{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_69764/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_69764","id":"gutenberg_69764","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/69764","summary":null,"tags":["Category: Philosophy & Ethics","Category: Research Methods/Statistics/Information Sys","Science -- Philosophy"],"text":"NOVUM ORGANON\nRENOVATUM.\n\nBY WILLIAM WHEWELL, D.D.,\n\nMASTER OF TRINITY COLLEGE, CAMBRIDGE, AND\nCORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.\n\nBEING THE SECOND PART OF THE PHILOSOPHY\nOF THE INDUCTIVE SCIENCES.\n\n_THE THIRD EDITION, WITH LARGE ADDITIONS._\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\nLONDON:\nJOHN W. PARKER AND SON, WEST STRAND.\n1858.\n\n\n\n\nIT is to our immortal countryman; Bacon, that we owe the broad\nannouncement of this grand and fertile principle; and the\ndevelopement of the idea, that the whole of natural philosophy\nconsists entirely of a series of inductive generalizations,\ncommencing with the most circumstantially stated particulars, and\ncarried up to universal laws, or axioms, which comprehend in their\nstatements every subordinate degree of generality; and of a\ncorresponding series of inverted reasoning from generals to\nparticulars, by which these axioms are traced back into their\nremotest consequences, and all particular propositions deduced from\nthem; as well those by whose immediate considerations we rose to\ntheir discovery, as those of which we had no previous knowledge.\n\nHERSCHEL, _Discourse on Natural Philosophy_, Art. 96.\n\n\n\nCAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.\n\n\n\n{{iii}}\nPREFACE.\n\n\nEVEN if Bacon's _Novum Organon_ had possessed the character to which\nit aspired as completely as was possible in its own day, it would at\npresent need renovation: and even if no such book had ever been\nwritten, it would be a worthy undertaking to determine the\nmachinery, intellectual, social and material, by which human\nknowledge can best be augmented. Bacon could only divine how\nsciences might be constructed; we can trace, in their history, how\ntheir construction has taken place. However sagacious were his\nconjectures, the facts which have really occurred must give\nadditional instruction: however large were his anticipations, the\nactual progress of science since his time has illustrated them in\nall their extent. And as to the structure and operation of the\n_Organ_ by which truth is to be collected from nature,--that is, the\nMethods by which science is to be promoted--we know that, though\nBacon's general maxims are sagacious and animating, his particular\nprecepts failed in his hands, and are now practically useless. This,\nperhaps, was not wonderful, seeing that they were, as I have said,\nmainly derived from conjectures respecting knowledge and the\nprogress of knowledge; but at {iv} the present day, when, in several\nprovinces of knowledge, we have a large actual progress of solid\ntruth to look back upon, we may make the like attempt with the\nprospect of better success, at least on that ground. It may be a\ntask, not hopeless, to extract from the past progress of science the\nelements of an effectual and substantial method of Scientific\nDiscovery. The advances which have, during the last three centuries,\nbeen made in the physical sciences;--in Astronomy, in Physics, in\nChemistry, in Natural History, in Physiology;--these are allowed by\nall to be real, to be great, to be striking; may it not be that the\nsteps of progress in these different cases have in them something\nalike? May it not be that in each advancing movement of such\nknowledge there is some common principle, some common process? May\nit not be that discoveries are made by an _Organ_ which has\nsomething uniform in its working? If we can shew that this is so, we\nshall have the _New Organ_, which Bacon aspired to construct,\n_renovated_ according to our advanced intellectual position and\noffice.\n\nIt was with the view of opening the way to such an attempt that I\nundertook that survey of the past progress of physical knowledge, of\nwhich I have given the results in the _History of the Sciences_, and\nthe _History of Scientific Ideas_[1\\P]; the former containing the\nhistory of the sciences, so far as it depends on {v} observed\n_Facts_; the latter containing the history of those _Ideas_ by which\nsuch Facts are bound into Theories.\n\n[Note 1\\P: Published in two former editions as part of the\n_Philosophy of the Inductive Sciences_ (b. i--x.).]\n\nIt can hardly happen that a work which treats of Methods of\nScientific Discovery, shall not seem to fail in the positive results\nwhich it offers. For an Art of Discovery is not possible. At each\nstep of the investigation are needed Invention, Sagacity,\nGenius,--elements which no art can give. We may hope in vain, as\nBacon hoped, for an Organ which shall enable all men to construct\nScientific Truths, as a pair of compasses enables all men to\nconstruct exact circles[2\\P]. This cannot be. The practical results\nof the Philosophy of Science must be rather classification and\nanalysis of what has been done, than precept and method for future\ndoing. Yet I think that the methods of discovery which I have to\nrecommend, though gathered from a wider survey of scientific\nhistory, both as to subjects and as to time, than (so far as I am\naware) has been elsewhere attempted, are quite as definite and\npractical as any others which have been proposed; with the great\nadditional advantage of being the methods by which all great\ndiscoveries in science have really been made. This may be said, for\ninstance, of _the Method of Gradation_ and _the Method of Natural\nClassification_, spoken of b. iii. c. viii; and in a narrower sense,\nof _the Method of Curves_, _the Method of_ {vi} _Means_, _the Method\nof Least Squares_ and _the Method of Residues_, spoken of in chap.\nvii. of the same Book. Also the Remarks on the _Use of Hypotheses_\nand on the _Tests of Hypotheses_ (b. ii. c. v.) point out features\nwhich mark the usual course of discovery.\n\n[Note 2\\P: _Nov. Org._ lib. i. aph. 61.]\n\nBut one of the principal lessons resulting from our views is\nundoubtedly this:--that different sciences may be expected to\nadvance by different modes of procedure, according to their present\ncondition; and that in many of these sciences, an Induction\nperformed by any of the methods which have just been referred to is\nnot the next step which we may expect to see made. Several of the\nsciences may not be in a condition which fits them for such a\n_Colligation of Facts_; (to use the phraseology to which the\nsucceeding analysis has led me). The Facts may, at the present time,\nrequire to be more fully observed, or the Idea by which they are to\nbe colligated may require to be more fully unfolded.\n\nBut in this point also, our speculations are far from being barren\nof practical results. The examination to which we have subjected\neach science, gives us the means of discerning whether what is\nneeded for the further progress of the science, has its place in the\nObservations, or in the Ideas, or in the union of the two. If\nobservations be wanted, the Methods of Observation, given in b. iii.\nc. ii. may be referred to. If those who are to make the next\ndiscoveries need, for that purpose, a developement of their Ideas,\nthe modes in which such a developement has usually taken {vii} place\nare treated of in Chapters iii. and iv. of that Book.\n\nNo one who has well studied the history of science can fail to see\nhow important a part of that history is the explication, or as I\nmight call it, the _clarification_ of men's Ideas. This, the\nmetaphysical aspect of each of the physical sciences, is very far\nfrom being, as some have tried to teach, an aspect which it passes\nthrough at an early period of progress, and previously to the stage\nof positive knowledge. On the contrary, the metaphysical movement is\na necessary part of the inductive movement. This, which is evidently\nso by the nature of the case, was proved by a copious collection of\nhistorical evidences, in the _History of Scientific Ideas_. The ten\nBooks of that History contain an account of the principal\nphilosophical controversies which have taken place in all the\nphysical sciences, from Mathematics to Physiology. These\ncontroversies, which must be called _metaphysical_ if anything be so\ncalled, have been conducted by the greatest discoverers in each\nscience, and have been an essential part of the discoveries made.\nPhysical discoverers have differed from barren speculators, not by\nhaving _no_ metaphysics in their heads, but by having _good_\nmetaphysics in their heads while their adversaries had bad; and by\nbinding their metaphysics to their physics, instead of keeping the\ntwo asunder. I trust that the _History of Scientific Ideas_ is of\nsome value, even as a record of a number of remarkable\ncontroversies; but I conceive that it also contains an indisputable\nproof that there {viii} is, in progressive science, a metaphysical\nas well as a physical element;--ideas as well as facts;--thoughts as\nwell as things. Metaphysics is the process of ascertaining that\nthought is consistent with itself: and if it be not so, our\nsupposed knowledge is not knowledge.\n\nIn Chapter vi. of the Second Book, I have spoken of _the Logic of\nInduction_. Several writers[3\\P] have quoted very emphatically my\nassertion that the Logic of Induction does not exist in previous\nwriters: using it as an introduction to Logical Schemes of their\nown. They seem to have overlooked the fact that at the same time\nthat I noted the deficiency, I offered a scheme which I think fitted\nto supply this want. And I am obliged to say that I do not regard\nthe schemes proposed by any of those gentlemen as at all\nsatisfactory for the purpose. But I must defer to a future occasion\nany criticism of authors who have written on the subjects here\ntreated. A critical notice of such authors formed the Twelfth Book\nof the former edition of the _Philosophy of the Sciences_. I have\nthere examined the opinions concerning the Nature of Real Knowledge\nand the mode of acquiring it, which have been promulgated in all\nages, from Plato and Aristotle, to Roger Bacon, to Francis Bacon, to\nNewton, to Herschel. Such a survey, with the additions which I\nshould now have to make to it, may hereafter be put forth as a\nseparate book: but I {ix} have endeavoured to confine the present\nvolume to such positive teaching regarding Knowledge and Science as\nresults from the investigations pursued in the other works of this\nseries. But with regard to this matter, of the _Logic of Induction_,\nI may venture to say, that we shall not find anything deserving the\nname explained in the common writers on Logic, or exhibited under\nthe ordinary Logical Forms. _That_ in previous writers which comes\nthe nearest to the notice of such a Logic as the history of science\nhas suggested and verified, is the striking declaration of Bacon in\ntwo of his Aphorisms (b. i. aph. civ. cv.).\n\n[Note 3\\P: Apelt _Die Theorie der Induction_: Gratry _Logique_.]\n\n\"There will be good hopes for the Sciences then, and not till then,\nwhen by a true SCALE or Ladder, and by successive steps, following\ncontinuously without gaps or breaks, men shall ascend from\nparticulars to the narrower Propositions, from those to intermediate\nones, rising in order one above another, and at last to the most\ngeneral.\n\n\"But in establishing such propositions, we must devise some other\nFORM OF INDUCTION than has hitherto been in use; and this must be\none which serves not only to prove and discover _Principles_, (as very\ngeneral Propositions are called,) but also the narrower and the\nintermediate, and in short, all true Propositions.\"\n\nAnd he elsewhere speaks of successive FLOORS of Induction.\n\nAll the truths of an extensive science form a Series of such Floors,\nconnected by such Scales or Ladders; and a part of the Logic of\nInduction consists, as I {x} conceive, in the construction of a\n_Scheme_ of such Floors. Converging from a wide basis of various\nclasses of particulars, at last to one or a few general truths,\nthese schemes necessarily take the shape of a Pyramid. I have\nconstructed such Pyramids for Astronomy and for Optics[4\\P]; and the\nillustrious Von Humboldt in speaking of the former subject, does me\nthe honour to say that my attempt in that department is perfectly\nsuccessful[5\\P]. The Logic of Induction contains other portions,\nwhich may be seen in the following work, b. ii. c. vi.\n\n[Note 4\\P: See the Tables at the end of book ii.]\n\n[Note 5\\P: _Cosmos_, vol. ii. n. 35.]\n\nI have made large additions to the present edition, especially in\nwhat regards the Application of Science, (b. iii. c. ix.) and the\nLanguage of Science. The former subject I am aware that I have\ntreated very imperfectly. It would indeed, of itself, furnish\nmaterial for a large work; and would require an acquaintance with\npractical arts and manufactures of the most exact and extensive\nkind. But even a general observer may see how much more close the\nunion of Art with Science is now than it ever was before; and what\nlarge and animating hopes this union inspires, both for the progress\nof Art and of Science. On another subject also I might have dilated\nto a great extent,--what I may call (as I have just now called it)\nthe _social_ machinery for the advancement of science. There can be\nno doubt that at certain stages of sciences, {xi} Societies and\nAssociations may do much to promote their further progress; by\ncombining their observations, comparing their views, contributing to\nprovide material means of observation and calculation, and dividing\nthe offices of observer and generalizer. We have had in Europe in\ngeneral, and especially in this country, very encouraging examples\nof what may be done by such Associations. For the present I have\nonly ventured to propound one Aphorism on the subject, namely this;\n(Aph. LV.) That it is worth considering whether a continued and\nconnected system of observation and calculation, like that of\nAstronomy, might not be employed in improving our knowledge of other\nsubjects; as Tides, Currents, Winds, Clouds, Rain, Terrestrial\nMagnetism, Aurora Borealis, composition of crystals, and the like.\nIn saying this, I have mentioned those subjects which are, as\nappears to me, most likely to profit by continued and connected\nobservations.\n\nI have thrown the substance of my results into Aphorisms, as Bacon\nhad done in his _Novum Organum_. This I have done, not in the way of\ndelivering dogmatic assertions or oracular sentences; for the\nAphorisms are all supported by reasoning, and were, in fact, written\nafter the reasoning, and extracted from it. I have adopted this mode\nof gathering results into compact sentences, because it seems to\nconvey lessons with additional clearness and emphasis.\n\nI have only to repeat what I have already said; that this task of\nadapting the _Novum Organum_ to the {xii} present state of Physical\nScience, and of constructing a _Newer Organ_ which may answer the\npurposes at which Bacon aimed, seems to belong to the present\ngeneration; and being here founded upon a survey of the past history\nand present condition of the Physical Sciences, will I hope, not be\ndeemed presumptuous.\n\n TRINITY LODGE,\n\n 1 _November_, 1858.\n\n\n\n{{xiii}}\nTABLE OF CONTENTS.\n\n\n PAGE\nPREFACE **iii\n\n\n\nBOOK I.\nAPHORISMS CONCERNING IDEAS.\n\nAPHORISMS I.--XVIII. Ideas in general 5--7\n XIX.--XLIV. Ideas in the Pure Sciences 8--12\n XLV.--LV. Ideas in the Mechanical Sciences 13--15\n LVI.--LXXI. Ideas in the Secondary Mechanical\n Sciences. 15--18\n LXXII.--**LXXIII. Ideas in the Mechanico-chemical\n Sciences 18\n LXXIV.--LXXIX. Ideas in Chemistry 18\n LXXX.--LXXXI. Ideas in Morphology 19\n **LXXXII.--C. Ideas in Classificatory Science 20--23\n CI.--CVI. Ideas in Biology 23--24\n CVII.--CXVII. Ideas in Pal\u00e6ontology 24--26\n\nBOOK II.\nOF KNOWLEDGE.\n\nCHAP. I. OF TWO PRINCIPAL PROCESSES BY WHICH SCIENCE IS\n CONSTRUCTED 27\n\nCHAP. II. OF THE EXPLICATION OF CONCEPTIONS 30\n _Sect._ I. _The Historical Progress._\n _Art._ 1. The Explication of Conceptions,\n 2. Has taken place historically by discussions.\n{xiv}\n _Art._ 3. False Doctrines when exposed appear impossible:\n 4. But were plausible before\n 5. Men's Minds gradually cleared.\n _Sect._ II. _Use of definitions._\n _Art._ 6. Controversies about Definitions.\n 7. Not arbitrary Definitions.\n 8. Attention to Facts requisite.\n 9. Definition is not essential.\n 10. The omission of Definition not always blameable.\n _Sect._ III. _Use of Axioms._\n _Art._ 11. Axioms serve to express Ideas.\n _Sect._ IV. _Clear and appropriate Ideas._\n _Art._ 12. We must see the Axioms clearly.\n 13. Inappropriate Ideas cannot lead to Truth.\n 14. The fault is in the Conceptions.\n 15. Rules cannot teach Discovery;\n 16. But are not useless.\n 17. Discussion as well as Facts needed.\n _Sect._ V. _Accidental Discoveries._\n _Art._ 18. No Scientific Discovery is accidental.\n 19. Such accidents do not happen to common Men.\n 20. Examples.\n 21. So far Explication of Conceptions.\n\nCHAP. III. OF FACTS AS THE MATERIALS OF SCIENCE 50\n _Art._ 1. Facts must be true.\n 2. Facts not separable from Ideas.\n 3. The Ideas must be distinct.\n 4. Conceptions of the Intellect only to be admitted.\n 5. Facts are to be observed with reference to\n Space and Time:\n 6. And also to other Ideas.\n 7. The Decomposition of Facts.\n{xv}\n _Art._ 8. This step is not sufficient.\n 9. It introduces Technical Terms,\n 10. And Classification.\n 11. The materials of Science.\n\nCHAP. IV. OF THE COLLIGATION OF FACTS 59\n _Art._ 1. Facts are colligated by Conceptions.\n 2. Science begins with common Observation.\n 3. Facts must be decomposed.\n 4. What Ideas first give Sciences.\n 5. Facts must be referred to Ideas.\n 6. Sagacity needed.\n 7. Discovery made by Guesses.\n 8. False Hypotheses preluding to true ones.\n 9. New Hypotheses not mere modifications of old ones.\n 10. Hypotheses may have superfluous parts.\n 11. Hypotheses to be compared with Facts.\n 12. Secondary Steps.\n\nCHAP. V. OF CERTAIN CHARACTERISTICS OF SCIENTIFIC INDUCTION 70\n _Sect._ I. _Invention a part of Induction._\n _Art._ 1. Induction the source of Knowledge.\n 2. Induction involves a New Element.\n 3. Meaning of Induction.\n 4. The New Element is soon forgotten.\n 5. Induction includes a Definition and a Proposition.\n _Sect._ II. _Use of Hypotheses._\n _Art._ 6. Discoveries made by Guesses,\n 7. Which must be compared with Facts.\n 8. Hypotheses are suspected.\n 9. Hypotheses may be useful though inaccurate.\n _Sect._ III. _Tests of Hypotheses._\n _Art._ 10. True Hypotheses foretel Phenomena,\n 11. Even of different kinds.--Consilience of Inductions.\n{xvi}\n _Art._ 12. True Theories tend to Simplicity.\n 13. Connexion of the last Tests.\n\nCHAP. VI. OF THE LOGIC OF INDUCTION 97\n _Art._ 1. Steps of Generalization,\n 2. May be expressed by _Tables_.\n 3. Which exhibit Inductive Steps;\n 4. And the Consilience of Inductions;\n 5. And the tendency to Simplicity;\n 6. And the names of Discoverers;\n 7. And the Verifications of Theory;\n 8. By means of several easy steps.\n 9. This resembles Book-keeping.\n 10. The Logic of Induction.\n 11. Attention at each step required.\n 12. General Truths are not mere additions of\n particulars:\n 13. But a new view is introduced.\n 14. Formula of Inductive Logic:\n 15. May refer to Definition.\n 16. Formula inadequate.\n 17. Deductive Connexion of Steps.\n 18. Relation of Deductive and Inductive Reasoning.\n 19. The Criterion of Truth.\n 20. Theory and Fact.\n 21. Higher and Lower Generalizations.\n\nCHAP. VII. OF LAWS OF PHENOMENA AND OF CAUSES 118\n _Art._ 1. Knowledge of Laws of Phenomena.\n 2. _Formal_ and _Physical_ Sciences.\n 3. Causes in Astronomy.\n 4. Different Mechanical Causes in other Sciences.\n 5. Chemical and Vital Forces as Causes.\n 6. Difference of these kinds of Force.\n 7. Difficulty of conceiving new Causes.\n 8. Men willingly take old Causes.\n 9. Is the Magnetic Fluid real?\n 10. Are Causes to be sought? (Comte's Doctrine.)\n 11. Both Laws and Causes to be studied.\n{xvii}\n\nCHAP. VIII. OF ART AND SCIENCE 129\n _Art._ 1. Art precedes Science.\n 2. Contrast of Art and Science.\n 3. Instinct and Insight.\n 4. Difference of Art and Instinct.\n 5. Does Art involve Science?\n 6. Science unfolds Principles.\n 7. Science may improve Art.\n 8. Arts not classified with Sciences.\n\nCHAP. IX. OF THE CLASSIFICATION OF SCIENCES 136\n _Art._ 1. Use and Limits of such Classification.\n 2. Classification depends on the Ideas.\n 3. This points out Transitions.\n 4. The Classification.\n\nINDUCTIVE TABLE OF ASTRONOMY 140\n\nINDUCTIVE TABLE OF OPTICS 140\n\nBOOK III.\nOF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.\n\nCHAP. I. INTRODUCTION 141\n _Art._ 1. Object of this Book.\n 2. An Art of Discovery not possible.\n 3. Use of Methods.\n 4. Series of Six Processes.\n 5. Methods of Observation and Induction.\n\nCHAP. II. OF METHODS OF OBSERVATION 145\n _Art._ 1. Referring to Number, Space, and Time.\n 2. Observations are never perfect.\n 3. (I.) _Number is naturally exact_.\n 4. (II.) _Measurement of Space_.\n 5. Instruments Invented in Astronomy,\n 6. And improved.\n{xviii}\n _Art._ 7. Goniometer.\n 8. Standard of Length.\n 10. (III.) _Measurement of Time_.\n 11. Unit of Time.\n 12. Transit Instrument.\n 13. Chronometers.\n 14. (IV.) _Conversion of Space and Time_.\n 15. Space may Measure Time.\n 16. Time may Measure Space.\n 17. (V.) _The Method of Repetition_.\n 18. The Method of Coincidences.\n 19. Applied to Pendulums.\n 20. (VI.) _Measurement of Weight_.\n 21. Standard of Weight.\n 22. (VII.) _Measurement of Secondary Qualities_.\n 23. \"The Howl\" in Harmonics.\n 24. (VIII.) _Manipulation_.\n 25. Examples in Optics.\n 26. (IX.) _The Education of the Senses_,\n 27. By the Study of Natural History.\n 28. Preparation for Ideas.\n\nCHAP. III. OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS;\n _and first_ OF INTELLECTUAL EDUCATION 164\n _Art._ 1. (I.) _Idea of Space_.\n 2. Education by Geometry.\n 3. (II.) _Idea of Number_.\n 4. Effect of the usual Education.\n 5. (III.) _Idea of Force_.\n 6. Study of Mechanics needed,\n 7. To make Newton intelligible.\n 8. No _Popular_ Road.\n 9. (IV.) _Chemical Ideas_.\n 10. (V.) _Natural History Ideas_.\n 11. Natural Classes to be taught.\n 12. Mathematical Prejudices,\n 13. To be corrected by Natural History.\n 14. Method of Natural History,\n 15. Resembles common language.\n{xix}\n _Art._ 16. Its Lessons.\n 17. (VI.) _Well-established Ideas alone to be used_.\n 18. How are Ideas cleared?\n\nCHAP. IV. OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS,\n _continued_.--OF THE DISCUSSION OF IDEAS 180\n _Art._ 1. Successive Clearness,\n 2. Produced by Discussion.\n 3. Examples.\n 4. Disputes not useless,\n 5. Although \"metaphysical.\"\n 6. Connected with Facts.\n\nCHAP. V. ANALYSIS OF THE PROCESS OF INDUCTION 186\n _Sect._ I. _The Three Steps of Induction._\n _Art._ 1. Methods may be useful.\n 2. The three Steps.\n 3. Examples.\n 4. Mathematical names of the Steps.\n _Sect._ II. _Of the Selection of the Fundamental Idea._\n _Art._ 5. Examples.\n 6. The Idea to be found by trying,\n 7. Till the Discovery is made;\n 8. Preluded by Guesses.\n 9. Idea and Facts homogeneous.\n 10. Idea tested by the Facts.\n\nCHAP. VI. GENERAL RULES FOR THE CONSTRUCTION OF THE CONCEPTION 195\n _Art._ 1. First: for Quantity.\n 2. Formula and Coefficients found together.\n 3. Example. Law of Cooling.\n 4. Determined by Experiment.\n 5. Progressive Series of Numbers.\n 6. Recurrent Series.\n 7. Use of Hypotheses.\n 8. Even with this there are difficulties.\n{xv}\n\nCHAP. VII. SPECIAL METHODS OF INDUCTION APPLICABLE TO QUANTITY 202\n _Sect._ I. _The Method of Curves._\n _Art._ 1. Its Process.\n 2. Its Use.\n 3. With imperfect Observations.\n 4. It corrects Observations.\n 5. _Obstacles_. (I.) Ignorance of the argument.\n 6. (II.) Combination of Laws.\n _Sect._ II. _The Method of Means._\n _Art._ 7. Its Relation to the Method of Curves.\n 8. Its process.\n 9. _Argument_ required to be known.\n 10. Use of the Method.\n 11. Large masses of Observations used.\n 12. Proof of the Use of the Method.\n _Sect._ III. _The Method of Least Squares._\n _Art._ 13. Is a Method of Means.\n 14. Example.\n _Sect._ IV. _The Method of Residues._\n _Art._ 15. Occasion for its Use.\n 16. Its Process.\n 17. Examples.\n 18. Its Relation to the Method of Means.\n 19. Example.\n 20. \"Residual Phenomena.\"\n\nCHAP. VIII. METHODS OF INDUCTION DEPENDING ON RESEMBLANCE 220\n _Sect._ I. _The Law of Continuity._\n _Art._ 1. Its Nature and Application,\n 2. To Falling Bodies,\n 3. To Hard Bodies,\n 4. To Gravitation.\n 5. The Evidence.\n{xxi}\n _Sect._ II. _The Method of Gradation._\n _Art._ 6. Occasions of its Use.\n 7. Examples.\n 8. Not enjoined by Bacon.\n 9. Other Examples.\n 10. Its Value in Geology.\n 11. Limited Results.\n _Sect._ III. _The Method of Natural Classification._\n _Art._ 12. Examples of its Use.\n 13. Its Process.\n 14. Negative Results.\n 15. Is opposed to Arbitrary Definitions.\n 16. Propositions and Definitions correlative.\n 17. Definitions only provisional.\n\nCHAP. IX. OF THE APPLICATION OF INDUCTIVE TRUTHS 233\n _Art._ 1. This forms the Sequel of Discovery.\n 2. Systematic Verification of Discoveries.\n 3. Correction of Coefficients.\n 4. Astronomy a Model.\n 5. Verification by new cases.\n 6. Often requires fresh calculation.\n 7. Cause of Dew.\n 8. Useful Applications.\n\nCHAP. X. OF THE INDUCTION OF CAUSES 247\n _Art._ 1. Is to be pursued.\n 2. Induction of Substance.\n 3. Induction of Force.\n 4. Induction of Polarity.\n 5. Is Gravity Polar?\n 6. Induction of Ulterior Causes.\n 7. Of the Supreme Cause.\n{xxii}\n\nBOOK IV,\nOF THE LANGUAGE OF SCIENCE.\n\nINTRODUCTION 257\n\n APHORISMS CONCERNING THE LANGUAGE OF SCIENCE.\n\n_Aphorism_ I. Relative to the Ancient Period 258\n _Art._ 1. Common Words.\n 2. Descriptive Terms.\n 3. Theoretical Terms.\n_Aphorism_ II. Relative to the Modern Period 269\n _Art._ 1. Systematic Nomenclature.\n 2. Systematic Terminology.\n 3. Systematic Modification.\n_Aphorisms_ (III. IV. V. VI. VII) relative to the\n Application of Common Words 278\n_Aphorisms_ (VIII. IX. X. XI. XII. XIII.) relative to the\n Construction of New Terms 285\n_Aphorism_ XIV. Binary Nomenclature 307\n XV. Linn\u00e6an Maxims 308\n XVI. Numerical Names 309\n XVII. Names of more than two Steps 310\n XVIII. No arbitrary _Terms_ 311\n XIX. Forms fixed by Convention 314\n XX. _Form_ of Terms 318\n _Art._ 1. Terms derived from Latin and Greek.\n 2. German Terms.\n 3. Descriptive Terms.\n 4. Nomenclature. Zoology.\n 5. ------------- Mineralogy.\n 6. ------------- Botany.\n 7. ------------- Chemistry.\n 8. ------------- Crystallography.\n{xxiii}\n_Aphorism_ XXI. Philological Rules 328\n _Art._ 1. Hybrids.\n 2. Terminations of Substantives.\n 3. Formations of Substantives (names of things).\n 4. Abstract Substantives.\n 5. Rules of derivation from Greek and Latin.\n 6. Modification of Terminations.\n_Aphorism_ XXII. Introduction of Changes 341\n\nFURTHER ILLUSTRATIONS OF THE APHORISMS ON SCIENTIFIC\n LANGUAGE, FROM THE RECENT COURSE OF SCIENCES.\n\n1. BOTANY.\n_Aphorism_ XXIII. Multiplication of Genera 346\n\n2. COMPARATIVE ANATOMY.\n_Aphorism_ XXIV. Single Names to be used 353\n XXV. The History of Science is the History\n of its Language 355\n XXVI. Algebraical Symbols 357\n XXVII. Algebraical Analogies 364\n XXVIII. Capricious Derivations 365\n XXIX. Inductions are our Definitions 368\n\n\n\n{{1}}\nNOVUM ORGANON RENOVATUM.\n\n\n\n\nDE Scientiis tum demum bene sperandum est, quando per SCALAM veram\net per gradus continuos, et non intermissos aut hiulcos, a\nparticularibus ascendetur ad Axiomata minora, et deinde ad media,\nalia aliis superiora, et postremo demum ad generalissima.\n\nIn constituendo autem Axiomate, Forma INDUCTIONIS alia quam adhuc in\nusu fuit, excogitanda est; et qu\u00e6 non ad Principia tantum (qu\u00e6\nvocant) probanda et invenienda, sed etiam ad Axiomata minora, et\nmedia, denique omnia.\n\n BACON, _Nov. Org._, Aph. civ. cv.\n\n\n\n{{3}}\nNOVUM ORGANON RENOVATUM.\n\n\nTHE name _Organon_ was applied to the works of Aristotle which\ntreated of Logic, that is, of the method of establishing and proving\nknowledge, and of refuting errour, by means of Syllogisms. Francis\nBacon, holding that this method was insufficient and futile for the\naugmentation of real and useful knowledge, published his _Novum\nOrganon_, in which he proposed for that purpose methods from which\nhe promised a better success. Since his time real and useful\nknowledge has made great progress, and many Sciences have been\ngreatly extended or newly constructed; so that even if Bacon's\nmethod had been the right one, and had been complete as far as the\nprogress of Science up to his time could direct it, there would be\nroom for the revision and improvement of the methods of arriving at\nscientific knowledge.\n\nInasmuch as we have gone through the _Histories_ of the principal\n_Sciences_, from the earliest up to the present time, in a previous\nwork, and have also traced the _History of Scientific Ideas_ in\nanother work, it may perhaps be regarded as not too presumptuous if\nwe attempt this revision and improvement of the methods by which\nSciences must rise and grow. This {4} is our task in the present\nvolume; and to mark the reference of this undertaking to the work of\nBacon, we name our book _Novum Organon Renovatum_.\n\nBacon has delivered his precepts in Aphorisms, some of them stated\nnakedly, others expanded into dissertations. The general results at\nwhich we have arrived by tracing the history of Scientific Ideas are\nthe groundwork of such Precepts as we have to give: and I shall\ntherefore begin by summing up these results in Aphorisms, referring\nto the former work for the historical proof that these Aphorisms are\ntrue.\n\n\n\n{{5}}\nNOVUM ORGANON RENOVATUM.\n\n\n\nBOOK I.\n\nAPHORISMS CONCERNING IDEAS DERIVED FROM THE HISTORY OF IDEAS.\n\n\nI.\n\n_MAN is the Interpreter of Nature, Science the right\ninterpretation._ (_History of Scientific Ideas_: Book I. Chapter 1.)\n\nII.\n\n_The_ Senses _place before us the_ Characters _of the Book of\nNature; but these convey no knowledge to us, till we have discovered\nthe Alphabet by which they are to be read._ (Ibid. I. 2.)\n\nIII.\n\n_The_ Alphabet, _by means of which we interpret Phenomena, consists\nof the_ Ideas _existing in our own minds; for these give to the\nphenomena that coherence and significance which is not an object of\nsense._ (I. 2.)\n\nIV.\n\n_The antithesis of_ Sense _and_ Ideas _is the foundation of the\nPhilosophy of Science. No knowledge can exist without the union, no\nphilosophy without the separation, of these two elements._ (I. 2.)\n{6}\n\nV.\n\nFact _and_ Theory _correspond to Sense on the one hand, and to Ideas\non the other, so far as we are_ conscious _of our Ideas: but all facts\ninvolve ideas_ unconsciously; _and thus the distinction of Facts and\nTheories is not tenable, as that of Sense and Ideas is._ (I. 2.)\n\nVI.\n\n_Sensations and Ideas in our knowledge are like Matter and Form in\nbodies. Matter cannot exist without Form, nor Form without Matter:\nyet the two are altogether distinct and opposite. There is no\npossibility either of separating, or of confounding them. The same\nis the case with Sensations and Ideas._ (I. 2.)