as well as upon that Idea\nof Chemical Affinity which we are here considering; and the\ndiscussion of its evidence and truth must be for the present\ndeferred.\n\n[Note 26\\6: Dumas, _Phil. Chim._ p. 198.]\n\n9. The two principles just explained,--that Affinity is\nDefinite as to the Kind, and as to the Quantity of the\nelements which it unites,--have here been stated as results\nof experimental investigation. That they could never have\nbeen clearly understood, and therefore never firmly\nestablished, without laborious and exact experiments, is\ncertain; but yet we may venture to say that being once fully\nknown, they may seem to thoughtful men to possess an\nevidence beyond that of mere experiment. For how, in fact,\ncan we conceive combinations, otherwise than as definite in\nkind and quantity? If we were to suppose each element\nready to combine with any other indifferently, and\nindifferently in any quantity, we should have a world in\n{26} which all would be confusion and indefiniteness. There\nwould be no fixed kinds of bodies. Salts, and stones, and\nores, would approach to and graduate into each other by\ninsensible degrees. Instead of this, we know that the world\nconsists of bodies distinguishable from each other by\ndefinite differences, capable of being classified and named,\nand of having general propositions asserted concerning them.\nAnd as we cannot conceive a world in which this should not\nbe the case, it would appear that we cannot conceive a state\nof things in which the laws of the combination of elements\nshould not be of that definite and measured kind which we\nhave above asserted.\n\nThis will, perhaps, appear more clearly by stating our\nfundamental convictions respecting chemical composition in\nanother form, which I shall, therefore, proceed to do.\n\n10. _Chemical Composition determines Physical\nProperties._--However obscure and incomplete may be our\nconception of the internal powers by which the ultimate\nparticles of bodies are held together, it involves, at\nleast, this conviction:--that these powers are what\ndetermine bodies to be bodies, and therefore contain the\nreason of all the properties which, as bodies, they possess.\nThe forces by which the particles of a body are held\ntogether, also cause it to be hard or soft, heavy or light,\nopake or transparent, black or red; for if these forces are\nnot the cause of these peculiarities, what can be the cause?\nBy the very supposition which we make respecting these\nforces, they include all the relations by which the parts\nare combined into a whole, and therefore they, and they\nonly, must determine all the attributes of the whole. The\nfoundation of all our speculations respecting the intimate\nconstitution of bodies must be this principle, that their\ncomposition determines their properties.\n\nAccordingly we find our chemists reasoning from this\nprinciple with great confidence, even in doubtful cases.\nThus Davy, in his researches concerning the diamond, says:\n'That some chemical difference must exist between the\nhardest and most beautiful of the {27} gems and charcoal,\nbetween a non-conductor and a conductor of electricity, it\nis scarcely possible to doubt: and it seems reasonable to\nexpect that a very refined or perfect chemistry will confirm\n_the analogies of nature_; and show that bodies cannot be\nthe same in their composition or chemical nature, and yet\ntotally different in their chemical properties.' It is\nobvious that the principle here assumed is so far from being\na mere result of experience, that it is here appealed to to\nprove that all previous results of experience on this\nsubject must be incomplete and inaccurate; and that there\nmust be some chemical difference between charcoal and\ndiamond, though none had hitherto been detected.\n\n11. In what manner, according to what rule, the chemical\ncomposition shall determine the kind of the substance, we\ncannot reasonably expect to determine by mere conjecture or\nassumption, without a studious examination of natural bodies\nand artificial compounds. Yet even in the most recent times,\nand among men of science, we find that an assumption of the\nmost arbitrary character has in one case been mixed up with\nthis indisputable principle, that the elementary composition\ndetermines the kind of the substance. In the classification\nof minerals, one school of mineralogists have rightly taken\nit as their fundamental principle that the chemical\ncomposition shall decide the position of the mineral in the\nsystem. But they have appended to this principle,\narbitrarily and unjustifiably, the maxim that the element\nwhich is _largest in quantity_ shall fix the class of the\nsubstance. To make such an assumption is to renounce, at\nonce, all hope of framing a system which shall be governed\nby the resemblances of the things classified; for how can we\npossibly know beforehand that fifty-five per cent, of iron\nshall give a substance its predominant properties, and that\nforty-five per cent, shall not? Accordingly, the systems of\nmineralogical arrangement which have been attempted in this\nway, (those of Ha\u00fcy, Phillips, and others,) have been found\ninconsistent with themselves, ambiguous, and incapable of\nleading to any general truths. {28}\n\n12. _Chemical Composition and Crystalline Form\ncorrespond._--Thus the physical properties of bodies depend\nupon their chemical composition, but in a manner which a\ngeneral examination of bodies with reference to their\nproperties and their composition can alone determine. We\nmay, however, venture to assert further, that the more\ndefinite the properties are, the more distinct may we expect\nto find this dependence. Now the most definite of the\nproperties of bodies are those constant properties which\ninvolve relations of space; that is, their figure. We speak\nnot, however, of that external figure, derived from external\ncircumstances, which, so far from being constant and\ndefinite, is altogether casual and arbitrary; but of that\nfigure which arises from their internal texture, and which\nshows itself not only in the regular forms which they\nspontaneously assume, but in the disposition of the parts to\nseparate in definite directions, and no others. In short,\nthe most definite of the properties of perfect chemical\ncompounds is their _crystalline structure_; and therefore it\nis evident that the crystalline structure of each body, and\nthe forms which it affects, must be in a most intimate\ndependence upon its chemical composition.\n\nHere again we are led to the brink of another theory;--that\nof crystalline structure, which has excited great interest\namong philosophers ever since the time of Ha\u00fcy. But this\ntheory involves, besides that idea of chemical composition\nwith which we are here concerned, other conceptions, which\nenter into the relations of figure. These conceptions,\ngoverned principally by the Idea of Symmetry, must be\nunfolded and examined before we can venture to discuss any\ntheory of crystallization: and we shall proceed to do this\nas soon as we have first duly considered the Idea of\nSubstance and its consequences.\n\n\n\n{{29}}\nCHAPTER III.\n\nOF THE IDEA OF SUBSTANCE.\n\n\n1. _Axiom of the Indestructibility of Substance._--WE now\ncome to an Idea of which the history is very different from\nthose of which we have lately been speaking. Instead of\nbeing gradually and recently brought into a clear light, as\nhas been the case with the Ideas of Polarity and Affinity,\nthe Idea of Substance has been entertained in a distinct\nform from the first periods of European speculation. That\nthis is so, is proved by our finding a principle depending\nupon this Idea current as an axiom among the early\nphilosophers of Greece:--namely, that _nothing can be\nproduced out of nothing_. Such an axiom, more fully stated,\namounts to this: that the substance of which a body consists\nis incapable of being diminished (and consequently incapable\nof being augmented) in quantity, whatever apparent changes\nit may undergo. Its forms, its distribution, its qualities,\nmay vary, but the substance itself is identically the same\nunder all these variations.\n\nThe axiom just spoken of was the great principle of the\nphysical philosophy of the Epicurean school, as it must be\nof every merely material philosophy. The reader of Lucretius\nwill recollect the emphasis with which it is repeatedly\nasserted in his poem:\n E nilo nil gigni, in nilum nil posse reverti;\n Nought comes of nought, nor ought returns to nought.\n\nThose who engaged in these early attempts at physical\nspeculation were naturally much pleased with the clearness\nwhich was given to their notions of change, composition, and\ndecomposition, by keeping steadily hold of the Idea of\nSubstance, as marked by this {30} fundamental axiom. Nor has\nits authority ever ceased to be acknowledged. A philosopher\nwas asked[27\\6], What is the weight of smoke? He answered,\n'Subtract the weight of the ashes from the weight of the\nwood which is burnt, and you have the weight of the smoke.'\nThis reply would be assented to by all; and it assumes as\nincontestable that even under the action of fire, the\nmaterial, the substance, does not perish, but only changes\nits form.\n\n[Note 27\\6: Kant, _Kritik der R. V._ p. 167.]\n\nThis principle of the indestructibility of substance might\neasily be traced in many reasonings and researches, ancient\nand modern. For instance, when the chemist works with the\n_retort_, he places the body on which he operates in one\npart of an inclosed cavity, which, by its bendings and\ncommunications, separates at the same time that it confines,\nthe products which result from the action of fire: and he\nassumes that this process is an analysis of the body into\nits ingredients, not a creation of anything which did not\nexist before, or a destruction of anything which previously\nexisted. And he assumes further, that the total quantity of\nthe substance thus analysed is the sum of the quantities of\nits ingredients. This principle is the very basis of\nchemical speculation, as we shall hereafter explain more fully.\n\n2. _The Idea of Substance._--The axiom above spoken of\ndepends upon the Idea of Substance, which is involved in all\nour views of external objects. We unavoidably assume that\nthe qualities and properties which we observe are properties\nof _things_;--that the adjective implies a\nsubstantive;--that there is, besides the external characters\nof things, something _of which_ they are the characters. An\napple which is red, and round, and hard, is not merely\nredness, and roundness, and hardness: these circumstances\nmay all alter while the apple remains the same apple. Behind\nor under the appearances which we see, we conceive something\nof which we think; or, to use the metaphor which obtained\ncurrency among the ancient philosophers, the {31} attributes\nand qualities which we observe are supported by and inherent\nin something: and this something is hence called a\n_substratum_ or _substance_,--that which stands _beneath_\nthe apparent qualities and supports them.\n\nThat we have such an _Idea_, using the term 'Idea' in the\nsense in which I have employed it throughout these\ndisquisitions, is evident from what has been already said.\nThe Axiom of the Indestructibility of Substance proves the\nexistence of the Idea of Substance, just as the Axioms of\nGeometry and Arithmetic prove the existence of the Ideas of\nSpace and Number. In the case of Substance, as of space or\nnumber, the ideas cannot be said to be borrowed from\nexperience, for the axioms have an authority of a far more\ncomprehensive and demonstrative character than any which\nexperience can bestow. The axiom that nothing can be\nproduced from nothing and nothing destroyed, is so far from\nbeing a result of experience, that it is apparently\ncontradicted by the most obvious observation. It has, at\nfirst, the air of a paradox; and by those who refer to it,\nit is familiarly employed to show how fallacious common\nobservation is. The assertion is usually made in this\nform;--that nothing is created and nothing annihilated,\n_notwithstanding_ that the common course of our experience\nappears to show the contrary. The principle is not an\nempirical, but a necessary and universal truth;--is\ncollected, not from the evidence of our senses, but from the\noperation of our ideas. And thus the universal and\nundisputed authority of the axiom proves the existence of\nthe Idea of Substance.\n\n3. _Locke's Denial of the Idea of Substance._--I shall not\nattempt to review the various opinions which have been\npromulgated respecting this Idea: but it may be worth our\nwhile to notice briefly the part which it played in the\ngreat controversy concerning the origin of our ideas which\nLocke's _Essay_ occasioned. Locke's object was to disprove\nthe existence of all ideas not derived from Sensation or\nReflection: and since the idea of substance as distinct from\nexternal qualities, is {32} manifestly not derived directly\nfrom sensation, nor by any very obvious or distinct process\nfrom reflection, Locke was disposed to exclude the idea as\nmuch as possible. Accordingly, in his argumentation against\nInnate Ideas[28\\6], he says plainly, 'the idea of substance,\nwhich we neither have nor can have by sensation or\nreflection.' And the inference which he draws is, 'that we\nhave no such clear idea at all.' What then, it may be asked,\ndo we mean by the word _substance_? This also he answers,\nthough somewhat strangely, 'We signify nothing by the word\n_substance_, but only an uncertain supposition of we know\nnot what, _i. e._ of something whereof we have no particular\ndistinct positive idea, which we take to be the substratum,\nor support, of those ideas we know.' That while he indulged\nin this tautological assertion of our ignorance and\nuncertainty, he should still have been compelled to\nacknowledge that the word substance had some meaning, and\nshould have been driven to explain it by the identical\nmetaphors of 'substratum' and 'support,' is a curious proof\nhow impossible it is entirely to reject this idea.\n\n[Note 28\\6: _Essay_, b. i. c. iv. s. 18.]\n\nBut as we have already seen, the supposition of the\nexistence of substance is so far from being uncertain, that\nit carries with it irresistible conviction, and substance is\nnecessarily conceived as something which cannot be produced\nor destroyed. It may be easily supposed, therefore, that\nwhen the controversy between Locke and his assailants came\nto this point, he would be in some difficulty. And, indeed,\nthough with his accustomed skill in controversy, he managed\nto retain a triumphant tone, he was driven from his main\npoints. Thus he repels the charge that he took the being of\nsubstance to be doubtful[29\\6]. He says, 'Having everywhere\naffirmed and built upon it that man is a substance, I cannot\nbe supposed to question or doubt of the being of substance,\ntill I can question or doubt of my own being.' He attempts\nto make a stand by saying that _being_ of things does not\ndepend upon our {33} _ideas_; but if he had been asked how,\nwithout having an _idea_ of substance, he _knew_ substance\nto _be_, it is difficult to conceive what answer he could\nhave made. Again, he had said that our idea of substance\narises from our 'accustoming ourselves to suppose' a\nsubstratum of qualities. Upon this his adversary, Bishop\nStillingfleet, very properly asks, Is this custom grounded\nupon true reason or no? To which Locke replies, that it is\ngrounded upon this: That we cannot conceive how simple ideas\nof sensible qualities should subsist alone; and therefore we\nsuppose them to exist in, and to be supported by some common\nsubject, which support we denote by the name substance. Thus\nhe allows, not only that we necessarily assume the reality\nof substance, but that we cannot conceive qualities without\nsubstance; which are concessions so ample as almost to\ninclude all that any advocate for the Idea of Substance need\ndesire.\n\n[Note 29\\6: _Essay_, b. ii. c. ii. and _First Letter to the\nBishop of Worcester_.]\n\nPerhaps Locke, and the adherents of Locke, in denying that\nwe have an idea of substance in general, were latently\ninfluenced by finding that they could not, by any effort of\nmind, call up any _image_ which could be considered as an\nimage of substance in general. That in this sense we have no\nidea of substance, is plain enough; but in the same sense we\nhave no idea of space in general, or of time, or number, or\ncause, or resemblance. Yet we certainly have such a power of\nrepresenting to our minds space, time, number, cause,\nresemblance, as to arrive at numerous truths by means of\nsuch representations. These general representations I have\nall along called Ideas, nor can I discover any more\nappropriate word; and in this sense, we have also, as has\nnow been shown, an Idea of Substance.\n\n4. _Is all Material Substance heavy?_--The principle that\nthe quantity of the substance of any body remains unchanged\nby our operations upon it, is, as we have said, of universal\nvalidity. But then the question occurs, how are we to\nascertain the quantity of substance, and thus, to apply the\nprinciple in particular cases. In the case above mentioned,\nwhere {34} smoke was to be weighed, it was manifestly\nassumed that the quantity of the substance might be known by\nits weight; and that the total quantity being unchanged, the\ntotal weight also would remain the same. Now on what grounds\ndo we make this assumption? Is all material substance heavy?\nand if we can assert this to be so, on what grounds does the\ntruth of the assertion rest? These are not idle questions of\nbarren curiosity; for in the history of that science\n(Chemistry) to which the Idea of Substance is principally\napplicable, nothing less than the fate of a comprehensive\nand long established theory (the Phlogiston theory) depended\nupon the decision of this question. When it was urged that\nthe reduction of a metal from a calcined to a metallic form\ncould not consist in the _addition_ of phlogiston, because\nthe metal was lighter than the calx had been; it was replied\nby some, that this was not conclusive, for that phlogiston\nwas a principle of levity, diminishing the weight of the\nbody to which it was added. This reply was, however,\nrejected by all the sounder philosophers, and the force of\nthe argument finally acknowledged. But why was this\nsuggestion of a substance having no weight, or having\nabsolute levity, repudiated by the most reflective\nreasoners? It is assumed, it appears, that all matter must\nbe heavy; what is the ground of this assumption?\n\nThe ground of such an assumption appears to be the\nfollowing. Our idea of substance includes in it this:--that\nsubstance is a quantity capable of addition; and thus\ncapable of making up, by composition, a sum equal to all its\nparts. But substance, and the quantity of substance, can be\nknown to us only by its attributes and qualities. And the\nqualities which are capable constantly and indefinitely of\nincrease and diminution by increase and diminution of the\nparts, must be conceived inseparable from the substance. For\nthe qualities, if removable from the substance at all, must\nbe removable by some operation performed upon the substance;\nand by the idea of substance, all such operations are only\nequivalent to separation, junction, and union of parts.\nHence those characters {35} which thus universally increase\nand diminish by addition and subtraction of the things\nthemselves, belong to the substance of the things. They are\nmeasures of its quantity, and are not merely its separable\nqualities.\n\nThe weight of bodies is such a character. However we\ncompound or divide bodies, we compound and divide their\nweight in the same manner. We may dismember a body into the\nminutest parts; but the sum of the weights of the parts is\nalways equal to the whole weight of the body. The weight of\na body can be in no way increased or diminished, except by\nadding something to it or taking something from it. If we\nbake a brick, we do not conceive that the change of colour\nor of hardness, implies that anything has been created or\ndestroyed. It may easily be that the parts have only assumed\na new arrangement; but if the brick have lost weight, we\nsuppose that something (moisture for instance) has been\nremoved elsewhere.\n\nThus weight is apprehended as essential to matter. In\nconsidering the dismemberment or analysis of bodies, we\nassume that there must be some criterion of the quantity of\nsubstance; and this criterion can possess no other\nproperties than their weight possesses. If we assume an\nelement which has no weight, or the weight of which is\nnegative, as some of the defenders of phlogiston attempted\nto do, we put an end to all speculation on such subjects.\nFor if weight is not the criterion of the quantity of one\nelement, phlogiston for instance, why is weight the\ncriterion of the quantity of any other element? We may, by\nthe same right, assume any other real or imaginary element\nto have levity instead of gravity; or to have a peculiar\nintensity of gravity which makes its weight no index of its\nquantity. In short, if we do this, we deprive of all\npossibility of application our notions of element, analysis,\nand composition; and violate the postulates on which the\nquestions are propounded which we thus attempt to decide.\n\nWe must, then, take a constant and quantitative property of\nmatter, such as weight is, to be an index {36} of the\nquantity of matter or of substance to which it belongs. I do\nnot here speak of the question which has sometimes been\nproposed, whether the _weight_ or the _inertia_ of bodies be\nthe more proper measure of the quantity of matter. For the\nmeasure of inertia is regulated by the same assumption as\nthat of substance:--that the quantity of the whole must be\nequal to the quantity of all the parts: and inertia is\nmeasured by weight, for the same reason that substance is so.\n\nHaving thus established the certainty, and ascertained the\ninterpretation of the fundamental principle which the Idea\nof Substance involves, we are prepared to consider its\napplication in the science upon which it has a peculiar\nbearing.\n\n\n\n{{37}}\nNOTE TO CHAPTER III.\n\n\n[3rd Ed.]--[THE doctrine here propounded, that All Matter is\nHeavy, has been opposed by Sir William Hamilton of\nEdinburgh. (_Works of Reid_, note, p. 853.) This writer is a\nman of unquestionable acuteness and of very extensive\nreading; but his acuteness shows itself in barren\nontological distinctions, which appear to me to be of the\nsame character as the speculations of the eminent Schoolmen\nof the most sterile periods of the dark ages. That he should\nhave no conception of progressive or inductive science is\nnot wonderful, when we recollect that he holds, as an\nimportant part of his philosophy, that the study of\nmathematics perverts and obscures the mind. But it may be of\nsome interest to consider his objections to the doctrine\nhere maintained.\n\nHe says, 1st, that our reasoning assumes that we must\nnecessarily have it in our power to ascertain the Quantity\nof Matter; whereas this may be a problem out of the reach of\nhuman determination.\n\nTo this I reply, that my reasoning _does_ assume that there\nis a science, or sciences, which make assertions concerning\nthe Quantity of Matter: Mechanics and Chemistry are such\nsciences. My assertion is, that to make such sciences\npossible, Quantity of Matter must be proportional to Weight.\nIf my opponent deny that Mechanics and Chemistry can exist\nas sciences, he may invalidate my proof; but not otherwise.\n\n2. He says that there are two conceivable ways of estimating\nthe Quantity of Matter: by the Space occupied, and by the\nWeight or Inertia; and that I assume the second measure\ngratuitously.\n\nTo which I reply, that the most elementary steps in\nMechanics and in Chemistry contradict the notion that {38}\nthe Quantity of Matter is proportionate to the Space. They\nproceed necessarily on a distinction between Space and\nMatter:--between mere Extension and material Substance.\n\n3. He allows that we cannot make the Extension of a body the\nmeasure of the Quantity of Matter, because, he says, we do\nnot know if 'the compressing force' is such as to produce\n'the closest compression.' That is, he assumes a compressing\nforce, assumes a closest compression, assumes a peculiar\n(and very improbable) atomic hypothesis; and all this to\nsupply a reason why we are not to believe the first simple\nprinciple of Mechanics and Chemistry.\n\n4. He speaks of 'a series of apparent fluids (as Light or\nits vehicle, the Calorific, the Electro-galvanic, and\nMagnetic agents) which we can neither denude of their\ncharacter of substance, nor clothe with the attribute of\nweight.'\n\nTo which my reply is, that precisely because I cannot\n'clothe' these agents with the attribute of Weight, I _do_\n'denude them of the character of Substance.' They are not\nsubstances, but agencies. These Imponderable Agents are not\nproperly called 'Imponderable Fluids.' This I conceive that\nI have proved; and the proof is not shaken by denying the\nconclusion without showing any defect in the reasoning.\n\n5. Finally, my critic speaks about 'a logical canon,' and\nabout 'a criterion of truth, subjectively necessary and\nobjectively certain;' which matters I shall not waste the\nreader's time by discussing.]\n\n\n\n{{39}}\nCHAPTER IV.\n\nAPPLICATION OF THE IDEA OF SUBSTANCE IN CHEMISTRY.\n\n\n1. _A Body is Equal to the Sum of its Elements._--FROM the\nearliest periods of chemistry the balance has been\nfamiliarly used to determine the proportions of the\ningredients and of the compound; and soon after the middle\nof the last century, this practice was so studiously\nfollowed, that Wenzel and Richter were thereby led to the\ndoctrine of Definite Proportions. But yet the full value and\nsignificance of the balance, as an indispensable instrument\nin chemical researches, was not understood till the gaseous,\nas well as solid and fluid ingredients were taken into the\naccount. When this was done, it was found that the\nprinciple, that the whole is equal to the sum of its parts,\nof which, as we have seen, the necessary truth, in such\ncases, flows from the idea of substance, could be applied in\nthe most rigorous manner. And conversely, it was found that\nby the use of the balance, the chemist could decide, in\ndoubtful cases, which was a whole, and which were parts.\n\nFor chemistry considers all the changes which belong to her\nprovince as compositions and decompositions of elements; but\nstill the question may occur, whether an observed change be\nthe one or the other. How can we distinguish whether the\nprocess which we contemplate be composition or\ndecomposition?--whether the new body be formed by addition\nof a new, or subtraction of an old element? Again; in the\ncase of decomposition, we may inquire, What are the ultimate\nlimits of our analysis? If we decompound bodies into others\nmore and more simple, how far can we carry this succession\n{40} of processes? How far can we proceed in the road of\nanalysis? And in our actual course, what evidence have we\nthat our progress, as far as it has gone, has carried us\nfrom the more complex to the more simple?\n\nTo this we reply, that the criterion which enables us to\ndistinguish, decidedly and finally, whether our process have\nbeen a mere analysis of the proposed body into its\ningredients, or a synthesis of some of them with some new\nelement, is the principle stated above, that the weight of\nthe whole is equal to the weight of all the parts. And no\nprocess of chemical analysis or synthesis can be considered\ncomplete till it has been verified by this fact;--by finding\nthat the weight of the compound is the weight of its\nsupposed ingredients; or, that if there be an element which\nwe think we have detached from the whole, its loss is\nbetrayed by a corresponding diminution of weight.\n\nI have already noticed what an important part this principle\nhas played in the great chemical controversy which ended in\nthe establishment of the oxygen theory. The calcination of a\nmetal was decided to be the union of oxygen with the metal,\nand not the separation of phlogiston from it, because it was\nfound that in the process of calcination, the weight of the\nmetal increased, and increased exactly as much as the weight\nof ambient air diminished. When oxygen and hydrogen were\nexploded together, and a small quantity of water was\nproduced, it was held that this was really a synthesis of\nwater, because, when very great care was taken with the\nprocess, the weight of the water which resulted was equal to\nthe weight of the gases which disappeared.\n\n2. _Lavoisier._--It was when gases came to be considered as\nentering largely into the composition of liquid and solid\nbodies, that extreme accuracy in weighing was seen to be so\nnecessary to the true understanding of chemical processes.\nIt was in this manner discovered by Lavoisier and his\ncontemporaries that oxygen constitutes a large ingredient of\ncalcined metals, of acids, and of water. A countryman of\nLavoisier[30\\6] {41} has not only given most just praise to\nthat great philosopher for having constantly tested all his\nprocesses by a careful and skilful use of the balance, but\nhas also claimed for him the merit of having introduced the\nmaxim, that in chemical operations nothing is created and\nnothing lost. But I think it is impossible to deny that this\nmaxim is assumed in all the attempts at analysis made by his\ncontemporaries, as well as by him. This maxim is indeed\nincluded in any clear notion of analysis: it could not be\nthe result of the researches of any one chemist, but was the\ngoverning principle of the reasonings of all. Lavoisier,\nhowever, employed this principle with peculiar assiduity and\nskill. In applying it, he does not confine himself to mere\nadditions and subtractions of the quantities of ingredients;\nbut often obtains his results by more complex processes. In\none of his investigations he says, 'I may consider the\ningredients which are brought together, and the result which\nis obtained as an algebraical equation; and if I\nsuccessively suppose each of the quantities of this equation\nto be unknown, I can obtain its value from the rest: and\nthus I can rectify the experiment by the calculation, and\nthe calculation by the experiment. I have often taken\nadvantage of this method, in order to correct the first\nresults of my experiments, and to direct me in repeating\nthem with proper precautions.'\n\n[Note 30\\6: M. Dumas, _Le\u00e7ons de la Philosophie Chimique_.\n1837. p. 157.]\n\nThe maxim, that the whole is equal to the sum of all its\nparts, is thus capable of most important and varied\nemployment in chemistry. But it may be applied in another\nform to the exclusion of a class of speculations which are\noften put forwards.\n\n3. _Maxim respecting Imponderable Elements._--Several of the\nphenomena which belong to bodies, as heat, light,\nelectricity, magnetism, have been explained hypothetically\nby assuming the existence of certain fluids; but these\nfluids have never been shown to have weight. Hence such\nhypothetical fluids have been termed _imponderable\nelements_. It is however plain, that so long as these fluids\nappear to be without weight, they are not _elements_ of\nbodies in the same {42} sense as those elements of which we\nhave hitherto been speaking. Indeed we may with good reason\ndoubt whether those phenomena depend upon transferable\nfluids at all. We have seen strong reason to believe that\nlight is not matter, but only motion; and the same thing\nappears to be probable with regard to heat. Nor is it at all\ninconceivable that a similar hypothesis respecting\nelectricity and magnetism should hereafter be found tenable.\nNow if heat, light, and those other agents, be not matter,\nthey are not _elements_ in such a sense as to be included in\nthe principle referred to above, That the body is equal to\nthe sum of its elements. Consequently the maxim just stated,\nthat in chemical operations nothing is created, nothing\nannihilated, does not apply to Light and Heat. They are not\n_things_. And whether heat can be produced where there was\nno heat before, and light struck out from darkness, the\nideas of which we are at present treating do not enable us\nto say. In reasoning respecting chemical synthesis and\nanalysis therefore, we shall only make confusion by\nattempting to include in our conception the Light and Heat\nwhich are produced and destroyed. Such phenomena may be very\nproper subjects of study, as indeed they undoubtedly are;\nbut they cannot be studied to advantage by considering them\nas sharing the nature of composition and decomposition.\n\nAgain: in all attempts to explain the processes of nature,\nthe proper course is, first to measure the facts with\nprecision, and then to endeavour to understand their cause.\nNow the facts of chemical composition and decomposition, the\nweights of the ingredients and of the compounds, are facts\nmeasurable with the utmost precision and certainty. But it\nis far otherwise with the light and heat which accompany\nchemical processes. When combustion, deflagration,\nexplosion, takes place, how can we measure the light or the\nheat? Even in cases of more tranquil action, though we can\napply the thermometer, what does the thermometer tell us\nrespecting the _quantity_ of the heat? Since then we have no\nmeasure which is of any value as {43} regards such\ncircumstances in chemical changes, if we attempt to account\nfor these phenomena _on chemical principles_, we introduce,\ninto investigations in themselves perfectly precise and\nmathematically rigorous, another class of reasonings, vague\nand insecure, of which the only possible effect is to\nvitiate the whole reasoning, and to make our conclusions\ninevitably erroneous.\n\nWe are led then to this maxim: that _imponderable fluids\nare_ not _to be admitted as chemical elements of bodies_[31\\6].\n\n[Note 31\\6: See the answer to Sir William Hamilton's\nobjections, at the end of the last chapter.\n\nSince we are thus warned by a sound view of the nature of\nscience, from considering chemical affinity as having any\nhold upon imponderable elements, we are manifestly still\nmore decisively prohibited from supposing mechanical impulse\nor pressure to have any effect upon such elements. To make\nthis supposition, is to connect the most subtle and\nincorporeal objects which we know in nature by the most\ngross material ties. This remark seems to be applicable to\nM. Poisson's hypothesis that the electric fluid is retained\nat the surface of bodies by the pressure of the\natmosphere.]\n\n4. It appears, I think, that our best and most philosophical\nchemists have proceeded upon this principle in their\ninvestigations. In reasoning concerning the constitution of\nbodies and the interpretation of chemical changes, the\nattempts to include in these interpretations the heat or\ncold produced, by the addition or subtraction of a certain\nhypothetical 'caloric,' have become more and more rare among\nmen of science. Such statements, and the explanations often\nput forwards of the light and heat which appear under\nvarious circumstances in the form of fire, must be\nconsidered as unessential parts of any sound theory.\nAccordingly we find Mr. Faraday gradually relinquishing such\nviews. In January, 1834, he speaks generally of an\nhypothesis of this kind[32\\6]: 'I cannot refrain from\nrecalling here the beautiful idea put forth, I believe by\nBerzelius, in his development of his views of the\nelectro-chemical theory of affinity, that the heat and light\nevolved during cases of powerful combination {44} are the\nconsequence of the electric discharge which is at that\nmoment taking place.' But in April of the same year[33\\6],\nhe observes, that in the combination of oxygen and hydrogen\nto produce water, electric powers to a most enormous amount\nare for the time active, but that the flame which is\nproduced gives but feeble traces of such powers. 'Such\nphenomena,' therefore, he adds, 'may not, cannot, be taken\nas evidences of the nature of the action; but are merely\nincidental results, incomparably small in relation to the\nforces concerned, and supplying no information of the way in\nwhich the particles are active on each other, or in which\ntheir forces are finally arranged.'\n\n[Note 32\\6: _Researches_, 870.]\n\n[Note 33\\6: _Researches_, 960.]\n\nIn pursuance of this maxim, we must consider as an\nunessential part of the oxygen theory that portion of it,\nmuch insisted upon by its author at the time, in which when\nsulphur, for instance, combined with oxygen to produce\nsulphuric acid, the combustion was accounted for by means of\nthe _caloric_ which was supposed to be _liberated_ from its\ncombination with oxygen.\n\n5. _Controversy of the Composition of Water._--There is\nanother controversy of our times to which we may with great\npropriety apply the maxim now before us. After the glory of\nhaving first given a true view of the composition of water\nhad long rested tranquilly upon the names of Cavendish and\nLavoisier, a claim was made in favour of James Watt as the\nreal author of this discovery by his son, (Mr J. Watt,) and\nhis eulogist, (M. Arago[34\\6]). It is not to our purpose\nhere to discuss the various questions which have arisen on\nthis subject respecting priority of publication, and\nrespecting the translation of opinions published at one time\ninto the language of another period. But if we look at\nWatt's own statement of his views, given soon after those of\nCavendish had been published, we shall perceive that it is\nmarked by a violation of this maxim: we shall find that he\ndoes admit imponderable fluids {45} as chemical elements;\nand thus shows a vagueness and confusion in his idea of\nchemical composition. With such imperfection in his views,\nit is not surprising that Watt, not only did not anticipate,\nbut did not apprehend quite precisely the discovery of\nCavendish and Lavoisier. Watt's statement of his views is as\nfollows[35\\6]:--'Are we not authorized to conclude that\nwater is composed of dephlogisticated air and phlogiston\ndeprived of part of their latent or elementary heat; that\ndephlogisticated or pure air is composed of water deprived\nof its phlogiston and united to elementary heat and light;\nand that the latter are contained in it in a latent state,\nso as not to be sensible to the thermometer or to the eye;\nand if light be only a modification of heat, or a\ncircumstance attending it, or a component part of the\ninflammable air, then pure or dephlogisticated air is\ncomposed of water deprived of its phlogiston and united to\nelementary heat?'\n\n[Note 34\\6: \u00c9loge de James Watt, _Annuaire du Bur. des\nLong._ 1839.]\n\n[Note 35\\6: _Phil. Trans._ 1784, p. 332.]\n\nWhen we compare this doubtful and hypothetical statement,\ninvolving so much that is extraneous and heterogeneous, with\nthe conclusion of Cavendish, in which there is nothing\nhypothetical or superfluous, we may confidently assent to\nthe decision which has been pronounced by one[36\\6] of our\nown time in favour of Cavendish. And we may with pleasure\nrecognize, in this enlightened umpire, a due appreciation of\nthe value of the maxim on which we are now insisting.\n'Cavendish,' says Mr. Vernon Harcourt, 'pared off {46} from\nthe hypotheses their theories of combustion, and _affinities\nof imponderable for ponderable matter_, as complicating\nchemical with physical considerations.'\n\n[Note 36\\6: The Rev. W. Vernon Harcourt, Address to the\nBritish Association, 1839.--Since the first edition of this\nwork was published, and also since the second edition of the\n_History of the Inductive Sciences_, Mr. Watt's\ncorrespondence bearing upon the question of the Composition\nof Water has been published by Mr. Muirhead. I do not find,\nin this publication, any reason for withdrawing what I have\nstated in the text above: but with reference to the\nstatement in the _History_, it appears that Mr. Cavendish's\nclaim to the discovery was not uncontested in his own time.\nMr. Watt had looked at the composition of water, as a\nproblem to be solved, perhaps more distinctly than Mr.\nCavendish had done; and he conceived himself wronged by Mr.\nCavendish's putting forwards his experiment as the first\nsolution of this problem.]\n\n6. _Relation of Heat to Chemistry._--But while we thus\ncondemn the attempts to explain the thermotical phenomena of\nchemical processes by means of chemical considerations, it\nmay be asked if we are altogether to renounce the hope of\nunderstanding such phenomena? It is plain, it may be said,\nthat heat generated in chemical changes is always a very\nimportant circumstance, and can sometimes be measured, and\nperhaps reduced to laws; are we prohibited from speculating\nconcerning the causes of such circumstances and such laws?\nAnd to this we reply, that we may properly attempt to\nconnect chemical with thermotical processes, _so far as_ we\nhave obtained a clear and probable view of the nature of the\nthermotical processes. When our theory of Thermotics is\ntolerably complete and certain, we may with propriety\nundertake to connect it with our theory of Chemistry. But at\npresent we are not far enough advanced in our knowledge of\nheat to make this attempt with any hope of success. We can\nhardly expect to understand the part which heat plays in the\nunion of two bodies, when we cannot as yet comprehend in\nwhat manner it produces the liquefaction or vaporization of\none body. We cannot look to account for Gay Lussac and\nDalton's Law, that all gases expand equally by heat, till we\nlearn how heat causes a gas to expand. We cannot hope to see\nthe grounds of Dulong and Petit's Law, that the specific\nheat of all atoms is the same, till we know much more, not\nonly about atoms, but about specific heat. We have as yet no\nthermotical theory which even professes to account for all\nthe prominent facts of the subject[37\\6]: and the theories\nwhich have been proposed are of the most diverse kind.\nLaplace assumes particles of bodies surrounded by\natmospheres of caloric[38\\6]; Cauchy makes heat consist in\nlongitudinal vibrations of the ether of which transverse\nvibrations {47} produce light: in Amp\u00e8re's theory[39\\6],\nheat consists in the vibrations of the particles of bodies.\nAnd so long as we have nothing more certain in our\nconceptions of heat than the alternative of these and other\nprecarious hypotheses, how can we expect to arrive at any\nreal knowledge, by connecting the results of such hypotheses\nwith the speculations of Chemistry, of which science the\ntheory is at least equally obscure?\n\n[Note 37\\6: _Hist. Ind. Sci._ b. x. c. 4.]\n\n[Note 38\\6: _Ib._]\n\n[Note 39\\6: _Hist. Ind. Sci._ b. x. c. 4.]\n\nThe largest attempts at chemical theory have been made in\nthe form of the Atomic Theory, to which I have just had\noccasion to allude. I must, therefore, before quitting the\nsubject, say a few words respecting this theory.\n\n\n\n{{48}}\nCHAPTER V.\n\nTHE ATOMIC THEORY.\n\n\n1. _The Atomic Theory considered on Chemical Grounds._--WE\nhave already seen that the combinations which result from\nchemical affinity are definite, a certain quantity of one\ningredient uniting, not with an uncertain, but with a\ncertain quantity of another ingredient. But it was found, in\naddition to this principle, that one ingredient would often\nunite with another in different proportions, and that, in\nsuch cases, these proportions are multiples one of another.\nIn the three salts formed by potassa with oxalic acid, the\nquantities of acid which combine with the same quantity of\nalkali are exactly in the proportion of the numbers 1, 2, 4.\nAnd the same rule of the existence of multiple proportions\nis found to obtain in other cases.\n\nIt is obvious that such results will be accounted for, if we\nsuppose that the base and the acid consist each of numerous\ndefinite equal particles, and that the formation of the\nsalts above mentioned consists in the combination of one\nparticle of the base with one particle of acid, with two\nparticles of acid, and with four particles of acid,\nrespectively. But further; as we have already stated,\nchemical affinity is not only definite, but reciprocal. The\nproportions of potassa and soda which form neutral salts\nbeing 590 and 391 in one case, they are so in all cases.\nThese numbers represent _proportions_ of weight in which the\ntwo bases, potassa and soda, enter into analogous\ncombinations; 590 of potassa is _equivalent_ to 391 of soda.\nThese facts with regard to combination are still expressed\nby the above supposition of equal particles, assuming that\nthe weights of a {49} particle of potassa and of soda are in\nthe proportion of 590 to 391.\n\nBut we pursue our analysis further. We find that potassa is\na compound of a metallic base, potassium, and of oxygen, in\nthe proportion of 490 to 100; we suppose, then, that the\nparticle of potassa consists of a particle of potassium and\na particle of oxygen; and these latter particles, since we\nsee no present need to suppose them divided, potassium and\noxygen being simple bodies, we may call _atoms_, and assume to\nbe indivisible. And by supposing all simple bodies to\nconsist of such atoms, and compounds to be formed by the\nunion of two, or three, or more of such atoms, we explain\nthe occurrence of definite and multiple proportions, and we\nconstruct the Atomic Theory.\n\n2. _Hypothesis of Atoms._--So far as the assumption of such\natoms as we have spoken of serves to express those laws of\nchemical composition which we have referred to, it is a\nclear and useful generalization. But if the Atomic Theory be\nput forwards (and its author, Dr. Dalton, appears to have\nput it forwards with such an intention,) as asserting that\nchemical elements are really composed of _atoms_, that is,\nof such particles not further divisible, we cannot avoid\nremarking, that for such a conclusion, chemical research has\nnot afforded, nor can afford, any satisfactory evidence\nwhatever. The smallest observable quantities of ingredients,\nas well as the largest, combine according to the laws of\nproportions and equivalence which have been cited above. How\nare we to deduce from such facts any inference with regard\nto the existence of certain smallest possible particles? The\nTheory, when dogmatically taught as a physical truth,\nasserts that all observable quantities of elements _are_\ncomposed of proportional numbers of particles which can no\nfurther be subdivided; but all which observation teaches us\nis, that if there be such particles, they are smaller than\nthe smallest observable quantities. In chemical experiment,\nat least, there is not the slightest positive evidence for\nthe existence of such atoms. The assumption of _indivisible_\nparticles, smaller than the smallest {50} observable, which\ncombine, particle with particle, will explain the phenomena;\nbut the assumption of particles bearing this proportion, but\n_not_ possessing the property of indivisibility, will explain\nthe phenomena at least equally well. The decision of the\nquestion, therefore, whether the Atomic Hypothesis be the\nproper way of conceiving the chemical combinations of\nsubstances, must depend, not upon chemical facts, but upon\nour conception of Substance. In this sense the question is\nan ancient and curious controversy, and we shall hereafter\nhave to make some remarks upon it.\n\n3. _Chemical Difficulties of the Hypothesis._--But before\ndoing this, we may observe that there is no small difficulty\nin reconciling this hypothesis with the facts of chemistry.\nAccording to the theory, all salts, compounded of an acid\nand a base, are analogous in their atomic constitution; and\nthe number of atoms in one such compound being known or\nassumed, the number of atoms in other salts may be\ndetermined. But when we proceed in this course of reasoning\nto other bodies, as metals, we find ourselves involved in\ndifficulties. The protoxide of iron is a base which,\naccording to all analogy, must consist of one atom of iron\nand one of oxygen: but the peroxide of iron is also a base,\nand it appears by the analysis of this substance that it\nmust consist of _two-thirds_ of an atom of iron and one atom\nof oxygen. Here, then, our indivisible atoms must be\ndivisible, even upon chemical grounds. And if we attempt to\nevade this difficulty by making the peroxide of iron consist\nof two atoms of iron and three of oxygen, we have to make a\ncorresponding alteration in the theoretical constitution of\nall bodies analogous to the protoxide; and thus we overturn\nthe very foundation of the theory. Chemical facts,\ntherefore, not only do not prove the Atomic Theory as a\nphysical truth, but they are not, according to any\nmodification yet devised of the theory, reconcileable with\nits scheme.\n\nNearly the same conclusions result from the attempts to\nemploy the Atomic Hypothesis in expressing another important\nchemical law;--the law of the {51} combinations of gases\naccording to definite proportions of their volumes,\nexperimentally established by Gay Lussac[40\\6]. In order to\naccount for this law, it has been very plausibly suggested\nthat all gases, under the same pressure, contain an equal\nnumber of atoms in the same space; and that when they\ncombine, they unite atom to atom. Thus one volume of\nchlorine unites with one volume of hydrogen, and forms\nhydrochloric acid[41\\6]. But then this hydrochloric acid\noccupies the space of the two volumes; and therefore the\nproper number of particles cannot be supplied, and the\nuniform distribution of atoms in all gases maintained,\nwithout dividing into two each of the compound particles,\nconstituted of an atom of chlorine and an atom of hydrogen.\nAnd thus in this case, also, the Atomic Theory becomes\nuntenable if it be understood to imply the indivisibility of\nthe atoms.\n\n[Note 40\\6: _Hist. Ind. Sc._ b. xiv. c. 8.]\n\n[Note 41\\6: Dumas, _Phil. Chim._ 263.]\n\nIn all these attempts to obtain distinct physical conception\nof chemical union by the aid of the Atomic Hypothesis, the\natoms are conceived to be associated by certain forces of\nthe nature of mechanical attractions. But we have already\nseen[42\\6] that no such mode of conception can at all\nexplain or express the facts of chemical combination; and\ntherefore it is not wonderful that when the Atomic Theory\nattempts to give an account of chemical relations by\ncontemplating them under such an aspect, the facts on which\nit grounds itself should be found not to authorize its\npositive doctrines; and that when these doctrines are tried\nupon the general range of chemical observation, they should\nprove incapable of even expressing, without\nself-contradiction, the laws of phenomena.\n\n[Note 42\\6: See Chapter I. of this book.]\n\n4. _Grounds of the Atomic Doctrine._--Yet the doctrine of\natoms, or of substance as composed of indivisible particles,\nhas in all ages had great hold upon the minds of physical\nspeculators; nor would this doctrine ever have suggested\nitself so readily, or have been maintained so tenaciously,\nas the true mode of {52} conceiving chemical combinations,\nif it had not been already familiar to the minds of those\nwho endeavour to obtain a general view of the constitution\nof nature. The grounds of the assumption of the atomic\nstructure of substance are to be found rather in the idea of\nsubstance itself, than in the experimental laws of chemical\naffinity. And the question of the existence of atoms, thus\ndepending upon an idea which has been the subject of\ncontemplation from the very infancy of philosophy, has been\ndiscussed in all ages with interest and ingenuity. On this\nvery account it is unlikely that the question, so far as it\nbears upon chemistry, should admit of any clear and final\nsolution. Still it will be instructive to look back at some\nof the opinions which have been delivered respecting this\ndoctrine.\n\n5. _Ancient Prevalence of the Atomic Doctrine._--The\ndoctrine that matter consists of minute, simple,\nindivisible, indestructible particles as its ultimate\nelements, has been current in all ages and countries,\nwhenever the tendency of man to wide and subtle speculations\nhas been active. I need not attempt to trace the history of\nthis opinion in the schools of Greece and Italy. It was the\nleading feature in the physical tenets of the Epicureans,\nand was adopted by their Roman disciples, as the poem of\nLucretius copiously shows us. The same tenet had been held\nat still earlier periods, in forms more or less definite, by\nother philosophers. It is ascribed to Democritus, and is\nsaid to have been by him derived from Leucippus. But this\ndoctrine is found also, we are told[43\\6], among the\nspeculations of another intellectual and acute race, the\nHindoos. According to some of their philosophical writers,\nthe ultimate elements of matter are atoms, of which it is\nproved by certain reasonings, that they are each one-sixth\nof one of the motes that float in the sunbeam.\n\n[Note 43\\6: By Mr. Colebrook. _Asiatic Res._ 1824.]\n\nThis early prevalence of controversies of the widest and\ndeepest kind, which even in our day remain undecided, has in\nit nothing which need surprize us; or, at least, it has in\nit nothing which is not in conformity {53} with the general\ncourse of the history of philosophy. As soon as any ideas\nare clearly possessed by the human mind, its activity and\nacuteness in reasoning upon them are such, that the\nfundamental antitheses and ultimate difficulties which\nbelong to them are soon brought into view. The Greek and\nIndian philosophers had mastered completely the Idea of\nSpace, and possessed the Idea of Substance in tolerable\ndistinctness. They were, therefore, quite ready, with their\nlively and subtle minds, to discuss the question of the\nfinite and infinite divisibility of matter, so far as it\ninvolved only the ideas of space and of substance, and this\naccordingly they did with great ingenuity and perseverance.\n\nBut the ideas of Space and of Substance are far from being\nsufficient to enable men to form a complete general view of\nthe constitution of matter. We must add to these ideas, that\nof mechanical Force with its antagonist Resistance, and that\nof the Affinity of one kind of matter for another. Now the\nformer of these ideas the ancients possessed in a very\nobscure and confused manner; and of the latter they had no\napprehension whatever. They made vague assumptions\nrespecting the impact and pressure of atoms on each other;\nbut of their mutual attraction and repulsion they never had\nany conception, except of the most dim and wavering kind;\nand of an affinity different from mere local union they did\nnot even dream. Their speculations concerning atoms,\ntherefore, can have no value for us, except as a part of the\nhistory of science. If their doctrines appear to us to\napproach near to the conclusions of our modern philosophy,\nit must be because our modern philosophy is that philosophy\nwhich has not fully profited by the additional light which\nthe experiments and meditations of later times have thrown\nupon the constitution of matter.\n\n6. _Bacon._--Still, when modern philosophers look upon the\nAtomic Theory of the ancients in a general point of view\nmerely, without considering the special conditions which\nsuch a theory must fulfil, in order to represent the\ndiscoveries of modern times, they are {54} disposed to\nregard it with admiration. Accordingly we find Francis Bacon\nstrongly expressing such a feeling. The Atomic Theory is\nselected and dwelt upon by him as the chain which connects\nthe best parts of the physical philosophy of the ancient and\nthe modern world. Among his works is a remarkable\ndissertation _On the Philosophy of Democritus, Parmenides,\nand Telesius_: the last mentioned of whom was one of the\nrevivers of physical science in modern times. In this work\nhe speaks of the atomic doctrine of Democritus as a\nfavourable example of the exertions of the undisciplined\nintellect. 'H\u00e6c ipsa placita, quamvis paulo emendatiora,\ntalia sunt qualia esse possunt illa qu\u00e6 ab intellectu sibi\npermisso, nec continenter et gradatim sublevato, profecta\nvidentur.'--'These doctrines, thus [in an ancient fable]\npresented in a better form, are such glimpses of truth as\ncan be obtained by the intellect left to its own natural\nimpulses, and not ascending by successive and connected\nsteps,' [as the Baconian philosophy directs]. 'Accordingly,'\nhe adds, 'the doctrine of Atoms, from its going a step\nbeyond the period in which it was advanced, was ridiculed by\nthe vulgar, and severely handled in the disputations of the\nlearned, notwithstanding the profound acquaintance with\nphysical science by which its author was allowed to be\ndistinguished, and from which he acquired the character of a\nmagician.'\n\n'However,' he continues, 'neither the hostility of\nAristotle, with all his skill and vigour in disputation,\n(though, like the Ottoman sultans, he laboured to destroy\nall his brother philosophers that he might rest undisputed\nmaster of the throne of science,) nor the majestic and lofty\nauthority of Plato, could effect the subversion of the\ndoctrine of Democritus. And while the opinions of Plato and\nAristotle were rehearsed with loud declamation and\nprofessorial pomp in the schools, this of Democritus was\nalways held in high honour by those of a deeper wisdom, who\nfollowed in silence a severer path of contemplation. In the\ndays of Roman speculation it kept its ground and its favour;\nCicero everywhere speaks of its author with the {55}\ngreatest praise; and Juvenal, who, like poets in general,\nprobably expressed the prevailing judgment of his time,\nproclaims his merit as a noble exception to the general\nstupidity of his countrymen.\n . . . . Cujus prudentia monstrat\n Magnos posse viros et magna exempla daturos\n Vervecum in patri\u00e2 crassoque sub aere nasci.\n\n'The destruction of this philosophy was not effected by\nAristotle and Plato, but by Genseric and Attila, and their\nbarbarians. For then, when human knowledge had suffered\nshipwreck, those fragments of the Aristotelian and Platonic\nphilosophy floated on the surface like things of some\nlighter and emptier sort, and so were preserved; while more\nsolid matters went to the bottom, and were almost lost in\noblivion.'\n\n7. _Modern Prevalence of the Atomic Doctrine._--It is our\nbusiness here to consider the doctrine of Atoms only in its\nbearing upon existing physical sciences, and I must\ntherefore abstain from tracing the various manifestations of\nit in the schemes of hypothetical cosmologists;--its place\namong the _vortices_ of Descartes, its exhibition in the\n_monads_ of Leibnitz. I will, however, quote a passage from\nNewton to show the hold it had upon his mind.\n\nAt the close of his _Opticks_ he says, 'All these things\nbeing considered, it seems probable to me that God, in the\nbeginning, formed matter in solid, massy, hard,\nimpenetrable, moveable particles, of such sizes and figures,\nand with such other properties, and in such proportions to\nspace, as most conduced to the end for which He formed them;\nand that the primitive particles, being solids, are\nincomparably harder than any porous bodies compounded of\nthem, even so very hard as never to wear or break in pieces;\nno ordinary power being able to divide what God had made one\nin the first creation. While the particles continue entire,\nthey may compose bodies of one and the same nature and\ntexture in all ages: but should they wear away or break in\npieces, the nature of things depending on them would be\nchanged. Water and earth composed {56} of old worn particles\nand fragments of particles would not be of the same nature\nand texture now with water and earth composed of entire\nparticles in the beginning. And therefore that nature may be\nlasting, the changes of corporeal things are to be placed\nonly in the various separations and new associations and\nmotions of these permanent particles; compounded bodies\nbeing apt to break, not in the midst of solid particles, but\nwhere those particles are laid together and only touch in a\nfew points.'\n\nWe shall hereafter see how extensively the atomic doctrine\nhas prevailed among still more recent philosophers. Not only\nhave the chemists assumed it as the fittest form for\nexhibiting the principles of multiple proportions; but the\nphysical mathematicians, as Laplace and Poisson, have made\nit the basis of their theories of heat, electricity,\ncapillary action; and the crystallographers have been\nsupposed to have established both the existence and the\narrangement of such ultimate molecules.\n\nIn the way in which it has been employed by such writers,\nthe hypothesis of ultimate particles has been of great use,\nand is undoubtedly permissible. But when we would assert\nthis theory, not as a convenient hypothesis for the\nexpression or calculation of the laws of nature, but as a\nphilosophical truth respecting the constitution of the\nuniverse, we find ourselves checked by difficulties of\nreasoning which we cannot overcome, as well as by\nconflicting phenomena which we cannot reconcile. I will\nattempt to state briefly the opposing arguments on this\nquestion.\n\n8. _Arguments for and against Atoms._--The leading arguments\non the two sides of the question, in their most general\nform, may be stated as follows:\n\n_For_ the Atomic Doctrine.--The appearances which nature\npresents are compounded of many parts, but if we go on\nresolving the larger parts into smaller, and so on\nsuccessively, we must at last come to something simple. For\nthat which is compound can be so no otherwise than by\ncomposition of what is simple; and if we suppose all\ncomposition to be removed, which {57} hypothetically we may\ndo, there can remain nothing but a number of simple\nsubstances, capable of composition, but themselves not\ncompounded. That is, matter being dissolved, resolves itself\ninto atoms.\n\n_Against_ the Atomic Doctrine.--Space is divisible without\nlimit, as may be proved by Geometry; and matter occupies\nspace, therefore matter is divisible without limit, and no\nportion of matter is indivisible, or an _atom_.\n\nAnd to the argument on the other side just stated, it is\nreplied that we cannot even hypothetically divest a body of\ncomposition, if by composition we mean the relation of point\nto point in space. However small be a particle, it is\ncompounded of parts having relation in space.\n\nThe Atomists urge again, that if matter be infinitely\ndivisible, a finite body consists of an infinite number of\nparts, which is a contradiction. To this it is replied, that\nthe finite body consists of an infinite number of parts in\nthe same sense in which the parts are infinitely small,\nwhich is no contradiction.\n\nBut the opponents of the Atomists not only rebut, but retort\nthis argument drawn from the notion of infinity. Your atoms,\nthey say, are indivisible by any finite force; therefore\nthey are infinitely hard; and thus your finite particles\npossess infinite properties. To this the Atomists are wont\nto reply, that they do not mean the hardness of their\nparticles to be infinite, but only so great as to resist all\nusual natural forces. But here it is plain that their\nposition becomes untenable; for, in the first place, their\nassumption of this precise degree of hardness in the\nparticles is altogether gratuitous; and in the next place,\nif it were granted, such particles are not atoms, since in\nthe next moment the forces of nature may be augmented so as\nto divide the particle, though hitherto undivided.\n\nSuch are the arguments for and against the Atomic Theory in\nits original form. But when these atoms are conceived, as\nthey have been by Newton, and commonly by his followers, to\nbe solid, hard particles exerting attractive and repulsive\nforces, a new set of {58} arguments come into play. Of\nthese, the principal one may be thus stated: According to\nthe Atomic Theory thus modified, the properties of bodies\ndepend upon the attractions and repulsions of the particles.\nTherefore, among other properties of bodies, their hardness\ndepends upon such forces. But if the hardness _of the\nbodies_ depends upon the forces, the repulsion, for\ninstance, of the particles, upon what does the hardness _of\nthe particles_ depend? what progress do we make in\nexplaining the properties of bodies, when we assume the same\nproperties in our explanation? and to what purpose do we\nassume that the particles are hard?\n\n9. _Transition to Boscovich's Theory._--To this difficulty\nit does not appear easy to offer any reply. But if the\nhardness and solidity of the particles be given up as an\nincongruous and untenable appendage to the Newtonian view of\nthe Atomic Theory, we are led to the theory of Boscovich,\naccording to which matter consists not of solid particles,\nbut of mere mathematical centers of force. According to this\ntheory, each body is composed of a number of geometrical\npoints from which emanate forces, following certain\nmathematical laws in virtue of which the forces become, at\ncertain small distances attractive, at certain other\ndistances repulsive, and at greater distances attractive\nagain. From these forces of the points arise the cohesion of\nthe parts of the same body, the resistance which it exerts\nagainst the pressure of another body, and finally the\nattraction of gravitation which it exerts upon bodies at a\ndistance.\n\nThis theory is at least a homogeneous and consistent theory,\nand it is probable that it may be used as an instrument for\ninvestigating and expressing true laws of nature; although,\nas we have already said, the attempt to identify the forces\nby which the particles of bodies are bound together with\nmechanical attraction, appears to be a confusion of two\nseparate ideas[44\\6].\n\n[Note 44\\6: 'Boscovich's Theory,' that all bodies may be\nconsidered as consisting of a mere collection of centers of\nforces, may be so conceived as possibly to involve an\nexplanation of all the powers which their parts exert, (such\npowers, namely, as those which produce optical, thermotical\nand chemical phenomena;) but this theory cannot supply an\nexplanation of the mechanical properties of a body as a\nwhole, especially of its _inertia_. A collection of mere\ncenters of force can have no inertia. If two bodies are\nconsidered as two collections of centers of force, the one\nattracting the other, there is in this view nothing to limit\nor determine the velocity with which the one body will\napproach the other. A world composed of such bodies is not a\n_material_ world: for matter (as we have already seen in\nbook iii. chapter v.) implies not only force, but something\nwhich resists the action of force.]\n\n{59} 10. _Use of the Molecular Hypothesis._--In this form,\nrepresenting matter as a collection of molecules or centers\nof force, the Atomic Theory has been abundantly employed in\nmodern times as an hypothesis on which calculations\nrespecting the elementary forces of bodies might be\nconducted. When thus employed it is to be considered as\nexpressing the principle that the properties of bodies\ndepend upon forces emanating from immovable points of their\nmass. This view of the way in which the properties of bodies\nare to be treated by the mechanical philosopher was\nintroduced by Newton, and was a natural sequel to the\nsuccess which he had obtained by reasoning concerning\ncentral forces on a large scale. I have already quoted his\nPreface to the _Principia_, in which he says, 'Many things\ninduce me to believe that the rest of the phenomena of\nnature, as well as those of astronomy, may depend upon\ncertain forces by which the particles of bodies, in virtue\nof causes not yet known, are urged towards each other and\ncohere in regular figures, or are mutually repelled and\nrecede; and philosophers, knowing nothing of these forces,\nhave hitherto failed in their examination of nature.' Since\nthe time of Newton, this line of speculation has been\nfollowed with great assiduity, and by some mathematicians\nwith great success. In particular Laplace has shown that the\nhypothesis may, in many instances, be made a much closer\nrepresentation of nature, if we suppose the forces exerted\nby the particles to decrease so rapidly with the increasing\ndistance from them, that {60} the force is finite only at\ndistances imperceptible to our senses, and vanishes at all\nremoter points. He has taught the method of expressing and\ncalculating such forces, and he and other mathematicians of\nhis school have applied this method to many of the most\nimportant questions of physics; as capillary action, the\nelasticity of solids, the conduction and radiation of heat.\nThe explanation of many apparently unconnected and curious\nobserved facts by these mathematical theories gives a strong\nassurance that its essential principles are true. But it\nmust be observed that the actual constitution of bodies as\ncomposed of distinct and separate particles is by no means\nproved by these coincidences. The assumption, in the\nreasoning, of certain centers of force acting at a distance,\nis to be considered as nothing more than a method of\nreducing to calculation that view of the constitution of\nbodies which supposes that they exert force at _every_\npoint. It is a mathematical artifice of the same kind as the\nhypothetical division of a body into infinitesimal parts, in\norder to find its center of gravity; and no more implies a\nphysical reality than that hypothesis does.\n\n11. _Poisson's Inference._--When, therefore, M. Poisson, in\nhis views of Capillary Action, treats this hypothetical\ndistribution of centers of force as if it were a physical\nfact, and blames Laplace for not taking account of their\ndifferent distribution at the surface of the fluid and below\nit[45\\6], he appears to push the claims of the molecular\nhypothesis too far. The only ground for the assumption of\nseparate centers, is that we can thus explain the action of\nthe whole mass. The intervals between the centers nowhere\nenter into this explanation: and therefore we can have no\nreason for assuming these intervals different in one part of\nthe fluid and in the other. M. Poisson asserts that the\ndensity of the fluid diminishes when we approach very near\nthe surface; but he allows that this diminution is not\ndetected by experiment, and that the formul\u00e6 on {61} his\nsupposition, so far as the results go, are identical with\nthose of Laplace. It is clear, then, that his doctrine\nconsists merely in the assertion of the necessary truth of a\npart of the hypothesis which cannot be put to the test of\nexperiment. It is true, that so long as we have before us\nthe hypothesis of separate centers, the particles very near\nthe surface are not in a condition symmetrical with that of\nthe others: but it is also true that this hypothesis is only\na step of calculation. There results, at one period of the\nprocess of deduction, a stratum of smaller density at the\nsurface of the fluid; but at a succeeding point of the\nreasoning the thickness of this stratum vanishes; it has no\nphysical existence.\n\n[Note 45\\6: Poisson, _Th\u00e9orie de l'Action Capillaire_.]\n\nThus the _molecular_ hypothesis, as used in such cases, does\nnot differ from the doctrine of forces acting at _every\npoint_ of the mass; and this principle, which is common to\nboth the opposite views, is the true part of each.\n\n12. _Wollaston's Argument._--An attempt has been made in\nanother case, but depending on nearly the same arguments, to\nbring the doctrine of ultimate atoms to the test of\nobservation. In the case of the air, we know that there _is_\na diminution of density in approaching the upper surface of\nthe atmosphere, if it have a surface: but it is held by some\nthat except we allow the doctrine of ultimate molecules, it\nwill not be bounded by any surface, but will extend to an\ninfinite distance. This is the reasoning of Wollaston[46\\6].\n'If air consists of any ultimate particles no longer\ndivisible, then must the expansion of the medium composed of\nthem cease at that distance where the force of gravity\ndownwards is equal to the resistance arising from the\nrepulsive force of the medium.' But if there be no such\nultimate particles, every stratum will require a stratum\nbeyond it to prevent by its weight a further expansion, and\nthus the atmosphere {62} must extend to an infinite\ndistance. And Wollaston conceived that he could learn from\nobservation whether the atmosphere was thus diffused through\nall space; for if so, it must, he argued, be accumulated\nabout the larger bodies of the system, as Jupiter and the\nSun, by the law of universal gravitation; and the existence\nof an atmosphere about these bodies, might, he remarked, be\ndetected by its effects in producing refraction. His result\nis, that 'all the phenomena accord entirely with the\nsupposition that the earth's atmosphere is of finite extent,\nlimited by the weight of ultimate atoms of definite\nmagnitude, no longer divisible by repulsion of their parts.'\n\n[Note 46\\6: _Phil. Trans._ 1822, p. 89.]\n\nA very little reflection will show us that such a line of\nreasoning cannot lead to any result. For we know nothing of\nthe law which connects the density with the compressing\nforce, in air so extremely rare as we must suppose it to be\nnear the boundary of the atmosphere. Now there are possible\nlaws of dependence of the density upon the compressing force\nsuch that the atmosphere would terminate in virtue of the\nlaw without any assumption of atoms. This may be proved by\nmathematical reasoning. If we suppose the density of air to\nbe as the square root of the compressing force, it will\nfollow that at the very limits of the atmosphere, the strata\nof equal thickness may observe in their densities such a law\nof proportion as is expressed by the numbers 7, 5, 3,\n1[47\\6].\n\n[Note 47\\6: For the compressing force on each being as the\nwhole weight beyond it, it will be for the four highest\nstrata, 16, 9, 4 and 1, of which the square roots are as 4,\n3, 2, 1, or, as 8, 6, 4, 2; and though these numbers are not\nexactly as the densities 7, 5, 3, 1, those who are a little\nacquainted with mathematical reasoning, will see that the\ndifference arises from taking so small a number of strata.