\n\nVII.\n\n_Ideas are not_ trans_formed, but_ in_formed Sensations; for without\nideas, sensations have no form._ (I. 2.)\n\nVIII.\n\n_The Sensations are the_ Objective, _the Ideas the_ Subjective _part\nof every act of perception or knowledge._ (I. 2.)\n\nIX.\n\n_General Terms denote_ Ideal Conceptions, _as a_ circle, _an_ orbit,\n_a_ rose. _These are not_ Images _of real things, as was held by the\nRealists, but Conceptions: yet they are conceptions, not bound\ntogether by mere_ Name, _as the Nominalists held, but by an Idea._\n(I. 2.)\n\nX.\n\n_It has been said by some, that all Conceptions are merely_ states\n_or_ feelings of the mind, _but this assertion only tends to\nconfound what it is our business to distinguish._ (I. 2.)\n\nXI.\n\n_Observed Facts are connected so as to produce new truths, by\nsuperinducing upon them an Idea: and such truths are obtained_ by\nInduction. (I. 2.) {7}\n\nXII.\n\n_Truths once obtained by legitimate Induction are Facts: these Facts\nmay be again connected, so as to produce higher truths: and thus we\nadvance to_ Successive Generalizations. (I. 2.)\n\nXIII.\n\n_Truths obtained by Induction are made compact and permanent by\nbeing expressed in_ Technical Terms. (I. 3.)\n\nXIV.\n\n_Experience cannot conduct us to universal and necessary\ntruths:--Not to universal, because she has not tried all cases:--Not\nto necessary, because necessity is not a matter to which experience\ncan testify._ (I. 5.)\n\nXV.\n\n_Necessary truths derive their necessity from the_ Ideas _which they\ninvolve; and the existence of necessary truths proves the existence\nof Ideas not generated by experience._ (I. 5.)\n\nXVI.\n\n_In Deductive Reasoning, we cannot have any truth in the conclusion\nwhich is not virtually contained in the premises._ (I. 6.)\n\nXVII.\n\n_In order to acquire any exact and solid knowledge, the student must\npossess with perfect precision the ideas appropriate to that part of\nknowledge: and this precision is tested by the student's_ perceiving\n_the axiomatic evidence of the_ axioms _belonging to each_\nFundamental Idea. (I. 6.)\n\nXVIII.\n\n_The Fundamental Ideas which it is most important to consider, as\nbeing the Bases of the Material Sciences, are the Ideas of_ Space,\nTime (_including Number_), Cause (_including Force and Matter_),\nOutness _of Objects, and_ Media _of Perception of Secondary\nQualities,_ Polarity (_Contrariety_), {8} _Chemical_ Composition\n_and_ Affinity, Substance, Likeness _and Natural_ Affinity, Means\nand Ends (_whence the Notion of Organization_), Symmetry, _and the\nIdeas of_ Vital Powers. (I. 8.)\n\nXIX.\n\n_The Sciences which depend upon the Ideas of Space and Number are_\nPure _Sciences, not_ Inductive _Sciences: they do not infer special\nTheories from Facts, but deduce the conditions of all theory from\nIdeas. The Elementary Pure Sciences, or Elementary Mathematics, are\nGeometry, Theoretical Arithmetic and Algebra._ (II. 1.)\n\nXX.\n\n_The Ideas on which the Pure Sciences depend, are those of_ Space\n_and_ Number; _but Number is a modification of the conception of\nRepetition, which belongs to the Idea of_ Time. (II. 1.)\n\nXXI.\n\n_The_ Idea of Space _is not derived from experience, for experience\nof external objects_ pre_supposes bodies to exist in Space, Space is a\ncondition under which the mind receives the impressions of sense,\nand therefore the relations of space are necessarily and universally\ntrue of all perceived objects. Space is a_ form _of our perceptions,\nand regulates them, whatever the_ matter _of them may be._ (II. 2.)\n\nXXII.\n\n_Space is not a General Notion collected by abstraction from\nparticular cases; for we do not speak of_ Spaces _in general, but of\nuniversal or absolute_ Space. _Absolute Space is infinite. All\nspecial spaces are_ in _absolute space, and are parts of it._ (II. 3.)\n\nXXIII.\n\n_Space is not a real object or thing, distinct from the objects\nwhich exist in it; but it is a real condition of the existence of\nexternal objects._ (II. 3.) {9}\n\nXXIV.\n\n_We have an_ Intuition _of objects in space; that is, we contemplate\nobjects as_ made up _of spatial parts, and apprehend their spatial\nrelations by the same act by which we apprehend the objects\nthemselves._ (II. 3.)\n\nXXV.\n\nForm _or Figure is space limited by boundaries. Space has\nnecessarily_ three _dimensions, length, breadth, depth; and no\nothers which cannot be resolved into these._ (II. 3.)\n\nXXVI.\n\n_The Idea of Space is exhibited for scientific purposes, by the_\nDefinitions _and_ Axioms _of Geometry; such, for instance, as\nthese:--the_ Definition of a Right Angle, _and_ of a Circle;--_the_\nDefinition of Parallel Lines, _and the_ Axiom _concerning\nthem;--the_ Axiom _that_ two straight lines cannot inclose a space.\n_These Definitions are necessary, not arbitrary; and the Axioms are\nneeded as well as the Definitions, in order to express the necessary\nconditions which the Idea of Space imposes._ (II. 4.)\n\nXXVII.\n\n_The Definitions and Axioms of Elementary Geometry do not_\ncompletely _exhibit the Idea of Space. In proceeding to the Higher\nGeometry, we may introduce other additional and independent Axioms;\nsuch as that of Archimedes, that_ a curve line which joins two\npoints is less than any broken line joining the same points and\nincluding the curve line. (II. 4.)\n\nXXVIII.\n\n_The perception of a_ solid object _by sight requires that act of\nmind by which, from figure and shade, we infer distance and position\nin space. The perception of_ figure _by sight requires that act of\nmind by which we give an outline to each object._ (II. 6.) {10}\n\nXXIX.\n\n_The perception of Form by touch is not an impression on the passive\nsense, but requires an act of our muscular frame by which we become\naware of the position of our own limbs. The perceptive faculty\ninvolved in this act has been called_ the muscular sense. (II. 6.)\n\nXXX.\n\n_The_ Idea of Time _is not derived from experience, for experience\nof changes_ pre_supposes occurrences to take place in Time. Time is\na condition under which the mind receives the impressions of sense,\nand therefore the relations of time are necessarily and universally\ntrue of all perceived occurrences. Time is a_ form _of our\nperceptions, and regulates them, whatever the_ matter _of them may\nbe._ (II. 7.)\n\nXXXI.\n\n_Time is not a General Notion collected by abstraction from\nparticular cases. For we do not speak of particular_ Times _as\nexamples of time in general, but as parts of a single and infinite_\nTime. (II. 8.)\n\nXXXII.\n\n_Time, like Space, is a form, not only of perception, but of_\nIntuition. _We consider the whole of any time as_ equal _to the_ sum\n_of the parts; and an occurrence as_ coinciding _with the portion of\ntime which it occupies._ (II. 8.)\n\nXXXIII.\n\n_Time is analogous to Space of_ one dimension: _portions of both\nhave a beginning and an end, are long or short. There is nothing in\nTime which is analogous to Space of two, or of three, dimensions,\nand thus nothing which corresponds to Figure._ (II. 8.)\n\nXXXIV.\n\n_The Repetition of a set of occurrences, as, for example, strong and\nweak, or long and short sounds, according to a_ {11} _steadfast order,\nproduces_ Rhythm, _which is a conception peculiar to Time, as Figure\nis to Space._ (II. 8.)\n\nXXXV.\n\n_The simplest form of Repetition is that in which there is no\nvariety, and thus gives rise to the conception of_ Number. (II. 8.)\n\nXXXVI.\n\n_The simplest numerical truths are seen by Intuition; when we\nendeavour to deduce the more complex from these simplest, we employ\nsuch maxims as these_:--If equals be added to equals the wholes are\nequal:--If equals be subtracted from equals the remainders are\nequal:--The whole is equal to the sum of all its parts. (II. 9.)\n\nXXXVII.\n\n_The Perception of Time involves a constant and latent kind of\nmemory, which may be termed a_ Sense of Succession. _The Perception\nof Number also involves this Sense of Succession, although in small\nnumbers we appear to apprehend the units simultaneously and not\nsuccessively._ (II. 10.)\n\nXXXVIII.\n\n_The Perception of Rhythm is not an impression on the passive sense,\nbut requires an act of thought by which we connect and group the\nstrokes which form the Rhythm._ (II. 10.)\n\nXXXIX.\n\nIntuitive _is opposed to_ Discursive _reason. In intuition, we obtain\nour conclusions by dwelling upon_ one _aspect of the fundamental\nIdea; in discursive reasoning, we combine_ several _aspects of the\nIdea,_ (_that is, several axioms,_) _and reason from the\ncombination._ (II. 11.)\n\nXL.\n\n_Geometrical deduction_ (_and deduction in general_) _is called_\nSynthesis, _because we introduce, at successive steps, the_ {12}\n_results of new principles. But in reasoning on the relations of\nspace, we sometimes go on_ separating _truths into their component\ntruths, and these into other component truths; and so on: and this\nis geometrical_ Analysis. (II. 11.)\n\nXLI.\n\n_Among the foundations of the Higher Mathematics, is the_ Idea of\nSymbols _considered as general_ Signs _of Quantity. This idea of a\nSign is distinct from, and independent of other ideas. The Axiom to\nwhich we refer in reasoning by means of Symbols of quantity is\nthis_:--The interpretation of such symbols must be perfectly\ngeneral. _This Idea **and Axiom are the bases of Algebra in its most\ngeneral form._ (II. 12.)\n\nXLII.\n\n_Among the foundations of the Higher Mathematics is also the_ Idea\nof a Limit. _The Idea of a Limit cannot be superseded by any other\ndefinitions or Hypotheses, The Axiom which we employ in introducing\nthis Idea into our reasoning is this_:--What is true up to the Limit\nis true at the Limit. _This Idea and Axiom are the bases of all\nMethods of Limits, Fluxions, Differentials, Variations, and the\nlike._ (II. 12.)\n\nXLIII.\n\n_There is a_ pure _Science of Motion, which does not depend upon\nobserved facts, but upon the Idea of motion. It may also be termed_\nPure Mechanism, _in opposition to Mechanics Proper, or_ Machinery,\n_which involves the mechanical conceptions of force and matter. It\nhas been proposed to name this Pure Science of Motion,_ Kinematics.\n(II. 13.)\n\nXLIV.\n\n_The pure Mathematical Sciences must be successfully cultivated, in\norder that the progress of the principal Inductive Sciences may take\nplace. This appears in the case of Astronomy, in which Science, both\nin ancient and in modern times, each advance of the theory has\ndepended upon the_ {13} _previous solution of problems in pure\nmathematics. It appears also inversely in the Science of the Tides,\nin which, at present, we cannot advance in the theory, because we\ncannot solve the requisite problems in the Integral Calculus._\n(II. 14.)\n\nXLV.\n\n_The_ Idea of Cause, _modified into the conceptions of mechanical\ncause, or Force, and resistance to force, or Matter, is the\nfoundation of the Mechanical Sciences; that is, Mechanics,_\n(_including Statics and Dynamics,_) _Hydrostatics, and Physical\nAstronomy._ (III. 1.)\n\nXLVI.\n\n_The Idea of Cause is not derived from experience; for in judging of\noccurrences which we contemplate, we consider them as being,\nuniversally and necessarily, Causes and Effects, which a finite\nexperience could not authorize us to do. The Axiom, that every event\nmust have a cause, is true independently of experience, and beyond\nthe limits of experience._ (III. 2.)\n\nXLVII.\n\n_The Idea of Cause is expressed for purposes of science by these\nthree Axioms_:--Every Event must have a Cause:--Causes are measured\nby their Effects:--Reaction is equal and opposite to Action.\n(III. 4.)\n\nXLVIII.\n\n_The Conception of Force involves the Idea of Cause, as applied to\nthe motion and rest of bodies. The conception of_ force _is suggested\nby muscular action exerted: the conception of_ matter _arises from\nmuscular action resisted. We necessarily ascribe to all bodies\nsolidity and inertia, since we conceive Matter as that which cannot\nbe compressed or moved without resistance._ (III. 5.)\n\nXLIX.\n\n_Mechanical Science depends on the Conception of Force; and is\ndivided into_ Statics, _the doctrine of Force preventing_ {14}\n_motion, and_ Dynamics, _the doctrine of Force producing motion._\n(III. 6.)\n\nL.\n\n_The Science of Statics depends upon the Axiom, that Action and\nReaction are equal, which in Statics assumes this form_:--When two\nequal weights are supported on the middle point between them, the\npressure on the fulcrum is equal to the sum of the weights.\n(III. 6.)\n\nLI.\n\n_The Science of Hydrostatics depends upon the Fundamental Principle\nthat_ fluids press equally in all directions. _This principle\nnecessarily results from the conception of a Fluid, as a body of\nwhich the parts are perfectly moveable in all directions. For since\nthe Fluid is a body, it can transmit pressure; and the transmitted\npressure is equal to the original pressure, in virtue of the Axiom\nthat Reaction is equal to Action. That the Fundamental Principle is\nnot derived from experience, is plain both from its evidence and\nfrom its history._ (III. 6.)\n\nLII.\n\n_The Science of Dynamics depends upon the three Axioms above stated\nrespecting Cause. The First Axiom,--that every change must have a\nCause,--gives rise to the First Law of Motion,--that_ a body not\nacted upon by a force will move with a uniform velocity in a\nstraight line. _The Second Axiom,--that Causes are measured by their\nEffects,--gives rise to the Second Law of Motion,--that_ when a\nforce acts upon a body in motion, the effect of the force is\ncompounded with the previously existing motion. _The Third\nAxiom,--that_ Reaction is equal and opposite to Action,--_gives rise\nto the Third Law of Motion, which is expressed in the same terms as\nthe Axiom; Action and Reaction being understood to signify momentum\ngained and lost._ (III. 7.) {15}\n\nLIII.\n\n_The above Laws of Motion, historically speaking, were established\nby means of experiment: but since they have been discovered and\nreduced to their simplest form, they have been considered by many\nphilosophers as self-evident. This result is principally due to the\nintroduction and establishment of terms and definitions, which\nenable us to express the Laws in a very simple manner._ (III. 7.)\n\nLIV.\n\n_In the establishment of the Laws of Motion, it happened, in several\ninstances, that Principles were assumed as self-evident which do not\nnow appear evident, but which have since been demonstrated from the\nsimplest and most evident principles. Thus it was assumed that_ a\nperpetual motion is impossible;--_that_ the velocities of bodies\nacquired by falling down planes or curves of the same vertical\nheight are equal;--_that_ the actual descent of the center of\ngravity is equal to its potential ascent. _But we are not hence to\nsuppose that these assumptions were made without ground: for since\nthey really follow from the laws of motion, they were probably, in\nthe minds of the discoverers, the results of undeveloped\ndemonstrations which their sagacity led them to divine._ (III. 7.)\n\nLV.\n\n_It is a_ Paradox _that Experience should lead us to truths\nconfessedly universal, and apparently necessary, such as the Laws of\nMotion are. The_ Solution _of this paradox is, that these laws are\ninterpretations of the Axioms of Causation. The axioms are\nuniversally and necessarily true, but the right interpretation of\nthe terms which they involve, is learnt by experience. Our Idea of\nCause supplies the_ Form, _Experience, the_ Matter, _of these Laws._\n(III. 8.)\n\nLVI.\n\nPrimary _Qualities of Bodies are those which we can conceive as\ndirectly perceived;_ Secondary _Qualities are those_ {16} _which we\nconceive as perceived by means of a Medium._ (IV. 1.)\n\nLVII.\n\n_We necessarily perceive bodies as_ without _us; the Idea of_\nExternality _is one of the conditions of perception._ (IV. 1.)\n\nLVIII.\n\n_We necessarily assume a_ Medium _for the perceptions of Light,\nColour, Sound, Heat, Odours, Tastes; and this Medium_ must _convey\nimpressions by means of its mechanical attributes._ (IV. 1.)\n\nLIX.\n\n_Secondary Qualities are not_ extended _but_ intensive: _their effects\nare not augmented by addition of parts, but by increased operation\nof the medium. Hence they are not measured directly, but by_ scales;\n_not by_ units, _but by_ degrees. (IV. 4.)\n\nLX.\n\n_In the Scales of Secondary Qualities, it is a condition_ (_in order\nthat the scale may be complete,_) _that every example of the quality\nmust either_ agree _with one of the degrees of the Scale, or lie\nbetween two_ contiguous _degrees._ (IV. 4.)\n\nLXI.\n\n_We perceive_ by means of _a medium and_ by means of _impressions on\nthe nerves: but we do not_ (_by our senses_) _perceive either the\nmedium or the impressions on the nerves._ (IV. 1.)\n\nLXII.\n\n_The_ Prerogatives of the Sight _are, that by this sense we\nnecessarily and immediately apprehend the_ position _of its objects:\nand that from visible circumstances, we_ infer _the_ distance _of\nobjects from us, so readily that we seem to perceive and not to\ninfer._ (IV. 2.) {17}\n\nLXIII.\n\n_The_ Prerogatives of the Hearing _are, that by this sense we\nperceive relations perfectly precise and definite between two notes,\nnamely,_ Musical Intervals (_as an_ Octave, _a_ Fifth); _and that\nwhen two notes are perceived together, they are comprehended as\ndistinct,_ (_a_ Chord,) _and as having a certain relation,_ (Concord\n_or_ Discord.) (IV. 2.)\n\nLXIV.\n\n_The Sight cannot decompose a compound colour into simple colours,\nor distinguish a compound from a simple colour. The Hearing cannot\ndirectly perceive the place, still less the distance, of its\nobjects: we infer these obscurely and vaguely from audible\ncircumstances._ (IV. 2.)\n\nLXV.\n\n_The_ First Paradox of Vision _is, that we see objects_ upright,\n_though the images on the retina are_ inverted. _The solution is,\nthat we do not see the image on the retina at all, we only see by\nmeans of it._ (IV. 2.)\n\nLXVI.\n\n_The_ Second Paradox of Vision _is, that we see objects_ single,\n_though there are two images on the retinas, one in each eye. The\nexplanation is, that it is a Law of Vision that we see_ (_small or\ndistant_) _objects single, when their images fall on_ corresponding\npoints _of the two retinas._ (IV. 2.)\n\nLXVII.\n\n_The law of single vision for_ near _objects is this:--When the two\nimages in the two eyes are situated, part for part, nearly but not\nexactly, upon corresponding points, the object is apprehended as\nsingle and solid if the two objects are such as would be produced by\na single solid object seen by the eyes separately._ (IV. 2.)\n\nLXVIII.\n\n_The ultimate object of each of the Secondary Mechanical Sciences\nis, to determine the nature and laws of the processes_ {18} _by\nwhich the impression of the Secondary Quality treated of is\nconveyed: but before we discover the cause, it may be necessary to\ndetermine the_ laws _of the phenomena; and for this purpose a_\nMeasure _or_ Scale _of each quality is necessary._ (IV. 4.)\n\nLXIX.\n\n_Secondary qualities are measured by means of such effects as can be\nestimated in number or space._ (IV. 4.)\n\nLXX.\n\n_The Measure of Sounds, as high or low, is the_ Musical Scale, _or_\nHarmonic Canon. (IV. 4.)\n\nLXXI.\n\n_The Measures of Pure Colours are the_ Prismatic Scale; _the same,\nincluding_ Fraunhofer's Lines; _and_ Newton's Scale _of Colours. The\nprincipal Scales of Impure Colours are_ Werner's Nomenclature _of\nColours, and_ Merim\u00e9e's Nomenclature _of Colours_. (IV. 4.)\n\nLXXII.\n\n_The Idea of_ Polarity _involves the conception of contrary\nproperties in contrary directions:--the properties being, for\nexample, attraction and repulsion, darkness and light, synthesis and\nanalysis; and the contrary directions being those which are directly\nopposite, or, in some cases, those which are at right angles._\n(V. 1.)\n\nLXXIII. (Doubtful.)\n\n_Coexistent polarities are fundamentally identical._ (V. 2.)\n\nLXXIV.\n\n_The Idea of Chemical_ Affinity, _as implied in Elementary\nComposition, involves peculiar conceptions. It is not properly\nexpressed by assuming the qualities of bodies to_ resemble _those of\nthe elements, or to depend on the_ figure _of the elements, or on\ntheir_ attractions. (VI. 1.) {19}\n\nLXXV.\n\n_Attractions take place between bodies, Affinities between the\nparticles of a body. The former may be compared to the alliances of\nstates, the latter to the ties of family._ (VI. 2.)\n\nLXXVI.\n\n_The governing principles of Chemical Affinity are, that it is_\nelective; _that it is_ definite; _that it_ determines the properties\n_of the compound; and that_ analysis is possible. (VI. 2.)\n\nLXXVII.\n\n_We have an idea of_ Substance: _and an axiom involved in this Idea\nis, that_ the weight of a body is the sum of the weights of all its\nelements. (VI. 3.)\n\nLXXVIII.\n\n_Hence Imponderable Fluids are not to be admitted as chemical\nelements._ (VI. 4.)\n\nLXXIX.\n\n_The Doctrine of Atoms is admissible as a mode of expressing and\ncalculating laws of nature; but is not proved by any fact, chemical\nor physical, as a philosophical truth._ (VI. 5.)\n\nLXXX.\n\n_We have an Idea of_ Symmetry; _and an axiom involved in this Idea\nis, that in a symmetrical natural body, if there be a tendency to\nmodify any member in any manner, there is a tendency to modify all\nthe corresponding members in the same manner._ (VII. 1.)\n\nLXXXI.\n\n_All hypotheses respecting the manner in which the elements of\ninorganic bodies are arranged in space, must be constructed with\nregard to the general facts of crystallization._ (VII. 3.) {20}\n\nLXXXII.\n\n_When we consider any object as_ One, _we give unity to it by an act\nof thought. The condition which determines what this unity shall\ninclude, and what it shall exclude, is this;--that assertions\nconcerning the one thing shall be possible._ (VIII. 1.)\n\nLXXXIII.\n\n_We collect individuals into_ Kinds _by applying to them the Idea of\nLikeness. Kinds of things are not determined by definitions, but by\nthis condition:--that general assertions concerning such kinds of\nthings shall be possible._ (VIII. 1.)\n\nLXXXIV.\n\n_The_ Names _of kinds of things are governed by their use; and that\nmay be a right name in one use which is not so in another. A whale\nis not a_ fish _in natural history, but it is a_ fish _in commerce\nand law._ (VIII. 1.)\n\nLXXXV.\n\n_We take for granted that each kind of things has a special_\ncharacter _which may be expressed by a Definition. The ground of our\nassumption is this;--that reasoning must be possible._ (VIII. 1.)\n\nLXXXVI.\n\n_The \"Five Words,\"_ Genus, Species, Difference, Property, Accident,\n_were used by the Aristotelians, in order to express the\nsubordination of Kinds, and to describe the nature of Definitions\nand Propositions. In modern times, these technical expressions have\nbeen more referred to by Natural Historians than by Metaphysicians._\n(VIII. 1.)\n\nLXXXVII.\n\n_The construction of a Classificatory Science includes_ Terminology,\n_the formation of a descriptive language;_--Diataxis, _the Plan of\nthe System of Classification, called_ {21} _also the_\nSystematick;--Diagnosis, _the Scheme of the Characters by which the\ndifferent Classes are known, called also the_ Characteristick.\nPhysiography _is the knowledge which the System is employed to\nconvey. Diataxis includes_ Nomenclature. (VIII. 2.)\n\nLXXXVIII.\n\nTerminology _must be conventional, precise, constant; copious in\nwords, and minute in distinctions, according to the needs of the\nscience. The student must understand the terms,_ directly _according\nto the convention, not through the medium of explanation or\ncomparison._ (VIII. 2.)\n\nLXXXIX.\n\n_The_ Diataxis,_ or Plan of the System, may aim at a Natural or at\nan Artificial System. But no classes can be absolutely artificial,\nfor if they were, no assertions could be made concerning them._\n(VIII. 2.)\n\nXC.\n\n_An_ Artificial System _is one in which the_ smaller _groups_ (_the\nGenera_) _are_ natural; _and in which the_ wider _divisions_\n(_Classes, Orders_) _are constructed by the_ peremptory _application\nof selected Characters;_ (_selected, however, so as not to break up\nthe smaller groups._) (VIII. 2.)\n\nXCI.\n\n_A_ Natural System _is one which attempts to make_ all _the\ndivisions_ natural, _the widest as well as the narrowest; and\ntherefore applies_ no _characters_ peremptorily. (VIII. 2.)\n\nXCII.\n\n_Natural Groups are best described, not by any Definition which\nmarks their boundaries, but by a_ Type _which marks their center.\nThe Type of any natural group is an example which possesses in a\nmarked degree all the leading characters of the class._ (VIII. 2.)\n{22}\n\nXCIII.\n\n_A Natural Group is steadily fixed, though not precisely limited; it\nis given in position, though not circumscribed; it is determined,\nnot by a boundary without, but by a central point within;--not by\nwhat it strictly excludes, but by what it eminently includes;--by a\nType, not by a Definition._ (VIII. 2.)\n\nXCIV.\n\n_The prevalence of Mathematics as an element of education has made\nus think Definition the philosophical mode of fixing the meaning of\na word: if_ (_Scientific_) _Natural History were introduced into\neducation, men might become familiar with the fixation of the\nsignification of words by_ Types; _and this process agrees more\nnearly with the common processes by which words acquire their\nsignifications._ (VIII. 2.)\n\nXCV.\n\n_The attempts at Natural Classification are of three sorts;\naccording as they are made by the process of_ blind trial, _of_\ngeneral comparison, _or of_ subordination of characters. _The\nprocess of Blind Trial professes to make its classes by attention to\nall the characters, but without proceeding methodically. The process\nof General Comparison professes to enumerate all the characters, and\nforms its classes by the_ majority. _Neither of these methods can\nreally be carried into effect. The method of Subordination of\nCharacters considers some characters as_ more important _than\nothers; and this method gives more consistent results than the\nothers. This method, however, does not depend upon the Idea of\nLikeness only, but introduces the Idea of Organization or Function._\n(VIII. 2.)\n\nXCVI.\n\n_A_ Species _is a collection of individuals, which are descended\nfrom a common stock, or which resemble such a collection as much as\nthese resemble each other: the resemblance being opposed to a_\ndefinite _difference._ (VIII. 2.) {23}\n\nXCVII.\n\n_A_ Genus _is a collection of species which resemble each other more\nthan they resemble other species: the resemblance being opposed to\na_ definite _difference._ (VIII. 2.)\n\nXCVIII.\n\n_The_ Nomenclature _of a Classificatory Science is the collection of\nthe names of the Species, Genera, and other divisions. The_ binary\n_nomenclature, which denotes a species by the_ generic _and_ specific\n_name, is now commonly adopted in Natural History._ (VIII. 2.)\n\nXCIX.\n\n_The_ Diagnosis, _or Scheme of the Characters, comes, in the order\nof philosophy, after the Classification. The characters do not_ make\n_the classes, they only enable us to_ recognize _them. The Diagnosis\nis an Artificial Key to a Natural System._ (VIII. 2.)\n\nC.\n\n_The basis of all Natural Systems of Classification is the Idea of\nNatural Affinity. The Principle which this Idea involves is\nthis:--Natural arrangements, obtained from_ different _sets of\ncharacters, must_ coincide _with each other._ (VIII. 4.)\n\nCI.\n\n_In order to obtain a Science of Biology, we must analyse the Idea\nof Life. It has been proved by the biological speculations of past\ntime, that Organic Life cannot rightly be solved into Mechanical or\nChemical Forces, or the operation of a Vital Fluid, or of a Soul._\n(IX. 2.)\n\nCII.\n\n_Life is a System of Vital Forces; and the conception of such Forces\ninvolves a peculiar Fundamental Idea._ (IX. 3.) {24}\n\nCIII.\n\n_Mechanical, chemical, and vital Forces form an ascending\nprogression, each including the preceding. Chemical Affinity\nincludes in its nature Mechanical Force, and may often be\npractically resolved into Mechanical Force._ (_Thus the ingredients\nof gunpowder, liberated from their chemical union, exert great\nmechanical Force: a galvanic battery acting by chemical process does\nthe like._) _Vital Forces include in their nature both chemical\nAffinities and mechanical Forces: for Vital Powers produce both\nchemical changes,_ (_as digestion,_) _and motions which imply\nconsiderable mechanical force,_ (_as the motion of the sap and of\nthe blood._) (IX. 4.)\n\nCIV.\n\n_In_ voluntary _motions, Sensations produce Actions, and the\nconnexion is made by means of Ideas: in_ reflected _motions, the\nconnexion neither seems to be nor is made by means of Ideas: in_\ninstinctive _motions, the connexion is such as requires Ideas, but\nwe cannot believe the Ideas to exist._ (IX. 5.)\n\nCV.\n\n_The Assumption of a Final Cause in the structure of each part of\nanimals and plants is as inevitable as the assumption of an\nEfficient Cause for every event. The maxim that in organized bodies\nnothing is_ in vain, _is as necessarily true as the maxim that\nnothing happens_ by chance. (IX. 6.)\n\nCVI.\n\n_The Idea of living beings as subject to_ disease _includes a\nrecognition of a Final Cause in organization; for disease is a state\nin which the vital forces do not attain their_ proper ends. (IX. 7.)\n\nCVII.\n\n_The Pal\u00e6tiological Sciences depend upon the Idea of Cause: but the\nleading conception which they involve is that of_ historical cause,\n_not mechanical cause._ (X. 1.) {25}\n\nCVIII.\n\n_Each Pal\u00e6tiological Science, when complete, must possess three\nmembers: the_ Phenomenology, _the_ \u00c6tiology, _and the_ Theory. (X.\n2.)\n\nCIX.\n\n_There are, in the Pal\u00e6tiological Sciences, two antagonist\ndoctrines:_ Catastrophes _and_ Uniformity. _The doctrine of a_\nuniform course of nature _is tenable only when we extend the nation\nof Uniformity so far that it shall include Catastrophes._ (X. 3.)\n\nCX.\n\n_The Catastrophist constructs Theories, the Uniformitarian\ndemolishes them. The former adduces evidence of an Origin, the\nlatter explains the evidence away. The Catastrophist's dogmatism is\nundermined by the Uniformitarian's skeptical hypotheses. But when\nthese hypotheses are asserted dogmatically they cease to be\nconsistent with the doctrine of Uniformity._ (X. 3.)\n\nCXI.\n\n_In each of the Pal\u00e6tiological Sciences, we can ascend to remote\nperiods by a chain of causes, but in none can we ascend to a_\nbeginning _of the chain._ (X. 3.)\n\nCXII.\n\n_Since the Pal\u00e6tiological sciences deal with the conceptions of\nhistorical cause,_ History, _including_ Tradition, _is an important\nsource of materials for such sciences._ (X. 4.)\n\nCXIII.\n\n_The history and tradition which present to us the providential\ncourse of the world form a_ Sacred Narrative; _and in reconciling\nthe Sacred Narrative with the results of science, arise inevitable\ndifficulties which disturb the minds of those who reverence the\nSacred Narrative._ (X. 4.) {26}\n\nCXIV.\n\n_The disturbance of reverent minds, arising from scientific views,\nceases when such views become familiar, the Sacred Narrative being\nthen interpreted anew in accordance with such views._ (X. 4.)\n\nCXV.