\nIf we were to make the strata indefinitely thin, as to avoid\nerror we ought to do, the coincidence would be exact; and\nthus, according to this law, the series of strata terminates\nas we ascend, without any consideration of atoms.]\n\nIf it be asked how, on this hypothesis, the density of the\nhighest stratum can be as 1, since there is {63} nothing to\ncompress it, we answer that the upper part of the highest\nstratum compresses the lower, and that the density\ndiminishes continually to the surface, so that the need of\ncompression and the compressing weight vanish together.\n\nThe fallacy of concluding that because the height of the\natmosphere is finite, the weight of the highest stratum must\nbe finite, is just the same as the fallacy of those who\nconclude that when we project a body vertically upwards,\nbecause it occupies only a finite time in ascending to the\nhighest point, the velocity at the last instant of the\nascent must be finite. For it might be said, if the last\nvelocity of ascent be not finite, how can the body describe\nthe last particle of space in a finite time? and the answer\nis, that there is no last finite particle of space, and\ntherefore no last finite velocity.\n\n13. _Permanence of Properties of Bodies._--We have already\nseen that, in explaining the properties of matter as we find\nthem in nature, the assumption of solid, hard,\nindestructible particles is of no use or value. But we may\nremark, before quitting the subject, that Newton appears to\nhave had another reason for assuming such particles, and one\nwell worthy of notice. He wished to express, by means of\nthis hypothesis, the doctrine that the laws of nature do not\nalter with the course of time. This we have already seen in\nthe quotation from Newton. 'The ultimate particles of matter\nare indestructible, unalterable, impenetrable; for if they\ncould break or wear, the structure of material bodies now\nwould be different from that which it was when the particles\nwere new.' No philosopher will deny the truth which is thus\nconveyed by the assertion of atoms; but it is obviously\nequally easy for a person who rejects the atomic view, to\nstate this truth by saying that the forces which matter\nexerts do not vary with time, but however modified by the\nnew modifications of its form, are always unimpaired in\nquantity, and capable of being restored to their former mode\nof action. {64}\n\nWe now proceed to speculations in which the fundamental\nconceptions may, perhaps, be expressed, at least in some\ncases, by means of the arrangement of atoms; but in which\nthe philosophy of the subject appears to require a reference\nto a new Fundamental Idea.\n\n\n\n\n{{65}}\nBOOK VII.\n\n\nTHE\nPHILOSOPHY\nOF\nMORPHOLOGY,\nINCLUDING\nCRYSTALLOGRAPHY.\n\n\n\n\nCRYSTALLIZATION exhibits to us the effects of the natural\narrangement of the ultimate particles of various compound\nbodies; but we are scarcely yet sufficiently acquainted with\nchemical synthesis and analysis to understand the rationale\nof this process. The rhomboidal form may arise from the\nproper position of 4, 6, 8 or 9 globular particles, the\ncubic form from 8 particles, the triangular form from 3, 6\nor 10 particles, the hexahedral prism from 7 particles, &c.\nPerhaps, in due time we may be enabled to ascertain the\nnumber and order of elementary particles, constituting any\ngiven compound element, and from that determine the figure\nwhich it will prefer on crystallization, and _vice vers\u00e2_.\n\nJOHN DALTON, _Chemical Philosophy_ (1808), p. 210.\n\n\n\n{{67}}\nBOOK VII.\n\n\nTHE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY.\n\n\nCHAPTER I.\n\nEXPLICATION OF THE IDEA OF SYMMETRY.\n\n\n1. WE have seen in the History of the Sciences, that the\nprinciple which I have there termed[1\\7] the Principle of\nDeveloped and Metamorphosed Symmetry, has been extensively\napplied in botany and physiology, and has given rise to a\nprovince of science termed Morphology. In order to\nunderstand clearly this principle, it is necessary to obtain\na clear idea of the Symmetry of which we thus speak. But\nthis Idea of Symmetry is applicable in the inorganic, as\nwell as in the organic kingdoms of nature; it is presented\nto our eyes in the forms of minerals, as well as of flowers\nand animals; we must, therefore, take it under our\nconsideration here, in order that we may complete our view\nof Mineralogy, which, as I have repeatedly said, is an\nessential part of Chemical science. I shall accordingly\nendeavour to unfold the Idea of Symmetry with which we here\nhave to do.\n\n[Note 1\\7: _Hist. Ind. Sc._ b. xvii. c. vi.]\n\nIt will of course be understood that by the term _Symmetry_\nI here intend, not that more indefinite attribute of form\nwhich belongs to the domain of the fine arts, as when we\nspeak of the 'symmetry' of an edifice {68} or of a\nsculptured figure, but a certain definite relation or\nproperty, no less rigorous and precise than other relations\nof number and position, which is thus one of the sure guides\nof the scientific faculty, and one of the bases of our exact\nscience.\n\n2. In order to explain what Symmetry is in this sense, let\nthe reader recollect that the bodies of animals consist of\n_two_ equal and similar sets of members, the right and the\nleft side;--that some flowers consist of three or of five\nequal sets of organs, similarly and regularly disposed, as\nthe iris has _three_ straight petals, and three reflexed\nones, alternately disposed, the rose has _five_ equal and\nsimilar sepals of the calyx, and alternate with these, as\nmany petals of the corolla. This orderly and exactly similar\ndistribution of two, or three, or five, or any other number\nof parts, is Symmetry; and according to its various\nmodifications, the forms thus determined are said to be\n_symmetrical_ with various numbers of members. The\nclassification of these different kinds of symmetry has been\nmost attended to in Crystallography, in which science it is\nthe highest and most general principle by which the classes\nof forms are governed. Without entering far into the\ntechnicalities of the subject, we may point out some of the\nfeatures of such classes.\n\n[Illustration] The first of the figures (1) in the margin\nmay represent the summit of a crystal as it appears to an\neye looking directly down upon it; the center of the figure\nrepresents the summit of a pyramid, and the spaces of\nvarious forms which diverge from this point represent\nsloping sides of the pyramid. Now it will be observed that\nthe figure consists of three portions exactly similar to one\nanother, and that each part or member is repeated in each of\nthese portions. The faces, or pairs of faces, are repeated\nin _threes_, with exactly similar forms and angles. This\nfigure is said to be _three-membered_, or to have\n_triangular_ symmetry. The same kind of {69} symmetry may\nexist in a flower, as presented in the accompanying figure,\nand does, in fact, occur in a large class of flowers, as for\nexample, all the lily tribe. The next pair of figures (2)\nhave four equal and similar portions, and have their members\nor pairs of members four times repeated. Such figures are\ntermed _four-membered_, and are said to have _square_ or\n_tetragonal_ symmetry. The _pentagonal_ symmetry, formed by\n_five_ similar _members_, is represented in the next figures\n(3). It occurs abundantly in the vegetable world, but never\namong crystals; for the pentagonal figures which crystals\nsometimes assume, are never exactly regular. But there is\nstill another kind of symmetry (4) in which the opposite\nends are exactly similar to each other and also the opposite\nsides; this is _oblong_, or _two-and-two-membered_ symmetry.\nAnd finally, we have the case of _simple_ symmetry (5) in\nwhich the two sides of the object are exactly alike (in\nopposite positions) without any further repetition.\n[Illustration]\n\n3. These different kinds of symmetry occur in various ways\nin the animal, vegetable, and mineral kingdom. Vertebrate\nanimals have a right and a {70} left side exactly alike, and\nthus possess _simple_ symmetry. The same kind of symmetry\n(simple symmetry) occurs very largely in the forms of\nvegetables, as in most leaves, in _papilionaceous_,\n_personate_, and _labiate_ flowers. Among minerals, crystals\nwhich possess this symmetry are called _oblique-prismatic_,\nand are of very frequent occurrence. The _oblong_, or\n_two-and-two-membered_ symmetry belongs to _right-prismatic_\ncrystals; and may be seen in _cruciferous_ flowers, for\nthough these are cross-shaped, the cross has two longer and\ntwo shorter arms, or pairs of arms. The _square_ or\n_tetragonal_ symmetry occurs in crystals abundantly; to the\nvegetable world it appears to be less congenial; for though\nthere are flowers with four exactly similar and\nregularly-disposed petals, as the herb Paris (_Paris\nquadrifolia_), these flowers appear, from various\ncircumstances, to be deviations from the usual type of\nvegetable forms. The _trigonal_, or _three-membered_\nsymmetry is found abundantly both in plants and in crystals,\nwhile the _pentagonal_ symmetry, on the other hand, though\nby far the most common among flowers, nowhere occurs in\nminerals, and does not appear to be a possible form of\ncrystals. This pentagonal form further occurs in the animal\nkingdom, which the oblong, triangular, and square forms do\nnot. Many of Cuvier's _radiate_ animals appear in this\npentagonal form, as _echini_ and _pentacrinites_, which\nlatter have hence their name.\n\n4. The regular, or as they may be called, the _normal_ types\nof the vegetable world appear to be the forms which possess\ntriangular and pentagonal symmetry; from these the others\nmay be conceived to be derived, by transformations resulting\nfrom the expansion of one or more parts. Thus it is manifest\nthat if in a three-membered or five-membered flower, one of\nthe petals be expanded more than the other, it is\nimmediately reduced from pentagonal or trigonal, to simple\nsymmetry. And the oblong or two-and-two-membered symmetry of\nthe flowers of cruciferous plants, (in which the stamens are\nfour large and two small ones, arranged in regular\nopposition,) is held by botanists to result {71} from a\nnormal form with ten stamens; Meinecke explaining this by\nadhesion, and Sprengel by the metamorphosis of the stamens\ninto petals[2\\7].\n\n[Note 2\\7: Sprengel, _Gesch. d. Bot._ ii. 304.]\n\nIt is easy to see that these various kinds of symmetry\ninclude relations both of form and of number, but more\nespecially of the latter kind; and as this symmetry is often\nan important character in various classes of natural\nobjects, such classes have often curious numerical\nproperties. One of the most remarkable and extensive of\nthese is the distinction which prevails between\nmonocotyledonous and dicotyledonous plants; the number\n_three_ being the ground of the symmetry of the former, and\nthe number _five_, of the latter. Thus liliaceous and\nbulbous plants, and the like, have flowers of three or six\npetals, and the other organs follow the same numbers: while\nthe vast majority of plants are pentandrous, and with their\nfive stamens have also their other parts in fives. This\ngreat numerical distinction corresponding to a leading\ndifference of physiological structure cannot but be\nconsidered as a highly curious fact in phytology. Such\nproperties of numbers, thus connected in an incomprehensible\nmanner with fundamental and extensive laws of nature, give\nto numbers an appearance of mysterious importance and\nefficacy. We learn from history how strongly the study of\nsuch properties, as they are exhibited by the phenomena of\nthe heavens, took possession of the mind of Kepler; perhaps\nit was this which, at an earlier period, contributed in no\nsmall degree to the numerical mysticism of the Pythagoreans\nin antiquity, and of the Arabians and others in the middle\nages. In crystallography, numbers are the primary characters\nin which the properties of substances are expressed;--they\nappear, first, in that classification of forms which depends\non the degree of symmetry, that is, upon the number of\ncorrespondencies; and next, in the laws of derivation,\nwhich, for the most part, appear to be common in their\noccurrence in proportion to the numerical simplicity of\ntheir expression. But the manifestation {72} of a governing\nnumerical relation in the organic world strikes us as more\nunexpected; and the selection of the number _five_ as the\nindex of the symmetry of dicotyledonous plants and radiated\nanimals, (a number which is nowhere symmetrically produced\nin inorganic bodies,) makes this a new and remarkable\nillustration of the constancy of numerical relations. We may\nobserve, however, that the moment one of these radiate\nanimals has one of its five members expanded, or in any way\npeculiarly modified, (as happens among the echini), it is\nreduced to the common type of animals simply symmetrical,\nwith a right and left side.\n\n5. It is not necessary to attempt to enumerate all the kinds\nof Symmetry, since our object is only to explain what\nSymmetry is, and for this purpose enough has probably been\nsaid already. It will be seen, as soon as the notion of\nSymmetry in general is well apprehended, that it is or\nincludes a peculiar Fundamental Idea, not capable of being\nresolved into any of the ideas hitherto examined. It may be\nsaid, perhaps, that the Idea of Symmetry is a modification\nor derivative of our ideas of space and number;--that a\nsymmetrical shape is one which consists of parts exactly\nsimilar, repeated a certain number of times, and placed so\nas to correspond with each other. But on further reflection\nit will be seen that this repetition and correspondence of\nparts in symmetrical figures are something peculiar; for it\nis not _any_ repetition or any correspondence of parts to\nwhich we should give the name of symmetry, in the manner in\nwhich we are now using the term. Symmetrical arrangements\nmay, no doubt, be concerned with space and position, time\nand number; but there appears to be implied in them a\nFundamental Idea of regularity, of completeness, of complex\nsimplicity, which is not a mere modification of other ideas.\n\n6. It is, however, not necessary, in this and in similar\ncases, to determine whether the idea which we have before us\nbe a peculiar and independent Fundamental Idea or a\nmodification of other ideas, provided we clearly perceive\nthe evidence of those Axioms by {73} means of which the Idea\nis applied in scientific reasonings. Now in the application\nof the Idea of Symmetry to crystallography, phytology and\nzoology, we must have this idea embodied in some principle\nwhich asserts more than a mere geometrical or numerical\naccordance of members. We must have it involved in some\nvital or productive action, in order that it may connect and\nexplain the facts of the organic world. Nor is it difficult\nto enunciate such a principle. We may state it in this\nmanner. _All the symmetrical members of a natural product\nare, under like circumstances, alike affected by the natural\nformative power._ The parts which we have termed\n_symmetrical_, resemble each other, not only in their form\nand position, but also in the manner in which they are\nproduced and modified by natural causes. And this principle\nwe assume to be necessarily true, however unknown and\ninconceivable may be the causes which determine the\nphenomena. Thus it has not yet been found possible to\ndiscover or represent to ourselves, in any intelligible\nmanner, the forces by which the various faces of a crystal\nare consequent upon its primary form: for the hypothesis of\ntheir being built up of integrant molecules, as Ha\u00fcy held,\ncannot be made satisfactory. But though the mechanism of\ncrystals is still obscure, there is no doubt as to the\nprinciple which regulates their modifications. The whole of\ncrystallography rests upon this principle, that if one of\nthe primary planes or axes be modified in any manner, all\nthe symmetrical planes and axes must be modified in the same\nmanner. And though accidental mechanical or other causes may\ninterfere with the actual exhibition of such faces, we do\nnot the less assume their crystallographical reality, as\ninevitably implied in the law of symmetry of the\ncrystal[3\\7]. And we apply similar considerations to\norganized beings. We assume that in a regular flower, each\nof the similar {74} members has the same organization and\nsimilar powers of developement; and hence if among these\nsimilar parts some are much less developed than others, we\nconsider them as _abortive_; and if we wish to remove doubts\nas to what are symmetrical members in such a case, we make\nthe inquiry by tracing the anatomy of these members, or by\nfollowing them in their earlier states of developement, or\nin cases where their capabilities are magnified by\nmonstrosity or otherwise. The power of developement may be\nmodified by external causes, and thus we may pass from one\nkind of symmetry to another; as we have already remarked.\nThus a regular flower with pentagonal symmetry, growing on a\nlateral branch, has one petal nearest to the axis of the\nplant: if this petal be more or less expanded than the\nothers, the pentagonal symmetry is interfered with, and the\nflower may change to a symmetry of another kind. But it is\neasy to see that all such conceptions of expansion,\nabortion, and any other kind of metamorphosis, go upon the\nsupposition of identical faculties and tendencies in each\nsimilar member, in so far as such tendencies have any\nrelation to the symmetry. And thus the principle we have\nstated above is the basis of that which, in the History, we\ntermed the Principle of Developed and Metamorphosed\nSymmetry.\n\n[Note 3\\7: Some crystalline forms, instead of being\n_holohedral_ (provided with their whole number of faces),\nare _hemihedral_ (provided with only half their number of\nfaces). But in these hemihedral forms the half of the faces\nare still _symmetrically_ suppressed.]\n\nWe shall not at present pursue the other applications of\nthis Idea of Symmetry, but we shall consider some of the\nresults of its introduction into Crystallography.\n\n\n\n{{75}}\nCHAPTER II.\n\nAPPLICATION OF THE IDEA OF SYMMETRY TO CRYSTALS.\n\n\n1. MINERALS and other bodies of definite chemical\ncomposition often exhibit that marked regularity of form and\nstructure which we designate by terming them _Crystals_; and\nin such crystals, when we duly study them, we perceive the\nvarious kinds of symmetry of which we have spoken in the\nprevious chapter. And the different kinds of symmetry which\nwe have there described are now usually distinguished from\neach other, by writers on crystallography. Indeed it is\nmainly to such writers that we are indebted for a sound and\nconsistent classification of the kinds and degrees of\nsymmetry of which forms are capable. But this classification\nwas by no means invented as soon as mineralogists applied\nthemselves to the study of crystals. These first attempts to\narrange crystalline forms were very imperfect; those, for\nexample, of Linn\u00e6us, Werner, Rom\u00e9 de Lisle, and Ha\u00fcy. The\nessays of these writers implied a classification at once\ndefective and superfluous. They reduced all crystals to one\nor other of certain _fundamental forms_; and this procedure\nmight have been a perfectly good method of dividing\ncrystalline forms into classes, if the fundamental forms had\nbeen selected so as to exemplify the different kinds of\nsymmetry. But this was not the case. Ha\u00fcy's fundamental or\n'primitive' forms, were, for instance, the following: the\n_parallelepiped_, the _octahedron_, the _tetrahedron_, the\n_regular hexagonal prism_, the _rhombic dodecahedron_, and\nthe _double hexagonal pyramid_. Of these, the _octahedron_,\nthe _tetrahedron_, the _rhombic dodecahedron_, all belong to\nthe {76} same kind of symmetry (the TESSULAR systems); also\nthe _hexagonal prism_ and the _hexagonal pyramid_ both\nbelong to the RHOMBIC system; while the _parallelepiped_ is\nso employed as to include all kinds of symmetry.\n\nIt is, however, to be recollected that Ha\u00fcy, in his\nselection of primitive forms, not only had an eye to the\nexternal form of the crystal and to its degree and kind of\nregularity, but also made his classification with an\nespecial reference to the _cleavage_ of the mineral, which\nhe considered as a primary element in crystalline analysis.\nThere can be no doubt that the cleavage of a crystal is one\nof its most important characters: it is a relation of form\nbelonging to the interior, which is to be attended to no\nless than the form of the exterior. But still, the cleavage\nis to be regarded only as determining the degree of\ngeometrical symmetry of the body, and not as defining a\nspecial geometrical figure to which the body _must_ be\nreferred. To have looked upon it in the latter light, was a\nmistake of the earlier crystallographic speculators, on\nwhich we shall shortly have to remark.\n\n2. I have said that the reference of crystals to Primitive\nForms might have been well employed as a mode of expressing\na just classification of them. This follows as a consequence\nfrom the application of the Principle stated in the last\nchapter, that _all symmetrical members are alike affected_.\nThus we may take an upright triangular prism as the\nrepresentative of the rhombic system, and if we then suppose\none of the upper edges to be cut off, or truncated, we must,\nby the Principle of Symmetry, suppose the other two upper\nedges to be truncated in precisely the same manner. By this\ntruncation we may obtain the upper part of a rhombohedron;\nand by truncations of the same kind, symmetrically affecting\nall the analogous parts of the figure, we may obtain any\nother form possessing three-membered symmetry. And the same\nis true of any of the other kinds of symmetry, provided we\nmake a proper selection of a fundamental form. And this was\nreally the method employed by Demeste, Werner, and Rom\u00e9 de\nLisle. They {77} assumed a Primitive Form, and then\nconceived other forms, such as they found in nature, to be\nderived from the Primitive Form by truncation of the edges,\nacumination of the corners, and the like processes. This\nmode of conception was a perfectly just and legitimate\nexpression of the general Idea of Symmetry.\n\n3. The true view of the degrees of symmetry was, as I have\nalready said, impeded by the attempts which Ha\u00fcy and others\nmade to arrive at primitive forms by the light which\ncleavage was supposed to throw upon the structure of\nminerals. At last, however, in Germany, as I have narrated\nin the History of Mineralogy[4\\7], Weiss and Mohs introduced\na classification of forms implying a more philosophical\nprinciple, dividing the forms into Systems; which, employing\nthe terms of the latter writer, we shall call the\n_tessular_, the _pyramidal_ or _square pyramidal_, the\n_prismatic_ or _oblong_, and the _rhombohedral_ systems.\n\n[Note 4\\7: _Hist. Ind. Sc._ b. xv. c. iv.]\n\nOf these forms, the three latter may be at once referred to\nthose kinds of symmetry of which we have spoken in the last\nchapter. The _rhombohedral_ system has _triangular_\nsymmetry, or is three-membered: the _pyramidal_ has _square_\nsymmetry, or is four-membered: the _prismatic_ has _oblong_\nsymmetry, and is two-and-two-membered. But the kinds of\nsymmetry which were spoken of in the former chapter, do not\nexhaust the idea when applied to minerals. For the symmetry\nwhich was there explained was such only as can be exhibited\non a surface, whereas the forms of crystals are solid. Not\nonly have the right and left parts of the upper surface of a\ncrystal relations to each other; but the upper surface and\nthe lateral faces of the crystal have also their relations;\nthey may be different, or they may be alike. If we take a\ncube, and hold it so that four of its faces are vertical,\nnot only are all these four sides exactly similar, so as to\ngive square symmetry; but also we may turn the cube, so that\nany one of these four sides shall become the top, and still\nthe four sides which are thus made vertical, though {78} not\nthe same which were vertical before, are still perfectly\nsymmetrical. Thus this cubical figure possesses more than\nsquare symmetry. It possesses square symmetry in a vertical\nas well as in a horizontal sense. It possesses a symmetry\nwhich has the same relation to a _cube_ which four-membered\nsymmetry has to a _square_. And this kind of symmetry is\ntermed the _cubical_ or _tessular_ symmetry. All the other\nkinds of symmetry have reference to an axis, about which the\ncorresponding parts are disposed; but in tessular symmetry\nthe horizontal and vertical axes are also symmetrical, or\ninterchangeable; and thus the figure may be said to have no\naxis at all.\n\n4. It has already been repeatedly stated that, by the very\nidea of symmetry, all the incidents of form must affect\nalike all the corresponding parts. Now in crystals we have,\namong these incidents, not only external figure, but\n_cleavage_, which may be considered as internal figure.\nCleavage, then, must conform to the degree of symmetry of\nthe figure. Accordingly cleavage, no less than form, is to\nbe attended to in determining to what system a mineral\nbelongs. If a crystal were to occur as a square prism or\npyramid, it would not on that account necessarily belong to\nthe square pyramidal system. If it were found that it was\ncleavable parallel to one side of the prism, but not in the\ntransverse direction, it has only oblong symmetry; and the\nequality of the sides which makes it square is only\naccidental.\n\nThus no cleavage is admissible in any system of\ncrystallization which does not agree with the degree of\nsymmetry of the system. On the other hand, _any_ cleavage\nwhich _is_ consistent with the symmetry of the system, is\n(hypothetically at least) allowable. Thus in the oblong\nprismatic system we may have a cleavage parallel to one side\nonly of the prism; or parallel to both, but of different\ndistinctness; or parallel to the two diagonals of the prism\nbut of the same distinctness; or we may have both these\ncleavages together. In the rhombohedral system, the cleavage\nmay be parallel to the sides of the rhombohedron, as in Calc\n{79} Spar: or, in the same system, the cleavage, instead of\nbeing thus oblique to the axis, may be along the axis in\nthose directions which make equal angles with each other:\nthis cleavage easily gives either a triangular or a\nhexagonal prism. Again, in the tessular system, the cleavage\nmay be parallel to the surface of the cube, which is thus\nreadily separable into other cubes, as in Galena; or the\ncleavage may be such as to cut off the solid angle of the\ncube, and since there are eight of these, such cleavage\ngives us an octahedron, which, however, may be reduced to a\ntetrahedron, by rejecting all parallel faces, as being mere\nrepetitions of the same cleavage; this is the case with\nFluor Spar: or the cube of the tessular system may be\ncleavable in planes which truncate all the edges of the\ncube; and as these are twelve, we thus obtain the\ndodecahedron with rhombic faces: this occurs in Zinc Blende.\nAnd thus we see the origin of Ha\u00fcy's various primitive\nforms, the tetrahedron, octahedron, and rhombic\ndodecahedron, all belonging to the tessular system:--they\nare, in fact, different cleavage forms of that system.\n\n5. I do not dwell upon other incidents of crystals which\nhave reference to form, nor upon the lustre, smoothness, and\nstriation of the surfaces. To all such incidents the general\nprinciple applies, that similar parts are similarly\naffected; and hence, if any parts are found to be constantly\nand definitely different from other parts of the same sort,\nthey are not similar parts; and the symmetry is to be\ninterpreted with reference to this difference.\n\nWe have now to consider the inferences which have been drawn\nfrom these incidents of crystallization, with regard to the\nintimate structure of bodies.\n\n\n\n{{80}}\nCHAPTER III.\n\nSPECULATIONS FOUNDED UPON THE SYMMETRY OF CRYSTALS.\n\n\n1. WHEN a crystal, as, for instance, a crystal of Galena,\n(sulphuret of lead,) is readily divisible into smaller\ncubes, and these into smaller ones, and so on without limit,\nit is very natural to represent to ourselves the original\ncube as really consisting of small cubical elements; and to\nimagine that it is a philosophical account of the physical\nstructure of such a substance to say that it is made up of\ncubical molecules. And when the Galena crystal has\nexternally the form of a cube, there is no difficulty in\nsuch a conception; for the surface of the crystal is also\nconceived as made up of the surfaces of its cubical\nmolecules. We conceive the crystal so constituted, as we\nconceive a wall built of bricks.\n\nBut if, as often happens, the Galena crystal be an\noctahedron, a further consideration is requisite in order to\nunderstand its structure, pursuing still the same\nhypothesis. The mineral is still, as in the other case,\nreadily cleavable into small cubes, having their corners\nturned to the faces of the octahedron. Therefore these faces\ncan no longer be conceived as made up of the faces of\ncubical elements of which the whole is constituted. If we\nsuppose a pile of such small cubes to be closely built\ntogether, but with decreasing width above, so as to form a\npyramid, the face of such a pyramid will no longer be plane;\nit will consist of a great number of the corners or edges of\nthe small elementary cubes. It would appear at first sight,\ntherefore, that such a face cannot represent the smooth\npolished surface of a crystal. {81}\n\nBut when we come to look more closely, this difficulty\ndisappears. For how large are these elementary cubes? We\ncannot tell, even supposing they really have any size. But\nwe know that they must be, at any rate, very small; so small\nas to be inappreciable by our senses, for our senses find no\nlimit to the divisibility of minerals by cleavage. Hence the\nsurface of the pyramid above described would not consist of\nvisible corners or edges, but would be roughened by specks\nof imperceptible size; or rather, by supposing these specks\nto become still smaller, the roughness becomes smoothness.\nAnd thus we may have a crystal with a smooth surface, made\nup of small cubes in such a manner that their surfaces are\nall oblique to the surface of the crystal.\n\nHa\u00fcy, struck by some instances in which the supposition of\nsuch a structure of crystals appeared to account happily for\nseveral of their relations and properties, adopted and\npropounded it as a general theory. The small elements, of\nwhich he supposed crystals to be thus built up, he termed\n_integrant molecules_. The form of these molecules might or\nmight not be the same as the _primitive form_ with which his\nconstruction was supposed to begin; but there was, at any\nrate, a close connexion between these forms, since both of\nthem were founded on the cleavage of the mineral. The tenet\nthat crystals are constituted in the manner which I have\nbeen describing, I shall call the _Theory of Integrant\nMolecules_, and I have now to make some remarks on the\ngrounds of this theory.\n\n2. In the case of which I have spoken, the mineral used as\nthe example, Galena, readily splits into cubes, and cubes\nare easily placed together so as to fit each other, and fill\nthe space which they occupy. The same is the case in the\nmineral which suggested to Ha\u00fcy his theory, namely, Calc\nSpar. The crystals of this substance are readily divisible\ninto rhombohedrons, a form like a brick with oblique angles;\nand such bricks can be built together so as to produce\ncrystals of all the immense varieties of form which Calc\nSpar presents. This kind of masonry is equally possible in\nmany other {82} minerals; but as we go through the mineral\nkingdom in our survey, we soon find cases which offer\ndifficulties. Some minerals cleave only in two directions,\nsome in one only; in such cases we cannot by cleavage obtain\nan integrant molecule of definite form; one of its\ndimensions, at least, must remain indeterminate and\narbitrary. Again, in some instances, we have more than three\ndifferent planes of cleavage, as in Fluor Spar, where we\nhave four. The solid, bounded by four planes, is a\ntetrahedron; or if we take four _pairs_ of parallel faces,\nan octahedron. But if we attempt to take either of these\nforms for our integrant molecule, we are met by this\ndifficulty: that a collection of such forms will not fill\nspace. Perhaps this difficulty will be more readily\nconceived by the general reader if it be contemplated with\nreference to plane figures. It will readily be seen that a\nnumber of equal squares may be put together so as to fill\nthe space which they occupy; but if we take a number of\nequal regular octagons, we may easily convince ourselves\nthat no possible arrangement can make them cover a flat\nspace without leaving blank spots between. In like manner\noctahedrons or tetrahedrons cannot be arranged in solid\nspace so as to fill it. They necessarily leave vacancies.\nHence the structure of Fluor Spar, and similar crystals, was\na serious obstacle in the way of the theory of integrant\nmolecules. That theory had been adopted in the first\ninstance because portions of the crystal, obtained by\ncleavage, could be built up into a solid mass; but this\nground of the theory failed altogether in such instances as\nI have described, and hence the theory, even upon the\nrepresentations of its adherents, had no longer any claim to\nassent.\n\nThe doctrine of Integral Molecules, however, was by no means\ngiven up at once, even in such instances. In this and in\nother subjects, we may observe that a theory, once\nconstructed and carried into detail, has such a hold upon\nthe minds of those who have been in the habit of applying\nit, that they will attempt to uphold it by introducing\nsuppositions inconsistent with {83} the original foundations\nof the theory. Thus those who assert the Atomic Theory,\nreconcile it with facts by taking the _halves of atoms_; and\nthus the Theory of Integrant Molecules was maintained for\nFluor Spar, by representing the elementary octahedrons of\nwhich crystals are built up, as touching each other only by\nthe _edges_. The contact of surface with surface amongst\nintegrant molecules had been the first basis of the theory;\nbut this supposition being here inapplicable, was replaced\nby one which made the theory no longer a representation of\nthe facts (the cleavages), but a mere geometrical\nconstruction. Although, however, the inapplicability of the\ntheory to such cases was thus, in some degree, disguised to\nthe disciples of Ha\u00fcy, it was plain that, in the face of\nsuch difficulties, the Theory of Integrant Molecules could\nnot hold its place as a philosophical truth. But it still\nanswered the purpose (a very valuable one, and one to which\ncrystallography is much indebted,) of an instrument for\ncalculating the geometrical relations of the parts of\ncrystals to each other: for the integrant molecules were\nsupposed to be placed layer above layer, each layer as we\nascend, _decreasing_ by a certain number of molecules and\nrows of molecules; and the calculation of these _laws of\ndecrement_ was, in fact, the best mode then known of\ndetermining the positions of the faces. The Theory of\nDecrements served to express and to determine, in a great\nnumber of the most obvious cases, _the laws of phenomena_ in\ncrystalline forms, though the Theory of Integrant Molecules\ncould not be maintained as a just view of the structure of\ncrystals.\n\n3. The Theory of Integrant Molecules, however, involved this\njust and important principle: that a true view of the\nintimate structure of crystals must include and explain the\nfacts of crystallization, that is, crystalline form and\ncleavage; and that it must take these into account,\naccording to their degree of _Symmetry_. So far all theories\nconcerning the elements of crystals must agree. And it was\nsoon seen that this was, in reality, all that had been\nestablished by the investigations of Ha\u00fcy and his school. I\nhave already, in the {84} _History_, quoted Weiss's\nreflections on making this step. 'When in 1809,' he\nsays[5\\7], 'I published my Dissertation, I shared the common\nopinion as to the necessity of the assumption, and the\nreality of the existence of a primitive form, at least in a\nsense not very different from the usual sense of the\nexpression.' He then proceeds to relate that he sought a\nground for such an opinion, independent of the doctrine of\n_Atoms_, which he, in common with a great number of\nphilosophers of that time in his own country, was disposed\nto reject, inclining to believe that the properties of\nbodies were determined by _Forces_ which acted in them, and\nnot by _Molecules_ of which they were composed. He adds,\nthat in pursuing this train of thought, he found, 'that out\nof his Primitive Forms there was gradually unfolded to his\nhands that which really governs them, and is not affected by\ntheir casual fluctuations; namely, the Fundamental Relations\nof their Dimensions,' or as we now may call them, _Axes of\nSymmetry_. With reference to these Axes, he found, as he\ngoes on to say, that 'a multiplicity of internal\nOppositions, necessarily and mutually interdependent, are\ndeveloped in the crystalline mass, each Relation having its\nown Polarity; so that the Crystalline Character is\nco-extensive with these Polarities.' The character of these\npolarities, whether manifested in crystalline faces,\ncleavage, or any other incidents of crystallization, is\nnecessarily displayed in the degree and kind of Symmetry\nwhich the crystal possesses: and thus this Symmetry, in all\nour speculations concerning the structure of crystals,\nnecessarily takes the place of that enumeration of Primitive\nForms which were rejected as inconsistent with observed\nfacts, and destitute of sound scientific principle.\n\n[Note 5\\7: _Acad. Berlin._ 1816, p. 307.]\n\nI may just notice here what I have stated in the History of\nMineralogy[6\\7], that the distinction of systems of\ncrystallization, as introduced by Weiss and Mohs, was\nstrikingly confirmed by Sir David Brewster's discoveries\nrespecting the optical properties of minerals. {85} The\nsplendid phenomena which were produced by passing polarized\nlight through crystals, were found to vary according as the\ncrystals were of the Rhombohedral, Square Pyramidal, Oblong\nPrismatic, or Tessular System. The Optical Symmetry exactly\ncorresponded with the Geometrical Symmetry. In the two\nformer Systems were crystals _uniaxal_ in respect of their\noptical properties; the oblong prismatic, was _biaxal_;\nwhile in the tessular, the want of a predominant axis\nprevented the phenomena here spoken of from occurring at\nall. The optical experiments must have led, and would have\nled, to a classification of crystals into the above systems\nor something nearly equivalent, even had they not been\nalready so arranged by attention to their forms.\n\n[Note 6\\7: _Hist. Ind. Sc._ b. xv. c. v.]\n\n4. While in Germany Weiss and Mohs with their disciples,\nwere gradually rejecting what was superfluous in the\nprevious crystallographical hypotheses, philosophers in\nEngland were also trying to represent to themselves the\nconstitution of crystals in a manner which should be free\nfrom the obviously arbitrary and untenable fictions of the\nHa\u00fcyian school. These attempts, however, were not crowned\nwith much success. One mode of representing the structure of\ncrystals which suggested itself, was to reject the\npolyhedral forms which Ha\u00fcy gave to his integrant molecules,\nand to conceive the elements of crystals as _spheres_, the\nproperties of the crystal being determined not by the\n_surfaces_, but by the _position_ of the elements. This was\ndone by Wollaston, in the _Philosophical Transactions_ for\n1813. He applied this view to the tessular system, in which,\nindeed, the application is not difficult; and he showed that\noctahedral and tetrahedral figures may be deduced from\nsymmetrical arrangements of equal spherules. But though in\ndoing this, he manifested a perception of the conditions of\nthe problem, he appeared to lose his hold on the real\nquestion when he tried to pass on to other systems of\ncrystallization. For he accounted for the rhombohedral\nsystem by supposing the spheres changed into _spheroids_.\nSuch a procedure involved him in a gratuitous and useless\nhypothesis: for to what purpose do we introduce the {86}\narrangement of atoms (instead of their figure,) as a mode of\nexplaining the symmetry of the crystallization, when at the\nnext step we ascribe to the atom, by an arbitrary fiction, a\nsymmetry of figure of the same kind as that which we have to\nexplain? It is just as easy, and as allowable, to assume an\nelementary rhombohedron, as to assume elementary spheroids,\nof which the rhombohedrons are constructed.\n\n5. Many hypotheses of the same kind might be adduced,\ndevised both by mineralogists and chemists. But almost all\nsuch speculations have been pursued with a most surprising\nneglect of the principle which obviously is the only sound\nbasis on which they can proceed. The principle is\nthis:--that _All hypotheses concerning the arrangement of\nthe elementary atoms of bodies in space must be constructed\nwith reference to the general facts of crystallization_. The\ntruth and importance of this principle can admit of no\ndoubt. For if we make any hypothesis concerning the mode of\nconnexion of the elementary particles of bodies, this must\nbe done with the view of representing to ourselves the\nforces which connect them, and the results of these forces\nas manifested in the properties of the bodies. Now the\nforces which connect the particles of bodies so as to make\nthem crystalline, are manifestly chemical forces. It is only\ndefinite chemical compounds which crystallize; and in\ncrystals the force of cohesion by which the particles are\nheld together cannot in any way be distinguished or\nseparated from the chemical force by which their elements\nare combined. The elements are understood to be combined,\nprecisely because the result is a definite, apparently\nhomogeneous substance. The properties of the compound bodies\ndepend upon the elements and their mode of combination; for,\nin fact, these include everything on which they can depend.\nThere are no other circumstances than these which can affect\nthe properties of a body. Therefore all those properties\nwhich have reference to space, namely, the crystalline\nproperties, cannot depend upon anything else than the\narrangement of the elementary molecules in space. These {87}\nproperties are the facts which any hypothesis of the\narrangement of molecules must explain, or at least render\nconceivable; and all such hypotheses, all constructions of\nbodies by supposed arrangements of molecules, can have no\nother philosophical object than to account for facts of this\nkind. If they do not do this, they are mere arbitrary\ngeometrical fictions, which cannot be in any degree\nconfirmed or authorised by an examination of nature, and are\ntherefore not deserving of any regard.\n\n6. Those philosophers who have endeavoured to represent the\nmode in which bodies are constructed by the combination of\ntheir chemical atoms, have often undertaken to show, not\nonly that the atoms are combined, but also in what positions\nand configurations they are combined. And it is truly\nremarkable, as I have already said, that they have done\nthis, almost in every instance, without any consideration of\nthe crystalline character of the resulting combinations;\nfrom which alone we receive any light as to the relation of\ntheir elements in space. Thus Dr. Dalton, in his _Elements\nof Chemistry_, in which he gave to the world the Atomic\nTheory as a representation of the doctrine of definite and\nmultiple proportions, also published a large collection of\nDiagrams, exhibiting what he conceived to be the\nconfiguration of the atoms in a great number of the most\ncommon combinations of chemical elements. Now these\nhypothetical diagrams do not in any way correspond, as to\nthe nature of their symmetry, with the compounds, as we find\nthem displaying their symmetry when they occur crystallized.\nCarbonate of lime has in reality a triangular symmetry,\nsince it belongs to the rhombohedral system; Dr. Dalton's\ncarbonate of lime would be an oblique rhombic prism or\npyramid. Sulphate of baryta is really two-and-two membered;\nDr. Dalton's diagram makes it two-and-one membered. Alum is\nreally octahedral or tessular; but according to the diagram\nit could not be so, since the two ends of the atom are not\nsymmetrical. And the same want of correspondence between the\nfacts and the hypothesis runs through the whole {88} system.\nIt need not surprise us that the theoretical arrangement of\natoms does not explain the facts of _crystallization_; for\nto produce such an explanation would be a second step in\nscience quite as great as the first, the discovery of the\natomic theory in its _chemical_ sense. But we may allow\nourselves to be surprised that an utter discrepance between\nall the facts of crystallization and the figures assumed in\nthe theory, did not suggest any doubt as to the soundness of\nthe mode of philosophizing by which this part of the theory\nwas constructed.\n\n7. Some little accordance between the hypothetical\narrangements of chemical atoms and the facts of\ncrystallization, does appear to have been arrived at by some\nof the theorists to whom we here refer, although by no means\nenough to show a due conviction of the importance of the\nprinciple stated above. Thus Wollaston, in the Essay above\nnoticed, after showing that a symmetrical arrangement of\nequal spherules would give rise to octahedral and other\ntessular figures, remarks, very properly, that the metals,\nwhich are simple bodies, crystallize in such forms. M.\nAmp\u00e8re[7\\7] also, in 1814, published a brief account of an\nhypothesis of a somewhat similar nature, and stated himself\nto have developed this speculation in a Memoir which has not\nyet, so far as I am aware, been published. In this notice he\nconceives bodies to be compounded of _molecules_, which,\narranged in a polyhedral form, constitute _particles_. These\n_representative forms_ of the particles depend on chemical\nlaws. Thus the particles of oxygen, of hydrogen, and of\nazote, are composed each of four molecules. Hence it is\ncollected that the particles of nitrous gas are composed of\ntwo molecules of oxygen and two of azote; and similar\nconclusions are drawn respecting other substances. These\nconclusions, though expressed by means of the polyhedrons\nthus introduced, are supported by chemical, rather than by\ncrystallographical comparisons. The author does, indeed,\nappeal to the crystallization of sal {89} ammoniac as an\nargument[8\\7]; but as _all_ the forms which he introduces\nappear to belong to the _tessular_ system of\ncrystallization, there is, in his reasonings, nothing\ndistinctive; and therefore nothing, crystallographically\nspeaking, of any weight on the side of this theory.\n\n[Note 7\\7: _Ann. de Chimie_, tom. xc. p. 43.]\n\n[Note 8\\7: _Ann. de Chimie_, tom. xc. p. 83.]\n\n8. Any hypothesis which should introduce any principle of\nchemical order among the actual forms of minerals, would\nwell deserve attention. At first sight, nothing can appear\nmore anomalous than the forms which occur. We have, indeed,\none broad fact, which has an encouraging aspect, the\ntessular forms in which the pure metals crystallize. The\nhighest degree of chemical and of geometrical simplicity\ncoincide: irregularity disappears precisely where it is\nexcluded by the consideration above stated, that the\nsymmetry of chemical composition must determine the symmetry\nof crystalline form[9\\7].\n\n[Note 9\\7: Inasmuch as this law, that the simple metals\ncrystallize in tessular forms, is the most signal example of\nthat connexion between the chemical nature of a body and its\ncrystalline form, I in the former Edition stated it with as\nmuch generality as I could find any ground for, and I should\nhave been glad if I could have added confirmation of the\nlaw, derived from later observations. But the most recent\ninvestigations of crystallographers appear to have afforded\nexceptions rather than examples of the rule. Arsenic and\nTellurium are said to be _rhombohedral_. Antimony, stated by\nHa\u00fcy to be octahedral (and therefore tessular), has been\nfound by more modern observers to be _rhombohedral_. Tin has\nbeen obtained by Professor Miller in beautiful crystals\nbelonging to the _pyramidal_ system. Professor N\u00f6ggerath has\nobserved in Zinc, after cooling from fusion, hexagonal\ncleavage, rendering it probable that the mineral\ncrystallized in _rhombohedrons_ having their axes vertical,\nlike ice. G. Rose conceives it highly probable that Osmium\nand Iridium are _rhombohedral_. (Poggendorf. Bd. liv.)\n\nBut all the more perfect metals are tessular; namely, Gold,\nSilver, Mercury, Platinum, Iron, Copper; also Bismuth [?]\nPerhaps the observation in which the crystallization of Zinc\nis affected by its position is, on that very account, no\nsufficient evidence of its free crystallization. We can\nhardly conceive a collection of perfectly simple, similar\nparticles to crystallize so as to have one pre-eminent axis,\nwithout some extraneous action affecting them.]\n\nBut if we go on to any other class of crystalline forms, we\nsoon find ourselves lost in our attempts to {90} follow any\nthread of order. We have indeed many large groups connected\nby obvious analogies; as the rhombohedral carbonates of\nlime, magnesia, iron, manganese;--the prismatic carbonates\nand sulphates of lime, baryta, strontia, lead. But even in\nthese, we cannot form any plausible hypothesis of the\narrangement of the elements; and in other cases to which we\nnaturally turn, we can find nothing but confusion. For\ninstance, if we examine the oxides of metals:--those of iron\nare rhombohedral and tessular; those of copper, tessular;\nthose of tin, of titanium, of manganese, square pyramidal;\nthose of antimony, prismatic; and we have other forms for\nother substances.\n\nIt may be added, that if we take account of the optical\nproperties which, as we have already stated, have constant\nrelations to the crystalline forms, the confusion is still\nfurther increased; for the optical dimensions vary in\namount, though not in symmetry, where chemistry can trace no\ndifference of composition.\n\n9. We will not quit the subject, however, without noticing\nthe much more promising aspect which it has assumed by the\ndetection of such groups as are referred to in the last\narticle; or in other words, by Mitscherlich's discovery of\n_Isomorphism_. According to that discovery, there are\nvarious elements which may take the place of each other in\ncrystalline bodies, either without any alteration of the\ncrystalline form, or at most with only a slight alteration\nof its dimensions. Such a group of elements we have in the\nearths lime and magnesia, the protoxides of iron and\nmanganese: for the carbonates of all these bases occur\ncrystallized in forms of the rhombohedral system, the\ncharacteristic angle being nearly the same in all. Now lime\nand magnesia, by the discoveries of modern chemistry, are\nreally oxides of metals; and therefore all these carbonates\nhave a similar chemical constitution, while they have also a\nsimilar crystalline form. Whether or no we can devise any\narrangement of molecules by which this connexion of the\nchemical and the geometrical property can be represented, we\ncannot help {91} considering the connexion as an extremely\nimportant fact in the constitution of bodies; and such facts\nare more likely than any other to give us some intelligible\nview of the relations of the ultimate parts of bodies. The\nsame may be said of all the other isomorphous or\nplesiomorphous groups[10\\7]. For instance, we have a number\nof minerals which belong to the same system of\ncrystallization, but in which the chemical composition\nappears at first sight to be very various: namely, spinelle,\npleonaste, gahnite, franklinite, chromic iron oxide,\nmagnetic iron oxide: but Abich has shown that all these may\nbe reduced to a common chemical formula;--they are bioxides\nof one set of bases, combined with trioxides of another set.\nPerhaps some mathematician may be able to devise some\ngeometrical arrangement of such a group of elements which\nmay possess the properties of the tessular system.\nHypothetical arrangements of atoms, thus expressing both the\nchemical and the crystalline symmetry which we know to\nbelong to the substance, would be valuable steps in\nanalytical science; and when they had been duly verified,\nthe hypotheses might easily be divested of their atomic\ncharacter.\n\n[Note 10\\7: See _Hist. Ind. Sc._ b. xv. c. vi.]\n\nThus, as we have already said, mineralogy, understood in its\nwider sense, as the counterpart of chemistry, has for one of\nits main objects to discover those Relations of the Elements\nof bodies which have reference to Space. In this research,\nthe foundation of all sound speculation is the kind and\ndegree of Symmetry of form which we find in definite\nchemical compounds: and the problem at present before the\ninquirer is, to devise such arrangements of molecules as\nshall answer the conditions alike of Chemistry and of\nCrystallography.\n\nWe now proceed to the Classificatory Sciences, of which\nMineralogy is one, though hitherto by far the least\nsuccessful.\n\n\n\n{{93}}\nBOOK VIII.\n\n\nTHE\nPHILOSOPHY\nOF THE\nCLASSIFICATORY SCIENCES.\n\n\n\n\nWHERE a certain apparent difference between things (although\nperhaps in itself of little moment) answers to we know not\nwhat number of other differences, pervading not only their\nknown properties but properties yet undiscovered, it is not\noptional but imperative to recognise this difference as the\nfoundation of a specific distinction.\n\nJOHN S. MILL, _System of Logic_, b. 1, ch. vii. \u00a7 4.\n\n\n\n{{95}}\nBOOK VIII.\n\n\nTHE PHILOSOPHY OF THE CLASSIFICATORY SCIENCES.\n\n\nCHAPTER I.\n\nTHE IDEA OF LIKENESS AS GOVERNING THE USE OF COMMON NAMES.\n\n\n1. _Object of the Chapter._--NOT only the Classificatory\nSciences, but the application of names to things in the\nrudest and most unscientific manner, depends upon our\napprehending them as _like_ each other. We must therefore\nendeavour to trace the influence and operation of the Idea\nof Likeness in the common use of language, before we speak\nof the conditions under which it acquires its utmost\nexactness and efficacy.\n\nIt will be my object to show in this, as in previous cases,\nthat the impressions of sense are apprehended by acts of the\nmind; and that these mental acts necessarily imply certain\nrelations which may be made the subjects of speculative\nreasoning. We shall have, if we can, to seize and bring into\nclear view the principles which the relation of _like_ and\n_unlike_ involves, and the mode in which these principles\nhave been developed.\n\n2. _Unity of the Individual._--But before we can attend to\nseveral things as like or unlike, we must be able to\napprehend each of these by itself as _one thing_. {96} It\nmay at first sight perhaps appear that this apprehension\nresults immediately from the impressions on our senses,\nwithout any act of our thoughts. A very little attention,\nhowever, enables us to see that thus to single out special\nobjects requires a mental operation as well as a sensation.\nHow, for example, without an exertion of mental activity,\ncan we see one tree, in a forest where there are many? We\nhave, spread before us, a collection of colours and forms,\ngreen and brown, dark and light, irregular and straight:\nthis is all that sensation gives or can give. But we\nassociate one brown trunk with one portion of the green\nmass, excluding the rest, although the neighbouring leaves\nare both nearer in contiguity and more similar in appearance\nthan is the stem. We thus have before us one tree; but this\nunity is given by the mind itself. We see the green and the\nbrown, but we must _make_ the tree before we can see _it_.\n\nThat this composition of our sensations so as to form _one\nthing_ implies an act of our own, will perhaps be more\nreadily allowed, if we once more turn our attention to the\nmanner in which we sometimes attempt to imitate and record\nthe objects of sight, by drawing. When we do this, as we\nhave already observed, we mark this unity of each object, by\ndrawing a line to separate the parts which we include from\nthose which we exclude;--an _Outline_. This line corresponds\nto nothing which we see; the beginner in drawing has great\ndifficulty in discerning it; he has in fact to make it. It\nis, as has been said by a painter of our own time[1\\8], a\nfiction: but it is a fiction employed to mark a real act of\nthe mind; to designate the singleness of the object in our\nconception. As we have said elsewhere, we see lines, but\nespecially outlines, by mentally drawing them ourselves.\n\n[Note 1\\8: Phillips _On Painting_,--Design.]\n\nThe same act of conception which the outline thus represents\nand commemorates in visible objects,--the same combination\nof sensible impressions into a unit,--is exercised also with\nregard to the objects of all {97} our senses: and the\nsingleness thus given to each object, is a necessary\npreliminary to its being named or represented in any other\nway.\n\nBut it may be said, Is it then by an arbitrary act of our\nown that we put together the branches of the same tree, or\nthe limbs of the same animal? Have we equally the power and\nthe right to make the branch of the fir a part of the\nneighbouring oak? Can we include in the outline of a man any\nobject with which he happens to be in contact?\n\nSuch suppositions are manifestly absurd. And the answer is,\nthat though we give unity to objects by an act of thought,\nit is not by an _arbitrary_ act; but by a process subject to\ncertain conditions;--to conditions which exclude such\nincongruous combinations as have just been spoken of.\n\nWhat are these conditions which regulate our apprehension of\nan object as one?--which determine what portion of our\nimpressions does, and what portion does not belong to the\nsame thing?\n\n3. _Condition of Unity._--I reply, that the primary and\nfundamental condition is, that we must be able to make\nintelligible assertions respecting the object, and to\nentertain that belief of which assertions are the\nexposition. A tree _grows_, _sheds_ its leaves in autumn,\nand _buds_ again in the spring, _waves_ in the wind, or\n_falls_ before the storm. And to the tree belong all those\nparts which must be included in order that such\ndeclarations, and the thought which they convey, shall have\na coherent and permanent meaning. Those are _its_ branches\nwhich wave and fall with _its_ trunk; those are _its_ leaves\nwhich grow on _its_ branches. The permanent connexions which\nwe observe,--permanent, among unconnected changes which\naffect the surrounding appearances,--are what we bind\ntogether as belonging to one object. This permanence is the\ncondition of our conceiving the object _as_ one. The\nconnected changes may always be described by means of\nassertions; and the connexion is seen in the identity of the\nsubject of successive predications; in the possibility of\napplying many verbs to one substantive. We may {98}\ntherefore express the condition of the unity of an object to\nbe this: that _assertions concerning the object shall be\npossible_: or rather we should say, that the acts of belief\nwhich such assertions enunciate shall be possible.\n\nIt may seem to be superfluous to put in a form so abstract\nand remote, the grounds of a process apparently so simple as\nour conceiving an object to be one. But the same condition\nto which we have thus been led, as the essential principle\nof the unity of objects, namely, that propositions shall be\npossible, will repeatedly occur in the present chapter; and\nit may serve to illustrate our views, to show that this\ncondition pervades even the simplest cases.\n\n4. _Kinds._--The mental synthesis of which we have thus\nspoken, gives us our knowledge of _individual_ things; it\nenables me to apprehend that particular tree or man which I\nnow see, or, by the help of memory, the tree or the man I\nsaw yesterday. But the knowledge with which we have mainly\nhere to do is not a knowledge of individuals but of kinds;\nof such classes as are indicated by common names. We have to\nmake assertions concerning a tree or a man in general,\nwithout regarding what is peculiar to this man or that tree.\n\nNow it is clear that certain individual objects are all\ncalled _man_, or all called _tree_, in virtue of some\nresemblance which they have. If we had not the power of\nperceiving in the appearances around us, likeness and\nunlikeness, we could not consider objects as distributed\ninto kinds at all. The impressions of sense would throng\nupon us, but being uncompared with each other, they would\nflow away like the waves of the sea, and each vanish from\nour contemplation when the sensation faded. That we do\napprehend surrounding objects as belonging to permanent\nkinds, as being men and horses, oaks and roses, arises from\nour having the idea of likeness, and from our applying it\nhabitually, and so far as such a classification requires.\n\nNot only can we employ the idea of likeness in this manner,\nbut we apply it incessantly and universally to {99} the\nwhole mass and train of our sensations. For we have no\nexternal sensations to which we cannot apply some language\nor other; and all language necessarily implies recognition\nof resemblances. We cannot call an object _green_ or _round_\nwithout comparing in our thoughts its colour or its shape,\nwith a shape and a colour seen in other objects. All our\nsensations, therefore, without any exception of kind or\ntime, are subject to this constant process of\nclassification; and the idea of likeness is perpetually\noperating to distribute them into kinds, at least so far as\nthe use of language requires.\n\nWe come then again to the question, Upon what principle,\nunder what conditions, is the Idea of Likeness thus\noperative? What are the limits of the classes thus formed?\nWhere does that similarity end, which induces and entitles\nus to call a thing a _tree_? What universal rule is there\nfor the application of common names, so that we may not\napply them wrongly?\n\n5. _Not made by Definitions._--Perhaps some one might expect\nin answer to these inquiries a definition or a series of\ndefinitions;--might imagine that some description of a tree\nmight be given which might show when the term was applicable\nand when it was not; and that we might construct a body of\nrules to which such descriptions must conform. But on\nconsideration it will be clear that the real solution of our\ndifficulty cannot be obtained in such a manner. For _first_;\nsuch descriptions must be given in words, and must therefore\nsuppose that we have already satisfied ourselves how words\nare to be used. If we define a tree to be 'a living thing\nwithout the power of voluntary motion,' we shall be called\nupon to define 'a living thing;' and it is manifest that\nthis renewal of the demand for definition might be repeated\nindefinitely; and, therefore, we cannot in this way come to\na final principle. And in the _next_ place, most of those\nwho use language, even with great precision and consistency,\nwould find it difficult or impossible to give good\ndefinitions even of a few of the general names which they\nuse; and therefore their practice cannot be regulated by any\n{100} tacit reference to such definitions. That definitions\nof terms are of great use and importance in their right\nplace, we shall soon see; but their place is not to regulate\nthe use of common language.\n\nWhat then, once more, is this regulative principle? What\nrules do men follow in the use of words, so as commonly to\navoid confusion and ambiguity? How do they come to\nunderstand each other so well as they ordinarily do,\nrespecting the limits of classes never defined, and which\nthey cannot define? What is the common Convention, or\nCondition to which they conform?\n\n6. _Condition of the Use of Terms._--To this we reply, that\nthe Condition which regulates the use of language, is, that\nit shall be capable of being used;--that is, that general\nassertions shall be possible. The term _tree_ is applicable\nas far as it is useful in expressing our knowledge\nconcerning trees:--thus we know that trees are fixed in the\nground, have a solid stem, branches, leaves, and many other\nproperties. With regard to all the objects which surround\nus, we have an immense store of knowledge of such\nproperties, and we employ the names of the objects in such a\nmanner as enables us to express these properties.\n\nBut the connexion of such properties is variable and\nindefinite. Some properties are constantly combined, others\noccasionally only. The leaves of different oaks resemble\neach other, the branches resemble far less, and may differ\nvery widely. The term _oak_ does not enable us to say that all\noaks have straight branches or all crooked. Terms can only\nexpress properties as far as they are constant. Not only,\ntherefore, the accumulation of a vast mass of knowledge of\nthe properties and attributes of objects, but also an\nobservation of the habitual _connexion_ of such properties\nis needed, to direct us to the consistent application of\nterms:--to enable us to apply them so as to express truths.\nBut here again we are largely provided with the requisite\nknowledge and observation by the common course of our\nexistence. The unintermitting stream of experience supplies\nus with an incalculable {101} amount of such observed\nconnexions. All men have observed that the associations of\nthe same form of leaves are more constant than of the same\nform of branches;--that though persons walk in different\nattitudes, none go on all fours; and thus the term _oak_ is\nso applied as to include those cases in which the leaves are\nalike in form though the branches be unlike; and though we\nshould refuse to apply the term _man_ to a class of\ncreatures which habitually and without compulsion used four\nlegs, we make no scruple of affixing it to persons of very\ndifferent figures. The whole of human experience being\ncomposed of such observed connexions, we have thus materials\neven for the immense multiplicity of names which human\nlanguage contains; all which names are, as we have said,\nregulated in their application by the condition of their\nexpressing such experience.\n\nThus amid the countless combinations of properties and\ndivisions of classes which the structure of language\nimplies, scarcely any are arbitrary or capricious. A word\nwhich expressed a mere wanton collection of unconnected\nattributes could hardly be called a _word_; for of such a\ncollection of properties no truth could be asserted, and the\nword would disappear, for want of some occasion on which it\ncould be used. Though much of the fabric of language\nappears, not unnaturally, fantastical and purely\nconventional, it is in fact otherwise. The associations and\ndistinctions of phraseology are not more fanciful than is\nrequisite to make them correspond to the apparent caprices\nof nature or of thought; and though much in language may be\ncalled conventional, the conventions exist for the sake of\nexpressing some truth or opinion, and not for their own\nsake. The principle, that _the condition of the use of terms\nis the possibility of general, intelligible, consistent\nassertions_, is true in the most complete and extensive sense.\n\n7. _Terms may have different Uses._--The Terms with which we\nare here most concerned are Names of Classes of natural\nobjects; and when we say that the principle and the limit of\nsuch Names are their use in expressing propositions\nconcerning the classes, it is {102} clear that much will\ndepend on the kind of propositions which we mainly have to\nexpress: and that the same name may have different limits,\naccording to the purpose we have in view. For example, is\nthe _whale_ properly included in the general term _fish_?\nWhen men are concerned in catching marine animals, the main\nfeatures of the process are the same however the animals may\ndiffer; hence whales are classed with fishes, and we speak\nof the _whale-fishery_. But if we look at the analogies of\norganization, we find that, according to these, the whale is\nclearly not a fish, but a _beast_, (confining this term, for\nthe sake of distinctness, to suckling beasts or _mammals_).\nIn Natural History, therefore, the whale is not included\namong fish. The indefinite and miscellaneous propositions\nwhich language is employed to enunciate in the course of\ncommon practical life, are replaced by a more coherent and\nsystematic collection of properties, when we come to aim at\nscientific knowledge. But we shall hereafter consider the\nprinciple of the classifications of Natural History; our\npresent subject is the application of the Idea of Likeness\nin common practice and common language.\n\n8. _Gradation of Kinds._--Common names, then, include many\nindividuals associated in virtue of resemblances, and of\npermanently connected properties; and such names are\napplicable as far as they serve to express such properties.\nThese collections of individuals are termed _Kinds_,\n_Sorts_, _Classes_.\n\nBut this association of particulars is capable of degrees.\nAs individuals by their resemblances form Kinds, so kinds of\nthings, though different, may resemble each other so as to\nbe again associated in a higher Class; and there may be\nseveral successive steps of such classification. _Man_,\n_horse_, _tree_, _stone_, are each a name of a Kind; but\n_animal_ includes the two first and excludes the others;\n_living thing_ is a term which includes _animal_ and _tree_\nbut not _stone_; _body_ includes all the four. And such a\nsubordination of kinds may be traced very widely in the\narrangements of language. {103}\n\nThe condition of the use of the wider is the same as that of\nthe narrower Names of Classes;--they are good as far as they\nserve to express true propositions. In common language,\nthough such an order of generality may in a variety of\ninstances be easily discerned, it is not systematically and\nextensively referred to; but this subordination and\ngraduated comprehensiveness is the essence of the methods\nand nomenclatures of Natural History, as we shall soon have\nto show.\n\nBut such subordination is not without its use, even in\ncommon cases, and when it is expressed in the terms of\ncommon language. Thus _organized body_ is a term which\nincludes plants and animals; _animal_ includes beasts,\nbirds, fishes; _beast_ includes horses and dogs; _dogs_,\nagain, are greyhounds, spaniels, terriers.\n\n9. _Characters of Kinds._--Now when we have such a Series of\nNames and Classes, we find that we take for granted\nirresistibly that each class has some _Character_ which\ndistinguishes it from other classes included in the superior\ndivision. We ask what kind of beast a dog is; what kind of\nanimal a beast is; and we assume that such questions admit\nof answer;--that each kind has some mark or marks by which\nit may be described. And such descriptions may be given: an\nanimal is an organized body _having sensation and volition_;\nman is a _reasonable_ animal. Whether or no we assent to the\nexactness of these definitions, we allow the propriety of\ntheir form. If we maintain these definitions to be wrong, we\nmust believe some others to be right, however difficult it\nmay be to hit upon them. We entertain a conviction that\nthere must be, among things so classed and named, a\npossibility of defining each.\n\nNow what is the foundation of this postulate? What is the\nground of this assumption, that there must exist a\ndefinition which we have never seen, and which perhaps no\none has seen in a satisfactory form? The knowledge of this\ndefinition is by no means necessary to our using the word\nwith propriety; for any one can make true assertions about\ndogs, but who can define a {104} dog? And yet if the\ndefinition be not necessary to enable us to use the word,\nwhy is it necessary at all? I allow that we possess an\nindestructible conviction that there must be such a\ncharacter of each kind as will supply a definition; but I\nask, on what this conviction rests.\n\nI reply, that our persuasion that there must needs be\ncharacteristic marks by which things can be defined in\nwords, is founded on the assumption of _the necessary\npossibility of reasoning_.\n\nThe reference of any object or conception to its class\nwithout definition, may give us a persuasion that it shares\nthe properties of its class, but such classing does not\nenable us to reason upon those properties. When we consider\nman as an animal, we ascribe to him in thought the\nappetites, desires, affections, which we habitually include\nin our notion of animal: but except we have expressed these\nin some definition or acknowledged description of the term\n_animal_, we can make no use of the persuasion in\nratiocination. But if we have described animals as 'being\nimpelled to action by appetites and passions,' we can not\nonly think, but say, 'man is an animal, and therefore he is\nimpelled to act by appetites and passions.' And if we add a\nfurther definition, that 'man is a reasonable animal,' and\nif it appear that 'reason implies conformity to a rule of\naction,' we can then further infer that man's nature is to\nconform the results of animal appetite and passion to a rule\nof action.\n\nThe possibility of pursuing any such train of reasoning as\nthis, depends on the definitions, of _animal_ and of _man_,\nwhich we have introduced; and the possibility of reasoning\nconcerning the objects around us being inevitably assumed by\nus from the constitution of our nature, we assume\nconsequently the possibility of such definitions as may thus\nform part of our deduction, and the existence of such\ndefining characters.\n\n10. _Difficulty of Definitions._--But though men are, on\nsuch grounds, led to make constant and importunate _demands_\nfor definitions of the terms which they employ in their\nspeculations, they are, in fact, far {105} from being able\nto carry into complete effect the postulate on which they\nproceed, that they must be able to find definitions which by\nlogical consequence shall lead to the truths they seek. The\npostulate overlooks the process by which our classes of\nthings are formed and our names applied. This process\nconsisting, as we have already said, in observing permanent\nconnexions of properties, and in fixing them by the\nattribution of names, is of the nature of the process of\nInduction, of which we shall afterwards have to speak. And\nthe postulate is so far true, that this process of induction\nbeing once performed, its result may usually be expressed by\nmeans of a few definitions, and may thus lead by a deduction\nto a train of real truths.\n\nBut in the subjects where we principally find such a\nsubordination of classes as we have spoken of, this process\nof deduction is rarely of much prominence: for example, in\nthe branches of natural history. Yet it is in these subjects\nthat the existence and importance of these characteristic\nmarks, which we have spoken of, principally comes into view.\nIn treating of these marks, however, we enter upon methods\nwhich are technical and scientific, not popular and common.\nAnd before we make this transition, we have a remark to make\non the manner in which writers, without reference to physics\nor natural history, have spoken of kinds, their\nsubordination, and their marks.\n\n11. '_The Five Words._'--These things,--the Nature and\nRelations of Classes,--were, in fact, the subjects of minute\nand technical treatment by the logicians of the school of\nAristotle. Porphyry wrote an Introduction to the\n_Categories_ of that philosopher, which is entitled _On the\nFive Words_. The 'Five Words' are _Genus_, _Species_,\n_Difference_, _Property_, _Accident_. Genus and Species are\nsuperior and inferior classes, and are stated[2\\8] to be\ncapable of repeated subordination. The 'most {106} general\nGenus' is the widest class; the 'most special Species' the\nnarrowest. Between these are intermediate classes, which are\nGenera with regard to those below, and Species with regard\nto those above them. Thus Being is the most general Genus;\nunder this is Body; under Body is Living Body; under this\nagain Animal; under Animal is Rational Animal, or Man; under\nMan are Socrates and Plato, and other individual men.\n\n[Note 2\\8: Porphyr. _Isagog._ c. 23.]\n\nThe _Difference_ is that which is added to the genus to make\nthe species; thus Rational is the Difference by which the\ngenus Animal is made the species Man; the Difference in this\nTechnical sense is the 'Specific,' or species-making\nDifference[3\\8]. It forms the Definition for the purposes of\nlogic, and corresponds to the 'Character' (specific or\ngeneric) of the Natural Historians. Indeed several of them,\nas, for instance, Linn\u00e6us, in his _Philosophia Botanica_,\nalways call these Characters the _Difference_, by a\ntraditional application of the Peripatetic terms of art.\n\n[Note 3\\8: \u03b5\u1f30\u03b4\u03bf\u03c0\u03bf\u03b9\u03cc\u03c2.]\n\nOf the other two words, the Property is that which though\nnot employed in defining the class, belongs to every part of\nit[4\\8]: it is, 'What happens to all the class, to it alone,\nand at all times; as _to be capable of laughing_ is a\nProperty of man.'\n\n[Note 4\\8: _Isagog._ c. 4]\n\nThe Accident is that which may be present and absent without\nthe destruction of the subject, as to sleep is an Accident\n(a thing which happens) to man.\n\nI need not dwell further on this system of technicalities.\nThe most remarkable points in it are those which I have\nalready noticed; the doctrine of the successive\nSubordination of genera, and the fixing attention upon the\nSpecific Difference. These doctrines, though invented in\norder to make reasoning more systematic, and at a period\nanterior to the existence of any Classificatory Science,\nhave, by a curious contrast with the intentions of their\nfounders, been of scarcely {107} any use in sciences of\n_Reasoning_, but have been amply applied and developed in\nthe _Natural History_ which arose in later times.\n\nWe must now treat of the principles on which this science\n(Natural History) proceeds, and explain what peculiar and\ntechnical processes it employs in addition to those of\ncommon thought and common language.\n\n\n\n{{108}}\nCHAPTER II.\n\nTHE METHODS OF NATURAL HISTORY, AS REGULATED BY THE IDEA OF\nLIKENESS.\n\n\nSECT. I.--_Natural History in general._\n\n1. _Idea of Likeness in Natural History._--THE various\nbranches of Natural History, in so far as they are\nclassificatory sciences merely, and do not depend upon\nphysiological views, rest upon the same Idea of Likeness\nwhich is the ground of the application of the names, more or\nless general, of common language. But the nature of science\nrequires that, for her purposes, this Idea should be applied\nin a more exact and rigourous manner than in its common and\npopular employment; just as occurs with regard to the other\nIdeas on which science is founded;--for instance, as the\nidea of space gives rise, in popular use, to the relations\nimplied in the prepositions and adjectives which refer to\nposition and form, and in its scientific development gives\nrise to the more precise relations of geometry.\n\nThe way in which the Idea of Likeness has been applied, so\nas to lead to the construction of a science, is best seen in\nBotany: for, in the Classification of Animals, we are\ninevitably guided by a consideration of the _function_ of\nparts; that is, by an idea of _purpose_, and not of likeness\nmerely: and in Mineralogy, the attempts at classification on\nthe principles of Natural History have been hitherto very\nimperfectly successful. But in Botany we have an example of\na branch of knowledge in which systematic classification has\nbeen effected with great beauty and advantage; and in which\nthe peculiarities and principles on which such {109}\nclassification must depend have been carefully studied. Many\nof the principal botanists, as Linn\u00e6us, Adanson, Decandolle,\nhave not only practically applied, but have theoretically\nenunciated, what they held to be the sound maxims of\nclassificatory science: and have thus enabled us to place\nbefore the reader with confidence the philosophy of this\nkind of science.\n\n2. _Condition of its Use._--We may begin by remarking that\nthe Idea of Likeness, in its systematic employment, is\ngoverned by the same principle which we have already spoken\nof as regulating the distribution of things into kinds, and\nthe assignment of names in unsystematic thought and speech;\nnamely, the condition that _general propositions shall be\npossible_. But as in this case the propositions are to be of\na scientific form and exactness, the likeness must be\ntreated with a corresponding precision; and its consequences\ntraced by steady and distinct processes. Naturalists must,\nfor their purposes, employ the resemblances of objects in a\ntechnical manner. This technical process may be considered\nas consisting of three steps;--The fixation of the\nresemblances; The use of them in making a classification;\nThe means of applying the classification. These three steps\nmay be spoken of as the _Terminology_, the _Plan of the\nSystem_, and the _Scheme of the Characters_.\n\n\nSECT. II.--_Terminology._[5\\8]\n\n[Note 5\\8: Decandolle and others use the term _Glossology_\ninstead of Terminology, to avoid the blemish of a word\ncompounded of two parts taken from different languages. The\nconvenience of treating the termination _ology_ (and a few\nother parts of compounds) as not restricted to Greek\ncombinations, is so great, that I shall venture, in these\ncases, to disregard this philological scruple.]\n\n3. _Terminology_ signifies the collection of _terms_, or\ntechnical words, which belong to the science. But in fixing\nthe meaning of the terms, at least of the descriptive terms,\nwe necessarily fix, at the same time, the perceptions and\nnotions which the terms are to {110} convey; and thus the\nTerminology of a classificatory science exhibits the\nelements of its substance as well as of its language. A\nlarge but indispensable part of the study of botany (and of\nmineralogy and zoology also,) consists in the acquisition of\nthe peculiar vocabulary of the science.\n\nThe meaning of technical terms can be fixed in the first\ninstance only by convention, and can be made intelligible\nonly by presenting to the senses that which the terms are to\nsignify. The knowledge of a colour by its name can only be\ntaught through the eye. No description can convey to a\nhearer what we mean by _apple-green_ or _French grey_. It\nmight, perhaps, be supposed that, in the first example, the\nterm _apple_, referring to so familiar an object,\nsufficiently suggests the colour intended. But it may easily\nbe seen that this is not true; for apples are of many\ndifferent hues of green, and it is only by a conventional\nselection that we can appropriate the term to one special\nshade. When this appropriation is once made, the term refers\nto the sensation, and not to the parts of this term; for\nthese enter into the compound merely as a help to the\nmemory, whether the suggestion be a natural connexion as in\n'apple-green,' or a casual one as in 'French grey.' In order\nto derive due advantage from technical terms of this kind,\nthey must be associated _immediately_ with the perception to\nwhich they belong; and not connected with it through the\nvague usages of common language. The memory must retain the\nsensation; and the technical word must be understood as\ndirectly as the most familiar word, and more distinctly.\nWhen we find such terms as _tin-white_ or _pinchbeck-brown_,\nthe metallic colour so denoted ought to start up in our\nmemory without delay or search.\n\nThis, which it is most important to recollect with respect\nto the simpler properties of bodies, as colour and form, is\nno less true with respect to more compound notions. In all\ncases the term is fixed to a peculiar meaning by convention;\nand the student, in order to use the word, must be\ncompletely familiar with the convention, so that he has no\nneed to frame {111} conjectures from the word itself. Such\nconjectures would always be insecure, and often erroneous.\nThus the term _papilionaceous_, applied to a flower, is\nemployed to indicate, not only a resemblance to a butterfly,\nbut a resemblance arising from five petals of a certain\npeculiar shape and arrangement; and even if the resemblance\nto a butterfly were much stronger than it is in such cases,\nyet if it were produced in a different way, as, for example,\nby one petal, or two only, instead of a 'standard,' two\n'wings,' and a 'keel' consisting of two parts more or less\nunited into one, we should no longer be justified in\nspeaking of it as a 'papilionaceous' flower.\n\nThe formation of an exact and extensive descriptive language\nfor botany has been executed with a degree of skill and\nfelicity, which, before it was attained, could hardly have\nbeen dreamt of as attainable. Every part of a plant has been\nnamed; and the form of every part, even the most minute, has\nhad a large assemblage of descriptive terms appropriated to\nit, by means of which the botanist can convey and receive\nknowledge of form and structure, as exactly as if each\nminute part were presented to him vastly magnified. This\nacquisition was part of the Linn\u00e6an Reform, of which we have\nspoken in the _History_. 'Tournefort,' says Decandolle[6\\8],\n'appears to have been the first who really perceived the\nutility of fixing the sense of terms in such a way as always\nto employ the same word in the same sense, and always to\nexpress the same idea by the same word; but it was Linn\u00e6us\nwho really created and fixed this botanical language, and\nthis is his fairest claim to glory, for by this fixation of\nlanguage he has shed clearness and precision over all parts\nof the science.'\n\n[Note 6\\8: _Theor. Elem._ p. 327.]\n\nIt is not necessary here to give any detailed account of the\nterms of botany. The fundamental ones have been gradually\nintroduced, as the parts of plants were more carefully and\nminutely examined. Thus the flower was successively\ndistinguished into the _calyx_, {112} the _corolla_, the\n_stamens_, and the _pistils_: the sections of the corolla\nwere termed _petals_ by Columna; those of the calyx were\ncalled _sepals_ by Necker[7\\8]. Sometimes terms of greater\ngenerality were devised; as _perianth_ to include the calyx\nand corolla, whether one or both of these were present[8\\8];\n_pericarp_ for the part inclosing the grain, of whatever\nkind it be, fruit, nut, pod, &c. And it may easily be\nimagined that descriptive terms may, by definition and\ncombination, become very numerous and distinct. Thus leaves\nmay be called _pinnatifid_[9\\8], _pinnatipartite_,\n_pinnatisect_, _pinnatilobate_, _palmatifid_,\n_palmatipartite_, &c., and each of these words designates\ndifferent combinations of the modes and extent of the\ndivisions of the leaf with the divisions of its outline. In\nsome cases arbitrary numerical relations are introduced into\nthe definition: thus a leaf is called _bilobate_[10\\8] when\nit is divided into two parts by a notch; but if the notch go\nto the middle of its length, it is _bifid_; if it go near\nthe base of the leaf, it is _bipartite_; if to the base, it\nis _bisect_. Thus, too, a pod of a cruciferous plant is a\n_silica_[11\\8] if it be four times as long as it is broad,\nbut if it be shorter than this it is a _silicula_. Such\nterms being established, the form of the very complex leaf\nor frond of a fern is exactly conveyed by the following\nphrase: 'fronds rigid pinnate, pinn\u00e6 recurved subunilateral\npinnatifid, the segments linear undivided or bifid\nspinuloso-serrate[12\\8].'\n\n[Note 7\\8: Decandolle, 329]\n\n[Note 8\\8: For this Erhart and Decandolle use _Perigone_.]\n\n[Note 9\\8: Dec. 318.]\n\n[Note 10\\8: _Ib._ 493.]\n\n[Note 11\\8: _Ib._ 422.]\n\n[Note 12\\8: Hooker, _Brit. Flo._ p. 457. _Hymenophyllum\nWilsoni_, Scottish filmy-fern, abundant in the highlands of\nScotland and about Killarney.]\n\nOther characters, as well as form, are conveyed with the\nlike precision: Colour by means of a classified scale of\ncolours, as we have seen in speaking of the Measures of\nSecondary Qualities; to which, however, we must add, that\nthe naturalist employs arbitrary names, (such as we have\nalready quoted,) and not mere numerical exponents, to\nindicate a certain number of {113} selected colours. This\nwas done with most precision by Werner, and his scale of\ncolours is still the most usual standard of naturalists.\nWerner also introduced a more exact terminology with regard\nto other characters which are important in mineralogy, as\nlustre, hardness. But Mohs improved upon this step by giving\na numerical scale of hardness, in which _talc_ is 1,\n_gypsum_ 2, _calc spar_ 3, and so on, as we have already\nexplained in the History of Mineralogy. Some properties, as\nspecific gravity, by their definition give at once a\nnumerical measure; and others, as crystalline form, require\na very considerable array of mathematical calculation and\nreasoning, to point out their relations and gradations. In\nall cases the features of likeness in the objects must be\nrightly apprehended, in order to their being expressed by a\ndistinct terminology. Thus no terms could describe crystals\nfor any purpose of natural history, till it was discovered\nthat in a class of minerals the proportion of the faces\nmight vary, while the angle remained the same. Nor could\ncrystals be described so as to distinguish species, till it\nwas found that the derived and primitive forms are connected\nby very simple relations of space and number. The discovery\nof the mode in which characters must be apprehended so that\nthey may be considered as _fixed_ for a class, is an\nimportant step in the progress of each branch of Natural\nHistory; and hence we have had, in the History of Mineralogy\nand Botany, to distinguish as important and eminent persons\nthose who made such discoveries, Rom\u00e9 de Lisle and Ha\u00fcy,\nCesalpinus and Gesner.\n\nBy the continued progress of that knowledge of minerals,\nplants, and other natural objects, in which such persons\nmade the most distinct and marked steps, but which has been\nconstantly advancing in a more gradual and imperceptible\nmanner, the most important and essential features of\nsimilarity and dissimilarity in such objects have been\nselected, arranged, and fitted with names; and we have thus\nin such departments, systems of Terminology which fix our\nattention upon the resemblances which it is proper to\nconsider, and {114} enable us to convey them in words. We\nhave now to speak of the mode in which such resemblances\nhave been employed in the construction of a Systematic\nClassification.\n\n\nSECT. III. _The Plan of the System._\n\n4. The collection of sound views and maxims by which the\nresemblances of natural objects are applied so as to form a\nscientific classification, is a department of the philosophy\nof natural history which has been termed by some writers (as\nDecandolle), _Taxonomy_, as containing the _Laws_ of the\n_Taxis_ (_arrangement_). By some Germans this has been\ndenominated _Systematik_; if we could now form a new\nsubstantive after the analogy of the words _Logick_,\n_Rhetorick_, and the like, we might call it _Systematick_.\nBut though our English writers commonly use the expression\n_Systematical Botany_ for the Botany of Classification, they\nappear to prefer the term _Diataxis_ for the method of\nconstructing the classification. The rules of such a branch\nof science are curious and instructive.\n\nIn framing a Classification of objects we must attend to\ntheir resemblances and differences. But here the question\noccurs, to _what_ resemblances and differences? for a\ndifferent selection of the points of resemblance would give\ndifferent results: a plant frequently agrees in leaves with\none group of plants, in flowers with another. Which set of\ncharacters are we to take as our guide?\n\nThe view already given of the regulative principle of all\nclassification, namely, that it must enable us to assert\ntrue and general propositions, will obviously occur as\napplicable here. The object of a scientific Classification\nis to enable us to enunciate scientific truths: we must\ntherefore classify according to those resemblances of\nobjects (plants or any others) which bring to light such\ntruths.\n\nBut this reply to the inquiry, 'On what characters of\nresemblance we are to found our system,' is still too\ngeneral and vague to be satisfactory. It carries us, {115}\nhowever, as far as this;--that since the truths we are to\nattend to are scientific truths, governed by precise and\nhomogeneous relations, we must not found our scientific\nClassification on casual, indefinite, and unconnected\nconsiderations. We must not, for instance, be satisfied with\ndividing plants, as Dioscorides does, into _aromatic_,\n_esculent_, _medicinal_ and _vinous_; or even with the long\nprevalent distribution into _trees_, _shrubs_, and _herbs_;\nsince in these subdivisions there is no consistent\nprinciple.\n\n5. _Latent Reference to Natural Affinity._--But there may be\nseveral kinds of truths, all exact and coherent, which may\nbe discovered concerning plants or any other natural\nobjects; and if this should be the case, our rule leaves us\nstill at a loss in what manner our classification is to be\nconstructed. And, historically speaking, a much more serious\ninconvenience has been this;--that the task of\nclassification of plants was necessarily performed when the\ngeneral laws of their form and nature were very little\nknown; or rather, when the existence of such laws was only\njust beginning to be discerned. Even up to the present day,\nthe general propositions which botanists are able to assert\nconcerning the structure and properties of plants, are\nextremely imperfect and obscure.\n\nWe are thus led to this conclusion:--that the Idea of\nLikeness could not be applied so as to give rise to a\nscientific Classification of plants, till considerable\nprogress was made in studying the general relations of\nvegetable form and life; and that the selection of the\nresemblances which should be taken into account, must depend\nupon the nature of the relations which were then brought\ninto view.\n\nBut this amounts to saying that, in the consideration of the\nClassification of vegetables, other Ideas must be called\ninto action as well as the Idea of Likeness. The additional\ngeneral views to which the more intimate study of plants\nleads, must depend, like all general truths, upon some\nregulating Idea which gives unity to scattered facts. No\nprogress could be made in botanical knowledge without the\n{116} operation of such principles: and such additional\nIdeas must be employed, besides those of mere likeness and\nunlikeness, in order to point out that Classification which\nhas a real scientific value.\n\nAccordingly, in the classificatory sciences, Ideas other\nthan Likeness do make their appearance. Such Ideas in botany\nhave influenced the progress of the science, even before\nthey have been clearly brought into view. We have especially\nthe Idea of Affinity, which is the basis of all Natural\nSystems of Classification, and which we shall consider in a\nsucceeding chapter. The assumption that there _is_ a Natural\nSystem, an assumption made by all philosophical botanists,\nimplies a belief in the existence of Natural Affinity, and\nis carried into effect by means of principles which are\ninvolved in that Idea. But as the formation of all systems\nof classification must involve, in a great degree, the Idea\nof Resemblance and Difference, I shall first consider the\neffect of that Idea, before I treat specially of Natural\nAffinity.\n\n6. _Natural Classes._--Many attempts were made to classify\nvegetables before the rules which govern a natural system\nwere clearly apprehended. Botanists agree in esteeming some\ncharacters as of more value than others, before they had\nagreed upon any general rules or principles for estimating\nthe relative importance of the characters. They were\nconvinced of the necessity of adding other considerations to\nthat of Resemblance, without seeing clearly what these\nothers ought to be. They aimed at a Natural Classification,\nwithout knowing distinctly in what manner it was to be\nNatural.\n\nThe attempts to form _Natural Classes_, therefore, in the\nfirst part of their history, belong to the Idea of Likeness,\nthough obscurely modified, even from an early period, by the\nIdeas of Affinity, and even of Function and of Development.\nHence Natural Classes may, to a certain extent, be treated\nof in this place.\n\nNatural Classes are opposed to Artificial Classes which are\nunderstood to be regulated by an _assumed_ {117} character.\nYet no classes can be so absolutely Artificial in this\nsense, as to be framed upon characters _arbitrarily_\nassumed; for instance, no one would speak of a class of\nshrubs defined by the circumstance of each having a hundred\nleaves: for of such a class no assertion could be made, and\ntherefore the class could never come under our notice. In\nwhat sense then are Artificial Classes to be understood, as\nopposed to Natural?\n\n7. _Artificial Classes._--To this question, the following is\nthe answer. When Natural Classes of a certain small extent\nhave been formed, a system may be devised which shall be\nregulated by a few selected characters, and which shall not\ndissever these small Natural Classes, but conform to them as\nfar as they go. If these selected characters be then made\nabsolute and imperative, and if we abandon all attempt to\nobtain Natural Classes of any higher order and wider extent,\nwe form an Artificial System.\n\nThus in the Linn\u00e6an System of Botanical Classification, it\nis assumed that certain natural groups, namely, Species and\nGenera, are established; it is conceived, moreover, that the\ndivision of Classes according to the number of stamens and\nof pistils does not violate the natural connexions of\nSpecies and Genera. This arrangement, according to the\nnumber of stamens and pistils, (further modified in certain\ncases by other considerations,) is then made the ground of\nall the higher divisions of plants, and thus we have an\nArtificial System.\n\nIt has been objected to this view, that the Linn\u00e6an\nArtificial System does not in all cases respect the\nboundaries of genera, but would, if rigorously applied,\ndistribute the species of the same genus into different\nartificial classes; it would divide, for instance, the\ngenera _Valeriana_, _Geranium_[13\\8], &c. To this we must\nreply, that so far as the Linn\u00e6an System does this, it is an\nimperfect Artificial System. Its great merit is in its\nmaking such a disjunction in comparatively so {118} few\ncases; and in the artificial characters being, for the most\npart, obvious and easily applied.\n\n[Note 13\\8: Decand. _Theor. Elem._ p. 45.]\n\n8. _Are Genera Natural_?--It has been objected also that\nGenera are not Natural groups. Linn\u00e6us asserts in the most\npositive manner that they are[14\\8]. On which Adanson\nobserves[15\\8], 'I know not how any Botanist can maintain\nsuch a thesis: that which is certain is, that up to the\npresent time no one has been able to prove it, nor to give\nan exact definition of a natural genus, but only of an\nartificial.' He then brings several arguments to confirm\nthis view.\n\n[Note 14\\8: _Phil. Bot._ Art. 165.]\n\n[Note 15\\8: _Famille de Ph._ Pref. cv.]\n\nBut we are to observe, in answer to this, that Adanson\nimproperly confounds the recognition of the existence of a\nnatural group with the invention of a technical mark or\ndefinition of it. Genera are groups of species associated in\nvirtue of natural affinity, of general resemblance, of real\npropinquity: of such groups, certain selected characters,\none or few, may usually be discovered, by which the species\nmay be referred to their groups. These Artificial characters\ndo not constitute, but indicate the genus: they are the\n_Diagnosis_, not the basis of the _Diataxis_: and they are\nalways subject to be rejected, and to have others\nsubstituted for them, when they violate the natural\nconnexion of species which a minute and enlarged study\ndiscovers.\n\nIt is, therefore, no proof that Genera are not Natural, to\nsay that their artificial characters are different in\ndifferent systems. Such characters are only different\nattempts to confine the variety of nature within the limits\nof definition. Nor is it sufficient to say that these groups\nthemselves are different in different writers; that some\nbotanists make genera what others make only species; as\n_Pedicularis_, _Rhinanthus_, _Euphrasia_,\n_Antirrhinum_[16\\8]. This discrepancy shows only that the\nnatural arrangement is not yet completely known, even in the\nsmaller groups; a conclusion to which we need not refuse our\nassent. But in {119} opposition to these negatives, the\nmanner in which Genera have been established proves that\nthey are regulated by the principle of being natural, and by\nthat alone. For they are not formed according to any _\u00e0\npriori_ rule. The Botanist does not take any selected or\narbitrary part or parts of the plants, and marshal his\ngenera according to the differences of this part. On the\ncontrary, the divisions of genera are sometimes made by\nmeans of the flower; sometimes by means of the fruit: the\nanthers, the stamens, the seeds, the pericarp, and the most\nvaried features of these parts, are used in the most\nmiscellaneous and unsystematic manner. Linn\u00e6us has indeed\nlaid down a maxim that the characteristic differences of\ngenera must reside in the fructification[17\\8]: but Adanson\nhas justly remarked[18\\8], that an arbitrary restriction\nlike this makes the groups artificial: and that in some\nfamilies other characters are more essential than those of\nthe fructification; as the leaves in the families of\n_Aparine\u00e6_ and _Leguminos\u00e6_, and the disposition of the\nflowers in _Labiat\u00e6_. And Naturalists are so far from\nthinking it sufficient to distribute species into genera by\n_arbitrary_ marks, that we find them in many cases lamenting\nthe absence of good _natural_ marks: as in the families of\n_Umbellifer\u00e6_, where Linn\u00e6us declared that any one who could\nfind good characters of genera would deserve great\nadmiration, and where it is only of late that good\ncharacters have been discovered and the arrangement\nsettled[19\\8] by means principally of the ribs of the\nfruit[20\\8].\n\n[Note 16\\8: Adanson, p. cvi.]\n\n[Note 17\\8: _Phil. Bot._ Art. 162.]\n\n[Note 18\\8: Adanson, Pref. p. cxx.]\n\n[Note 19\\8: Lindley, _Nat. Syst._ p. 5.]\n\n[Note 20\\8: In like manner we find Cuvier saying of Rondelet\nthat he has 'un _sentiment_ tr\u00e8s vrai des genres.' _Hist.\nIchth._ p. 39.]\n\nIt is thus clear that Genera are not established on any\nassumed or preconceived basis. What, then, is the principle\nwhich regulates botanists when they try to fix genera? What\nis the arrangement which they thus wish for, without being\nable to hit upon it? What is the tendency which thus drives\nthem from the corolla to the anthers, from the flower to the\nfruit, {120} from the fructification to the leaves? It is\nplain that they seek something, not of their own devising\nand creating;--not anything merely conventional and\nsystematic; but something which they conceive to exist in\nthe relations of the plants themselves;--something which is\nwithout the mind, not within;--in nature, not in art;--in\nshort, a Natural Order.\n\nThus the regulative principle of a Genus, or of any other\nnatural group is, that it is, or is supposed to be, natural.\nAnd by reference to this principle as our guide, we shall be\nable to understand the meaning of that indefiniteness and\nindecision which we frequently find in the descriptions of\nsuch groups, and which must appear so strange and\ninconsistent to any one who does not suppose these\ndescriptions to assume any deeper ground of connexion than\nan arbitrary choice of the botanist. Thus in the family of\nthe Rose-tree, we are told that the _ovules_ are _very\nrarely_ erect[21\\8], the _stigmata_ are _usually_ simple. Of\nwhat use, it might be asked, can such loose accounts be? To\nwhich the answer is, that they are not inserted in order to\ndistinguish the species, but in order to describe the\nfamily, and the total relations of the ovules and of the\nstigmata of the family are better known by this general\nstatement. A similar observation may be made with regard to\nthe Anomalies of each group, which occur so commonly, that\nMr. Lindley, in his _Introduction to the Natural System of\nBotany_, makes the 'Anomalies' an article in each Family.\nThus, part of the character of the Rosace\u00e6 is that they have\nalternate _stipulate_ leaves, and that the _albumen_ is\n_obliterated_: but yet in _Lowea_, one of the genera of this\nfamily, the stipul\u00e6 are _absent_; and the albumen is\n_present_ in another, _Neillia_. This implies, as we have\nalready seen, that the artificial character (or _diagnosis_\nas Mr. Lindley calls it) is imperfect. It is, though very\nnearly, yet not exactly, commensurate with the natural\ngroup: and hence, in certain cases, this character is made\nto yield to the general weight of natural affinities.\n\n[Note 21\\8: Lindley, _Nat. Syst._ p. 81.]\n\n{121} 9. _Difference of Natural History and\nMathematics._--These views,--of classes determined by\ncharacters which cannot be expressed in words,--of\npropositions which state, not what happens in all cases, but\nonly usually,--of particulars which are included in a class\nthough they transgress the definition of it, may very\nprobably surprise the reader. They are so contrary to many\nof the received opinions respecting the use of definitions\nand the nature of scientific propositions, that they will\nprobably appear to many persons highly illogical and\nunphilosophical. But a disposition to such a judgment arises\nin a great measure from this;--that the mathematical and\nmathematico-physical sciences have, in a great degree,\ndetermined men's views of the general nature and form of\nscientific truth; while Natural History has not yet had time\nor opportunity to exert its due influence upon the current\nhabits of philosophizing. The apparent indefiniteness and\ninconsistency of the classifications and definitions of\nNatural History belongs, in a far higher degree, to all\nother except mathematical speculations: and the modes in\nwhich approximations to exact distinctions and general\ntruths have been made in Natural History, may be worthy our\nattention, even for the light they throw upon the best modes\nof pursuing truth of all kinds.\n\n10. _Natural Groups given by Type not by Definition._--The\nfurther development of this suggestion must be considered\nhereafter. But we may here observe, that though in a Natural\nGroup of objects a definition can no longer be of any use as\na regulative principle, classes are not, therefore, left\nquite loose, without any certain standard or guide. The\nclass is steadily fixed, though not precisely limited; it is\ngiven, though not circumscribed; it is determined, not by a\nboundary line without, but by a central point within; not by\nwhat it strictly excludes, but by what it eminently\nincludes; by an example, not by a precept; in short, instead\nof Definition we have a _Type_ for our director.\n\nA Type is an example of any class, for instance, a species\nof a genus, which is considered as eminently {122}\npossessing the characters of the class. All the species\nwhich have a greater affinity with this Type-species than\nwith any others, form the genus, and are ranged about it,\ndeviating from it in various directions and different\ndegrees. Thus a genus may consist of several species, which\napproach very near the type, and of which the claim to a\nplace with it is obvious; while there may be other species\nwhich straggle further from this central knot, and which yet\nare clearly more connected with it than with any other. And\neven if there should be some species of which the place is\ndubious, and which appear to be equally bound by two generic\ntypes, it is easily seen that this would not destroy the\nreality of the generic groups, any more than the scattered\ntrees of the intervening plain prevent our speaking\nintelligibly of the distinct forests of two separate hills.\n\nThe Type-species of every genus, the Type-genus of every\nfamily, is, then, one which possesses all the characters and\nproperties of the genus in a marked and prominent manner.\nThe Type of the Rose family has alternate stipulate leaves,\nwants the albumen, has the ovules not erect, has the\nstigmata simple, and besides these features, which\ndistinguish it from the exceptions or varieties of its\nclass, it has the features which make it prominent in its\nclass. It is one of those which possess clearly several\nleading attributes; and thus, though we cannot say of any\none genus that it _must_ be the Type of the family, or of\nany one species that it _must_ be the Type of the genus, we\nare still not wholly to seek: the Type must be connected by\nmany affinities with most of the others of its group; it\nmust be near the center of the crowd, and not one of the\nstragglers.\n\n11. It has already been repeatedly stated, as the great rule\nof all classification, that the classification must serve to\nassert general propositions. It may be asked _what_\npropositions we are able to enunciate by means of such\nclassifications as we are now treating of. And the answer\nis, that the collected knowledge of the characters, habits,\nproperties, organization, and {123} functions of these\ngroups and families, as it is found in the best botanical\nworks, and as it exists in the minds of the best botanists,\nexhibits to us the propositions which constitute the\nscience, and to the expression of which the classification\nis to serve. All that is not strictly definition, that is,\nall that is not artificial character, in the descriptions of\nsuch classes, is a statement of truths, more or less\ngeneral, more or less precise, but making up, together, the\npositive knowledge which constitutes the science. As we have\nsaid, the consideration of the properties of plants in order\nto form a system of classification, has been termed\nTaxonomy, or the Systematick of Botany; all the parts of the\ndescriptions, which, taking the system for granted, convey\nadditional information, are termed the _Physiography_ of the\nscience; and the same terms may be applied in the other\nbranches of Natural History.\n\n12. _Artificial and Natural Systems._--If I have succeeded\nin making it apparent that an artificial system of\ncharacters necessarily implies natural classes which are not\nsevered by the artificial marks, we shall now be able to\ncompare the nature and objects of the Artificial and Natural\nSystems; points on which much has been written in recent times.\n\nThe Artificial System is one which is, or professes to be,\nentirely founded upon marks selected according to the\ncondition which has been stated, of not violating certain\nnarrow natural groups; namely in the Linn\u00e6an system, the\nnatural genera of plants. The marks which form the basis of\nthe system, being thus selected, are applied rigorously and\nuniversally without any further regard to any other\ncharacters or indications of affinity. Thus in the Linn\u00e6an\nsystem, which depends mainly on the number of male organs or\nstamens, and on the number of female organs or styles, the\nlargest divisions, or the Classes, are arranged according to\nthe number of the stamens, and are _monandria_, _diandria_,\n_triandria_, _tetrandria_, _pentandria_, _hexandria_, and so\non: the names being formed of the Greek numerical words, and\nof the word which implies _male_. And the Orders of each of\nthese Classes are {124} distinguished by the number of\nstyles, and are called _monogynia_, _digynia_, _trigynia_,\nand so on, the termination of these words meaning _female_.\nAnd so far as this numerical division and subdivision go on,\nthe system is a rigorous system, and strictly artificial.\n\nBut the condition that the artificial system shall leave\ncertain natural affinities untouched, makes it impossible to\ngo through the vegetable kingdom by a method of mere\nnumeration of stamens and styles. The distinction of flowers\nwith twenty and with thirty stamens is not a fixed\ndistinction: flowers of one and the same kind, as roses,\nhave, some fewer than the former, some more than the latter\nnumber. The Artificial System, therefore, must be modified.\nAnd there are various relations of connexion and proportion\namong the stamina which are more permanent and important\nthan their mere number. Thus flowers with two longer and two\nshorter stamens are not placed in the class _tetrandria_,\nbut are made a separate class _didynamia_; those with four\nlonger and two shorter are in like manner _tetradynamia_,\nnot _hexandria_; those in **which the filaments are bound\ninto two bundles are _diadelphia_. All these and other\nclasses are deviations from the plan of the earlier Classes,\nand are so far defects of the artificial system; but they\nare deviations requisite in order that the system may leave\na basis of natural groups, without which it would not be a\nSystem of _Vegetables_. And as the division is still founded\non some properties of the stamens, it combines not ill with\nthat part of the system which depends on the number of them.\nThe Classes framed in virtue of these various considerations\nmake up an Artificial System which is tolerably coherent.\n\n'But since the Artificial System thus regards natural\ngroups, in what does it differ from a Natural System?' It\ndiffers in this:--That though it allows certain subordinate\nnatural groups, it merely allows _these_, and does not\nendeavour to ascend to any wider natural groups. It takes\nall the _higher_ divisions of its scheme from its artificial\ncharacters, its stamens and pistils, without looking to any\nnatural affinities. It {125} accepts natural _Genera_, but\nit does not seek natural _Families_, or Orders, or Classes.\nIt _assumes_ natural groups, but does not _investigate_ any;\nit forms wider and higher groups, but professes to frame\nthem arbitrarily.\n\nBut then, on the other hand, the question occurs, 'This\nbeing the case, what can be the use of the Artificial\nSystem?' If its characters, in the higher stages of\nclassification, be arbitrary, how can it lead us to the\nnatural relations of plants? And the answer is, that it does\nso in virtue of the original condition, that there shall be\ncertain natural relations which the artificial system shall\nnot transgress; and that its use arises from the facility\nwith which we can follow the artificial arrangement as far\nas it goes. We can count the stamens and pistils, and thus\nwe know the Class and Order of our plant; and we have then\nto discover its Genus and Species by means less symmetrical\nbut more natural. The Artificial System, though arbitrary in\na certain degree, brings us to a Class in which the whole of\neach Genus is contained, and there we can find the proper\nGenus by a suitable method of seeking. No Artificial System\ncan conduct us into the extreme of detail, but it can place\nus in a situation where the detail is within our reach. We\ncannot find the house of a foreign friend by its latitude\nand longitude; but we may be enabled, by a knowledge of the\nlatitude and longitude, to find the city in which he dwells,\nor at least the island; and we then can reach his abode by\nfollowing the road or exploring the locality. The Artificial\nSystem is such a method of travelling by latitude and\nlongitude; the Natural System is that which is guided by a\nknowledge of the country.\n\nThe Natural System, then, is that which endeavours to\narrange by the natural affinities of objects; and more\nespecially, which attempts to ascend from the lower natural\ngroups to the higher; as for example from genera to natural\nfamilies, orders, and classes. But as we have already\nhinted, these expressions of natural affinities, natural\ngroups, and the like, when {126} considered in reference to\nthe idea of resemblance alone, without studying analogy or\nfunction, are very vague and obscure. We must notice some of\nthe attempts which were made under the operation of this\nimperfect view of the subject.\n\n\nSECT. IV.--_Modes of framing Natural Systems._\n\n13. Decandolle[22\\8] distinguishes the attempts at Natural\nClassifications into three sorts: those of _blind trial_\n(_t\u00e2tonnement_), those of _general comparison_, and those of\n_subordination of characters_. The two former do not depend\ndistinctly upon any principle, except resemblance; the third\nrefers us to other views, and must be considered in a future\nchapter.\n\n[Note 22\\8: _Theor. Elem._ art 41.]\n\n_Method of Blind Trial._--The notion of the existence of\nnatural classes dependent on the general resemblance of\nplants,--of an affinity showing itself in different parts\nand various ways,--though necessarily somewhat vague and\nobscure, was acted upon at an early period, as we have seen\nin the formation of genera; and was enunciated in general\nterms soon after. Thus Magnolius[23\\8] says that he discerns\nin plants an affinity, by means of which they may be\narranged in families: 'Yet it is impossible to obtain from\nthe fructification alone the Characters of these families;\nand I have therefore chosen those parts of plants in which\nthe principal characteristic marks are found, as the root,\nthe stem, the flower, the seed. In some plants there is even\na certain resemblance; an affinity which does not consist in\nthe parts considered separately, but in their totality; an\naffinity which may be felt but not expressed; as we see in\nthe families of agrimonies and cinquefoils, which every\nbotanist will judge to be related, though they differ by\ntheir roots, their leaves, their flowers, and their seeds.'\n\n[Note 23\\8: Dec. _Theor. Elem._ art. 42. Petri Magnoli,\n_Prodromus Hist. Gen. Plant._ 1689.]\n\n{127} This obscure feeling of a resemblance on the whole, an\naffinity of an indefinite kind, appears fifty years later in\nLinn\u00e6us's attempts. 'In the Natural Classification,' he\nsays[24\\8], 'no _\u00e0 priori_ rule can be admitted, no part of\nthe fructification can be taken exclusively into\nconsideration; but only the simple symmetry of all its\nparts.' Hence though he proposed Natural Families, and even\nstated the formation of such Families to be the first and\nlast object of all Methods, he never gave the Characters of\nthose groups, or connected them by any method. He even\ndeclared it to be impossible to lay down such a system of\ncharacters. This persuasion was the result of his having\nrefused to admit into his mind any Idea more profound than\nthat notion of Resemblance of which he had made so much and\nsuch successful use; he would not attempt to unravel the\nIdeas of Symmetry and of Function on which the clear\nestablishment of natural relations must depend. He even\ndespised the study of the inner organization of plants; and\nreckoned[25\\8] the _Anatomici_, who studied the anatomy and\nphysiology of plants and the laws of vegetation, among the\n_Botanophili_, the mere amateurs of his science.\n\n[Note 24\\8: Dec. _Theor. Elem._ art 42.]\n\n[Note 25\\8: _Phil. Bot._ s. 44.]\n\nThe same notion of general resemblance and affinity,\naccompanied with the same vagueness, is to be found in the\nwriter who least participated in the general admiration of\nLinn\u00e6us, Buffon. Though it was in a great measure his love\nof higher views which made him dislike what he considered\nthe pedantry of the Swedish school, he does not seem to have\nobtained a clearer sight of the principle of the natural\nmethod than his rival, except that he did not restrict his\nCharacters to the fructification. Things must be arranged by\ntheir resemblances and differences, (he says in 1750[26\\8],)\n'but the resemblances and differences must be taken not from\none part but from the whole; and we must attend to the form,\nthe size, the habit, the number and position of the parts,\neven the substance {128} of the part; and we must make use\nof these elements in greater or smaller number, as we have need.'\n\n[Note 26\\8: Adanson, p. clvi. Buffon, _Hist. Nat._ t. i. p. 21.]\n\n14. _Method of General Comparison._--A countryman of Buffon,\nwho shared with him his depreciating estimate of the Linn\u00e6an\nsystem, and his wish to found a natural system upon a\nbroader basis, was Adanson; and he invented an ingenious\nmethod of apparently avoiding the vagueness of the practice\nof following the general feeling of resemblance. This method\nconsisted in making many Artificial Systems, in each of\nwhich plants were arranged by some one part; and then\ncollecting those plants which came near each other in the\ngreatest number of those Artificial Systems, as plants\nnaturally the most related. Adanson gives an account[27\\8]\nof the manner in which this system arose in his mind. He had\ngone to Senegal, animated by an intense zeal for natural\nhistory; and there, amid the luxuriant vegetation of the\ntorrid zone, he found that the methods of Linn\u00e6us and\nTournefort failed him altogether as means of arranging his\nnew botanical treasures. He was driven to seek a new system.\n'For this purpose,' he says, 'I examined plants in all their\nparts, without omitting any, from the roots to the embryo,\nthe folding of the leaves in the bud, their mode of\nsheathing[28\\8], the situation and folding of the embryo and\nof its radicle in the seed, relatively to the fruit; in\nshort, a number of particulars which few botanists notice. I\nmade in the first place a complete description of each\nplant, putting each of its parts in separate articles, in\nall its details; when new species occurred I put down the\npoints in which they differed, omitting those in which they\nagreed. By means of the aggregate of these comparative\ndescriptions, I perceived that plants arranged themselves\ninto classes or families which could not be artificial or\narbitrary, not being founded upon one or two parts, which\nmight change at certain limits, but on all the parts; so\nthat the disproportion of one of these parts was corrected\nand balanced by the introduction of another.' Thus the\nprinciple of Resemblance {129} was to suffice for the\ngeneral arrangement, not by means of a new principle, as\nSymmetry or Organization, which should regulate its\napplication, but by a numeration of the peculiarities in\nwhich the resemblance consisted.\n\n[Note 27\\8: Pref. p. clvii.]\n\n[Note 28\\8: 'Leur mani\u00e8re de s'engainer.']\n\nThe labour which Adanson underwent in the execution of this\nthought was immense. By taking each Organ, and considering\nits situation, figure, number, &c., he framed sixty-five\nArtificial Systems; and collected his Natural Families by a\nnumerical combination of these. For example, his\n_sixty-fifth_ Artificial System[29\\8] is that which depends\nupon the situation of the Ovary with regard to the Flower;\naccording to this system he frames _ten_ Artificial Classes,\nincluding _ninety-three_ Sections: and of these Sections the\nresulting Natural Arrangement retains _thirty-five_, above\none-third: the same estimate is applied in other cases.\n\n[Note 29\\8: Adanson, Pref. p. cccxii.]\n\nBut this attempt to make Number supply the defects which the\nvague notion of Resemblance introduces, however ingenious,\nmust end in failure. For, as Decandolle observes[30\\8], it\nsupposes that we know, not only all the Organs of plants,\nbut all the points of view in which it is possible to\nconsider them; and even if this assumption were true, which\nit is not, and must long be very far from being, the\nprinciple is altogether vicious; for it supposes that all\nthese points of view, and all the resulting artificial\nsystems are of equal importance:--a supposition manifestly\nerroneous. We are thus led back to the consideration of the\n_Relative Importance_ of Organs and their qualities, as a\nbasis for the classification of plants, which no Artificial\nMethod can supersede; and thus we find the necessity of\nattending to something besides mere external and detached\nResemblance. The method of General Comparison cannot, any\nmore than the method of Blind Trial, lead us, with any\ncertainty or clearness, to the Natural Method. Adanson's\nFamilies are held by the best botanists to be, for the\ngreater part, Natural; but his hypotheses are unfounded; and\nhis success is {130} probably more due to the dim feeling of\nAffinity, by which he was unconsciously guided, than to the\nhelp he derived from his numerical processes.\n\n[Note 30\\8: Dec. _Theor. Elem._ p. 67.]\n\nIn a succeeding chapter I shall treat of that Natural\nAffinity on which a Natural System must really be founded.\nBut before proceeding to this higher subject, we must say a\nfew words on some of the other parts of the philosophy of\nNatural History,--the Gradation of Groups, the Nomenclature,\nthe Diagnosis, and the application of the methods to other\nsubjects.\n\n\nSECT. V.--_Gradation of Groups._\n\n15. It has been already noticed (last chapter,) that even\nthat vague application of the idea of resemblance which\ngives rise to the terms of common language, introduces a\nsubordination of classes, as _man_, _animal_, _body_,\n_substance_. Such a subordination appears in a more precise\nform when we employ this idea in a scientific manner as we\ndo in Natural History. We have then a series of divisions,\neach inclusive of the lower ones, which are expressed by\nvarious metaphors in different writers. Thus some have gone\nas far as eight terms of the series[31\\8], and have taken,\nfor the most part, military names for them; as _Hosts_,\n_Legions_, _Phalanxes_, _Centuries_, _Cohorts_, _Sections_,\n_Genera_, _Species_. But the most received series is\n_Classes_, _Orders_, _Genera_, and _Species_; in which,\nhowever, we often have other terms interpolated, as\n_Sub-genera_, or Sections of genera. The expressions\n_Family_ and _Tribe_, are commonly appropriated to natural\ngroups; and we speak of the Vegetable, Animal, Mineral\n_Kingdom_; but the other metaphors of Provinces, Districts,\n&c., which this suggests, have not been commonly used[32\\8].\n\n[Note 31\\8: Adanson, p. cvi.]\n\n[Note 32\\8: _Sub-Kingdom_ has recently been employed by\nsome naturalists.]\n\nIt will of course be understood that each ascending step of\nclassification is deduced by the same process from the one\nbelow. A Genus is a collection of Species which resemble\neach other more than they {131} resemble other species; an\nOrder is a collection of Genera having, in like manner, the\nfirst degree of resemblance, and so on. How close or how\nwide the Degrees of Resemblance are, must depend upon the\nnature of the objects compared, and cannot possibly be\nprescribed beforehand. Hence the same term, _Class_ and\n_Order_ for instance, may imply, in different provinces of\nnature, very different degrees of resemblance. The Classes\nof Animals are Insects, Birds, Fish, Beasts, &c. The Orders\nof Beasts are _Ruminants_, _Tardigrades_, _Plantigrades_,\n&c. The two Classes of Plants (according to the Natural\nOrder[33\\8]) are _Vascular_ and _Cellular_, the latter\nhaving neither sexes, flowers, nor spiral vessels. The\nVascular Plants are divided into Orders, as _Umbellifer\u00e6_,\n_Ranunculace\u00e6_, &c.; but between this Class and its Orders\nare interposed two other steps:--two Sub-classes,\n_Dicotyledonous_ and _Monocotyledonous_, and two Tribes of\neach: _Angiospermi\u00e6_, _Gymnospermi\u00e6_ of the first; and\n_Petaloide\u00e6_, _Glumaci\u00e6_ of the second. Such interpolations\nare modifications of the general formula of subordination,\nfor the purpose of accommodating it to the most prominent\nnatural affinities.\n\n[Note 33\\8: Lindley.]\n\n16. _Species._--As we have already seen in tracing the\nprinciples of the Natural Method, when by the intimate study\nof plants we seek to give fixity and definiteness to the\nnotion of resemblance and affinity on which all these\ndivisions depend, we are led to the study of Organization\nand Analogy. But we make a reference to physiological\nconditions even from the first, with regard to the lowest\nstep of our arrangement, the _Species_; for we consider it a\nproof of the impropriety of separating two Species, if it be\nshown that they can by any course of propagation, culture,\nand treatment, the one pass into the other. It is in this\nway, for example, that it has been supposed to be\nestablished that the common Primrose, Oxlip, Polyanthus, and\nCowslip, are all the same species. Plants which thus, in\nvirtue of external circumstances, as soil, {132} exposure,\nclimate, exhibit differences which may disappear by changing\nthe circumstances, are called _Varieties_ of the species.\nAnd thus we cannot say that a Species is a collection of\nindividuals which possess the First Degree of Resemblance;\nfor it is clear that a primrose resembles another primrose\nmore than it does a cowslip; but this resemblance only\nconstitutes a Variety. And we find that we must necessarily\ninclude in our conception of Species, the notion of\npropagation from the same stock. And thus a Species has been\nwell defined[34\\8]: 'The collection of the individuals\ndescended from one another, or from common parents, and of\nthose which resemble these as much as these resemble each\nother.' And thus the sexual doctrine of plants, or rather\nthe consideration of them as things which propagate their\nkind, (whether by seed, shoot, or in any other way,) is at\nthe basis of our classifications.\n\n[Note 34\\8: Cuv. _R\u00e8gne Animal_, p. 19.]\n\n17. The First permanent Degree of Resemblance among\norganized beings is thus that which depends on this relation\nof generation, and we might expect that the groups which are\nconnected by this relation would derive their names from the\nnotion of generation. It is curious that both in Greek and\nLatin languages and in our own, the words which have this\norigin (\u03b3\u03ad\u03bd\u03bf\u03c2, _genus_, _kind_,) do not, in the phraseology\nof science at least, denote the nearest degree of\nrelationship, but have other terms subordinate to them,\nwhich appear etymologically to indicate a mere resemblance\nof appearance (\u03b5\u1f36\u03b4\u03bf\u03c2, _species_, _sort_); and these latter\nterms are appropriated to the groups resulting from\npropagation. Probably the reason of this is, that the former\nterms (_genus_, &c.) had been applied so widely and loosely\nbefore the scientific fixation of terms, that to confine\nthem to what we call _species_ would have been to restrict\nthem in a manner too unusual to be convenient.\n\n18. _Varieties. Races._--The Species, as we have said, is\nthe collection of individuals which resemble each other as\nmuch as do the offspring of a common {133} stock. But within\nthe limits of this boundary, there are often observable\ndifferences permanent enough to attract our notice, though\ncapable of being obliterated by mixture in the course of\ngeneration. Such different groups are called _Varieties_.\nThus the Primrose and Cowslip, as has been stated above, are\nfound to be varieties of the same plant; the Poodle and the\nGreyhound are well marked varieties of the species _dog_.\nSuch differences are hereditary, and it may be long doubtful\nwhether such hereditary differences are varieties only, or\ndifferent species. In such cases the term _Race_ has been\napplied.\n\n\nSECT. VI.--_Nomenclature._\n\n19. The Nomenclature of any branch of Natural History is the\ncollection of names of all its species; which, when they\nbecome extremely numerous, requires some artifice to make it\npossible to recollect or apply them. The known species of\nplants, for example, were 10,000 at the time of Linn\u00e6us, and\nare now probably 60,000. It would be useless to endeavour to\nframe and employ separate names for each of these species.\n\nThe division of the objects into a subordinated system of\nclassification enables us to introduce a Nomenclature which\ndoes not require this enormous number of names. The artifice\nemployed to avoid this inconvenience is to name a Species by\nmeans of two (or it might be more) steps of the successive\ndivision. Thus in Botany, each of the genera has its name,\nand the species are marked by the addition of some epithet\nto the name of the genus. In this manner about 1,700 generic\nnames, with a moderate number of specific names, were found\nby Linn\u00e6us sufficient to designate with precision all the\nspecies of vegetables known at his time. And this _Binary\nMethod_ of Nomenclature has been found so convenient that it\nhas been universally adopted in every other department of\nthe Natural History of organized beings.\n\nMany other modes of Nomenclature have been tried, but no\nother has at all taken root. Linn\u00e6us himself {134} appears\nat first to have intended marking each species by the\nGeneric Name accompanied by a characteristic Descriptive\nPhrase; and to have proposed the employment of a _trivial_\nSpecific Name, as he termed it, only as a method of\noccasional convenience. The use of these _trivial names_,\nhas, however, become universal, as we have said, and is by\nmany persons considered the greatest improvement introduced\nat the Linn\u00e6an reform.\n\nBoth Linn\u00e6us and other writers (as Adanson) have given many\nmaxims with a view of regulating the selection of generic\nand specific names. The maxims of Linn\u00e6us were intended as\nmuch as possible to exclude barbarism and confusion, and\nhave, upon the whole, been generally adopted; though many of\nthem were objected to by his contemporaries (Adanson and\nothers[35\\8]), as capricious or unnecessary innovations.\nMany of the names, introduced by Linn\u00e6us, certainly appear\nfanciful enough: thus he gives the name of _Bauhinia_ to a\nplant with leaves in pairs, because the Bauhins were a pair\nof brothers; _Banisteria_ is the name of a climbing plant,\nin honour of Banister, who travelled among mountains. But\nsuch names, once established by adequate authority, lose all\ntheir inconvenience, and easily become permanent; and hence\nthe reasonableness of the Linn\u00e6an rule[36\\8], that as such a\nperpetuation of the names of persons by the names of plants\nis the only honour botanists have to bestow, it ought to be\nused with care and caution.\n\n[Note 35\\8: Pp. cxxix. clxxii.]\n\n[Note 36\\8: _Phil Bot._ s. 239.]\n\nThe generic name must, as Linn\u00e6us says, be fixed[37\\8]\nbefore we attempt to form a specific name; 'the latter\nwithout the former is like the clapper without the bell.'\nThe name of the genus being established, the species may be\nmarked by adding to it 'a single word taken at will from any\nquarter;' that is, not involving a description or any\nessential property of the plant, but a casual or arbitrary\nappellation[38\\8]. Thus the {135} various species of\n_Hieracium_[39\\8] are _Hieracium Alpinum_, _H. Halleri_, _H.\nPilosella_, _H. dubium_, _H. murorum_, &c. where we see how\ndifferent may be the kind of origin of the words.\n\n[Note 37\\8: _Ib._ s. 222.]\n\n[Note 38\\8: _Ib._ s. 260.]\n\n[Note 39\\8: Hooker, _Fl. Scot._ 228.]\n\nAttempts have been made at various times to form the name of\nspecies from those of genera in some more symmetrical\nmanner. Thus some have numbered the species of genus, 1, 2,\n3, &c.; but this method is liable to the inconveniences,\nfirst, that it offers nothing for the memory to take hold\nof; and second, that if a new species intermediate between 1\nand 2, 2 and 3, &c., be discovered, it cannot be put in its\nplace. It has also been proposed to mark the species by\naltering the termination of the genus. Thus Adanson[40\\8],\ndenoting a genus by the name _Fonna_ (_Lychnidea_),\nconceived he might mark five of its species by altering the\nlast vowel, _Fonna_, _Fonna-e_, _Fonna-i_, _Fonna-o_,\n_Fonna-u_; then others by _Fonna-ha_, _Fonna-ka_, and so on.\nThis course would be liable to the same evils which have\nbeen noticed as belonging to the numerical method.\n\n[Note 40\\8: Pref. clxxvi.]\n\nThe names of plants (and the same is true of animals) have\nin common practice been binary only, consisting of a generic\nand a specific name. The Class and Order have not been\nadmitted to form part of the appellation of the species.\nIndeed it is easy to see that a name which must be identical\nin so many instances as that of an Order would be, would be\nfelt as superfluous and burdensome. Accordingly, Linn\u00e6us\nmakes it a precept[41\\8], that the name of the Class and the\nOrder must not be expressed but understood: and hence, he\nsays, Royen, who took _Lilium_ for the name of a Class,\nrightly rejected it as a generic name, and substituted\n_Lirium_, with the Greek termination.\n\n[Note 41\\8: _Phil. Bot._ s. 215.]\n\nYet we must not too peremptorily assume such maxims as these\nto be universal for all classificatory sciences. It is very\npossible that it may be found advisable to use _three_\nterms, that of order, genus and {136} species, in\ndesignating minerals, as is done in Mohs's nomenclature; for\nexample, _Rhombohedral Calc Haloide_, _Paratomous Hal\nBaryte_.\n\nIt is possible also that it may be found useful in the same\nscience to mark some of the steps of classification by the\ntermination. Thus it has been proposed to confine the\ntermination _ite_ to the Order _Silicides_ of Naumann, as\nApophyll_ite_, Stilb_ite_, Leuc_ite_, &c., and to use names\nof different form in other orders, as Talc _Spar_ for\nBrennerite, Pyramidal Titanium _Oxide_ for Octahedrite. Some\nsuch method appears to be the most likely to give us a\ntolerable mineralogical nomenclature.\n\n\nSECT. VII.--_Diagnosis._\n\n20. German Naturalists speak of a part of the general method\nwhich they call the _Characteristik_ of Natural History, and\nwhich is distinguished from the _Systematik_ of the science.\nThe _Systematick_ arranges the objects by means of all their\nresemblances, the _Characteristick_ enables us to detect\ntheir place in the arrangement by means of a few of their\ncharacters. What these characters are to be, must be\ndiscovered by observation of the groups and divisions of the\nsystem when they are formed. To construct a collection of\nsuch characters as shall be clear and fixed, is a useful,\nand generally a difficult task; for there is usually no\napparent connexion between the marks which are used in\ndiscriminating the groups, and the nature of the groups\nthemselves. They are assumed only because the naturalist,\nextensively and exactly acquainted with the groups and the\nproperties of the objects which compose them, sees, by a\nsurvey of the field, that these marks divide it properly.\n\nThe Characteristick has been termed by some English\nBotanists the _Diagnosis_ of plants; a word which we may\nconveniently adopt. The Diagnosis of any genus or species is\ndifferent according to the system we follow. Thus in the\nLinn\u00e6an System the Diagnosis of the Rose is in the first\nplace given by its Class and Order: it is {137} Icosandrous,\nand Polygynous; and then the Generic Distinction is that the\ncalyx is five-cleft, the tube urceolate, including many\nhairy achenia, the receptacle villous[42\\8]. In the Natural\nSystem the Rose-Tribe are distinguished as being[43\\8]\n'Polypetalous dicotyledons, with lateral styles, superior\nsimple ovaria, regular perigynous stamens, exalbuminous\ndefinite seeds, and alternate stipulate leaves.' And the\ntrue Roses are further distinguished by having 'Nuts,\nnumerous, hairy, terminated by the persistent lateral style\nand inclosed within the fleshy tube of the calyx,' &c.\n\n[Note 42\\8: Lindley, _Nat. Syst._ p. 149.]\n\n[Note 43\\8: _Ib._ pp. 81, 3.]\n\nIt will be observed that in a rigorous Artificial System the\n_Systematick_ coincides with the _Characteristick_; the\n_Diataxis_ with the _Diagnosis_; the reason why a plant is\nput in a division is identical with the mode by which it is\nknown to be in the division. The Rose is in the class\n_icosandria_, because it has many stamens inserted in the\ncalyx; and when we see such a set of stamens we immediately\nknow the class. But this is not the case with the Diagnosis\nof Natural Families. Thus the genera _Lamium_ and\n_Galeopsis_ (Dead Nettle and Hemp Nettle) are each formed\ninto a separate group in virtue of their general\nresemblances and differences, and not because the former has\none tooth on each side of the lower lip, and the latter a\nnotch in its upper lip, though they are distinguished by\nthese marks.\n\nThus so far as our Systems are natural, (which, as we have\nshown, all systems to a certain extent must be), the\nCharacteristick is distinct both from a Natural and an\nArtificial System; and is, in fact, an Artificial Key to a\nNatural System. As being Artificial, it takes as few\ncharacters as possible; as being Natural, its characters are\nnot selected by any general or prescribed rule, but follow\nthe natural affinities. The Botanists who have made any\nsteps in the formation of a natural method of plants since\nLinn\u00e6us, have all attempted to give a Diagnosis\ncorresponding to the Diataxis of their method.\n\n\n\n{{138}}\nCHAPTER III.\n\nAPPLICATION OF THE NATURAL HISTORY METHOD TO MINERALOGY.\n\n\n1. THE philosophy of the Sciences of Classification has had\ngreat light thrown upon it by discussions concerning the\nmethods which are used in Botany: for that science is one of\nthe most complete examples which can be conceived of the\nconsistent and successful application of the principles and\nideas of Classification; and this application has been made\nin general without giving rise to any very startling\nparadoxes, or disclosing any insurmountable difficulties.\nBut the discussions concerning methods of Mineralogical\nClassification have been instructive for quite a different\nreason: they have brought into view the boundaries and the\ndifficulties of the process of Classification; and have\npresented examples in which every possible mode of\nclassifying appeared to involve inextricable contradictions.\nI will notice some of the points of this kind which demand\nour attention, referring to the works published recently by\nseveral mineralogists.\n\nIn the History of Mineralogy we noticed the attempt made by\nMohs and other Germans to apply to minerals a method of\narrangement similar to that which has been so successfully\nemployed for plants. The survey which we have now taken of\nthe grounds of that method will point out some of the\nreasons of the very imperfect success of this attempt. We\nhave already said that the _Terminology_ of Mineralogy was\nmaterially reformed by Werner; and including in this branch\nof the subject (as we must do) the Crystallography of later\nwriters, it may be considered as to a great extent complete.\nOf the attempts at a Natural arrangement, that of Mohs\nappears to proceed by the {139} method of _blind trial_, the\nundefinable perception of relationship, by which the\nearliest attempts at a Natural Arrangement of plants were\nmade. Breithaupt however, has made (though I do not know\nthat he has published) an essay in a mode which corresponds\nvery nearly to Adanson's process of _multiplied\ncomparisons_. Having ascertained the specific gravity and\nhardness of all the species of minerals, he arranged them in\na table, representing by two lines at right angles to each\nother these two numerical quantities. Thus all minerals were\ndistributed according to two co-ordinates representing\nspecific gravity and hardness. He conceived that the groups\nwhich were thus brought together were natural groups. On\nboth these methods, and on all similar ones, we might\nobserve, that in minerals as in plants, the mere general\nnotion of Likeness cannot lead us to a real arrangement:\nthis notion requires to have precision and aim given it by\nsome other relation;--by the relation of Chemical\nComposition in minerals, as by the relation of Organic\nFunction in vegetables. The physical and crystallographical\nproperties of minerals must be studied with reference to\ntheir constitution; and they must be arranged into Groups\nwhich have some common Chemical Character, before we can\nconsider any advance as made towards a Natural Arrangement.\n\nIn reality, it happens in Mineralogy as it happened in\nBotany, that those speculators are regulated by an obscure\nperception of this ulterior relation, who do not profess to\nbe regulated by it. Several of the Orders of Mohs have\nreally great unity of chemical character, and thus have good\nevidence of their being really Natural Orders.\n\n2. Supposing the Diataxis of minerals thus obtained, Mohs\nattempted the Diagnosis; and his _Characteristick of the\nMineral Kingdom_, published in Dresden, in 1820, was the\nfirst public indication of his having constructed a system.\nFrom the nature of a Characteristick, it is necessarily\nbrief, and without any ostensible principle; but its\nimportance was duly appreciated by the author's countrymen.\nSince that {140} time, many attempts have been made at\nimproved arrangements of minerals, but none, I think,\n(except perhaps that of Breithaupt,) professing to proceed\nrigorously on the principles of Natural History;--to arrange\nby means of external characters, neglecting altogether, or\nrather postponing, the consideration of chemical properties.\nBy relaxing from this rigour, however, and by combining\nphysical and chemical considerations, arrangements have been\nobtained (for example, that of Naumann,) which appear more\nlikely than the one of Mohs to be approximations to an\nultimate really natural system. Naumann's Classes are\n_Hydrolytes_, _Haloides_, _Silicides_, _Metal Oxides_,\n_Metals_, _Sulphurides_, _Anthracides_, with subdivisions of\nOrders, as _Anhydrous unmetallic Silicides_. It may be\nremarked that the designations of these are mostly chemical.\nAs we have observed already, Chemistry, and Mineralogy in\nits largest sense, are each the necessary supplement of the\nother. If Chemistry furnish the Nomenclature, Mineralogy\nmust supply the Physiography: if the Arrangement be founded\non External Characters and the Names be independent of\nChemistry, the chemical composition of each species is an\nimportant scientific Truth respecting it.\n\n3. The inquiry may actually occur, whether any subordination\nof groups in the mineral kingdom has really been made out.\nThe ancient chemical arrangements, for instance, that of\nHa\u00fcy, though professing to distribute minerals according to\nClasses, Orders, Genera, and Species, were not only\narbitrary, but inapplicable; for the first postulate of any\nmethod, that the species should have constant characters of\nunity and difference, was not satisfied. It was not\nascertained that carbonate of lime was really\ndistinguishable in all cases from carbonate of magnesia, or\nof iron; yet these species were placed in remote parts of\nthe system: and the above carbonates made just so many\nspecies; although, if they were distinct from one another at\nall, they were further distinguishable into additional\nspecies. Even now, we may, perhaps, say that the limits of\nmineralogical species, and their laws of fixity, are {141}\nnot yet clearly seen. For the discoveries of the isomorphous\nrelations and of the optical properties of minerals have\nrather shown us in what direction the object lies, than led\nus to the goal. It is clear that, in the mineral kingdom,\nthe Definition of Species, borrowed from the laws of the\ncontinuation of the kind, which holds throughout the organic\nworld, fails us altogether, and must be replaced by some\nother condition: nor is it difficult to see that the\ndefinite atomic relations of the chemical constituents, and\nthe definite crystalline angle, must supply the principles\nof the _Specific_ Identity for minerals. Yet the exact\nlimits of definiteness in both these cases (when we admit\nthe effect of mechanical mixtures, &c.) have not yet been\ncompletely disentangled. Moreover, any _arbitrary_\nassumption (as the allowance of a certain per-centage of\nmixture, or a certain small deviation in the angle,) is\naltogether contrary to the philosophy of the Natural System,\nand can lead to no stable views. It is only by laborious,\nextensive, and minute research, that we can hope to attain\nto any solid basis of arrangement.