\n\n_A new interpretation of the Sacred Narrative, made for the purpose\nof reconciling it with doctrines of science, should not be insisted\non till such doctrines are clearly proved; and when they are so\nproved, should be frankly accepted, in the confidence that a\nreverence for the Sacred Narrative is consistent with a reverence\nfor the Truth._ (X. 4.)\n\nCXVI.\n\n_In contemplating the series of causes and effects which constitutes\nthe world, we necessarily assume a_ First Cause _of the whole\nseries._ (X. 5.)\n\nCXVII.\n\n_The Pal\u00e6tiological Sciences point backwards with lines which are\nbroken, but which all converge to the_ same _invisible point: and\nthis point is the Origin of the Moral and Spiritual, as well as of\nthe Natural World._ (X. 5.)\n\n\n\n\nNOVUM ORGANON RENOVATUM.\n\n\n{{27}}\nBOOK II.\n\nOF THE CONSTRUCTION OF SCIENCE.\n\n\n\nCHAPTER I.\n\nOF TWO PRINCIPAL PROCESSES BY WHICH SCIENCE IS CONSTRUCTED.\n\n\nAPHORISM I.\n\n_THE two processes by which Science is constructed are the_\nExplication of Conceptions, _and the_ Colligation of Facts.\n\n\nTO the subject of the present and next Book all that has preceded is\nsubordinate and preparatory. In former works we have treated of the\nHistory of Scientific Discoveries and of the History of Scientific\nIdeas. We have now to attempt to describe the manner in which\ndiscoveries are made, and in which Ideas give rise to knowledge. It\nhas already been stated that Knowledge requires us to possess both\nFacts and Ideas;--that every step in our knowledge consists in\napplying the Ideas and Conceptions furnished by our minds to the\nFacts which observation and experiment offer to us. When our\nConceptions are clear and distinct, when our Facts are certain and\nsufficiently numerous, and when the Conceptions, being suited to the\nnature of the {28} Facts, are applied to them so as to produce an\nexact and universal accordance, we attain knowledge of a precise and\ncomprehensive kind, which we may term _Science_. And we apply this\nterm to our knowledge still more decidedly when, Facts being thus\nincluded in exact and general Propositions, such Propositions are,\nin the same manner, included with equal rigour in Propositions of a\nhigher degree of Generality; and these again in others of a still\nwider nature, so as to form a large and systematic whole.\n\nBut after thus stating, in a general way, the nature of science, and\nthe elements of which it consists, we have been examining with a\nmore close and extensive scrutiny, some of those elements; and we\nmust now return to our main subject, and apply to it the results of\nour long investigation. We have been exploring the realm of Ideas;\nwe have been passing in review the difficulties in which the\nworkings of our own minds involve us when we would make our\nconceptions consistent with themselves: and we have endeavoured to\nget a sight of the true solutions of these difficulties. We have now\nto inquire how the results of these long and laborious efforts of\nthought find their due place in the formation of our Knowledge. What\ndo we gain by these attempts to make our notions distinct and\nconsistent; and in what manner is the gain of which we thus become\npossessed, carried to the general treasure-house of our permanent\nand indestructible knowledge? After all this battling in the world\nof ideas, all this struggling with the shadowy and changing forms of\nintellectual perplexity, how do we secure to ourselves the fruits of\nour warfare, and assure ourselves that we have really pushed\nforwards the frontier of the empire of Science? It is by such an\nappropriation, that the task which we have had in our hands during\nthe two previous works, (the _History of the Inductive Sciences_ and\nthe _History of Scientific Ideas_,) must acquire its real value and\ntrue place in our design.\n\nIn order to do this, we must reconsider, in a more definite and\nprecise shape, the doctrine which has already been laid down;--that\nour Knowledge consists {29} in applying Ideas to Facts; and that the\nconditions of real knowledge are that the ideas be distinct and\nappropriate, and exactly applied to clear and certain facts. The\nsteps by which our knowledge is advanced are those by which one or\nthe other of these two processes is rendered more complete;--by\nwhich _Conceptions_ are _made more clear_ in themselves, or by which\nthe Conceptions more strictly _bind together the Facts_. These two\nprocesses may be considered as together constituting the whole\nformation of our knowledge; and the principles which have been\nestablished in the History of Scientific Ideas bear principally upon\nthe former of these two operations;--upon the business of elevating\nour conceptions to the highest possible point of precision and\ngenerality. But these two portions of the progress of knowledge are\nso clearly connected with each other, that we shall deal with them\nin immediate succession. And having now to consider these operations\nin a more exact and formal manner than it was before possible to do,\nwe shall designate them by certain constant and technical phrases.\nWe shall speak of the two processes by which we arrive at science,\nas _the Explication of Conceptions_ and _the Colligation of Facts_:\nwe shall show how the discussions in which we have been engaged have\nbeen necessary in order to promote the former of these offices; and\nwe shall endeavour to point out modes, maxims, and principles by\nwhich the second of the two tasks may also be furthered.\n\n\n\n{{30}}\nCHAPTER II.\n\nOF THE EXPLICATION OF CONCEPTIONS.\n\n\nAPHORISM II.\n\n_The Explication of Conceptions, as requisite for the progress of\nscience, has been effected by means of discussions and controversies\namong scientists; often by debates concerning definitions; these\ncontroversies have frequently led to the establishment of a\nDefinition; but along with the Definition, a corresponding\nProposition has always been expressed or implied. The essential\nrequisite for the advance of science is the clearness of the\nConception, not the establishment of a Definition. The construction\nof an exact Definition is often very difficult. The requisite\nconditions of clear Conceptions may often be expressed by Axioms as\nwell as by Definitions._\n\n\nAPHORISM III.\n\n_Conceptions, for purposes of science, must be_ appropriate _as well\nas clear: that is, they must be modifications of_ that _Fundamental\nIdea, by which the phenomena can really be interpreted. This maxim\nmay warn us from errour, though it may not lead to discovery.\nDiscovery depends upon the previous cultivation or natural clearness\nof the appropriate Idea, and therefore_ no discovery is the work of\naccident.\n\n\nSECT. I.--_Historical Progress of the Explication of Conceptions._\n\n1. WE have given the appellation of _Ideas_ to certain comprehensive\nforms of thought,--as _space_, _number_, _cause_, _composition_,\n_resemblance_,--which we apply to the phenomena which we\ncontemplate. But the special modifications of these ideas which are\n{31} exemplified in particular facts, we have termed _Conceptions_;\nas _a circle_, _a square number_, _an accelerating force_, _a\nneutral combination_ of elements, a _genus_. Such Conceptions\ninvolve in themselves certain necessary and universal relations\nderived from the Ideas just enumerated; and these relations are an\nindispensable portion of the texture of our knowledge. But to\ndetermine the contents and limits of this portion of our knowledge,\nrequires an examination of the Ideas and Conceptions from which it\nproceeds. The Conceptions must be, as it were, carefully _unfolded_,\nso as to bring into clear view the elements of truth with which they\nare marked from their ideal origin. This is one of the processes by\nwhich our knowledge is extended and made more exact; and this I\nshall describe as the _Explication of Conceptions_.\n\nIn the several Books of the History of Ideas we have discussed a\ngreat many of the Fundamental Ideas of the most important existing\nsciences. We have, in those Books, abundant exemplifications of the\nprocess now under our consideration. We shall here add a few general\nremarks, suggested by the survey which we have thus made.\n\n2. Such discussions as those in which we have been engaged\nconcerning our fundamental Ideas, have been the course by which,\nhistorically speaking, those Conceptions which the existing sciences\ninvolve have been rendered so clear as to be fit elements of exact\nknowledge. Thus, the disputes concerning the various kinds and\nmeasures of _Force_ were an important part of the progress of the\nscience of Mechanics. The struggles by which philosophers attained a\nright general conception of _plane_, of _circular_, of _elliptical\nPolarization_, were some of the most difficult steps in the modern\ndiscoveries of Optics. A Conception of the _Atomic Constitution_ of\nbodies, such as shall include what we know, and assume nothing more,\nis even now a matter of conflict among Chemists. The debates by\nwhich, in recent times, the Conceptions of _Species_ and _Genera_\nhave been rendered more exact, have improved the science of Botany:\nthe imperfection of the science of {32} Mineralogy arises in a great\nmeasure from the circumstance, that in that subject, the Conception\nof a _Species_ is not yet fixed. In Physiology, what a vast advance\nwould that philosopher make, who should establish a precise,\ntenable, and consistent Conception of _Life_!\n\nThus discussions and speculations concerning the import of very\nabstract and general terms and notions, may be, and in reality have\nbeen, far from useless and barren. Such discussions arose from the\ndesire of men to impress their opinions on others, but they had the\neffect of making the opinions much more clear and distinct. In\ntrying to make others understand them, they learnt to understand\nthemselves. Their speculations were begun in twilight, and ended in\nthe full brilliance of day. It was not easily and at once, without\nexpenditure of labour or time, that men arrived at those notions\nwhich now form the elements of our knowledge; on the contrary, we\nhave, in the history of science, seen how hard, discoverers, and the\nforerunners of discoverers, have had to struggle with the\nindistinctness and obscurity of the intellect, before they could\nadvance to the critical point at which truth became clearly visible.\nAnd so long as, in this advance, some speculators were more forward\nthan others, there was a natural and inevitable ground of difference\nof opinion, of argumentation, of wrangling. But the tendency of all\nsuch controversy is to diffuse truth and to dispel errour. Truth is\nconsistent, and can bear the tug of war; Errour is incoherent, and\nfalls to pieces in the struggle. True Conceptions can endure the\nsun, and become clearer as a fuller light is obtained; confused and\ninconsistent notions vanish like visionary spectres at the break of\na brighter day. And thus all the controversies concerning such\nConceptions as science involves, have ever ended in the\nestablishment of the side on which the truth was found.\n\n3. Indeed, so complete has been the victory of truth in most of\nthese instances, that at present we can hardly imagine the struggle\nto have been necessary. The very essence of these triumphs is that\nthey lead us to regard the views we reject as not only false, {33}\nbut inconceivable. And hence we are led rather to look back upon the\nvanquished with contempt than upon the victors with gratitude. We\nnow despise those who, in the Copernican controversy, could not\nconceive the apparent motion of the sun on the heliocentric\nhypothesis;--or those who, in opposition to Galileo, thought that a\nuniform force might be that which generated a velocity proportional\nto the space;--or those who held there was something absurd in\nNewton's doctrine of the different refrangibility of differently\ncoloured rays;--or those who imagined that when elements combine,\ntheir sensible qualities must be manifest in the compound;--or those\nwho were reluctant to give up the distinction of vegetables into\nherbs, shrubs, and trees. We cannot help thinking that men must have\nbeen singularly dull of comprehension, to find a difficulty in\nadmitting what is to us so plain and simple. We have a latent\npersuasion that we in their place should have been wiser and more\nclear-sighted;--that we should have taken the right side, and given\nour assent at once to the truth.\n\n4. Yet in reality, such a persuasion is a mere delusion. The persons\nwho, in such instances as the above, were on the losing side, were\nvery far, in most cases, from being persons more prejudiced, or\nstupid, or narrow-minded, than the greater part of mankind now are;\nand the cause for which they fought was far from being a manifestly\nbad one, till it had been so decided by the result of the war. It is\nthe peculiar character of scientific contests, that what is only an\nepigram with regard to other warfare is a truth in this;--They who\nare defeated are really in the wrong. But they may, nevertheless, be\nmen of great subtilty, sagacity, and genius; and we nourish a very\nfoolish self-complacency when we suppose that we are their\nsuperiors. That this is so, is proved by recollecting that many of\nthose who have made very great discoveries have laboured under the\nimperfection of thought which was the obstacle to the next step in\nknowledge. Though Kepler detected with great acuteness the Numerical\nLaws of the solar system, he laboured in {34} vain to conceive the\nvery simplest of the Laws of Motion by which the paths of the\nplanets are governed. Though Priestley made some important steps in\nchemistry, he could not bring his mind to admit the doctrine of a\ngeneral Principle of Oxidation. How many ingenious men in the last\ncentury rejected the Newtonian Attraction as an impossible chimera!\nHow many more, equally intelligent, have, in the same manner, in our\nown time, rejected, I do not now mean as false, but as\ninconceivable, the doctrine of Luminiferous Undulations! To err in\nthis way is the lot, not only of men in general, but of men of great\nendowments, and very sincere love of truth.\n\n5. And those who liberate themselves from such perplexities, and who\nthus go on in advance of their age in such matters, owe their\nsuperiority in no small degree to such discussions and controversies\nas those to which we now refer. In such controversies, the\nConceptions in question are turned in all directions, examined on\nall sides; the strength and the weakness of the maxims which men\napply to them are fully tested; the light of the brightest minds is\ndiffused to other minds. Inconsistency is unfolded into\nself-contradiction; axioms are built up into a system of necessary\ntruths; and ready exemplifications are accumulated of that which is\nto be proved or disproved, concerning the ideas which are the basis\nof the controversy.\n\nThe History of Mechanics from the time of Kepler to that of\nLagrange, is perhaps the best exemplification of the mode in which\nthe progress of a science depends upon such disputes and\nspeculations as give clearness and generality to its elementary\nconceptions. This, it is to be recollected, is the kind of progress\nof which we are now speaking; and this is the principal feature in\nthe portion of scientific history which we have mentioned. For\nalmost all that was to be done by reference to observation, was\nexecuted by Galileo and his disciples. What remained was the task of\ngeneralization and simplification. And this was promoted in no small\ndegree by the various controversies which took place within that\nperiod concerning {35} mechanical conceptions:--as, for example, the\nquestion concerning the measure of the Force of Percussion;--the war\nof the _Vis Viva_;--the controversy of the Center of\nOscillation;--of the independence of Statics and Dynamics;--of the\nprinciple of Least Action;--of the evidence of the Laws of\nMotion;--and of the number of Laws really distinct. None of these\ndiscussions was without its influence in giving generality and\nclearness to the mechanical ideas of mathematicians: and therefore,\nthough remote from general apprehension, and dealing with very\nabstract notions, they were of eminent use in the perfecting the\nscience of Mechanics. Similar controversies concerning fundamental\nnotions, those, for example, which Galileo himself had to maintain,\nwere no less useful in the formation of the science of Hydrostatics.\nAnd the like struggles and conflicts, whether they take the form of\ncontroversies between several persons, or only operate in the\nefforts and fluctuations of the discoverer's mind, are always\nrequisite, before the conceptions acquire that clearness which makes\nthem flt to appear in the enunciation of scientific truth. This,\nthen, was one object of the History of Ideas;--to bring under the\nreader's notice the main elements of the controversies which have\nthus had so important a share in the formation of the existing body\nof science, and the decisions on the controverted points to which\nthe mature examination of the subject has led; and thus to give an\nabundant exhibition of that step which we term the Explication of\nConceptions.\n\n\nSECT. II.--_Use of Definitions._\n\n6. The result of such controversies as we have been speaking of,\noften appears to be summed up in a _Definition_; and the controversy\nitself has often assumed the form of a battle of definitions. For\nexample, the inquiry concerning the Laws of Falling Bodies led to\nthe question whether the proper Definition of a _uniform force_ is,\nthat it generates a velocity proportional to the _space_ from rest,\nor to the _time_. The controversy of the _Vis Viva_ was, what was\nthe {36} proper Definition of the _measure of force_. A principal\nquestion in the classification of minerals is, what is the\nDefinition of a _mineral species_. Physiologists have endeavoured to\nthrow light on their subject, by Defining _organization_, or some\nsimilar term.\n\n7. It is very important for us to observe, that these controversies\nhave never been questions of insulated and _arbitrary_ Definitions,\nas men seem often tempted to suppose them to have been. In all cases\nthere is a tacit assumption of some Proposition which is to be\nexpressed by means of the Definition, and which gives it its\nimportance. The dispute concerning the Definition thus acquires a\nreal value, and becomes a question concerning true and false. Thus\nin the discussion of the question, What is a Uniform Force? it was\ntaken for granted that 'gravity is a uniform force:'--in the debate\nof the _Vis Viva_, it was assumed that 'in the mutual action of\nbodies the whole effect of the force is unchanged:'--in the\nzoological definition of Species, (that it consists of individuals\nwhich have, or may have, sprung from the same parents,) it is\npresumed that 'individuals so related resemble each other more than\nthose which are excluded by such a definition;' or perhaps, that\n'species so defined have permanent and definite differences.' A\ndefinition of Organization, or of any other term, which was not\nemployed to express some principle, would be of no value.\n\nThe establishment, therefore, of a right Definition of a Term may be\na useful step in the Explication of our Conceptions; but this will\nbe the case _then_ only when we have under our consideration some\nProposition in which the Term is employed. For then the question\nreally is, how the Conception shall be understood and defined in\norder that the Proposition may be true.\n\n8. The establishment of a Proposition requires an attention to\nobserved Facts, and can never be rightly derived from our\nConceptions alone. We must hereafter consider the necessity which\nexists that the Facts should be rightly bound together, as well as\nthat our Conceptions should be clearly employed, in order to {37}\nlead us to real knowledge. But we may observe here that, in such\ncases at least as we are now considering, the two processes are\nco-ordinate. To unfold our Conceptions by the means of Definitions,\nhas never been serviceable to science, except when it has been\nassociated with an immediate _use_ of the Definitions. The endeavour\nto define a uniform Force was combined with the assertion that\n'gravity is a uniform force:' the attempt to define Accelerating\nForce was immediately followed by the doctrine that 'accelerating\nforces may be compounded:' the process of defining Momentum was\nconnected with the principle that 'momenta gained and lost are\nequal:' naturalists would have given in vain the Definition of\nSpecies which we have quoted, if they had not also given the\n'characters' of species so separated. Definition and Proposition are\nthe two handles of the instrument by which we apprehend truth; the\nformer is of no use without the latter. Definition may be the best\nmode of explaining our Conception, but that which alone makes it\nworth while to explain it in any mode, is the opportunity of using\nit in the expression of Truth. When a Definition is propounded to us\nas a useful step in knowledge, we are always entitled to ask what\nPrinciple it serves to enunciate. If there be no answer to this\ninquiry, we define and give clearness to our conceptions in vain.\nWhile we labour at such a task, we do but light up a vacant\nroom;--we sharpen a knife with which we have nothing to cut;--we\ntake exact aim, while we load our artillery with blank\ncartridge;--we apply strict rules of grammar to sentences which have\nno meaning.\n\nIf, on the other hand, we have under our consideration a proposition\nprobably established, every step which we can make in giving\ndistinctness and exactness to the Terms which this proposition\ninvolves, is an important step towards scientific truth. In such\ncases, any improvement in our Definition is a real advance in the\nexplication of our Conception. The clearness of our impressions\ncasts a light upon the Ideas which we contemplate and convey to\nothers. {38}\n\n9. But though _Definition_ may be subservient to a right explication\nof our conceptions, it is _not essential_ to that process. It is\nabsolutely necessary to every advance in our knowledge, that those\nby whom such advances are made should possess clearly the\nconceptions which they employ: but it is by no means necessary that\nthey should unfold these conceptions in the words of a formal\nDefinition. It is easily seen, by examining the course of Galileo's\ndiscoveries, that he had a distinct conception of the _Moving Force_\nwhich urges bodies downwards upon an inclined plane, while he still\nhesitated whether to call it _Momentum_, _Energy_, _Impetus_, or\n_Force_, and did not venture to offer a Definition of the thing\nwhich was the subject of his thoughts. The Conception of\n_Polarization_ was clear in the minds of many optical speculators,\nfrom the time of Huyghens and Newton to that of Young and Fresnel.\nThis Conception we have defined to be 'Opposite properties depending\nupon opposite positions;' but this notion was, by the discoverers,\nthough constantly assumed and expressed by means of superfluous\nhypotheses, never clothed in definite language. And in the mean\ntime, it was the custom, among subordinate writers on the same\nsubjects, to say, that the term _Polarization_ had no definite\nmeaning, and was merely an expression of our ignorance. The\nDefinition which was offered by Ha\u00fcy and others of a _Mineralogical\nSpecies_;--'The same elements combined in the same proportions, with\nthe same fundamental form;'--was false, inasmuch as it was incapable\nof being rigorously applied to any one case; but this defect did not\nprevent the philosophers who propounded such a Definition from\nmaking many valuable additions to mineralogical knowledge, in the\nway of identifying some species and distinguishing others. The right\nConception which they possessed in their minds prevented their being\nmisled by their own very erroneous Definition. The want of any\nprecise Definitions of _Strata_, and _Formations_, and _Epochs_,\namong geologists, has not prevented the discussions which they have\ncarried on upon such subjects from being highly serviceable {39} in\nthe promotion of geological knowledge. For however much the apparent\nvagueness of these terms might leave their arguments open to cavil,\nthere was a general understanding prevalent among the most\nintelligent cultivators of the science, as to what was meant in such\nexpressions; and this common understanding sufficed to determine\nwhat evidence should be considered conclusive and what inconclusive,\nin these inquiries. And thus the distinctness of Conception, which\nis a real requisite of scientific progress, existed in the minds of\nthe inquirers, although Definitions, which are a partial and\naccidental evidence of this distinctness, had not yet been hit upon.\nThe Idea had been developed in men's minds, although a clothing of\nwords had not been contrived for it, nor, perhaps, the necessity of\nsuch a vehicle felt: and thus that essential condition of the\nprogress of knowledge, of which we are here speaking, existed; while\nit was left to the succeeding speculators to put this unwritten Rule\nin the form of a verbal Statute.\n\n10. Men are often prone to consider it as a thoughtless _omission_\nof an essential circumstance, and as a _neglect_ which involves some\nblame, when knowledge thus assumes a form in which Definitions, or\nrather Conceptions, are implied but are not expressed. But in such a\njudgment, they assume _that_ to be a matter of choice requiring\nattention only, which is in fact as difficult and precarious as any\nother portion of the task of discovery. To _define_, so that our\nDefinition shall have any scientific value, requires no small\nportion of that sagacity by which truth is detected. As we have\nalready said, Definitions and Propositions are co-ordinate in their\nuse and in their origin. In many cases, perhaps in most, the\nProposition which contains a scientific truth, is apprehended with\nconfidence, but with some vagueness and vacillation, before it is\nput in a positive, distinct, and definite form.--It is thus known to\nbe true, before it can be enunciated in terms each of which is\nrigorously defined. The business of Definition is part of the\nbusiness of discovery. When it has been clearly seen what ought to\nbe our Definition, it {40} must be pretty well known what truth we\nhave to state. The Definition, as well as the discovery, supposes a\ndecided step in our knowledge to have been made. The writers on\nLogic in the middle ages, made Definition the last stage in the\nprogress of knowledge; and in this arrangement at least, the history\nof science, and the philosophy derived from the history, confirm\ntheir speculative views. If the Explication of our Conceptions ever\nassume the form of a Definition, this will come to pass, not as an\narbitrary process, or as a matter of course, but as the mark of one\nof those happy efforts of sagacity to which all the successive\nadvances of our knowledge are owing.\n\n\nSECT. III.--_Use of Axioms._\n\n11. Our Conceptions, then, even when they become so clear as the\nprogress of knowledge requires, are not adequately expressed, or\nnecessarily expressed at all, by means of Definitions. We may ask,\nthen, whether there is any _other mode_ of expression in which we\nmay look for the evidence and exposition of that peculiar exactness\nof thought which the formation of Science demands. And in answer to\nthis inquiry, we may refer to the discussions respecting many of the\nFundamental Ideas of the sciences contained in our _History_ of such\nIdeas. It has there been seen that these Ideas involve many\nelementary truths which enter into the texture of our knowledge,\nintroducing into it connexions and relations of the most important\nkind, although these elementary truths cannot be deduced from any\nverbal definition of the idea. It has been seen that these\nelementary truths may often be enunciated by means of _Axioms_,\nstated in addition to, or in preference to, Definitions. For\nexample, the Idea of Cause, which forms the basis of the science of\nMechanics, makes its appearance in our elementary mechanical\nreasonings, not as a Definition, but by means of the Axioms that\n'Causes are measured by their effects,' and that 'Reaction is equal\nand opposite to action.' Such axioms, tacitly assumed or {41}\noccasionally stated, as maxims of acknowledged validity, belong to\nall the Ideas which form the foundations of the sciences, and are\nconstantly employed in the reasoning and speculations of those who\nthink clearly on such subjects. It may often be a task of some\ndifficulty to detect and enunciate in words the Principles which are\nthus, perhaps silently and unconsciously, taken for granted by those\nwho have a share in the establishment of scientific truth: but\ninasmuch as these Principles are an essential element in our\nknowledge, it is very important to our present purpose to separate\nthem from the associated materials, and to trace them to their\norigin. This accordingly I attempted to do, with regard to a\nconsiderable number of the most prominent of such Ideas, in the\n_History_. The reader will there find many of these Ideas resolved\ninto Axioms and Principles by means of which their effect upon the\nelementary reasonings of the various sciences may be expressed. That\nWork is intended to form, in some measure, a representation of the\nIdeal Side of our physical knowledge;--a Table of those contents of\nour Conceptions which are not received directly from facts;--an\nexhibition of Rules to which we know that truth must conform.\n\n\nSECT. IV.--_Clear and appropriate Ideas._\n\n12. In order, however, that we may see the necessary cogency of\nthese rules, we must possess, clearly and steadily, the Ideas from\nwhich the rules flow. In order to perceive the necessary relations\nof the Circles of the Sphere, we must possess clearly the Idea of\nSolid Space:--in order that we may see the demonstration of the\ncomposition of forces, we must have the Idea of Cause moulded into a\ndistinct Conception of Statical Force. This is that _Clearness of\nIdeas_ which we stipulate for in any one's mind, as the first\nessential condition of his making any new step in the discovery of\ntruth. And we now see what answer we are able to give, if we are\nasked for a Criterion of this Clearness of {42} Idea. The Criterion\nis, that the person shall _see_ the necessity of the Axioms belonging\nto each Idea;--shall accept them in such a manner as to perceive the\ncogency of the reasonings founded upon them. Thus, a person has a\nclear Idea of Space who follows the reasonings of geometry and fully\napprehends their conclusiveness. The Explication of Conceptions,\nwhich we are speaking of as an essential part of real knowledge, is\nthe process by which we bring the Clearness of our Ideas to bear\nupon the Formation of our knowledge. And this is done, as we have\nnow seen, not always, nor generally, nor principally, by laying down\na Definition of the Conception; but by acquiring such a possession\nof it in our minds as enables, indeed compels us, to admit, along\nwith the Conception, all the Axioms and Principles which it\nnecessarily implies, and by which it produces its effect upon our\nreasonings.\n\n13. But in order that we may make any real advance in the discovery\nof truth, our Ideas must not only be clear, they must also be\n_appropriate_. Each science has for its basis a different class of\nIdeas; and the steps which constitute the progress of one science\ncan never be made by employing the Ideas of another kind of science.