\n\n4. Still, though there are many doubts respecting\nmineralogical species, a large number of such species are so\nfar fixed that they may be supposed capable of being united\nunder the higher divisions of a system with approximate\ntruth. Of these higher divisions, those which have been\ntermed _Orders_ appear to tend to something like a fixed\nchemical character. Thus the _Haloids_ of Naumann, and\nmostly those of Mohs, are combinations of an oxide with an\nacid, and thus resemble Salts, whence their name. The\nSilicides contain most of Mohs's _Spaths_: and the Orders\n_Pyrites_, _Glance_, and _Blende_, are common to Naumann and\nMohs; being established by the latter on a difference of\nexternal character, which difference is, indeed, very\nmanifest; and being included by the former in one chemical\n_Class_, _Sulphurides_. The distinctions of _Hydrous_ and\n_Anhydrous_, _Metallic_ and _Unmetallic_, are, of course,\nchemical distinctions, but occur as the differences of\nOrders in Naumann's mixed system. {142}\n\nWe may observe that some French writers, following Ha\u00fcy's\nlast edition, use, instead of _metallic_ and _unmetallic_,\n_autopside metallic_ and _heteropside metallic_; meaning by\nthis phraseology to acknowledge the discovery that earths,\netc., _are_ metallic, though they do not _appear_ to be so,\nwhile metals both are and appear metallic. But this seems to\nbe a refinement not only useless but absurd. For what is\ngained by adding the word _metallic_, which is common to\nall, and therefore makes no distinction? If certain metals\nare distinguished by their _appearing_ to be metals, this\nappearance is a reason for giving them the peculiar name,\n_metals_. Nothing is gained by first bringing earths and\nmetals together, and then immediately separating them again\nby new and inconvenient names. No proposition can be\nexpressed better by calling _earths_, _heteropside metallic\nsubstances_, and therefore such nomenclature is to be\nrejected.\n\nGranting, then, that the Orders of the best recent\nmineralogical systems approximate to natural groups, we are\nled to ask whether the same can be said of the Genera of the\nNatural History systems, such as those of Mohs and\nBreithaupt. And here I must confess that I see no principle\nin these Genera; I have failed to apprehend the conceptions\nby the application of which they have been constructed: I\nshall therefore not pass any further judgment upon them. The\nsubordination of Mineralogical Species to Orders is a\nmanifest gain to science: in the interposition of Genera I\nsee nothing but a source of confusion.\n\n5. In Mineralogy, as in other branches of natural history, a\nreformed arrangement ought to give rise to a reformed\nNomenclature; and for this, there is more occasion at\npresent in Mineralogy than there was in Botany at the worst\nperiod, at least as far as the extent of the subject allows.\nThe characters of minerals are much more dimly and\nunfrequently developed than those of plants; hence arbitrary\nchemical arrangements, which could not lead to any natural\ngroups, and therefore not to any good names, prevailed till\nrecently; and this state of things produced an anarchy {143}\nin which every man did what seemed right in his own\neyes,--proposed species without any ascertained distinction,\nand without a thought of subordination, and gave them\narbitrary names; and thus with only about two or three\nhundred known species, we have thousands upon thousands of\nnames, of anomalous form and uncertain application.\n\nMohs has attempted to reform the Nomenclature of the subject\nin a mode consistent with his attempt to reform the System.\nIn doing this, he has fatally transgressed a rule always\ninsisted upon by the legislators of Botany, of altering\nusual names as little as possible; and his names are both so\nnovel and so cumbrous, that they appear to have little\nchance of permanent currency. They are, perhaps, more\nunwieldy than they need to be, by referring, as we have\nsaid, to three of the steps of his classification, the\nSpecies, Genus, and Order. We may, however, assert\nconfidently, from the whole analogy of natural history, that\nno good names can be found which do not refer to at least\n_two_ terms of the arrangement. This rule has been\npractically adopted to a great extent by Naumann, who gives\nto most of his Haloids the name _Spar_, as Calc spar, Iron\nspar, &c.; to all his Oxides the terminal word _Erz_\n(_Ore_); and to the species of the orders _Kies_\n(_Pyrites_), _Glance_, and _Blende_, these names. It has\nalso been theoretically assented to by Beudant, who proposes\nthat we should say _silicate stilbite_, _silicate chabasie_;\n_carbonate calcaire_, _carbonate witherite_; _sulphate\ncouperose_, &c. One great difficulty in this case would\narise from the great number of _silicides_; it is not likely\nthat any names would obtain a footing which tacked the term\n_silicide_ to another word for each of these species. The\nartifice which I have proposed, in order to obviate this\ndifficulty, is that we should make the names of the\nsilicides, and those alone, end in _ite_ or _lite_, which a\nlarge proportion of them do already.\n\nBy this and a few similar contrivances, we might, I\nconceive, without any inconvenient change, introduce into\nMineralogy a systematic nomenclature. {144}\n\n6. I shall now proceed to make a few remarks on a work on\nMineralogy more recent than those which I have above\nnoticed, and written with express reference to such\ndifficulties as I have been discussing. I allude to the\ntreatise of M. Necker, _Le R\u00e8gne Mineral ramen\u00e9 aux Methods\nd'Histoire Naturelle_[44\\8], which also contains various\ndissertations on the Philosophy of Classification in\ngeneral, and its application to Mineralogy in particular.\n\n[Note 44\\8: Paris, 1835.]\n\nM. Necker remarks very justly, that Mineralogy, as it has\nhitherto been treated, differs from all other branches of\nNatural History in this:--that while it is invested with all\nthe forms of the sciences of classification,--Classes,\nDivisions, Genera, and the like,--the properties of those\nbodies to which the mineralogical student's attention is\ndirected have no bearing whatever on the classification. A\nperson, he remarks[45\\8], might be perfectly well acquainted\nwith all the characters of minerals which Werner or Ha\u00fcy\nexamined so carefully, and might yet be quite unable to\nassign to any mineral its place in the divisions of their\nmethods. There is[46\\8] a complete separation between the\nstudy of mineralogical characters and the recognition of the\nname and systematic place of a mineral. Those who know\n_mineralogy_ well, may know _minerals_ ill, or hardly at\nall; the systematist may be in such knowledge vastly\ninferior to the mineral-dealer or the miner. In this respect\nthere is a complete contrast between this science and other\nclassificatory sciences.\n\n[Note 45\\8: _R\u00e8gne Mineral_, p. 3.]\n\n[Note 46\\8: _Ib._ p. 8.]\n\nAgain, in the best-known systems of Mineralogy, (as those of\nWerner and Ha\u00fcy,). the bodies which are grouped together as\nbelonging to the same division, have not, as they have in\nother classificatory sciences, any resemblance. The\ndifferent members of the larger classes are united by the\ncommon possession of some abstract property,--as, that they\nall contain iron. This is a property to which no common\ncircumstance in the bodies themselves corresponds. What is\nthere common to the minerals named oxidulous iron, sulphuret\n{145} of iron, carbonate of iron, sulphate of iron, except\nthat they all contain iron? And when we have classed these\nbodies together, what general assertion can we make\nconcerning them, except that which is the ground of our\nclassification, that they contain iron? They have nothing in\ncommon with iron or with each other in any other way.\n\nAgain, as these classes have no general properties, all the\nproperties are particular to the species; and the\ndescriptions of these necessarily become both tediously\nlong, and inconveniently insulated.\n\n7. These inconveniences arise from making Chemical\nComposition the basis of Mineralogical Classification\nwithout giving Chemical Analysis the first place among\nMineral Properties. Shall we, then, correct this omission,\nso far as it has affected mineralogical systems? Shall we\nteach the student the chemical analysis of minerals, and\nthen direct him to classify them according to the results of\nhis analysis[47\\8]?\n\n[Note 47\\8: _R\u00e8gne Mineral_, p. 18.]\n\nBut why should we do this? To what purpose, or on what\nground, do we arrange the results of chemical analysis\naccording to the forms and subordination of natural history?\nIs not Chemistry a science distinct from Natural History?\nAre not the sciences opposed? Is not natural history\nconfined to organic bodies? Can mere chemical elements and\ntheir combinations be, with any propriety or consistency,\narranged into Species, Genera, and Families? What is the\nprinciple on which genera and species depend? Do not Species\nimply Individuals? What is an Individual in the case of a\nchemical substance?\n\n8. We thus find some of the widest and deepest questions of\nthe philosophy of classification brought under our\nconsideration when we would provide a method for the\nclassification of minerals. The answers to these questions\nare given by M. Necker; and I shall state some of his\nopinions; taking the liberty of adding such remarks as are\nsuggested by referring the subject {146} to those principles\nwhich have already been established in this work.\n\nM. Necker asserts[48\\8] that the distinctions of different\nSciences depend, not on the objects they consider, but on\nthe different and independent points of view on which they\nproceed. Each science has its logic, that is, its mode of\napplying the general rules of human reason to its own\nspecial case. It has been said by some[49\\8], that in\nminerals, natural history and chemistry contemplate common\nobjects, and thus form a single science. But do chemistry\nand natural history consider minerals in the same point of view?\n\n[Note 48\\8: _R\u00e8gne Mineral_, p. 23.]\n\n[Note 49\\8: _Ib._ p. 27.]\n\nThe answer is, that they do not. Physics and Chemistry\nconsider the properties of bodies in an abstract manner; as,\ntheir composition, their elements, their mutual actions,\nwith the laws of these; their forces, as attraction,\naffinity; all which objects are abstract ideas. In these\ncases we have nothing to do with bodies themselves, but as\nthe vehicles of the powers and properties which we\ncontemplate.\n\nNatural History, on the other hand, has to do with natural\nbodies: their properties are not considered abstractedly,\nbut only as characters. If the properties are abstracted, it\nis but for a moment. Natural history has to describe and\nclass bodies as they are. All which cannot be perceived by\nthe senses, belongs not to its domain, as molecules, atoms,\nelements.\n\nNatural history[50\\8] may have recourse to physics or\nchemistry in order to recognize those properties of bodies\nwhich serve as characters; but natural history is not, on\nthat account, physics or chemistry. Classification is the\nessential business of the natural historian[51\\8], to which\ntask chemistry and physics are only instrumental, and the\nfurther account of properties only complementary.\n\n[Note 50\\8: _Ib._ p. 37.]\n\n[Note 51\\8: _Ib._ p. 41.]\n\nIt has been said, in support of the doctrine that chemistry\nand mineralogy are identical, that chemistry does not\nneglect external characters. 'The chemist in {147}\ndescribing sulphur, mentions its colour, taste, odour,\nhardness, transparence, crystalline form, specific gravity;\nhow does he then differ from the mineralogist?' But to this\nit is replied, that these notices of the external characters\nof this or any substance are introduced in chemistry merely\nas convenient marks of recognition; whereas they are\nessential in mineralogy. If we had taken the account given\nof several substances instead of one, we should have seen\nthat the chemist and the naturalist consider them in ways\naltogether different. The chemist will make it his business\nto discover the mutual action of the substances; he will\ncombine them, form new products, determine the proportions\nof the elements. The mineralogist will divide the substances\ninto groups according to their properties, and then\nsubdivide these groups, till he refers each substance to its\nspecies. Exterior and physical characters are merely\naccessory and subordinate for the chemist; chemistry is\nmerely instrumental for the mineralogist.\n\nThis view agrees with that to which we have been led by our\nprevious reasonings; and may, according to our principles,\nbe expressed briefly by saying, that the Idea which\nChemistry has to apply is the Idea of Elementary\nComposition, while Natural History applies the Idea of\nGraduated Resemblances, and thus performs the task of\nclassification.\n\n9. The question occurs[52\\8], whether Natural History can be\napplied to Inorganic Substances? And the answer to this\nquestion is, that it can be applied, if there are such\nthings as inorganic individuals, since the resemblances and\ndifferences with which natural history has to do are the\nresemblances and differences of individuals.\n\n[Note 52\\8: _R\u00e8gne Mineral_, p. 46.]\n\nWhat is an Individual? It certainly is not that which is so\nsimple that it cannot be divided. Individual animals are\ncomposed of many parts. But if we examine, we shall find\nthat our Idea of an Individual is, that it is a whole\ncomposed of parts, which {148} are not similar to the whole,\nand have not an independent existence, while the whole has\nan independent existence and a definite form[53\\8].\n\n[Note 53\\8: _R\u00e8gne Mineral_, p. 52.]\n\nWhat then is the Mineralogical Individual? At first, while\nminerals were studied for their use, the most precious of\nthe substances which they contained was looked upon as the\ncharacteristic of the mineral. The smallest trace of silver\nmade a mineral an _ore of silver_. Thus forms and properties\nwere disregarded, and _substance_ was considered as\nidentical with _mineral_. And hence[54\\8] Daubenton refused\nto recognize _species_ in the mineral kingdom, because he\nrecognized no individuals. He proposed to call _sorts_ what\nwe call species. In this way of considering minerals, there\nare no individuals.\n\n[Note 54\\8: _Ib._ p. 54.]\n\n10. But still this is not satisfactory: for if we take a\nwell-formed and distinct crystal, this clearly _is_ an\nindividual[55\\8].\n\n[Note 55\\8: _Ib._ p. 56.]\n\nIt may be objected, that the crystal is divisible (according\nto the theory of crystallography) into smaller solids; that\nthese small solids are really the simple objects; and that\nactual crystals are formed by combinations of these\nmolecules according to certain laws.\n\nBut, as we have already said, an individual is such, not\nbecause it cannot be divided, but because it cannot be\ndivided into parts similar to the whole. As to the division\nof the form into its component _laws_, this is an abstract\nproceeding, foreign to natural history[56\\8]. Therefore\nthere is so far nothing to prevent a crystal from being an\nindividual.\n\n[Note 56\\8: _Ib._ p. 58.]\n\n11. We cannot (M. Necker goes on to remark) consider the\n_Integrant Molecules_ as individuals. These are useful\nabstractions, but abstractions only, which we must not deal\nwith as real objects. Ha\u00fcy himself warns us[57\\8] that his\ndoctrine of increments is a purely abstract conception, and\nthat nature, in fact, follows a different process.\nAccordingly, Weiss and Mohs express laws identical with\nthose of Ha\u00fcy, without even {149} speaking of molecules; and\nWollaston and Davy have deemed it probable that the\nmolecules are not polyhedrons, but spheres or spheroids.\nSuch mere creations of the mind can never be treated as\nindividuals. If the maxim of natural history,--that the\nSpecies is a collection of Individuals--be applied so as to\nmake those individuals mere abstractions; or if, instead of\nIndividuals, we take such an abstraction as Substance or\nMatter, the course of natural history is altogether\nviolated. And yet this errour has hitherto generally\nprevailed; and mineralogists have classified, not things,\nbut abstract ideas[58\\8].\n\n[Note 57\\8: _Ib._ p. 61.]\n\n[Note 58\\8: _R\u00e8gne Mineral_, p. 67.]\n\n12. But it may be said[59\\8], will not the small solids\nobtained by Cleavage better answer the idea of individuals?\nTo this it is replied, that these small solids have no\nindependent existence. They are only the result of a mode of\ndivision. They are never found separate and independent. The\nsecondary forms which they compose are determined by various\ncircumstances (the nature of the solution, &c.); and the\ncleavage which produces these small solids is only one\nresult among many, from the crystalline forces[60\\8].\n\n[Note 59\\8: _Ib._ p. 69.]\n\n[Note 60\\8: _Ib._ p. 71.]\n\nThus neither Integrant Molecules, nor Solids obtained by\nCleavage, can be such mineralogical Individuals as the\nspirit of natural history requires. Hence it appears that we\nmust take the real Crystals for Individuals[61\\8].\n\n[Note 61\\8: _Ib._ p. 73.]\n\n13. We must, however, reject crystals (generally large ones)\nwhich are obviously formed of several smaller ones of a\nsimilar form (as occurs so often in quartz and calc spar).\nWe must also distinguish cases in which a large regular form\nis composed of smaller but different regular forms (as\noctahedrons of fluor spar made up of cubes). Here the small\ncomponent forms are the individuals. Also we must notice the\ncases[62\\8] in which we have a natural crystal, similar to\nthe primary form. Here the face will show whether {150} the\nbody is a result obtained by cleavage or a natural individual.\n\n[Note 62\\8: _Ib._ p. 75.]\n\n14. It will be objected[63\\8], that the crystalline form\nought not to be made the dominant character in mineralogy,\nsince it rarely occurs perfect. To this it is replied, that\neven if the application of the principle be difficult, still\nit has been shown to be the only true principle, and\ntherefore we have no alternative. But further[64\\8], it is\nnot true that amorphous substances are more numerous than\ncrystals. In Leonhard's _Manual of Oryctognosy_, there are\n377 mineral substances. Of these, 281 have a crystalline\nstructure, and 96 only have not been found in a regular form.\n\n[Note 63\\8: _R\u00e8gne Mineral_, p. 79.]\n\n[Note 64\\8: _Ib._ p. 82.]\n\nAgain, the 281 crystalline forms have each its varieties,\nsome of which are crystalline, and some are not so. Now the\ncrystalline varieties amount to 1453, and the uncrystalline\nto 186 only. Thus mineralogy, according to the view of it\nhere presented, has a sufficiently wide field[65\\8].\n\n[Note 65\\8: _Ib._ p. 84.]\n\n15. It will be objected[66\\8], that according to this mode\nof proceeding, we must reject from our system all\nnon-crystalline minerals. But we reply, that if the mass be\ncomposed of crystals, the size of the crystals makes no\ndifference. Now lamellar and other compact masses are very\ngenerally groups of crystals in various positions.\nIndividuals mutilated and mixed together are not the less\nindividuals; and therefore such masses may be treated as\nobjects of natural history.\n\n[Note 66\\8: _Ib._ p. 86.]\n\nIf we cannot refer all rocks to crystalline species, those\nwhich elude our method may appear as an appendix,\ncorresponding to those plants which botanists call _genera\nincert\u00e6 sedis_[67\\8].\n\n[Note 67\\8: _Ib._ p. 91.]\n\nBut these genera and species will often be afterwards\nremoved into the crystalline part of the system, by being\nidentified with crystalline species. Thus _pyrope_, &c.,\nhave been referred to _garnet_, and _basalt_, {151} _wacke_,\n&c., to compound rocks. Thus veins of _Dolerite_, visibly\ncomposed of two or three elements, pass to an apparently\nsimple state by becoming fine-grained[68\\8].\n\n[Note 68\\8: _R\u00e8gne Mineral_, p. 93.]\n\n16. Finally[69\\8], we have to ask, are artificial crystals\nto enter into our classification? M. Necker answers, No;\nbecause they are the result of art, like mules, mestizos,\nhybrids, and the like.\n\n[Note 69\\8: _Ib._ p. 95.]\n\n17. Upon these opinions, we may observe, that they appear to\nbe, in the main, consistent with the soundest philosophy.\nThat each natural crystal is an individual, is a doctrine\nwhich is the only basis of Mineralogy as a Natural\nHistorical Science; yet the imperfections and confused\nunions of crystals make this principle difficult to apply.\nPerhaps it may be expressed in a more precise manner by\nreferring to the crystalline forces, and to the axes by\nwhich their operation is determined, rather than to the\nexternal form. _That_ portion of a mineral substance is a\nmineralogical _individual_ which is determined by\ncrystalline forces acting to the _same axes_. In this way we\navoid the difficulty arising from the absence of faces, and\nenable ourselves to use either cleavage, or optical\nproperties, or any others, as indications of the identity of\nthe individual. The individual extends so far as the polar\nforces extend by which crystalline form is determined,\nwhether or not those forces produce their full effect,\nnamely, a perfectly circumscribed polyhedron.\n\n18. There is only one material point on which our principles\nlead us to differ from M. Necker;--the propriety of\nincluding _artificial crystals_ in our mineralogical\nclassification. To exclude them, as he does, is a conclusion\nso entirely at variance with the whole course of his own\nreasonings, that it is difficult to conceive that he would\npersist in his conclusion, if his attention were drawn to\nthe question more steadily. For, as he justly says[70\\8],\neach science has its appropriate domain, determined by its\npeculiar point of view. Now artificial and natural crystals\nare considered in the same point of view, (namely, with\nreference to {152} crystalline, physical, and optical\nproperties, as subservient to classification,) and ought,\ntherefore, to belong to the same science. Again, he\nsays[71\\8], that Chemistry would reject as useless all\nnotice of the physical properties and external characters of\nsubstances, if a _special science_ were to take charge of\nthe description and classification of these products. But\nsuch a special science must be Mineralogy; for we cannot\nwell make one science of the classification of natural, and\nanother of that of artificial substances: or if we do, the\ntwo sciences will be identical in method and principles, and\nwill extend over each other's boundaries, so that it will be\nneither useful nor possible to distinguish them. Again, M.\nNecker's own reasonings on the selection of the individual\nin mineralogy are supported by well chosen examples[72\\8];\nbut these examples are taken from artificial salts; as, for\ninstance, common salt crystallizing in different mixtures.\nAgain, the analogy of mules and mestizos, as products of\nart, with chemical compounds, is not just. Chemical\ncompounds correspond rather to natural species, propagated\nby man under the most natural circumstances, in order that\nhe may study the laws of their production[73\\8].\n\n[Note 70\\8: _Ib._ p. 23.]\n\n[Note 71\\8: _R\u00e8gne Mineral_, p. 36.]\n\n[Note 72\\8: _Ib._ p. 71.]\n\n[Note 73\\8: We may remark that M. Necker, in his own\narrangement of minerals, inserts among his species Iron and\nLead, which do not occur Native.]\n\n19. But the decisive argument against the separation of\nnatural and artificial crystals in our schemes of\nclassification is, that we _cannot_ make such a separation.\nSubstances which were long known only as the products of the\nlaboratory, are often discovered, after a time, in natural\ndeposits. Are the crystals which are found in a forgotten\nretort or solution to be considered as belonging to a\ndifferent science from those which occur in a deserted mine?\nAnd are the crystals which are produced where man has turned\na stream of water or air out of its course, to be separated\nfrom natural crystals, when the composition, growth, and\nproperties, are exactly the same in both? And again: How\nmany natural crystals can we already produce by {153}\nsynthesis! How many more may we hope to imitate hereafter!\nM. Necker himself states[74\\8], that Mitscherlich found, in\nthe scori\u00e6 of the mines of Sweden and Germany, artificial\nminerals having the same composition and the same\ncrystalline form with natural minerals: as silicates of\niron, lime, and magnesia, agreeing with Peridot; bisilicate\nof iron, lime, and magnesia, agreeing with Pyroxene; red\noxide of copper; oxide of zinc; protoxide of iron (_fer\noxydul\u00e9_); sulphurets of iron, zinc, lead; arseniuret of\nnickel; black mica. These were accidental results of fusion.\nBut M. Berthier, by bringing together the elements in proper\nquantities, has succeeded in composing similar minerals, and\nhas thus obtained artificial silicates, with the same forms\nand the same characters as natural silicates. Other chemists\n(M. Haldat, M. Becquerel) have, in like manner, obtained, by\nartificial processes, other crystals, known previously as\noccurring naturally. How are these crystals, thus identical\nwith natural minerals, to be removed out of the domain of\nmineralogy, and transferred to a science which shall\nclassify artificial crystals only? If this be done, the\nmineralogist will not be able to classify any specimen till\nhe has human testimony whether it was found naturally\noccurring or produced by chemical art. Or is the other\nalternative to be taken, and are these crystals to be given\nup to mineralogy because they occur naturally also? But what\ncan be more unphilosophical than to refer to separate\nsciences the results of chemical processes closely allied,\nand all but identical? The chemist constructs bisilicates,\nand these are classified by the mineralogist: but if he\nconstructs a trisilicate, it belongs to another science. All\nthese intolerable incongruities are avoided by acknowledging\nthat artificial, as well as natural, crystals belong to the\ndomain of mineralogy. It is, in fact, the _name_ only of\n_Mineralogy_ which appears to discover any inconsistency in\nthis mode of proceeding. Mineralogy is the {154}\nrepresentative of a science which has a wider office than\nmineralogists first contemplated; but which must exist, in\norder that the body of science may be complete. There must,\nas we have already said, be a Science, the object of which\nis to classify bodies by their physical characters, in order\nthat we may have some means of asserting chemical truths\nconcerning bodies; some language in which we may express the\npropositions which chemical analysis discovers. And this\nScience will have its object prescribed, not by any\naccidental or arbitrary difference of the story belonging to\neach specimen;--not by knowing whether the specimen was\nfound in the mine or in the laboratory; produced by\nattempting to imitate nature, or to do violence to her:--but\nwill have its course determined by its own character. The\nrange and boundaries of this Science will be regulated by\nthe Ideas with which it deals. Like all other sciences, it\nmust extend to everything to which its principles apply. The\nlimits of the province which it includes are fixed by the\nconsideration that it must be a connected whole. No previous\ndefinition, no historical accident, no casual phrase, can at\nall stand in the way of philosophical consistency;--can make\nthis Science exclude what that includes, or oblige it to\nadmit what that rejects. And thus, whatever we call our\nScience;--whether we term it External Chemistry, Mineralogy,\nthe Natural History of Inorganic Bodies;--since it can be\nnothing but the Science of the Classification of Inorganic\nBodies of definite forms and properties, it must classify\nall such bodies, whether or not they be minerals, and\nwhether or not they be natural.\n\n[Note 74\\8: _R\u00e8gne Mineral_, p. 151.]\n\n20. In the application of the principles of classification\nto minerals, the question occurs, What are to be considered\nas mineral _Species_? By Species we are to understand,\naccording to the usage of other parts of natural history,\nthe lowest step of our subordinate divisions;--the most\nlimited of the groups which have definite distinctions. What\ndefinite distinctions of groups of objects of any kind\nreally occur in nature, is to be learnt from an examination\nof nature: and the {155} result of our inquiries will be\nsome general principle which connects the members of each\ngroup, and distinguishes the members of groups which, though\ncontiguous, are different. In the classification of\norganized bodies, the rule which thus presides over the\nformation of Species is the principle of _reproduction_.\nThose animals and those plants are of the same Species which\nare produced from a common stock, or which resemble each\nother as much as the progeny of a common stock. Accordingly\nin practice, if any questions arise whether two varieties of\nform in organic things be of the same or different species,\nit is settled by reference to the fact of reproduction; and\nwhen it is ascertained that the two forms come within the\nhabitual and regular limits of a common circle of\nreproduction, they are held to be of the same species. Now\nin crystals, this principle of reproduction disappears\naltogether, and the basis of the formation of species must\nbe sought elsewhere. We must have some other principle to\nreplace the reproduction which belongs only to organic life.\nThis principle will be, we may expect, one which secures the\npermanence and regularity of mineral forms, as the\nreproductive power does of animal and vegetable. Such a\nprinciple is the _Power of Crystallization_. The forces of\nwhich solidity, cohesion, and crystallization are the\nresult, are those which give to minerals their permanent\nexistence and their physical properties; and ever since the\ndiscovery of the distinctions of Crystalline Forms and\nCrystalline Systems, it is certain that this force\ndistinguishes groups of crystals in the most precise and\ndefinite manner. The rhombohedral carbonates of lime and of\niron, for instance, are distinguished exactly by the angles\nof their rhombohedrons. And if, in the case of any proposed\ncrystal, we should doubt to which kind the specimen belongs,\nthe measurement of the angles of cleavage would at once\ndecide the question. The principle of Crystallization\ntherefore appears, from analogy, to be exactly fitted to\ntake the place of the principle of organic Generation. The\nforces which make the individual permanent and its\nproperties definite, here stand in the place of the forces\n{156} which preserve the race, while individuals are\ngenerated and die.\n\n21. According to this view, the different Modifications of\nthe _same_ crystalline form would be _Varieties_ only of the\nsame Species. All the various solids, for example, which are\nproduced by the different laws of derivation of rhombohedral\ncarbonate of lime, would fall within the same Species. And\nthis appears to be required by the general analogy of\nNatural History. For these differences of form, produced by\nthe laws of crystalline derivation, are not _definite_. The\nfaces which are added to one form in order to produce\nanother, may be of any size, small or large, and thus the\ncrystal which represents one modification passes by\ninsensible degrees to another. The forms of calc spar, which\nwe call _dog-tooth spar_, _cannon spar_, _nail-head spar_,\nand the like, appear at first, no doubt, distinct enough;\nbut so do the races of dogs. And we find, in the mineral as\nin the animal, that the distinction is obliterated by taking\nsuch intermediate steps as really occur. And if a _fragment_\nof any of these crystals is given us, we can determine that\nit is rhombohedral carbonate of lime; but it is not\npossible, in general, to determine to which of the kinds of\ncrystals it has belonged.\n\n22. Notwithstanding these considerations, M. Necker has\ntaken for his basis of mineral species[75\\8] the _Secondary_\nModifications, and not the Primary Forms. Thus _cubical\ngalena_, _octahedral galena_, and _triform galena_, are,\nwith him, three _species_ of crystals.\n\n[Note 75\\8: _R\u00e8gne Mineral_, p. 396.]\n\nOn this I have to observe, as I have already done, that on\nthis principle we have no _definite_ distinction of species;\nfor these forms may and do pass into each other: among\ncubo-octahedrons of galena occur cubes and octahedrons, as\none face or another vanishes, and the transition is\ninsensible. We shall, on this principle, find almost always\nthree or four species in the same tuft of crystals; for\nalmost every individual in such assemblages may exhibit a\ndifferent combination of {157} secondary faces. Again, in\ncases where the secondary laws are numerous, it would be\nimpracticable to enumerate all their combinations, and\nimpossible therefore to give a list of species. Accordingly\nM. Necker[76\\8] gives seventy-one Species of _spath\ncalcaire_, and then says, 'Nous n'avons pas \u00e9numer\u00e9 la\ndixi\u00e8me partie des esp\u00e8ces connues de ce genre, qui se\nmontent \u00e0 plus de huit cents.' Again, in many substances, of\nwhich few crystals are found, every new specimen would be a\nnew species; if indeed it were perfect enough to be referred\nto a species at all. But from a specimen without perfect\nexternal form, however perfect in crystalline character,\nalthough everything else might be known,--angles, optical\nproperties, physical properties, and chemical\nconstitution,--the species could not be determined. Thus M.\nNecker says[77\\8] of the micas, 'Quant aux esp\u00e8ces propre \u00e0\nchaque genre, la lacune sera presque compl\u00e8te; car jusqu'ici\nles cristaux entiers de Mica et de Talc n'ont pas \u00e9t\u00e9 fort communs.'\n\n[Note 76\\8: _R\u00e8gne Mineral_, p. 364.]\n\n[Note 77\\8: _Ib._ ii. 414.]\n\nThese inconveniences arise from neglecting the leading rule\nof natural history, that the _predominant principle_ of the\nexistence of an object must determine the Species; whether\nthis principle be Reproduction operating for Development, or\nCrystallization operating for Permanence of form. We may add\nto the above statement of inconveniences this;--that if M.\nNecker's view of mineralogical species be adopted, the\ndistinction of Species is vague and indefinite, while that\nof Genera is perfectly precise and rigorous;--an aspect of\nthe system entirely at variance with other parts of Natural\nHistory; for in all these the Species is a more definite\ngroup than the Genus.\n\nThis result follows, as has already been said, from M.\nNecker's wish to have individuals marked by external form.\nIf, instead of this, we are contented to take for an\nindividual that portion of a mass, of whatever form, which\nis connected by the continuous influence of the same\ncrystalline forces, by whatever incidents these forces may\nbe manifested, (as cleavage, {158} physical and optical\nproperties, and the like,) our mode of proceeding avoids all\nthe above inconveniences, applies alike to the most perfect\nand most imperfect specimens, and gives a result agreeable\nto the general analogy of natural history, and the rules of\nits methods[78\\8].\n\n[Note 78\\8: I will not again enter into the subject of\nNomenclature; but I may remark that M. Necker has adopted\n(i. 415) the Nomenclature of Beudant, latinizing the names,\nand thus converting each into a single word. He has also\nintroduced, besides the names of Genera, names of Families\ntaken from the _typical_ Genus. Thus the Family of\n_Carbonidiens_ contains the following genera:\n_Calcispathum_, _Magnesispathum_, _Dolomispathum_,\n_Ferrispathum_, _&c._, _Malachita_, _Azuria_, _Gaylusacia_.]\n\nI now quit the subject of mere Resemblance, and proceed to\ntreat of that natural affinity which Natural Systems of\nClassification for organic bodies must involve.\n\n\n\n{{159}}\nCHAPTER IV.\n\nOF THE IDEA OF NATURAL AFFINITY.\n\n\n1. IN the Second Chapter of this Book it was shown that\nalthough the Classificatory Sciences proceed ostensibly upon\nthe Idea of Resemblance as their main foundation, they\nnecessarily take for granted in the course of their progress\na further Idea of Natural Affinity. This appeared[79\\8] by a\ngeneral consideration of the nature of Science, by the\nrecognition of natural species and genera, even in\nArtificial Systems of Classification[80\\8], and by the\n**attempts of botanists to form a Natural System. It further\nappeared that among the processes by which endeavours have\nbeen made to frame a Natural System, some, as the method of\n_Blind Trial_ and the method of _General Comparison_, have\nbeen altogether unsuccessful, being founded only upon a\ncollection of resemblances, casual in the one case and\narbitrary in the other. In neither of these processes is\nthere employed any general principle by which we may be\ndefinitely directed as to what resemblances we should\nemploy, or by which the result at which we arrive may be\nverified and confirmed. Our object in the present chapter is\nto show that the Idea of Natural Affinity supplies us with a\nprinciple which may answer such purposes.\n\n[Note 79\\8: Art. 5.]\n\n[Note 80\\8: Art. 7.]\n\nI shall first consider the Idea of Affinity as exemplified\nin organized beings. In doing this, we may appear to take\nfor granted Ideas which have not yet come under our\ndiscussion, as the Ideas of Organization, and Vital\nFunction; but it will be found that the principle to which\nwe are led is independent of these additional Ideas. {160}\n\n2. We have already seen that the attempts to discover the\ndivisions which result from this Natural Affinity have led\nto the consideration of the _Subordination of Characters_.\nIt is easy to see that some organs are more essential than\nothers to the existence of an organized being; the organs of\nnutrition, for example, more essential than those of\nlocomotion. But at the same time it is clear that any\n_arbitrary_ assumption of a certain scale of relative values\nof different kinds of characters will lead only to an\nArtificial System. This will happen, if, for example, we\nbegin by declaring the nutritive to be superior in\nimportance to the reproductive functions. It is clear that\nthis relation of importance of organs and functions must be\ncollected by the study of the organized beings; and cannot\nbe determined _\u00e0 priori_, without depriving us of all right\nto expect a general accordance between our system and the\narrangement of nature. We see, therefore, that our notion of\nNatural Affinity involves in it this consequence;--that it\nis not to be made out by an arbitrary subordination of characters.\n\n3. The functions and actions of living things which we\nseparate from each other in our consideration, cannot be\nsevered in nature. Each function is essential; Life implies\na collection of movements, and ceases when any of these\nmovements is stopped. A change in the organization\nsubservient to one set of functions may lead necessarily to\na change in the organization belonging to others. We can\noften see this necessary connexion; and from a comparison of\nthe forms of organized beings,--from the way in which their\nstructure changes in passing from one class to another, we\nare led to the conviction that there is some general\nprinciple which connects and graduates all such changes.\nWhen the circulatory system changes, the nervous system\nchanges also: when the mode of locomotion changes, the\nrespiration is also modified.\n\n4. These corresponding changes may be considered as ways in\nwhich the living thing is fitted to its mode of life; as\nmarks of _adaptation to a purpose_; or, as it has been\notherwise expressed, as results of the {161} _conditions of\nexistence_. But at the present moment, we put forward these\ncorrespondencies in a different light. We adduce them as\nillustrations of what we mean by Affinity, and what we\nconsider as the tendency of a Natural Classification. It has\nsometimes been asserted that if we were to classify any of\nthe departments of organized nature by means of one\nfunction, and then by means of another, the two\nclassifications, if each strictly consistent with itself,\nwould be consistent with each other. Such an assertion is\nperhaps more than we are entitled to make with confidence;\nbut it shows very well what is meant by Affinity. The\ndisposition to believe such a general identity of all\npartial natural classifications, shows how readily we fix\nupon the notion of Affinity, as a general result of the\ncauses which determine the forms of living things. When\nthese causes or principles, of whatever nature they are\nconceived to be, vary so as to modify one part of the\norganization of the being, they also modify another: and\nthus the groups which exhibit this variation of the\nfundamental principles of form, are the same, whether the\nmanifestation of the change be sought in one part or in\nanother of the organized structure. The groups thus formed\nare related by Affinity; and in proportion as we find the\nevidence of more functions and more organs to the propriety\nof our groups, we are more and more satisfied that they are\nNatural Classes. It appears, then, that our Idea of Affinity\ninvolves the conviction of the _Coincidence of natural\narrangements formed on different functions_; and this,\nrather than the principle of the Subordination of some\ncharacters to others, is the true ground of the natural\nmethod of Classification.\n\n5. For example, Cuvier, after speaking of the Subordination\nof Characters as the guide which he intends to follow in his\narrangement of animals, interprets this principle in such a\nmanner[81\\8] as to make it agree nearly with the one just\nstated: 'In pursuance of what has been said on methods in\ngeneral, we now require to {162} know what characters in\nanimals are the most influential, and therefore those which\nmust be made the grounds of the primary divisions.' 'These,'\nhe says, 'it is clear must be those which are taken from the\nanimal functions;--sensation and motion:'--But how does he\nconfirm this? Not by showing that the animal functions are\nindependent of, or predominant over, the vegetative, but by\nobserving that they follow the same gradations.\n'Observation,' he continues, 'confirms this view, by showing\nthat the degrees of development and complication of the\nanimal functions agree with those of the vegetative. The\nheart and the organs of the circulation are a sort of center\nfor the vegetative functions, as the brain and the trunk of\nthe nervous system are for the animal functions. Now we see\nthese two systems descend in the scale, and disappear the\none with the other. In the lowest animals, when there are no\nlonger any distinct nerves, there are also no longer\ndistinct fibres, and the organs of digestion are simply\nhollowed out in the homogeneous mass of the body. The\nmuscular system disappears even before the nervous, in\ninsects; but in general the distribution of the medullary\nmasses corresponds to that of the muscular instruments; a\nspinal cord, on which knots or ganglions represent so many\nbrains, corresponds to a body divided into numerous rings\nand supported on pairs of members placed at different points\nof the length, and so on.\n\n[Note 81\\8: _R\u00e8gne Animal_, p. 55.]\n\n'This _correspondence_ of the general forms which result\nfrom the arrangement of the motive organs, from the\ndistribution of the nervous masses, and from the energy of\nthe circulatory system, must therefore form the ground of\nthe first great sections by which we divide the animal kingdom.'\n\n6. Decandolle takes the same view. There must be, he says,\n_an equilibrium_ of the different functions[82\\8]. And he\nexemplifies this by the case of the distinction of\nmonocotyledonous and dicotyledonous plants, which being at\nfirst established by means of the organs of {163}\nreproduction, was afterwards found to coincide with the\ndistinction of endogenous and exogenous, which depends on\nthe process of nutrition. 'Thus,' he adds, '_the natural\nclasses founded on one of the great functions of the\nvegetable are necessarily the same as those which are\nfounded upon the other function_; and I find here a very\nuseful criterion to ascertain whether a class is natural:\nnamely, in order to announce that it is so, it must be\narrived at by the two roads which vegetable organization\npresents. Thus I affirm,' he says, 'that the division of\nmonocotyledons from dicotyledons, and the distinction of\nGramine\u00e6 from Cyperace\u00e6, are real, because in these cases, I\narrive at the same result by the reproductive and the\nnutritive organs; while the distinction of monopetalous and\npolypetalous, of Rhodorace\u00e6 and Ericine\u00e6, appears to me\nartificial, because I can arrive at it only by the\nreproductive organs.'\n\n[Note 82\\8: _Theor. Elem._ p. 79.]\n\nThus the Correspondence of the indications of different\nfunctions is the criterion of Natural Classes; and this\ncorrespondence may be considered as one of the best and most\ncharacteristic marks of the fundamental Idea of Affinity.\nAnd the Maxim by which all Systems professing to be natural\nmust be tested is this:--that the _arrangement obtained from\none set of characters coincides with the arrangement\nobtained from another set_.\n\nThis Idea of Affinity, as a natural connexion among various\nspecies, of which connexion all particular resemblances are\nindications, has principally influenced the attempts at\nclassifying the animal kingdom. The reason why the\nclassification in this branch of Natural History has been\nmore easy and certain than that of the vegetable world is,\nas Decandolle says[83\\8], that besides the functions of\nnutrition and reproduction, which animals have in common\nwith plants, they have also in addition the function of\nsensation; and thus have a new means of verification and\nconcordance. But we may add, as a further reason, that the\nfunctions of {164} animals are necessarily much more obvious\nand intelligible to us than those of vegetables, from their\nclear resemblance to the operations which take place in our\nown bodies, to which our attention has necessarily been\nstrongly directed.\n\n[Note 83\\8: _Theor. Elem._ p. 80.]\n\n7. The question here offers itself, whether this Idea of\nNatural Affinity is applicable to inorganic as well as to\norganic bodies;--whether there be Natural Affinities among\nMinerals. And to this we are now enabled to reply by\nconsidering whether or not the principle just stated is\napplicable in such cases. And the conclusion to which our\nprinciple leads us is,--that there are such Natural\nAffinities among Minerals, since there are different sets of\ncharacters which may be taken, (and have by different\nwriters been taken,) as the basis of classification. The\nhardness, specific gravity, colour, lustre, crystallization,\nand other _external_ characters, as they are termed, form\none body of properties according to which minerals may be\nclassified; as has in fact been done by Mohs, Breithaupt,\nand others. The _chemical_ constitution of the substances,\non the other hand, may be made the principle of their\narrangement, as was done by Ha\u00fcy, and more recently, and on\na different scheme, by Berzelius. Which of these is the true\nand natural classification? To this we answer, that _each_\nof these arrangements is true and natural, then, and then\nonly, when it coincides with the other. An arrangement by\nexternal characters which gives us classes possessing a\ncommon chemical character;--a chemical order which brings\ntogether like and separates unlike minerals;--such\nclassifications have the evidence of truth in their\nagreement with one another. Every classification of minerals\nwhich does not aim at and tend to such a result, is so far\nmerely arbitrary; and cannot be subservient to the\nexpression of general chemical and mineralogical truths,\nwhich is the proper purpose of such a classification.\n\n8. In the History of Mineralogy I have related the advances\nwhich have been made among mineralogists and chemists in\nmodern times towards a System {165} possessing this\ncharacter of truth. I have there described the mixed systems\nof Werner and Ha\u00fcy;--the attempt made by Mohs to form a pure\nNatural History system;--the first and second attempt of\nBerzelius to form a pure chemical system; and the failure of\nboth these attempts. But the distinct separation of the two\nelements of which science requires the coincidence threw a\nvery useful light upon the subject; and the succeeding mixed\nsystems, such as that of Naumann, approached much nearer to\nthe true conditions of the problem than any of the preceding\nones had done. Thus, as I have stated, several of Naumann's\ngroups have both a common chemical character and great\nexternal resemblances. Such are his _Anhydrous Unmetallic\nHaloids_--his _Anhydrous Metallic Haloids_--_Hydrous\nMetallic Haloids_--_Oxides_ of metals--_Pyrites_--_Glances_--\nBlendes_. The existence of such groups shows that we may hope\nultimately to obtain a classification of minerals which shall\nbe both chemically significant, and agreeable to the methods\nof Natural History: although when we consider how very imperfect\nas yet our knowledge of the chemical composition of minerals is,\nwe can hardly flatter ourselves that we shall arrive at such a\nresult very soon.\n\nWe have thus seen that in Mineralogy, as well as in the\nsciences which treat of organized bodies, we may apply the\nIdea of Natural Affinity; of which the fundamental maxim is,\nthat _arrangements obtained from different sets of\ncharacters must coincide_.\n\nSince the notion of Affinity is thus applicable to inorganic\nas well as to organic bodies, it is plain that it is not a\nmere modification of the Idea of Organization or Function,\nalthough it may in some of its aspects appear to approach\nnear to these other Ideas. But these Ideas, or others which\nare the foundation of them, necessarily enter in a very\nprominent and fundamental manner into all the other parts of\nNatural History. To the consideration of these, therefore,\nwe shall now proceed.\n\n\n\n\n{{167}}\nBOOK IX.\n\n\nTHE\nPHILOSOPHY\nOF\nBIOLOGY.\n\n\n\n\nLA vie est donc un TOURBILLON plus ou moins rapide, plus ou\nmoins compliqu\u00e9, dont la direction est constante, et qui\nentraine toujours des molecules de m\u00eames sorts, mais o\u00f9 les\nmolecules individuelles entrent et d'o\u00f9 elles sortent\ncontinuellement, de mani\u00e8re que la _Forme_ du corps vivant\nlui est plus essentielle que sa _Mati\u00e8re_.\n\nTant que ce mouvement subsiste, le corps o\u00f9 il s'exerce est\n_vivant_; _il vit_. Lorsque le mouvement s'arr\u00eate sans\nretour, le corps _meurt_.\n\nCUVIER, _R\u00e8gne Animal_, s. 12.\n\n\nI REMEMBER, upon asking our famous Harvey, what induced him\nto think of a circulation of the blood, he said, that\nobserving the valves in the veins of many parts of the body,\nso placed as to give a free passage to the blood towards the\nheart, but to oppose the passage of the venal blood the\ncontrary way, he imagined that so provident a cause as\nnature had not thus placed so many valves without design;\nand as no design seemed more probable than that the blood\ncould not well, because of the interposing valves, be sent\nby the veins to the limbs, it should be sent through the\narteries and return through the veins when valves did not\noppose its course that way.\n\nBOYLE, _On the Final Causes of Natural Things_. On the\nProposition: _'Tis often allowable for a naturalist, from the\nmanifest and apposite uses of the parts of animal bodies, to\ncollect some of the particular ends for which the Creator\ndesigned them: and in some cases we may, from the known\nnature and structure of the parts, draw particular\nconjectures about the particular offices of them._\n\n\n\n{{169}}\nBOOK IX.\n\n\nTHE PHILOSOPHY OF BIOLOGY.\n\n\nCHAPTER I.\n\nANALOGY OF BIOLOGY WITH OTHER SCIENCES.\n\n\n1. IN the History of the Sciences, after treating of the\nSciences of Classification, we proceeded to what are there\ntermed the Organical Sciences, including in this term\nPhysiology and Comparative Anatomy. A peculiar feature in\nthis group of sciences is that they involve the notion of\n_living_ things. The notion of _Life_, however vague and\nobscure it may be in men's minds, is apprehended as a\npeculiar Idea, not resolvable into any other Ideas, such,\nfor instance, as Matter and Motion. The separation between\nliving creatures and inert matter, between organized and\nunorganized beings, is conceived as a positive and\ninsurmountable barrier. The two classes of objects are\nconsidered as of a distinct kind, produced and preserved by\ndifferent forces. Whether the Idea of Life is really thus\noriginal and fundamental, and whether, if so, it be one Idea\nonly, or involve several, it must be the province of true\nphilosophy to determine. What we shall here offer may be\nconsidered as an attempt to contribute something to the\ndetermination of these questions; but we shall perhaps be\nable to make it appear that science is at present only in\nthe course of its progress towards a complete solution of\nsuch problems.\n\nSince the main feature of those sciences of which we have\nnow to examine the philosophy is, that they {170} involve\nthe Idea of Life, it would be desirable to have them\ndesignated by a name expressive of that circumstance. The\nword _Physiology_, by which they have most commonly been\ndescribed, means _the Science of Nature_; and though it\nwould be easy to explain, by reference to history, the train\nof thought by which the word was latterly restricted to\n_Living Nature_, it is plain that the name is,\netymologically speaking, loose and improper. The term\n_Biology_, which means exactly what we wish to express, _the\nScience of Life_, has often been used, and has of late\nbecome not uncommon among good winters. I shall therefore\nventure to employ it, in most cases, rather than the word\n_Physiology_.\n\n2. As I have already intimated, one main inquiry belonging\nto the Philosophy of Biology, is concerning the Fundamental\nIdea or Ideas which the science involves. If we look back at\nthe course and the results of our disquisitions respecting\nother sciences in this work, and assume, as we may\nphilosophically do, that there will be some general analogy\nbetween those sciences and this, in their development and\nprogress, we shall be enabled to anticipate in some measure\nthe nature of the view which we shall now have to take. We\nhave seen that in other subjects the Fundamental Ideas on\nwhich science depended, and the Conceptions derived from\nthese, were at first vague, obscure, and confused;--that by\ngradual steps, by a constant union of thought and\nobservation, these conceptions become more and more clear,\nmore and more definite;--and that when they approached\ncomplete distinctness and precision, there were made great\npositive discoveries into which these conceptions entered;\nand thus the new precision of thought was fixed and\nperpetuated in some conspicuous and lasting truths. Thus we\nhave seen how the first confused mechanical conceptions\n(Force, and the like,) were, from time to time, growing\nclearer, down to the epoch of Newton;--how true conceptions\nof Genera and of wider classes, gradually unfolded\nthemselves among the botanists of the sixteenth and\nseventeenth centuries;--how the idea of Substance became\nsteady enough to govern the {171} theories of chemists only\nat the epoch of Lavoisier;--how the Idea of Polarity,\nalthough often used by physicists and chemists, is even now\nsomewhat vague and indistinct in the minds of the greater\npart of speculators. In like manner we may expect to find\nthat the Idea of Life, if indeed _that_ be the governing\nIdea of the Science which treats of Living Things, will be\nfound to have been gradually approaching towards a distinct\nand definite form among the physiologists of all ages up to\nthe present day. And if this be the case, it may not be\nconsidered superfluous, with reference to so interesting a\nsubject, if we employ some space in tracing historically the\nsteps of this progress;--the changes by which the originally\nloose notion of Life, or of Vital Powers, became more nearly\nan Idea suited to the purposes of science.\n\n3. But we may safely carry this analogy between Biology and\nother sciences somewhat further. We have seen, in other\nsciences, that while men in their speculations were thus\ntending towards a certain peculiar Idea, but before they as\nyet saw clearly that it was peculiar and independent, they\nnaturally and inevitably clothed their speculations in\nconceptions borrowed from some other extraneous idea. And\nthe unsatisfactoriness of all such attempts, and the\nnecessary consequence of this, a constant alteration and\nsuccession of such inappropriate hypotheses, were\nindications and aids of the progress which was going on\ntowards a more genuine form of the science. For instance, we\nhave seen that in chemistry, so long as men refused to\nrecognize a peculiar and distinct kind of power in the\n_Affinity_ which binds together the elements of bodies, they\nframed to themselves a series of hypotheses, each\nconstructed according to the prevalent ideas of the time, by\nwhich they tried to represent the relation of the compound\nto the ingredients:--first, supposing that the elements\nbestowed upon the whole qualities _resembling_ their\nown:--then giving up this supposition, and imagining that\nthe properties of the body depended upon the _shape_ of the\ncomponent particles;--then, as their view expanded, assuming\nthat it was {172} not the shape, but the mechanical _forces_\nof the particles which gave the body its attributes;--and\nfinally acquiescing in, or rather reluctantly admitting, the\nidea of _Affinity_, conceived as a peculiar power, different\nnot only from material contact, but from any mechanical or\ndynamical attraction.\n\nNow we cannot but think it very natural, if we find that the\nhistory of Biology offers a series of occurrences of the\nsame nature. The notions of Life in general, or of any Vital\nFunctions or Vital Forces in particular, are obviously very\nloose and vague as they exist in the minds of most men. The\ndiscrepancies and controversies respecting the definitions\nof all such terms, which are found in all works on\nphysiology, afford us abundant evidence that these notions\nare not, at least not generally, apprehended with complete\nclearness and steadiness. We shall therefore find approaches\nand advances, intermediate steps, gradually leading up to\nthe greatest degree of distinctness which has yet been\nattained. And in those stages of imperfect apprehension in\nwhich the notions of Life and of Vital Powers are still too\nloose and unformed to be applied independently, we may\nexpect to find them supported and embodied by means of\nhypotheses borrowed from other subjects, and thus, made so\ndistinct and substantial as to supply at least a temporary\npossibility of scientific reasoning upon the laws of life.\n\n4. For example, if we suppose that men begin to speculate\nupon the properties of living things, not acknowledging a\npeculiar Vital Power, but making use successively of the\nknowledge supplied by the study of other subjects, we may\neasily imagine a series of hypotheses along which they would pass.\n\nThey would probably, first, in this as in other sciences,\nhave their thoughts occupied by vague and _mystical_ notions\nin which material and spiritual agency, natural and\nsupernatural events, were mixed together without\ndiscrimination, and without any clear notion at all. But as\nthey acquired a more genuine perception of the nature of\n**knowledge, they would naturally try to explain vital\nmotions and processes by means of {173} such forces as they\nhad learnt the existence of from other sciences. They might\nfirst have a _mechanical_ hypothesis, in which the\nmechanical _Forces_ of the solids and fluids which compose\norganized bodies should be referred to, as the most\nimportant influences in the process of life. They might then\nattend to the actions which the fluids exercise in virtue of\ntheir _Affinity_, and might thus form a _chemical_ theory.\nWhen they had proved the insufficience of these hypotheses,\nborrowed from the powers which matter exhibits in other\ncases, they might think themselves authorized to assume some\npeculiar power or agency, still material, and thus they\nwould have the hypothesis of a _Vital Fluid_. And if they\nwere driven to reject this, they might think that there was\nno resource but to assume an immaterial principle of life,\nand thus they would arrive at the doctrine of an _Animal Soul_.\n\nNow, through the cycle of hypotheses which we have thus\nsupposed, physiology has actually passed. The conclusions to\nwhich the most philosophical minds have been led by a survey\nof this progress is, that by the failure of all these\ntheories, men have exhausted this path of inquiry, and shown\nthat scientific truth is to be sought in some other manner.\nBut before I proceed further to illustrate this result, it\nwill be proper, as I have already stated, to exhibit\nhistorically the various hypotheses which I have described.\nIn doing this I shall principally follow the _History of\nMedicine_ of Sprengel. It is only by taking for my guide a\nphysiologist of acknowledged science and judgment, that I\ncan hope, on such a subject, to avoid errours of detail. I\nproceed now to give in succession an account of the\nMystical, the Iatrochemical, the Iatromathematical, and the\nVital-Fluid Schools; and finally of the Psychical School,\nwho hold the Vital Powers to be derived from the Soul\n(_Psyche_).\n\n\n\n{{174}}\nCHAPTER II.\n\nSUCCESSIVE BIOLOGICAL HYPOTHESES.\n\n\nSECT. I.--_The Mystical School._\n\nIN order to abbreviate as much as can conveniently be done\nthe historical view which I have now to take, I shall\naltogether pass over the physiological speculations of the\nancients, and begin my survey with the general revival of\nscience in modern times.\n\nWe need not dwell long on the fantastical and unsubstantial\ndoctrines concerning physiology which prevailed in the\nsixteenth century, and which flowed in a great measure from\nthe fertile but ill-regulated imaginations of the\ncultivators of Alchemy and Magic. One of the prominent\ndoctors of this school is the celebrated Paracelsus, whose\ndoctrines contained a combination of biblical\ninterpretations, visionary religious notions, fanciful\nanalogies, and bold experiments in practical medicine. The\nopinion of a close but mystical resemblance of parts between\nthe universe and the human body,--the _Macrocosm_ and the\n_Microcosm_,--as these two things, thus compared, were\ntermed, had probably come down from the Neoplatonists; it\nwas adopted by the Paracelsists[1\\9], and connected with\nvarious astrological dreams and cabbalistic riddles. A\nsuccession of later Paracelsists[2\\9], Rosicrucians, and\nother fanatics of the same kind, continued into the\nseventeenth century. Upon their notions was founded the\npretension of curing wounds by a sympathetic powder, which\nSir Kenelm Digby, among others, asserted; while animal\nmagnetism, and the transfer of diseases from one person to\nanother[3\\9], were maintained by others of this {175}\nschool. They held, too, the doctrines of _astral bodies_\ncorresponding to each terrestrial body; and of the\n_signatures_ of plants, that is, certain features in their\nexternal form by which their virtues might be known. How\nlittle advantage or progress real physiology could derive\nfrom speculations of this kind may be seen from this, that\ntheir tendency was to obliterate the distinction between\nliving and lifeless things: according to Paracelsus, all\nthings are alive, eat, drink, and excrete; even minerals and\nfluids[4\\9]. According to him and his school, besides\nmaterial and immaterial beings, there are _elementary\nSpirit_s which hold an intermediate place, _Sylvans_,\n_Nymphs_, _Gnomes_, _Salamanders_, &c. by whose agency\nvarious processes of enchantment may be achieved, and things\napparently supernatural explained. Thus this spiritualist\nscheme dealt with a world of its own by means of fanciful\ninventions and mystical visions, instead of making any step\nin the study of nature.\n\n[Note 1\\9: Spr. iii. 456.]\n\n[Note 2\\9: _Ib._ iv. 270.]\n\n[Note 3\\9: _Ib._ iv. 276.]\n\n[Note 4\\9: Spr. iii. 458. Parac. _De Vita Rerum Naturalium_, p. 889.]\n\nPerhaps, however, one of the most fantastical of the\ninventions of Paracelsus may be considered as indicating a\nperception of a peculiar character in the vital powers.\nAccording to him, the business of digestion is performed by\na certain demon whom he calls _Arch\u00e6us_, who has his abode\nin the stomach, and who, by means of his alchemical\nprocesses, separates the nutritive from the harmful part of\nour food, and makes it capable of assimilation[5\\9]. This\nfanciful notion was afterwards adopted and expanded by Van\nHelmont[6\\9]. According to him the stomach and spleen are\nboth under the direction of this Master-spirit, and these\ntwo organs form a sort of _Duumvirate_ in the body.\n\n[Note 5\\9: _Ib._ iii. 468.]\n\n[Note 6\\9: _Ib._ iv. 302.]\n\nBut though we may see in such writers occasional gleams of\nphysiological thought, the absence of definite physical\nrelations in the speculations thus promulgated was\nnecessarily intolerable to men of sound understanding and\nscientific tendencies. Such men naturally took hold of that\npart of the phenomena of life which could be most distinctly\nconceived, and {176} which could be apparently explained by\nmeans of the sciences then cultivated; and this was the part\nwhich appeared to be reducible to chemical conceptions and\ndoctrines. It will readily be supposed that the processes of\nchemistry have a considerable bearing upon physiological\nprocesses, and might, till their range was limited by a\nsound investigation, be supposed to have still more than\nthey really had; and thus a Physiology was formed which\ndepended mainly upon Chemistry, and the school which held\nthis doctrine has been called the _Iatrochemical_ School.\n\n\nSECT. II.--_The Iatrochemical School._\n\nThat all physical properties, and therefore chemical\nrelations, have a material influence on physiological\nresults, was already recognized, though dimly, in the\nGalenic doctrine of the 'four elementary qualities.' But at\nthe time of Paracelsus, chemical action was more distinctly\nthan before separated from other kinds of physical action;\nand therefore a physiological doctrine, founded upon\nchemistry, and freed from the extravagance and mysticism of\nthe Paracelsists, was a very promising path of speculation.\nAndrew Libavius[7\\9] of Halle, in Saxony, Physician and\nTeacher in the Gymnasium at Koberg, is pointed out by\nSprengel as the person who began to cultivate chemistry, as\ndistinct from the theosophic fantasies of his predecessors;\nand Angelus Sala of Vienna[8\\9], as his successor. The\nlatter has the laudable distinction of having rejected the\nprevalent conceits about a potable gold, a universal\nmedicine, and the like[9\\9]. In Germany already at the\nbeginning of the seventeenth century a peculiar chair of\n_Chymiatria_ was already created at Marpurg: and many in\nvarious places pursued the same studies, till, in the middle\nof the seventeenth century, we come to Lemery[10\\9], the\nprincipal reformer of pharmaceutical chemistry. But we are\nnot here so much concerned {177} with the practical as with\nthe theoretical parts of Iatrochemistry; and hence we pass\non to Sylvius[11\\9] and his system.\n\n[Note 7\\9: Spr. iii. 550.]\n\n[Note 8\\9: _Ib._ iv. 281.]\n\n[Note 9\\9: _Ib._ iv. 283.]\n\n[Note 10\\9: _Ib._ iv. 291.]\n\n[Note 11\\9: Spr. iv. 336.]\n\nThe opinion that chemistry had an important bearing upon\nphysiology did not, however, begin with Sylvius. Paracelsus,\namong his extravagant absurdities, did some service to\nmedicine by drawing attention to this important truth. He\nused[12\\9] chemical principles for the explanation of\nparticular diseases: most or all diseases according to him,\narise from the effervescence of salts, from the combustion\nof sulphur, or from the coagulation of mercury. His\nmedicines were chemical preparations; and it was[13\\9] an\nundeniable advantage of the Paracelsian doctrine that\nchemistry thus became indispensable to the physician. We\nstill retain a remnant of the chemical nomenclature of\nParacelsus in the term _tartar_, denoting the stony\nconcretion which forms on the teeth[14\\9]. According to him\nthere is a certain substance, the basis of all diseases\nwhich arise from a thickening of the juices and a collection\nof earthy matter; and this substance he calls _Tartarus_,\nbecause 'it burns like the fire of hell.' Helmont, the\nsuccessor of Paracelsus in many absurdities, also followed\nhim in the attempt to give a chemical account, however loose\nand wild, of the functions of the human body; and is by\nSprengel considered, with all his extravagancies, as a\nmeritorious and important discoverer. The notion of the\nfermentation of fluids[15\\9], and of the a\u00ebrial product\nthence resulting, to which he gave the name of _Gas_, forms\nan important part of his doctrines; and of the six\ndigestions which he assumes, the _first_ prepares an acid,\nwhich is neutralized by the gall when it reaches the\nduodenum, and this constitutes the _second_ digestion.\n\n[Note 12\\9: _Ib._ iii. 472.]\n\n[Note 13\\9: _Ib._ iii. 482.]\n\n[Note 14\\9: _Ib._ iii. 475.]\n\n[Note 15\\9: Vol. v. 315.]\n\nI have already, in the History of Chemistry[16\\9], stated,\nthat the doctrine of the opposition of acid and alkali, the\ngreat step which theoretical chemistry owes to Sylvius, was\nfirst brought into view as a physiological {178} tenet,\nalthough we had then to trace its consequences in another\nscience. The explanation of all the functions of the animal\nsystem, both healthy and morbid, by means of this and other\nchemical doctrines, and the prescription of methods of cure\nfounded upon such explanations, form the scheme of the\n_iatrochemical_ school; a school which almost engrossed the\nfavour of European physicians during the greater part of the\nseventeenth century.\n\n[Note 16\\9: _Hist. Ind. Sc._ b. xiii. c. 2.]\n\nSylvius taught medicine at Leyden, from the year 1658, with\nso much success, that Boerhaave alone surpassed him[17\\9].\nHis notions, although he piqued himself on their\noriginality, were manifestly suggested in no small degree\n(as all such supposed novelties are) by the speculations of\nhis predecessors, and the spirit of the times. Like\nHelmont[18\\9], he considers digestion as consisting in a\nfermentation; but he states it more definitely as the\neffervescence of an acid, supplied by the saliva and the\npancreatic juice, with the alkali of the gall. By various\nother hypothetical processes, all of a chemical nature, the\nblood becomes a collection of various juices, which are the\nsubjects of the speculations of the iatrochemists, to the\nentire neglect of the solid parts of the body. Diseases were\naccounted for by a supposed prevalence of one or the other\nof the acrid principles, the acid or the alkaline: and\nSylvius[19\\9] was bold enough to found upon these hypotheses\npractical methods of cure, which were in the highest degree\nmischievous.\n\n[Note 17\\9: Spr. iv. 336.]\n\n[Note 18\\9: _Ib._ 338.]\n\n[Note 19\\9: _Ib._ iv. 345.]\n\nThe Sylvian doctrine was often combined with some of the\nnotions of the Cartesian system of philosophy; but this\nmixture I shall not notice, since my present object is to\ntrace the history of a mere chemical physiology as one of\nthe unsuccessful attempts at a philosophy of life. With\nvarious modifications, this doctrine was diffused over\nEurope. It gave rise to several controversies, which turned\nupon the questions of the novelty of the doctrine, and the\nuse of chemical remedies to which it pointed, as well as\nupon its {179} theoretical truth. We need not dwell long\nupon these controversies, although they were carried on with\nno small vehemence in their time. Thus the school of Paris\nopposed all innovation, remained true to the Galenic\ndogmatism, and declared itself earnestly against all\ncombination of chemistry with medicine; and even against the\nchemical preparation of medicaments. Guy Patin, a celebrated\nand learned professor of that day, declares[20\\9] that the\nchemists are no better than forgers, and ought to be\npunished as such. The use of antimonial medicines was a main\npoint of dispute between the iatrochemists and their\nopponents; Patin maintained that more men had been destroyed\nby antimony than by the thirty years' war of Germany; and\nendeavoured to substantiate this assertion by collecting all\nsuch cases in his _Martyrologium Antimonii_. It must have\nbeen a severe blow to Patin when[21\\9] in 1666, the Doctors\nof the Faculty of Paris, assembled by command of the\nparliament, declared, by a majority of ninety-two voices,\nthat the use of antimonial medicines was allowable and\nlaudable, and when all attempts to set aside this decision failed.\n\n[Note 20\\9: Spr. 349.]\n\n[Note 21\\9: _Ib._ iv. 350.]\n\nFlorentius Schuyl of Leyden sought to recommend the\niatrochemical doctrines, by maintaining that they were to be\nfound in the Hippocratic writings; nor was it difficult to\ngive a chemical interpretation of the humoral pathology of\nthe ancients. The Italian[22\\9] physicians also, for the\nmost part, took this line, and attempted to show the\nagreement of the principles of the ancient school of\nmedicine with the new chemical notions. This, indeed, is the\nusual manner in which the diffusion of new theoretical ideas\nbecomes universal.\n\n[Note 22\\9: _Ib._ 368.]\n\nThe progress of the chemical school of medicine in\nEngland[23\\9] requires our more especial notice. Willis was\nthe most celebrated champion of this sect. He assumed, but\nwith modifications of his own, the three Paracelsian\nprinciples, Salt, Sulphur, and Mercury; considered digestion\nas the effect of an acid, and {180} explained other parts of\nthe animal economy by distillation, fermentation, and the\nlike. All diseases arise from the want of the requisite\n_ferment_; and the physician, he says[24\\9], may be compared\nto a vintner, since both the one and the other have to take\ncare that the necessary fermentations go on, that no foreign\nmatter mixes itself with the wine of life, to interrupt or\nderange those operations. In the middle of the seventeenth\ncentury, medicine had reached a point in which the life of\nthe animal body was considered as merely a chemical process;\nthe wish to explain everything on known principles left no\nrecognized difference between organized and unorganized\nbodies, and diseases were treated according to this delusive\nnotion. The condition of chemistry itself during this\nperiod, though not one of brilliant progress, was\nsufficiently stable and flourishing to give a plausibility\nto any speculation which was founded on chemical principles;\nand the real influence of these principles in the animal\nframe could not be denied.\n\n[Note 23\\9: _Ib._ 353.]\n\n[Note 24\\9: Spr. 354.]\n\nThe iatrochemists were at first resisted, as we have seen,\nby the adherents of the ancient schools; they were attacked\non various grounds, and finally deposed from them ascendancy\nby another sect, which we have to speak of, as the\niatromathematical, or mechanical school. This sect was no\nless unsatisfactory and erroneous in its positive doctrines\nthan the chemists had been; for the animal frame is no more\na mere machine than a mere laboratory: but it promoted the\ncause of truth, by detecting and exposing the insufficient\nexplanations and unproved assertions of the reigning theory.\n\nBoyle was one of the persons who first raised doubts against\nthe current chemical doctrines of his time, as we have\nelsewhere noted; but his objections had no peculiar\nphysiological import. Herman Coming[25\\9], the most learned\nphysician of his time, a contemporary with Sylvius, took a\nview more pertinent to our present object; for he not only\nrejected the alchemical {181} and hermetical medicines, but\ntaught expressly that chemistry, in its then existing\ncondition, was better fitted to be of use in the practice of\npharmacy, than in the theories of physiology and pathology.\nHe made the important assertion, also, that chemical\nprinciples do not pre-exist _as such_ in the animal body;\nand that there are higher powers which operate in the\norganic world, and which do not depend on the form and\nmixture of matter.\n\n[Note 25\\9: _Ib._ iv. 361.]\n\nAttempts were made to prove the acid and alkaline nature of\nthe fluids of the human body by means of experiments, as by\nJohn Viridet of Geneva[26\\9], and by Raimond\nVieussens[27\\9], the latter of whom maintained that he had\nextracted an acid from the blood, and detected a ferment in\nthe stomach. In opposition to him, Hecquet, a disciple of\nthe iatromathematical school, endeavoured to prove that\ndigestion was performed, not by means of fermentation, but\nby trituration. Hecquet's own opinions cannot be defended;\nbut his objections to the chemical doctrines, and his\nassertion of the difference of chemical and organical\nprocesses, are evidences of just thought[28\\9].\n\n[Note 26\\9: Spr. iv. 329.]\n\n[Note 27\\9: _Ib._ 350, (1715).]\n\n[Note 28\\9: _Ib._ 401.]\n\nThe most important opponents of the iatrochemical school\nwere Pitcairn in England, Bohn and Hoffman in Germany, and\nBoerhaave in Holland. These eminent physicians, about the\nend of the seventeenth century, argued on the same grounds\nof observation, that digestion is not fermentation, and that\nthe Sylvian accounts of the origin of diseases by means of\nacid and alkali are false. The arguments and authority of\nthese and other persons finally gained an ascendancy in the\nmedical world, and soon after this period we may consider\nthe reign of the chemical school of physiology as past. In\nfact, the attempts to prove its assertions experimentally\nwere of the feeblest kind, and it had no solid basis on\nwhich it could rest, so as to resist the shock of the next\nhypothesis which the progress of the physical sciences might\nimpel against it. We may, therefore, now consider the\nopinion of the mere {182} chemical nature of the vital\nprocesses as disproved, and we proceed next to notice the\nhistory of another unsuccessful essay to reduce vital\nactions to known actions of another kind.\n\n\nSECT. III.--_The Iatromathematical School._\n\nIn the first Section of this chapter, we enumerated the\nbiological hypotheses which at first present themselves, as\nthe mystical, the mechanical, the chemical. We might have\nexpected that they should occur to men's minds in the order\nthus stated: and in fact they did so; for the physiology of\nthe ancient materialists, as Democritus and Lucretius, is\nmechanical so far as it is at all distinct in its views, and\nthus the mechanical preceded the chemical doctrine. But in\nmodern times, the fluid or chemical physiology was developed\nbefore the solid or mechanical: of which the reason appears\nto have been this;--that Mechanics and Chemistry began to\nassume a scientific character about the same time; and that\nof the two, Chemistry not only appeared at first sight more\napplicable to the functions of the body, because all the\nmore rapid changes appear to be connected with modifications\nof the fluids of the animal system, but also, by its wider\nrange of facts and more indefinite principles, afforded a\nbetter temporary refuge for the mind when perplexed by the\ndifficulties and mysteries which spring out of the\nspeculations concerning life. But if Chemistry was thus at\nfirst a more inviting field for the physiologist, Mechanics\nsoon became more attractive in virtue of the splendid\nresults obtained by the schools of Galileo and Newton. And\nwhen the insufficiency of chemical physiology was discovered\nby trial, as we have seen it was, the hope naturally arose,\nthat the mechanical principles which had explained so many\nof the phenomena of the external universe might also be\nfound, applicable to the smaller world of material\nlife;--that the _microcosm_ as well as the _macrocosm_ might\nhave its mechanical principles. From this hope sprung the\n{183} Iatromathematical School, or school of Mechanical\nPhysiologists.\n\nWe may, however, divide this school into two parts, the\nItalian, and the Cartesio-Newtonian sect. The former\nemployed themselves in calculating and analysing a number of\nthe properties of the animal frame which are undoubtedly\nmechanical; the latter, somewhat intoxicated by the supposed\ntriumphs of the corpuscular philosophy, endeavoured to\nextend these to physiology, and for this purpose introduced\ninto the subject many arbitrary and baseless hypotheses. I\nwill very briefly mention some of the writers of both these sects.\n\nThe main points to which the Italian or genuine Mechanical\nPhysiologists attended, were the application of mechanical\ncalculations to the force of the muscles, and of hydraulical\nreasonings to the motion of the fluids of the animal system.\nThe success with which Galileo and his disciples had pursued\nthese branches of mechanical philosophy, and the ascendancy\nwhich they had obtained, first in Italy, and then in other\nlands, made such speculations highly interesting. Borelli\nmay be considered as the first great name in his line, and\nhis book, _De Motu Animalium_, (_Opus Posthumum_, Rom\u00e6,\n1680,) is even now a very instructive treatise on the forces\nand action of the bones and muscles. This, certainly one of\nthe most valuable portions of mechanical physiology, has not\neven yet been so fully developed as it deserves, although\nJohn Bernoulli[29\\9] and his son Daniel[30\\9] applied to it\nthe resources of analysis, and Pemberton[31\\9] in England,\npursued the same subject. Other of these mechanico-physiological\nproblems consisted in referring the pressure of the blood\nand of the breath to hydrostatical principles. In this\nmanner Borelli was led to assert that the muscles of the\nheart exert a force of 180,000 pounds[32\\9]. But a little\nlater, Keill reduced this force {184} to a few ounces[33\\9].\nKeill and others attempted to determine, on similar\nprinciples, the velocity of the blood; we need not notice\nthe controversies which thus arose, since there is not\ninvolved in them any peculiar physiological principle.\n\n[Note 29\\9: _De Motu Musculorum_.]\n\n[Note 30\\9: _Act. Acad. Petrop._]\n\n[Note 31\\9: _Course of Physiology_, 1773.]\n\n[Note 32\\9: Spr. iv. 110.]\n\n[Note 33\\9: Spr. iv. 443.]\n\nThe peculiar character of the iatromathematical school, as\nan attempt at physiological theory, is more manifest in its\nother section, which we have called the Cartesio-Newtonian.\nThe Cartesian system pretended to account for the\nappearances and changes of bodies by means of the size,\nfigure, and motion of their minute particles. And though\nthis system in its progress towards the intellectual empire\nof Europe was suddenly overturned by the rise of the\nNewtonian philosophy, these corpuscular doctrines rather\ngained than lost by the revolution; for the Newtonian\nphilosophy enlarged the powers of the corpuscular\nhypothesis, by adding the effects of the attractive and\nrepulsive forces of particles to those of their form and\nmotion. By this means, although Newton's discoveries did not\nin fact augment the probability of the corpuscular\nhypothesis, they so far increased its plausibility, that\nthis hypothesis found favour both with Newton himself and\nhis contemporaries, no less than it had done with the\nCartesians.\n\nThe attempt to apply this corpuscular hypothesis to\nphysiology was made by Des Cartes himself. The general\ncharacter of such speculations may easily be guessed[34\\9].\nThe secretions are effected by the organs operating after\nthe manner of sieves. Bound particles pass through\ncylindrical tubes, pyramidal ones through triangular pores,\ncubical particles through square apertures, and thus\ndifferent kinds of matter are separated. Similar\nspeculations were pursued by other mathematicians: the\nvarious diameter of the vessels[35\\9], their curvatures,\nfolds, and angles, were made subjects of calculation.\nBellini, Donzellini, Gulielmini, in Italy; Perrault, Dodart,\nin France; Cole, Keill, Jurin, in England, were the\nprincipal cultivators of such studies. {185} In the earlier\npart of the eighteenth century, physiological theorists\nconsidered it as almost self-evident that their science\nrequired them to reason concerning the size and shape of the\nparticles of the fluids, the diameter and form of the\ninvisible vessels. Such was, for instance, the opinion of\nCheyne[36\\9], who held that acute fevers arise from the\nobstruction of the glands, which occasions a more vehement\nmotion of the blood. Mead, the physician of the King, and\nthe friend of Newton, in like manner explained the effects\nof poisons by hypotheses concerning the form of their\nparticles[37\\9], as we have already seen in speaking of chemistry.\n\n[Note 34\\9: _Ib._ 329.]\n\n[Note 35\\9: _Ib._ 432.]\n\n[Note 36\\9: Spr. iv. 223.]\n\n[Note 37\\9: _ Mechanical Account of Poisons_, 1702.]\n\nIt is not necessary for us to dwell longer on this subject,\nor to point out the total insufficiency of the mere\nmechanical physiology. The iatrochemists had neglected the\neffect of the solids of the living frame; the\niatromathematicians attended only to these[38\\9]. And even\nthese were considered only as canals, as cords, as levers,\nas lifeless machines. These reasoners never looked for any\npowers of a higher order than the cohesion, the resistance,\nthe gravity, the attraction, which operate in inert matter.\nIf the chemical school assimilated the physician to a\nvintner or brewer, the mechanical physiologists made him an\nhydraulic engineer; and, in fact, several of the\niatromathematicians were at the same time teachers of\nengineering and of medicine.\n\n[Note 38\\9: Spr. iv. 419.]\n\nSeveral of the reasoners of this school combined chemical\nwith their mechanical principles; but it would throw no\nadditional light upon the subject to give any account of\nthese, and I shall therefore go on to speak of the next form\nof the attempt to explain the processes of life.\n\n\nSECT. IV.--_The Vital-Fluid School._\n\nI speak here, not of that opinion which assumes some kind of\nfluid or ether as the means of {186} communication along the\n_nerves_ in particular, but of the hypothesis that _all_ the\npeculiar functions of _life_ depend upon some subtile\nethereal substance diffused through the frame;--not of a\n_Nervous_ Fluid, but of a _Vital_ Fluid. Again, I\ndistinguish this opinion from the doctrine of an\n_immaterial_ vital power or principle, an Animal Soul, which\nwill be the subject of the next Section: nor is this\ndistinction insignificant; for a material element, however\nsubtile, however much spiritualized, must still act\neverywhere according to the same laws; whereas we do not\nconceive an immaterial spirit or soul to be subject to this\nnecessity.\n\nThe iatromathematical school could explain to their own\nsatisfaction how motions, once begun, were transferred and\nmodified; but in many organs of the living frame there\nseemed to be a power of beginning motion, which is beyond\nall mere mechanical action. This led to the assumption of a\nPrinciple of a higher kind, though still material. Such a\nPrinciple was asserted by Frederick Hoffmann, who was born\nat Halle, in 1660[39\\9], and became Professor of Medicine at\nthe newly established University there in 1694. According to\nhim[40\\9], the reason of the greater activity of organized\nbodies lies in the influence of a material substance of\nextreme subtilty, volatility, and energy. This is, he holds,\nno other than the Ether, which, diffused through all nature,\nproduces in plants the bud, the secretion and motion of the\njuices, and is separated from the blood and lodged in the\nbrain of animals[41\\9]. From this, acting through the\nnerves, must be derived all the actions of the organs in the\nanimal frame; for when the influence of the nerve upon the\nmuscle ceases, muscular motion ceases also.\n\n[Note 39\\9: Spr. v. 254.]\n\n[Note 40\\9: _Ib._ v. 257.]\n\n[Note 41\\9: _De Differenti\u00e2 Organismi et Mechanismi_, pp. 48, 67.]\n\nThe mode of operation of this vital fluid was, however, by\nno means steadily apprehended by Hoffmann and his followers.\nIts operations are so far mechanical[42\\9] that all effects\nare reduced to motion, yet they {187} cannot be explained\naccording to known mechanical laws. At one time the effects\nare said to take place according to laws of a Higher\nMechanics which are still to be discovered[43\\9]. At another\ntime, in complete contradiction of the general spirit of the\nsystem, metaphysical conceptions are introduced: each\nparticle of the vital fluid is said to have a determined\n_idea_ of the whole mechanism and organism[44\\9], and\naccording to this, it forms the body and preserves it by its\nmotion. By means of this fluid the soul operates upon the\nbody, and the instincts and the passions have their source\nin this material sensitive soul. This attribution of ideas\nto the particles of the fluid is less unaccountable when we\nrecollect that something of the same kind is admitted into\nLeibnitz's system, whose Monads have also ideas.\n\n[Note 42\\9: Spr. v. 262, 3.]\n\n[Note 43\\9: Hoffmann, _Opp._ Vol. v. p. 123.]\n\n[Note 44\\9: _De Diff. Organ. et Mechan._ p. 81.]\n\nNotwithstanding its inconsistencies, Hoffmann's system was\nreceived with very general favour both in Germany and in the\nrest of Europe; the more so, inasmuch as it fell in very\nwell with the philosophy both of Leibnitz and of Newton. The\nNewtonians were generally inclined to identify the Vital\nFluid with the Ether, of which their master was so strongly\ndisposed to assume the existence: and indeed he himself\nsuggested this identification.\n\nWhen the discoveries made respecting Electricity in the\ncourse of the eighteenth century had familiarized men with\nthe notion of a pervading subtile agent, invisible,\nintangible, yet producing very powerful effects in every\npart of nature, physiologists also caught at the suggestion\nof such an agent, and tried, by borrowing or imitating it,\nto aid the imperfection of their notions of the vital\npowers. The Vital Principle[45\\9] was imagined to be a\nsubstance of the same kind, by some to be the same\nsubstance, with the Electric Fluid. By its agency all these\nprocesses in organized bodies were accounted for which\ncannot be {188} explained by mechanical or chemical laws, as\nthe secretion of various matters (tears, milk, bile, &c.)\nfrom an homogeneous fluid, the blood; the production of\nanimal heat, digestion, and the like. According to John\nHunter, this attenuated substance pervaded the blood itself,\nas well as the solid organic frame; and the changes which\ntake place in the blood which has flowed out of the veins\ninto a basin are explained by saying that it is, for a time,\ntill this vital fluid evaporates, truly alive.\n\n[Note 45\\9: Prichard, _On the Doctrine of a Vital\nPrinciple_, p. 12.]\n\nThe notion of a Vital Fluid appears also to be favourably\nlooked upon by Cuvier; although with him this doctrine is\nmainly put forwards in the form of a Nervous Fluid. Yet in\nthe following passage he extends the operation of such an\nagent to all the vital functions[46\\9]: 'We have only to\nsuppose that all the medullary and nervous parts produce the\nNervous Agent, and that they alone conduct it; that is, that\nit can only be transmitted by them, and that it is changed\nor consumed by their actions. Then everything appears\nsimple. A detached portion of muscle preserves for some time\nits irritability, on account of the portion of nerve which\nalways adheres to it. The sensibility and the irritability\nreciprocally exhaust each other by their exercise, because\nthey change or consume the same agent. All the interior\nmotions of digestion, secretion, excretion, participate in\nthis exhaustion, or may produce it. All local excitation of\nthe nerves brings thither more blood by augmenting the\nirritability of the arteries, and the afflux of blood\naugments the real sensibility by augmenting the production\nof the nervous agent. Hence the pleasures of titillations,\nthe pains of inflammation. The particular sensations\nincrease in the same manner and by the same causes; and the\nimagination exercises, (still by means of the nerves,) upon\nthe internal fibres of the arteries or other parts, and\nthrough them on the sensations, an action analogous to that\nof the will upon the voluntary motions. As each exterior\nsense is exclusively disposed {189} to admit the substances\nwhich it is to perceive, so each interior organ, secretory\nor other, is also more excitable by some one agent than by\nanother: and hence arises what has been called the _proper\nsensibility_ or _proper life of the organs_; and the\ninfluence of specifics which, introduced into the general\ncirculation, affect only certain parts. In fine, if the\nnervous agent cannot become sensible to us, the reason is\nthat all sensation requires that this agent should be\naltered in some way or other; and it cannot alter itself.\n\n[Note 46\\9: _Hist. Sc. Nat. depuis_ 1789, i. 214.]\n\n'Such is the summary idea which we may at present form of\nthe mutual and general working of the vital powers in\nanimals.'\n\nAgainst the doctrine of a Vital Fluid as one uniform\nmaterial agent pervading the organic frame, an argument has\nbeen stated which points out extremely well the\nphilosophical objection to such an hypothesis[47\\9]. If the\nVital Principle be the _same_ in all parts of the body, how\ndoes it happen, it is asked, that the secretions are so\n_different_? How do the particles in the blood, separated\nfrom their old compounds and united into new ones, under the\nsame influence, give origin to all the different fluids\nwhich are produced by the glands? The liver secretes bile,\nthe lacrymal gland, tears, and so on. Is the Vital Principle\ndifferent in all these organs? To assert this, is to\nmultiply nominal principles without limit, and without any\nadvance in the explanation of facts. Is the Vital Principle\nthe same, but its operation modified by the structure of the\norgan? We have then two unknown causes, the Vital Principle\nand the Organic Structure, to account, for the effect. By\nsuch a multiplication of hypotheses nothing is gained. We\nmay as well say at once, that the structure of the organ,\nacting by laws yet unknown, is the cause of the peculiar\nsecretion. It is as easy to imagine this structure acting to\nproduce the whole effect, as it is to imagine it modifying\nthe activity of another agent. Thus the hypothesis of the\nVital Fluid in this form explains nothing, and does not in\nany {190} way help onwards the progress of real biological\nknowledge.\n\n[Note 47\\9: Prichard, _On a Vital Principle_, p. 98.]\n\nThe hypothesis of an _immaterial_ vital principle must now be\nconsidered.\n\n\nSECT. V.--_The Psychical School._\n\nThe doctrine of an Animal Soul as the principle which makes\nthe operations of organic different from those of inorganic\nmatter, is quite distinct from, and we may say independent\nof, the doctrine of the soul as the intelligent, moral,\nresponsible part of man's nature. It is the former doctrine\nalone of which we have here to speak, and those who thus\nhold the existence of an immaterial agent as the cause of\nthe phenomena of life, I term the _Psychical School_.\n\nSuch a view of the constitution of living things is very\nancient. For instance, Aristotle's Treatise '_On the Soul_,'\ngoes entirely upon the supposition that the Soul is the\ncause of motion, and he arrives at the conclusion that there\nare different _parts_ in the Soul; the _nutritive_ or\n_vegetative_, the _sensitive_, and the _rational_[48\\9].\n\n[Note 48\\9: Aristotle. \u03a0\u03b5\u03c1\u1f76 \u03a8\u03c5\u03c7\u1fc6\u03c2, ii. 2.]\n\nBut this doctrine is more instructive to us, when it appears\nas the antagonist of other opinions concerning the nature of\nlife. In this form it comes before us as promulgated by\nStahl, whom we have already noticed as one of the great\ndiscoverers in chemistry. Born in the same year as Hoffmann,\nand appointed at his suggestion professor at the same time\nin the same new university of Halle, he soon published a\nrival physiological theory. In a letter to Lucas Schr\u00f6ck,\nthe president of the Academy of Naturalists, he describes\nthe manner in which he was led to form a system for\nhimself[49\\9]. Educated in the tenets of Sylvius and Willis,\naccording to which all diseases are derived from the acidity\nof the fluids, Stahl, when a young student, often wondered\nhow these fluids, so liable to be polluted and corrupted,\nare so wonderfully preserved through innumerable external\ninfluences, and seem to {191} be far less affected by these\nthan by age, constitution, passion. No material cause could,\nhe thought, produce such effects. No attention to mechanism\nor chemistry alone could teach us the true nature and laws\nof organization.\n\n[Note 49\\9: Spr. v. 303.]\n\nSo far as Stahl recognized the influence, in living bodies,\nof something beyond the range of mechanics and chemistry,\nthere can be no doubt of the sound philosophy of his views;\nbut when he proceeds to found a positive system of\nphysiology, his tenets become more precarious. The basis of\nhis theory is this[50\\9]: the body has, as body, no power to\nmove itself, and must always be put in motion by immaterial\nsubstances. All motion is a spiritual act[51\\9]. The source\nof all activity in the organic body, from which its\npreservation, the permanency of its composition, and all its\nother functions proceed, is an immaterial being, which Stahl\ncalls the _Soul_; because, as he says, when the effects are\nso similar, he will not multiply powers without necessity.\nOf this principle, he says, as the Hippocratians said of\nNature, that 'it does without teaching what it ought to\ndo[52\\9],' and does it 'without consideration[53\\9].' These\nancient tenets Stahl interprets in such a manner that even\nthe involuntary motions proceed from the soul, though\nwithout reflection or clear consciousness. It is indeed\nevident, that there are many customary motions and\nsensations which are perfectly rational, yet not the objects\nof distinct consciousness: and thus instinctive motions, and\nthose of which we are quite unconscious, may still be\nconnected with reason. The questions which in this view\noffer themselves, as, how the soul passes from the mother to\nthe child, he dismisses as unprofitable[54\\9]. He considers\nnutrition and secretion as the work of the soul. The\ncorpuscular theory and the doctrine of animal spirits {192}\nare, he rightly observes, mere hypotheses, which are\narbitrary in their character, and only shift the difficulty.\nFor, if the animal spirits are not matter, how can they\nexplain the action of an immaterial substance on the body;\nand if they are matter, how are they themselves acted on?\n\n[Note 50\\9: Spr. v. 308]\n\n[Note 51\\9: _Ib._ v. 314.]\n\n[Note 52\\9: Stahl, \u03c0\u03b5\u03c1\u1f76 \u03c6\u03cd\u03c3\u03b5\u03c9\u03c2 \u1f00\u03c0\u03b1\u03af\u03b4\u03b5\u03c5\u03c4\u03bf\u03c5.]\n\n[Note 53\\9: \u03bf\u1f50\u03ba \u1f10\u03ba \u03b4\u03b9\u03b1\u03bd\u03bf\u03af\u03b7\u03c2.]\n\n[Note 54\\9: This was of course an obvious problem. Harvey,\n_On Generation_ Exercise 27, p. 148, teaches, 'That the egg\nis not the production of the womb, but of the soul.']\n\nThis doctrine of the action of the soul on the body, was\naccepted by many persons, especially by the\niatromathematicians, who could not but feel the\ninsufficiency of their system without some such supplement:\nsuch were Cheyne and Mead. In Germany, Stahl's disciples in\nphysiology were for the most part inconsiderable\npersons[55\\9]. Several Englishmen who speculated concerning\nthe metaphysics as well as the physiology of Sensation and\nMotion, inclined to this psychical view, as Porterfield and\nWhytt. Among the French, Boissier de Sauvages was the most\nzealous defender of the Stahlian system. Actions, he\nsays[56\\9], which belong to the preservation of life are\ndetermined by a moral not a mechanical necessity. They\nproceed from the soul, but cannot be controlled by it, as\nthe starting from fear, or the trembling at danger. Unzer, a\nphysician at Altona[57\\9], was also a philosophical\nStahlian[58\\9].\n\n[Note 55\\9: Spr. v. 339, &c.]\n\n[Note 56\\9: _Ib._ 358.]\n\n[Note 57\\9: A.D. 1799]\n\n[Note 58\\9: Spr. v. 360.]\n\nWe need not dwell on the opposition which was offered to\nthis theory, first by Hoffmann, and afterwards by Haller.\nThe former of these had promulgated, as we have seen, the\nrival theory of a Nervous Fluid, the latter was the\nprincipal assertor of the doctrine of Irritability, an\nimportant theory on which we may afterwards have to touch.\nHaller's animosity against the Stahlian hypothesis is a\nremarkable feature in one who is in general so tolerant in\nhis judgment of opinions. His arguments are taken from the\nabsence of the control of the will over the vital actions,\nfrom the want of consciousness accompanying these actions,\nfrom the uniformity of them in different conditions of the\nmind, and from the small sensibility of {193} the heart\nwhich is the source of the vital actions. These objections,\nand the too decided distinction which Haller made between\nvoluntary and involuntary muscles, were very satisfactorily\nanswered by Whytt and Platner. In particular it was urged\nthat the instinctive actions of brutes are inexplicable by\nmeans of mechanism, and may be compared with the necessary\nvital actions of the human body. Neither kind are\naccidental, neither kind are voluntary, both are performed\nwithout reflection.\n\nWithout tracing further the progress of the Psychical\nDoctrine, I shall borrow a few reflections upon it from\nSprengel[59\\9]:--\n\n'When the opponents of the Stahlian system repeat\nincessantly that the assumption of a psychical cause in\ncorporeal effects is a metaphysical speculation which does\nnot belong to medicine, they talk to no purpose. The states\nof the soul are objects of our internal experience, and\ninterest the physician too nearly to allow him to neglect\nthem. The innumerable unconscious efforts of the soul, the\npowerful and daily effects of the passions upon the body,\ntoo often put to confusion those who would expel into the\nregion of metaphysics the dispositions of the mind. The\nconnexion of our knowledge of the soul, as gathered from\nexperience, with our knowledge of the human body, is far\ncloser than the mechanical and chemical physiologists\nsuspect.\n\n[Note 59\\9: Spr. v. 383.]\n\n'The strongest objection against the psychical system, and\none which has never been sufficiently answered by any of its\nadvocates, is the universality of organic effects in the\n_vegetable_ kingdom. The comparison of the physiology of\nplants with the physiology of animals puts the latter in its\ntrue light. Without absolutely trifling with the word\n_soul_, we cannot possibly derive from a soul the organic\noperations of vegetables. But just as little can we, as some\nStahlians have done, draw a sharp line between plants and\nanimals, and ascribe the processes of the former to mere\nmechanism, while {194} we derive the operations of the\nlatter from an intellectual principle. Not to mention that\nsuch a line is not possible, the rise of the sap and the\nalteration of the fluids of plants cannot be derived\nentirely from material causes as their highest origin.'\n\nThus, I may add, this psychical theory, however difficult to\ndefend in its detail, does in its generalities express some\nimportant truths respecting the vital powers. It not only,\nlike the last theory, gives unity to the living body, but it\nmarks, more clearly than any other theory, the wide interval\nwhich separates mechanical and chemical from vital action,\nand fixes our attention upon the new powers which the\nconsideration of life compels us to assume. It not only\nreminds us that these powers are elevated above the known\nlaws of the material world, but also that they are closely\nconnected with the world of thought and feeling, of will and\nreason; and thus it carries us, in a manner in which none of\nthe preceding theories have done, to a true conception of a\nliving, conscious, sentient, active individual.\n\nAt the same time we cannot but allow that the life of\nplants and of the lower orders of animals shows us very\nclearly that, in order to arrive at any sound and consistent\nknowledge respecting life, we must form some conception of\nit from which all the higher attributes which the term\n'soul' involves, are utterly and carefully excluded; and\ntherefore we cannot but come to the conclusion that the\npsychical school are right mainly in this; that in ascribing\nthe functions of life to a _soul_, they mark strongly and\njustly the impossibility of ascribing them to any known\nattributes of _body_.\n\n\n\n{{195}}\nCHAPTER III.\n\nATTEMPTS TO ANALYSE THE IDEA OF LIFE.\n\n\n1. _Definitions of Life._--WE have seen in the preceding\nchapter that all attempts to obtain a distinct conception of\nthe nature of Life in general have ended in failure, and\nproduced nothing beyond a negative result. And the\nconjecture may now naturally occur, that the cause of this\nfailure resides in an erroneous mode of propounding to\nourselves the problem. Instead of contemplating Life as a\nsingle Idea, it may perhaps be proper to separate it into\nseveral component notions: instead of seeking for one cause\nof all vital operations, it may be well to look at the\nseparate vital functions, and to seek their causes. When the\nview of this possibility opens upon us, how shall we\nendeavour to verify it, and to take advantage of it?\n\nLet us, as one obvious course, take some of the attempts\nwhich have been made to _define_ Life, and let us see\nwhether they appear to offer to us any analysis of the idea\ninto component parts. Such definitions, when they proceed\nfrom men of philosophical minds, are the ultimate result of\na long course of thought and observation; and by no means\ndeserve to be slighted as arbitrary selections of\nconditions, or empty forms of words.\n\n2. Life has been defined by Stahl[60\\9], 'The condition by\nwhich a body resists a natural tendency to chemical changes,\nsuch as putrefaction.' In like manner, M. von Humboldt[61\\9]\ndefines living bodies to be 'those which, notwithstanding\nthe constant operation {196} of causes tending to change\ntheir form, are hindered by a certain inward power from\nundergoing such change.' The first of these definitions\namounts only to the assertion, that vital processes are not\nchemical; a negative result, which we may accept as true,\nbut which is, as we have seen, a barren truth. The second\nappears to be, in its import, identical with the first. An\n_inward_ principle can only be understood as distinguished\nfrom known external powers, such as mechanical and chemical\nagencies. Or if, by an internal principle, we mean such a\nprinciple as that of which we are _conscious_ within\nourselves, we ascribe a soul to all living things: an\nhypothesis which we have seen is not more effective than the\nformer in promoting the progress of biological science.\nNearly the same criticism applies to such definitions as\nthat of Kant: that 'Life is an internal faculty producing\nchange, motion, and action.'\n\n[Note 60\\9: Treviranus, _Biologie_, p. 19. Stahlii, _**Theor.\nMed._ p. 254.]\n\n[Note 61\\9: _Aphorismen aus d. Chem. Physiol. der Pflanzen_, s. 1.]\n\nOther definitions refer us, not to some property residing in\nthe whole of an organized mass, but to the connexion and\nrelation of its parts. Thus M. von Humboldt[62\\9] has given\nanother definition of a living body: that 'it is a whole\nwhose parts, arbitrarily separated, no longer resist\nchemical changes.' But this additional assertion concerning\nthe parts, adds nothing of any value to the definition of\nthe whole. And in some of the lower kinds of plants and\nanimals it is hardly true as a fact.\n\n[Note 62\\9: _Versuche \u00fcber die gereitzte Muskel und\nNervenf\u00fcser_, b. ii. p. 433.]\n\n3. Another definition[63\\9] places the character of Life in\n'motions serviceable to the body moved.' To this it has been\nobjected[64\\9], that, on this definition, the earth and the\nplanets are living bodies. Perhaps it would be more\nphilosophical to object to the introduction of so loose a\nnotion as that of a property being _serviceable_ to a body.\nWe might also add, that if we speak of all vital functions\nas _motions_, we make an assumption quite unauthorized, and\nprobably false.\n\n[Note 63\\9: Erhard, R\u00f6schlaub's _Magazin der Heilkunde_, b.\ni. st. 1. p. 69.]\n\n[Note 64\\9: Treviranus, _Biologie_, p. 41.]\n\n{197} Other definitions refer the idea of Life to the idea\nof Organization. 'Life is the activity of matter according\nto laws of organization[65\\9].' We are then naturally led to\nask, What is Organization? In reply to this is given us the\nKantian definition of Organization, which I have already\nquoted elsewhere[66\\9], 'An organized product of nature is\nthat in which all the parts are mutually ends and\nmeans[67\\9].' That this definition involves exact\nfundamental ideas, and is capable of being made the basis of\nsound knowledge, I shall hereafter endeavour to show. But I\nmay observe that such a definition leads us somewhat\nfurther. If the parts of organized bodies are known to be\nmeans to certain ends, this must be known because they\nfulfil these ends, and produce certain effects by the\noperation of a certain cause or causes. The question then\nrecurs, what is _the cause_ which produces such effects as\ntake place in organized or living bodies? and this is\nidentical with the problem of which in the last chapter we\ntraced the history, and related the failure of physiologists\nin all attempts at its solution.\n\n[Note 65\\9: Schmid, _Physiologie_, b. ii. p. 274.]\n\n[Note 66\\9: _Hist. Ind. Sc._ b. xvii. c. viii. s. 2.]\n\n[Note 67\\9: Kant, _Urtheilskraft_, p. 296.]\n\n4. But what has been just said suggests to us that it may be\nan improvement to put our problem in another shape:--not to\ntake for granted that the cause of all vital processes is\none, but to suppose that there may be several separate\ncauses at work in a living body. If this be so, life is no\nlonger one kind of activity, but several. We have a number\nof operations which are somehow bound together, and life is\nthe totality of all these: in short, life is not one\nFunction, but a System of Functions.\n\n5. We are thus brought very near to the celebrated\ndefinition of life given by Bichat[68\\9]: 'Life is the sum\nof the functions by which death is resisted.' But upon the\ndefinition thus stated, we may venture to observe;--first,\nthat the introduction of the notion of {198} _death_ in\norder to define the notion of _life_ appears to be\nunphilosophical. We may more naturally define death with\nreference to life, as the cessation of life; or at least we\nmay consider life and death as correlative and\ninterdependent notions. Again, the word 'sum,' used in the\nway in which it here occurs, appears to be likely to convey\nan erroneous conception, as if the functions here spoken of\nwere simply added to each other, and connected by\nco-existence. It is plain that our idea of life involves\nmore than this: the functions are all clearly connected, and\nmutually depend on each other; nutrition, circulation,\nlocomotion, reproduction,--each has its influence upon all\nthe others. These functions not merely co-exist, but exist\nwith many mutual relations and connexions; they are\ncontinued so as to form, not merely a _sum_, but a _system_.\nAnd thus we are led to modify Bichat's definition, and to\nsay that _Life is the system of vital functions_.\n\n[Note 68\\9: _Physiological Researches on Life and Death_.]\n\n6. But it will be objected that by such a definition we\nexplain nothing: the notion of _vital functions_, it may be\nsaid, involves the idea of _life_, and thus brings us round\nagain to our starting-point. Or if not, at least it is as\nnecessary to define Vital Functions as to define Life\nitself, so that we have made little progress in our task.\n\nTo this we reply, that if any one seeks, upon such subjects,\nsome ultimate and independent definition from which he can,\nby mere reasoning, deduce a series of conclusions, he seeks\nthat which cannot be found. In the Inductive Sciences, a\nDefinition does not form the basis of reasoning, _but points\nout the course of investigation_. The definition must\ninclude words; and the meaning of these words must be sought\nin the progress and results of observations, as I have\nelsewhere said[69\\9]. 'The meaning of words is to be sought\nin the progress of thought; the history of science is our\ndictionary; the steps of scientific induction are our\ndefinitions.' It will appear, I think, that it is more easy\nfor us to form an idea of a separate Function of the {199}\nanimal frame, as Nutrition or Reproduction, than to\ncomprehend Life in general under any single idea. And when\nwe say that Life is a system of Vital Functions, we are of\ncourse directed to study these functions separately, and (as\nin all other subjects of scientific research) to endeavour\nto form of them such clear and definite ideas as may enable\nus to discover their laws.\n\n[Note 69\\9: _Hist. Ind. Sc._ b. xiii. c. ix.]\n\n7. The view to which we are thus led, of the most promising\nmode of conducting the researches of Biology, is one which\nthe greatest and most philosophical physiologists of modern\ntimes have adopted. Thus Cuvier considers this as the true\noffice of physiology at present. 'It belongs to modern\ntimes,' he says, 'to form a just classification of the vital\nphenomena; the task of the present time is to analyse the\nforces which belong to each organic element, and upon the\nzeal and activity which are given to this task, depends,\naccording to my judgment, the fortune of physiology[70\\9].'\nThis classification of the phenomena of life involves, of\ncourse, a distinction and arrangement of the vital\nfunctions; and the investigation of the powers by which\nthese functions are carried on, is a natural sequel to such\na classification.\n\n[Note 70\\9: _Hist. Sc. Nat. dep._ 1789, i. 218.]\n\n8. _Classification of Functions._--Attempts to classify the\nVital Functions of man were made at an early period, and\nhave been repeated in great number up to modern times. The\ntask of classification is exposed to the same difficulties,\nand governed by the same conditions, in this as in other\nsubjects. Here, as in the case of other things, there may be\nmany classifications which are moderately good and natural,\nbut there is only one which is the best and the true natural\nsystem. Here, as in other cases, one classification brings\ninto view one set of relations; another, another; and each\nmay be valuable for its special purpose. Here, as in other\ncases, the classes may be well constituted, though the\nboundary lines which divide them be somewhat indistinct, and\nthe order doubtful. Here, {200} as in other cases, we may\nhave approached to the natural classification without having\nattained it; and here, as in other cases, to _define_ our\nclasses is the last and hardest of our problems.\n\n9. The most ancient classification of the Functions of\nliving things[71\\9], is the division of them into _Vital_,\n_Natural_, and _Animal_. The Vital Functions are those which\ncannot be interrupted without loss of life, as\n_Circulation_, _Respiration_, and _Nervous Communication_.\nThe _Natural Functions_ are those which without the\nintervention of the will operate on their proper occasions\nto preserve the bodies of animals; they are _Digestion_,\n_Absorption_, _Nutrition_; to which was added _Generation_.\nThe _Animal_ Functions are those which involve perception\nand will, by which the animal is distinguished from the\nvegetable; they are _Sensibility_, _Locomotion_, and _Voice_.\n\n[Note 71\\9: _Dict. des Sciences Nat._ art. _Fonctions_.]\n\nThe two great grounds of this division, the distinction of\nfunctions which operate continually, and those which operate\noccasionally; and again, the distinction of functions which\ninvolve sensation and voluntary motion from those which do\nnot; are truly of fundamental importance, and gave a real\nvalue to this classification. It was, however, liable to\nobvious objections: namely, _First_, that the names of the\nclasses were ill chosen; for all the functions are natural,\nall are vital: _Second_, that the lines of demarcation\nbetween the classes are indefinite and ambiguous;\nRespiration is a _vital_ function, as being continually\nnecessary to life; but it is also a _natural_ function,\nsince it occurs in the formation of the nutritive fluid, and\nan _animal_ function, since it depends in part on the will.\nBut these objections were not fatal, for a classification\nmay be really sound and philosophical, though its boundary\nlines are vague, and its nomenclature ill selected. The\ndivision of the functions we have mentioned kept its ground\nlong; or was employed with a subdivision of one class, so as\nto make them four; the _vital_, _natural_, _animal_ and\n_sexual_ functions. {201}\n\n10. I pass over many intermediate attempts to classify the\nfunctions, and proceed to that of Bichat as that which is, I\nbelieve, the one most generally assented to in modern times.\nThe leading principle in the scheme of this celebrated\nphysiologist is the distinction between _organic_ and\n_animal_ life. This separation is nearly identical with the\none just noticed between the vital and animal functions; but\nBichat, by the contrasts which he pointed out between these\nclasses of functions, gave a decided prominence and\npermanence to the distinction. The Organic Life, which in\nanimals is analogous to the life of vegetables, and the\nAnimal Life, which implies sensation and voluntary motion,\nhave each its system of organs. The center of the animal\nlife is the brain, of the organic life, the heart. The\nformer is carried on by a symmetrical, the latter, by an\nunsymmetrical system of organs: the former produces\nintermitting, the latter continuous actions: and, in\naddition to these, other differences are pointed out. This\ndistinction of the two lives, being thus established, each\nis subdivided into two orders of Functions. The Animal\nFunctions are passive, as _Sensation_: or active, as\n_Locomotion_ and _Voice_; again, the Organic Functions are\nthose of Composition, which are concerned in taking matter\ninto the system; _Digestion_, _Absorption_, _Respiration_,\n_Circulation_, _Assimilation_; and those of Decomposition,\nwhich reject the materials when they have discharged their\noffice in the system; and these are again, _Absorption_,\n_Circulation_, and _Secretion_. To these are added\n_Calorification_, or the production of animal heat. It\nappears, from what has been said, that _Absorption_ and\n_Circulation_ (and we may add _Assimilation_ and\n_Secretion_, which are difficult to separate,) belong alike\nto the processes of composition and decomposition; nor in\ntruth, can we, with any rigour, separate the centripetal and\ncentrifugal movements in that vortex which, as we shall see,\nis an apt image of organic life.\n\nSeveral objections have been made to this classification:\nand in particular, to the terms thus employed. It has been\nasserted to be a perversion of language to {202} ascribe to\nanimals _two lives_, and to call the higher faculties in\nman, perception and volition, the _animal_ functions. But,\nas we have already said, when a classification is really\ngood, such objections, which bear only upon the mode in\nwhich it is presented, are by no means fatal: and it is\ngenerally acknowledged by all the most philosophical\ncultivators of biology, that this arrangement of the\nfunctions is better suited to the purposes of the science\nthan those which preceded it.\n\n11. But according to the principles which we have already\nlaid down, the solidity of such a classification is to be\nverified by its serving as a useful guide in biological\nresearches. If the arrangement which we have explained be\nreally founded in natural relations, it will be found that\nin proportion as physiologists have studied the separate\nfunctions above enumerated, their ideas of these functions,\nand of the powers by which they are carried on, have become\nmore and more clear;--have tended more and more to the\ncharacter of exact and rigorous science.\n\nTo examine how far this has been the case with regard to all\nthe separate functions, would be to attempt to estimate the\nvalue of all the principal physiological speculations of\nmodern times; a task far too vast and too arduous for any\none to undertake who has not devoted his life to such\nstudies. But it may properly come within the compass of our\npresent plan to show how, with regard to the broader lines\nof the above classification, there has been such a progress\nas we have above described, from more loose and inaccurate\nnotions of some of the vital functions to more definite and\nprecise ideas. This I shall attempt to point out in one or\ntwo instances.\n\n\n\n{{203}}\nCHAPTER IV.\n\nATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES, AND FIRST\nOF ASSIMILATION AND SECRETION.\n\n\nSECT. I.--_Course of Biological Research._\n\n1. IT is to be observed that at present I do not speak of\nthe progress of our knowledge with regard to the detail of\nthe processes which take place in the human body, but of the\napproach made to some distinct Idea of the specially vital\npart of each process. In the History of Physiology, it has\nbeen seen[72\\9] that all the great discoveries made respecting\nthe organs and motions of the animal frame have been\nfollowed by speculations and hypotheses connected with such\ndiscoveries. The discovery of the circulation of the blood\nled to theories of animal heat; the discovery of the motion\nof the chyle led to theories of digestion; the close\nexamination of the process of reproduction in plants and\nanimals led to theories of generation. In all these cases,\nthe discovery brought to light some portion of the process\nwhich was mechanical or chemical, but it also, in each\ninstance, served to show that the process was something more\nthan mechanical or chemical. The theory attempted to explain\nthe process by the application of known causes; but there\nalways remained some part of it which must unavoidably be\nreferred to an unknown cause. But though unknown, such a\ncause was not a hopeless object of study. As the vital\nfunctions became better and better understood, it was seen\nmore and more clearly at what precise points of the process\nit was necessary to assume a peculiar vital energy, and what\nsort of properties {204} this energy must be conceived to\npossess. It was perceived where, in what manner, in what\ndegree, mechanical and chemical agencies were modified,\nover-ruled, or counteracted, by agencies which must be\nhypermechanical and hyperchemical. And thus the discoveries\nmade in anatomy by a laborious examination of facts, pointed\nout the necessity of introducing new ideas, in order that\nthe facts might be intelligible. Observation taught much;\nand among other things, she taught that there was something\nwhich could not be observed, but which must, if possible, be\nconceived. I shall notice a few instances of this.\n\n[Note 72\\9: _Hist. Ind. Sc._ b. xvii.]\n\n\nSECT. II.--_Attempts to form a distinct Conception of\nAssimilation and Secretion._\n\n2. _The Ancients._--That plants and animals grow by taking\ninto their substance matter previously extraneous, is\nobvious to all: but as soon as we attempt to conceive this\nprocess distinctly in detail, we find that it involves no\ninconsiderable mystery. How does the same food become blood\nand flesh, bone and hair? Perhaps the earliest attempt to\nexplain this mystery, is that recorded by Lucretius[73\\9] as\nthe opinion of Anaxagoras, that food contains some bony,\nsome fleshy particles, some of blood, and so on. We might,\non this supposition, conceive that the mechanism of the body\nappropriates each kind of particle to its suitable place.\n\n[Note 73\\9: Lucr. i. 855. Nunc et Anaxagor\u00e6 scrutemur\n\u1f41\u03bc\u03bf\u03b9\u03bf\u03bc\u03ad\u03c1\u03b5\u03b9\u03b1\u03bd.]\n\nBut it is easy to refute this essay at philosophizing (as\nLucretius refutes it) by remarking that we do not find milk\nin grass, or blood in fruit, though such food gives such\nproducts in cattle and in men. In opposition to this\n'Homoiomereia,' the opinion that is forced upon us by the\nfacts is, that the process of nutrition is not a selection\nmerely, but an _assimilation_; the organized system does not\n_find_, but _make_, the additions to its structure. {205}\n\n3. _Buffon._--This notion of _assimilation_ may be variously\nexpressed and illustrated; and all that we can do here, in\norder to show the progress of thought, is to adduce the\nspeculations of those writers who have been most successful\nin seizing and marking its peculiar character. Buffon may be\ntaken as an example of the philosophy of his time on this\nsubject. 'The body of the animal,' says he[74\\9], 'is a kind\nof _interior mould_, in which the matter subservient to its\nincrease is modelled and assimilated to the whole, in such a\nway that, without occasioning any change in the order and\nproportion of the parts, there results an augmentation in\neach part taken separately. This increase, this development,\nif we would have a _clear idea_ of it, how can we obtain it,\nexcept by considering the body of the animal, and each of\nthe parts which is to be developed, as so many interior\nmoulds which only receive the accessory matter in the order\nwhich results from the position of all their parts? This\ndevelopment cannot take place, as persons sometimes persuade\nthemselves, by an addition to the outside; on the contrary,\nit goes on by an intimate susception which penetrates the\nmass; for, in the part thus developed, the size increases in\nall parts proportionally, so that the new matter must\npenetrate it in all its dimensions: and it is quite\nnecessary that this penetration of substance must take place\nin a certain order, and according to a certain measure; for\nif this were not so, some parts would develope themselves\nmore than others. Now what can there be which shall\nprescribe such a rule to the accessory matter except the\n_interior mould_?'\n\n[Note 74\\9: _Hist. Nat._ b. i. c. iii.]\n\nTo speak of a _mould_ simply, would convey a coarse\nmechanical notion, which could not be received as any useful\ncontribution to physiological speculation. But this\n_interior_ mould is, of course, to be understood\nfiguratively, not as an assemblage of cavities, but as a\ncollection of laws, shaping, directing, and modifying the\nnew matter; giving it not only form, but motion {206} and\nactivity, such as belong to the parts of an organic being.\n\n4. It must be allowed, however, that even with this\nexplanation, the comparison is very loose and insufficient.\nA _mould_ may be permitted to mean a collection of laws, but\nstill it can convey no conception except that of laws\nregulated by relations of space; and such a conception is\nvery plainly quite inadequate to the purpose. What can we\nconceive of the interior mould by which chyle is separated\nfrom the aliments at the pores of the lacteals, or tears\nsecreted in the lacrymatory gland?\n\nAn additional objection to this mode of expression of Buffon\nis, that it suggests to us only a single marked change in\nthe assimilated matter, not a continuous series of changes.\nYet the animal fluids and other substances are, in fact,\nundergoing a constant series of changes. Food becomes chyme,\nand chyme becomes chyle; chyle is poured into the blood;\nfrom the blood secretions take place, as the bile; the bile\nis poured into the digestive canal, and a portion of the\nmatter previously introduced is rejected out of the system.\nHere we must have a series of 'interior moulds;' and these\nmust impress matter at its ejection from the organic system\nas well as at its reception. But, moreover, it is probable\nthat none of the above transformations are quite abrupt.\nChange is going on between the beginning and the end of each\nstage of the nutritive circulation. To express the laws of\nthis continuous change, the image of an interior mould is\nquite unsuited. We must seek a better mode of conception.\n\n5. Vegetable and animal nutrition is, as we have said, a\nconstant circulation. The matter so assumed is not all\nretained: a perpetual subtraction accompanies a perpetual\naddition. There is an excretion as well as an\nintussusception. The matter which is assumed by the living\ncreature is retained only for a while, and is then parted\nwith. The individual is the same, but its parts are in a\nperpetual flux: they come and go. For a time the matter\nwhich belongs to the organic body is bound to it by certain\nlaws: but before it is thus bound, and {207} after it is\nloose, this matter may circulate about the universe in any\nother form. Life consists in a permanent influence over a\nperpetually changing set of particles.\n\n_Cuvier._--This condition also has been happily expressed,\nby means of a comparison, by another great naturalist. 'If,'\nsays Cuvier[75\\9], 'if, in order to obtain a just idea of\nthe essence of life, we consider it in the beings where its\neffects are most simple, we shall soon perceive that it\nconsists in the faculty which belongs to certain bodily\ncombinations to continue during a determinate time under a\ndeterminate form; constantly attracting into their\ncomposition a part of the surrounding substances, and giving\nup in return some part of their own substance.\n\n[Note 75\\9: _R\u00e8gne Animal_, i. 11.]\n\n'Life is thus a _vortex_, more or less rapid, more or less\ncomplex, which has a constant direction, and which always\ncarries along its stream particles of the same kinds; but in\nwhich the individual particles are constantly entering in\nand departing out; so that the _form_ of the living body is\nmore essential to it than its matter.\n\n'So long as this motion subsists, the body in which it takes\nplace is _alive_; it _lives_. When the motion stops finally,\nthe body _dies_. After death, the elements which compose the\nbody, given up to the ordinary chemical affinities, soon\nseparate, and the body which was alive is dissolved.'\n\nThis notion of a vortex[76\\9] which is permanent while the\nmatter which composes it constantly changes,--of peculiar\nforces which act in this vortex so long as it exists, and\nwhich give place to chemical forces when {208} the\ncirculatory motion ceases,--appears to express some of the\nleading conditions of the assimilative power of living\nthings in a simple and general manner, and thus tends to\ngive distinctness to the notion of this vital function.\n\n[Note 76\\9: The definition of life given by M. de Blainville\nappears to me not to differ essentially from that of Cuvier:\n'Un corps vivant est une sorte de foyer chimique o\u00f9 il-y-a \u00e0\ntous momens apport de nouvelles molecules et d\u00e9part de\nmolecules anciennes; o\u00f9 la composition n'est jamais fixe (si\nce n'est d'un certain nombre de parties veritablement mortes\nou en dep\u00f4t), mais toujours pour ainsi dire _in nisu_, d'o\u00f9\nmouvement plus ou moins lent et quelquefois\nchaleur.'--_Principes d'Anat._ 1822, t. i. p. 16.]\n\n6. But we may observe that this notion of a Vortex is still\ninsufficient. Particles are not only taken into the system\nand circulated through it for a time, but, as we have seen,\nthey are altered in character in a manner to us\nunintelligible, both at their first admission into the\nsystem and at every period of their progress through it. In\nthe vortex each particle is constantly _transformed_ while\nit whirls.\n\nIt may be said, perhaps, that this transformation of the\nkinds of matter may be conceived to be merely a new\narrangement of their particles, and that thus all the\nchanges which take place in the circulating substances are\nmerely so many additional windings in the course of the\nwhirling current. But to say this, is to take for granted\nthe atomic hypothesis in its rudest form. What right have we\nto assume that blood and tears, bile and milk, consist of\nlike particles of matter differently arranged? What can\narrangement, a mere relation of space, do towards explaining\nsuch differences? Is not the insufficiency, the absurdity of\nsuch an assumption proved by the whole course of science?\nAre not even chemical changes, according to the best views\nhitherto obtained, something more than a mere new\narrangement of particles? And are not vital as much beyond\nchemical, as chemical are beyond geometrical modifications?\nIt is not enough, then, to conceive life as a vortex. The\nparticles which are taken into the organic frame do more\nthan circulate there. They are, at every point of their\ncirculation, acted upon by laws of an unknown kind, changing\nthe nature of the substance which they compose. Life is a\nvortex in which vital forces act at every point of the\nstream: it is not only a current of whirling _matter_, but a\ncycle of recurring _powers_.\n\n7. _Matter and Form._--This image of a vortex is closely\nconnected with the representation of life offered {209} us\nby writers of a very different school. In Schelling's\n_Lectures on Academic Study_, he takes a survey of the\nvarious branches of human knowledge, determining according\nto his own principles the shape which each science must\nnecessarily assume. The peculiar character of organization,\naccording to him[77\\9], is that the matter is only an\naccident of the thing itself, and the organization consists\nin Form alone. But this Form, by its very opposition to\nMatter, ceases to be independent of it, and is only ideally\nseparable. In organization, therefore, substance and\naccident, matter and form, are completely identical[78\\9].\nThis notion, that in organization the Form is essential and\nthe Matter accidental, or, in other words, that the Form is\npermanent and the Matter fluctuating and transitory, agrees,\nif taken in the grossest sense of matter and form, with\nCuvier's image of a Vortex. In a whirlpool, or in a\nwaterfall, the form remains, the matter constantly passes\naway and is renewed. But we have already seen[79\\9] that in\nmetaphysical speculations in which matter and form are\nopposed, the word form is used in a far more extensive sense\nthan that which denotes a relation of space. It may indeed\ndesignate any change which matter can undergo; and we may\nvery allowably say that food and blood are the same matter\nunder different _forms_. Hence if we assert that _Life is a\nconstant Form of a circulating Matter_, we express Cuvier's\nnotion in a mode free from the false suggestion which\n'Vortex' conveys.\n\n[Note 77\\9: Lect. xiii. p. 288.]\n\n[Note 78\\9: I have not translated Schelling's words, but\ngiven their import as far as I could.]\n\n[Note 79\\9: Book i.]\n\n8. We may, however, still add something to this account of\nlife. The circulating parts of the system not only\ncirculate, but they form the non-circulating parts. Or\nrather, there are no non-circulating parts: all portions of\nthe frame circulate more or less rapidly. The food which we\ntake circulates rapidly in the fluids, more slowly in the\nflesh, still more slowly in the bones; but in all these\nparts it is taken into the system, {210} retained there for\nsome time, and finally replaced by other matter. But while\nit remains in the body, it exercises upon the other\ncirculating parts the powers by which their motion is\nproduced. Nutriment forms and supports the organs, and the\norgans carry fresh nutriment to its destination. The\npeculiar forces of the living body, and its peculiar\nstructure, are thus connected in an indescribable manner.\nThe forces produce the structure; the structure, again, is\nrequisite for the exertion of the forces. The Idea of an\nOrganic or Living Being includes this peculiar\ncondition--that its construction and powers are such, that\nit constantly appropriates to itself new portions of\nsubstance which, so appropriated, become indistinguishable\nparts of the whole, and serve to carry on subsequently the\nsame functions by which they were assimilated. And thus\n_Organic Life is a constant Form of a circulating Matter, in\nwhich the Matter and the Form determine each other by\npeculiar laws_ (_that is, by Vital Forces_).\n\n\nSECT. III.--_Attempts to conceive the forces of Assimilation\nand Secretion._\n\n9. I have already stated that in our attempts to obtain\nclear and scientific Ideas of Vital Forces, we have, in the\nfirst place, to seek to understand the course of change and\nmotion in each function, so as to see at what points of the\nprocess peculiar causes come into play; and next, to\nendeavour to obtain some insight into the peculiar character\nand attributes of these causes. Having spoken of the first\npart of this mode of investigation in regard to the general\nnutrition of organic bodies, I must now say a few words on\nthe second part.\n\nThe Forces here spoken of are _Vital_ Forces. From what has\nbeen said, we may see in some measure the distinction\nbetween forces of this kind and mechanical or chemical\nforces; the latter tend constantly to produce a final\ncondition, after which there is no further cause of change:\nmechanical forces tend to produce equilibrium; chemical\nforces tend to produce {211} composition or decomposition;\nand this point once reached, the matter in which these\nforces reside is altogether inert. But an organic body tends\nto a constant motion, and the highest activity of organic\nforces shows itself in continuous change. Again, in\nmechanical and chemical forces, the force of any aggregate\nis the sum of the forces of all the parts: the sum of the\nforces corresponds to the sum of the matter. But in organic\nbodies, the amount of effect does not depend on the matter,\nbut on the form: the particles lose their separate energy,\nin order to share in that of the system; they are not added,\nthey are _assimilated_.\n\n10. It is difficult to say whether anything has been gained\nto science by the various attempts to assign a fixed _name_\nto the vital force which is thus the immediate cause of\nAssimilation. It has been called _Organic Attraction_ or\n_Vital Attraction_, _Organic Affinity_ or _Vital Affinity_,\nbeing thus compared with mechanical Attraction or chemical\nAffinity. But, perhaps, as the process is certainly neither\nmechanical nor chemical, it is desirable to appropriate to\nit a peculiar name; and the name _Assimilation_, or _Organic\nAssimilation_, by the usage of good biological writers, is\ngenerally employed for this purpose, and may be taken as the\nstandard name of this Vital Force. To illustrate this, I\nwill quote a passage from the excellent _Elements of\nPhysiology_ of Professor M\u00fcller. 'In the process of\nnutrition is exemplified the fundamental principle of\n_organic assimilation_. Each elementary particle of an organ\nattracts similar particles from the blood, and by the\nchanges it produces in them, causes them to participate in\nthe vital principle of the organ itself. Nerves take up\nnervous substance, muscles, muscular substance: even morbid\nstructures have the assimilating power; warts in the skin\ngrow with their own peculiar structure; in an ulcer, the\nbase and border are nourished in a way conformable to the\nmode of action and secretion determined by the disease.'\n\n11. The Force of Organic Assimilation spoken of in the last\nparagraph denotes peculiarly the force by which each organ\nappropriates to itself a part of the {212} nutriment\nreceived into the system, and thus is maintained and\naugmented with the growth of the whole. But the growth of\nthe solid parts is only one portion of the function of\nnutrition; besides this, we must consider the motion and\nchanges of the fluids, and must ask what kind of forces may\nbe conceived to produce these. What are the powers by which\nchyle is _absorbed_ from the food, by which bile is\n_secreted_ from the blood, by which the circulating _motion_\nof these and all other fluids of the body are constantly\nmaintained? To the questions,--What are the forces by which\n_absorption_, _secretion_, and the _vital motions_, of\nfluids are produced?--no satisfactory answer has been\nreturned. Yet still some steps have been made, which it may\nbe instructive to point out.\n\n12. In _Absorption_ it would appear that a part of the\nagency is inorganic; for not only dead membranes, but\ninorganic substances, absorb fluids, and even absorb them\nwith elective forces, according to the ingredients, of the\nfluid. A force which is of this kind, and which has been\ntermed _Endosmose_, has been found to produce very curious\neffects. When a membrane separates two fluids, holding in\nsolution different ingredients, the fluids pass through the\nmembrane in an imperceptible manner, and mix or exchange\ntheir elements. The force which produces these effects is\ncapable of balancing a very considerable pressure. It\nappears, moreover, to depend, at least among other causes,\nupon attractions operating between the elements of the\nsolids and the fluids, as well as between the different\nfluids; and this force, though thus apparently of a\nmechanical and chemical nature, probably has considerable\ninfluence in vital phenomena.\n\n13. But still, though Endosmose may account in part for\nabsorption in some cases, it is certain that there is some\nother vital force at work in this process. There must be, as\nM\u00fcller says[80\\9], 'an organic attraction of a kind hitherto\nunknown.' 'If absorption,' he adds[81\\9], is to be explained\nin a manner analogous to {213} the laws of endosmose, it\nmust be supposed that a chemical affinity, resulting from\nthe vital process itself, is exerted between the chyme in\nthe intestines and the chyle in the lacteals, by which the\nchyle is enabled to attract the chyme without being itself\nattracted by it. But such affinity or attraction would be of\na vital nature, since it does not exist after death.'\n\n[Note 80\\9: _Physiology_, p. 299.]\n\n[Note 81\\9: _Ib._ p. 301.]\n\n14. If the force of absorption be thus mysterious in its\nnature, the force of _Secretion_ is still more so. In this\ncase we have an organ filled with a fine net-work of\nblood-vessels, and in the cavities of some _gland_, or open\npart, we have a new fluid formed, of a kind altogether\ndifferent from the blood itself. It is easily shown that\nthis cannot be explained by any action of pores or capillary\ntubes. But what conception can we form of the forces by\nwhich such a change is produced? Here, again, I shall borrow\nthe expressions of M\u00fcller, as presenting the last result of\nmodern physiology. He says[82\\9], 'The more probable\nsupposition is, that by virtue of imbibition, or the general\norganic porosity, the fluid portion of the blood becomes\ndiffused through the tissue of the secreting organ; that the\nexternal surface of the glandular canals exerts a chemical\nattraction on the elements of the fluid, infusing into them\nat the same time a tendency to unite in new combinations;\nand then repels them in a manner which is certainly quite\ninexplicable, towards the inner surface of the secreting\nmembrane, or glandular canals.' 'Although quite unsupported\nby facts,' he adds, 'this theory of attraction and repulsion\nis not without its analogy in physical phenomena; and it\nwould appear that very similar powers effect the elimination\nof the fluid in secretion, and cause it to be taken up by\nthe lymphatics in absorption.' He elsewhere says[83\\9],\n'Absorption seems to depend on an attraction the nature of\nwhich is unknown, but of which the very counterpart, as it\nwere, takes place in secretion; the fluids altered by the\nsecreting action being repelled towards the free side or\nopen surface only of the {214} secreting membranes, and then\npressed forwards by the successive portions of the fluids\nsecreted.'\n\n[Note 82\\9: _Physiology_, p. 464.]\n\n[Note 83\\9: _Ib._ p. 301.]\n\n15. With regard to the forces which produce the _Motion_ of\nabsorbed or secreted fluids along their destined course, it\nmay be seen, from the last quoted sentence, that the same\nvital force which changes the nature, also produces the\nmovement of the substance. The fluids are pressed forwards\nby the successive portions absorbed or secreted. That this\nis the sole cause, or at least a very powerful cause, of the\nmotion of the nutritive fluids in organic bodies, is easily\nshown by experience. It is found[84\\9] that the organs which\neffect the ascent of the sap in trees during the spring are\nthe terminal parts of the roots; that the whole force by\nwhich the sap is impelled upwards is the _vis a tergo_, as\nit has been called, the force pushing from behind, exerted\nin the roots. And thus the force which produces this motion\nis exerted exactly at those points where the organic body\nselects from the contiguous mass those particles which it\nabsorbs and appropriates. And the same may most probably be\ntaken for the cause of the motion of the lymph and chyle; at\nleast, M\u00fcller says[85\\9] that no other motive power has been\ndetected which impels those fluids in their course.\n\n[Note 84\\9: M\u00fcller, p. 300.]\n\n[Note 85\\9: _Ib._ p. 254.]\n\nThus, though we must confess the Vital Force concerned in\nAssimilation and Secretion to be unknown in its nature, we\nstill obtain a view of some of the attributes which it\ninvolves. It has mechanical efficacy, producing motions,\noften such as would require great mechanical force. But it\nexerts at the same point both an attraction and a repulsion,\nattracting matter on one side, and repelling it on the\nother; and in this circumstance it differs entirely from\nmechanical forces. Again, it is not only mechanical but\nchemical, producing a complete change in the nature of the\nsubstance on which it acts; to which we must add that the\nchanges produced by the vital forces are such as, for the\nmost part, our artificial chemistry {215} cannot imitate.\nBut, again, by the action of the vital force at any point of\nan organ, not only are fluids made to pass, and changed as\nthey pass, but the organ itself is maintained and\nstrengthened, so as to continue or to increase its\noperation: and thus the vital energy supports its activity\nby its action, and is augmented by being exerted.\n\nWe have thus endeavoured to obtain a view of some of the\npeculiar characters which belong to the Force of Organic\nAssimilation;--the Force by which life is kept up, conceived\nin the most elementary form to which we can reduce it by\nobservation and contemplation. It appears that it is a force\nwhich not only produces motion and chemical change, but also\n_vitalizes_ the matter on which it acts, giving to it the\npower of producing like changes on other matter, and so on\nindefinitely. It not only circulates the particles of\nmatter, but puts them in a stream of which the flow is\ndevelopment as well as movement.\n\nThe force of Organic Assimilation being thus conceived, it\nbecomes instructive to compare it with the force concerned\nin Generation, which we shall therefore endeavour to do.