\nNo genuine advance could ever be obtained in Mechanics by applying\nto the subject the Ideas of Space and Time merely:--no advance in\nChemistry, by the use of mere Mechanical Conceptions:--no discovery\nin Physiology, by referring facts to mere Chemical and Mechanical\nPrinciples. Mechanics must involve the Conception of\n_Force_;--Chemistry, the Conception of _Elementary\nComposition_;--Physiology, the Conception of _Vital Powers_. Each\nscience must advance by means of its appropriate Conceptions. Each\nhas its own field, which extends as far as its principles can be\napplied. I have already noted the separation of several of these\nfields by the divisions of the Books of the _History_ of Ideas. The\nMechanical, the Secondary Mechanical, the Chemical, the\nClassificatory, the Biological Sciences form so many great Provinces\nin the Kingdom of knowledge, each in a great measure possessing its\nown peculiar fundamental principles. Every attempt to build up a\n{43} new science by the application of principles which belong to an\nold one, will lead to frivolous and barren speculations.\n\nThis truth has been exemplified in all the instances in which subtle\nspeculative men have failed in their attempts to frame new sciences,\nand especially in the essays of the ancient schools of philosophy in\nGreece, as has already been stated in the History of Science.\nAristotle and his followers endeavoured in vain to account for the\nmechanical relation of forces in the lever by applying the\n_inappropriate_ geometrical conceptions of the properties of the\ncircle:--they speculated to no purpose about the elementary\ncomposition of bodies, because they assumed the _inappropriate_\nconception of _likeness_ between the elements and the compound,\ninstead of the genuine notion of elements merely _determining_ the\nqualities of the compound. And in like manner, in modern times, we\nhave seen, in the history of the fundamental ideas of the\nphysiological sciences, how all the _inappropriate_ mechanical and\nchemical and other ideas which were applied in succession to the\nsubject failed in bringing into view any genuine physiological\ntruth.\n\n14. That the real cause of the failure in the instances above\nmentioned lay in the _Conceptions_, is plain. It was not ignorance\nof the facts which in these cases prevented the discovery of the\ntruth. Aristotle was as well acquainted with the fact of the\nproportion of the weights which balance on a Lever as Archimedes\nwas, although Archimedes alone gave the true mechanical reason for\nthe proportion.\n\nWith regard to the doctrine of the Four Elements indeed, the\ninapplicability of the conception of composition of qualities,\nrequired, perhaps, to be proved by some reference to facts. But this\nconception was devised at first, and accepted by succeeding times,\nin a blind and gratuitous manner, which could hardly have happened\nif men had been awake to the necessary condition of our\nknowledge;--that the conceptions which we introduce into our\ndoctrines are not arbitrary or accidental notions, but certain\npeculiar modes of {44} apprehension strictly determined by the\nsubject of our speculations.\n\n15. It may, however, be said that this injunction that we are to\nemploy _appropriate_ Conceptions only in the formation of our\nknowledge, cannot be of practical use, because we can only determine\nwhat Ideas _are_ appropriate, by finding that they truly combine the\nfacts. And this is to a certain extent true. Scientific discovery\nmust ever depend upon some happy thought, of which we cannot trace\nthe origin;--some fortunate cast of intellect, rising above all\nrules. No maxims can be given which inevitably lead to discovery. No\nprecepts will elevate a man of ordinary endowments to the level of a\nman of genius: nor will an inquirer of truly inventive mind need to\ncome to the teacher of inductive philosophy to learn how to exercise\nthe faculties which nature has given him. Such persons as Kepler or\nFresnel, or Brewster, will have their powers of discovering truth\nlittle augmented by any injunctions respecting Distinct and\nAppropriate Ideas; and such men may very naturally question the\nutility of rules altogether.\n\n16. But yet the opinions which such persons may entertain, will not\nlead us to doubt concerning the value of the attempts to analyse and\nmethodize the process of discovery. Who would attend to Kepler if he\nhad maintained that the speculations of Francis Bacon were\nworthless? Notwithstanding what has been said, we may venture to\nassert that the Maxim which points out the necessity of Ideas\nappropriate as well as clear, for the purpose of discovering truth,\nis not without its use. It may, at least, have a value as a caution\nor prohibition, and may thus turn us away from labours certain to be\nfruitless. We have already seen, in the _History_ of Ideas, that\nthis maxim, if duly attended to, would have at once condemned, as\nwrongly directed, the speculations of physiologists of the\nmathematical, mechanical, chemical, and vital-fluid schools; since\nthe Ideas which the teachers of these schools introduce, cannot\nsuffice for the purposes of physiology, which seeks truths\nrespecting the vital powers. Again, {45} it is clear from similar\nconsiderations that no definition of a mineralogical species by\nchemical characters alone can answer the end of science, since we\nseek to make mineralogy, not an analytical but a classificatory\nscience[1\\2]. Even before the appropriate conception is matured in\nmen's minds so that they see clearly what it is, they may still have\nlight enough to see what it is not.\n\n[Note 1\\2: This agrees with what M. Necker has well observed in his\n_R\u00e8gne Mineral_, that those who have treated mineralogy as a merely\nchemical science, have substituted the analysis of substances for\nthe classification of individuals. See _History of Ideas_, b. viii.\nchap. iii.]\n\n17. Another result of this view of the necessity of appropriate\nIdeas, combined with a survey of the history of science is, that\nthough for the most part, as we shall see, the progress of science\nconsists in accumulating and combining Facts rather than in debating\nconcerning Definitions; there are still certain periods when the\n_discussion_ of Definitions may be the most useful mode of\ncultivating some special branch of science. This discussion is of\ncourse always to be conducted by the light of facts; and, as has\nalready been said, along with the settlement of every good\nDefinition will occur the corresponding establishment of some\nProposition. But still at particular periods, the want of a\nDefinition, or of the clear conceptions which Definition supposes,\nmay be peculiarly felt. A good and tenable Definition of _Species_\nin Mineralogy would at present be perhaps the most important step\nwhich the science could make. A just conception of the nature of\n_Life_, (and if expressed by means of a Definition, so much the\nbetter,) can hardly fail to give its possessor an immense advantage\nin the speculations which now come under the considerations of\nphysiologists. And controversies respecting Definitions, in these\ncases, and such as these, may be very far from idle and\nunprofitable.\n\nThus the knowledge that Clear and Appropriate Ideas are requisite\nfor discovery, although it does not lead to any very precise\nprecepts, or supersede the value of natural sagacity and\ninventiveness, may still {46} be of use to us in our pursuit after\ntruth. It may show us what course of research is, in each stage of\nscience, recommended by the general analogy of the history of\nknowledge; and it may both save us from hopeless and barren paths of\nspeculation, and make us advance with more courage and confidence,\nto know that we are looking for discoveries in the manner in which\nthey have always hitherto been made.\n\n\nSECT. V.--_Accidental Discoveries._\n\n18. Another consequence follows from the views presented in this\nChapter, and it is the last I shall at present mention. _No\nscientific discovery_ can, with any justice, be considered _due to\naccident_. In whatever manner facts may be presented to the notice\nof a discoverer, they can never become the materials of exact\nknowledge, except they find his mind already provided with precise\nand suitable conceptions by which they may be analysed and\nconnected. Indeed, as we have already seen, facts cannot be observed\nas Facts, except in virtue of the Conceptions which the\nobserver[2\\2] himself unconsciously supplies; and they are not Facts\nof Observation for any purpose of Discovery, except these familiar\nand unconscious acts of thought be themselves of a just and precise\nkind. But supposing the Facts to be adequately observed, they can\nnever be combined into any new Truth, except by means of some new\nConceptions, clear and appropriate, such as I have endeavoured to\ncharacterize. When the observer's mind is prepared with such\ninstruments, a very few facts, or it may be a single one, may bring\nthe process of discovery into action. But in such cases, this\nprevious condition of the intellect, and not the single fact, is\nreally the main and peculiar cause of the success. The fact is\nmerely the occasion by which the engine of discovery is brought into\nplay sooner or later. It is, as I have elsewhere said, only the\nspark which discharges a gun already loaded and pointed; and there\n{47} is little propriety in speaking of such an accident as the\ncause why the bullet hits the mark. If it were true that the fall of\nan apple was the occasion of Newton's pursuing the train of thought\nwhich led to the doctrine of universal gravitation, the habits and\nconstitution of Newton's intellect, and not the apple, were the real\nsource of this great event in the progress of knowledge. The common\nlove of the marvellous, and the vulgar desire to bring down the\ngreatest achievements of genius to our own level, may lead men to\nascribe such results to any casual circumstances which accompany\nthem; but no one who fairly considers the real nature of great\ndiscoveries, and the intellectual processes which they involve, can\nseriously hold the opinion of their being the effect of accident.\n\n[Note 2\\2: B. i. of this vol. Aphorism III.]\n\n19. Such accidents never happen to common men. Thousands of men,\neven of the most inquiring and speculative men, had seen bodies\nfall; but who, except Newton, ever followed the accident to such\nconsequences? And in fact, how little of his train of thought was\ncontained in, or even directly suggested by, the fall of the apple!\nIf the apple fall, said the discoverer, 'why should not the moon,\nthe planets, the satellites, fall?' But how much previous\nthought,--what a steady conception of the universality of the laws\nof motion gathered from other sources,--were requisite, that the\ninquirer should see any connexion in these cases! Was it by accident\nthat he saw in the apple an image of the moon, and of every body in\nthe solar system?\n\n20. The same observations may be made with regard to the other cases\nwhich are sometimes adduced as examples of accidental discovery. It\nhas been said, 'By the accidental placing of a rhomb of calcareous\nspar upon a book or line Bartholinus discovered the property of the\n_Double Refraction_ of light.' But Bartholinus could have seen no\nsuch consequence in the accident if he had not previously had a\nclear conception of _single refraction_. A lady, in describing an\noptical experiment which had been shown her, said of her teacher,\n'He told me to _increase and diminish_ {48} _the angle of\nrefraction_, and at last I found that he only meant me to move my\nhead up and down.' At any rate, till the lady had acquired the\nnotions which the technical terms convey, she could not have made\nBartholinus's discovery by means of his accident. 'By accidentally\ncombining two rhombs in different positions,' it is added, 'Huyghens\ndiscovered the _Polarization_ of Light.' Supposing that this\nexperiment had been made without design, what Huyghens really\nobserved was, that the images appeared and disappeared alternately\nas he turned one of the rhombs round. But was it an easy or an\nobvious business to analyze this curious alternation into the\ncircumstances of the rays of light having _sides_, as Newton\nexpressed it, and into the additional hypotheses which are implied\nin the term 'polarization'? Those will be able to answer this\nquestion, who have found how far from easy it is to understand\nclearly what is meant by 'polarization' in this case, now that the\nproperty is fully established. Huyghens's success depended on his\nclearness of thought, for this enabled him to perform the\nintellectual analysis, which never would have occurred to most men,\nhowever often they had 'accidentally combined two rhombs in\ndifferent positions.' 'By accidentally looking through a prism of\nthe same substance, and turning it round, Malus discovered the\npolarization of light by reflection.' Malus saw that, in some\npositions of the prism, the light reflected from the windows of the\nLouvre thus seen through the prism, became dim. A common man would\nhave supposed this dimness the result of accident; but Malus's mind\nwas differently constituted and disciplined. He considered the\nposition of the window, and of the prism; repeated the experiment\nover and over; and in virtue of the eminently distinct conceptions\nof space which he possessed, resolved the phenomena into its\ngeometrical conditions. A believer in accident would not have sought\nthem; a person of less clear ideas would not have found them. A\nperson must have a strange confidence in the virtue of chance, and\nthe worthlessness of intellect, who can say that {49} 'in all these\nfundamental discoveries appropriate ideas had no share,' and that\nthe discoveries 'might have been made by the most ordinary\nobservers.'\n\n21. I have now, I trust, shown in various ways, how the _Explication\nof Conceptions_, including in this term their clear development from\nFundamental Ideas in the discoverer's mind, as well as their precise\nexpression in the form of Definitions or Axioms, when that can be\ndone, is an essential part in the establishment of all exact and\ngeneral physical truths. In doing this, I have endeavoured to\nexplain in what sense the possession of clear and appropriate ideas\nis a main requisite for every step in scientific discovery. That it\nis far from being the only step, I shall soon have to show; and if\nany obscurity remain on the subject treated of in the present\nchapter, it will, I hope, be removed when we have examined the other\nelements which enter into the constitution of our knowledge.\n\n\n\n{{50}}\nCHAPTER III.\n\nOF FACTS AS THE MATERIALS OF SCIENCE.\n\n\nAPHORISM IV.\n\n_Facts are the materials of science, but all Facts involve Ideas.\nSince in observing Facts, we cannot exclude Ideas, we must, for the\npurposes of science, take care that the Ideas are clear and\nrigorously applied._\n\nAPHORISM V.\n\n_The last Aphorism leads to such Rules as the following:--That\nFacts, for the purposes of material science, must involve\nConceptions of the Intellect only, and not Emotions:--That Facts\nmust be observed with reference to our most exact conceptions,\nNumber, Place, Figure, Motion:--That they must also be observed with\nreference to any other exact conceptions which the phenomena\nsuggest, as Force, in mechanical phenomena, Concord, in musical._\n\nAPHORISM VI.\n\n_The resolution of complex Facts into precise and measured partial\nFacts, we call the_ Decomposition of Facts. _This process is\nrequisite for the progress of science, but does not necessarily lead\nto progress._\n\n\n1. WE have now to examine how Science is built up by the combination\nof Facts. In doing this, we suppose that we have already attained a\nsupply of definite and certain Facts, free from obscurity and doubt.\nWe must, therefore, first consider under what conditions Facts can\nassume this character.\n\nWhen we inquire what Facts are to be made the materials of Science,\nperhaps the answer which we {51} should most commonly receive would\nbe, that they must be _True Facts_, as distinguished from any mere\ninferences or opinions of our own. We should probably be told that\nwe must be careful in such a case to consider as Facts, only what we\nreally observe;--that we must assert only what we see; and believe\nnothing except upon the testimony of our senses.\n\nBut such maxims are far from being easy to apply, as a little\nexamination will convince us.\n\n2. It has been explained, in preceding works, that all perception of\nexternal objects and occurrences involves an active as well as a\npassive process of the mind;--includes not only Sensations, but also\nIdeas by which Sensations are bound together, and have a unity given\nto them. From this it follows, that there is a difficulty in\nseparating in our perceptions what we receive from without, and what\nwe ourselves contribute from within;--what we perceive, and what we\ninfer. In many cases, this difficulty is obvious to all: as, for\nexample, when we witness the performances of a juggler or a\nventriloquist. In these instances, we imagine ourselves to see and\nto hear what certainly we do not see and hear. The performer takes\nadvantage of the habits by which our minds supply interruptions and\ninfer connexions; and by giving us fallacious indications, he leads\nus to perceive as an actual fact, what does not happen at all. In\nthese cases, it is evident that we ourselves assist in making the\nfact; for we make one which does not really exist. In other cases,\nthough the fact which we perceive be true, we can easily see that a\nlarge portion of the perception is our own act; as when, from the\nsight of a bird of prey we infer a carcase, or when we read a\nhalf-obliterated inscription. In the latter case, the mind supplies\nthe meaning, and perhaps half the letters; yet we do not hesitate to\nsay that we actually _read_ the inscription. Thus, in many cases,\nour own inferences and interpretations enter into our facts. But\nthis happens in many instances in which it is at first sight less\nobvious. When any one has seen an oak-tree blown down by a strong\ngust of wind, he does not think of the occurrence {52} any otherwise\nthan as a _Fact_ of which he is assured by his senses. Yet by what\nsense does he perceive the Force which he thus supposes the wind to\nexert? By what sense does he distinguish an Oak-tree from all other\ntrees? It is clear upon reflexion, that in such a case, his own mind\nsupplies the conception of extraneous impulse and pressure, by which\nhe thus interprets the motions observed, and the distinction of\ndifferent kinds of trees, according to which he thus names the one\nunder his notice. The Idea of Force, and the idea of definite\nResemblances and Differences, are thus combined with the impressions\non our senses, and form an undistinguished portion of that which we\nconsider as the Fact. And it is evident that we can in no other way\nperceive Force, than by seeing motion; and cannot give a Name to any\nobject, without not only seeing a difference of single objects, but\nsupposing a difference of classes of objects. When we speak as if we\nsaw impulse and attraction, things and classes, we really see only\nobjects of various forms and colours, more or less numerous,\nvariously combined. But do we really perceive so much as this? When\nwe see the form, the size, the number, the motion of objects, are\nthese really mere impressions on our senses, unmodified by any\ncontribution or operation of the mind itself? A very little\nattention will suffice to convince us that this is not the case.\nWhen we see a windmill turning, it may happen, as we have elsewhere\nnoticed[3\\2], that we mistake the direction in which the sails turn:\nwhen we look at certain diagrams, they may appear either convex or\nconcave: when we see the moon first in the horizon and afterwards\nhigh up in the sky, we judge her to be much larger in the former\nthan in the latter position, although to the eye she subtends the\nsame angle. And in these cases and the like, it has been seen that\nthe errour and confusion which we thus incur arise from the mixture\nof acts of the mind itself with impressions on the senses. But such\nacts are, as we have also seen, _inseparable_ portions of the\nprocess {53} of perception. A certain activity of the mind is\ninvolved, not only in seeing objects erroneously, but in seeing them\nat all. With regard to solid objects, this is generally\nacknowledged. When we seem to see an edifice occupying space in all\ndimensions, we really see only a representation of it as it appears\nreferred by perspective to a surface. The inference of the solid\nform is an operation of our own, alike when we look at a reality and\nwhen we look at a picture. But we may go further. Is plane Figure\nreally a mere Sensation? If we look at a decagon, do we see at once\nthat it has ten sides, or is it not necessary for us to count them:\nand is not counting an act of the mind? All objects are seen in\nspace; all objects are seen as one or many: but are not the Idea of\nSpace and the Idea of Number requisite in order that we may thus\napprehend what we see? That these Ideas of Space and Number involve\na connexion derived from the mind, and not from the senses, appears,\nas we have already seen, from this, that those Ideas afford us the\nmaterials of universal and necessary truths:--such truths as the\nsenses cannot possibly supply. And thus, even the perception of such\nfacts as the size, shape, and number of objects, cannot be said to\nbe impressions of sense, distinct from all acts of mind, and cannot\nbe expected to be free from errour on the ground of their being mere\nobserved Facts.\n\n[Note 3\\2: _History of Ideas_, B. ii. c. vi. s. 6.]\n\nThus the difficulty which we have been illustrating, of\ndistinguishing Facts from inferences and from interpretations of\nfacts, is not only great, but amounts to an impossibility. The\nseparation at which we aimed in the outset of this discussion, and\nwhich was supposed to be necessary in order to obtain a firm\ngroundwork for science, is found to be unattainable. We cannot\nobtain a sure basis of Facts, by rejecting all inferences and\njudgments of our own, for such inferences and judgments form an\nunavoidable element in all Facts. We cannot exclude our Ideas from\nour Perceptions, for our Perceptions involve our Ideas.\n\n3. But still, it cannot be doubted that in selecting the Facts which\nare to form the foundation of Science, {54} we must reduce them to\ntheir most simple and certain form; and must reject everything from\nwhich doubt or errour may arise. Now since this, it appears, cannot\nbe done, by rejecting the Ideas which all Facts involve, in what\nmanner are we to conform to the obvious maxim, that the Facts which\nform the basis of Science must be perfectly definite and certain?\n\nThe analysis of facts into Ideas and Sensations, which we have so\noften referred to, suggests the answer to this inquiry. We are not\nable, nor need we endeavour, to exclude Ideas from our Facts; but we\nmay be able to discern, with perfect distinctness, the Ideas which\nwe include. We cannot observe any phenomena without applying to them\nsuch Ideas as Space and Number, Cause and Resemblance, and usually,\nseveral others; but we may avoid applying these Ideas in a wavering\nor obscure manner, and confounding Ideas with one another. We cannot\nread any of the inscriptions which nature presents to us, without\ninterpreting them by means of some language which we ourselves are\naccustomed to speak; but we may make it our business to acquaint\nourselves perfectly with the language which we thus employ, and to\ninterpret it according to the rigorous rules of grammar and analogy.\n\nThis maxim, that when Facts are employed as the basis of Science, we\nmust distinguish clearly the Ideas which they involve, and must\napply these in a distinct and rigorous manner, will be found to be a\nmore precise guide than we might perhaps at first expect. We may\nnotice one or two Rules which flow from it.\n\n4. In the first place. Facts, when used as the materials of physical\nScience, must be _referred to Conceptions of the Intellect only_,\nall emotions of fear, admiration, and the like, being rejected or\nsubdued. Thus, the observations of phenomena which are related as\nportents and prodigies, striking terrour and boding evil, are of no\nvalue for purposes of science. The tales of armies seen warring in\nthe sky, the sound of arms heard from the clouds, fiery dragons,\nchariots, swords seen in the air, may refer to meteorological\nphenomena; but the records of phenomena observed in the {55} state\nof mind which these descriptions imply can be of no scientific\nvalue. We cannot make the poets our observers.\n\n Armorum sonitum toto Germania c\u0153lo\n Audiit; insolitis tremuerunt motibus Alpes.\n Vox quoque per lucos vulgo exaudita silentes\n Ingens; et simulacra modis pallentia miris\n Visa sub obscurum noctis: pecudesque locut\u00e6.\n\nThe mixture of fancy and emotion with the observation of facts has\noften disfigured them to an extent which is too familiar to all to\nneed illustration. We have an example of this result, in the manner\nin which Comets are described in the treatises of the middle ages.\nIn such works, these bodies are regularly distributed into several\nclasses, accordingly as they assume the form of a sword, of a spear,\nof a cross, and so on. When such resemblances had become matters of\ninterest, the impressions of the senses were governed, not by the\nrigorous conceptions of form and colour, but by these assumed\nimages; and under these circumstances, we can attach little value to\nthe statement of what was seen.\n\nIn all such phenomena, the reference of the objects to the exact\nIdeas of Space, Number, Position, Motion, and the like, is the first\nstep of Science: and accordingly, this reference was established at\nan early period in those sciences which made an early progress, as,\nfor instance, Astronomy. Yet even in astronomy there appears to have\nbeen a period when the predominant conceptions of men in regarding\nthe heavens and the stars pointed to mythical story and supernatural\ninfluence, rather than to mere relations of space, time, and motion:\nand of this primeval condition of those who gazed at the stars, we\nseem to have remnants in the Constellations, in the mythological\nNames of the Planets, and in the early prevalence of Astrology. It\nwas only at a later period, when men had begun to measure the\nplaces, or at least to count the revolutions of the stars, that\nAstronomy had its birth.\n\n5. And thus we are led to another Rule:--that in collecting Facts\nwhich are to be made the basis of {56} Science, the Facts are to be\nobserved, as far as possible, _with reference to place, figure,\nnumber, motion_, and the like Conceptions; which, depending upon the\nIdeas of Space and Time, are the most universal, exact, and simple\nof our conceptions. It was by early attention to these relations in\nthe case of the heavenly bodies, that the ancients formed the\nscience of Astronomy: it was by not making precise observations of\nthis kind in the case of terrestrial bodies, that they failed in\nframing a science of the Mechanics of Motion. They succeeded in\nOptics as far as they made observations of this nature; but when\nthey ceased to trace the geometrical paths of rays in the actual\nexperiment, they ceased to go forwards in the knowledge of this\nsubject.\n\n6. But we may state a further Rule:--that though these relations of\nTime and Space are highly important in almost all Facts, we are not\nto confine ourselves to these: but are to consider the phenomena\n_with reference to other Conceptions also_: it being always\nunderstood that these conceptions are to be made as exact and\nrigorous as those of geometry and number. Thus the science of\nHarmonics arose from considering sounds with reference to _Concords_\nand _Discords_; the science of Mechanics arose from not only\nobserving motions as they take place in Time and Space, but further,\nreferring them to _Force_ as their _Cause_. And in like manner,\nother sciences depend upon other Ideas, which, as I have endeavoured\nto show, are not less fundamental than those of Time and Space; and\nlike them, capable of leading to rigorous consequences.\n\n7. Thus the Facts which we assume as the basis of Science are to be\nfreed from all the mists which imagination and passion throw round\nthem; and to be separated into those elementary Facts which exhibit\nsimple and evident relations of Time, or Space, or Cause, or some\nother Ideas equally clear. We resolve the complex appearances which\nnature offers to us, and the mixed and manifold modes of looking at\nthese appearances which rise in our thoughts, into limited,\ndefinite, and clearly-understood portions. This process we may term\nthe _Decomposition of Facts_. It is the {57} beginning of exact\nknowledge,--the first step in the formation of all Science. This\nDecomposition of Facts into Elementary Facts, clearly understood and\nsurely ascertained, must precede all discovery of the laws of\nnature.\n\n8. But though this step is necessary, it is not infallibly\nsufficient. It by no means follows that when we have thus decomposed\nFacts into Elementary Truths of observation, we shall soon be able\nto combine these, so as to obtain Truths of a higher and more\nspeculative kind. We have examples which show us how far this is\nfrom being a necessary consequence of the former step. Observations\nof the weather, made and recorded for many years, have not led to\nany general truths, forming a science of Meteorology: and although\ngreat numerical precision has been given to such observations by\nmeans of barometers, thermometers, and other instruments, still, no\ngeneral laws regulating the cycles of change of such phenomena have\nyet been discovered. In like manner the faces of crystals, and the\nsides of the polygons which these crystals form, were counted, and\nthus numerical facts were obtained, perfectly true and definite, but\nstill of no value for purposes of science. And when it was\ndiscovered what Element of the form of crystals it was important to\nobserve and measure, namely, the Angle made by two faces with each\nother, this discovery was a step of a higher order, and did not\nbelong to that department, of mere exact observation of manifest\nFacts, with which we are here concerned.\n\n9. When the Complex Facts which nature offers to us are thus\ndecomposed into Simple Facts, the decomposition, in general, leads\nto the introduction of _Terms_ and Phrases, more or less technical,\nby which these Simple Facts are described. When Astronomy was thus\nmade a science of measurement, the things measured were soon\ndescribed as _Hours_, and _Days_, and _Cycles_, _Altitude_ and\n_Declination_, _Phases_ and _Aspects_. In the same manner, in Music,\nthe concords had names assigned them, as _Diapente_, _Diatessaron_,\n_Diapason_; in studying Optics, the _Rays_ of light were spoken of\nas {58} having their course altered by _Reflexion_ and _Refraction_;\nand when useful observations began to be made in Mechanics, the\nobservers spoke of _Force_, _Pressure_, _Momentum_, _Inertia_, and\nthe like.