\n\n\nSECT. IV.--_Attempts to conceive the Process of Generation._\n\n16. At first sight the function of Nutrition appears very\ndifferent from the function of Generation. In the former\ncase we have merely the existing organs maintained or\nenlarged, and their action continued; in the latter, we have\na new individual produced and extricated from the parent.\nThe term _Reproduction_ has, no doubt, been applied, by\ndifferent writers, to both these functions;--to the\nprocesses by which an organ when mutilated, is restored by\nthe forces of the living body, and to the process by which a\nnew generation of individuals is produced which may be\nconsidered as taking the place of the old generation, as\nthese are gradually removed by death. But these are\nobviously different senses of the word. In the latter case,\nthe {216} term _Reproduction_ is figuratively used; for the\n_same_ individuals are not reproduced; but the species is\nkept up by the propagation of new individuals, as in\nnutrition the organ is kept up by the assimilation of new\nmatter. To escape ambiguity, I shall avoid using the term\n_Reproduction_ in the sense of _Propagation_.\n\n17. In Nutrition, as we have seen, the matter, which from\nbeing at first extraneous, is appropriated by the living\nsystem, and directed to the sustentation of the organs,\nundergoes a series of changes of which the detail eludes our\nobservation and apprehension. The nutriment which we receive\ncontributes to the growth of flesh and bone, viscera and\norgans of sense. But we cannot trace in its gradual changes\na visible preparation for its final office. The portion of\nmatter which is destined to repair the waste of the eye or\nthe skin, is not found assuming a likeness to the parts of\nthe eye or the structure of the skin, as it comes near the\nplace where it is moulded into its ultimate form. The new\nparts are insinuated among the old ones, in an obscure and\nimperceptible matter. We can trace their progress only by\ntheir effects. The organs _are_ nourished, and that is\nalmost all we can learn: we cannot discover _how_ this is\ndone. We cannot follow nature through a series of manifest\npreparations and processes to this result.\n\n18. In Generation the case is quite different. The young\nbeing is formed gradually and by a series of distinguishable\nprocesses. It is included within the parent before it is\nextruded, and approaches more or less to the likeness of the\nparent before it is detached. While it is still an embryo,\nit shares in the nutriment which circulates through the\nsystem of the mother; but its destination is already clear.\nWhile the new and the old parts, in every other portion of\nthe mother, are undistinguishably mixed together, this new\npart, the f\u0153tus, is clearly distinct from the rest of the\nsystem, and becomes rapidly more and more so, as the time\ngoes on. And thus there is formed, not a new part, but a new\nwhole; it is not an organ which is kept up, but an offspring\nwhich is prepared. The progeny is {217} included in the\nparent, and is gradually fitted to be separated from it. The\nyoung is at first only the development of a part of the\norganization of the mother;--of a germ, an ovule. But it is\nnot developed like other organs, retaining its general form.\nIt does not become merely a larger bud, a larger ovule; it\nis entirely changed; it becomes--from a bud--a blossom, a\nflower, a fruit, a seed; from an ovule it becomes an egg, a\nchick, a bird; or it may be, a f\u0153tus, a child. The original\nrudiment is not merely nourished, but unfolded and\ntransformed through the most marked and remote changes,\ngradually tending to the form of the new individual.\n\n19. But this is not all. The f\u0153tus is, as we have said, a\ndevelopment of a portion of the mother's organization. But\nthe f\u0153tus (supposing it female) is a likeness of the mother.\nThe mother, even before conception, contains within herself\nthe germs of her progeny; the female f\u0153tus, therefore, at a\ncertain stage of development, will contain also the germs of\npossible progeny; and thus we may have the germs of future\ngenerations, pre-existing and included successively within\none another. And this state of things, which thus suggests\nitself to us as possible, is found to be the case in facts\nwhich observation supplies. Anatomists have traced ovules in\nthe unborn f\u0153tus, and thus we have three generations\nincluded one within another.\n\n20. Supposing we were to stop here, the process of\npropagation might appear to be altogether different from\nthat of nutrition. The latter, as we have seen, may be in\nsome measure illustrated by the image of a _vortex_; the\nformer has been represented by the image of a series of\ngerms, _sheathed_ one within another successively, and this\nwithout any limit. This view of the subject has been termed\nthe doctrine of the _Pre-existence of germs_; and has been\ndesignated by German writers by a term 'Einschachtelungs-theorie'\ndescriptive of the successive sheathing of which I have\nspoken. Imitating this term, we may call it _the Theory of\nsuccessive inclusion_. It has always had many {218}\nadherents; and has been, perhaps, up to the present time,\nthe most current opinion on the subject of generation.\nCuvier inclines to this opinion[86\\9]. 'Fixed forms\nperpetuating themselves by generation distinguish the\nspecies of living things. These forms do not produce\nthemselves, do not change themselves. Life supposes them to\nexist already; its flame can be lighted only in organization\npreviously prepared; and the most profound meditations and\nthe most delicate researches terminate alike in the mystery\nof the _pre-existence of germs_.'\n\n[Note 86\\9: _R\u00e8gne Animal_, p. 20.]\n\n21. Yet this doctrine is full of difficulty. It is, as\nCuvier says, a mysterious view of the subject;--so\nmysterious, that it can hardly be accepted by us, who seek\ndistinct conceptions as the basis of our philosophy. Can it\nbe true, not only that the germ of the offspring is\noriginally included in the parent, but also the germs of\n_its_ progeny, and so on without limit:--so that each\nfruitful individual contains in itself an infinite\ncollection of future possible individuals;--a reserve of\ninfinite succeeding generations? This is hard to admit. Have\nwe no alternative? What is the opposite doctrine?\n\n22. The opposite doctrine deserves at least some notice. It\nextends, to the production of a new individual, the\nconception of growth by nutrition. According to this view,\nwe suppose propagation to take place, not as in the view\njust spoken of, by inclusion and extrusion, but by\nassimilation and development;--not by the material\npre-existence of germs, but by the communication of vital\nforces to new matter. This opinion appears to be entertained\nby some of the most eminent physiologists of the present\ntime. Thus, M\u00fcller says, 'The organic force is also\ncreative. The organic force which resides in the whole, and\non which the existence of each part depends, has also the\nproperty of generating, from organic matter, the parts\nnecessary to the whole.' Life, he adds, is not merely a\nharmony of the {219} parts. On the contrary, the harmonious\naction of the parts subsists only by the influence of a\nforce pervading all parts of the body. 'This force exists\nbefore the harmonizing parts, which are in fact formed by it\nduring the development of the embryo.' And again; 'The\ncreative force exists in the germ, and creates in it the\nessential force of the future animal. The germ is\n_potentially_ the whole animal: during the development of\nthe germ the parts which constitute the actual whole are\nproduced.'\n\n23. In this view, we extend to the reproduction of an\nindividual the same conception of organic assimilation which\nwe have already arrived at, as the best notion we can form\nof the force by which the reproduction and sustentation of\nparts takes place. And is not such an extension really very\nconsistent? If a living thing can appropriate to itself\nextraneous matter, invest it with its own functions, and\nthus put it in the stream of constant development, may we\nnot conceive the development of a new _whole_ to take place\nin this way as well as of a _part_? If the organized being\ncan infuse into new matter its vital forces, is there any\ncontradiction in supposing this infusion to take place in\nthe full measure which is requisite for the production of a\nnew individual? The force of organic assimilation is\ntransferred to the very matter on which it acts; it may be\ntransferred so that the operation of the forces produces not\nonly an organ, but a system of organs.\n\n24. This identification of the forces which operate in\nNutrition and Generation may at first seem forced and\nobscure, in consequence of the very strong apparent\ndifferences of the two processes which we have already\nnoticed. But this defect in the doctrine is remedied by the\nconsideration of what may be considered as intermediate\ncases. It is not true that, in the nutrition of special\norgans, the matter is always conveyed to its ultimate\ndestination without being on its way moulded into the form\nwhich it is finally to bear, as the embryo is moulded into\nthe form of the {220} future individual. On the contrary,\nthere are cases in which the waste of the organs is supplied\nby the growth of new ones, which are prepared and formed\nbefore they are used, just as the offspring is prepared and\nformed before it is separated from the parent. This is the\ncase with the teeth of many animals, and especially with the\nteeth of animals of the crocodile kind. Young teeth grow\nnear the root of the old ones, like buds on the stem of a\nplant; and as these become fully developed, they take the\nplace of the parent tooth when that dies and is cast away.\nAnd these new teeth in their turn are succeeded by others\nwhich germinate from them. Several generations of such\nteeth, it is said as many as four, have been detected by\nanatomists, visibly existing at the same time; just as\nseveral generations of germs of individuals have been, as we\nalready stated, observed included in one another. But this\ncase of the teeth appears to show very strikingly how\ninsufficient such observations are to establish the doctrine\nof successive inclusion, or of the pre-existence of germs.\nAre we to suppose that every crocodile's tooth includes in\nitself the germs of an infinite number of possible teeth, as\nin the theory of pre-existing germs every individual\nincludes an infinite number of individuals? If this be true\nof teeth, we must suppose that organ to follow laws entirely\ndifferent from almost every other organ; for no one would\napply to the other organs in general such a theory of\nreproduction. But if such a theory be not maintained\nrespecting the teeth, how can we maintain the theory of the\npre-existing germs of individuals, which has no\nrecommendation except that of accounting for exactly the\nsame phenomena?\n\nIt would seem, then, that we are, by the closest\nconsideration of the subject, led to conceive the forces by\nwhich generation is produced, as forces which vitalize\ncertain portions of matter, and thus prepare them for\ndevelopment according to organic forms; and thus the\nconception of this Generative Force is identified with the\nconception of the Force of Organic Assimilation, to {221}\nwhich we were led by the consideration of the process of\nnutrition.\n\nI shall not attempt to give further distinctness and fixity\nto this conception of one of the vital forces; but I shall\nproceed to exemplify the same analysis of life by some\nremarks upon another Vital Process, and the Forces of which\nit exhibits the operation.\n\n\n\n{{222}}\nCHAPTER V.\n\nATTEMPTS TO FORM IDEAS OF SEPARATE VITAL FORCES,\n_continued_.--VOLUNTARY MOTION.\n\n\n1. WE formerly noticed the distinctions of _organic_ and\n_animal_ functions, organic and animal forces, as one of the\nmost marked distinctions to which physiologists have been\nled in their analysis of the vital powers. I have now taken\none of the former, the _organic_ class of functions, namely,\nNutrition; and have endeavoured to point out in some measure\nthe peculiar nature of the vital forces by which this\nfunction is carried on. It may serve to show the extent and\nthe difficulty of this subject, if, before quitting it, I\noffer a few remarks suggested by a function belonging to the\nother class, the _animal_ functions. This I shall briefly do\nwith respect to _Voluntary Motion_.\n\n2. In the History of Physiology, I have already related the\nprogress of the researches by which the organs employed in\nvoluntary motion became known to anatomists. It was\nascertained to the satisfaction of all physiologists, that\nthe immediate agents in such motion are the muscles; that\nthe muscles are in some way contracted, when the nerves\nconvey to them the agency of the will; and that thus the\nlimbs are moved. It was ascertained, also, that the nerves\nconvey sensations from the organs of sense inwards, so as to\nmake these sensations the object of the animal's\nconsciousness. In man and the higher animals, these\nimpressions upon the nerves are all conveyed to one internal\norgan, the brain; and from this organ all impressions of the\nwill appear to proceed; and thus the brain is {223} the\ncenter of animal life, towards which sensations converge,\nand from which volitions diverge.\n\nBut this being the process, we are led to inquire how far we\ncan obtain any knowledge, or form any conception, of the\nvital forces by means of which the process is carried on.\nAnd here I have further stated in the History[87\\9], that\nthe transfer of sensations and volitions along the nerves\nwas often represented as consisting in the motion of a\nNervous Fluid. I have related that the hypothesis of such a\nfluid, conveying its impressions either by motions of\ntranslation or of vibration, was countenanced by many great\nnames, as Newton, Haller, and even Cuvier. But I have\nventured to express my doubt whether this hypothesis can\nhave much value: 'for,' I have said, 'this principle cannot\nbe mechanical, chemical, or physical, and therefore cannot\nbe better understood by embodying it in a fluid. The\ndifficulty we have in conceiving what the force _is_, is not\ngot rid of by explaining the machinery by which it is\n_transferred_.'\n\n[Note 87\\9: _Hist. Ind. Sc._ b. xvii. c. v. s. 2.]\n\n3. I may add, that no succeeding biological researches\nappear to have diminished the force of these considerations.\nIn modern times, attempts have repeatedly been made to\nidentify the nervous fluid with electricity or galvanism.\nBut these attempts have not been satisfactory or conclusive\nof the truth of such an identity: and Professor M\u00fcller\nprobably speaks the judgment of the most judicious\nphysiologists, when he states it as his opinion, after\nexamining the evidence[88\\9], 'That the vital actions of the\nnerves are not attended with the development of any galvanic\ncurrents which our instruments can detect; and that the laws\nof action of the nervous principle are totally different\nfrom those of electricity.'\n\n[Note 88\\9: _Elem. Phys._ p. 640.]\n\nThat the powers by which the nerves are the instruments of\nsensation, and the muscles of motion, are vital endowments,\nincapable of being expressed or explained by any comparison\nwith mechanical, chemical, and electrical forces, is the\nresult which we should {224} expect to find, judging from\nthe whole analogy of science; and which thus is confirmed by\nthe history of physiology up to the present time. We\nnaturally, then, turn to inquire whether such peculiar vital\npowers have been brought into view with any distinctness and\nclearness.\n\n4. The property by which muscles, under proper stimulation,\ncontract and produce motion, has been termed _Irritability_\nor _Contractility_; the property by which nerves are\nsusceptible of their appropriate impressions has been termed\n_Sensibility_. A very few words on each of these subjects\nmust suffice.\n\n_Irritability._--I have, in the History of Physiology[89\\9],\nnoticed that Glisson, a Cambridge professor, distinguished\nthe Irritation of muscles as a peculiar property, different\nfrom any merely mechanical or physical action. I have\nmentioned, also, that he divides Irritation into _natural_,\n_vital_, and _animal_; and points out, though briefly, the\ngraduated differences of Irritability in different organs.\nAlthough these opinions did not at first attract much\nnotice, about seventy years afterwards attention was\npowerfully called to this vital force, _Irritability_, by\nHaller. I shall borrow Sprengel's reflections on this subject.\n\n[Note 89\\9: _Hist. Ind. Sc._ b. xvii. c. v.]\n\n'Hitherto men had been led to see more and more clearly that\nthe cause of the bodily functions, the fundamental power of\nthe animal frame, is not to be sought in the mechanism, and\nstill less in the mixture of the parts. In this conviction,\nthey had had recourse partly to the quite supersensuous\nprinciple of the Soul, partly to the half-material principle\nof the Animal Spirits, in order to explain the bodily\nmotions. Glisson alone saw the necessity of assuming an\nOriginal Power in the fibres, which, independent of the\ninfluence of the animal spirits, should produce contraction\nin them. And Gorter first held that this Original Power was\nnot to be confined to the muscles, but to be extended to all\nparts of the living body. {225}\n\n'But as yet the laws of this Power were not known, nor had\nmen come to an understanding whether it were fully distinct\nfrom the elasticity of the parts, or by what causes it was\nput in action. They had neither instituted observations nor\nexperiments which established its relation to other assumed\nforces of the body. There was still wanting a determination\nof the peculiar seat of this power, and experiments to trace\nits gradual differences in different parts of the body. In\naddition to other causes, the necessity of the assumption of\nsuch a power was felt the more, in consequence of the\nprevalence of Leibnitz's doctrine of the activity of matter;\nbut it was an occult quality, and remained so till Haller,\nby numerous experiments and solid observations, placed in a\nclear light the peculiarities of the powers of the animal body.'\n\n5. Perhaps, however, Haller did more in the way of\ndetermining experimentally the limits and details of the\napplication of this idea of Irritability as a peculiar\nattribute, than in developing the Idea itself. In that way\nhis merits were great. As early as the year 1739, he\npublished his opinion upon Irritability as the cause of\nmuscular motion, which he promulgated again in 1743. But\nfrom the year 1747 he was more attentive to the\npeculiarities of Irritability, and its difference from the\neffect of the nerves. In the first edition of his\n_Physiology_, which appeared in 1747, he distinguished three\nkinds of Force in muscles,--the Dead Force, the Innate\nForce, and the Nervous Power. The first is identical with\nthe elastic force of dead matter, and remains even after\ndeath. The _innate force_ continues only a short time after\ndeath, and discloses itself especially by alternate\noscillations; the motions which arise from this are much\nmore lively than those which arise from mere elasticity:\nthey are not excited by tension, nor by pressure, nor by any\nmechanical alteration, but only by _irritation_. The\n_nervous force_ of the muscle is imparted to it from without\nby the nerves; it preserves the _irritability_, which cannot\nlong subsist without the influence of the nervous force, but\nis not identical with it. {226}\n\nIn the year 1752, Haller laid before the Society of\nG\u00f6ttingen the result of one hundred and ninety experiments;\nfrom which it appears to what parts of the animal system\nIrritability and Nervous Power belong. These I need not\nenumerate. He also investigated with care its gradations in\nthose parts which do possess it. Thus the heart possesses it\nin the highest degree, and other organs follow in their\norder.\n\n6. Haller's doctrine was, that there resides in the muscles\na peculiar vital power by which they contract, and that this\npower is distinct from the attributes of the nerves. And\nthis doctrine has been accepted by the best physiologists of\nmodern times. But this distinction of the _irritability_ of\nthe muscles from the _sensibility_ of the nerves became\nsomewhat clearer by giving to the former attribute the name\nof _Contractility_. This accordingly was done; it is, for\nexample, the phraseology used by Bichat. By speaking of\n_animal sensibility_ and _animal contractility_, the passive\nand the active element of the processes of animal life are\nclearly separated and opposed to each other. The sensations\nwhich we feel, and the muscular action which we exert, may\nbe closely and inseparably connected, yet still they are\nclearly distinguishable. We can easily in our apprehension\nseparate the titillation felt in the nose on taking snuff,\nfrom the action of the muscles in sneezing; or the\nperception of an object falling towards the eye, from the\nexertion which shuts the eye-lid; although in these cases\nthe passive and active part of the process are almost or\nquite inseparable in fact. And this clear separation of the\nactive from the passive power is something, it would seem,\npeculiar to the Animal Vital Powers; it is a character by\nwhich they differ, not only from mechanical, chemical, and\nall other merely physical forces, but even from Organic\nVital Powers.\n\n7. But this difference between the Animal and the Organic\nVital Powers requires to be further insisted upon, for it\nappears to have been overlooked or denied by very eminent\nphysiologists. For instance, Bichat classifies the Vital\nPowers as Animal Sensibility, {227} Animal Contractility,\nOrganic Sensibility, Organic Contractility.\n\nNow the view which suggests itself to us, in agreement with\nwhat has been said, is this:--that though Animal Sensibility\nand Animal Contractility are clearly and certainly distinct,\nOrganic Sensibility and Organic Contractility are neither\nseparable in fact nor in our conception, but together make\nup a single Vital Power. That they are not separable in fact\nis, indeed, acknowledged by Bichat himself. 'The organic\ncontractility,' he says[90\\9], 'can never be separated from\nthe sensibility of the same kind; the reaction of the\nexcreting tubes is immediately connected with the action\nwhich the secreted fluids exercise upon them: the\ncontraction of the heart must necessarily succeed the influx\nof the blood into it.' It is not wonderful, therefore, that\nit should have happened, as he complains, that 'authors have\nby no means separated these two things, either in their\nconsideration or in language.' We cannot avoid asking, Are\nOrganic Sensibility and Organic Contractility really\nanything more than two different aspects of the same thing,\nlike action and reaction in mechanics, which are only two\nways of considering the action which takes place at a point;\nor like the positive and negative electricities, which, as\nwe have seen, always co-exist and correspond to each other?\n\n[Note 90\\9: _Life and Death_, p. 94.]\n\n8. But we may observe, moreover, that Bichat, by his use of\nthe term Contractility, includes in it powers to which it\ncannot with any propriety be applied. Why should we suppose\nthat the vital powers of absorption, secretion,\nassimilation, are of such a nature that the name\n_contractility_ may be employed to describe them? We have\nseen, in the last chapter, that the most careful study of\nthese powers leads us to conceive them in a manner\naltogether removed from any notion of contraction. Is it not\nthen an abuse of language which cannot possibly lead to\nanything but {228} confusion, to write thus[91\\9]: 'The\ninsensible organic contractility is that, by virtue of which\nthe excreting tubes react upon their respective fluids, the\nsecreting organs upon the blood which flows into them, the\nparts where nutrition is performed upon the nutritive\njuices, and the lymphatics upon the substances which excite\ntheir open extremities'? In the same manner he\nascribes[92\\9] to the peculiar sensibility of each organ the\npeculiarity of its products and operations. An increased\nabsorption is produced by an increased susceptibility of the\n'absorbent orifices.' And thus, in this view, each organic\npower may be contemplated either as sensibility or as\ncontractility, and may be supposed to be rendered more\nintense by magnifying either of these its aspects; although,\nin fact, neither can be conceived to be increased without an\nexactly commensurate increase of the other.\n\n[Note 91\\9: _Life and Death_, p. 95.]\n\n[Note 92\\9: _Ib._ p. 90.]\n\n9. This opinion, unfounded as it thus appears to be, that\nall the different organic vital powers are merely different\nkinds of Contractility or Excitability, was connected with\nthe doctrines of Brown and his followers, which were so\ncelebrated in the last century, that all diseases arise from\nincrease or from diminution of the Vital Force. The\nconsiderations which have already offered themselves would\nlead us to assent to the judgment which Cuvier has\npronounced upon this system. 'The theory of excitation,' he\nsays, 'so celebrated in these later times by its influence\nupon pathology and therapeutick, is at bottom only a\nmodification of that, in which, including under a common\nname Sensibility and Irritability,' and we may add, applying\nthis name to all the Vital Powers, 'the speculator takes\nrefuge in an abstraction so wide, that if, by it, he\nsimplifies medicine, he by it annihilates all positive\nphysiology[93\\9].'\n\n[Note 93\\9: _Hist. des Sc. Nat. depuis_ 1789, i. 219.]\n\n10. The separation of the nervous influence and the muscular\nirritability, although it has led to many highly instructive\nspeculations, is not without its {229} difficulties, when\nviewed with reference to the Idea of Vital Power. If the\nirritability of each muscle reside in the muscle itself, how\ndoes it differ from a mere mechanical force, as elasticity?\nBut, in point of fact, it is certain that the muscular\nirritability of the animal body is not an attribute of the\nmuscle itself independent of its connexion with the system.\nNo muscle, or other part, removed from the body, _long_\npreserves its irritability. This power cannot subsist\npermanently, except in connexion with an organic whole. This\ncondition peculiarly constitutes irritability a _living_\nforce: and this condition would be satisfied by considering\nthe force as derived from the nervous system; but it appears\nthat though the nervous system has the most important\ninfluence upon all vital actions, the muscular irritability\nmust needs be considered as something distinct. And thus the\nIrritability or Contractility of the muscle is a peculiar\nendowment of the texture, but it is at the same time an\nendowment which can only co-exist with life; it is, in\nshort, a peculiar Vital Power.\n\n11. This necessity of the union of the muscle with the whole\nnervous system, in order that it may possess irritability,\nwas the meaning of the true part of Stahl's psychical\ndoctrine; and the reason why he and his adherents persisted\nin asserting the power of the soul even over involuntary\nmotions. This doctrine was the source of much controversy in\nlater times.\n\n'But,' says Cuvier[94\\9], 'this opposition of opinion may be\nreconciled by the intimate union of the nervous substance\nwith the fibre and the other contractile organic elements,\nand by their reciprocal action;--doctrines which had been\npresented with so much probability by physiologists of the\nScotch school, but which were elevated above the rank of\nhypotheses only by the observations of more recent times.\n\n[Note 94\\9: _Hist. des Sc. Nat. depuis_ 1789, i. 213.]\n\n'The fibre does not contract by itself, but by the influence\nof the nervous filaments, which are always united with it.\nThe change which produces the {230} contraction cannot take\nplace without the concurrence of both these substances; and\nit is further necessary that it should be occasioned each\ntime by an exterior cause, by a stimulant.\n\n'The Will is one of these stimulants; but it only excites\nthe Irritability, it does not constitute it; for in the case\nof persons paralytic from apoplexy, the Irritability\nremains, though the power of the Will over it is gone. Thus\n_irritability_ depends in part on the _nerve_, but not on\nthe _sensibility_: this last is another property, still more\nadmirable and occult than the irritability; but it is only\none among several functions of the nervous system. It would\nbe an abuse of words to extend this denomination to\nfunctions unaccompanied by perception.'\n\n12. Supposing, then, that Contractility is established as a\npeculiar Vital Power residing in the muscles, we may ask\nwhether we can trace with any further exactness the seat and\nnature of this power. It would be unsuitable to the nature\nof the present work to dwell upon the anatomical discussions\nbearing upon this point. I will only remark that some\nanatomists maintain[95\\9] that muscles are contracted by\nthose fibres assuming a zigzag form, which at first were\nstraight. Others (Professor Owen and Dr. A. Thompson) doubt\nthe accuracy of this observation; and conceive that the\nmuscular fibre becomes shorter and thicker, but does not\ndeviate from a right line. We may remark that the latter\nkind of action appears to be more elementary in its nature.\nWe can, as a matter of geometry, conceive a straight line\nthrown into a zigzag shape by muscular contractions taking\nplace between remote parts of it; but it is difficult to\nconceive by what _elementary_ mode of action a straight\nfibre could bend itself at certain points, and at certain\npoints only; since the elementary force must act at every\npoint of the fibre, and not at certain selected points.\n\n[Note 95\\9: M\u00fcller, _Elem. Phys._ p. 887.]\n\n13. A circumstance which remarkably marks the difference\nbetween the vital force of Contractility, {231} inherent in\nmuscles, and any merely dead or mechanical force, is this;\nthat in assuming their contractile state, muscles exert a\ntension which they could not themselves support or convey if\nnot strengthened by their vital irritability. They are\ncapable of raising weights by their exertion, which will\ntear them asunder when the power of contraction is lost by\ndeath. This has induced Cuvier and other physiologists[96\\9]\nto believe 'that in the moment of action, the particles that\ncompose a fibre, not only approach towards each other\nlongitudinally, but that their cohesive attraction becomes\ninstantaneously much greater than it was before: for without\nsuch an increase of cohesive force, the tendency to shorten\ncould not, as it would appear, prevent the fibre from being\ntorn.' We see here the difficulty, or rather the\nimpossibility, of conceiving muscular contractility as a\nmere mechanical force; and perhaps there is little hope of\nany advantage by calling in the aid of chemical hypothesis\nto solve the mechanical difficulty. Cuvier conjectures that\na sudden change in the chemical composition may thus so\nquickly and powerfully augment the cohesion. But we may ask,\nare not a chemical synthesis and analysis, suddenly\nperformed by a mere act of the will, as difficult to\nconceive as a sudden increase and decrease of mechanical\npower directly produced by the same cause?\n\n[Note 96\\9: Prichard, _Vital Prin._ p. 126.]\n\n14. _Sensibility._ The nerves are the organs and channels of\nSensibility. By means of them we receive our sensations,\nwhether of mere pleasure and pain, or of qualities which we\nascribe to external objects, as a bitter taste, a sweet\nodour, a shrill sound, a red colour, a hard or a hot feeling\nof touch. Some of these sensations are but obscurely the\nobjects of our consciousness; as for example the feeling\nwhich our feet have of the ground, or the sight which our\neyes have of neighbouring objects, when we walk in a\nreverie. In these cases the sensations, though obscure,\nexist; for they {232} serve to balance and guide us as we\nwalk. In other cases, our sensations are distinctly and\ndirectly the objects of our attention.\n\nBut our Sensations, as we have already said, we ascribe as\nQualities to external objects. By our senses we perceive\nobjects, and thus our _sensations_ become _perceptions_. We\nhave not only the sensation of _round_, _purple_, and\n_green_, repeated and varied, but the perception of a _bunch\nof grapes_ partly ripe and partly unripe. We have not only\nsensations of noise and of variously-coloured specks rapidly\nchanging their places, but we have perceptions, by sound and\nsight, of a stone rolling down the hill and crushing the\nshrubs in its path. We scarcely ever dwell upon our\nSensations; our thoughts are employed upon Objects. We\nregard the impressions upon our nerves, not for what they\n_are_, but for what they _tell_ us.\n\nBut in what Language do the impressions upon the nerves thus\nspeak to us of an external world,--of the forms and\nqualities and actions of objects? How is it that by the aid\nof our nervous system we become acquainted not only with\nimpressions but with _things_; that we learn not only the\nrelation of objects to us, but to one another?\n\n15. It has been shown at some length in the previous Books,\nthat the mode in which Sensations are connected in our minds\nso as to convey to us the knowledge of Objects and their\nRelations, is by being contemplated with reference to\n_Ideas_. Our Sensations, connected by the Idea of Space,\nbecome Figures; connected by the Idea of Time, they become\nCauses and Effects; connected by the Idea of Resemblance,\nthey become Individuals and Kinds; connected by the Idea of\nOrganization, they become Living Things. It has been shown\nthat without these Ideas there can be no connexion among our\nsensations, and therefore no perception of Figure, Action,\nKind, or in short, of bodies under any aspect whatever.\nSensations are the rude _Matter_ of our perceptions; and are\nnothing, except so far as they have _Form_ given them by\nIdeas. {233} But thus moulded by our Ideas, Sensation\nbecomes the source of an endless store of important\nKnowledge of every possible kind.\n\n16. But one of the most obvious uses of our perceptions and\nour knowledge is to direct our Actions. It is suitable to\nthe condition of our being that when we perceive a bunch of\ngrapes, we should be able to pluck and eat the ripe ones;\nthat when we perceive a stone rushing down the side of a\nhill, we should be able to move so as to avoid it. And this\nmust be done by moving our limbs; in short, by the use of\nour muscles. And thus Sensation leads, not directly, but\nthrough the medium of Ideas, to muscular Contraction. I say\nthat sensation and Muscular action are in such cases\nconnected through the medium of Ideas. For when we proceed\nto pluck the grape which we see, the _sensation_ does not\ndetermine the motion of the hand by any necessary\ngeometrical or mechanical conditions, as an impression made\nupon a machine determines its motions; but the _perception_\nleads us to stretch forth the hand to that part of space,\nwherever it is, where we _know_ that the grape is; and this,\nnot in any determinate path, but, it may be, avoiding or\nremoving intervening obstacles, which we also _perceive_.\nThere is in every such case a connexion between the\nsensation and the resulting action, not of a material but of\na mental kind. The cause and the effect are bound together,\nnot by physical but by intellectual ties.\n\n17. And thus in such cases, between the two _vital_\noperations, Sensation and Muscular Action, there intervenes,\nas an intermediate step, Perception or Knowledge, which is\nnot merely vital but _ideal_. But this is not all; there is\nstill another mental part of the process which may be\nreadily distinguished from that which we have described. An\nact of the _Will_, a Volition, is that, in the Mind, which\nimmediately determines the action of the Muscles of the\nBody. And thus Will intervenes between Knowledge and Action;\nand the cycle of operations which take place when animals\nact with reference to external objects is {234}\nthis:--Sensation, Perception, Volition, Muscular\nContraction.\n\n18. To attempt further to analyse the mental part of this\ncycle does not belong to the present part of our work. But\nwe may remark here, as we have already remarked in the\nHistory[97\\9], how irresistibly we are led by physiological\nresearches into the domain of thought and mind. We pass from\nthe body to the soul, from physics to metaphysics; from\nbiology to psychology; from things to persons; from nouns to\npronouns. I have there noticed the manner in which Cuvier\nexpresses this transition by the introduction of the\npronoun: 'The impression of external objects upon the ME,\nthe production of a sensation, of an image, is a mystery\nimpenetrable to our thoughts.'\n\n[Note 97\\9: _Hist. Ind. Sc._ b. xvii. c. v. s. 2.]\n\n19. But to return to the merely biological part of our\nspeculations. We have arrived, it will be perceived, at this\nresult: that in animal actions there intervenes between the\ntwo terms of Sensation and Muscular Contraction, an\nintermediate process; which may be described as a\ncommunication to and from a Center. The Center is the seat\nof the sentient and volent faculties, and is of a\n_hyperphysical_ nature. But the existence of such a Center\nas a necessary element in the functions of the _animal_ life\nis a truth which is important in biology. This indeed may be\ntaken as the peculiar character of animal, as distinguished\nfrom merely _organic_ powers. Accordingly, it is so stated\nby Bichat. For although he superfluously, as I have tried to\nshow, introduces into his list of vital powers an organic\nsensibility, he still draws the distinction of which I have\nspoken; 'in the animal life, Sensibility is the faculty of\nreceiving an Impression _plus_ that of referring it to a\ncommon Center[98\\9].'\n\n[Note 98\\9: _Life and Death_, p. 84.]\n\n20. But since Sensibility and Contractility are thus\nconnected by reference to a common Center, we may ask,\nbefore quitting the subject, what are the different forms\nwhich this reference assumes? Is the connexion {235} always\nattended by the distinct steps of Knowledge and Will,--by a\nclear act of consciousness, as in the case which we have\ntaken, of plucking a grape; or may these steps become\nobscure, or vanish altogether?\n\nWe need not further illustrate the _conscious_ connexion.\nSuch actions as we have described are called _voluntary_\nactions. In extreme cases, the mental part of the process is\nobvious enough. But we may gradually pass from these to\ncases in which the mental operation is more and more obscure.\n\nIn walking, in speaking, in eating, in breathing, our\nmuscular exertions are directed by our sensations and\nperceptions: yet in such processes, how dimly are we\nconscious of perceptive and directive power! How the mind\nshould be able to exercise such a power, and yet should be\nscarcely or not at all conscious of its exercise, is a very\ncurious problem. But in all or in most of the instances just\nmentioned, the solution of this problem appears to depend\nupon psychological rather than biological principles, and\ntherefore does not belong to this place.\n\n21. But in cases at the other extreme (unconscious actions)\nthe mental part of the operation vanishes altogether. In\nmany animals, even after decapitation, the limbs shrink when\nirritated. The motions of the iris are determined by the\ninfluence of light on our eyes, without our being aware of\nthe motions. Here Sensations produce Motions, but with no\ntrace of intervening Perception or Will. The Sensation\nappears to be _reflected_ back from the central element of\nanimal life, in the form of a Muscular Contraction; but in\nthis case the Sensation is not modified or regulated by any\n_Idea_. These reflected motions have no reference to\nrelations of space or force among surrounding objects. They\nare blind and involuntary, like the movements of convulsion,\ndepending for direction and amount only on the position and\ncircumstances of the limb itself with its muscles. Here the\nCentre from which the reflection takes place is merely\n_animal_, not intellectual.\n\nIn this case some physiologists have doubted whether the\nreflection of the sensation in the form of a muscular {236}\ncontraction does really take place from the Center; and have\nconceived that sensorial impressions might affect motor\nnerves without any communication with the nervous Center.\nBut on this subject we may, I conceive, with safety adopt\nthe decision of Professor M\u00fcller, deliberately given after a\ncareful examination of the subject: 'When impressions made\nby the action of external stimuli on sensitive nerves give\nrise to motions in other parts, these motions are never the\nresult of the _direct_ reaction of the sensitive and motor\nfibres of the nerves on each other; the irritation is\nconveyed by the sensitive fibres to the brain and spinal\ncord, and is by these communicated to the motor fibres.'\n\n22. Thus we have two extreme cases of the connexion of\nsensation with muscular action; in one of which the\nconnexion clearly _is_, and in the other it as clearly _is\nnot_, determined by relations of Ideas, in its transit\nthrough the nervous Center. There is another highly curious\ncase standing intermediate between these two, and extremely\ndifficult to refer to either. I speak of the case of _Instinct_.\n\nInstinct leads to actions which are _such as if they were\ndetermined by Ideas_. The lamb follows its mother by\ninstinct; but the motions by which it does this, the special\nmuscular exertions, depend entirely upon the geometrical and\nmechanical relations of external bodies, as the form of the\nground, and the force of the wind. The contractions of the\nmuscles which are requisite in order that the creature may\nobey its instinct, vary with every variation of these\nexternal conditions;--are not determined by any rule or\nnecessity, but by properties of Space and Force. Thus the\naction is not governed by Sensations directly, but by\nsensations moulded by Ideas. And the same is the case with\nother cases of instinct. The dog hunts by instinct; but he\nhunts certain kinds of animals merely, thus showing that his\ninstinct acts according to Resemblances and Differences; he\ncrosses the field repeatedly to find the track of his prey\nby scent; thus recognizing the relations of Space with\nreference to the track; he leaps, adjusting his Force to\n{237} the distance and height of the leap with mechanical\nprecision; and thus he practically recognizes the Ideas of\nResemblance, Space, and Force.\n\nBut have animals such Ideas? In any proper sense in which we\ncan speak of possessing Ideas, it appears plain that they\nhave not. Animals cannot, at any time, be said properly to\npossess ideas, for ideas imply the possibility of\n_speculative_ knowledge.\n\n23. But even if we allow to animals only the _practical_\npossession of Ideas, we have still a great difficulty\nremaining. In the case of man, his ideas are unfolded\ngradually by his intercourse with the external world. The\nchild learns to distinguish forms and positions by a\nrepeated and incessant use of his hands and eyes; he learns\nto walk, to run, to leap, by slow and laborious degrees; he\ndistinguishes one man from another, and one animal from\nanother, only after repeated mistakes. Nor can we conceive\nthis to be otherwise. How should the child know at once what\nmuscles he is to exert in order to touch with his hand a\ncertain visible object? How should he know what muscles to\nexert that he may stand and not fall, till he has tried\noften? How should he learn to direct his attention to the\ndifferences of different faces and persons, till he is\nroused by some memory, or hope which implies memory? It\nseems to us as if the sensations could not, without\nconsiderable practice, be rightly referred to Ideas of\nSpace, Force, Resemblance, and the like.\n\nYet that which thus appears impossible, is in fact done by\nanimals. The lamb almost immediately after its birth follows\nits mother, accommodating the actions of its muscles to the\nform of the ground. The chick, just escaped from the shell,\npicks up a minute insect, directing its beak with the\ngreatest accuracy. Even the human infant seeks the breast\nand exerts its muscles in sucking, almost as soon as it is\nborn. Hence, then, we see that Instinct produces at once\nactions regulated by Ideas, or, at least, which take place\n_as if_ they were regulated by Ideas; although the Ideas\ncannot have been developed by exercise, and only appear to\nexist so far as such actions are concerned. {238}\n\n24. The term _Instinct_ may properly be opposed to\n_Insight_. The former implies an inward principle of action,\nimplanted within a creature and practically impelling it,\nbut not capable of being developed into a subject of\ncontemplation. While the instinctive actions of animals are\ndirected by such a principle, the deliberate actions of man\nare governed by insight: he can contemplate the ideal\nrelations on which the result of his action depends. He can\nin his mind map the path he will follow, and estimate the\nforce he will exert, and class the objects he has to deal\nwith, and determine his actions by the relations which he\nthus has present to his mind. He thus possesses Ideas not\nonly practically, but speculatively. And knowing that the\nIdeas by which he commonly directs his actions, Space,\nCause, Resemblance, and the like, have been developed to\nthat degree of clearness in which he possesses them by the\nassiduous exercise of the senses and the mind from the\nearliest stage of infancy, and that these Ideas are capable\nof being still further unfolded into long trains of\nspeculative truth, he is unable to conceive the manner in\nwhich animals possess such Ideas as their instinctive\nactions disclose:--Ideas which neither require to be\nunfolded nor admit of unfolding; which are adequate for\npractical purposes without any previous exercise, and\ninadequate for speculative purposes with whatever labour\ncultivated.\n\nI have ventured to make these few remarks on Instinct since\nit may, perhaps, justly be considered as the last province\nof Biology, where we reach the boundary line of Psychology.\nI have now, before quitting this subject, only one other\nprinciple to speak of.\n\n\n\n{{239}}\nCHAPTER VI.\n\nOF THE IDEA OF FINAL CAUSES.\n\n\n1. BY an examination of those notions which enter into all\nour reasonings and judgments on living things, it appeared\nthat we conceive animal life as a vortex or cycle of moving\nmatter in which the form of the vortex determines the\nmotions, and these motions again support the form of the\nvortex: the stationary parts circulate the fluids, and the\nfluids nourish the permanent parts. Each portion ministers\nto the others, each depends upon the other. The parts make\nup the whole, but the existence of the whole is essential to\nthe preservation of the parts. But parts existing under such\nconditions are _organs_, and the whole is _organized_. This\nis the fundamental conception of organization. 'Organized\nbeings,' says the physiologist[99\\9], 'are composed of a\nnumber of essential and mutually dependent parts.' 'An\norganized product of nature,' says the great\nmetaphysician[100\\9], 'is that in which all the parts are\nmutually ends and means.'\n\n[Note 99\\9: M\u00fcller, _Elem._ p. 18.]\n\n[Note 100\\9: Kant, _Urtheilskraft_, p. 296.]\n\n2. It will be observed that we do not content ourselves with\nsaying that in such a whole, all the parts are _mutually\ndependent_. This might be true even of a mechanical\nstructure; it would be easy to imagine a framework in which\neach part should be necessary to the support of each of the\nothers; for example, an arch of several stones. But in such\na structure, the parts have no properties which they derive\nfrom the whole. They are beams or stones when separate; they\nare no more when joined. But the same is not the case in an\norganized whole. The limb of an animal separated {240} from\nthe body, loses the properties of a limb, and soon ceases to\nretain even its form.\n\n3. Nor do we content ourselves with saying that the parts\nare _mutually causes and effects_. This is the case in\nmachinery. In a clock, the pendulum by means of the\nescapement causes the descent of the weight, the weight by\nthe same escapement keeps up the motion of the pendulum. But\nthings of this kind may happen by accident. Stones slide\nfrom a rock down the side of a hill and cause it to be\nsmooth; the smoothness of the slope causes stones still to\nslide. Yet no one would call such a slide an organized\nsystem. The system is organized, when the effects which take\nplace among the parts are _essential to our conception of\nthe whole_; when the whole would not _be_ a whole, nor the\nparts, parts, except these effects were produced; when the\neffects not only happen in fact, but are included in the\nidea of the object; when they are not only seen, but\nforeseen; not only expected, but intended: in short when,\ninstead of being causes and effects, they are _ends_ and\n_means_, as they are termed in the above definition.\n\nThus we necessarily include, in our Idea of Organization,\nthe notion of an End, a Purpose, a Design; or, to use\nanother phrase which has been peculiarly appropriated in\nthis case, a _Final Cause_. This idea of a Final Cause is an\nessential condition in order to the pursuing our researches\nrespecting organized bodies.\n\n4. This Idea of Final Cause is not _deduced_ from the\nphenomena by reasoning, but is _assumed_ as the only\ncondition under which we can reason on such subjects at all.\nWe do not deduce the Idea of Space, or Time, or efficient\nCause from the phenomena about us, but necessarily look at\nphenomena as subordinate to these Ideas from the beginning\nof our reasoning. It is true, our ideas of relations of\nSpace, and Time, and Force, may become much more clear by\nour familiarizing ourselves with particular phenomena: but\nstill, the Fundamental Ideas are not generated, but\nunfolded; not extracted from the external world, but evolved\nfrom the world within. In like manner, in the contemplation\nof organic structures, we consider {241} each part as\nsubservient to some use, and we cannot study the structure\nas organic without such a conception. This notion of\nadaptation,--this Idea of an End,--may become much more\nclear and impressive by seeing it exemplified in particular\ncases. But still, though suggested and evoked by special\ncases, it is not furnished by them. If it be not supplied by\nthe mind itself, it can never be logically deduced from the\nphenomena. It is not a portion of the facts which we study,\nbut it is a principle which connects, includes, and renders\nthem intelligible; as our other Fundamental Ideas do the\nclasses of facts to which they respectively apply.\n\n5. This has already been confirmed by reference to fact; in\nthe History of Physiology, I have shown that those who\nstudied the structure of animals were irresistibly led to\nthe conviction that the parts of this structure have each\nits end or purpose;--that each member and organ not merely\nproduces a certain effect or answers a certain use, but is\nso framed as to impress us with the persuasion that it was\nconstructed _for_ that use:--that it was _intended_ to\nproduce the effect. It was there seen that this persuasion\nwas repeatedly expressed in the most emphatic manner by\nGalen;--that it directed the researches and led to the\ndiscoveries of Harvey;--that it has always been dwelt upon\nas a favourite contemplation, and followed as a certain\nguide, by the best anatomists;--and that it is inculcated by\nthe physiologists of the profoundest views and most\nextensive knowledge of our own time. All these persons have\ndeemed it a most certain and important principle of\nphysiology, that in every organized structure, plant or\nanimal, each intelligible part has its allotted\noffice:--each organ is designed for its appropriate\nfunction:--that nature, in these cases, produces nothing in\nvain: that, in short, each portion of the whole arrangement\nhas its _final cause_; an End to which it is adapted, and in\nthis End, the reason that it is where and what it is.\n\n6. This Notion of Design in organized bodies must, I say, be\nsupplied by the student of organization out of his own mind:\na truth which will become clearer if {242} we attend to the\nmost conspicuous and acknowledged instances of _design_. The\nstructure of the Eye, in which the parts are curiously\nadjusted so as to produce a distinct image on the retina, as\nin an optical instrument;--the Trochlear Muscle of the eye,\nin which the tendon passes round a support and turns back,\nlike a rope round a pulley;--the prospective contrivances\nfor the preservation of animals, provided long before they\nare wanted, as the Milk of the mother, the Teeth of the\nchild, the Eyes and Lungs of the f\u0153tus:--these arrangements,\nand innumerable others, call up in us a persuasion that\nDesign has entered into the plan of animal form and\nprogress. And if we bring in our minds this conception of\nDesign, nothing can more fully square with and fit it, than\nsuch instances as these. But if we did not already possess\nthe Idea of Design;--if we had not had our notion of\nmechanical contrivance awakened by inspection of optical\ninstruments, or pulleys, or in some other way:--if we had\nnever been conscious ourselves of providing for the\nfuture;--if this were the case, we could not recognize\ncontrivance and prospectiveness in such instances as we have\nreferred to. The facts are, indeed, admirably in accordance\nwith these conceptions, when the two are brought together:\nbut the facts and the conceptions come together from\ndifferent quarters--from without and from within.\n\n7. We may further illustrate this point by referring to the\nrelations of travellers who tell us that when consummate\nexamples of human mechanical contrivance have been set\nbefore savages, they have appeared incapable of apprehending\nthem as proofs of design. This shows that in such cases the\nIdea of Design had not been developed in the minds of the\npeople who were thus unintelligent: but it no more proves\nthat such an idea does not naturally and necessarily arise,\nin the progress of men's minds, than the confused manner in\nwhich the same savages apprehend the relations of space, or\nnumber, or cause, proves that these ideas do not naturally\nbelong to their intellects. All men have these ideas; and it\nis because they {243} cannot help referring their sensations\nto such ideas, that they apprehend the world as existing in\ntime and space, and as a series of causes and effects. It\nwould be very erroneous to say that the belief of such\ntruths is obtained by logical reasoning from facts. And in\nlike manner we cannot logically deduce design from the\ncontemplation of organic structures; although it is\nimpossible for us, when the facts are clearly before us, not\nto find a reference to design operating in our minds.\n\n8. Again; the evidence of the doctrine of Final Causes as a\nfundamental principle of Biology may be obscured and\nweakened in some minds by the constant habit of viewing this\ndoctrine with suspicion as unphilosophical and at variance\nwith Morphology. By cherishing such views, it is probable\nthat many persons, physiologists and others, have gradually\nbrought themselves to suppose that many or most of the\narrangements which are familiarly adduced as instances of\ndesign may be accounted for, or explained away;--that there\nis a certain degree of prejudice and narrowness of\ncomprehension in that lively admiration of the adaptation of\nmeans to ends which common minds derive from the spectacle\nof organic arrangements. And yet, even in persons accustomed\nto these views, the strong and natural influence of the Idea\nof a Final Cause, the spontaneous recognition of the\nrelation of Means to an End as the assumption which makes\norganic arrangements intelligible, breaks forth when we\nbring before them a new case, with regard to which their\ngenuine convictions have not yet been modified by their\nintellectual habits. I will offer, as an example which may\nserve to illustrate this, the discoveries recently made with\nregard to the process of Suckling in the Kangaroo. In the\ncase of this, as of other pouched animals, the young animal\nis removed, while very small and imperfectly formed, from\nthe womb to the pouch, in which the teats are, and is there\nplaced with its lips against one of the nipples. But the\nyoung animal taken altogether is not so large as the nipple,\nand is therefore incapable of sucking after the manner of\ncommon mammals. Here is a difficulty: {244} how is it\novercome?--By an appropriate _contrivance_: the nipple,\nwhich in common mammals is not furnished with any muscle, is\nin the kangaroo provided with a powerful extrusory muscle by\nwhich the mother can inject the milk into the mouth of her\noffspring. And again; in order to give attachment to this\nmuscle there is a bone which is not found in animals of\nother kinds. But this mode of solving the problem of\nsuckling so small a creature introduces another difficulty.\nIf the milk is injected into the mouth of the young one,\nwithout any action of its own muscles, what is to prevent\nthe fluid entering the windpipe and producing suffocation?\nHow is this danger avoided?--By another appropriate\n_contrivance_: there is a funnel in the back of the throat\nby which the air passage is completely separated from the\npassage for nutriment, and the injected milk passes in a\ndivided stream on each side of the larynx to the\n\u0153sophagus[101\\9]. And as if to show that this apparatus is\nreally formed with a view to the wants of the young one, the\nstructure alters in the course of the animal's growth; and\nthe funnel, no longer needed, is modified and disappears.\n\n[Note 101\\9: Mr. Owen, in _Phil. Trans._ 1834, p. 348.]\n\nWith regard to this and similar examples, the remark which I\nwould urge is this:--that no one, however prejudiced or\nunphilosophical he may in general deem the reference to\nFinal Causes, can, at the first impression, help regarding\nthis curious system of arrangement as the Means to an End.\nSo contemplated, it becomes significant, intelligible,\nadmirable: without such a principle, it is an unmeaning\ncomplexity, a collection of contradictions, producing an\nalmost impossible result by a portentous conflict of\nchances. The parts of this apparatus cannot have produced\none another: one part is in the mother; another part in the\nyoung one: without their harmony they could not be\neffective; but nothing except design can operate to make\nthem harmonious. They are _intended_ to work together; and\nwe cannot resist the conviction of this intention when the\nfacts first come before us. Perhaps {245} there may\nhereafter be physiologists who, tracing the gradual\ndevelopment of the parts of which we have spoken, and the\nanalogies which connect them with the structures of other\nanimals, may think that this development, these analogies,\naccount for the conformation we have described; and may\nhence think lightly of the explanation derived from the\nreference to Final Causes. Yet surely it is clear, on a calm\nconsideration of the subject, that the latter explanation is\nnot disturbed by the former; and that the observer's first\nimpression, that this is 'an irrefragable evidence of\ncreative foresight[102\\9],' can never be obliterated;\nhowever much it may be obscured in the minds of those who\nconfuse this view by mixing it with others which are utterly\nheterogeneous to it, and therefore cannot be contradictory.\n\n[Note 102\\9: Mr. Owen, in _Phil. Trans._ 1834, p. 349.]\n\n9. I have elsewhere[103\\9] remarked how physiologists, who\nthus look with suspicion and dislike upon the introduction\nof Final Causes into physiology, have still been unable to\nexclude from their speculations causes of this kind. Thus\nCabanis says[104\\9], 'I regard with the great Bacon, the\nphilosophy of Final Causes as sterile; but I have elsewhere\nacknowledged that it was very difficult for the most\ncautious man never to have recourse to them in his\nexplanations.' Accordingly, he says, 'The partisans of Final\nCauses nowhere find arguments so strong in favour of their\nway of looking at nature as in the laws which preside and\nthe circumstances of all kinds which concur in the\nreproduction of living races. In no case do the means\nemployed appear so clearly relative to the end.' And it\nwould be easy to find similar acknowledgments, express or\nvirtual, in other writers of the same kind. Thus Bichat,\nafter noting the difference between the organic sensibility\nby which the organs are made to perform their offices, and\nthe animal sensibility of which the {246} nervous center is\nthe seat, says[105\\9], 'No doubt it will be asked,\n_why_'--that is, as we shall see, for what _end_--'the\norgans of internal life have received from nature an\ninferior degree of sensibility only, and why they do not\ntransmit to the brain the impressions which they receive,\nwhile all the acts of the animal life imply this\ntransmission? The reason is simply this, that all the\nphenomena which establish our connexions with surrounding\nobjects _ought to be_, and are in fact, under the influence\nof the Will; while all those which serve for the purpose of\nassimilation only, escape, and _ought_ indeed to escape,\nsuch influence.' The _reason_ here assigned is the Final\nCause; which, as Bichat justly says, we cannot help asking\nfor.\n\n[Note 103\\9: _Bridgewater Treatise_, p. 352.]\n\n[Note 104\\9: _Rapports du Physique et du Moral_, i. 299.]\n\n[Note 105\\9: _Life and Death_, (trans.) p. 32.]\n\n10. Again; I may quote from the writer last mentioned\nanother remark, which shows that in the organical sciences,\nand in them alone, the Idea of forces as Means acting to an\nEnd, is inevitably assumed and acknowledged as of supreme\nauthority. In Biology alone, observes Bichat[106\\9], have we\nto contemplate the state of _Disease_. 'Physiology is to the\nmovements of living bodies, what astronomy, dynamics,\nhydraulics, &e., are to those of inert matter: but these\nlatter sciences have no branches which correspond to them as\nPathology corresponds to Physiology. For the same reason all\nnotion of a Medicament is repugnant to the physical\nsciences. A Medicament has for its object to bring the\nproperties of the system back to their Natural Type; but the\nphysical properties never depart from this Type, and have no\nneed to be brought back to it: and thus there is nothing in\nthe physical sciences which holds the place of Therapeutick\nin Physiology.' Or, as we might express it otherwise, of\ninert forces we have no conception of what they _ought to\ndo_, except what they _do_. The forces of gravity,\nelasticity, affinity, never act in a _diseased_ manner; we\nnever conceive them as failing in their purpose; for we do\nnot conceive them as having any purpose which is answered by\none mode of their action rather than {247} another. But with\n_organical_ forces the case is different; they are\nnecessarily conceived as acting for the preservation and\ndevelopment of the system in which they reside. If they do\nnot do this, they fail, they are deranged, diseased. They\nhave for their object to conform the living being to a\ncertain type; and if they cause or allow it to deviate from\nthis type, their action is distorted, morbid, contrary to\nthe ends of nature. And thus this conception of organized\nbeings as susceptible of disease, implies the recognition of\na state of health, and of the organs and the vital forces as\nmeans for preserving this normal condition. The state of\nhealth, and of perpetual development, is necessarily\ncontemplated as the Final Cause of the processes and powers\nwith which the different parts of plants and animals are\nendowed.\n\n[Note 106\\9: _Anatomie G\u00e9n\u00e9rale_, i. liii.]\n\n11. This Idea of a Final Cause is applicable as a\nfundamental and regulative idea to our speculations\nconcerning organized creatures only. That there is a purpose\nin many other parts of the creation, we find abundant reason\nto believe, from the arrangements and laws which prevail\naround us. But this persuasion is not to be allowed to\nregulate and direct our reasonings with regard to inorganic\nmatter, of which conception the relation of means and end\nforms no essential part. In mere Physics, Final Causes, as\nBacon has observed, are not to be admitted as a principle of\nreasoning. But in the organical sciences, the assumption of\ndesign and purpose in every part of every whole, that is,\nthe pervading idea of Final Cause, is the basis of sound\nreasoning and the source of true doctrine.\n\n12. The Idea of Final Cause, of end, purpose, design,\nintention, is altogether different from the Idea of Cause,\nas Efficient Cause, which we formerly had to consider; and\non this account the use of the word Cause in this phrase has\nbeen objected to. If the idea be clearly entertained and\nsteadily applied, the word is a question of subordinate\nimportance. The term Final Cause has been long familiarly\nused, and appears not likely to lead to confusion. {248}\n\n13. The consideration of Final Causes, both in physiology\nand in other subjects, has at all times attracted much\nattention, in consequence of its bearing upon the belief of\nan Intelligent Author of the Universe. I do not intend, in\nthis place, to pursue the subject far in this view: but\nthere is one antithesis of opinion, already noticed in the\nHistory of Physiology, on which I will again make a few\nremarks[107\\9].\n\n[Note 107\\9: _Hist. Ind. Sc._ b. xvii. c. viii. On the\nDoctrine of Final Causes in Physiology.]\n\nIt has appeared to some persons that the mere aspect of\norder and symmetry in the works of nature--the contemplation\nof comprehensive and consistent law--is sufficient to lead\nus to the conception of a design and intelligence producing\nthe order and carrying into effect the law. Without here\nattempting to decide whether this is true, we may discern,\nafter what has been said, that the conception of Design,\narrived at in this manner, is altogether different from that\nIdea of Design which is suggested to us by organized bodies,\nand which we describe as the doctrine of Final Causes. The\nregular form of a crystal, whatever beautiful symmetry it\nmay exhibit, whatever general laws it may exemplify, does\nnot prove design in the same manner in which design is\nproved by the provisions for the preservation and growth of\nthe seeds of plants, and of the young of animals. The law of\nuniversal gravitation, however wide and simple, does not\nimpress us with the belief of a purpose, as does that\npropensity by which the two sexes of each animal are brought\ntogether. If it could be shown that the symmetrical\nstructure of a flower results from laws of the same kind as\nthose which determine the regular forms of crystals, or the\nmotions of the planets, the discovery might be very striking\nand important, but it would not at all come under our idea\nof Final Cause.\n\n14. Accordingly, there have been, in modern times, two\ndifferent schools of physiologists, the one proceeding upon\nthe idea of Final Causes, the other school {249} seeking in\nthe realm of organized bodies wide laws and analogies from\nwhich that idea is excluded. All the great biologists of\npreceding times, and some of the greatest of modern times,\nhave belonged to the former school; and especially Cuvier,\nwho may be considered as the head of it. It was solely by\nthe assiduous application of this principle of Final Cause,\nas he himself constantly declared, that he was enabled to\nmake the discoveries which have rendered his name so\nillustrious, and which contain a far larger portion of\nimportant anatomical and biological truth than it ever\nbefore fell to the lot of one man to contribute to the science.\n\nThe opinions which have been put in opposition to the\nprinciple of Final Causes have, for the most part, been\nstated vaguely and ambiguously. Among the most definite of\nsuch principles, is that which, in the History of the\nsubject, I have termed the Principle of Metamorphosed and\nDeveloped Symmetry, upon which has been founded the science\nof Morphology.\n\nThe reality and importance of this principle are not to be\ndenied by us: we have shown how they are proved by its\napplication in various sciences, and especially in botany.\nBut those advocates of this principle who have placed it in\nantithesis to the doctrine of Final Causes, have, by this\nmeans, done far more injustice to their own favourite\ndoctrine than damage to the one which they opposed. The\nadaptation of the bones of the skeleton to the muscles, the\nprovision of fulcrums, projecting processes, channels, so\nthat the motions and forces shall be such as the needs of\nlife require, cannot possibly become less striking and\nconvincing, from any discovery of general analogies of one\nanimal frame with another, or of laws connecting the\ndevelopment of different parts. Whenever such laws are\ndiscovered, we can only consider them as the means of\nproducing that adaptation which we so much admire. Our\nconviction that the Artist works intelligently, is not\ndestroyed, though it may be modified and transferred, when\nwe obtain a sight of his tools. Our discovery of laws cannot\ncontradict our persuasion of ends; our Morphology cannot\nprejudice our Teleology. {250}\n\n15. The irresistible and constant apprehension of a purpose\nin the forms and functions of animals has introduced into\nthe writings of speculators on these subjects various forms\nof expression, more or less precise, more or less\nfigurative; as, that 'animals are framed with a view to the\npart which they have to play;'--that 'nature does nothing in\nvain;' that 'she employs the best means for her ends;' and\nthe like. However metaphorical or inexact any of these\nphrases may be in particular, yet taken altogether, they\nconvey, clearly and definitely enough to preclude any\nserious errour, a principle of the most profound reality and\nof the highest importance in the organical sciences. But\nsome adherents of the morphological school of which 1 have\nspoken reject, and even ridicule, all such modes of\nexpression. 'I know nothing,' says M. Geoffroy Saint\nHilaire, 'of animals which have to play a part in nature. I\ncannot make of nature an intelligent being who does nothing\nin vain; who acts by the shortest mode; who does all for the\nbest.' The philosophers of this school, therefore, do not,\nit would seem, feel any of the admiration which is\nirresistibly excited in all the rest of mankind at the\ncontemplation of the various and wonderful adaptations for\nthe preservation, the enjoyment, the continuation of the\ncreatures which people the globe;--at the survey of the\nmechanical contrivances, the chemical agencies, the\nprospective arrangements, the compensations, the minute\nadaptations, the comprehensive interdependencies, which\nzoology and physiology have brought into view, more and\nmore, the further their researches have been carried. Yet\nthe clear and deep-seated conviction of the reality of these\nprovisions, which the study of anatomy produces in its most\nprofound and accurate cultivators, cannot be shaken by any\nobjections to the metaphors or terms in which this\nconviction is clothed. In regard to the Idea of a Purpose in\norganization, as in regard to any other idea, we cannot\nfully express our meaning by phrases borrowed from any\nextraneous source; but that impossibility arises precisely\nfrom the circumstance of its being a Fundamental Idea which\nis inevitably assumed in our {251} representation of each\nspecial fact. The same objection has been made to the idea\nof mechanical _force_, on account of its being often\nexpressed in metaphorical language; for writers have spoken\nof an _energy_, _effort_, or _solicitation_ to motion; and\nbodies have been said to be _animated_ by a force. Such\nlanguage, it has been urged, implies volition, and the act\nof animated beings. But the idea of Force as distinct from\nmere motion,--as the Cause of motion, or of tendency to\nmotion,--is not on that account less real. We endeavour in\nvain to conduct our mechanical reasonings without the aid of\nthis idea, and must express it as we can. Just as little can\nwe reason concerning organized beings without assuming that\neach part has its function, each function its purpose; and\nso far as our phrases imply this, they will not mislead us,\nhowever inexact, or however figurative they be.\n\n16. The doctrine of a purpose in Organization has been\nsometimes called the doctrine of _the Conditions of\nExistence_; and has been stated as teaching that each animal\nmust be so framed as to contain in its structure the\nConditions which its existence requires. When expressed in\nthis manner, it has given rise to the objection, that it\nmerely offers an identical proposition; since no animal can\nexist without such conditions. But in reality, such\nexpressions as those just quoted give an inadequate\nstatement of the Principle of a Final Cause. For we discover\nin innumerable cases, arrangements in an animal, of which we\nsee, indeed, that they are subservient to its well being;\nbut the nature of which we never should have been able at\nall to conjecture, from considering what was necessary to\nits existence, and which strike us, no less by their\nunexpectedness than by their adaptation: so far are they\nfrom being presented by any perceptible necessity. Who would\nventure to say that the trochlear muscle, or the power of\narticulate speech, must occur in man, because they are the\nnecessary conditions of his existence? When, indeed, the\ngeneral scheme and mode of being of an animal are known, the\nexpert and profound anatomist can reason concerning the\nproportions and {252} form of its various parts and organs,\nand prove in some measure what their relations must be. We\ncan assert, with Cuvier, that certain forms of the viscera\nrequire certain forms of the teeth, certain forms of the\nlimbs, certain powers of the senses. But in all this, the\nfunctions of self-nutrition and digestion are supposed\nalready existing as ends: and it being taken for granted, as\nthe only conceivable basis of reasoning, that the organs are\nmeans to these ends, we may discover what modifications of\nthese organs are necessarily related to and connected with\neach other. Instead of terming this rule of speculation\nmerely 'the Principle of the Conditions of Existence,' we\nmight term it 'the Principle of the conditions of organs as\n_Means_ adapted to animal existence as their _End_.' And how\nfar this principle is from being a mere barren truism, the\nextraordinary discoveries made by the great assertor of the\nprinciple, and universally assented to by naturalists,\nabundantly prove. The vast extinct creation which is\nrecalled to life in Cuvier's great work, the _Ossemens\nFossiles_, cannot be the consequence of a mere identical\nproposition.