\n\n10. When we take phenomena in which the leading Idea is Resemblance,\nand resolve them into precise component Facts, we obtain some kind\nof Classification; as, for instance, when we lay down certain Rules\nby which particular trees, or particular animals are to be known.\nThis is the earliest form of Natural History; and the Classification\nwhich it involves is that which corresponds, nearly or exactly, with\nthe usual Names of the objects thus classified.\n\n11. Thus the first attempts to render observation certain and exact,\nlead to a decomposition of the obvious facts into Elementary Facts,\nconnected by the Ideas of Space, Time, Number, Cause, Likeness, and\nothers: and into a Classification of the Simple Facts; a\nclassification more or less just, and marked by Names either common\nor technical. Elementary Facts, and Individual Objects, thus\nobserved and classified, form the materials of Science; and any\nimprovement in Classification or Nomenclature, or any discovery of a\nConnexion among the materials thus accumulated, leads us fairly\nwithin the precincts of Science. We must now, therefore, consider\nthe manner in which Science is built up of such materials;--the\nprocess by which they are brought into their places, and the texture\nof the bond which unites and cements them.\n\n\n\n{{59}}\nCHAPTER IV.\n\nOF THE COLLIGATION OF FACTS.\n\n\nAPHORISM VII.\n\n_Science begins with_ common _observation of facts; but even at this\nstage, requires that the observations be precise. Hence the sciences\nwhich depend upon space and number were the earliest formed. After\ncommon observation, come Scientific_ Observation _and_ Experiment.\n\nAPHORISM VIII.\n\n_The Conceptions by which Facts are bound together, are suggested by\nthe sagacity of discoverers. This sagacity cannot be taught. It\ncommonly succeeds by guessing; and this success seems to consist in\nframing several_ tentative hypotheses _and selecting the right one.\nBut a supply of appropriate hypotheses cannot be constructed by\nrule, nor without inventive talent._\n\nAPHORISM IX.\n\n_The truth of tentative hypotheses must be tested by their\napplication to facts. The discoverer must be ready, carefully to try\nhis hypotheses in this manner, and to reject them if they will not\nbear the test, in spite of indolence and vanity._\n\n\n1. FACTS such as the last Chapter speaks of are, by means of such\nConceptions as are described in the preceding Chapter, bound\ntogether so as to give rise to those general Propositions of which\nScience consists. Thus the Facts that the planets revolve {60} about\nthe sun in certain periodic times and at certain distances, are\nincluded and connected in Kepler's Law, by means of such Conceptions\nas the _squares of numbers_, the _cubes of distances_, and the\n_proportionality_ of these quantities. Again the existence of this\nproportion in the motions of any two planets, forms a set of Facts\nwhich may all be combined by means of the Conception of a certain\n_central accelerating force_, as was proved by Newton. The whole of\nour physical knowledge consists in the establishment of such\npropositions; and in all such cases, Facts are bound together by the\naid of suitable Conceptions. This part of the formation of our\nknowledge I have called the _Colligation of Facts_: and we may apply\nthis term to every case in which, by an act of the intellect, we\nestablish a precise connexion among the phenomena which are\npresented to our senses. The knowledge of such connexions,\naccumulated and systematized, is Science. On the steps by which\nscience is thus collected from phenomena we shall proceed now to\nmake a few remarks.\n\n2. Science begins with _Common_ Observation of facts, in which we\nare not conscious of any peculiar discipline or habit of thought\nexercised in observing. Thus the common perceptions of the\nappearances and recurrences of the celestial luminaries, were the\nfirst steps of Astronomy: the obvious cases in which bodies fall or\nare supported, were the beginning of Mechanics; the familiar aspects\nof visible things, were the origin of Optics; the usual distinctions\nof well-known plants, first gave rise to Botany. Facts belonging to\nsuch parts of our knowledge are noticed by us, and accumulated in\nour memories, in the common course of our habits, almost without our\nbeing aware that we are observing and collecting facts. Yet such\nfacts may lead to many scientific truths; for instance, in the first\nstages of Astronomy (as we have shown in the _History_) such facts\nled to Methods of Intercalation and Rules of the Recurrence of\nEclipses. In succeeding stages of science, more especial attention\nand preparation on the part of the observer, and a selection of\ncertain {61} _kinds_ of facts, becomes necessary; but there is an\nearly period in the progress of knowledge at which man is a physical\nphilosopher, without seeking to be so, or being aware that he is so.\n\n3. But in all stages of the progress, even in that early one of\nwhich we have just spoken, it is necessary, in order that the facts\nmay be fit materials of any knowledge, that they should be\ndecomposed into Elementary Facts, and that these should be observed\nwith precision. Thus, in the first infancy of astronomy, the\nrecurrence of phases of the moon, of places of the sun's rising and\nsetting, of planets, of eclipses, was observed to take place at\nintervals of certain definite numbers of days, and in a certain\nexact order; and thus it was, that the observations became portions\nof astronomical science. In other cases, although the facts were\nequally numerous, and their general aspect equally familiar, they\nled to no science, because their exact circumstances were not\napprehended. A vague and loose mode of looking at facts very easily\nobservable, left men for a long time under the belief that a body,\nten times as heavy as another, falls ten times as fast;--that\nobjects immersed in water are always magnified, without regard to\nthe form of the surface;--that the magnet exerts an irresistible\nforce;--that crystal is always found associated with ice;--and the\nlike. These and many others are examples how blind and careless men\ncan be, even in observation of the plainest and commonest\nappearances; and they show us that the mere faculties of perception,\nalthough constantly exercised upon innumerable objects, may long\nfail in leading to any exact knowledge.\n\n4. If we further inquire what was the favourable condition through\nwhich some special classes of facts were, from the first, fitted to\nbecome portions of science, we shall find it to have been\nprincipally this;--that these facts were considered with reference\nto the Ideas of Time, Number, and Space, which are Ideas possessing\npeculiar definiteness and precision; so that with regard to them,\nconfusion and indistinctness are hardly possible. The interval from\nnew moon to new {62} moon was always a particular number of days:\nthe sun in his yearly course rose and set near to a known succession\nof distant objects: the moon's path passed among the stars in a\ncertain order:--these are observations in which mistake and\nobscurity are not likely to occur, if the smallest degree of\nattention is bestowed upon the task. To count a number is, from the\nfirst opening of man's mental faculties, an operation which no\nscience can render more precise. The relations of space are nearest\nto those of number in obvious and universal evidence. Sciences\ndepending upon these Ideas arise with the first dawn of intellectual\ncivilization. But few of the other Ideas which man employs in the\nacquisition of knowledge possess this clearness in their common use.\nThe Idea of _Resemblance_ may be noticed, as coming next to those of\nSpace and Number in original precision; and the Idea of _Cause_, in\na certain vague and general mode of application, sufficient for the\npurposes of common life, but not for the ends of science, exercises\na very extensive influence over men's thoughts. But the other Ideas\non which science depends, with the Conceptions which arise out of\nthem, are not unfolded till a much later period of intellectual\nprogress; and therefore, except in such limited cases as I have\nnoticed, the observations of common spectators and uncultivated\nnations, however numerous or varied, are of little or no effect in\ngiving rise to Science.\n\n5. Let us now suppose that, besides common everyday perception of\nfacts, we turn our attention to some other occurrences and\nappearances, with a design of obtaining from them speculative\nknowledge. This process is more peculiarly called _Observation_, or,\nwhen we ourselves occasion the facts, _Experiment_. But the same\nremark which we have already made, still holds good here. These\nfacts can be of no value, except they are resolved into those exact\nConceptions which contain the essential circumstances of the case.\nThey must be determined, not indeed necessarily, as has sometimes\nbeen said, 'according to Number, Weight, and Measure;' for, as we\nhave endeavoured to show {63} in the preceding Books[4\\2], there are\nmany other Conceptions to which phenomena may be subordinated, quite\ndifferent from these, and yet not at all less definite and precise.\nBut in order that the facts obtained by observation and experiment\nmay be capable of being used in furtherance of our exact and solid\nknowledge, they must be apprehended and analysed according to some\nConceptions which, applied for this purpose, give distinct and\ndefinite results, such as can be steadily taken hold of and reasoned\nfrom; that is, the facts must be referred to Clear and Appropriate\nIdeas, according to the manner in which we have already explained\nthis condition of the derivation of our knowledge. The phenomena of\nlight, when they are such as to indicate sides in the ray, must be\nreferred to the Conception of _polarization_; the phenomena of\nmixture, when there is an alteration of qualities as well as\nquantities, must be combined by a Conception of _elementary\ncomposition_. And thus, when mere position, and number, and\nresemblance, will no longer answer the purpose of enabling us to\nconnect the facts, we call in other Ideas, in such cases more\nefficacious, though less obvious.\n\n[Note 4\\2: _Hist. of Sci. Id._ Bs. v. vi. vii. viii. ix. x.]\n\n6. But how are we, in these cases, to discover such Ideas, and to\njudge which will be efficacious, in leading to a scientific\ncombination of our experimental data? To this question, we must in\nthe first place answer, that the first and great instrument by which\nfacts, so observed with a view to the formation of exact knowledge,\nare combined into important and permanent truths, is that peculiar\nSagacity which belongs to the genius of a Discoverer; and which,\nwhile it supplies those distinct and appropriate Conceptions which\nlead to its success, cannot be limited by rules, or expressed in\ndefinitions. It would be difficult or impossible to describe in\nwords the habits of thought which led Archimedes to refer the\nconditions of equilibrium on the Lever to the Conception of\n_pressure_, while Aristotle could not see in them anything more than\nthe results {64} of the strangeness of the properties of the\ncircle;--or which impelled Pascal to explain by means of the\nConception of the _weight of air_, the facts which his predecessors\nhad connected by the notion of nature's horrour of a vacuum;--or\nwhich caused Vitello and Roger Bacon to refer the magnifying power\nof a convex lens to the bending of the rays of light towards the\nperpendicular by _refraction_, while others conceived the effect to\nresult from the matter of medium, with no consideration of its form.\nThese are what are commonly spoken of as felicitous and inexplicable\nstrokes of inventive talent; and such, no doubt, they are. No rules\ncan ensure to us similar success in new cases; or can enable men who\ndo not possess similar endowments, to make like advances in\nknowledge.\n\n7. Yet still, we may do something in tracing the process by which\nsuch discoveries are made; and this it is here our business to do.\nWe may observe that these, and the like discoveries, are not\nimproperly described as happy _Guesses_; and that Guesses, in these\nas in other instances, imply various suppositions made, of which\nsome one turns out to be the right one. We may, in such cases,\nconceive the discoverer as inventing and trying many conjectures,\ntill he finds one which answers the purpose of combining the\nscattered facts into a single rule. The discovery of general truths\nfrom special facts is performed, commonly at least, and more\ncommonly than at first appears, by the use of a series of\nSuppositions, or _Hypotheses_, which are looked at in quick\nsuccession, and of which the one which really leads to truth is\nrapidly detected, and when caught sight of, firmly held, verified,\nand followed to its consequences. In the minds of most discoverers,\nthis process of invention, trial, and acceptance or rejection of the\nhypothesis, goes on so rapidly that we cannot trace it in its\nsuccessive steps. But in some instances, we can do so; and we can\nalso see that the other examples of discovery do not differ\nessentially from these. The same intellectual operations take place\nin other cases, although this often happens so instantaneously that\nwe lose the trace of the {65} progression. In the discoveries made\nby Kepler, we have a curious and memorable exhibition of this\nprocess in its details. Thanks to his communicative disposition, we\nknow that he made nineteen hypotheses with regard to the motion of\nMars, and calculated the results of each, before he established the\ntrue doctrine, that the planet's path is an ellipse. We know, in\nlike manner, that Galileo made wrong suppositions respecting the\nlaws of falling bodies, and Mariotte, concerning the motion of water\nin a siphon, before they hit upon the correct view of these cases.\n\n8. But it has very often happened in the history of science, that\nthe erroneous hypotheses which preceded the discovery of the truth\nhave been made, not by the discoverer himself, but by his\nprecursors; to whom he thus owed the service, often an important one\nin such cases, of exhausting the most tempting forms of errour. Thus\nthe various fruitless suppositions by which Kepler endeavoured to\ndiscover the law of reflection, led the way to its real detection by\nSnell; Kepler's numerous imaginations concerning the forces by which\nthe celestial motions are produced,--his 'physical reasonings' as he\ntermed them,--were a natural prelude to the truer physical\nreasonings of Newton. The various hypotheses by which the suspension\nof vapour in air had been explained, and their failure, left the\nfield open for Dalton with his doctrine of the mechanical mixture of\ngases. In most cases, if we could truly analyze the operation of the\nthoughts of those who make, or who endeavour to make discoveries in\nscience, we should find that many more suppositions pass through\ntheir minds than those which are expressed in words; many a possible\ncombination of conceptions is formed and soon rejected. There is a\nconstant invention and activity, a perpetual creating and selecting\npower at work, of which the last results only are exhibited to us.\nTrains of hypotheses are called up and pass rapidly in review; and\nthe judgment makes its choice from the varied group.\n\n9. It would, however, be a great mistake to suppose that the\nhypotheses, among which our choice thus {66} lies, are constructed\nby an enumeration of obvious cases, or by a wanton alteration of\nrelations which occur in some first hypothesis. It may, indeed,\nsometimes happen that the proposition which is finally established\nis such as may be formed, by some slight alteration, from those\nwhich are justly rejected. Thus Kepler's elliptical theory of Mars's\nmotions, involved relations of lines and angles much of the same\nnature as his previous false suppositions: and the true law of\nrefraction so much resembles those erroneous ones which Kepler\ntried, that we cannot help wondering how he chanced to miss it. But\nit more frequently happens that new truths are brought into view by\nthe application of new Ideas, not by new modifications of old ones.\nThe cause of the properties of the Lever was learnt, not by\nintroducing any new _geometrical_ combination of lines and circles,\nbut by referring the properties to genuine _mechanical_ Conceptions.\nWhen the Motions of the Planets were to be explained, this was done,\nnot by merely improving the previous notions, of cycles of time, but\nby introducing the new conception of _epicycles_ in space. The\ndoctrine of the Four Simple Elements was expelled, not by forming\nany new scheme of elements which should impart, according to new\nrules, their sensible qualities to their compounds, but by\nconsidering the elements of bodies as _neutralizing_ each other. The\nFringes of Shadows could not be explained by ascribing new\nproperties to the single rays of light, but were reduced to law by\nreferring them to the _interference_ of several rays.\n\nSince the true supposition is thus very frequently something\naltogether diverse from all the obvious conjectures and\ncombinations, we see here how far we are from being able to reduce\ndiscovery to rule, or to give any precepts by which the want of real\ninvention and sagacity shall be supplied. We may warn and encourage\nthese faculties when they exist, but we cannot create them, or make\ngreat discoveries when they are absent.\n\n10. The Conceptions which a true theory requires are very often\nclothed in a _Hypothesis_ which connects {67} with them several\nsuperfluous and irrelevant circumstances. Thus the Conception of the\nPolarization of Light was originally represented under the image of\nparticles of light having their poles all turned in the same\ndirection. The Laws of Heat may be made out perhaps most\nconveniently by conceiving Heat to be a _Fluid_. The Attraction of\nGravitation might have been successfully applied to the explanation\nof facts, if Newton had throughout treated Attraction as the result\nof an _Ether_ diffused through space; a supposition which he has\nnoticed as a possibility. The doctrine of Definite and Multiple\nProportions may be conveniently expressed by the hypothesis of\n_Atoms_. In such cases, the Hypothesis may serve at first to\nfacilitate the introduction of a new Conception. Thus a pervading\nEther might for a time remove a difficulty, which some persons find\nconsiderable, of imagining a body to exert force at a distance. A\nParticle with Poles is more easily conceived than Polarization in\nthe abstract. And if hypotheses thus employed will really explain\nthe facts by means of a few simple assumptions, the laws so obtained\nmay afterwards be reduced to a simpler form than that in which they\nwere first suggested. The general laws of Heat, of Attraction, of\nPolarization, of Multiple Proportions, are now certain, whatever\nimage we may form to ourselves of their ultimate causes.\n\n11. In order, then, to discover scientific truths, suppositions\nconsisting either of new Conceptions, or of new Combinations of old\nones, are to be made, till we find one supposition which succeeds in\nbinding together the Facts. But how are we to find this? How is the\ntrial to be made? What is meant by 'success' in these cases? To this\nwe reply, that our inquiry must be, whether the Facts have the same\nrelation in the Hypothesis which they have in reality;--whether the\nresults of our suppositions agree with the phenomena which nature\npresents to us. For this purpose, we must both carefully observe the\nphenomena, and steadily trace the consequences of our assumptions,\ntill we can {68} bring the two into comparison. The Conceptions\nwhich our hypotheses involve, being derived from certain Fundamental\nIdeas, afford a basis of rigorous reasoning, as we have shown in the\nBooks of the _History_ of those Ideas. And the results to which this\nreasoning leads, will be susceptible of being verified or\ncontradicted by observation of the facts. Thus the Epicyclical\nTheory of the Moon, once assumed, determined what the moon's place\namong the stars ought to be at any given time, and could therefore\nbe tested by actually observing the moon's places. The doctrine that\nmusical strings of the same length, stretched with weights of 1, 4,\n9, 16, would give the musical intervals of an octave, a fifth, a\nfourth, in succession, could be put to the trial by any one whose\near was capable of appreciating those intervals: and the inference\nwhich follows from this doctrine by numerical reasoning,--that there\nmust be certain imperfections in the concords of every musical\nscale,--could in like manner be confirmed by trying various modes of\n_Temperament_. In like manner all received theories in science, up\nto the present time, have been established by taking up some\nsupposition, and comparing it, directly or by means of its remoter\nconsequences, with the facts it was intended to embrace. Its\nagreement, under certain cautions and conditions, of which we may\nhereafter speak, is held to be the evidence of its truth. It answers\nits genuine purpose, the Colligation of Facts.\n\n12. When we have, in any subject, succeeded in one attempt of this\nkind, and obtained some true Bond of Unity by which the phenomena\nare held together, the subject is open to further prosecution; which\nulterior process may, for the most part, be conducted in a more\nformal and technical manner. The first great outline of the subject\nis drawn; and the finishing of the resemblance of nature demands a\nmore minute pencilling, but perhaps requires less of genius in the\nmaster. In the pursuance of this task, rules and precepts may be\ngiven, and features and leading circumstances pointed out, of which\nit may often be useful to the inquirer to be aware. {69}\n\nBefore proceeding further, I shall speak of some characteristic\nmarks which belong to such scientific processes as are now the\nsubject of our consideration, and which may sometimes aid us in\ndetermining when the task has been rightly executed.\n\n\n\n{{70}}\nCHAPTER V.\n\nOF CERTAIN CHARACTERISTICS OF SCIENTIFIC INDUCTION.\n\n\nAPHORISM X.\n\n_The process of scientific discovery is cautious and rigorous, not\nby abstaining from hypotheses, but by rigorously comparing\nhypotheses with facts, and by resolutely rejecting all which the\ncomparison does not confirm._\n\nAPHORISM XI.\n\n_Hypotheses may be useful, though involving much that is\nsuperfluous, and even erroneous: for they may supply the true bond\nof connexion of the facts; and the superfluity and errour may\nafterwards be pared away._\n\nAPHORISM XII.\n\n_It is a test of true theories not only to account for, but to\npredict phenomena._\n\nAPHORISM XIII.\n\nInduction _is a term applied to describe the process of a true\nColligation of Facts by means of an exact and appropriate\nConception._ An Induction _is also employed to denote the_\nproposition _which results from this process._\n\nAPHORISM XIV.\n\nThe Consilience of Inductions _takes place when an Induction,\nobtained from one class of facts, coincides with an Induction,\nobtained from another different class. This_ {71} _Consilience is a\ntest of the truth of the Theory in which it occurs._\n\nAPHORISM XV.\n\n_An Induction is not the mere_ sum _of the Facts which are colligated.\nThe Facts are not only brought together, but seen in a new point of\nview. A new mental Element is_ superinduced; _and a peculiar\nconstitution and discipline of mind are requisite in order to make\nthis Induction._\n\nAPHORISM XVI.\n\n_Although in Every Induction a new conception is superinduced upon\nthe Facts; yet this once effectually done, the novelty of the\nconception is overlooked, and the conception is considered as a part\nof the fact._\n\n\nSECT. I.--_Invention a part of Induction._\n\n1. THE two operations spoken of in the preceding chapters,--the\nExplication of the Conceptions of our own minds, and the Colligation\nof observed Facts by the aid of such Conceptions,--are, as we have\njust said, inseparably connected with each other. When united, and\nemployed in collecting knowledge from the phenomena which the world\npresents to us, they constitute the mental process of _Induction_;\nwhich is usually and justly spoken of as the genuine source of all\nour _real general knowledge_ respecting the external world. And we\nsee, from the preceding analysis of this process into its two\nconstituents, from what origin it derives each of its characters. It\nis _real_, because it arises from the combination of Real Facts, but\nit is _general_, because it implies the possession of General Ideas.\nWithout the former, it would not be knowledge of the External World;\nwithout the latter, it would not be Knowledge at all. When Ideas and\nFacts are separated from each other, the neglect of Facts gives rise\nto empty speculations, idle subtleties, visionary inventions, false\nopinions concerning the laws of phenomena, disregard of the true\naspect of nature: {72} while the want of Ideas leaves the mind\noverwhelmed, bewildered, and stupified by particular sensations,\nwith no means of connecting the past with the future, the absent\nwith the present, the example with the rule; open to the impression\nof all appearances, but capable of appropriating none. Ideas are the\n_Form_, facts the _Material_, of our structure. Knowledge does not\nconsist in the empty mould, or in the brute mass of matter, but in\nthe rightly-moulded substance. Induction gathers general truths from\nparticular facts;--and in her harvest, the corn and the reaper, the\nsolid ears and the binding band, are alike requisite. All our\nknowledge of nature is obtained by Induction; the term being\nunderstood according to the explanation we have now given. And our\nknowledge is then most complete, then most truly deserves the name\nof Science, when both its elements are most perfect;--when the Ideas\nwhich have been concerned in its formation have, at every step, been\nclear and consistent; and when they have, at every step also, been\nemployed in binding together real and certain Facts. Of such\nInduction, I have already given so many examples and illustrations\nin the two preceding chapters, that I need not now dwell further\nupon the subject.\n\n2. Induction is familiarly spoken of as the process by which we\ncollect a _General Proposition_ from a number of _Particular Cases_:\nand it appears to be frequently imagined that the general\nproposition results from a mere juxta-position of the cases, or at\nmost, from merely conjoining and extending them. But if we consider\nthe process more closely, as exhibited in the cases lately spoken\nof, we shall perceive that this is an inadequate account of the\nmatter. The particular facts are not merely brought together, but\nthere is a New Element added to the combination by the very act of\nthought by which they are combined. There is a Conception of the\nmind introduced in the general proposition, which did not exist in\nany of the observed facts. When the Greeks, after long observing the\nmotions of the planets, saw that these motions might be rightly\nconsidered as produced by the motion of one {73} wheel revolving in\nthe inside of another wheel, these Wheels were Creations of their\nminds, added to the Facts which they perceived by sense. And even if\nthe wheels were no longer supposed to be material, but were reduced\nto mere geometrical spheres or circles, they were not the less\nproducts of the mind alone,--something additional to the facts\nobserved. The same is the case in all other discoveries. The facts\nare known, but they are insulated and unconnected, till the\ndiscoverer supplies from his own stores a Principle of Connexion.\nThe pearls are there, but they will not hang together till some one\nprovides the String. The distances and periods of the planets were\nall so many separate facts; by Kepler's Third Law they are connected\ninto a single truth: but the Conceptions which this law involves\nwere supplied by Kepler's mind, and without these, the facts were of\nno avail. The planets described ellipses round the sun, in the\ncontemplation of others as well as of Newton; but Newton conceived\nthe deflection from the tangent in these elliptical motions in a new\nlight,--as the effect of a Central Force following a certain law;\nand then it was, that such a force was discovered truly to exist.\n\nThus[5\\2] in each inference made by Induction, there is introduced\nsome General Conception, which is given, not by the phenomena, but\nby the mind. The conclusion is not contained in the premises, but\nincludes them by the introduction of a New Generality. In order to\nobtain our inference, we travel beyond the cases which we have\nbefore us; we consider them as mere exemplifications of some Ideal\nCase in which the relations are complete and intelligible. We take a\nStandard, and measure the facts by it; and this Standard is\nconstructed by us, not offered by Nature. We assert, for example,\nthat a body left to itself will move on with unaltered velocity; not\nbecause our senses ever disclosed to us a body doing this, but\nbecause (taking this as our Ideal Case) we find that all {74} actual\ncases are intelligible and explicable by means of the Conception of\n_Forces_, causing change and motion, and exerted by surrounding\nbodies. In like manner, we see bodies striking each other, and thus\nmoving and stopping, accelerating and retarding each other: but in\nall this, we do not perceive by our senses that abstract quantity,\n_Momentum_, which is always lost by one body as it is gained by\nanother. This Momentum is a creation of the mind, brought in among\nthe facts, in order to convert their apparent confusion into order,\ntheir seeming chance into certainty, their perplexing variety into\nsimplicity. This the Conception of _Momentum gained and lost_ does:\nand in like manner, in any other case in which a truth is\nestablished by Induction, some Conception is introduced, some Idea\nis applied, as the means of binding together the facts, and thus\nproducing the truth.\n\n[Note 5\\2: I repeat here remarks made at the end of the _Mechanical\nEuclid_, p. 178.]\n\n3. Hence in every inference by Induction, there is some Conception\n_superinduced_ upon the Facts: and we may henceforth conceive this\nto be the peculiar import of the term _Induction_. I am not to be\nunderstood as asserting that the term was originally or anciently\nemployed with this notion of its meaning; for the peculiar feature\njust pointed out in Induction has generally been overlooked. This\nappears by the accounts generally given of Induction. 