\n\n17. It has been objected, also, that the doctrine of Final\nCauses supposes us to be acquainted with the intentions of\nthe Creator; which, it is insinuated, is a most presumptuous\nand irrational basis for our reasonings. But there can be\nnothing presumptuous or irrational in reasoning on that\nbasis, which if we reject, we cannot reason at all. If men\nreally can discern, and cannot help discerning, a design in\ncertain portions of the works of creation, this perception\nis the soundest and most satisfactory ground for the\nconvictions to which it leads. The Ideas which we\nnecessarily employ in the contemplation of the world around\nus, afford us the only natural means of forming any\nconception of the Creator and Governor of the Universe; and\nif we are by such means enabled to elevate our thoughts,\nhowever inadequately, towards Him, where is the presumption\nof doing so? or rather, where is the wisdom of refusing to\nopen our minds to contemplations so animating and elevating,\nand yet {253} so entirely convincing? We possess the ideas\nof Time and Space, under which all the objects of the\nuniverse present themselves to us; and in virtue of these\nideas thus possessed, we believe the Creator to be eternal\nand omnipotent. When we find that we, in like manner,\npossess the idea of a Design in Creation, and that with\nregard to ourselves, and creatures more or less resembling\nourselves, we cannot but contemplate their constitution\nunder this idea, we cannot abstain from ascribing to the\nCreator the infinite profundity and extent of design to\nwhich all these special instances belong as parts of a whole.\n\n18. I have here considered Design as manifest in\norganization only: for in that field of speculation it is\nforced upon us as contained in all the phenomena, and as the\nonly mode of our understanding them. The existence of Final\nCauses has often been pointed out in other portions of the\ncreation;--for instance, in the apparent adaptations of the\nvarious parts of the earth and of the solar system to each\nother and to organized beings. In these provinces of\nspeculation, however, the principle of Final Causes is no\nlonger the basis and guide, but the sequel and result of our\nphysical reasonings. If in looking at the universe, we\nfollow the widest analogies of which we obtain a view, we\nsee, however dimly, reason to believe that all its laws are\nadapted to each other, and intended to work together for the\nbenefit of its organic population, and for the general\nwelfare of its rational tenants. On this subject, however,\nnot immediately included in the principle of Final Causes as\nhere stated, I shall not dwell. I will only make this\nremark; that the assertion appears to be quite unfounded,\nthat as science advances from point to point, Final Causes\nrecede before it, and disappear one after the other. The\nprinciple of design changes its mode of application indeed,\nbut it loses none of its force. We no longer consider\nparticular facts as produced by special interpositions, but\nwe consider design as exhibited in the establishment and\nadjustment of the laws by which particular facts are\nproduced. We do not look upon each particular {254} cloud as\nbrought near us that it may drop fatness on our fields; but\nthe general adaptation of the laws of heat, and air, and\nmoisture, to the promotion of vegetation, does not become\ndoubtful. We do not consider the sun as less intended to\nwarm and vivify the tribes of plants and animals, because we\nfind that, instead of revolving round the earth as an\nattendant, the earth along with other planets revolves round\nhim. We are rather, by the discovery of the general laws of\nnature, led into a scene of wider design, of deeper\ncontrivance, of more comprehensive adjustments. Final\ncauses, if they appear driven further from us by such an\nextension of our views, embrace us only with a vaster and\nmore majestic circuit: instead of a few threads' connecting\nsome detached objects, they become a stupendous net-work,\nwhich is wound round and round the universal frame of things.\n\n19. I now quit the subject of Biology, and with it the\ncircle of sciences depending upon separate original Ideas\nand permanent relations. If from the general relations which\npermanently prevail and constantly recur among the objects\naround us, we turn to the inquiry of what has actually\nhappened,--if from Science we turn to History,--we find\nourselves in a new field. In this region of speculation we\ncan rarely obtain a complete and scientific view of the\nconnexion between objects and events. The past History of\nMan, of the Arts, of Languages, of the Earth, of the Solar\nSystem, offers a vast series of problems, of which perhaps\nnot one has been rigorously solved. Still, man, as his\nspeculative powers unfold themselves, cannot but feel\nprompted and invited to employ his thoughts even on these\nproblems. He cannot but wish and endeavour to understand the\nconnexion between the successive links of such chains of\nevents. He attempts to form a Science which shall be\napplicable to each of these Histories; and thus he begins to\nconstruct the class of sciences to which I now, in the last\nplace, proceed.\n\n\n\n\n{{255}}\nBOOK X.\n\n\nTHE\nPHILOSOPHY\nOF\nPAL\u00c6TIOLOGY.\n\n\n\n\n\u03c4\u1f74\u03bd \u03bc\u1f72\u03bd \u03bf\u1f56\u03bd \u03c4\u03bf\u03b9\u03b1\u03cd\u03c4\u03b7\u03bd _\u0391\u1f30\u03c4\u03b9\u03bf\u03bb\u03bf\u03b3\u03af\u03b1\u03bd_ \u1f27\u03c4\u03c4\u03bf\u03bd \u1f04\u03bd \u03c4\u03b9\u03c2 \u1f00\u03c0\u03bf\u03b4\u03ad\u03be\u03b1\u03b9\u03c4\u03bf\u00b7\n\u03bc\u1fb6\u03bb\u03bb\u03bf\u03bd _\u03b4\u1fbd \u1f00\u03c0\u1f78 \u03c4\u1ff6\u03bd \u03c6\u03b1\u03bd\u03b5\u03c1\u03c9\u03c4\u03ad\u03c1\u03c9\u03bd_ \u03ba\u03b1\u1f76 \u03c4\u1ff6\u03bd \u03ba\u03b1\u03b8\u1fbd \u1f21\u03bc\u03ad\u03c1\u03b1\u03bd \u03c4\u03c1\u03cc\u03c0\u03bf\u03bd\n\u03c4\u03b9\u03bd\u1f70 \u1f41\u03c1\u03c9\u03bc\u03ad\u03bd\u03c9\u03bd \u1f00\u03bd\u03b1\u03c0\u03c4\u03ad\u03bf\u03bd \u03c4\u1f78\u03bd \u03bb\u03cc\u03b3\u03bf\u03bd. \u039a\u03b1\u1f76 \u03b3\u1f70\u03c1 \u03ba\u03b1\u03c4\u03b1\u03ba\u03bb\u03c5\u03c3\u03bc\u03bf\u1f76, \u03ba\u03b1\u1f76\n\u03c3\u03b5\u03b9\u03c3\u03bc\u03bf\u1f76, \u03ba\u03b1\u1f76 \u1f00\u03bd\u03b1\u03c6\u03c5\u03c3\u03ae\u03bc\u03b1\u03c4\u03b1, \u03ba\u03b1\u1f76 \u1f00\u03bd\u03bf\u03b9\u03b4\u03ae\u03c3\u03b5\u03b9\u03c2 \u03c4\u1fc6\u03c2 \u1f51\u03c6\u03ac\u03bb\u03bf\u03c5 \u03b3\u1fc6\u03c2,\n\u03bc\u03b5\u03c4\u03b5\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03c3\u03b9 \u03ba\u03b1\u1f76 \u03c4\u1f74\u03bd \u03b8\u03ac\u03bb\u03b1\u03c4\u03c4\u03b1\u03bd\u00b7 \u03b1\u1f31 \u03b4\u1f72 \u03c3\u03c5\u03bd\u03b9\u03b6\u03ae\u03c3\u03b5\u03b9\u03c2 \u03c4\u03b1\u03c0\u03b5\u03b9\u03bd\u03bf\u1fe6\u03c3\u03b9\u03bd\n\u03b1\u1f50\u03c4\u03ae\u03bd.\n\nSTRABO, _Geogr._ 1. p. 54.\n\n\nIT is therefore, not so much what these forms of the earth\nactually are, as what they are continually becoming, that we\nhave to observe; nor is it possible thus to observe them\nwithout an instinctive reference to the first state out of\nwhich they have been brought.... Yet to such questions\ncontinually suggesting themselves, it is never possible to\ngive a complete answer. For a certain distance, the past\nwork of existing forces can be traced; but then gradually\nthe mist gathers, and the footsteps of more gigantic\nagencies are traceable in the darkness; and still as we\nendeavour to penetrate further and further into departed\ntime, the thunder of the Almighty power sounds louder and\nlouder, and the clouds gather broader and more fearfully,\nuntil at last the Sinai of the world is seen altogether upon\na smoke, and the fence of its foot is reached, where none\ncan break through.\n\nRUSKIN, _Modern Painters_, Vol. IV. p. 143.\n\n\n\n{{257}}\nBOOK X.\n\n\nTHE PHILOSOPHY OF PAL\u00c6TIOLOGY.\n\n\nCHAPTER I.\n\nOF PAL\u00c6TIOLOGICAL SCIENCES IN GENERAL.\n\n\n1. I HAVE already stated in the _History of the\nSciences_[1\\10], that the class of Sciences which I\ndesignate as _Pal\u00e6tiological_ are those in which the object\nis to ascend from the present state of things to a more\nancient condition, from which the present is derived by\nintelligible causes. As conspicuous examples of this class\nwe may take Geology, Glossology or Comparative Philology,\nand Comparative Arch\u00e6ology. These provinces of knowledge\nmight perhaps be intelligibly described as _Histories_; the\nHistory of the Earth,--the History of Languages,--the\nHistory of Arts. But these phrases would not fully describe\nthe sciences we have in view; for the object to which we now\nsuppose their investigations to be directed is, not merely\nto ascertain what the series of events has been, as in the\ncommon forms of History, but also how it has been brought\nabout. These sciences are to treat of causes as well as of\neffects. Such researches might be termed _Philosophical\nHistory_; or, in order to mark more distinctly that the\n_causes_ of events are the leading object of attention,\n_\u00c6tiological History_. But since {258} it will be more\nconvenient to describe this class of sciences by a single\nappellation, I have taken the liberty of proposing to call\nthem[2\\10] the _Pal\u00e6tiological_ Sciences.\n\n[Note 1\\10: B. xviii. Introd.]\n\n[Note 2\\10: A philological writer, in a very interesting\nwork (Mr. Donaldson, in his _New Cratylus_, p. 12),\nexpresses his dislike of this word, and suggests that I must\nmean _pal\u00e6-\u00e6tiological_. I think the word is more likely to\nobtain currency in the more compact and euphonious form in\nwhich I have used it. It has been adopted by Mr. Winning, in\nhis _Manual of Comparative Philology_, and more recently, by\nother writers.]\n\nWhile Pal\u00e6ontology describes the beings which have lived in\nformer ages without investigating their causes, and\n_\u00c6tiology_ treats of causes without distinguishing\nhistorical from mechanical causation; _Pal\u00e6tiology_ is a\ncombination of the two sciences; exploring, by means of the\nsecond, the phenomena presented by the first. The portions\nof knowledge which I include in this term are\npal\u00e6ontological \u00e6tiological sciences.\n\n2. All these sciences are connected by this bond;--that they\nall endeavour to ascend to a past state, by considering what\nis the present state of things, and what are the causes of\nchange. Geology examines the existing appearance of the\nmaterials which form the earth, infers from them previous\nconditions, and speculates concerning the forces by which\none condition has been made to succeed another. Another\nscience, cultivated with great zeal and success in modern\ntimes, compares the languages of different countries and\nnations, and by an examination of their materials and\nstructure, endeavours to determine their descent from one\nanother: this science has been termed _Comparative\nPhilology_, or _Ethnography_; and by the French,\n_Linguistique_, a word which we might imitate in order to\nhave a single name for the science, but the Greek derivative\n_Glossology_ appears to be more convenient in its form. The\nprogress of the Arts (Architecture and the like);--how one\nstage of the culture produced another; and how far we can\ntrace their maturest and most complete condition to their\nearliest form in various nations;--are problems of great\ninterest belonging to another subject, which we may for the\npresent term {259} _Comparative Arch\u00e6ology_. I have already\nnoticed, in the History[3\\10] how the researches into the\norigin of natural objects, and those relating to works of\nart, pass by slight gradations into each other; how the\nexamination of the changes which have affected an ancient\ntemple or fortress, harbour or river, may concern alike the\ngeologist and the antiquary. Cuvier's assertion that the\ngeologist is an antiquary of a new order, is perfectly\ncorrect, for both are pal\u00e6tiologists.\n\n[Note 3\\10: B. xviii. Introd.]\n\n3. We are very far from having exhausted, by this\nenumeration, the class of sciences which are thus connected.\nWe may easily point out many other subjects of speculation\nof the same kind. As we may look back towards the first\ncondition of our planet, we may in like manner turn our\nthoughts towards the first condition of the solar system,\nand try whether we can discern any traces of an order of\nthings antecedent to that which is now established; and if\nwe find, as some great mathematicians have conceived,\nindications of an earlier state in which the planets were\nnot yet gathered into their present forms, we have, in the\npursuit of this train of research, a pal\u00e6tiological portion\nof Astronomy. Again, as we may inquire how languages, and\nhow man, have been diffused over the earth's surface from\nplace to place, we may make the like inquiry with regard to\nthe races of plants and animals, founding our inferences\nupon the existing geographical distribution of the animal\nand vegetable kingdoms: and thus the Geography of Plants and\nof Animals also becomes a portion of Pal\u00e6tiology. Again, as\nwe can in some measure trace the progress of Arts from\nnation to nation and from age to age, we can also pursue a\nsimilar investigation with respect to the progress of\nMythology, of Poetry, of Government, of Law. Thus the\nphilosophical history of the human race, viewed with\nreference to these subjects, if it can give rise to\nknowledge so exact as to be properly called Science, will\nsupply Sciences belonging to the class I am now to consider. {260}\n\n4. It is not an arbitrary and useless proceeding to\nconstruct such a Class of Sciences. For wide and various as\ntheir subjects are, it will be found that they have all\ncertain principles, maxims, and rules of procedure in\ncommon; and thus may reflect light upon each other by being\ntreated of together. Indeed it will, I trust, appear, that\nwe may by such a juxtaposition of different speculations,\nobtain most salutary lessons. And questions, which, when\nviewed as they first present themselves under the aspect of\na special science, disturb and alarm men's minds, may\nperhaps be contemplated more calmly, as well as more\nclearly, when they are considered as general problems of\npal\u00e6tiology.\n\n5. It will at once occur to the reader that, if we include\nin the circuit of our classification such subjects as have\nbeen mentioned,--politics and law, mythology and poetry,--we\nare travelling very far beyond the material sciences within\nwhose limits we at the outset proposed to confine our\ndiscussion of principles. But we shall remain faithful to\nour original plan; and for that purpose shall confine\nourselves, in this work, to those pal\u00e6tiological sciences\nwhich deal with material things. It is true, that the\ngeneral principles and maxims which regulate these sciences\napply also to investigations of a parallel kind respecting\nthe products which result from man's imaginative and social\nendowments. But although there may be a similarity in the\ngeneral form of such portions of knowledge, their materials\nare so different from those with which we have been hitherto\ndealing, that we cannot hope to take them into our present\naccount with any profit. Language, Government, Law, Poetry,\nArt, embrace a number of peculiar Fundamental Ideas,\nhitherto not touched upon in the disquisitions in which we\nhave been engaged; and most of them involved in far greater\nperplexity and ambiguity, the subject of controversies far\nmore vehement, than the Ideas we have hitherto been\nexamining. We must therefore avoid resting any part of our\nphilosophy upon sciences, or supposed sciences, which treat\nof such subjects. To attend to this caution, {261} is the\nonly way in which we can secure the advantage we proposed to\nourselves at the outset, of taking, as the basis of our\nspeculations, none but systems of undisputed truths, clearly\nunderstood and expressed[4\\10]. We have already said that we\nmust, knowingly and voluntarily, resign that livelier and\nwarmer interest which doctrines on subjects of Polity or Art\npossess, and content ourselves with the cold truths of the\nmaterial sciences, in order that we may avoid having the\nvery foundations of our philosophy involved in controversy,\ndoubt, and obscurity.\n\n[Note 4\\10: See Introd. p. 9.]\n\n6. We may remark, however, that the necessity of rejecting\nfrom our survey a large portion of the researches which the\ngeneral notion of Pal\u00e6tiology includes, suggests one\nconsideration which adds to the interest of our task. We\nbegan our inquiry with the trust that any sound views which\nwe should be able to obtain respecting the nature of Truth\nin the physical sciences, and the mode of discovering it,\nmust also tend to throw light upon the nature and prospects\nof knowledge of all other kinds;--must be useful to us in\nmoral, political, and philological researches. We stated\nthis as a confident anticipation; and the evidence of the\njustice of our belief already begins to appear. We have\nseen, in the last Book, that biology leads us to psychology,\nif we choose to follow the path; and thus the passage from\nthe material to the immaterial has already unfolded itself\nat one point; and we now perceive that there are several\nlarge provinces of speculation which concern subjects\nbelonging to man's immaterial nature, and which are governed\nby the same laws as sciences altogether physical. It is not\nour business here to dwell on the prospects which our\nphilosophy thus opens to our contemplation; but we may allow\nourselves, in this last stage of our pilgrimage among the\nfoundations of the physical sciences, to be cheered and\nanimated by the ray {262} that thus beams upon us, however\ndimly, from a higher and brighter region.\n\nBut in our reasonings and examples we shall mainly confine\nourselves to the physical sciences; and for the most part to\nGeology, which in the _History_ I have put forwards as the\nbest representative of the Pal\u00e6tiological Sciences.\n\n\n\n{{263}}\nCHAPTER II.\n\nOF THE THREE MEMBERS OF A PAL\u00c6TIOLOGICAL SCIENCE.\n\n\n1. _Divisions of such Sciences._--IN each of the Sciences of\nthis class we consider some particular order of phenomena\nnow existing:--from our knowledge of the causes of change\namong such phenomena, we endeavour to infer the causes which\nhave made this order of things what it is:--we ascend in\nthis manner to some previous stage of such phenomena;--and\nfrom that, by a similar course of inference, to a still\nearlier stage, and to its causes. Hence it will be seen that\neach such science will consist of two parts,--the knowledge\nof the Phenomena, and the knowledge of their Causes. And\nsuch a division is, in fact, generally recognized in such\nsciences: thus we have History, and the Philosophy of\nHistory; we have Comparison of Languages, and the Theories\nof the Origin and Progress of Language; we have Descriptive\nGeology, and Theoretical or Physical Geology. In all these\ncases, the relation between the two parts in these several\nprovinces of knowledge is nearly the same; and it may, on\nsome occasions at least, be useful to express the\ndistinction in a uniform or general manner. The\ninvestigation of Causes has been termed _\u00c6tiology_ by\nphilosophical writers, and this term we may use, in\ncontradistinction to the mere _Phenomenology_ of each such\ndepartment of knowledge. And thus we should have _Phenomenal\nGeology_ and _\u00c6tiological Geology_, for the two divisions of\nthe science which we have above termed _Descriptive_ and\n_Theoretical Geology_.\n\n2. _The Study of Causes._--But our knowledge respecting the\ncauses which actually _have_ produced any {264} order of\nphenomena must be arrived at by ascertaining what the causes\nof change in such matters _can_ do. In order to learn, for\nexample, what share earthquakes, and volcanoes, and the\nbeating of the ocean against its shores, ought to have in\nour Theory of Geology, we must make out what effects these\nagents of change are able to produce. And this must be done,\nnot hastily, or unsystematically, but in a careful and\nconnected manner; in short, this study of the causes of\nchange in each order of phenomena must become a distinct\nbody of Science, which must include a large amount of\nknowledge, both comprehensive and precise, before it can be\napplied to the construction of a theory. We must have an\n\u00c6tiology corresponding to each order of phenomena.\n\n3. _\u00c6tiology._--In the History of Geology, I have spoken of\nthe necessity for such an \u00c6tiology with regard to geological\nphenomena: this necessity I have compared with that which,\nat the time of Kepler, required the formation of a separate\nscience of Dynamics (the doctrine of the Causes of Motion),\nbefore Physical Astronomy could grow out of Phenomenal\nAstronomy. In pursuance of this analogy, I have there given\nthe name of _Geological Dynamics_ to the science which\ntreats of the causes of geological change in general. But,\nas I have there intimated, in a large portion of the subject\nthe changes are so utterly different in their nature from\nany modification of motion, that the term _Dynamics_, so\napplied, sounds harsh and strange. For in this science we\nhave to treat, not only of the subterraneous forces by which\nparts of the earth's crust are shaken, elevated, or\nruptured, but also of the causes which may change the\nclimate of a portion of the earth's surface, making a\ncountry hotter or colder than in former ages; again, we have\nto treat of the causes which modify the forms and habits of\nanimals and vegetables, and of the extent to which the\neffects of such causes can proceed; whether, for instance,\nthey can extinguish old species and produce new. These and\nother similar investigations would not be naturally included\nin the notion of _Dynamics_; and therefore it {265} might\nperhaps be better to use the term _\u00c6tiology_ when we wish to\ngroup together all those researches which have it for their\nobject to determine the laws of such changes. In the same\nmanner the Comparison and History of Languages, if it is to\nlead to any stable and exact knowledge, must have appended\nto it an \u00c6tiology, which aims at determining the nature and\nthe amount of the causes which really do produce changes in\nlanguage; as colonization, conquest, the mixture of races,\ncivilization, literature, and the like. And the same rule\napplies to all sciences of this class. We shall now make a\nfew remarks on the characteristics of such branches of\nscience as those to which we are led by the above\nconsiderations.\n\n4. _Phenomenology requires Classification. Phenomenal\nGeology._--The Phenomenal portions of each science imply\nClassification, for no description of a large and varied\nmass of phenomena can be useful or intelligible without\nclassification. A representation of phenomena, in order to\nanswer the purposes of science, must be systematic.\nAccordingly, in giving the History of Descriptive or\nPhenomenal Geology, I have called it _Systematic Geology_,\njust as Classificatory Botany is termed _Systematic Botany_.\nMoreover, as we have already seen, Classification can never\nbe an arbitrary process, but always implies some natural\nconnexion among the objects of the same Class; for if this\nconnexion did not exist, the Classes could not be made the\nsubjects of any true assertion. Yet though the classes of\nphenomena which our system acknowledges must be such as\nalready exist in nature, the discovery of these classes is,\nfor the most part, very far from obvious or easy. To detect\nthe true principles of Natural Classes, and to select marks\nby which these may be recognized, are steps which require\ngenius and good fortune, and which fall to the lot only of\nthe most eminent persons in each science. In the History, I\nhave pointed out Werner, William Smith, and Cuvier, as the\nthree great authors of Systematic Geology of Europe. The\nmode of classifying the materials of the earth's surface\nwhich was found, by these philosophers, fitted to {266}\nenunciate such general facts as came under their notice, was\nto consider the rocks and other materials as divided into\nsuccessive layers or strata, superimposed one on another,\nand variously inclined and broken. The German geologist\ndistinguished his strata for the most part by their\nmineralogical character; the other two, by the remains of\nanimals and plants which the rocks contained. After a\nbeginning had thus been made in giving a genuine scientific\nform to phenomenal geology, other steps followed in rapid\nsuccession, as has already been related in the\nHistory[5\\10]. The Classification of the Strata was fixed by\na suitable Nomenclature. Attempts were made to apply to\nother countries the order of strata which had been found to\nprevail in that first studied: and in this manner it was\nascertained what rocks in distant regions are the synonyms,\nor _Equivalents_[6\\10],--of each other. The knowledge thus\ncollected and systematized was exhibited in the form of\nGeological Maps.\n\n[Note 5\\10: _Hist. Ind. Sc._ b. xviii. c. iii.]\n\n[Note 6\\10: _Ib._ sect. 4.]\n\nMoreover, among the phenomena of geology we have Laws of\nNature as well as Classes. The general form of\nmountain-chains; the relations of the direction and\ninclination of different chains to each other; the general\nfeatures of mineral veins, faults, and fissures; the\nprevalent characters of slaty cleavage;--were the subjects\nof laws established, or supposed to be established, by\nextensive observation of facts. In like manner the organic\nfossils discovered in the strata were found to follow\ncertain laws with reference to the climate which they\nappeared to have lived in; and the evidence which they gave\nof a regular zoological development. And thus, by the\nassiduous labours of many accomplished and active\nphilosophers, Descriptive or Phenomenal Geology was carried\ntowards a state of completeness.\n\n5. _Phenomenal Uranography._--In like manner in other\npal\u00e6tiological researches, as soon as they approach to an\nexact and scientific form, we find the necessity of\nconstructing in the first place a science of {267}\nclassification and exact description, by means of which the\nphenomena may be correctly represented and compared; and of\nobtaining by this step a solid basis for an inquiry into the\ncauses which have produced them. Thus the Pal\u00e6tiology of the\nSolar System has, in recent times, drawn the attention of\nspeculators; and a hypothesis has been started, that our sun\nand his attendant planets have been produced by the\ncondensation of a mass of diffused matter, such as that\nwhich constitutes the nebulous patches which we observe in\nthe starry heavens. But the sagest and most enlightened\nastronomers have not failed to acknowledge, that to verify\nor to disprove this conjecture, must be the work of many\nages of observation and thought. They have perceived also\nthat the first step of the labour requisite for the\nadvancement of this portion of science must be to obtain and\nto record the most exact knowledge at present within our\nreach, respecting the phenomena of these nebul\u00e6, with which\nwe thus compare our own system; and, as a necessary element\nof such knowledge, they have seen the importance of a\nclassification of these objects, and of others, such as\nDouble Stars, of the same kind. Sir William Herschel, who\nfirst perceived the bearing of the phenomena of nebul\u00e6 upon\nthe history of the solar system, made the observation of\nsuch objects his business, with truly admirable zeal and\nskill; and in the account of the results of his labours,\ngave a classification of Nebul\u00e6; separating them into,\nfirst, _Clusters of Stars_; second, _Resolvable Nebul\u00e6_;\nthird, _Proper Nebul\u00e6_; fourth, _Planetary Nebul\u00e6_; fifth,\n_Stellar Nebul\u00e6_; sixth, _Nebulous Stars_[7\\10]. And since,\nin order to obtain from these remote appearances, any\nprobable knowledge respecting our own system, we must\ndiscover whether they undergo any changes in the course of\nages, he devoted himself to the task of forming a record of\ntheir number and appearance in his own time, that thus the\nastronomers of succeeding generations might have a {268}\ndefinite and exact standard with which to compare their\nobservations. Still, this task would have been executed only\nfor that part of the heavens which is visible in this\ncountry, if this Hipparchus of the Nebul\u00e6 and Double Stars\nhad not left behind him a son who inherited all his father's\nzeal and more than his father's knowledge. Sir John Herschel\nin 1833 went to the Cape of Good Hope to complete what Sir\nWilliam Herschel left wanting; and in the course of five\nyears observed with care all the nebul\u00e6 and double stars of\nthe Southern hemisphere. This great _Herschelian Survey of\nthe Heavens_, the completion of which is the noblest\nmonument ever erected by a son to a father, must necessarily\nbe, to all ages, the basis of all speculations concerning\nthe history and origin of the solar system; and has\ncompleted, so far as at present it can be completed, the\nphenomenal portion of Astronomical Pal\u00e6tiology.\n\n[Note 7\\10: _Phil. Trans._ 1786 and 1789, and Sir J.\nHerschel's _Astronomy_, Art. 616.]\n\n6. _Phenomenal Geography of Plants and Animals._--Again,\nthere is another Pal\u00e6tiological Science, closely connected\nwith the speculations forced upon the geologist by the\norganic fossils which he discovers imbedded in the strata of\nthe earth;--namely, the Science which has for its object the\nCauses of the Diffusion and Distribution of the various\nkinds of Plants and Animals. And the science also has for\nits first portion and indispensable foundation a description\nand classification of the existing phenomena. Such portions\nof science have recently been cultivated with great zeal and\nsuccess, under the titles of the _Geography of Plants_, and\nthe _Geography of Animals_. And the results of the inquiries\nthus undertaken have assumed a definite and scientific form\nby leading to a division of the earth's surface into a\ncertain number of botanical and zoological _Provinces_, each\nprovince occupied by its own peculiar vegetable and animal\npopulation. We find, too, in the course of these\ninvestigations, various general laws of the phenomena\noffered to our notice; such, for instance, as this:--that\nthe difference of the animals originally occupying each\nprovince, which is clear and entire for the higher orders of\n{269} animals and plants, becomes more doubtful and\nindistinct when we descend to the lower kinds of\norganizations; as Infusoria and Zoophytes[8\\10] in the\nanimal kingdom, Grasses and Mosses among vegetables. Again,\nother laws discovered by those who have studied the\ngeography of plants are these:--that countries separated\nfrom each other by wide tracts of sea, as the opposite\nshores of the Mediterranean, the islands of the Indian and\nPacific Oceans, have usually much that is common in their\nvegetation:--and again, that in parallel climates, analogous\ntribes replace each other. It would be easy to adduce other\nlaws, but those already stated may serve to show the great\nextent of the portions of knowledge which have just been\nmentioned, even considered as merely Sciences of Phenomena.\n\n[Note 8\\10: Prichard, _Researches into the Physical History\nof Mankind_, i. 55, 28.]\n\n7. _Phenomenal Glossology._--It is not my purpose in the\npresent work to borrow my leading illustrations from any\nportions of knowledge but those which are concerned with the\nstudy of material nature; and I shall, therefore, not dwell\nupon a branch of research, singularly interesting, and\nclosely connected with the one just mentioned, but dealing\nwith relations of thought rather than of things;--I mean the\nPal\u00e6tiology of Language;--the theory, so far as the facts\nenable us to form a theory, of the causes which have led to\nthe resemblances and differences of human speech in various\nregions and various ages. This, indeed, would be only a\nportion of the study of the history and origin of the\ndiffusion of animals, if we were to include man among the\nanimals whose dispersion we thus investigate; for language\nis one of the most clear and imperishable records of the\nearly events in the career of the human race. But the\npeculiar nature of the faculty of speech, and the ideas\nwhich the use of it involves, make it proper to treat\n_Glossology_ as a distinct science. And of this science, the\nfirst part must necessarily be, as in the other sciences of\nthis order, a {270} classification and comparison of\nlanguages governed in many respects by the same rules, and\npresenting the same **difficulties, as other sciences of\nclassification. Such, accordingly, has been the procedure of\nthe most philosophical glossologists. They have been led to\nthrow the languages of the earth into certain large classes\nor _Families_, according to various kinds of resemblance; as\nthe _Semitic_ Family, to which belong Hebrew, Arabic,\nChaldean, Syrian, Phoenician, Ethiopian, and the like; the\n_Indo-European_, which includes Sanskrit, Persian, Greek,\nLatin, and German; the _Monosyllabic_ languages, Chinese,\nTibetan, Birman, Siamese; the _Polysynthetic_ languages, a\nclass including most of the North-American Indian dialects;\nand others. And this work of classification has been the\nresult of the labour and study of many very profound\nlinguists, and has advanced gradually from step to step.\nThus the Indo-European Family was first formed on an\nobservation of the coincidences between Sanskrit, Greek, and\nLatin; but it was soon found to include the Teutonic\nlanguages, and more recently Dr. Prichard[9\\10] has shown\nbeyond doubt that the Celtic must be included in the same\nFamily. Other general resemblances and differences of\nlanguages have been marked by appropriate terms: thus August\nvon Schlegel has denominated them _synthetical_ and\n_analytical_, according as they form their conjugations and\ndeclensions by auxiliary verbs and prepositions, or by\nchanges in the word itself: and the _polysynthetic_\nlanguages are so named by M. Duponceau, in consequence of\ntheir still more complex mode of inflexion. Nor are there\nwanting, in this science also, general laws of phenomena;\nsuch, for instance, is the curious rule of the interchange\nof consonants in the cognate words of Greek, Gothic, and\nGerman, which has been discovered by James Grimm. All these\nremarkable portions of knowledge, and the great works which\nhave appeared on Glossology, such, for example, as the\n_Mithridates_ of Adelung and Vater, contain, for their\nlargest, and {271} hitherto probably their most valuable\npart, the phenomenal portion of the science, the comparison\nof languages as they now are. And beyond all doubt, until we\nhave brought this Comparative Philology to a considerable\ndegree of completeness, all our speculations respecting the\ncauses which have operated to produce the languages of the\nearth must be idle and unsubstantial dreams.\n\n[Note 9\\10: Dr Prichard, _On the Eastern Origin of the\nCeltic Nations_. 1831.]\n\nThus in all Pal\u00e6tiological Sciences, in all attempts to\ntrace back the history and discover the origin of the\npresent state of things, the portion of the science which\nmust first be formed is that which classifies the phenomena,\nand discovers general laws prevailing among them. When this\nwork is performed, and not till then, we may begin to\nspeculate successfully concerning causes, and to make some\nprogress in our attempts to go back to an origin. We must\nhave a _Phenomenal_ science preparatory to each\n_\u00c6tiological_ one.\n\n8. _The Study of Phenomena leads to Theory._--As we have\njust said, we cannot, in any subject, speculate successfully\nconcerning the causes of the present state of things, till\nwe have obtained a tolerably complete and systematic view of\nthe phenomena. Yet in reality men have not in any instance\nwaited for this completeness and system in their knowledge\nof facts before they have begun to form theories. Nor was it\nnatural, considering the speculative propensities of the\nhuman mind, and how incessantly it is endeavouring to apply\nthe Idea of Cause, that it should thus restrain itself. I\nhave already noticed this in the History of Geology. 'While\nwe have been giving an account,' it is there said, 'of the\nobjects with which Descriptive Geology is occupied, it must\nhave been felt how difficult it is, in contemplating such\nfacts, to confine ourselves to description and\nclassification. Conjectures and reasonings respecting the\ncauses of the phenomena force themselves upon us at every\nstep; and even influence our classification and\nnomenclature. Our Descriptive Geology impels us to construct\na Physical Geology.' And the same is the case with regard to\nthe other subjects which I have mentioned. The mere {272}\nconsideration of the different degrees of condensation of\ndifferent Nebul\u00e6 led Herschel and Laplace to contemplate the\nhypothesis that our solar system is a condensed Nebula.\nImmediately upon the division of the earth's surface into\nbotanical and zoological provinces, and even at an earlier\nperiod, the opposite hypotheses of the Origin of all the\nanimals of each kind from a single pair, and of their\noriginal diffusion all over the earth, were under\ndiscussion. And the consideration of the families of\nlanguages irresistibly led to speculations concerning the\nFamilies of the earliest human inhabitants of the earth. In\nall cases the contemplation of a very few phenomena, the\ndiscovery of a very few steps in the history, made men wish\nfor and attempt to form a theory of the history from the\nvery beginning of things.\n\n9. _No sound Theory without \u00c6tiology._--But though man is\nthus impelled by the natural propensities of his intellect\nto trace each order of things to its causes, he does not at\nfirst discern the only sure way of obtaining such knowledge:\nhe does not suspect how much labour and how much method are\nrequisite for success in this undertaking: he is not aware\nthat for each order of phenomena he must construct, by the\naccumulated results of multiplied observation and distinct\nthought, a separate \u00c6iology. Thus, as I have elsewhere\nremarked[10\\10], when men had for the first time become\nacquainted with some of the leading phenomena of Geology,\nand had proceeded to speculate concerning the past changes\nand revolutions by which such results had been produced,\nthey forthwith supposed themselves able to judge what would\nbe the effects of any of the obvious agents of change, as\nWater or Volcanic Fire. It did not at first occur to them to\nsuspect that their common and extemporaneous judgment on\nsuch points was by no means sufficient for sound knowledge.\nThey did not foresee that, before they could determine what\nshare these or any other causes had had in producing the\npresent condition of the earth, they must create {273} a\nspecial science whose object should be to estimate the\ngeneral laws and effects of such assumed causes;--that\nbefore they could obtain any sound Geological Theory, they\nmust carefully cultivate Geological \u00c6tiology.\n\n[Note 10\\10: _Hist. Ind. Sc._ b. xviii. c. v. sect. 1.]\n\nThe same disposition to proceed immediately from the facts\nto the theory, without constructing, as an intermediate\nstep, a Science of Causes, might be pointed out in the other\nsciences of this order. But in all of them this errour has\nbeen corrected by the failures to which it led. It soon\nappeared, for instance, that a more careful inquiry into the\neffects which climate, food, habit and circumstances can\nproduce in animals, was requisite in order to determine how\nthe diversities of animals in different countries have\noriginated. The \u00c6tiology of Animal Life (if we may be\nallowed to give this name to that study of such causes of\nchange which is at present so zealously cultivated, and\nwhich yet has no distinctive designation, except so far as\nit coincides with the _Organic Geological Dynamics_ of our\nHistory) is now perceived to be a necessary portion of all\nattempts to construct a history of the earth and its\ninhabitants.\n\n10. _Cause, in Pal\u00e6tiology._--We are thus led to contemplate\na class of Sciences which are commenced with the study of\nCauses. We have already considered sciences which depended\nmainly upon the Idea of Cause, namely, the Mechanical\nSciences. But it is obvious that the Idea of Cause in the\nresearches now under our consideration must be employed in a\nvery different way from that in which we applied it\nformerly. Force is the _Cause_ of motion, because force at\nall times and under all circumstances, if not counteracted,\nproduces motion; but the Cause of the present condition and\nelevation of the Alps, whatever it was, was manifested in a\nseries of events of which each happened but once, and\noccupied its proper place in the series of time. The former\nis _mechanical_, the latter _historical_, _cause_. In our\npresent investigations, we consider the events which we\ncontemplate, of whatever order they be, as forming a chain\nwhich is extended {274} from the beginning of things down to\nthe present time; and the causes of which we now speak are\nthose which connect the successive links of this chain.\nEvery occurrence which has taken place in the history of the\nsolar system, or the earth, or its vegetable and animal\ncreation, or man, has been at the same time effect and\ncause;--the effect of what preceded, the cause of what\nsucceeded. By being effect and cause, it has occupied some\ncertain portion of time; and the times which have thus been\noccupied by effects and causes, summed up and taken\naltogether, make up the total of Past Time. The Past has\nbeen a series of events connected by this historical\ncausation, and the Present is the last term of this series.\nThe problem in the Pal\u00e6tiological Sciences, with which we\nare here concerned, is, to determine the manner in which\neach term is derived from the preceding, and thus, if\npossible, to calculate backwards to the origin of the series.\n\n11. _Various kinds of Cause._--Those modes by which one term\nin the natural series of events is derived from\nanother,--the forms of historical causation,--the kinds of\nconnexion between the links of the infinite chain of\ntime,--are very various; nor need we attempt to enumerate\nthem. But these kinds of causation being distinguished from\neach other, and separately studied, each becomes the subject\nof a separate \u00c6tiology. Thus the causes of change in the\nearth's surface, residing in the elements, fire and water,\nform the main subject of Geological \u00c6tiology. The \u00c6tiology\nof the vegetable and animal kingdoms investigates the causes\nby which the forms and distribution of species of plants and\nanimals are affected. The study of causes in Glossology\nleads to an \u00c6tiology of Language, which shall distinguish,\nanalyse, and estimate the causes by which certain changes\nare produced in the languages of nations; in like manner we\nmay expect to have an \u00c6tiology of Art, which shall\nscrutinise the influences by which the various forms of art\nhave each given birth to its successor: by which, for\nexample, there have been brought into being those various\nforms of architecture which we term Egyptian, {275} Doric,\nIonic, Roman, Byzantine, Romanesque, Gothic, Italian,\nElizabethan. It is easily seen by this slight survey how\nmanifold and diverse are the kinds of cause which the\nPal\u00e6tiological Sciences bring under our consideration. But\nin each of those sciences we shall obtain solid and complete\nsystems of knowledge, only so far as we study, with steady\nthought and careful observation, that peculiar kind of cause\nwhich is appropriate to the phenomena under our\nconsideration.\n\n12. _Hypothetical Order of Pal\u00e6tiological Causes._--The\nvarious kinds of historical cause are not only connected\nwith each other by their common bearing upon the historical\nsciences, but they form a kind of progression which we may\nrepresent to ourselves as having acted in succession in the\nhypothetical history of the earth and its inhabitants. Thus\nassuming, merely as a momentary hypothesis, the origin of\nthe Solar System by the condensation of a Nebula, we have to\ncontemplate, first, the causes by which the luminous\nincandescent diffused mass of which a nebula is supposed to\nbe constituted, is gradually condensed, cooled, collected\ninto definite masses, solidified, and each portion made to\nrevolve about its axis, and the whole to travel about\nanother body. We have no difficulty in ascribing the\nglobular form of each mass to the mutual attraction of its\nparticles: but when this form was once assumed, and covered\nwith a solid crust, are there, we may ask, in the\nconstitution of such a body, any causes at work by which the\ncrust might be again broken up and portions of it displaced,\nand covered with other matter? Again, if we can thus explain\nthe origin of the Earth, can we with like success account\nfor the presence of the Atmosphere and the Waters of earth\nand ocean? Supposing this done, we have then to consider by\nwhat causes such a body could become stocked with vegetable\nand animal Life; for there have not been wanting persons,\nextravagant speculators, no doubt, who have conceived that\neven this event in the history of the world might be the\nwork of natural causes. Supposing an origin given to life\n{276} upon our earth, we have then, brought before us by\ngeological observations, a series of different forms of\nvegetable and animal existence; occurring in different\nstrata, and, as the phenomena appear irresistibly to prove,\nexisting at successive periods: and we are compelled to\ninquire what can have been the causes by which the forms of\neach period have passed into those of the next. We find,\ntoo, that strata, which must have been at first horizontal\nand continuous, have undergone enormous dislocations and\nruptures, and we have to consider the possible effect of\naqueous and volcanic causes to produce such changes in the\nearth's crust. We are thus led to the causes which have\nproduced the present state of things on the earth; and these\nare causes to which we may hypothetically ascribe, not only\nthe form and position of the inert materials of the earth,\nbut also the nature and distribution of its animal and\nvegetable population. Man too, no less than other animals,\nis affected by the operation of such causes as we have\nreferred to, and must, therefore, be included in such\nspeculations. But man's history only begins, where that of\nother animals ends, with his mere existence. They are\nstationary, he is progressive. Other species of animals,\nonce brought into being, continue the same through all ages;\nman is changing, from age to age, his language, his\nthoughts, his works. Yet even these changes are bound\ntogether by laws of causation; and these causes too may\nbecome objects of scientific study. And such causes, though\nnot to be dwelt upon now, since we permit ourselves to found\nour philosophy upon the material sciences only, must still,\nwhen treated scientifically, fall within the principles of\nour philosophy, and must be governed by the same general\nrules to which all science is subject. And thus we are led\nby a close and natural connexion, through a series of\ncauses, extending from those which regulate the\nimperceptible changes of the remotest nebul\u00e6 in the heavens,\nto those which determine the diversities of language, the\nmutations of art, and even the progress of civilization,\npolity, and literature. {277}\n\nWhile I have been speaking of this supposed series of\nevents, including in its course the formation of the earth,\nthe introduction of animal and vegetable life, and the\nrevolutions by which one collection of species has succeeded\nanother, it must not be forgotten, that though I have thus\nhypothetically spoken of these events as occurring by force\nof natural causes, this has been done only that the true\nefficacy of such causes might be brought under our\nconsideration and made the subject of scientific\nexamination. It may be found, that such occurrences as these\nare quite inexplicable by the aid of any natural causes with\nwhich we are acquainted; and thus, the result of our\ninvestigations, conducted with strict regard to scientific\nprinciples, may be, that we must either contemplate\nsupernatural influences as part of the past series of\nevents, or declare ourselves altogether unable to form this\nseries into a connected chain.\n\n13. _Mode of Cultivating \u00c6tiology:--In Geology._--In what\nmanner, it may be asked, is \u00c6tiology, with regard to each\nsubject such as we have enumerated, to be cultivated? In\norder to answer this question, we must, according to our\nmethod of proceeding, take the most successful and complete\nexamples which we possess of such portions of science. But\nin truth, we can as yet refer to few examples of this kind.\nIn Geology, it is only very recently, and principally\nthrough the example and influence of Sir Charles Lyell, that\nthe \u00c6tiology has been detached from the descriptive portion\nof the science; and cultivated with direct attention: in\nother sciences the separation has hardly yet been made. But\nif we examine what has already been done in Geological\n\u00c6tiology, or as in the History it is termed, _Geological\nDynamics_, we shall find a number of different kinds of\ninvestigation which, by the aid of our general principles\nrespecting the formation of sciences, may suffice to supply\nvery useful suggestions for \u00c6tiology in general.\n\nIn Geological \u00c6tiology, causes have been studied, in many\ninstances, by attending to their action in the phenomena of\nthe present state of things, and by inferring {278} from\nthis the nature and extent of the action which they may have\nexercised in former times. This has been done, for example,\nby Von Hoff, Sir Charles Lyell, and others, with regard to\nthe operations of rivers, seas, springs, glaciers, and other\naqueous causes of change, Again, the same course has been\nfollowed by the same philosophers with respect to volcanoes,\nearthquakes, and other violent agents. Sir Charles Lyell has\nattempted to show, too, that there take place, in our own\ntime, not only violent agitations, but slow motions of parts\nof the earth's crust, of the same kind and order with those\nwhich have assisted in producing all anterior changes.\n\nBut while we thus seek instruction in the phenomena of the\npresent state of things, we are led to the question, What\nare the limits of this 'present' period? For instance, among\nthe currents of lava which we trace as part of the shores of\nItaly and Sicily, _which_ shall we select as belonging to\nthe existing order of things? In going backwards in time,\nwhere shall we draw the line? and why at such particular\npoint? These questions are important, for our estimate of\nthe efficacy of known causes will vary with the extent of\nthe effects which we ascribe to them. Hence the mode in\nwhich we group together rocks is not only a step in\ngeological classification, but is also important to\n\u00c6tiology. Thus, when the vast masses of trap rocks in the\nWestern Isles of Scotland and in other countries, which had\nbeen maintained by the Wernerians to be of aqueous origin,\nwere, principally by the sagacity and industry of\nMacculloch, identified as to their nature with the products\nof recent volcanoes, the amount of effect which might\njustifiably be ascribed to volcanic agency was materially\nextended.\n\nIn other cases, instead of observing the current effects of\nour geological causes, we have to estimate the results from\nwhat we know of the causes themselves; as when, with\nHerschel, we calculate the alterations in the temperature of\nthe earth which astronomical changes may possibly produce;\nor when, with Fourier, we try to calculate the rate of\ncooling of the earth's {279} surface, on the hypothesis of\nan incandescent central mass. In other cases, again, we are\nnot able to calculate the effects of our causes rigorously,\nbut estimate them as well as we can; partly by physical\nreasonings, and partly by comparison with such analogous\ncases as we can find in the present state of things. Thus\nSir Charles Lyell infers the change of climate which would\nresult if land were transferred from the neighbourhood of\nthe poles to that of the equator, by reasonings on the power\nof land and water to contain and communicate heat, supported\nby a reference to the different actual climates of places,\nlying under the same latitude, but under different\nconditions as to the distribution of land and water.\n\nThus our \u00c6tiology is constructed partly from calculation and\nreasoning, partly from phenomena. But we may observe that\nwhen we reason from phenomena to causes, we usually do so by\nvarious steps; often ascending from phenomena to mere laws\nof phenomena, before we can venture to connect the\nphenomenon confidently with its cause. Thus the law of\nsubterranean heat, that it increases in descending below the\nsurface, is now well established, although the doctrine\nwhich ascribes this effect to a central heat is not\nuniversally assented to.\n\n14. _In the Geography of Plants and Animals._--We may find\nin other subjects also, considerable contributions towards\n\u00c6tiology, though not as yet a complete System of Science.\nThe \u00c6tiology of Vegetables and Animals, indeed, has been\nstudied with great zeal in modern times, as an essential\npreparative to geological theory; for how can we decide\nwhether any assumed causes have produced the succession of\nspecies which we find in the earth's strata, except we know\nwhat effect of this kind given causes can produce?\nAccordingly, we find in Sir Charles Lyell's _Treatise on\nGeology_ the most complete discussion of such questions as\nbelong to these subjects:--for example, the question whether\nspecies can be transmuted into other species by the\nlong-continued influence of external causes, as climate,\nfood, domestication, combined with internal {280} causes, as\nhabits, appetencies, progressive tendencies. We may observe,\ntoo, that as we have brought before us, the inquiry what\nchange difference of climate can produce in any species, we\nhave also the inverse problem, how far a different\ndevelopment of the species, or a different collection of\nspecies, proves a difference of climate. In the same way,\nthe geologist of the present day considers the question,\nwhether, in virtue of causes now in action, species are from\ntime to time extinguished; and in like manner, the\ngeologists of an earlier period discussed the question, now\nlong completely decided, whether fossil species in general\nare really extinct species.\n\n15. _In Languages._--Even with reference to the \u00c6tiology of\nLanguage, although this branch of science has hardly been\nconsidered separately from the glossological investigations\nin which it is employed or assumed to be employed, it might\nperhaps be possible to point out causes or conditions of\nchange which, being general in their nature, must operate\nupon all languages alike. Changes made for the sake of\neuphony when words are modified and combined, occur in all\ndialects. Who can doubt that such changes of consonants as\nthose by which the Greek roots become Gothic, and the\nGothic, German, have for their cause some general principle\nin the pronunciation of each language? Again, we might\nattempt to decide other questions of no small interest. Have\nthe terminations of verbs arisen from the accretion of\npronouns; or, on the other hand, does the modification of a\nverb imply a simpler mental process than the insulation of a\npronoun, as Adam Smith has maintained? Again, when the\nlanguage of a nation is changed by the invasion and\npermanent mixture of an enemy of different speech, is it\ngenerally true that it is changed from a synthetic to an\nanalytical structure? I will mention only one more of these\nwide and general glossological inquiries. Is it true, as Dr.\nPrichard has suggested[11\\10], that languages have become\nmore permanent as we come down {281} towards later times?\nMay we justifiably suppose, with him, that in the very\nearliest times, nations, when they had separated from one\nstock, might lose all traces of this common origin out of\ntheir languages, though retaining strong evidences of it in\ntheir mythology, social forms, and arts, as appears to be\nthe case with the ancient Egyptians and the Indians[12\\10].\n\n[Note 11\\10: _Researches_, ii. 221.]\n\n[Note 12\\10: _Researches_, ii. 192.]\n\nLarge questions of this nature cannot be treated profitably\nin any other way than by an assiduous study of the most\nvaried forms of living and dead languages. But on the other\nhand, the study of languages should be prosecuted not only\nby a direct comparison of one with another, but also with a\nview to the formation of a science of causes and general\nprinciples, embracing such discussions as I have pointed\nout. It is only when such a science has been formed, that we\ncan hope to obtain any solid and certain results in the\nPal\u00e6tiology of Language;--to determine, with any degree of\nsubstantial proof, what is the real evidence which the\nwonderful faculty of speech, under its present developments\nand forms, bears to the events which have taken place in its\nown history, and in the history of man since his first origin.\n\n16. _Construction of Theories._--When we have thus obtained,\nwith reference to any such subject as those we have here\nspoken of, these two portions of science, a Systematic\nDescription of the Facts, and a rigorous Analysis of the\nCauses,--the _Phenomenology_ and the _\u00c6tiology_ of the\nsubject,--we are prepared for the third member which\ncompletes the science, the _Theory_ of the actual facts. We\ncan then take a view of the events which really have\nhappened, discerning their connexion, interpreting their\nevidence, supplying from the context the parts which are\nunapparent. We can account for known facts by intelligible\ncauses; we can infer latent facts from manifest effects, so\nas to obtain a distinct insight into the whole history of\nevents up to the present time, and to see the last result of\nthe whole in the present condition of things. {282} The term\n_Theory_, when rigorously employed in such sciences as those\nwhich we here consider, bears nearly the sense which I have\nadopted: it implies a consistent and systematic view of the\nactual facts, combined with a true apprehension of their\nconnexion and causes. Thus if we speak of 'a Theory of Mount\nEtna,' or 'a Theory of the Paris Basin,' we mean a connected\nand intelligible view of the events by which the rocks in\nthese localities have come into their present condition.\nUndoubtedly the term _Theory_ has often been used in a\nlooser sense; and men have put forth '_Theories of the\nEarth_,' which, instead of including the whole mass of\nactual geological facts and their causes, only assigned, in\na vague manner, some causes by which some few phenomena\nmight, it was conceived, be accounted for. Perhaps the\nportion of our Pal\u00e6tiological Sciences which we now wish to\ndesignate, would be more generally understood if we were to\ndescribe it as _Theoretical_ or _Philosophical History_; as\nwhen we talk of 'the Theoretical History of Architecture,'\nor 'the Philosophical History of Language.' And in the same\nmanner we might speak of the Theoretical History of the\nAnimal and Vegetable Kingdoms; meaning, a distinct account\nof the events which have produced the present distribution\nof species and families. But by whatever phrase we describe\nthis portion of science, it is plain that such a Theory,\nsuch a Theoretical History, must result from the application\nof causes well understood to facts well ascertained. And if\nthe term _Theory_ be here employed, we must recollect that\nit is to be understood, not in its narrower sense as opposed\nto facts, but in its wider signification, as including all\nknown facts and differing from them only in introducing\namong them principles of intelligible connexion. The\nTheories of which we now speak are true _Theories_,\nprecisely because they are identical with the total system\nof the _Facts_.\n\n17. _No sound Pal\u00e6tiological Theory yet extant._--It is not\nto disparage unjustly the present state of science, to say\nthat as yet no such theory exists on any subject. 'Theories\nof the Earth' have been {283} repeatedly published; but when\nwe consider that even the facts of geology have been\nobserved only on a small portion of the earth's surface, and\neven within those narrow bounds very imperfectly studied, we\nshall be able to judge how impossible it is that geologists\nshould have yet obtained a well-established Theoretical\nHistory of the changes which have taken place in the crust\nof the terrestrial globe from its first origin. Accordingly,\nI have ventured in my History to designate the most\nprominent of the Theories which have hitherto prevailed as\n_premature_ geological theories[13\\10]: and we shall soon\nsee that geological theory has not advanced beyond a few\nconjectures, and that its cultivators are at present mainly\noccupied with a controversy in which the two extreme\nhypotheses which first offer themselves to men's minds are\nopposed to each other. And if we have no theoretical History\nof the Earth which merits any confidence, still less have we\nany theoretical History of Language, or of the Arts, which\nwe can consider as satisfactory. The Theoretical History of\nthe Vegetable and Animal Kingdoms is closely connected with\nthat of the Earth on which they subsist, and must follow the\nfortunes of Geology. And thus we may venture to say that no\nPal\u00e6tiological Science, as yet, possesses all its three\nmembers. Indeed most of them are very far from having\ncompleted and systematized their Phenomenology: in all, the\ncultivation of \u00c6tiology is but just begun, or is not begun;\nin all, the Theory must reward the exertions of future,\nprobably of distant, generations.\n\n[Note 13\\10: _Hist. Ind. Sc._ b. xviii. c. vii. sect. 3.]\n\nBut in the mean time we may derive some instruction from the\ncomparison of the two antagonist hypotheses of which I have spoken.\n\n\n\n{{284}}\nCHAPTER III.\n\nOF THE DOCTRINE OF CATASTROPHES AND THE DOCTRINE OF\nUNIFORMITY.\n\n\n1. _Doctrine of Catastrophes._--I HAVE already shown, in the\nHistory of Geology, that the attempts to frame a theory of\nthe earth have brought into view two completely opposite\nopinions:--one, which represents the course of nature as\n_uniform_ through all ages, the causes which produce change\nhaving had the same intensity in former times which they\nhave at the present day;--the other opinion, which sees, in\nthe present condition of things, evidences of\n_catastrophes_;--changes of a more sweeping kind, and\nproduced by more powerful agencies than those which occur in\nrecent times. Geologists who held the latter opinion,\nmaintained that the forces which have elevated the Alps or\nthe Andes to their present height could not have been any\nforces which are now in action: they pointed to vast masses\nof strata hundreds of miles long, thousands of feet thick,\nthrown into highly-inclined positions, fractured,\ndislocated, crushed: they remarked that upon the shattered\nedges of such strata they found enormous accumulations of\nfragments and rubbish, rounded by the action of water, so as\nto denote ages of violent aqueous action: they conceived\nthat they saw instances in which whole mountains of rock in\na state of igneous fusion, must have burst the earth's crust\nfrom below: they found that in the course of the revolutions\nby which one stratum of rock was placed upon another, the\nwhole collection of animal species which tenanted the earth\nand the seas had been removed, and a new set of living\nthings introduced in its place: finally, they found, above\nall the strata, {285} vast masses of sand and gravel\ncontaining bones of animals, and apparently the work of a\nmighty deluge. With all these proofs before their eyes, they\nthought it impossible not to judge that the agents of change\nby which the world was urged from one condition to another\ntill it reached its present state must have been more\nviolent, more powerful, than any which we see at work around\nus. They conceived that the evidence of 'catastrophes' was\nirresistible.\n\n2. _Doctrine of Uniformity._--I need not here repeat the\nnarrative (given in the History[14\\10]) of the process by\nwhich this formidable array of proofs was, in the minds of\nsome eminent geologists, weakened, and at last overcome.\nThis was done by showing that the sudden breaks in the\nsuccession of strata were apparent only, the discontinuity\nof the series which occurred in one country being removed by\nterms interposed in another locality:--by urging that the\ntotal effect produced by existing causes, taking into\naccount the accumulated result of long periods, is far\ngreater than a casual speculator would think possible:--by\nmaking it appear that there are in many parts of the world\nevidences of a slow and imperceptible rising of the land\nsince it was the habitation of now existing species:--by\nproving that it is not universally true that the strata\nseparated in time by supposed catastrophes contain distinct\nspecies of animals:--by pointing out the limited fields of\nthe supposed diluvial action:--and finally, by remarking\nthat though the _creation_ of species is a mystery, the\n_extinction_ of species is going on in our own day.\nHypotheses were suggested, too, by which it was conceived\nthat the change of climate might be explained, which, as the\nconsideration of the fossil remains seemed to show, must\nhave taken place between the ancient and the modern times.\nIn this manner the whole evidence of catastrophes was\nexplained away: the notion of a series of paroxysms of\nviolence in the causes of change was represented as a\ndelusion arising from our {286} contemplating short periods\nonly, in the action of present causes: length of time was\ncalled in to take the place of intensity of force: and it\nwas declared that Geology need not despair of accounting for\nthe revolutions of the earth, as Astronomy accounts for the\nrevolutions of the heavens, by the universal action of\ncauses which are close at hand to us, operating through time\nand space without variation or decay.\n\n[Note 14\\10: _Hist. Ind. Sc._ b. xviii. c. viii. sect. 2.]\n\nAn antagonism of opinions, somewhat of the same kind as\nthis, will be found to manifest itself in the other\nPal\u00e6tiological Sciences as well as in Geology; and it will\nbe instructive to endeavour to balance these opposite\ndoctrines. I will mention some of the considerations which\nbear upon the subject in its general form.\n\n3. _Is Uniformity probable \u00e0 priori?_--The doctrine of\nUniformity in the course of nature has sometimes been\nrepresented by its adherents as possessing a great degree of\n_\u00e0 priori_ probability. It is highly unphilosophical, it has\nbeen urged, to assume that the causes of the geological\nevents of former times were of a different kind from causes\nnow in action, if causes of this latter kind can in any way\nbe made to explain the facts. The analogy of all other\nsciences compels us, it was said, to explain phenomena by\nknown, not by unknown, causes. And on these grounds the\ngeological teacher recommended[15\\10] 'an earnest and\npatient endeavour to reconcile the indications of former\nchange with the evidence of gradual mutations now in\nprogress.'\n\n[Note 15\\10: Lyell, 4th ed. b. iv. c. i. p. 328.]\n\nBut on this we may remark, that if by _known_ causes we mean\ncauses acting with the same intensity which they have had\nduring historical times, the restriction is altogether\narbitrary and groundless. Let it be granted, for instance,\nthat many parts of the earth's surface are now undergoing an\nimperceptible rise. It is not pretended that the rate of\nthis elevation is rigorously uniform; what, then, are the\nlimits of its velocity? Why may it not increase so as to\nassume that character of violence which we may term a {287}\n_catastrophe_ with reference to all changes hitherto\nrecorded? Why may not the rate of elevation be such that we\nmay conceive the strata to assume _suddenly_ a position\nnearly vertical? And is it, in fact, easy to conceive a\nposition of strata nearly vertical, a position which occurs\nso frequently, to be _gradually_ assumed? In cases where the\nstrata are nearly vertical, as in the Isle of Wight, and\nhundreds of other places, or where they are actually\ninverted, as sometimes occurs, are not the causes which have\nproduced the effect as truly known causes, as those which\nhave raised the coasts where we trace the former beach in an\nelevated terrace? If the latter case proves _slow_\nelevation, does not the former case prove _rapid_ elevation?\nIn neither case have we any measure of the time employed in\nthe change; but does not the very nature of the results\nenable us to discern, that if one was gradual, the other was\ncomparatively sudden?\n\nThe causes which are now elevating a portion of Scandinavia\ncan be called known _causes_, only because we know the\n_effect_. Are not the causes which have elevated the Alps\nand the Andes known causes in the same sense? We know\nnothing in either case which confines the intensity of the\nforce within any limit, or prescribes to it any law of\nuniformity. Why, then, should we make a merit of cramping\nour speculations by such assumptions? Whether the causes of\nchange do act uniformly;--whether they oscillate only within\nnarrow limits;--whether their intensity in former times was\nnearly the same as it now is;--these are precisely the\nquestions which we wish Science to answer to us impartially\nand truly: where is then the wisdom of 'an earnest and\npatient endeavour' to secure an _affirmative_ reply?\n\nThus I conceive that the assertion of an _\u00e0 priori_ claim to\nprobability and philosophical spirit in favour of the\ndoctrine of uniformity, is quite untenable. We must learn\nfrom an examination of all the facts, and not from any\nassumption of our own, whether the course of nature be\nuniform. The limit of intensity being really unknown,\ncatastrophes are just as probable {288} as uniformity. If a\nvolcano may repose for a thousand years, and then break out\nand destroy a city; why may not another volcano repose for\nten thousand years, and then destroy a continent; or if a\ncontinent, why not the whole habitable surface of the earth?\n\n4. _Cycle of Uniformity indefinite._--But this argument may\nbe put in another form. When it is said that the course of\nnature is uniform, the assertion is not intended to exclude\ncertain smaller variations of violence and rest, such as we\nhave just spoken of;--alternations of activity and repose in\nvolcanoes; or earthquakes, deluges, and storms, interposed\nin a more tranquil state of things. With regard to such\noccurrences, terrible as they appear at the time, they may\nnot much affect the average rate of change; there may be a\n_cycle_, though an irregular one, of rapid and slow change;\nand if such cycles go on succeeding each other, we may still\ncall the order of nature uniform, notwithstanding the\nperiods of violence which it involves. The maximum and\nminimum intensities of the forces of mutation alternate with\none another; and we may estimate the average course of\nnature as that which corresponds to something between the\ntwo extremes.\n\nBut if we thus attempt to maintain the uniformity of nature\nby representing it as a series of _cycles_, we find that we\ncannot discover, in this conception, any solid ground for\nexcluding catastrophes. What is the length of that cycle,\nthe repetition of which constitutes uniformity? What\ninterval from the maximum to the minimum does it admit of?\nWe may take for our cycle a hundred or a thousand years, but\nevidently such a proceeding is altogether arbitrary. We may\nmark our cycles by the greatest known paroxysms of volcanic\nand terremotive agency, but this procedure is no less\nindefinite and inconclusive than the other.\n\nBut further; since the cycle in which violence and repose\nalternate is thus indefinite in its length and in its range\nof activity, what ground have we for assuming more than one\nsuch cycle, extending from the origin of things to the\npresent time? Why may we not suppose the maximum force of\nthe causes of change {289} to have taken place at the\nearliest period, and the tendency towards the minimum to\nhave gone on ever since? Or instead of only one cycle, there\nmay have been several, but of such length that our\nhistorical period forms a portion only of the last;--the\nfeeblest portion of the latest cycle. And thus violence and\nrepose may alternate upon a scale of time and intensity so\nlarge, that man's experience supplies no evidence enabling\nhim to estimate the amount. The course of things is\n_uniform_, to an Intelligence which can embrace the\nsuccession of several cycles, but it is _catastrophic_ to\nthe contemplation of man, whose survey can grasp a part only\nof one cycle. And thus the hypothesis of uniformity, since\nit cannot exclude degrees of change, nor limit the range of\nthese degrees, nor define the interval of their recurrence,\ncannot possess any essential simplicity which, previous to\ninquiry, gives it a claim upon our assent superior to that\nof the opposite catastrophic hypothesis.