'Induction,'\nsays Aristotle[6\\2], 'is when by means of one extreme term[7\\2] we\ninfer the other extreme term to be true of the middle term.' Thus,\n(to take such exemplifications as belong to our subject,) from\nknowing that Mercury, Venus, Mars, describe ellipses about the Sun,\nwe infer that all Planets describe ellipses about the Sun. In making\nthis inference syllogistically, we assume that the evident\nproposition, 'Mercury, Venus, Mars, do what all Planets do,' may be\ntaken _conversely_, 'All {75} Planets do what Mercury, Venus, Mars,\ndo.' But we may remark that, in this passage, Aristotle (as was\nnatural in his line of discussion) turns his attention entirely to\nthe _evidence_ of the inference; and overlooks a step which is of\nfar more importance to our knowledge, namely, the _invention_ of the\nsecond extreme term. In the above instance, the particular\nluminaries, Mercury, Venus, Mars, are one logical _Extreme_; the\ngeneral designation Planets is the _Middle Term_; but having these\nbefore us, how do we come to think of _description of ellipses_,\nwhich is the other Extreme of the syllogism? When we have once\ninvented this 'second Extreme Term,' we may, or may not, be\nsatisfied with the evidence of the syllogism; we may, or may not, be\nconvinced that, so far as this property goes, the extremes are\nco-extensive with the middle term[8\\2]; but the _statement_ of the\nsyllogism is the important step in science. We know how long Kepler\nlaboured, how hard he fought, how many devices he tried, before he\nhit upon this _Term_, the Elliptical Motion. He rejected, as we\nknow, many other 'second extreme Terms,' for example, various\ncombinations of epicyclical constructions, because they did not\nrepresent with sufficient accuracy the special facts of observation.\nWhen he had established his premiss, that 'Mars does describe an\nEllipse about the Sun,' he does not hesitate to _guess_ at least\nthat, in this respect, he might _convert_ the other premiss, and\nassert that 'All the Planets do what Mars does.' But the main\nbusiness was, the inventing and verifying the proposition respecting\nthe Ellipse. The Invention of the Conception was the great step in\nthe _discovery_; the Verification of the Proposition was the great\nstep in the _proof_ of the discovery. If Logic consists in pointing\nout the conditions of proof, the Logic of Induction must consist in\nshowing what are the conditions of proof, in such inferences as\nthis: but this subject must be pursued in the next chapter; I now\nspeak principally of the act of {76} _Invention_, which is requisite\nin every inductive inference.\n\n[Note 6\\2: _Analyt. Prior._ lib. ii. c. xxiii. \u03a0\u03b5\u03c1\u1f76 \u03c4\u1fc6\u03c2 \u1f10\u03c0\u03b1\u03b3\u03c9\u03b3\u1fc6\u03c2.]\n\n[Note 7\\2: The syllogism here alluded to would be this:--\n Mercury, Venus, Mars, describe ellipses about the Sun;\n All Planets do what Mercury, Venus, Mars, do;\n Therefore all Planets describe ellipses about the Sun.]\n\n[Note 8\\2: \u0395\u1f30 \u03bf\u1f56\u03bd \u1f00\u03bd\u03c4\u03b9\u03c3\u03c4\u03c1\u03ad\u03c6\u03b5\u03b9 \u03c4\u1f78 \u0393 \u03c4\u1ff7 \u0392 \u03ba\u03b1\u1f76 \u03bc\u1f74 \u1f51\u03c0\u03b5\u03c1\u03c4\u03b5\u03af\u03bd\u03b5\u03b9 \u03c4\u1f78\n\u03bc\u03ad\u03c3\u03bf\u03bd.--Aristot. _Ibid._]\n\n4. Although in every inductive inference, an act of invention is\nrequisite, the act soon slips out of notice. Although we bind\ntogether facts by superinducing upon them a new Conception, this\nConception, once introduced and applied, is looked upon as\ninseparably connected with the facts, and necessarily implied in\nthem. Having once had the phenomena bound together in their minds in\nvirtue of the Conception, men can no longer easily restore them back\nto the detached and incoherent condition in which they were before\nthey were thus combined. The pearls once strung, they seem to form a\nchain by their nature. Induction has given them a unity which it is\nso far from costing us an effort to preserve, that it requires an\neffort to imagine it dissolved. For instance, we usually represent\nto ourselves the Earth as _round_, the Earth and the Planets as\n_revolving_ about the Sun, and as _drawn_ to the Sun by a Central\nForce; we can hardly understand how it could cost the Greeks, and\nCopernicus, and Newton, so much pains and trouble to arrive at a\nview which to us is so familiar. These are no longer to us\nConceptions caught hold of and kept hold of by a severe struggle;\nthey are the simplest modes of conceiving the facts: they are really\nFacts. We are willing to _own_ our obligation to those discoverers,\nbut we hardly _feel_ it: for in what other manner (we ask in our\nthoughts) could we represent the facts to ourselves?\n\nThus we see why it is that this step of which we now speak, the\nInvention of a new Conception in every inductive inference, is so\ngenerally overlooked that it has hardly been noticed by preceding\nphilosophers. When once performed by the discoverer, it takes a\nfixed and permanent place in the understanding of every one. It is a\nthought which, once breathed forth, permeates all men's minds. All\nfancy they nearly or quite knew it before. It oft was thought, or\nalmost thought, though never till now expressed. Men accept it and\nretain it, and know it cannot be taken {77} from them, and look upon\nit as their own. They will not and cannot part with it, even though\nthey may deem it trivial and obvious. It is a secret, which once\nuttered, cannot be recalled, even though it be despised by those to\nwhom it is imparted. As soon as the leading term of a new theory has\nbeen pronounced and understood, all the phenomena change their\naspect. There is a standard to which we cannot help referring them.\nWe cannot fall back into the helpless and bewildered state in which\nwe gazed at them when we possessed no principle which gave them\nunity. Eclipses arrive in mysterious confusion: the notion of a\n_Cycle_ dispels the mystery. The Planets perform a tangled and mazy\ndance; but _Epicycles_ reduce the maze to order. The Epicycles\nthemselves run into confusion; the conception of an _Ellipse_ makes\nall clear and simple. And thus from stage to stage, new elements of\nintelligible order are introduced. But this intelligible order is so\ncompletely adopted by the human understanding, as to seem part of\nits texture. Men ask Whether Eclipses follow a Cycle; Whether the\nPlanets describe Ellipses; and they imagine that so long as they do\nnot _answer_ such questions rashly, they take nothing for granted.\nThey do not recollect how much they assume in _asking_ the\nquestion:--how far the conceptions of Cycles and of Ellipses are\nbeyond the visible surface of the celestial phenomena:--how many\nages elapsed, how much thought, how much observation, were needed,\nbefore men's thoughts were fashioned into the words which they now\nso familiarly use. And thus they treat the subject, as we have seen\nAristotle treating it; as if it were a question, not of invention,\nbut of proof; not of substance, but of form: as if the main thing\nwere not _what_ we assert, but _how_ we assert it. But for our\npurpose, it is requisite to bear in mind the feature which we have\nthus attempted to mark; and to recollect that, in every inference by\ninduction, there is a Conception supplied by the mind and\nsuperinduced upon the Facts.\n\n5. In collecting scientific truths by Induction, we often find (as\nhas already been observed) a Definition {78} and a Proposition\nestablished at the same time,--introduced together, and mutually\ndependent on each other. The combination of the two constitutes the\nInductive act; and we may consider the Definition as representing\nthe superinduced Conception, and the Proposition as exhibiting the\nColligation of Facts.\n\n\nSECT. II.--_Use of Hypotheses._\n\n6. To discover a Conception of the mind which will justly represent\na train of observed facts is, in some measure, a process of\nconjecture, as I have stated already; and as I then observed, the\nbusiness of conjecture is commonly conducted by calling up before\nour minds several suppositions, and selecting that one which most\nagrees with what we know of the observed facts. Hence he who has to\ndiscover the laws of nature may have to invent many suppositions\nbefore he hits upon the right one; and among the endowments which\nlead to his success, we must reckon that fertility of invention\nwhich ministers to him such imaginary schemes, till at last he finds\nthe one which conforms to the true order of nature. A facility in\ndevising hypotheses, therefore, is so far from being a fault in the\nintellectual character of a discoverer, that it is, in truth, a\nfaculty indispensable to his task. It is, for his purposes, much\nbetter that he should be too ready in contriving, too eager in\npursuing systems which promise to introduce law and order among a\nmass of unarranged facts, than that he should be barren of such\ninventions and hopeless of such success. Accordingly, as we have\nalready noticed, great discoverers have often invented hypotheses\nwhich would not answer to all the facts, as well as those which\nwould; and have fancied themselves to have discovered laws, which a\nmore careful examination of the facts overturned.\n\nThe tendencies of our speculative nature[9\\2], carrying {79} us\nonwards in pursuit of symmetry and rule, and thus producing all true\ntheories, perpetually show their vigour by overshooting the mark.\nThey obtain something, by aiming at much more. They detect the order\nand connexion which exist, by conceiving imaginary relations of\norder and connexion which have no existence. Real discoveries are\nthus mixed with baseless assumptions; profound sagacity is combined\nwith fanciful conjecture; not rarely, or in peculiar instances, but\ncommonly, and in most cases; probably in all, if we could read the\nthoughts of discoverers as we read the books of Kepler. To try wrong\nguesses is, with most persons, the only way to hit upon right ones.\nThe character of the true philosopher is, not that he never\nconjectures hazardously, but that his conjectures are clearly\nconceived, and brought into rigid contact with facts. He sees and\ncompares distinctly the Ideas and the Things;--the relations of his\nnotions to each other and to phenomena. Under these conditions, it\nis not only excusable, but necessary for him, to snatch at every\nsemblance of general rule,--to try all promising forms of simplicity\nand symmetry.\n\n[Note 9\\2: I here take the liberty of characterizing inventive minds\nin general in the same phraseology which, in the History of Science,\nI have employed in reference to particular examples. These\nexpressions are what I have used in speaking of the discoveries of\nCopernicus.--_Hist. Ind. Sc._ b. v. c. ii.]\n\nHence advances in knowledge[10\\2] are not commonly made without the\nprevious exercise of some boldness and license in guessing. The\ndiscovery of new truths requires, undoubtedly, minds careful and\nscrupulous in examining what is suggested; but it requires, no less,\nsuch as are quick and fertile in suggesting. What is Invention,\nexcept the talent of rapidly calling before us the many\npossibilities, and selecting the appropriate one? It is true, that\nwhen we have rejected all the inadmissible suppositions, they are\noften quickly forgotten; and few think it necessary to dwell on\nthese discarded hypotheses, and on the process by which they were\ncondemned. But all who discover truths, must have reasoned upon many\nerrours to obtain each truth; {80} every accepted doctrine must have\nbeen one chosen out of many candidates. If many of the guesses of\nphilosophers of bygone times now appear fanciful and absurd, because\ntime and observation have refuted them, others, which were at the\ntime equally gratuitous, have been conformed in a manner which makes\nthem appear marvellously sagacious. To form hypotheses, and then to\nemploy much labour and skill in refuting them, if they do not\nsucceed in establishing them, is a part of the usual process of\ninventive minds. Such a proceeding belongs to the _rule_ of the\ngenius of discovery, rather than (as has often been taught in modern\ntimes) to the _exception_.\n\n[Note 10\\2: These observations are made on occasion of Kepler's\nspeculations, and are illustrated by reference to his\ndiscoveries.--_Hist. Ind. Sc._ b. v. c. iv. sect. 1.]\n\n7. But if it be an advantage for the discoverer of truth that he be\ningenious and fertile in inventing hypotheses which may connect the\nphenomena of nature, it is indispensably requisite that he be\ndiligent and careful in comparing his hypotheses with the facts, and\nready to abandon his invention as soon as it appears that it does\nnot agree with the course of actual occurrences. This constant\ncomparison of his own conceptions and supposition with observed\nfacts under all aspects, forms the leading employment of the\ndiscoverer: this candid and simple love of truth, which makes him\nwilling to suppress the most favourite production of his own\ningenuity as soon as it appears to be at variance with realities,\nconstitutes the first characteristic of his temper. He must have\nneither the blindness which cannot, nor the obstinacy which will\nnot, perceive the discrepancy of his fancies and his facts. He must\nallow no indolence, or partial views, or self-complacency, or\ndelight in seeming demonstration, to make him tenacious of the\nschemes which he devises, any further than they are confirmed by\ntheir accordance with nature. The framing of hypotheses is, for the\ninquirer after truth, not the end, but the beginning of his work.\nEach of his systems is invented, not that he may admire it and\nfollow it into all its consistent consequences, but that he may make\nit the occasion of a course of active experiment and observation.\nAnd if the results of this process {81} contradict his fundamental\nassumptions, however ingenious, however symmetrical, however elegant\nhis system may be, he rejects it without hesitation. He allows no\nnatural yearning for the offspring of his own mind to draw him aside\nfrom the higher duty of loyalty to his sovereign, Truth: to her he\nnot only gives his affections and his wishes, but strenuous labour\nand scrupulous minuteness of attention.\n\nWe may refer to what we have said of Kepler, Newton, and other\neminent philosophers, for illustrations of this character. In Kepler\nwe have remarked[11\\2] the courage and perseverance with which he\nundertook and executed the task of computing his own hypotheses:\nand, as a still more admirable characteristic, that he never allowed\nthe labour he had spent upon any conjecture to produce any\nreluctance in abandoning the hypothesis, as soon as he had evidence\nof its inaccuracy. And in the history of Newton's discovery that the\nmoon is retained in her orbit by the force of gravity, we have\nnoticed the same moderation in maintaining the hypothesis, after it\nhad once occurred to the author's mind. The hypothesis required that\nthe moon should fall from the tangent of her orbit every second\nthrough a space of sixteen feet; but according to his first\ncalculations it appeared that in fact she only fell through a space\nof thirteen feet in that time. The difference seems small, the\napproximation encouraging, the theory plausible; a man in love with\nhis own fancies would readily have discovered or invented some\nprobable cause of the difference. But Newton acquiesced in it as a\ndisproof of his conjecture, and 'laid aside at that time any further\nthoughts of this matter[12\\2].'\n\n[Note 11\\2: _Hist. Ind. Sc._ b. v. c. iv. sect. 1.]\n\n[Note 12\\2: _Hist. Ind. Sc._ b. vii. c. ii. sect. 3.]\n\n8. It has often happened that those who have undertaken to instruct\nmankind have not possessed this pure love of truth and comparative\nindifference to the maintenance of their own inventions. Men have\nfrequently adhered with great tenacity and vehemence to the\nhypotheses which they have once framed; and in their {82} affection\nfor these, have been prone to overlook, to distort, and to\nmisinterpret facts. In this manner, _Hypotheses_ have so often been\nprejudicial to the genuine pursuit of truth, that they have fallen\ninto a kind of obloquy; and have been considered as dangerous\ntemptations and fallacious guides. Many warnings have been uttered\nagainst the fabrication of hypotheses, by those who profess to teach\nphilosophy; many disclaimers of such a course by those who cultivate\nscience.\n\nThus we shall find Bacon frequently discommending this habit, under\nthe name of 'anticipation of the mind,' and Newton thinks it\nnecessary to say emphatically 'hypotheses non fingo.' It has been\nconstantly urged that the inductions by which sciences are formed\nmust be _cautious_ and _rigorous_; and the various imaginations\nwhich passed through Kepler's brain, and to which he has given\nutterance, have been blamed or pitied, as lamentable instances of an\nunphilosophical frame of mind. Yet it has appeared in the preceding\nremarks that hypotheses rightly used are among the helps, far more\nthan the dangers, of science;--that scientific induction is not a\n'cautious' or a 'rigorous' process in the sense of _abstaining from_\nsuch suppositions, but in _not adhering_ to them till they are\nconfirmed by fact, and in carefully seeking from facts confirmation\nor refutation. Kepler's distinctive character was, not that he was\npeculiarly given to the construction of hypotheses, but that he\nnarrated with extraordinary copiousness and candour the course of\nhis thoughts, his labours, and his feelings. In the minds of most\npersons, as we have said, the inadmissible suppositions, when\nrejected, are soon forgotten: and thus the trace of them vanishes\nfrom the thoughts, and the successful hypothesis alone holds its\nplace in our memory. But in reality, many other transient\nsuppositions must have been made by all discoverers;--hypotheses\nwhich are not afterwards asserted as true systems, but entertained\nfor an instant;--'tentative hypotheses,' as they have been called.\nEach of these hypotheses is followed by its corresponding train of\nobservations, from which it derives its power of leading to truth.\nThe hypothesis is {83} like the captain, and the observations like\nthe soldiers of an army: while he appears to command them, and in\nthis way to work his own will, he does in fact derive all his power\nof conquest from their obedience, and becomes helpless and useless\nif they mutiny.\n\nSince the discoverer has thus constantly to work his way onwards by\nmeans of hypotheses, false and true, it is highly important for him\nto possess talents and means for rapidly _testing_ each supposition as\nit offers itself. In this as in other parts of the work of\ndiscovery, success has in general been mainly owing to the native\ningenuity and sagacity of the discoverer's mind. Yet some Rules\ntending to further this object have been delivered by eminent\nphilosophers, and some others may perhaps be suggested. Of these we\nshall here notice only some of the most general, leaving for a\nfuture chapter the consideration of some more limited and detailed\nprocesses by which, in certain cases, the discovery of the laws of\nnature may be materially assisted.\n\n\nSECT. III.--_Tests of Hypotheses._\n\n9. A maxim which it may be useful to recollect is this;--that\n_hypotheses may often be of service to science, when they involve a\ncertain portion of incompleteness, and even of errour_. The object\nof such inventions is to bind together facts which without them are\nloose and detached; and if they do this, they may lead the way to a\nperception of the true rule by which the phenomena are associated\ntogether, even if they themselves somewhat misstate the matter. The\nimagined arrangement enables us to contemplate, as a whole, a\ncollection of special cases which perplex and overload our minds\nwhen they are considered in succession; and if our scheme has so\nmuch of truth in it as to conjoin what is really connected, we may\nafterwards duly correct or limit the mechanism of this connexion. If\nour hypothesis renders a reason for the agreement of cases really\nsimilar, we may afterwards find this reason to be {84} false, but we\nshall be able to translate it into the language of truth.\n\nA conspicuous example of such an hypothesis,--one which was of the\nhighest value to science, though very incomplete, and as a\nrepresentation of nature altogether false,--is seen in the _Doctrine\nof epicycles_ by which the ancient astronomers explained the motions\nof the sun, moon, and planets. This doctrine connected the places\nand velocities of these bodies at particular times in a manner which\nwas, in its general features, agreeable to nature. Yet this doctrine\nwas erroneous in its assertion of the _circular_ nature of all the\ncelestial motions, and in making the heavenly bodies revolve _round\nthe earth_. It was, however, of immense value to the progress of\nastronomical science; for it enabled men to express and reason upon\nmany important truths which they discovered respecting the motion of\nthe stars, up to the time of Kepler. Indeed we can hardly imagine\nthat astronomy could, in its outset, have made so great a progress\nunder any other form, as it did in consequence of being cultivated\nin this shape of the incomplete and false _epicyclical hypothesis_.\n\nWe may notice another instance of an exploded hypothesis, which is\ngenerally mentioned only to be ridiculed, and which undoubtedly is\nboth false in the extent of its assertion, and unphilosophical in\nits expression; but which still, in its day, was not without merit.\nI mean the doctrine of _Nature's horrour of a vacuum_ (_fuga\nvacui_), by which the action of siphons and pumps and many other\nphenomena were explained, till Mersenne and Pascal taught a truer\ndoctrine. This hypothesis was of real service; for it brought\ntogether many facts which really belong to the same class, although\nthey are very different in their first aspect. A scientific writer\nof modern times[13\\2] appears to wonder that men did not at once\ndivine the weight of the air, from which the phenomena formerly\nascribed to the _fuga vacui_ really result. 'Loaded, {85} compressed\nby the atmosphere,' he says, 'they did not recognize its action. In\nvain all nature testified that air was elastic and heavy; they shut\ntheir eyes to her testimony. The water rose in pumps and flowed in\nsiphons at that time, as it does at this day. They could not\nseparate the boards of a pair of bellows of which the holes were\nstopped; and they could not bring together the same boards without\ndifficulty, if they were at first separated. Infants sucked the milk\nof their mothers; air entered rapidly into the lungs of animals at\nevery inspiration; cupping-glasses produced tumours on the skin; and\nin spite of all these striking proofs of the weight and elasticity\nof the air, the ancient philosophers maintained resolutely that air\nwas light, and explained all these phenomena by the horrour which\nthey said nature had for a vacuum.' It is curious that it should not\nhave occurred to the author while writing this, that if these facts,\nso numerous and various, can all be accounted for by _one_\nprinciple, there is a strong presumption that the principle is not\naltogether baseless. And in reality is it not true that nature _does_\nabhor a vacuum, and does all she can to avoid it? No doubt this\npower is not unlimited; and moreover we can trace it to a mechanical\ncause, the pressure of the circumambient air. But the tendency,\narising from this pressure, which the bodies surrounding a space\nvoid of air have to rush into it, may be expressed, in no\nextravagant or unintelligible manner, by saying that nature has a\nrepugnance to a vacuum.\n\n[Note 13\\2: Deluc, _Modifications de l'Atmosph\u00e8re_, Partie 1.]\n\nThat imperfect and false hypotheses, though they may thus explain\n_some_ phenomena, and may be useful in the progress of science,\ncannot explain _all_ phenomena;--and that we are never to rest in\nour labours or acquiesce in our results, till we have found some\nview of the subject which _is_ consistent with _all_ the observed\nfacts;--will of course be understood. We shall afterwards have to\nspeak of the other steps of such a progress.\n\n10. Thus the hypotheses which we accept ought to explain phenomena\nwhich we have observed. But they {86} ought to do more than this:\nour hypotheses ought to _foretel_ phenomena which have not yet been\nobserved; at least all phenomena of the same kind as those which the\nhypothesis was invented to explain. For our assent to the hypothesis\nimplies that it is held to be true of all particular instances. That\nthese cases belong to past or to future times, that they have or\nhave not already occurred, makes no difference in the applicability\nof the rule to them. Because the rule prevails, it includes all\ncases; and will determine them all, if we can only calculate its\nreal consequences. Hence it will predict the results of new\ncombinations, as well as explain the appearances which have occurred\nin old ones. And that it does this with certainty and correctness,\nis one mode in which the hypothesis is to be verified as right and\nuseful.\n\nThe scientific doctrines which have at various periods been\nestablished have been verified in this manner. For example, the\n_Epicyclical Theory_ of the heavens was confirmed by its\n_predicting_ truly eclipses of the sun and moon, configurations of\nthe planets, and other celestial phenomena; and by its leading to\nthe construction of Tables by which the places of the heavenly\nbodies were given at every moment of time. The truth and accuracy of\nthese predictions were a proof that the hypothesis was valuable,\nand, at least to a great extent, true; although, as was afterwards\nfound, it involved a false representation of the structure of the\nheavens. In like manner, the discovery of the _Laws of Refraction_\nenabled mathematicians to _predict_, by calculation, what would be\nthe effect of any new form or combination of transparent lenses.\nNewton's hypothesis of _Fits of Easy Transmission and Easy\nReflection_ in the particles of light, although not confirmed by\nother kinds of facts, involved a true statement of the law of the\nphenomena which it was framed to include, and served to _predict_\nthe forms and colours of thin plates for a wide range of given\ncases. The hypothesis that Light operates by _Undulations_ and\n_Interferences_, afforded the means of _predicting_ results under a\nstill larger extent of conditions. In like manner in the {87}\nprogress of chemical knowledge, the doctrine of _Phlogiston_\nsupplied the means of _foreseeing_ the consequence of many\ncombinations of elements, even before they were tried; but the\n_Oxygen Theory_, besides affording predictions, at least equally\nexact, with regard to the general results of chemical operations,\nincluded all the facts concerning the relations of weight of the\nelements and their compounds, and enabled chemists to _foresee_ such\nfacts in untried cases. And the Theory of _Electromagnetic Forces_,\nas soon as it was rightly understood, enabled those who had mastered\nit to _predict_ motions such as had not been before observed, which\nwere accordingly found to take place.\n\nMen cannot help believing that the laws laid down by discoverers\nmust be in a great measure identical with the real laws of nature,\nwhen the discoverers thus determine effects beforehand in the same\nmanner in which nature herself determines them when the occasion\noccurs. Those who can do this, must, to a considerable extent, have\ndetected nature's secret;--must have fixed upon the conditions to\nwhich she attends, and must have seized the rules by which she\napplies them. Such a coincidence of untried facts with speculative\nassertions cannot be the work of chance, but implies some large\nportion of truth in the principles on which the reasoning is\nfounded. To trace order and law in that which has been observed, may\nbe considered as interpreting what nature has written down for us,\nand will commonly prove that we understand her alphabet. But to\npredict what has not been observed, is to attempt ourselves to use\nthe legislative phrases of nature; and when she responds plainly and\nprecisely to that which we thus utter, we cannot but suppose that we\nhave in a great measure made ourselves masters of the meaning and\nstructure of her language. The prediction of results, even of the\nsame kind as those which have been observed, in new cases, is a\nproof of real success in our inductive processes.\n\n11. We have here spoken of the prediction of facts _of the same\nkind_ as those from which our rule was collected. But the evidence\nin favour of our {88} induction is of a much higher and more\nforcible character when it enables us to explain and determine cases\nof a _kind different_ from those which were contemplated in the\nformation of our hypothesis. The instances in which this has\noccurred, indeed, impress us with a conviction that the truth of our\nhypothesis is certain. No accident could give rise to such an\nextraordinary coincidence. No false supposition could, after being\nadjusted to one class of phenomena, exactly represent a different\nclass, where the agreement was unforeseen and uncontemplated. That\nrules springing from remote and unconnected quarters should thus\nleap to the same point, can only arise from _that_ being the point\nwhere truth resides.\n\nAccordingly the cases in which inductions from classes of facts\naltogether different have thus _jumped together_, belong only to the\nbest established theories which the history of science contains. And\nas I shall have occasion to refer to this peculiar feature in their\nevidence, I will take the liberty of describing it by a particular\nphrase; and will term it the _Consilience of Inductions_.\n\nIt is exemplified principally in some of the greatest discoveries.\nThus it was found by Newton that the doctrine of the Attraction of\nthe Sun varying according to the Inverse Square of this distance,\nwhich explained Kepler's _Third Law_, of the proportionality of the\ncubes of the distances to the squares of the periodic times of the\nplanets, explained also his _First_ and _Second Laws_, of the\nelliptical motion of each planet; although no connexion of these\nlaws had been visible before. Again, it appeared that the force of\nuniversal Gravitation, which had been inferred from the\n_Perturbations_ of the moon and planets by the sun and by each\nother, also accounted for the fact, apparently altogether dissimilar\nand remote, of the _Precession of the equinoxes_. Here was a most\nstriking and surprising coincidence, which gave to the theory a\nstamp of truth beyond the power of ingenuity to counterfeit. In like\nmanner in Optics; the hypothesis of alternate Fits of easy\nTransmission and Reflection would explain {89} the colours of thin\nplates, and indeed was devised and adjusted for that very purpose;\nbut it could give no account of the phenomena of the fringes of\nshadows. But the doctrine of Interferences, constructed at first\nwith reference to phenomena of the nature of the _Fringes_,\nexplained also the _Colours of thin plates_ better than the\nsupposition of the Fits invented for that very purpose. And we have\nin Physical Optics another example of the same kind, which is quite\nas striking as the explanation of Precession by inferences from the\nfacts of Perturbation. The doctrine of Undulations propagated in a\nSpheroidal Form was contrived at first by Huyghens, with a view to\nexplain the laws of _Double Refraction_ in calc-spar; and was\npursued with the same view by Fresnel. But in the course of the\ninvestigation it appeared, in a most unexpected and wonderful\nmanner, that this same doctrine of spheroidal undulations, when it\nwas so modified as to account for the _directions_ of the two\nrefracted rays, accounted also for the positions of their _Planes of\nPolarization_[14\\2], a phenomenon which, taken by itself, it had\nperplexed previous mathematicians, even to represent.\n\n[Note 14\\2: _Hist. Ind. Sc._ b. ix. c. xi. sect. 4.]