\n\n5. _Uniformitarian Arguments are Negative only._--There is\nan opposite tendency in the mode of maintaining the\ncatastrophist and the uniformitarian opinions, which depends\nupon their fundamental principles, and shows itself in all\nthe controversies between them. The Catastrophist is\naffirmative, the Uniformitarian is negative in his\nassertions: the former is constantly attempting to construct\na theory; the latter delights in demolishing all theories.\nThe one is constantly bringing fresh evidence of some great\npast event, or series of events, of a striking and definite\nkind; his antagonist is at every step explaining away the\nevidence, and showing that it proves nothing. One geologist\nadduces his proofs of a vast universal deluge; but another\nendeavours to show that the proofs do not establish either\nthe universality or the vastness of such an event. The\ninclined broken edges of a certain formation, covered with\ntheir own fragments, beneath superjacent horizontal\ndeposits, are at one time supposed to prove a catastrophic\nbreaking up of the earlier strata; but this opinion is\ncontroverted by showing that the same formations, when\npursued into other countries, {290} exhibit a uniform\ngradation from the lower to the upper, with no trace of\nviolence. Extensive and lofty elevations of the coast,\ncontinents of igneous rock, at first appear to indicate\noperations far more gigantic than those which now occur; but\nattempts are soon made to show that time only is wanting to\nenable the present age to rival the past in the production\nof such changes. Each new fact adduced by the catastrophist\nis at first striking and apparently convincing; but as it\nbecomes familiar, it strikes the imagination less\npowerfully; and the uniformitarian, constantly labouring to\nproduce some imitation of it by the machinery which he has\nso well studied, at last in every case seems to himself to\nsucceed, so far as to destroy the effect of his opponent's\nevidence.\n\nThis is so with regard to more remote, as well as with\nregard to immediate evidences of change. When it is\nascertained that in every part of the earth's crust the\ntemperature increases as we descend below the surface, at\nfirst this fact seems to indicate a central heat: and a\ncentral heat naturally suggests an earlier state of the\nmass, in which it was incandescent, and from which it is now\ncooling. But this original incandescence of the globe of the\nearth is manifestly an entire violation of the present\ncourse of things; it belongs to the catastrophist view, and\nthe advocates of uniformity have to explain it away.\nAccordingly, one of them holds that this increase of heat in\ndescending below the surface may very possibly not go on all\nthe way to the center. The heat which increases at first as\nwe descend, may, he conceives, afterwards decrease; and he\nsuggests causes which may have produced such a succession of\nhotter and colder shells within the mass of the earth. I\nhave mentioned this suggestion in the History of Geology;\nand have given my reasons for believing it altogether\nuntenable[16\\10]. Other persons also, desirous of\nreconciling this subterraneous heat with the tenet of\nuniformity, have {291} offered another suggestion:--that the\nwarmth or incandescence of the interior parts of the earth\ndoes not arise out of an originally hot condition from which\nit is gradually cooling, but results from chemical action\nconstantly going on among the materials of the earth's\nsubstance. And thus new attempts are perpetually making, to\nescape from the cogency of the reasonings which send us\ntowards an original state of things different from the\npresent. Those who theorize concerning an origin go on\nbuilding up the fabric of their speculations, while those\nwho think such theories unphilosophical, ever and anon dig\naway the foundation of this structure. As we have already\nsaid, the uniformitarian's doctrines are a collection of\nnegatives.\n\n[Note 16\\10: _Hist. Ind. Sc._ b. xviii. c. v. sect. 5, and note.]\n\nThis is so entirely the case, that the uniformitarian would\nfor the most part shrink from maintaining as positive tenets\nthe explanations which he so willingly uses as instruments\nof controversy. He puts forward his suggestions as\ndifficulties, but he will not stand by them as doctrines.\nAnd this is in accordance with his general tendency; for any\nof his hypotheses, if insisted upon as positive theories,\nwould be found inconsistent with the assertion of\nuniformity. For example, the nebular hypothesis appears to\ngive to the history of the heavens an aspect which\nobliterates all special acts of creation, for, according to\nthat hypothesis, new planetary systems are constantly\nforming; but when asserted as the origin of our own solar\nsystem, it brings with it an original incandescence, and an\norigin of the organic world. And if, instead of using the\nchemical theory of subterraneous heat to neutralize the\nevidence of original incandescence, we assert it as a\npositive tenet, we can no longer maintain the infinite past\nduration of the earth; for chemical forces, as well as\nmechanical, tend to equilibrium; and that condition once\nattained, their efficacy ceases. Chemical affinities tend to\nform new compounds; and though, when many and various\nelements are mingled together, the play of synthesis and\nanalysis may go on for a long time, it must at last end. If,\nfor instance, a large portion of the earth's mass were\noriginally pure potassium, we {292} can imagine violent\nigneous action to go on so long as any part remained\nunoxidized; but when the oxidation of the whole has once\ntaken place, this action must be at an end; for there is in\nthe hypothesis no agency which can reproduce the deoxidized\nmetal. Thus a perpetual motion is impossible in chemistry,\nas it is in mechanics; and a theory of constant change\ncontinued through infinite time, is untenable when asserted\nupon chemical, no less than upon mechanical principles. And\nthus the Skepticism of the uniformitarian is of force only\nso long as it is employed against the Dogmatism of the\ncatastrophist. When the Doubts are erected into Dogmas, they\nare no longer consistent with the tenet of Uniformity. When\nthe Negations become Affirmations, the Negation of an Origin\nvanishes also.\n\n6. _Uniformity in the Organic World._--In speaking of the\nviolent and sudden changes which constitute catastrophes,\nour thoughts naturally turn at first to great _mechanical_\nand _physical_ effects;--ruptures and displacements of\nstrata; extensive submersions and emersions of land; rapid\nchanges of temperature. But the catastrophes which we have\nto consider in geology affect the _organic_ as well as the\ninorganic world. The sudden extinction of one collection of\nspecies, and the introduction of another in their place, is\na Catastrophe, even if unaccompanied by mechanical violence.\nAccordingly, the antagonism of the catastrophist and\nuniformitarian schools has shown itself in this department\nof the subject, as well as in the other. When geologists had\nfirst discovered that the successive strata are each\ndistinguished by appropriate organic fossils, they assumed\nat once that each of these collections of living things\nbelonged to a separate creation. But this conclusion, as I\nhave already said, Sir C. Lyell has attempted to invalidate,\nby proving that in the existing order of things, some\nspecies become extinct; and by suggesting it as possible,\nthat in the same order, it may be true that new species are\nfrom time to time produced, even in the present course of\nnature. And in this, as in the other part of the subject, he\ncalls in {293} the aid of vast periods of time, in order\nthat the violence of the changes may be softened down: and\nhe appears disposed to believe that the actual extinction\nand creation of species may be so slow as to excite no more\nnotice than it has hitherto obtained; and yet may be rapid\nenough, considering the immensity of geological periods, to\nproduce such a succession of different collections of\nspecies as we find in the strata of the earth's surface.\n\n7. _Origin of the present Organic World._--The last great\nevent in the history of the vegetable and animal kingdoms\nwas that by which their various tribes were placed in their\npresent seats. And we may form various hypotheses with\nregard to the sudden or gradual manner in which we may\nsuppose this distribution to have taken place. We may assume\nthat at the beginning of the present order of things, a\nstock of each species was placed in the vegetable or animal\n_province_ to which it belongs, by some cause out of the\ncommon order of nature; or we may take a uniformitarian view\nof the subject, and suppose that the provinces of the\norganic world derived their population from some anterior\nstate of things by the operation of natural causes.\n\nNothing has been pointed out in the existing order of things\nwhich has any analogy or resemblance, of any valid kind, to\nthat creative energy which must be exerted in the production\nof a new species. And to assume the introduction of new\nspecies as 'a part of the order of nature,' without pointing\nout any natural fact with which such an event can be\nclassed, would be to reject creation by an arbitrary act.\nHence, even on natural grounds, the most intelligible view\nof the history of the animal and vegetable kingdoms seems to\nbe, that each period which is marked by a distinct\ncollection of species forms a cycle; and that at the\nbeginning of each such cycle a creative power was exerted,\nof a kind to which there was nothing at all analogous in the\nsucceeding part of the same cycle. If it be urged that in\nsome cases the same species, or the same genus, runs through\ntwo geological formations, {294} which must, on other\ngrounds, be referred to different cycles of creative energy,\nwe may reply that the creation of many new species does not\nimply the extinction of all the old ones.\n\nThus we are led by our reasonings to this view, that the\npresent order of things was commenced by an act of creative\npower entirely different to any agency which has been\nexerted since. None of the influences which have modified\nthe present races of animals and plants since they were\nplaced in their habitations on the earth's surface can have\nhad any efficacy in producing them at first. We are\nnecessarily driven to assume, as the beginning of the\npresent cycle of organic nature, an event not included in\nthe course of nature. And we may remark that this necessity\nis the more cogent, precisely because other cycles have\npreceded the present.\n\n8. _Nebular Origin of the Solar System._--If we attempt to\napply the same antithesis of opinion (the doctrines of\nCatastrophe and Uniformity) to the other subjects of\npal\u00e6tiological sciences, we shall be led to similar\nconclusions. Thus, if we turn our attention to Astronomical\nPal\u00e6tiology, we perceive that the Nebular Hypothesis has a\nuniformitarian tendency. According to this hypothesis the\nformation of this our system of sun, planets, and\nsatellites, was a process of the same kind as those which\nare still going on in the heavens. One after another, nebul\u00e6\ncondense into separate masses, which begin to revolve about\neach other by mechanical necessity, and form systems of\nwhich our solar system is a finished example. But we may\nremark, that the uniformitarian doctrine on this subject\nrests on most unstable foundations. We have as yet only very\nvague and imperfect reasonings to show that by such\ncondensation a _material_ system such as ours could result;\nand the introduction of _organized_ beings into such a\nmaterial system is utterly out of the reach of our\nphilosophy. Here again, therefore, we are led to regard the\npresent order of the world as pointing towards an origin\naltogether of a different kind from anything which our\nmaterial science can grasp. {295}\n\n9. _Origin of Languages._--We may venture to say that we\nshould be led to the same conclusion once more, if we were\nto take into our consideration those pal\u00e6tiological sciences\nwhich are beyond the domain of matter; for instance, the\nHistory of Languages. We may explain many of the differences\nand changes which we become acquainted with, by referring to\nthe action of causes of change which still operate. But what\nglossologist will venture to declare that the efficacy of\nsuch causes has been uniform;--that the influences which\nmould a language, or make one language differ from others of\nthe same stock, operated formerly with no more efficacy than\nthey exercise now. 'Where,' as has elsewhere been asked, 'do\nwe now find a language in the process of formation,\nunfolding itself in inflexions, terminations, changes of\nvowels by grammatical relations, such as characterise the\noldest known languages?' Again, as another proof how little\nthe history of languages suggests to the philosophical\nglossologist the persuasion of a uniform action of the\ncauses of change, I may refer to the conjecture of Dr.\nPrichard, that the varieties of language produced by the\nseparation of one stock into several, have been greater and\ngreater as we go backwards in history:--that[17\\10] the\nformation of sister dialects from a common language (as the\nScandinavian, German, and Saxon dialects from the Teutonic,\nor the Gaelic, Erse and Welsh from the Celtic) belongs to\nthe first millennium before the Christian era; while the\nformation of cognate languages of the same family, as the\nSanskrit, Latin, Greek and Gothic, must be placed at least\ntwo thousand years before that era; and at a still earlier\nperiod took place the separation of the great families\nthemselves, the Indo-European, Semitic, and others, in which\nit is now difficult to trace the features of a common\norigin. No hypothesis except one of this kind will explain\nthe existence of the families, groups, and dialects of\nlanguages, which we find in existence. Yet this is an\nentirely different view from that which {296} the hypothesis\nof the uniform progress of change would give. And thus, in\nthe earliest stages of man's career, the revolutions of\nlanguage must have been, even by the evidence of the\ntheoretical history of language itself, of an order\naltogether different from any which have taken place within\nthe recent history of man. And we may add, that as the early\nstages of the progress of language must have been widely\ndifferent from those later ones of which we can in some\nmeasure trace the natural causes, we cannot place the origin\nof language in any point of view in which it comes under the\njurisdiction of natural causation at all.\n\n[Note 17\\10: _Researches_, ii. 224.]\n\n10. _No Natural Origin discoverable._--We are thus led by a\nsurvey of several of the pal\u00e6tiological sciences to a\nconfirmation of the principle formerly asserted[18\\10], That\nin no pal\u00e6tiological science has man been able to arrive at\na beginning which is homogeneous with the known course of\nevents. We can in such sciences often go very far\nback;--determine many of the remote circumstances of the\npast series of events;--ascend to a point which seems to be\nnear the origin;--and limit the hypotheses respecting the\norigin itself: but philosophers never have demonstrated,\nand, so far as we can judge, probably never will be able to\ndemonstrate, what was that primitive state of things from\nwhich the progressive course of the world took its first\ndeparture. In all these paths of research, when we travel\nfar backwards, the aspect of the earlier portions becomes\nvery different from that of the advanced part on which we\nnow stand; but in all cases the path is lost in obscurity as\nit is traced backwards towards its starting-point: it\nbecomes not only invisible, but unimaginable; it is not only\nan interruption, but an abyss, which interposes itself\nbetween us and any intelligible beginning of things.\n\n[Note 18\\10: _Hist. Ind. Sc._ b. xviii. c. vi. sect 5.]\n\n\n\n{{297}}\nCHAPTER IV.\n\nOF THE RELATION OF TRADITION TO PAL\u00c6TIOLOGY.\n\n\n1. _Importance of Tradition._--SINCE the Pal\u00e6tiological\nSciences have it for their business to study the train of\npast events produced by natural causes down to the present\ntime, the knowledge concerning such events which is supplied\nby the remembrance and records of man, in whatever form,\nmust have an important bearing upon these sciences. All\nchanges in the condition and extent of land and sea, which\nhave taken place within man's observation, all effects of\ndeluges, sea-waves, rivers, springs, volcanoes, earthquakes,\nand the like, which come within the reach of human history,\nhave a strong interest for the pal\u00e6tiologist. Nor is he less\nconcerned in all recorded instances of the modification of\nthe forms and habits of plants and animals, by the\noperations of man, or by transfer from one land to another.\nAnd when we come to the Pal\u00e6tiology of Language, of Art, of\nCivilization, we find our subject still more closely\nconnected with history; for in truth these are historical,\nno less than pal\u00e6tiological investigations. But, confining\nourselves at present to the material sciences, we may\nobserve that though the importance of the information which\ntradition gives us, in the sciences now under our\nconsideration, as, for instance, geology, has long been\ntacitly recognised; yet it is only recently that geologists\nhave employed themselves in collecting their historical\nfacts upon such a scale and with such comprehensive views as\nare required by the interest and use of collections of this\nkind. The Essay of Von {298} Hoff[19\\10], _On the Natural\nAlterations in the Surface of the Earth which are proved by\nTradition_, was the work which first opened the eyes of\ngeologists to the extent and importance of this kind of\ninvestigation. Since that time the same path of research has\nbeen pursued with great perseverance by others, especially\nby Sir C. Lyell; and is now justly considered as an\nessential portion of Geology.\n\n[Note 19\\10: Vol. i. 1822; vol. ii. 1824.]\n\n2. _Connexion of Tradition and Science._--Events which we\nmight naturally expect to have some bearing on geology, are\nnarrated in the historical writings which, even on mere\nhuman grounds, have the strongest claim to our respect as\nrecords of the early history of the world, and are confirmed\nby the traditions of various nations all over the globe;\nnamely, the formation of the earth and of its population,\nand a subsequent deluge. It has been made a matter of\ncontroversy how the narrative of these events is to be\nunderstood, so as to make it agree with the facts which an\nexamination of the earth's surface and of its vegetable and\nanimal population discloses to us. Such controversies, when\nthey are considered as merely arch\u00e6ological, may occur in\nany of the pal\u00e6tiological sciences. We may have to compare\nand to reconcile the evidence of existing phenomena with\nthat of historical tradition. But under some circumstances\nthis process of conciliation may assume an interest of\nanother kind, on which we will make a few remarks.\n\n3. _Natural and Providential History of the World._--We may\ncontemplate the existence of man upon the earth, his origin\nand his progress, in the same manner as we contemplate the\nexistence of any other race of animals; namely, in a purely\npal\u00e6tiological view. We may consider how far our knowledge\nof laws of causation enables us to explain his diffusion and\nmigration, his differences and resemblances, his actions and\nworks. And this is the view of man as a member of the\n_Natural_ Course of Things. {299}\n\nBut man, at the same time the contemplator and the subject\nof his own contemplation, endowed with faculties and powers\nwhich make him a being of a different nature from other\nanimals, cannot help regarding his own actions and\nenjoyments, his recollections and his hopes, under an aspect\nquite different from any that we have yet had presented to\nus. We have been endeavouring to place in a clear light the\nFundamental Ideas, such as that of Cause, on which depends\nour knowledge of the natural course of things. But there are\nother Ideas to which man necessarily refers his actions; he\nis led by his nature, not only to consider his own actions,\nand those of his fellow-men, as springing out of this or\nthat cause, leading to this or that material result; but\nalso as _good_ or _bad_, as what they _ought_ or _ought not_\nto be. He has Ideas of moral relations as well as those\nIdeas of material relations with which we have hitherto been\noccupied. He is a moral as well as a natural agent.\n\nContemplating himself and the world around him by the light\nof his Moral Ideas, man is led to the conviction that his\nmoral faculties were bestowed upon him by design and for a\npurpose; that he is the subject of a Moral Government; that\nthe course of the world is directed by the Power which\ngoverns it, to the unfolding and perfecting of man's moral\nnature; that this guidance may be traced in the career of\nindividuals and of the world; that there is a _Providential_\nas well as a Natural Course of Things.\n\nYet this view is beset by no small difficulties. The full\ndevelopment of man's moral faculties;--the perfection of his\nnature up to the measure of his own ideas;--the adaptation\nof his moral being to an ultimate destination, by its\ntransit through a world full of moral evil, in which evil\neach person has his share;--are effects for which the\neconomy of the world appears to contain no adequate\nprovision. Man, though aware of his moral nature, and ready\nto believe in an ultimate destination of purity and\nblessedness, is too feeble to resist the temptation of evil,\nand too helpless to restore his purity when once lost. He\ncannot but look for {300} some confirmation of that\nprovidential order which he has begun to believe; some\nprovision for those deficiencies in his moral condition\nwhich he has begun to feel.\n\nHe looks at the history of the world, and he finds that at a\ncertain period it offers to him the promise of what he\nseeks. When the natural powers of man had been developed to\ntheir full extent, and were beginning to exhibit symptoms of\ndecay;--when the intellectual progress of the world appeared\nto have reached its limit, without supplying man's moral\nneeds;--we find the great Epoch in the Providential History\nof the world. We find the announcement of a Dispensation by\nwhich man's deficiencies shall be supplied and his\naspirations fulfilled: we find a provision for the\npurification, the support, and the ultimate beatification of\nthose who use the provided means. And thus the providential\ncourse of the world becomes consistent and intelligible.\n\n4. _The Sacred Narrative._--But with the new Dispensation,\nwe receive, not only an account of its own scheme and\nhistory, but also a written narrative of the providential\ncourse of the world from the earliest times, and even from\nits first creation. This narrative is recognized and\nauthorized by the new dispensation, and accredited by some\nof the same evidences as the dispensation itself. That the\nexistence of such a sacred narrative should be a part of the\nprovidential order of things, cannot but appear natural;\nbut, naturally also, the study of it leads to some\ndifficulties.\n\nThe Sacred Narrative in some of its earliest portions speaks\nof natural objects and occurrences respecting them. In the\nvery beginning of the course of the world, we may readily\nbelieve (indeed, as we have seen in the last chapter, our\nscientific researches lead us to believe) that such\noccurrences were very different from anything which now\ntakes place;--different to an extent and in a manner which\nwe cannot estimate. Now the narrative must speak of objects\nand occurrences in the words and phrases which have derived\ntheir meaning from their application to the existing natural\nstate of things. When applied to an initial {301}\nsupernatural state therefore, these words and phrases cannot\nhelp being to us obscure and mysterious, perhaps ambiguous\nand seemingly contradictory.\n\n5. _Difficulties in interpreting the Sacred Narrative._--The\nmoral and providential relations of man's condition are so\nmuch more important to him than mere natural relations, that\nat first we may well suppose he will accept the Sacred\nNarrative, as not only unquestionable in its true import,\nbut also as a guide in his views even of mere natural\nthings. He will try to modify the conceptions which he\nentertains of objects and their properties, so that the\nSacred Narrative of the supernatural condition shall retain\nthe first meaning which he had put upon it in virtue of his\nown habits in the usage of language.\n\nBut man is so constituted that he cannot persist in this\nprocedure. The powers and tendencies of his intellect are\nsuch that he cannot help trying to attain true conceptions\nof objects and their properties by the study of things\nthemselves. For instance, when he at first read of a\nfirmament dividing the waters above from the waters below,\nhe perhaps conceived a transparent floor in the skies, on\nwhich the superior waters rested, which descend in rain; but\nas his observations and his reasonings satisfied him that\nsuch a floor could not exist, he became willing to allow (as\nSt. Augustine allowed) that the waters above the firmament\nare in a state of vapour. And in like manner in other\nsubjects, men, as their views of nature became more distinct\nand precise, modified, so far as it was necessary for\nconsistency's sake, their first rude interpretations of the\nSacred Narrative; so that, without in any degree losing its\nimport as a view of the providential course of the world, it\nshould be so conceived as not to contradict what they knew\nof the natural order of things.\n\nBut this accommodation was not always made without painful\nstruggles and angry controversies. When men had conceived\nthe occurrences of the Sacred Narrative in a particular\nmanner, they could not readily and willingly adopt a new\nmode of conception; and all attempts to recommend to them\nsuch novelties, they {302} resisted as attacks upon the\nsacredness of the Narrative. They had clothed their belief\nof the workings of Providence in certain images; and they\nclung to those images with the persuasion that, without\nthem, their belief could not subsist. Thus they imagined to\nthemselves that the earth was a flat floor, solidly and\nbroadly laid for the convenience of man; and they felt as if\nthe kindness of Providence was disparaged, when it was\nmaintained that the earth was a globe held together only by\nthe mutual attraction of its parts.\n\nThe most memorable instance of a struggle of this kind is to\nbe found in the circumstances which attended the\nintroduction of the Heliocentric Theory of Copernicus to\ngeneral acceptance. On this controversy I have already made\nsome remarks in the _History of Science_[20\\10], and have\nattempted to draw from it some lessons which may be useful\nto us when any similar conflict of opinions may occur. I\nwill here add a few reflections with a similar view.\n\n[Note 20\\10: B. v. c. iii. sect. 4.]\n\n6. _Such difficulties inevitable._--In the first place, I\nremark that such modifications of the current interpretation\nof the words of Scripture appear to be an inevitable\nconsequence of the progressive character of Natural Science.\nScience is constantly teaching us to describe known facts in\nnew language; but the language of Scripture is always the\nsame. And not only so, but the language of Scripture is\nnecessarily adapted to the common state of man's\nintellectual development, in which he is supposed not to be\npossessed of science. Hence the phrases used by Scripture\nare precisely those which science soon teaches man to\nconsider as inaccurate. Yet they are not, on that account,\nthe less fitted for their proper purpose: for if any terms\nhad been used, adapted to a more advanced state of\nknowledge, they must have been unintelligible among those to\nwhom the Scripture was first addressed. If the Jews had been\ntold that water existed in the clouds in small drops, they\nwould have marvelled that it did {303} not constantly\ndescend; and to have explained the reason of this, would\nhave been to teach Atmology in the sacred writings. If they\nhad read in their Scripture that the earth was a sphere,\nwhen it appeared to be a plain, they would only have been\ndisturbed in their thoughts or driven to some wild and\nbaseless imaginations, by a declaration to them so strange.\nIf the Divine Speaker, instead of saying that he would set\nhis bow in the clouds, had been made to declare that he\nwould give to water the property of refracting different\ncolours at different angles, how utterly unmeaning to the\nhearers would the words have been! And in these cases, the\nexpressions, being unintelligible, startling, and\nbewildering, would have been such as tended to unfit the\nSacred Narrative for its place in the providential\ndispensation of the world.\n\nAccordingly, in the great controversy which took place in\nGalileo's time between the defenders of the then customary\ninterpretations of Scripture, and the assertors of the\nCopernican system of the universe, when the innovators were\nupbraided with maintaining opinions contrary to Scripture,\nthey replied that Scripture was not intended to teach men\nastronomy, and that it expressed the acts of divine power in\nimages which were suited to the ideas of unscientific men.\nTo speak of the rising and setting and travelling of the\nsun, of the fixity and of the foundations of the earth, was\nto use the only language which would have made the Sacred\nNarrative intelligible. To extract from these and the like\nexpressions doctrines of science, was, they declared, in the\nhighest degree unjustifiable; and such a course could lead,\nthey held, to no result but a weakening of the authority of\nScripture in proportion as its credit was identified with\nthat of these modes of applying it. And this judgment has\nsince been generally assented to by those who most reverence\nand value the study of the designs of Providence as well as\nthat of the works of nature.\n\n7. _Science tells us nothing concerning Creation._--Other\napparent difficulties arise from the accounts given in the\nScripture of the first origin of the world {304} in which we\nlive: for example, Light is represented as created before\nthe Sun. With regard to difficulties of this kind, it\nappears that we may derive some instruction from the result\nto which we were led in the last chapter;--namely, that in\nthe sciences which trace the progress of natural\noccurrences, we can in no case go back to an origin, but in\nevery instance appear to find ourselves separated from it by\na state of things, and an order of events, of a kind\naltogether different from those which come under our\nexperience. The thread of induction respecting the natural\ncourse of the world snaps in our fingers, when we try to\nascertain where its beginning is. Since, then, science can\nteach us nothing positive respecting the beginning of\nthings, she can neither contradict nor confirm what is\ntaught by Scripture on that subject; and thus, as it is\nunworthy timidity in the lover of Scripture to fear\ncontradiction, so is it ungrounded presumption to look for\nconfirmation, in such cases. The providential history of the\nworld has its own beginning, and its own evidence; and we\ncan only render the system insecure, by making it lean on\nour material sciences. If any one were to suggest that the\nnebular hypothesis countenances the Scripture history of the\nformation of this system, by showing how the luminous matter\nof the sun might exist previous to the sun itself, we should\nact wisely in rejecting such an attempt to weave together\nthese two heterogeneous threads;--the one a part of a\nprovidential scheme, the other a fragment of a physical\nspeculation.\n\nWe shall best learn those lessons of the true philosophy of\nscience which it is our object to collect, by attending to\nportions of science which have gone through such crises as\nwe are now considering; nor is it requisite, for this\npurpose, to bring forwards any subjects which are still\nunder discussion. It may, however, be mentioned that such\nmaxims as we are now endeavouring to establish, and the one\nbefore us in particular, bear with a peculiar force upon\nthose Pal\u00e6tiological Sciences of which we have been treating\nin the present Book. {305}\n\n8. _Scientific views, when familiar, do not disturb the\nauthority of Scripture._--There is another reflection which\nmay serve to console and encourage us in the painful\nstruggles which thus take place, between those who maintain\ninterpretations of Scripture already prevalent and those who\ncontend for such new ones as the new discoveries of science\nrequire. It is this;--that though the new opinion is\nresisted by one party as something destructive of the credit\nof Scripture and the reverence which is its due, yet, in\nfact, when the new interpretation has been generally\nestablished and incorporated with men's current thoughts, it\nceases to disturb their views of the authority of the\nScripture or of the truth of its teaching. When the language\nof Scripture, invested with its new meaning, has become\nfamiliar to men, it is found that the ideas which it calls\nup are quite as reconcileable as the former ones were, with\nthe most entire acceptance of the providential dispensation.\nAnd when this has been found to be the case, all cultivated\npersons look back with surprise at the mistake of those who\nthought that the essence of the revelation was involved in\ntheir own arbitrary version of some collateral circumstance\nin the revealed narrative. At the present day, we can hardly\nconceive how reasonable men could ever have imagined that\nreligious reflections on the stability of the earth, and the\nbeauty and use of the luminaries which revolve round it,\nwould be interfered with by an acknowledgment that this rest\nand motion are apparent only[21\\10]. And thus the authority\nof revelation is not shaken by any changes introduced by the\nprogress of science in the mode of interpreting expressions\nwhich describe physical objects and occurrences; provided\nthe new interpretation is admitted at a proper season, and\nin a proper spirit; so as to soften, as much as possible,\nboth the public controversies and the private scruples which\nalmost inevitably accompany such an alteration.\n\n[Note 21\\10: I have here borrowed a sentence or two from my\nown _History_.]\n\n9. _When should old Interpretations be given up?_--But the\nquestion then occurs, What is the proper {306} season for a\nreligious and enlightened commentator to make such a change\nin the current interpretation of sacred Scripture? At what\nperiod ought the established exposition of a passage to be\ngiven up, and a new mode of understanding the passage, such\nas is, or seems to be, required by new discoveries\nrespecting the laws of nature, accepted in its place? It is\nplain, that to introduce such an alteration lightly and\nhastily would be a procedure fraught with inconvenience; for\nif the change were made in such a manner, it might be\nafterwards discovered that it had been adopted without\nsufficient reason, and that it was necessary to reinstate\nthe old exposition. And the minds of the readers of\nScripture, always to a certain extent and for a time\ndisturbed by the subversion of their long-established\nnotions, would be distressed without any need, and might be\nseriously unsettled. While, on the other hand, a too\nprotracted and obstinate resistance to the innovation, on\nthe part of the scriptural expositors, would tend to\nidentify, at least in the minds of many, the authority of\nthe Scripture with the truth of the exposition; and\ntherefore would bring discredit upon the revealed word, when\nthe established interpretation was finally proved to be\nuntenable.\n\nA rule on this subject, propounded by some of the most\nenlightened dignitaries of the Roman Catholic church, on the\noccasion of the great Copernican controversy begun by\nGalileo, seems well worthy of our attention. The following\nwas the opinion given by Cardinal Bellarmine at the\ntime:--'When a _demonstration_ shall be found to establish the\nearth's motion, it will be proper to interpret the sacred\nScriptures otherwise than they have hitherto been\ninterpreted in those passages where mention is made of the\nstability of the earth and movement of the heavens.' This\nappears to be a judicious and reasonable maxim for such\ncases in general. So long as the supposed scientific\ndiscovery is doubtful, the exposition of the meaning of\nScripture given by commentators of established credit is not\nwantonly to be disturbed: but when a scientific theory,\nirreconcileable with this ancient {307} interpretation, is\nclearly proved, we must give up the interpretation, and seek\nsome new mode of understanding the passage in question, by\nmeans of which it may be consistent with what we know; for\nif it be not, our conception of the things so described is\nno longer consistent with itself.\n\nIt may be said that this rule is indefinite, for who shall\ndecide when a new theory is completely demonstrated, and the\nold interpretation become untenable? But to this we may\nreply, that if the rule be assented to, its application will\nnot be very difficult. For when men have admitted as a\ngeneral rule, that the current interpretations of scriptural\nexpressions respecting natural objects and events may\npossibly require, and in some cases certainly will require,\nto be abandoned, and new ones admitted, they will hardly\nallow themselves to contend for such interpretations as if\nthey were essential parts of revelation; and will look upon\nthe change of exposition, whether it come sooner or later,\nwithout alarm or anger. And when men lend themselves to the\nprogress of truth in this spirit, it is not of any material\nimportance at what period a new and satisfactory\ninterpretation of the scriptural difficulty is found; since\na scientific exactness in our apprehension of the meaning of\nsuch passages as are now referred to is very far from being\nessential to our full acceptance of revelation.\n\n10. _In what Spirit should the Change be accepted?_--Still\nthese revolutions in scriptural interpretation must always\nhave in them something which distresses and disturbs\nreligious communities. And such uneasy feelings will take a\ndifferent shape, according as the community acknowledges or\nrejects a paramount interpretative authority in its\nreligious leaders. In the case in which the interpretation\nof the Church is binding upon all its members, the more\nplacid minds rest in peace upon the ancient exposition, till\nthe spiritual authorities announce that the time for the\nadoption of a new view has arrived; but in these\ncircumstances, the more stirring and inquisitive minds,\nwhich cannot refrain from the pursuit of new truths {308}\nand exact conceptions, are led to opinions which, being\ncontrary to those of the Church, are held to be sinful. On\nthe other hand, if the religious constitution of the\ncommunity allow and encourage each man to study and\ninterpret for himself the Sacred Writings, we are met by\nevils of another kind. In this case, although, by the\nunforced influence of admired commentators, there may\nprevail a general agreement in the usual interpretation of\ndifficult passages, yet as each reader of the Scripture\nlooks upon the sense which he has adopted as being his own\ninterpretation, he maintains it, not with the tranquil\nacquiescence of one who has deposited his judgment in the\nhands of his Church, but with the keenness and strenuousness\nof self-love. In such a state of things, though no judicial\nseverities can be employed against the innovators, there may\narise more angry controversies than in the other case.\n\nIt is impossible to overlook the lesson which here offers\nitself, that it is in the highest degree unwise in the\nfriends of religion, whether individuals or communities,\nunnecessarily to embark their credit in expositions of\nScripture on matters which appertain to natural Science. By\ndelivering physical doctrines as the teaching of revelation,\nreligion may lose much, but cannot gain anything. This maxim\nof practical wisdom has often been urged by Christian\nwriters. Thus St. Augustine says[22\\10]: 'In obscure matters\nand things far removed from our senses, if we read anything,\neven in the divine Scripture, which may produce diverse\nopinions without damaging the faith which we cherish, let us\nnot rush headlong by positive assertion to either the one\nopinion or the other; lest, when a more thorough discussion\nhas shown the opinion which we had adopted to be false, our\nfaith may fall with it: and we should be found contending,\nnot for the doctrine of the sacred Scriptures, but for our\nown; endeavouring to make our doctrine to be that of the\nScriptures, instead of taking the doctrine of the Scriptures\nto be ours.' And in nearly the same spirit, at the {309}\ntime of the Copernican controversy, it was thought proper to\nappend to the work of Copernicus a postil, to say that the\nwork was written to account for the phenomena, and that\npeople must not run on blindly and condemn either of the\nopposite opinions. Even when the Inquisition, in 1616,\nthought itself compelled to pronounce a decision upon this\nsubject, the verdict was delivered in very moderate\nlanguage;--that 'the doctrine of the earth's motion appeared\nto be contrary to Scripture:' and yet, moderate as this\nexpression is, it has been blamed by judicious members of\nthe Roman church as deciding a point such as religious\nauthorities ought not to pretend to decide; and has brought\nupon that church no ordinary weight of general condemnation.\nKepler pointed out, in his lively manner, the imprudence of\nemploying the force of religious authorities on such\nsubjects: _Acies dolabr\u00e6 in ferrum illisa, postea nec in\nlignum valet amplius. Capiat hoc cujus interest_. 'If you\n_will_ try to chop iron, the axe becomes unable to cut even\nwood. I warn those whom it concerns.'\n\n[Note 22\\10: Lib. i. _de Genesi_, cap. xviii.]\n\n11. _In what Spirit should the Change be urged?_--But while\nwe thus endeavour to show in what manner the interpreters of\nScripture may most safely and most properly accept the\ndiscoveries of science, we must not forget that there may be\nerrours committed on the other side also; and that men of\nscience, in bringing forward views which may for a time\ndisturb the minds of lovers of Scripture, should consider\nthemselves as bound by strict rules of candour, moderation,\nand prudence. Intentionally to make their supposed\ndiscoveries a means of discrediting, contradicting, or\nslighting the sacred Scriptures, or the authority of\nreligion, is in them unpardonable. As men who make the\nscience of Truth the business of their lives, and are\npersuaded of her genuine superiority, and certain of her\nultimate triumph, they are peculiarly bound to urge her\nclaims in a calm and temperate spirit; not forgetting that\nthere are other kinds of truth besides that which they\npeculiarly study. They may properly reject authority in\nmatters of science; but they are to leave {310} it its\nproper office in matters of religion. I may here again quote\nKepler's expressions: 'In Theology we balance authorities,\nin Philosophy we weigh reasons. A holy man was Lactantius\nwho denied that the earth was round; a holy man was\nAugustine, who granted the rotundity, but denied the\nantipodes; a holy thing to me is the Inquisition, which\nallows the smallness of the earth, but denies its motion;\nbut more holy to me is Truth; and hence I prove, from\nphilosophy, that the earth is round, and inhabited on every\nside, of small size, and in motion among the stars,--and\nthis I do with no disrespect to the Doctors.' I the more\nwillingly quote such a passage from Kepler, because the\nentire ingenuousness and sincere piety of his character does\nnot allow us to suspect him in anything of hypocrisy or\nlatent irony. That similar professions of respect may be\nmade ironically, we have a noted example in the celebrated\nIntroduction to _Galileo's Dialogue on the Copernican\nSystem_; probably the part which was most offensive to the\nauthorities. 'Some years ago,' he begins, 'a wholesome edict\nwas promulgated at Rome, which, in order to check the\nperilous scandals of the present age, imposed silence upon\nthe Pythagorean opinion of the mobility of the earth. There\nwere not wanting,' he proceeds, 'persons who rashly asserted\nthat this decree was the result, not of a judicious inquiry,\nbut of passion ill-informed; and complaints were heard that\ncouncillors, utterly unacquainted with astronomical\nobservation, ought not to be allowed, with their sudden\nprohibitions, to clip the wings of speculative intellects.\n_At the hearing of rash lamentations like these, my zeal\ncould not keep silence._' And he then goes on to say, that\nhe wishes, in his _Dialogue_, to show that the subject had\nbeen fully examined at Rome. Here the irony is quite\ntransparent, and the sarcasm glaringly obvious. I think we\nmay venture to say that this is not the temper in which\nscientific questions should be treated; although by some,\nperhaps, the prohibition of public discussion may be\nconsidered as justifying any evasion which is likely to pass\nunpunished. {311}\n\n12. _Duty of Mutual Forbearance._--We may add, as a further\nreason for mutual forbearance in such cases, that the true\ninterests of both parties are the same. The man of science\nis concerned, no less than any other person, in the truth\nand import of the divine dispensation; the religious man, no\nless than the man of science, is, by the nature of his\nintellect, incapable of believing two contradictory\ndeclarations. Hence they have both alike a need for\nunderstanding the Scripture in some way in which it shall be\nconsistent with their understanding of nature. It is for\ntheir common advantage to conciliate, as Kepler says, the\nfinger and the tongue of God, his works and his word. And\nthey may find abundant reason to bear with each other, even\nif they should adopt for this purpose different\ninterpretations, each finding one satisfactory to himself;\nor if any one should decline employing his thoughts on such\nsubjects at all. I have elsewhere[23\\10] quoted a passage\nfrom Kepler[24\\10] which appears to me written in a most\nsuitable spirit: 'I beseech my reader that, not unmindful of\nthe divine goodness bestowed upon man, he do with me praise\nand celebrate the wisdom of the Creator, which I open to him\nfrom a more inward explication of the form of the world,\nfrom a searching of causes, from a detection of the errours\nof vision; and that thus not only in the firmness and\nstability of the earth may we perceive with gratitude the\npreservation of all living things in nature as the gift of\nGod: but also that in its motion, so recondite, so\nadmirable, we may acknowledge the wisdom of the Creator. But\nwhoever is too dull to receive this science, or too weak to\nbelieve the Copernican system without harm to his piety,\nhim, I say, I advise that, leaving the school of astronomy,\nand condemning, if so he please, any doctrines of the\nphilosophers, he follow his own path, and desist from this\nwandering through the universe; and that, lifting up his\nnatural eyes, with which alone he can see, {312} he pour\nhimself out from his own heart in worship of God the\nCreator, being certain that he gives no less worship to God\nthan the astronomer, to whom God has given to see more\nclearly with his inward eyes, and who, from what he has\nhimself discovered, both can and will glorify God.'\n\n[Note 23\\10: _Bridgewater Tr._ p. 314.]\n\n[Note 24\\10: _Com. Stell. Mart._ Introd.]\n\n13. _Case of Galileo._--I may perhaps venture here to make a\nremark or two upon this subject with reference to a charge\nbrought against a certain portion of the _History of the\nInductive Sciences_. Complaint has been made[25\\10] that the\ncharacter of the Roman church, as shown in its behaviour\ntowards Galileo, is misrepresented in the account given of\nit in the History of Astronomy. It is asserted that Galileo\nprovoked the condemnation he incurred; first, by\npertinaciously demanding the assent of the ecclesiastical\nauthorities to his opinion of the consistency of the\nCopernican doctrine with Scripture; and afterwards by\ncontumaciously, and, as we have seen, contumeliously\nviolating the silence which the Church had enjoined upon\nhim. It is further declared that the statement which\nrepresents it as the habit of the Roman church to dogmatize\non points of natural science is unfounded; as well as the\nopinion that in consequence of this habit, new scientific\ntruths were promulgated less boldly in Italy than in other\ncountries. I shall reply very briefly on these subjects; for\nthe decision of them is by no means requisite in order to\nestablish the doctrines to which I have been led in the\npresent chapter, nor, I hope, to satisfy my reader that my\nviews have been collected from an impartial consideration of\nscientific history.\n\n[Note 25\\10: _Dublin Review_, No. ix. July, 1838, p. 72.]\n\nWith regard to Galileo, I do not think it can be denied that\nhe obtruded his opinions upon the ecclesiastical authorities\nin an unnecessary and imprudent manner. He was of an ardent\ncharacter, strongly convinced himself, and urged on still\nmore by the conviction which he produced among his\ndisciples, and {313} thus he became impatient for the\ntriumph of truth. This judgment of him has recently been\ndelivered by various independent authorities, and has\nundoubtedly considerable foundation[26\\10]. As to the\nquestion whether authority in matters of natural science\nwere habitually claimed by the authorities of the Church of\nRome, I have to allow that I cannot produce instances which\nestablish such a habit. We, who have been accustomed to have\ndaily before our eyes the Monition which the Romish editors\nof Newton thought it necessary to prefix--_C\u00e6terum latis a\nsummo Pontifice contra telluris motum Decretis, nos obsequi\nprofitemur_--were not likely to conjecture that this was a\nsolitary instance of the interposition of the Papal\nauthority on such subjects. But although it would be easy to\nfind declarations of heresy delivered by Romish\nUniversities, and writers of great authority, against tenets\nbelonging to the natural sciences, I am not aware that any\nother case can be adduced in which the Church or the Pope\ncan be shown to have pronounced such a sentence. I am well\ncontented to acknowledge this; for I should be far more\ngratified by finding myself compelled to hold up the\nseventeenth century as a model for the nineteenth in this\nrespect, than by having to sow enmity between the admirers\nof the past and the present through any disparaging\ncontrast[27\\10].\n\n[Note 26\\10: Besides the _Dublin Review_, I may quote the\n_Edinburgh Review_, which I suppose will not be thought\nlikely to have a bias in favour of the exercise of\necclesiastical authority in matters of science; though\ncertainly there is a puerility in the critic's phraseology\nwhich does not add to the weight of his judgment. 'Galileo\ncontrived to surround the truth with every variety of\nobstruction. The tide of knowledge, which had hitherto\nadvanced in peace, he crested with angry breakers, and he\ninvolved in its surf both his friends and his foes.'--_Ed.\nRev._ No. cxxiii. p. 126.]\n\n[Note 27\\10: I may add that the most candid of the adherents\nof the Church of Rome condemn the assumption of authority in\nmatters of science, made, in this one instance at least, by\nthe ecclesiastical tribunals. The author of the _Ages of\nFaith_ (book viii. p. 248), says, 'A Congregation, it is to\nbe lamented, declared the new system to be opposed to\nScripture, and therefore heretical.']\n\n{314} With respect to the attempt made in my History to\ncharacterize the intellectual habits of Italy as produced by\nher religious condition,--certainly it would ill become any\nstudent of the history of science to speak slightingly of\nthat country, always the mother of sciences, always ready to\ncatch the dawn and hail the rising of any new light of\nknowledge. But I think our admiration of this activity and\nacuteness of mind is by no means inconsistent with the\nopinion, that new truths were promulgated more boldly beyond\nthe Alps, and that the subtilty of the Italian intellect\nloved to insinuate what the rough German bluntly asserted.\nOf the decent duplicity with which forbidden opinions were\nhandled, the reviewer himself gives us instances, when he\nboasts of the liberality with which Copernican professors\nwere placed in important stations by the ecclesiastical\nauthorities, soon after the doctrine of the motion of the\nearth had been declared by the same authorities to be\ncontrary to Scripture. And in the same spirit is the process\nof demanding from Galileo a public and official recantation\nof opinions which he had repeatedly been told by his\necclesiastical superiors he might hold as much as he\npleased. I think it is easy to believe that among persons so\nlittle careful to reconcile public profession with private\nconviction, official decorum was all that was demanded. When\nGalileo had made his renunciation of the earth's motion on\nhis knees, he rose and said, as we are told, _E pur si\nmuove_--'and yet it _does_ move.' This is sometimes\nrepresented as the heroic soliloquy of a mind cherishing its\nconviction of the truth, in spite of persecution; I think we\nmay more naturally conceive it uttered as a playful epigram\nin the ear of a cardinal's secretary, with a full knowledge\nthat it would be immediately repeated to his master[28\\10].\n\n[Note 28\\10: I have somewhat further discussed the case of\nGalileo in the later editions of the _History_, book v.\nchap. iii. sect. 4.]\n\nBesides the Ideas involved in the material sciences, {315}\nof which we have already examined the principal ones, there\nis one Idea or Conception which our Sciences do not indeed\ninclude, but to which they not obscurely point; and the\nimportance of this Idea will make it proper to speak of it,\nthough this must be done very briefly.\n\n\n\n\n{{316}}\nCHAPTER V.\n\nOF THE CONCEPTION OF A FIRST CAUSE.\n\n\n1. AT the end of the last chapter but one, we were led to\nthis result,--that we cannot, in any of the Pal\u00e6tiological\nSciences, ascend to a beginning which is of the same nature\nas the existing cause of events, and which depends upon\ncauses that are still in operation. Philosophers never have\ndemonstrated, and probably never will be able to\ndemonstrate, what was the original condition of the solar\nsystem, of the earth, of the vegetable and animal worlds, of\nlanguages, of arts. On all these subjects the course of\ninvestigation, followed backwards as far as our materials\nallow us to pursue it, ends at last in an impenetrable\ngloom. We strain our eyes in vain when we try, by our\nnatural faculties, to discern an origin.\n\n2. Yet speculative men have been constantly employed in\nattempts to arrive at that which thus seems to be placed out\nof their reach. The Origin of Languages, the Origin of the\npresent Distribution of Plants and Animals, the Origin of\nthe Earth, have been common subjects of diligent and\npersevering inquiry. Indeed inquiries respecting such\nsubjects have been, at least till lately, the usual form\nwhich Pal\u00e6tiological researches have assumed. _Cosmogony_,\nthe Origin of the World, of which, in such speculations, the\nearth was considered as a principal part, has been a\nfavourite study both of ancient and of modern times: and\nmost of the attempts at Geology previous to the present\nperiod have been _Cosmogonies_ or _Geogonies_, rather than\nthat more genuine science which we have endeavoured to\ndelineate. Again: Glossology, though now an extensive body\nof solid knowledge, was {317} mainly brought into being by\ninquiries concerning the Original Language spoken by men;\nand the nature of the first separation and diffusion of\nlanguages, the first peopling of the earth by man and by\nanimals, were long sought after with ardent curiosity,\nalthough of course with reference to the authority of the\nScriptures, as well as the evidence of natural phenomena.\nIndeed the interest of such inquiries even yet is far from\nbeing extinguished. The disposition to explore the past in\nthe hope of finding, by the light of natural reasoning as\nwell as by the aid of revelation, the origin of the present\ncourse of things, appears to be unconquerable. 'What was the\nbeginning?' is a question which the human race cannot desist\nfrom perpetually asking. And no failure in obtaining a\nsatisfactory answer can prevent inquisitive spirits from\nagain and again repeating the inquiry, although the blank\nabyss into which it is uttered does not even return an echo.\n\n3. What, then, is the reason of an attempt so pertinacious\nyet so fruitless? By what motive are we impelled thus\nconstantly to seek what we can never find? Why are the\nerrour of our conjectures, the futility of our reasonings,\nthe precariousness of our interpretations, over and over\nagain proved to us in vain? Why is it impossible for us to\nacquiesce in our ignorance and to relinquish the inquiry?\nWhy cannot we content ourselves with examining those links\nof the chain of causes which are nearest to us,--those in\nwhich the connexion is intelligible and clear; instead of\nfixing our attention upon those remote portions where we can\nno longer estimate its coherence? In short, why did not men\nfrom the first take for the subject of their speculations\nthe Course of Nature rather than the Origin of Things?\n\nTo this we reply, that in doing what they have thus done, in\nseeking what they have sought, men are impelled by an\nintellectual necessity. They cannot conceive a Series of\nconnected occurrences without a Commencement; they cannot\nhelp supposing a cause for the Whole, as well as a cause for\neach part; they cannot be satisfied with a succession of\ncauses without {318} assuming a First Cause. Such an\nassumption is necessarily impressed upon our minds by our\ncontemplation of a series of causes and effects; that _there\nmust be a First Cause_, is accepted by all intelligent\nreasoners as an Axiom: and like other Axioms, its truth is\nnecessarily implied in the Idea which it involves.\n\n4. The evidence of this axiom may be illustrated in several\nways. In the first place, the axiom is assumed in the\nargument usually offered to prove the existence of the\nDeity. Since, it is said, the world now exists, and since\nnothing cannot produce something, something must have\nexisted from eternity. This Something is the First Cause: it\nis God.\n\nNow what I have to remark here is this:--the conclusiveness\nof this argument, as a proof of the existence of one\nindependent, immutable Deity, depends entirely upon the\nassumption of the axiom above stated. The World, a **series\nof causes and effects, exists: therefore there must be, not\nonly this series of causes and effects, but also a First\nCause. It will be easily seen, that without the axiom, that\nin every series of causes and effects there must be a First\nCause, the reasoning is altogether inconclusive.\n\n5. Or to put the matter otherwise: The argument for the\nexistence of the Deity was stated thus: Something exists,\ntherefore something must have existed from eternity.\n'Granted,' the opponent might say; 'but this something which\nhas existed from eternity, why may it not be this very\nseries of causes and effects which is now going on, and\nwhich appears to contain in itself no indication of\nbeginning or end?' And thus, without the assumption of the\nnecessity of a First Cause, the force of the argument may be\nresisted.\n\n6. But, it may be asked, how do those who have written to\nprove the existence of the Deity reply to such an objection\nas the one just stated? It is natural to suppose that, on a\nsubject so interesting and so long discussed, all the\nobvious arguments with their replies, have been fully\nbrought into view. What is the result in this case? {319}\n\nThe principal modes of replying to the above objection, that\nthe series of causes and effects which now exists, may have\nexisted from eternity, appear to be these.\n\nIn the first place, our minds cannot be satisfied with a\nseries of successive, dependent, causes and effects, without\nsomething first and independent. We pass from effect to\ncause, and from that to a higher cause, in search of\nsomething on which the mind can rest; but if we can do\nnothing but repeat this process, there is no use in it. We\nmove our limbs, but make no advance. Our question is not\nanswered, but evaded. The mind cannot acquiesce in the\ndestiny thus presented to it, of being referred from event\nto event, from object to object, along an interminable vista\nof causation and time. Now this mode of stating the\nreply,--to say that the mind _cannot thus be satisfied_,\nappears to be equivalent to saying that the mind is\nconscious of a Principle, in virtue of which such a view as\nthis must be rejected;--the mind takes refuge in the\nassumption of a First Cause, from an employment inconsistent\nwith its own nature.\n\n7. Or again, we may avoid the objection, by putting the\nargument for the existence of a Deity in this form: The\nseries of causes and effects which we call the _world_, or\nthe _course of nature_, may be considered as a _whole_, and\nthis whole must have a cause of its existence. The whole\ncollection of objects and events may be comprehended as a\nsingle effect, and of this effect there must be a cause.\nThis Cause of the Universe must be superior to, and\nindependent of the special events, which, happening in time,\nmake up the universe of which He is the cause. He must exist\nand exercise causation, before these events can begin: He\nmust be the First Cause.\n\nAlthough the argument is here somewhat modified in form, the\nsubstance is the same as before. For the assumption that we\nmay consider the whole series of causes and effects as a\n_single effect_, is equivalent to the assumption that\nbesides partial causes we must have a First Cause. And thus\nthe Idea of a First Cause, and {320} the axiom which asserts\nits necessity, are recognized in the usual argumentation on\nthis subject.\n\n8. This Idea of a First Cause, and the principle involved in\nthe Idea, have been the subject of discussion in another\nmanner. As we have already said, we assume as an axiom that\na First Cause must exist; and we assert that God, the First\nCause, exists eternal and immutable, by the necessity which\nthe axiom implies. Hence God is said to exist\nnecessarily;--to be a necessarily existing being. And when\nthis _necessary existence_ of God had been spoken of, it\nsoon began to be contemplated as a sufficient reason, and as\nan absolute demonstration of His existence; without any need\nof referring to the world as an effect, in order to arrive\nat God as the cause. And thus men conceived that they had\nobtained a proof of the existence of the Deity, _\u00e0 priori_,\nfrom Ideas, as well as _\u00e0 posteriori_, from Effects.\n\n9. Thus, Thomas Aquinas employs this reasoning to prove the\n_eternity_ of God[29\\10]: 'Oportet ponere aliquod primum\nnecessarium quod est per se ipsum necessarium; et hoc est\nDeus, cum sit prima causa ut dictum est: igitur Deus \u00e6ternus\nest, cum omne necessarium per se sit \u00e6ternum.' It is true\nthat the schoolmen never professed to be able to prove the\n_existence_ of the Deity _\u00e0 priori_: but they made use of\nthis conception of necessary existence in a manner which\napproached very near to such an attempt. Thus Suarez[30\\10]\ndiscusses the question, 'Utrum aliquo modo possit _\u00e0 priori_\ndemonstrari Deum esse.' And resolves the question in this\nmanner: 'Ad hunc ergo modum dicendum est: Demonstrato _\u00e0\nposteriori_ Deum esse ens necessarium et a se, ex hoc\nattributo posse _\u00e0 priori_ demonstrari pr\u00e6ter illud non\nposse esse aliud ens necessarium et a se, et consequenter\ndemonstrari Deum esse.'\n\n[Note 29\\10: Aquin. _Cont. Gentil._ lib. i. c. xiv. p. 21.]\n\n[Note 30\\10: _Metaphys._ tom. ii. disp. xxix. sect. 3, p. 28.]\n\nBut in modern times attempts were made by Descartes and\nSamuel Clarke, to prove the Divine {321} existence at once\n_\u00e0 priori_, from the conception of necessary existence;\nwhich, it was argued, could not subsist without actual\nexistence. This argumentation was acutely and severely\ncriticised by Dr. Waterland.\n\n10. Without dwelling upon a subject, the discussion of which\ndoes not enter into the design of the present work, I may\nremark that the question whether an _\u00e0 priori_ proof of the\nexistence of a First Cause be possible, is a question\nconcerning the nature of our Ideas, and the evidence of the\naxioms which they involve, of the same kind as many\nquestions which we have already had to discuss. Is our\nConception or Idea of a First Cause gathered from the\neffects we see around us? It is plain that we must answer,\nhere as in other cases, that the Idea is not extracted from\nthe phenomena, but assumed in order that the phenomena may\nbecome intelligible to the mind;--that the Idea is a\nnecessary one, inasmuch as it does not depend upon\nobservation for its evidence; but that it depends upon\nobservation for its development, since without some\nobservation, we cannot conceive the mind to be cognizant of\nthe relation of causation at all. In this respect, however,\nthe Idea of a First Cause is no less necessary than the\nideas of Space, or Time, or Cause in general. And whether we\ncall the reasoning derived from such a necessity an argument\n_\u00e0 priori_ or _\u00e0 posteriori_, in either case it possesses\nthe genuine character of demonstration, being founded upon\naxioms which command universal assent.\n\n11. I have, however, spoken of our _Conception_ rather than\nof our _Idea_ of a First Cause; for the notion of a First\nCause appears to be rather a modification of the Fundamental\nIdea of Cause, which was formerly discussed, than a separate\nand peculiar Idea. And the Axiom, _that there must be a\nFirst Cause_, is recognised by most persons as an\napplication of the general Axiom of Causation, _that every\neffect must have a Cause_; this latter Axiom being applied\nto the World, considered in its totality, as a single\nEffect. This distinction, however, between an Idea and a\nConception, is of no material consequence to our argument;\nprovided we {322} allow the maxim, that there must be a\nFirst Cause, to be necessarily and evidently true; whether\nit be thought better to speak of it as an independent Axiom,\nor to consider it as derived from the general Axiom of Causation.\n\n12. Thus we necessarily infer a First Cause, although the\nPal\u00e6tiological Sciences only point _towards_ it, and do not\nlead us _to_ it. But I must observe further; that in each of\nthe series of events which form the subject of\nPal\u00e6tiological research, the First Cause is the _same_.\nWithout here resting upon reasoning founded upon our\nConception of a First Cause, I may remark that this identity\nis proved by the close connexion of all the branches of\nnatural science, and the way in which the causes and the\nevents of each are interwoven with those which belong to the\nothers. We must needs believe that the First Cause which\nproduced the earth and its atmosphere is also the Cause of\nthe plants which clothe its surface; that the First Cause of\nthe vegetable and of the animal world are the same; that the\nFirst Cause which produced light produced also eyes; that\nthe First Cause which produced air and organs of\narticulation produced also language and the faculties by\nwhich language is rendered possible: and if _those_\nfaculties, then also all man's other faculties;--the powers\nby which, as we have said, he discerns right and wrong, and\nrecognises a providential as well as a natural course of\nthings. Nor can we think otherwise than that the Being who\ngave these faculties, bestowed them for some\npurpose;--bestowed them for that purpose which alone is\ncompatible with their nature:--the purpose, namely, of\nguiding and elevating man in his present career, and of\npreparing him for another state of being to which they\nirresistibly direct his hopes. And thus, although, as we\nhave said, no one of the Pal\u00e6tiological Sciences can be\ntraced continuously to an Origin, yet they not only each\npoint to an Origin, but all to the same Origin. Their lines\nare broken indeed, as they run backwards into the early\nperiods of the world, but yet they all appear to converge to\nthe same invisible point. And {323} this point, thus\nindicated by the natural course of things, can be no other\nthan that which is disclosed to us as the starting-point of\nthe providential course of the world; for we are persuaded\nby such reasons as have just been hinted, that the Creator\nof the natural world can be no other than the Author and\nGovernor and Judge of the moral and spiritual world.\n\n13. Thus we are led, by our material Sciences, and\nespecially by the Pal\u00e6tiological class of them, to the\nborders of a higher region, and to a point of view from\nwhich we have a prospect of other provinces of\nknowledge;--to contemplations in which other faculties of\nman are concerned besides his intellectual, other interests\ninvolved besides those of speculation. On these it does not\nbelong to our present plan to dwell: but even such a brief\nglance as we have taken of the connexion of material with\nmoral speculations may not be useless, since it may serve to\nshow that the principles of truth which we are now\nlaboriously collecting among the results of the physical\nsciences, may possibly find some application in those parts\nof knowledge towards which men most naturally look with\ndeeper interest and more serious reverence.\n\n\nWe have been employed hitherto in examining the materials of\nknowledge, Facts and Ideas;--Facts in our former History,\nand Ideas in the present History. We have dwelt at length on\nthis latter element; inasmuch as the consideration of it is,\non various accounts, and especially at the present time, by\nfar the most important, having hitherto been least\ndistinctly attended to as a special element of scientific\nknowledge.\n\nThere still remains an important task, with a view to which\nwe have undertaken this survey of the past course of human\nthought and discovery:--namely, the task of determining the\nprocesses by which these materials may actually be made to\nconstitute knowledge. {324} We have surveyed the stones\nwhich lie before us, partly built and partly ready for\nbuilding: we have found them exactly squared, and often\ncuriously covered with significant imagery and important\ninscriptions. We have now to discover how they may best be\nfitted into their places, and cemented together, so that\nrising stage above stage, they may grow at last into that\nfair and lofty temple of Truth, for which we cannot doubt\nthat they were intended by the Great Architect.\n\nThis task, the description of the processes by which\nScientific Truth is discovered and established, we shall, as\nhas already been said, entitle, in reference to previous\nattempts of the same kind, _Novum Organum Renovatum_.\n\n\nEND OF VOL. II.\n\n\n\n_Cambridge: Printed at the University Press._\n\n\n\n\nTranscriber's Note\n\nWhewell published the first edition of the _Philosophy of the\nInductive Sciences_ in 1840, as a companion to the 1837\n_History of the Inductive Sciences_. Revised second editions\nof both works appeared in 1847. The third editions saw a\nmajor reshaping of the _Philosophy_: a two volume _History\nof Scientific Ideas_ (1858 - the present text, relying upon\nresources kindly provided by the Internet Archive), _Novum\nOrganon Renovatum_ (1858), and _ On the Philosophy of\nDiscovery: chapters historical and critical_ (1860 - already\nin Project Gutenberg's collection: #5155).\n\nThe present text has combined the two volumes into one continuous\ntext. Footnotes are numbered by Book and marked [m\\n] where m =\nthe number of the note within the Book, and n = the number of the\nBook. In the original, notes were numbered by chapter. Page numbers\nappear in { }, or {{ }} where there is no printed number; where a\nword was hyphenated across pages the number has been placed before\nthe word.\n\nSuperscripts are marked with ^.\n\nThere is one significant problem to report. For Book IX chapter VI,\nthe Table of Contents lists 20 articles, but the actual text has\nonly 19 numbered paragraphs. The text version leaves this\ninconsistency untouched; in the htm version, a correction has been\nmade by numbering the paragraph beginning on p. 244 as #9, and\nrenumbering those that follow, thereby matching the descriptions in\nthe Table of Contents.\n\nOther corrections to the text are marked with ** and are listed\nbelow.\n\nLocation Text of printed edition Emendation\nVol. 1\np. 71 conlcusion conclusion\np. 87 vi. vii.\np. 157 sciences science\nnote 1\\3 Book 1. chap. xii. Book 3. chap. ii.\np. 231 Marriotte Mariotte\np. 377 Winter's Winterl's\nVol. 2\np. 22 ingedient ingredient\np. 124 wich which\np. 159 attemps attempts\np. 172 knowlege knowledge\nnote 60\\9 Their. Theor.\np. 270 dfficulties difficulties\np. 318 serious series","title":"History of scientific ideas","tradition":"philosophy-ethics","translated_text":null,"word_count":233803}