\n\nThe Theory of Universal Gravitation, and of the Undulatory Theory of\nLight, are, indeed, full of examples of this Consilience of\nInductions. With regard to the latter, it has been justly asserted\nby Herschel, that the history of the undulatory theory was a\nsuccession of _felicities_[15\\2]. And it is precisely the unexpected\ncoincidences of results drawn from distant parts of the subject\nwhich are properly thus described. Thus the Laws of the\n_Modification of polarization_ to which Fresnel was led by his\ngeneral views, accounted for the Rule respecting the _Angle at which\nlight is polarized_, discovered by Sir D. Brewster[16\\2]. The\nconceptions of the theory pointed out peculiar _Modifications_ of\nthe phenomena when _Newton's rings_ were produced by polarised\nlight, which modifications were {90} ascertained to take place in\nfact, by Arago and Airy[17\\2]. When the beautiful phenomena of\n_Dipolarized light_ were discovered by Arago and Biot, Young was\nable to declare that they were reducible to the general laws of\n_Interference_ which he had already established[18\\2]. And what was no\nless striking a confirmation of the truth of the theory, _Measures_\nof the same element deduced from various classes of facts were found\nto coincide. Thus the _Length_ of a luminiferous undulation,\ncalculated by Young from the measurement of _Fringes_ of shadows,\nwas found to agree very nearly with the previous calculation from\nthe colours of _Thin plates_[19\\2].\n\n[Note 15\\2: See _Hist. Ind. Sc._ b. ix. c. xii.]\n\n[Note 16\\2: _Ib._ c. xi. sect. 4.]\n\n[Note 17\\2: See _Hist. Ind. Sc._ b. ix. c. xiii. sect. 6.]\n\n[Note 18\\2: _Ib._ c. xi. sect. 5.]\n\n[Note 19\\2: _Ib._ c. xi. sect. 2.]\n\nNo example can be pointed out, in the whole history of science, so\nfar as I am aware, in which this Consilience of Inductions has given\ntestimony in favour of an hypothesis afterwards discovered to be\nfalse. If we take one class of facts only, knowing the law which\nthey follow, we may construct an hypothesis, or perhaps several,\nwhich may represent them: and as new circumstances are discovered,\nwe may often adjust the hypothesis so as to correspond to these\nalso. But when the hypothesis, of itself and without adjustment for\nthe purpose, gives us the rule and reason of a class of facts not\ncontemplated in its construction, we have a criterion of its\nreality, which has never yet been produced in favour of falsehood.\n\n12. In the preceding Article I have spoken of the hypothesis with\nwhich we compare our facts as being framed _all at once_, each of\nits parts being included in the original scheme. In reality,\nhowever, it often happens that the various suppositions which our\nsystem contains are _added_ upon occasion of different researches.\nThus in the Ptolemaic doctrine of the heavens, new epicycles and\neccentrics were added as new inequalities of the motions of the\nheavenly bodies were discovered; and in the Newtonian doctrine of\nmaterial rays of light, the supposition that these rays had {91}\n'fits,' was added to explain the colours of thin plates; and the\nsupposition that they had 'sides' was introduced on occasion of the\nphenomena of polarization. In like manner other theories have been\nbuilt up of parts devised at different times.\n\nThis being the mode in which theories are often framed, we have to\nnotice a distinction which is found to prevail in the progress of\ntrue and false theories. In the former class all the additional\nsuppositions _tend to simplicity_ and harmony; the new suppositions\nresolve themselves into the old ones, or at least require only some\neasy modification of the hypothesis first assumed: the system\nbecomes more coherent as it is further extended. The elements which\nwe require for explaining a new class of facts are already contained\nin our system. Different members of the theory run together, and we\nhave thus a constant convergence to unity. In false theories, the\ncontrary is the case. The new suppositions are something altogether\nadditional;--not suggested by the original scheme; perhaps difficult\nto reconcile with it. Every such addition adds to the complexity of\nthe hypothetical system, which at last becomes unmanageable, and is\ncompelled to surrender its place to some simpler explanation.\n\nSuch a false theory, for example, was the ancient doctrine of\neccentrics and epicycles. It explained the general succession of the\nPlaces of the Sun, Moon, and Planets; it would not have explained\nthe proportion of their Magnitudes at different times, if these\ncould have been accurately observed; but this the ancient\nastronomers were unable to do. When, however, Tycho and other\nastronomers came to be able to observe the planets accurately in all\npositions, it was found that _no_ combination of _equable_ circular\nmotions would exactly represent all the observations. We may see, in\nKepler's works, the many new modifications of the epicyclical\nhypothesis which offered themselves to him; some of which would have\nagreed with the phenomena with a certain degree of accuracy, but not\nwith so great a degree as Kepler, fortunately for the progress of\nscience, insisted upon obtaining. After these {92} epicycles had\nbeen thus accumulated, they all disappeared and gave way to the\nsimpler conception of an _elliptical_ motion. In like manner, the\ndiscovery of new inequalities in the Moon's motions encumbered her\nsystem more and more with new machinery, which was at last rejected\nall at once in favour of the _elliptical_ theory. Astronomers could\nnot but suppose themselves in a wrong path, when the prospect grew\ndarker and more entangled at every step.\n\nAgain; the Cartesian system of Vortices might be said to explain the\nprimary phenomena of the revolutions of planets about the sun, and\nsatellites about planets. But the elliptical form of the orbits\nrequired new suppositions. Bernoulli ascribed this curve to the\nshape of the planet, operating on the stream of the vortex in a\nmanner similar to the rudder of a boat. But then the motions of the\naphelia, and of the nodes,--the perturbations,--even the action of\ngravity towards the earth,--could not be accounted for without new\nand independent suppositions. Here was none of the simplicity of\ntruth. The theory of Gravitation, on the other hand, became more\nsimple as the facts to be explained became more numerous. The\nattraction of the sun accounted for the motions of the planets; the\nattraction of the planets was the cause of the motion of the\nsatellites. But this being assumed, the perturbations, and the\nmotions of the nodes and aphelia, only made it requisite to extend\nthe attraction of the sun to the satellites, and that of the planets\nto each other:--the tides, the spheroidal form of the earth, the\nprecession, still required nothing more than that the moon and sun\nshould attract the parts of the earth, and that these should attract\neach other;--so that all the suppositions resolved themselves into\nthe single one, of the universal gravitation of all matter. It is\ndifficult to imagine a more convincing manifestation of simplicity\nand unity.\n\nAgain, to take an example from another science;--the doctrine of\nPhlogiston brought together many facts in a very plausible\nmanner,--combustion, acidification, and others,--and very naturally\nprevailed for a while. {93} But the balance came to be used in\nchemical operations, and the facts of weight as well as of\ncombination were to be accounted for. On the phlogistic theory, it\nappeared that this could not be done without a new supposition, and\n_that_, a very strange one;--that phlogiston was an element not only\nnot heavy, but absolutely light, so that it diminished the weight of\nthe compounds into which it entered. Some chemists for a time\nadopted this extravagant view, but the wiser of them saw, in the\nnecessity of such a supposition to the defence of the theory, an\nevidence that the hypothesis of an element _phlogiston_ was\nerroneous. And the opposite hypothesis, which taught that oxygen was\nsubtracted, and not phlogiston added, was accepted because it\nrequired no such novel and inadmissible assumption.\n\nAgain, we find the same evidence of truth in the progress of the\nUndulatory Theory of light, in the course of its application from\none class of facts to another. Thus we explain Reflection and\nRefraction by undulations; when we come to Thin Plates, the\nrequisite 'fits' are already involved in our fundamental hypothesis,\nfor they are the length of an undulation: the phenomena of\nDiffraction also require such intervals; and the intervals thus\nrequired agree exactly with the others in magnitude, so that no new\nproperty is needed. Polarization for a moment appears to require\nsome new hypothesis; yet this is hardly the case; for the direction\nof our vibrations is hitherto arbitrary:--we allow polarization to\ndecide it, and we suppose the undulations to be transverse. Having\ndone this for the sake of Polarization, we turn to the phenomena of\nDouble Refraction, and inquire what new hypothesis they require. But\nthe answer is, that they require none: the supposition of transverse\nvibrations, which we have made in order to explain Polarization,\ngives us also the law of Double Refraction. Truth may give rise to\nsuch a coincidence; falsehood cannot. Again, the facts of\nDipolarization come into view. But they hardly require any new\nassumption; for the difference of optical elasticity of crystals in\ndifferent directions, {94} which is already assumed in uniaxal\ncrystals[20\\2], is extended to biaxal exactly according to the law\nof symmetry; and this being done, the laws of the phenomena, curious\nand complex as they are, are fully explained. The phenomena of\nCircular Polarization by internal reflection, instead of requiring a\nnew hypothesis, are found to be given by an interpretation of an\napparently inexplicable result of an old hypothesis. The Circular\nPolarization of Quartz and the Double Refraction does indeed appear\nto require a new assumption, but still not one which at all disturbs\nthe form of the theory; and in short, the whole history of this\ntheory is a progress, constant and steady, often striking and\nstartling, from one degree of evidence and consistence to another of\na higher order.\n\n[Note 20\\2: _Hist. Ind. Sc._ b. ix. c. xi. sect. 5.]\n\nIn the Emission Theory, on the other hand, as in the theory of solid\nepicycles, we see what we may consider as the natural course of\nthings in the career of a false theory. Such a theory may, to a\ncertain extent, explain the phenomena which it was at first\ncontrived to meet; but every new class of facts requires a new\nsupposition--an addition to the machinery: and as observation goes\non, these incoherent appendages accumulate, till they overwhelm and\nupset the original frame-work. Such has been the hypothesis of the\nMaterial Emission of light. In its original form, it explained\nReflection and Refraction: but the colours of Thin Plates added to\nit the Fits of easy Transmission and Reflection; the phenomena of\nDiffraction further invested the emitted particles with complex laws\nof Attraction and Repulsion; Polarization gave them Sides: Double\nRefraction subjected them to peculiar Forces emanating from the axes\nof the crystal: Finally, Dipolarization loaded them with the complex\nand unconnected contrivance of Moveable Polarization: and even when\nall this had been done, additional mechanism was wanting. There is\nhere no unexpected success, no happy coincidence, no convergence of\nprinciples from remote quarters. The philosopher builds {95} the\nmachine, but its parts do not fit. They hold together only while he\npresses them. This is not the character of truth.\n\nAs another example of the application of the Maxim now under\nconsideration, I may perhaps be allowed to refer to the judgment\nwhich, in the History of Thermotics, I have ventured to give\nrespecting Laplace's Theory of Gases. I have stated[21\\2], that we\ncannot help forming an unfavourable judgment of this theory, by\nlooking for that great characteristic of true theory; namely, that\nthe hypotheses which were assumed to account for _one class_ of\nfacts are found to explain _another class_ of a different nature.\nThus Laplace's first suppositions explain the connexion of\nCompression with Density, (the law of Boyle and Mariotte,) and the\nconnexion of Elasticity with Heat, (the law of Dalton and Gay\nLussac). But the theory requires other assumptions when we come to\nLatent Heat; and yet these new assumptions produce no effect upon\nthe calculations in any application of the theory. When the\nhypothesis, constructed with reference to the Elasticity and\nTemperature, is applied to another class of facts, those of Latent\nHeat, we have no Simplification of the Hypothesis, and therefore no\nevidence of the truth of the theory.\n\n[Note 21\\2: _Hist. Ind. Sc._ b. x. c. iv.]\n\n13. The last two sections of this chapter direct our attention to\ntwo circumstances, which tend to prove, in a manner which we may\nterm irresistible, the truth of the theories which they\ncharacterize:--the _Consilience of Inductions_ from different and\nseparate classes of facts;--and the progressive _Simplification of\nthe Theory_ as it is extended to new cases. These two Characters\nare, in fact, hardly different; they are exemplified by the same\ncases. For if these Inductions, collected from one class of facts,\nsupply an unexpected explanation of a new class, which is the case\nfirst spoken of, there will be no need for new machinery in the\nhypothesis to apply it to the newly-contemplated facts; and thus, we\nhave a case in which the system does not become {96} more complex\nwhen its application is extended to a wider field, which was the\ncharacter of true theory in its second aspect. The Consiliences of\nour Inductions give rise to a constant Convergence of our Theory\ntowards Simplicity and Unity.\n\nBut, moreover, both these cases of the extension of the theory,\nwithout difficulty or new suppositions, to a wider range and to new\nclasses of phenomena, may be conveniently considered in yet another\npoint of view; namely, as successive steps by which we gradually\nascend in our speculative views to a higher and higher point of\ngenerality. For when the theory, either by the concurrence of two\nindications, or by an extension without complication, has included a\nnew range of phenomena, we have, in fact, a new induction of a more\ngeneral kind, to which the inductions formerly obtained are\nsubordinate, as particular cases to a general proposition. We have\nin such examples, in short, an instance of _successive\ngeneralization_. This is a subject of great importance, and\ndeserving of being well illustrated; it will come under our notice\nin the next chapter.\n\n\n\n{{97}}\nCHAPTER VI.\n\nOF THE LOGIC OF INDUCTION.\n\n\nAPHORISM XVII.\n\n_The_ Logic of Induction _consists in stating the Facts and the\nInference in such a manner, that the Evidence of the Inference is\nmanifest: just as the Logic of Deduction consists in stating the\nPremises and the Conclusion in such a manner that the Evidence of\nthe Conclusion is manifest._\n\nAPHORISM XVIII.\n\n_The Logic of Deduction is exhibited by means of a certain Formula;\nnamely, a Syllogism; and every train of deductive reasoning, to be\ndemonstrative, must be capable of resolution into a series of such\nFormul\u00e6 legitimately constructed. In like manner, the Logic of\nInduction may be exhibited by means of certain_ Formul\u00e6; _and every\ntrain of inductive inference to be sound, must be capable of\nresolution into a scheme of such Formul\u00e6, legitimately constructed._\n\nAPHORISM XIX.\n\n_The_ inductive act of thought _by which several Facts are\ncolligated into one Proposition, may be expressed by saying:_ The\nseveral Facts are exactly expressed as one Fact, if, and only if, we\nadopt the Conceptions and the Assertion _of the Proposition._\n\n\nAPHORISM XX.\n\n_The One Fact, thus inductively obtained from several Facts, may be\ncombined with other Facts, and colligated with them by a new act of\nInduction. This process may be_ {98} _indefinitely repeated: and\nthese successive processes are the_ Steps _of Induction, or of_\nGeneralization, _from the lowest to the highest._\n\nAPHORISM XXI.\n\n_The relation of the successive Steps of Induction may be exhibited\nby means of an_ Inductive Table, _in which the several Facts are\nindicated, and tied together by a Bracket, and the Inductive\nInference placed on the other side of the Bracket; and this\narrangement repeated, so as to form a genealogical Table of each\nInduction, from the lowest to the highest._\n\nAPHORISM XXII.\n\n_The Logic of Induction is the_ Criterion of Truth _inferred from\nFacts, as the Logic of Deduction is the Criterion of Truth deduced\nfrom necessary Principles. The Inductive Table enables us to apply\nsuch a Criterion; for we can determine whether each Induction is\nverified and justified by the Facts which its Bracket includes; and\nif each induction in particular be sound, the highest, which merely\ncombines them all, must necessarily be sound also._\n\nAPHORISM XXIII.\n\n_The distinction of_ Fact _and_ Theory _is only relative. Events and\nphenomena, considered as Particulars which may be colligated by\nInduction, are_ Facts; _considered as Generalities already obtained\nby colligation of other Facts, they are_ Theories. _The same event\nor phenomenon is a Fact or a Theory, according as it is considered\nas standing on one side or the other of the Inductive Bracket._\n\n\n1. THE subject to which the present chapter refers is described by\nphrases which are at the present day familiarly used in speaking of\nthe progress of knowledge. We hear very frequent mention of\n_ascending from particular to general_ propositions, and from these\nto propositions still more general;--of {99} truths _included_ in\nother truths of a higher degree of generality;--of different _stages\nof generalization_;--and of the _highest step_ of the process of\ndiscovery, to which all others are subordinate and preparatory. As\nthese expressions, so familiar to our ears, especially since the\ntime of Francis Bacon, denote, very significantly, processes and\nrelations which are of great importance in the formation of science,\nit is necessary for us to give a clear account of them, illustrated\nwith general exemplifications; and this we shall endeavour to do.\n\nWe have, indeed, already explained that science consists of\nPropositions which include the Facts from which they were collected;\nand other wider Propositions, collected in like manner from the\nformer, and including them. Thus, that the stars, the moon, the sun,\nrise, culminate, and set, are facts _included_ in the proposition\nthat the heavens, carrying with them all the celestial bodies, have\na diurnal revolution about the axis of the earth. Again, the\nobserved monthly motions of the moon, and the annual motions of the\nsun, are _included_ in certain propositions concerning the movements\nof those luminaries with respect to the stars. But all these\npropositions are really _included_ in the doctrine that the earth,\nrevolving on its axis, moves round the sun, and the moon round the\nearth. These movements, again, considered as facts, are explained\nand _included_ in the statement of the forces which the earth exerts\nupon the moon, and the sun upon the earth. Again, this doctrine of\nthe forces of these three bodies is _included_ in the assertion,\nthat all the bodies of the solar system, and all parts of matter,\nexert forces, each upon each. And we might easily show that all the\nleading facts in astronomy are comprehended in the same\ngeneralization. In like manner with regard to any other science, so\nfar as its truths have been well established and fully developed, we\nmight show that it consists of a gradation of propositions,\nproceeding from the most special facts to the most general\ntheoretical assertions. We shall exhibit this gradation in some of\nthe principal branches of science. {100}\n\n2. This gradation of truths, successively included in other truths,\nmay be conveniently represented by Tables resembling the\ngenealogical tables by which the derivation of descendants from a\ncommon ancestor is exhibited; except that it is proper in this case\nto invert the form of the Table, and to make it converge to unity\ndownwards instead of upwards, since it has for its purpose to\nexpress, not the derivation of many from one, but the collection of\none truth from many things. Two or more co-ordinate facts or\npropositions may be ranged side by side, and joined by some mark of\nconnexion, (a bracket, as \u23df or \u23b5,) beneath which may be placed the\nmore general proposition which is collected by induction from the\nformer. Again, propositions co-ordinate with this more general one\nmay be placed on a level with it; and the combination of these, and\nthe result of the combination, may be indicated by brackets in the\nsame manner; and so on, through any number of gradations. By this\nmeans the streams of knowledge from various classes of facts will\nconstantly run together into a smaller and smaller number of\nchannels; like the confluent rivulets of a great river, coming\ntogether from many sources, uniting their ramifications so as to\nform larger branches, these again uniting in a single trunk. The\n_genealogical tree_ of each great portion of science, thus formed,\nwill contain all the leading truths of the science arranged in their\ndue co-ordination and subordination. Such Tables, constructed for\nthe sciences of Astronomy and of Optics, will be given at the end of\nthis chapter.\n\n3. The union of co-ordinate propositions into a proposition of a\nhigher order, which occurs in this Tree of Science wherever two\ntwigs unite in one branch, is, in each case, an example of\n_Induction_. The single proposition is collected by the process of\ninduction from its several members. But here we may observe, that\nthe image of a mere _union_ of the parts at each of these points,\nwhich the figure of a tree or a river presents, is very inadequate\nto convey the true state of the case; for in Induction, as we have\nseen, besides mere collection of particulars, there is always a _new\nconception_, a {101} principle of connexion and unity, supplied by\nthe mind, and superinduced upon the particulars. There is not merely\na juxta-position of materials, by which the new proposition contains\nall that its component parts contained; but also a formative act\nexerted by the understanding, so that these materials are contained\nin a new shape. We must remember, therefore, that our Inductive\nTables, although they represent the elements and the order of these\ninductive steps, do not fully represent the whole signification of\nthe process in each case.\n\n4. The principal features of the progress of science spoken of in\nthe last chapter are clearly exhibited in these Tables; namely, the\n_Consilience of Inductions_ and the constant Tendency to Simplicity\nobservable in true theories. Indeed in all cases in which, from\npropositions of considerable generality, propositions of a still\nhigher degree are obtained, there is a convergence of inductions;\nand if in one of the lines which thus converge, the steps be rapidly\nand suddenly made in order to meet the other line, we may consider\nthat we have an example of Consilience. Thus when Newton had\ncollected, from Kepler's Laws, the Central Force of the sun, and\nfrom these, combined with other facts, the Universal Force of all\nthe heavenly bodies, he suddenly turned round to include in his\ngeneralization the Precession of the Equinoxes, which he declared to\narise from the attraction of the sun and moon upon the protuberant\npart of the terrestrial spheroid. The apparent remoteness of this\nfact, in its nature, from the other facts with which he thus\nassociated it, causes this part of his reasoning to strike us as a\nremarkable example of _Consilience_. Accordingly, in the Table of\nAstronomy we find that the columns which contain the facts and\ntheories relative to the _sun_ and _planets_, after exhibiting\nseveral stages of induction within themselves, are at length\nsuddenly connected with a column till then quite distinct,\ncontaining the _precession of the equinoxes_. In like manner, in the\nTable of Optics, the columns which contain the facts and theories\nrelative to _double refraction_, and those which {102} include\n_polarization by crystals_, each go separately through several\nstages of induction; and then these two sets of columns are suddenly\nconnected by Fresnel's mathematical induction, that double\nrefraction and polarization arise from the same cause: thus\nexhibiting a remarkable _Consilience_.\n\n5. The constant _Tendency to Simplicity_ in the sciences of which the\nprogress is thus represented, appears from the form of the Table\nitself; for the single trunk into which all the branches converge,\ncontains in itself the substance of all the propositions by means of\nwhich this last generalization was arrived at. It is true, that this\nultimate result is sometimes not so simple as in the Table it\nappears: for instance, the ultimate generalization of the Table\nexhibiting the progress of Physical Optics,--namely, that Light\nconsists in Undulations,--must be understood as including some other\nhypotheses; as, that the undulations are transverse, that the ether\nthrough which they are propagated has its elasticity in crystals and\nother transparent bodies regulated by certain laws; and the like.\nYet still, even acknowledging all the complication thus implied, the\nTable in question evidences clearly enough the constant advance\ntowards unity, consistency, and simplicity, which have marked the\nprogress of this Theory. The same is the case in the Inductive Table\nof Astronomy in a still greater degree.\n\n6. These Tables naturally afford the opportunity of assigning to\neach of the distinct steps of which the progress of science\nconsists, the name of the _Discoverer_ to whom it is due. Every one\nof the inductive processes which the brackets of our Tables mark,\ndirects our attention to some person by whom the induction was first\ndistinctly made. These names I have endeavoured to put in their due\nplaces in the Tables; and the Inductive Tree of our knowledge in\neach science becomes, in this way, an exhibition of the claims of\neach discoverer to distinction, and, as it were, a Genealogical Tree\nof scientific nobility. It is by no means pretended that such a tree\nincludes the {103} names of all the meritorious labourers in each\ndepartment of science. Many persons are most usefully employed in\ncollecting and verifying truths, who do not advance to any new\ntruths. The labours of a number of such are included in each stage\nof our ascent. But such Tables as we have now before us will present\nto us the names of all the most eminent discoverers: for the main\nsteps of which the progress of science consists, are transitions\nfrom more particular to more general truths, and must therefore be\nrightly given by these Tables; and those must be the greatest names\nin science to whom the principal events of its advance are thus due.\n\n7. The Tables, as we have presented them, exhibit the course by\nwhich we pass from Particular to General through various gradations,\nand so to the most general. They display the order of _discovery_.\nBut by reading them in an inverted manner, beginning at the single\ncomprehensive truths with which the Tables end, and tracing these\nback into the more partial truths, and these again into special\nfacts, they answer another purpose;--they exhibit the process of\n_verification_ of discoveries once made. For each of our general\npropositions is true in virtue of the truth of the narrower\npropositions which it involves; and we cannot satisfy ourselves of\nits truth in any other way than by ascertaining that these its\nconstituent elements are true. To assure ourselves that the sun\nattracts the planets with forces varying inversely as the square of\nthe distance, we must analyse by geometry the motion of a body in an\nellipse about the focus, so as to see that such a motion does imply\nsuch a force. We must also verify those calculations by which the\nobserved places of each planet are stated to be included in an\nellipse. These calculations involve assumptions respecting the path\nwhich the earth describes about the sun, which assumptions must\nagain be verified by reference to observation. And thus, proceeding\nfrom step to step, we resolve the most general truths into their\nconstituent parts; and these again into their parts; and by testing,\nat each step, both the reality of the asserted ingredients and the\npropriety {104} of the conjunction, we establish the whole system of\ntruths, however wide and various it may be.\n\n8. It is a very great advantage, in such a mode of exhibiting\nscientific truths, that it resolves the verification of the most\ncomplex and comprehensive theories, into a number of small steps, of\nwhich almost any one falls within the reach of common talents and\nindustry. That _if_ the particulars of any one step be true, the\ngeneralization also is true, any person with a mind properly\ndisciplined may satisfy himself by a little study. That each of\nthese particular propositions _is_ true, may be ascertained, by the\nsame kind of attention, when this proposition is resolved into _its_\nconstituent and more special propositions. And thus we may proceed,\ntill the most general truth is broken up into small and manageable\nportions. Of these portions, each may appear by itself narrow and\neasy; and yet they are so woven together, by hypothesis and\nconjunction, that the truth of the parts necessarily assures us of\nthe truth of the whole. The verification is of the same nature as\nthe verification of a large and complex statement of great sums\nreceived by a mercantile office on various accounts from many\nquarters. The statement is separated into certain comprehensive\nheads, and these into others less extensive; and these again into\nsmaller collections of separate articles, each of which can be\ninquired into and reported on by separate persons. And thus at last,\nthe mere addition of numbers performed by these various persons, and\nthe summation of the results which they obtain, executed by other\naccountants, is a complete and entire security that there is no\nerrour in the whole of the process.\n\n9. This comparison of the process by which we verify scientific\ntruth to the process of Book-keeping in a large commercial\nestablishment, may appear to some persons not sufficiently dignified\nfor the subject. But, in fact, the possibility of giving this formal\nand business-like aspect to the evidence of science, as involved in\nthe process of successive generalization, is an inestimable\nadvantage. For if no one could pronounce concerning a wide and\nprofound theory except he who {105} could at once embrace in his\nmind the whole range of inference, extending from the special facts\nup to the most general principles, none but the greatest geniuses\nwould be entitled to judge concerning the truth or errour of\nscientific discoveries. But, in reality, we seldom need to verify\nmore than one or two steps of such discoveries at one time; and this\nmay commonly be done (when the discoveries have been fully\nestablished and developed,) by any one who brings to the task clear\nconceptions and steady attention. The progress of science is\ngradual: the discoveries which are successively made, are also\nverified successively. We have never any very large collections of\nthem on our hands at once. The doubts and uncertainties of any one\nwho has studied science with care and perseverance are generally\nconfined to a few points. If he can satisfy himself upon these, he\nhas no misgivings respecting the rest of the structure; which has\nindeed been repeatedly verified by other persons in like manner. The\nfact that science is capable of being resolved into separate\nprocesses of verification, is that which renders it possible to form\na great body of scientific truth, by adding together a vast number\nof truths, of which many men, at various times and by multiplied\nefforts, have satisfied themselves. The treasury of Science is\nconstantly rich and abundant, because it accumulates the wealth\nwhich is thus gathered by so many, and reckoned over by so many\nmore: and the dignity of Knowledge is no more lowered by the\nmultiplicity of the tasks on which her servants are employed, and\nthe narrow field of labour to which some confine themselves, than\nthe rich merchant is degraded by the number of offices which it is\nnecessary for him to maintain, and the minute articles of which he\nrequires an exact statement from his accountants.\n\n10. The analysis of doctrines inductively obtained, into their\nconstituent facts, and the arrangement of them in such a form that\nthe conclusiveness of the induction may be distinctly seen, may be\ntermed the _Logic of Induction_. By _Logic_ has generally been meant\na system which teaches us so to arrange our {106} reasonings that\ntheir truth or falsehood shall be evident in their form. In\n_deductive_ reasonings, in which the general principles are assumed,\nand the question is concerning their application and combination in\nparticular cases, the device which thus enables us to judge whether\nour reasonings are conclusive is the _Syllogism_; and this _form_,\nalong with the rules which belong to it, does in fact supply us with\na criterion of deductive or demonstrative reasoning. The _Inductive\nTable_, such as it is presented in the present chapter, in like\nmanner supplies the means of ascertaining the truth of our inductive\ninferences, so far as the form in which our reasoning may be stated\ncan afford such a criterion. Of course some care is requisite in\norder to reduce a train of demonstration into the form of a series\nof syllogisms; and certainly not less thought and attention are\nrequired for resolving all the main doctrines of any great\ndepartment of science into a graduated table of co-ordinate and\nsubordinate inductions. But in each case, when this task is once\nexecuted, the evidence or want of evidence of our conclusions\nappears immediately in a most luminous manner. In each step of\ninduction, our Table enumerates the particular facts, and states the\ngeneral theoretical truth which includes these and which these\nconstitute. The special act of attention by which we satisfy\nourselves that the facts _are_ so included,--that the general truth\n_is_ so constituted,--then affords little room for errour, with\nmoderate attention and clearness of thought.\n\n11. We may find an example of this _act of attention_ thus required,\nat any one of the steps of induction in our Tables; for instance, at\nthe step in the early progress of astronomy at which it was\ninferred, that the earth is a globe, and that the sphere of the\nheavens (relatively) performs a diurnal revolution round this globe\nof the earth. How was this established in the belief of the Greeks,\nand how is it fixed in our conviction? As to the globular form, we\nfind that as we travel to the north, the apparent pole of the\nheavenly motions, and the constellations which are near it, seem to\nmount higher, and as we proceed southwards they descend. {107}\nAgain, if we proceed from two different points considerably to the\neast and west of each other, and travel directly northwards from\neach, as from the south of Spain to the north of Scotland, and from\nGreece to Scandinavia, these two north and south lines will be much\nnearer to each other in their northern than in their southern parts.\nThese and similar facts, as soon as they are clearly estimated and\nconnected in the mind, are _seen to be consistent_ with a convex\nsurface of the earth, and with no other: and this notion is further\nconfirmed by observing that the boundary of the earth's shadow upon\nthe moon is always circular; it being supposed to be already\nestablished that the moon receives her light from the sun, and that\nlunar eclipses are caused by the interposition of the earth. As for\nthe assertion of the (relative) diurnal revolution of the starry\nsphere, it is merely putting the visible phenomena in an exact\ngeometrical form: and thus we establish and verify the doctrine of\nthe revolution of the sphere of the heavens about the globe of the\nearth, by contemplating it so as to see that it does really and\nexactly include the particular facts from which it is collected.\n\nWe may, in like manner, illustrate this mode of verification by any\nof the other steps of the same Table. Thus if we take the great\nInduction of Copernicus, the heliocentric scheme of the solar\nsystem, we find it in the Table exhibited as including and\nexplaining, _first_, the diurnal revolution just spoken of;\n_second_, the motions of the moon among the fixed stars; _third_,\nthe motions of the planets with reference to the fixed stars and the\nsun; _fourth_, the motion of the sun in the ecliptic. And the scheme\nbeing clearly conceived, we _see_ that all the particular facts\n_are_ faithfully represented by it; and this agreement, along with\nthe simplicity of the scheme, in which respect it is so far superior\nto any other conception of the solar system, persuade us that it is\nreally the plan of nature.\n\nIn exactly the same way, if we attend to any of the several\nremarkable discoveries of Newton, which form the principal steps in\nthe latter part of the Table, as for instance, the proposition that\nthe sun attracts all {108} the planets with a force which varies\ninversely as the square of the distance, we find it proved by its\nincluding three other propositions previously established;--_first_,\nthat the sun's mean force on different planets follows the specified\nvariation (which is proved from Kepler's third law); _second_, that\nthe force by which each planet is acted upon in different parts of\nits orbit tends to the sun (which is proved by the equable\ndescription of areas); _third_, that this force in different parts\nof the same orbit is also inversely as the square of the distance\n(which is proved from the elliptical form of the orbit). And the\nNewtonian generalization, when its consequences are mathematically\ntraced, is _seen_ to agree with each of these particular\npropositions, and thus is fully established.\n\n12. But when we say that the more general proposition _includes_ the\nseveral more particular ones, we must recollect what has before been\nsaid, that these particulars form the general truth, not by being\nmerely enumerated and added together, but by being seen _in a new\nlight_. No mere verbal recitation of the particulars can decide\nwhether the general proposition is true; a special act of thought is\nrequisite in order to determine how truly each is included in the\nsupposed induction. In this respect the Inductive Table is not like\na mere schedule of accounts, where the rightness of each part of the\nreckoning is tested by mere addition of the particulars. On the\ncontrary, the Inductive truth is never the mere _sum_ of the facts.\nIt is made into something more by the introduction of a new mental\nelement; and the mind, in order to be able to supply this element,\nmust have peculiar endowments and discipline. Thus looking back at\nthe instances noticed in the last article, how are we to see that a\nconvex surface of the earth is necessarily implied by the\nconvergence of meridians towards the north, or by the visible\ndescent of the north pole of the heavens as we travel south?\nManifestly the student, in order to see this, must have clear\nconceptions of the relations of space, either naturally inherent in\nhis mind, or established there by geometrical cultivation,--by {109}\nstudying the properties of circles and spheres. When he is so\nprepared, he will feel the force of the expressions we have used,\nthat the facts just mentioned are _seen to be consistent_ with a\nglobular form of the earth; but without such aptitude he will not\nsee this consistency: and if this be so, the mere assertion of it in\nwords will not avail him in satisfying himself of the truth of the\nproposition.\n\nIn like manner, in order to perceive the force of the Copernican\ninduction, the student must have his mind so disciplined by\ngeometrical studies, or otherwise, that he sees clearly how absolute\nmotion and relative motion would alike produce apparent motion. He\nmust have learnt to cast away all prejudices arising from the\nseeming fixity of the earth; and then he will see that there is\nnothing which stands in the way of the induction, while there is\nmuch which is on its side. And in the same manner the Newtonian\ninduction of the law of the sun's force from the elliptical form of\nthe orbit, will be evidently satisfactory to him only who has such\nan insight into Mechanics as to see that a curvilinear path must\narise from a constantly deflecting force; and who is able to follow\nthe steps of geometrical reasoning by which, from the properties of\nthe ellipse, Newton proves this deflection to be in the proportion\nin which he asserts the force to be. And thus in all cases the\ninductive truth must indeed be verified by comparing it with the\nparticular facts; but then this comparison is possible for him only\nwhose mind is properly disciplined and prepared in the use of those\nconceptions, which, in addition to the facts, the act of induction\nrequires.\n\n13. In the Tables some indication is given, at several of the steps,\nof the act which the mind must thus perform, besides the mere\nconjunction of facts, in order to attain to the inductive truth.\nThus in the cases of the Newtonian inductions just spoken of, the\ninferences are stated to be made 'By Mechanics;' and in the case of\nthe Copernican induction, it is said that, 'By the nature of motion,\nthe apparent motion is the same, whether the heavens or the earth\nhave a {110} diurnal motion; and the latter is more simple.' But\nthese verbal statements are to be understood as mere hints[22\\2]:\nthey cannot supersede the necessity of the student's contemplating\nfor himself the mechanical principles and the nature of motion thus\nreferred to.\n\n[Note 22\\2: In the Inductive Tables they are marked by an\nasterisk.]\n\n14. In the common or Syllogistic Logic, a certain _Formula_ of\nlanguage is used in stating the reasoning, and is useful in enabling\nus more readily to apply the Criterion of Form to alleged\ndemonstrations. This formula is the usual Syllogism; with its\nmembers, Major Premiss, Minor Premiss, and Conclusion. It may\nnaturally be asked whether in Inductive Logic there is any such\nFormula? whether there is any standard form of words in which we may\nmost properly express the inference of a general truth from\nparticular facts?\n\nAt first it might be supposed that the formula of Inductive Logic\nneed only be of this kind: 'These particulars, and all known\nparticulars of the same kind, are exactly included in the following\ngeneral proposition.' But a moment's reflection on what has just\nbeen said will show us that this is not sufficient: for the\nparticulars are not merely _included_ in the general proposition. It\nis not enough that they appertain to it by enumeration. It is, for\ninstance, no adequate example of Induction to say, 'Mercury\ndescribes an elliptical path, so does Venus, so do the Earth, Mars,\nJupiter, Saturn, Uranus; therefore all the Planets describe\nelliptical paths.' This is, as we have seen, the mode of stating the\n_evidence_ when the proposition is once suggested; but the Inductive\nstep consists in the _suggestion_ of a conception not before\napparent. When Kepler, after trying to connect the observed places\nof the planet Mars in many other ways, found at last that the\nconception of an _ellipse_ would include them all, he obtained a\ntruth by induction: for this conclusion was not obviously included\nin the phenomena, and had not been applied to these {111} facts\npreviously. Thus in our Formula, besides stating that the\nparticulars are included in the general proposition, we must also\nimply that the generality is constituted by a new Conception,--new\nat least in its application.\n\nHence our Inductive Formula might be something like the following:\n'These particulars, and all known particulars of the same kind, are\nexactly expressed by adopting the Conceptions and Statement of the\nfollowing Proposition.' It is of course requisite that the\nConceptions should be perfectly clear, and should precisely embrace\nthe facts, according to the explanation we have already given of\nthose conditions.\n\n15. It may happen, as we have already stated, that the Explication\nof a Conception, by which it acquires its due distinctness, leads to\na Definition, which Definition may be taken as the summary and total\nresult of the intellectual efforts to which this distinctness is\ndue. In such cases, the Formula of Induction may be modified\naccording to this condition; and we may state the inference by\nsaying, after an enumeration and analysis of the appropriate facts,\n'These facts are completely and distinctly expressed by adopting the\nfollowing Definition and Proposition.'\n\nThis Formula has been adopted in stating the Inductive Propositions\nwhich constitute the basis of the science of Mechanics, in a work\nintitled _The Mechanical Euclid_. The fundamental truths of the\nsubject are expressed in _Inductive Pairs_ of Assertions, consisting\neach of a Definition and a Proposition, such as the following:\n\nDEF.--A _Uniform Force_ is that which acting in the direction of the\nbody's motion, adds or subtracts equal velocities in equal times.\n\nPROP.--Gravity is a Uniform Force.\n\nAgain,\n\nDEF.--Two _Motions_ are _compounded_ when each produces its separate\neffect in a direction parallel to itself.\n\nPROP.--When any Force acts upon a body in motion, the motion which\nthe Force would produce in the {112} body at rest is compounded with\nthe previous motion of the body.\n\nAnd in like manner in other cases.\n\nIn these cases the proposition is, of course, established, and the\ndefinition realized, by an enumeration of the facts. And in the case\nof inferences made in such a form, the Definition of the Conception\nand the Assertion of the Truth are both requisite and are\ncorrelative to one another. Each of the two steps contains the\nverification and justification of the other. The Proposition derives\nits meaning from the Definition; the Definition derives its reality\nfrom the Proposition. If they are separated, the Definition is\narbitrary or empty, the Proposition vague or ambiguous.\n\n16. But it must be observed that neither of the preceding Formul\u00e6\nexpresses the full cogency of the inductive proof. They declare only\nthat the results can be clearly explained and rigorously deduced by\nthe employment of a certain Definition and a certain Proposition.\nBut in order to make the conclusion demonstrative, which in perfect\nexamples of Induction it is, we ought to be able to declare that the\nresults can be clearly explained and rigorously declared _only_ by\nthe Definition and Proposition which we adopt. And in reality, the\nconviction of the sound inductive reasoner does reach to this point.\nThe Mathematician asserts the Laws of Motion, seeing clearly that\nthey (or laws equivalent to them) afford the only means of clearly\nexpressing and deducing the actual facts. But this conviction, that\nthe inductive inference is not only consistent with the facts, but\nnecessary, finds its place in the mind gradually, as the\ncontemplation of the consequences of the proposition, and the\nvarious relations of the facts, becomes steady and familiar. It is\nscarcely possible for the student at once to satisfy himself that\nthe inference is thus inevitable. And when he arrives at this\nconviction, he sees also, in many cases at least, that there may be\nother ways of expressing the substance of the truth established,\nbesides that special Proposition which he has under his notice.\n{113}\n\nWe may, therefore, without impropriety, renounce the undertaking of\nconveying in our formula this final conviction of the necessary\ntruth of our inference. We may leave it to be thought, without\ninsisting upon saying it, that in such cases what _can_ be true,\n_is_ true. But if we wish to express the ultimate significance of\nthe Inductive Act of thought, we may take as our Formula for the\nColligation of Facts by Induction, this:--'The several Facts are\nexactly expressed as one Fact if, _and only if_, we adopt the\nConception and the Assertion' of the inductive inference.\n\n17. I have said that the mind must be properly disciplined in order\nthat it may see the necessary connexion between the facts and the\ngeneral proposition in which they are included. And the perception\nof this connexion, though treated as _one step_ in our inductive\ninference, may imply _many steps_ of demonstrative proof. The\nconnexion is this, that the particular case is included in the\ngeneral one, that is, may be _deduced_ from it: but this deduction\nmay often require many links of reasoning. Thus in the case of the\ninference of the law of the force from the elliptical form of the\norbit by Newton, the proof that in the ellipse the deflection from\nthe tangent is inversely as the square of the distance from the\nfocus of the ellipse, is a ratiocination consisting of several\nsteps, and involving several properties of Conic Sections; these\nproperties being supposed to be previously established by a\ngeometrical system of demonstration on the special subject of the\nConic Sections. In this and similar cases the Induction involves\nmany steps of Deduction. And in such cases, although the Inductive\nStep, the Invention of the Conception, is really the most important,\nyet since, when once made, it occupies a familiar place in men's\nminds; and since the Deductive Demonstration is of considerable\nlength and requires intellectual effort to follow it at every step;\nmen often admire the deductive part of the proposition, the\ngeometrical or algebraical demonstration, far more than that part in\nwhich the philosophical merit really resides. {114}\n\n18. Deductive reasoning is virtually a collection of syllogisms, as\nhas already been stated: and in such reasoning, the general\nprinciples, the Definitions and Axioms, necessarily stand at the\n_beginning_ of the demonstration. In an inductive inference, the\nDefinitions and Principles are the _final result_ of the reasoning,\nthe ultimate effect of the proof. Hence when an Inductive\nProposition is to be established by a proof involving several steps\nof demonstrative reasoning, the enunciation of the Proposition will\ncontain, explicitly or implicitly, principles which the\ndemonstration proceeds upon as axioms, but which are really\ninductive inferences. Thus in order to prove that the force which\nretains a planet in an ellipse varies inversely as the square of the\ndistance, it is taken for granted that the Laws of Motion are true,\nand that they apply to the planets. Yet the doctrine that this is\nso, as well as the law of the force, were established only by this\nand the like demonstrations. The doctrine which is the _hypothesis_\nof the deductive reasoning, is the _inference_ of the inductive\nprocess. The special facts which are the basis of the inductive\ninference, are the conclusion of the train of deduction. And in this\nmanner the deduction establishes the induction. The principle which\nwe gather from the facts is true, because the facts can be derived\nfrom it by rigorous demonstration. Induction moves upwards, and\ndeduction downwards, on the same stair.\n\nBut still there is a great difference in the character of their\nmovements. Deduction descends steadily and methodically, step by\nstep: Induction mounts by a leap which is out of the reach of\nmethod. She bounds to the top of the stair at once; and then it is\nthe business of Deduction, by trying each step in order, to\nestablish the solidity of her companion's footing. Yet these must be\nprocesses of the same mind. The Inductive Intellect makes an\nassertion which is subsequently justified by demonstration; and it\nshows its sagacity, its peculiar character, by enunciating the\nproposition when as yet the demonstration does not {115} exist: but\nthen it shows that it _is_ sagacity, by also producing the\ndemonstration.\n\nIt has been said that inductive and deductive reasoning are contrary\nin their scheme; that in Deduction we infer particular from general\ntruths; while in Induction we infer general from particular: that\nDeduction consists of many steps, in each of which we apply known\ngeneral propositions in particular cases; while in Induction we have\na single step, in which we pass from many particular truths to one\ngeneral proposition. And this is truly said; but though contrary in\ntheir motions, the two are the operation of the same mind travelling\nover the same ground. Deduction is a necessary part of Induction.\nDeduction justifies by calculation what Induction had happily\nguessed. Induction recognizes the ore of truth by its weight;\nDeduction confirms the recognition by chemical analysis. Every step\nof Induction must be confirmed by rigorous deductive reasoning,\nfollowed into such detail as the nature and complexity of the\nrelations (whether of quantity or any other) render requisite. If\nnot so justified by the supposed discoverer, it is _not_ Induction.\n\n19. Such Tabular arrangements of propositions as we have constructed\nmay be considered as the _Criterion of Truth_ for the doctrines\nwhich they include. They are the Criterion of Inductive Truth, in\nthe same sense in which Syllogistic Demonstration is the Criterion\nof Necessary Truth,--of the certainty of conclusions, depending upon\nevident First Principles. And that such Tables are really a\nCriterion of the truth of the propositions which they contain, will\nbe plain by examining their structure. For if the connexion which\nthe inductive process assumes be ascertained to be in each case real\nand true, the assertion of the general proposition merely collects\ntogether ascertained truths; and in like manner each of those more\nparticular propositions is true, because it merely expresses\ncollectively more special facts: so that the most general theory is\nonly the assertion of a great body of facts, duly classified and\nsubordinated. When we {116} assert the truth of the Copernican\ntheory of the motions of the solar system, or of the Newtonian\ntheory of the forces by which they are caused, we merely assert the\ngroups of propositions which, in the Table of Astronomical\nInduction, are included in these doctrines; and ultimately, we may\nconsider ourselves as merely asserting at once so many Facts, and\ntherefore, of course, expressing an indisputable truth.\n\n20. At any one of these steps of Induction in the Table, the\ninductive proposition is a _Theory_ with regard to the Facts which\nit includes, while it is to be looked upon as a _Fact_ with respect\nto the higher generalizations in which it is included. In any other\nsense, as was formerly shown, the opposition of _Fact_ and _Theory_\nis untenable, and leads to endless perplexity and debate. Is it a\nFact or a Theory that the planet Mars revolves in an Ellipse about\nthe Sun? To Kepler, employed in endeavouring to combine the separate\nobservations by the Conception of an Ellipse, it is a Theory; to\nNewton, engaged in inferring the law of force from a knowledge of\nthe elliptical motion, it is a Fact. There are, as we have already\nseen, no special attributes of Theory and Fact which distinguish\nthem from one another. Facts are phenomena apprehended by the aid of\nconceptions and mental acts, as Theories also are. We commonly call\nour observations _Facts_, when we apply, without effort or\nconsciousness, conceptions perfectly familiar to us: while we speak\nof Theories, when we have previously contemplated the Facts and the\nconnecting Conception separately, and have made the connexion by a\nconscious mental act. The real difference is a difference of\nrelation; as the same proposition in a demonstration is the\n_premiss_ of one syllogism and the _conclusion_ in another;--as the\nsame person is a father and a son. Propositions are Facts and\nTheories, according as they stand above or below the Inductive\nBrackets of our Tables.\n\n21. To obviate mistakes I may remark that the terms _higher_ and\n_lower_, when used of generalizations, are unavoidably represented\nby their opposites in our Inductive Tables. The highest\ngeneralization is that {117} which includes all others; and this\nstands the lowest on our page, because, reading downwards, that is\nthe place which we last reach.\n\nThere is a distinction of the knowledge acquired by Scientific\nInduction into two kinds, which is so important that we shall\nconsider it in the succeeding chapter.\n\n\n\n{{118}}\nCHAPTER VII.\n\nOF LAWS OF PHENOMENA AND OF CAUSES.\n\n\nAPHORISM XXIV.\n\n_Inductive truths are of two kinds_, Laws of Phenomena, _and_\nTheories of Causes. _It is necessary to begin in every science with\nthe Laws of Phenomena; but it is impossible that we should be\nsatisfied to stop short of a Theory of Causes. In Physical\nAstronomy, Physical Optics, Geology, and other sciences, we have\ninstances showing that we can make a great advance in inquiries\nafter true Theories of Causes._\n\n\n1. IN the first attempts at acquiring an exact and connected\nknowledge of the appearances and operations which nature presents,\nmen went no further than to learn _what_ takes place, not _why_ it\noccurs. They discovered an Order which the phenomena follow, Rules\nwhich they obey; but they did not come in sight of the Powers by\nwhich these rules are determined, the Causes of which this order is\nthe effect. Thus, for example, they found that many of the celestial\nmotions took place as if the sun and stars were carried round by the\nrevolutions of certain celestial spheres; but what causes kept these\nspheres in constant motion, they were never able to explain. In like\nmanner in modern times, Kepler discovered that the planets describe\nellipses, before Newton explained why they select this particular\ncurve, and describe it in a particular manner. The laws of\nreflection, refraction, dispersion, and other properties of light\nhave long been known; the causes of these laws are at present under\ndiscussion. And the same might be {119} said of many other sciences.\nThe discovery of _the Laws of Phenomena_ is, in all cases, the first\nstep in exact knowledge; these Laws may often for a long period\nconstitute the whole of our science; and it is always a matter\nrequiring great talents and great efforts, to advance to a knowledge\nof the _Causes_ of the phenomena.\n\nHence the larger part of our knowledge of nature, at least of the\ncertain portion of it, consists of the knowledge of the Laws of\nPhenomena. In Astronomy indeed, besides knowing the rules which\nguide the appearances, and resolving them into the real motions from\nwhich they arise, we can refer these motions to the forces which\nproduce them. In Optics, we have become acquainted with a vast\nnumber of laws by which varied and beautiful phenomena are governed;\nand perhaps we may assume, since the evidence of the Undulatory\nTheory has been so fully developed, that we know also the Causes of\nthe Phenomena. But in a large class of sciences, while we have\nlearnt many Laws of Phenomena, the causes by which these are\nproduced are still unknown or disputed. Are we to ascribe to the\noperation of a fluid or fluids, and if so, in what manner, the facts\nof heat, magnetism, electricity, galvanism? What are the forces by\nwhich the elements of chemical compounds are held together? What are\nthe forces, of a higher order, as we cannot help believing, by which\nthe course of vital action in organized bodies is kept up? In these\nand other cases, we have extensive departments of science; but we\nare as yet unable to trace the effects to their causes; and our\nscience, so far as it is positive and certain, consists entirely of\nthe laws of phenomena.\n\n2. In those cases in which we have a division of the science which\nteaches us the doctrine of the causes, as well as one which states\nthe rules which the effects follow, I have, in the _History_,\ndistinguished the two portions of the science by certain terms. I\nhave thus spoken of _Formal_ Astronomy and _Physical_ Astronomy. The\nlatter phrase has long been commonly employed to describe that\ndepartment of Astronomy which deals with {120} those forces by which\nthe heavenly bodies are guided in their motions; the former\nadjective appears well suited to describe a collection of rules\ndepending on those ideas of space, time, position, number, which\nare, as we have already said, the _forms_ of our apprehension of\nphenomena. The laws of phenomena may be considered as _formul\u00e6_,\nexpressing results in terms of those ideas. In like manner, I have\nspoken of Formal Optics and Physical Optics; the latter division\nincluding all speculations concerning the machinery by which the\neffects are produced. Formal Acoustics and Physical Acoustics may be\ndistinguished in like manner, although these two portions of science\nhave been a good deal mixed together by most of those who have\ntreated of them. Formal Thermotics, the knowledge of the laws of the\nphenomena of heat, ought in like manner to lead to Physical\nThermotics, or the Theory of Heat with reference to the cause by\nwhich its effects are produced;--a branch of science which as yet\ncan hardly be said to exist.\n\n3. What _kinds of cause_ are we to admit in science? This is an\nimportant, and by no means an easy question. In order to answer it,\nwe must consider in what manner our progress in the knowledge of\ncauses has hitherto been made. By far the most conspicuous instance\nof success in such researches, is the discovery of the causes of the\nmotions of the heavenly bodies. In this case, after the formal laws\nof the motions,--their conditions as to space and time,--had become\nknown, men were enabled to go a step further; to reduce them to the\nfamiliar and general cause of motion--mechanical force; and to\ndetermine the laws which this force follows. That this was a step in\naddition to the knowledge previously possessed, and that it was a\nreal and peculiar truth, will not be contested. And a step in any\nother subject which should be analogous to this in astronomy;--a\ndiscovery of causes and forces as certain and clear as the discovery\nof universal gravitation;--would undoubtedly be a vast advance upon\na body of science consisting only of the laws of phenomena. {121}\n\n4. But although physical astronomy may well be taken as a standard\nin estimating the value and magnitude of the advance from the\nknowledge of phenomena to the knowledge of causes; the peculiar\nfeatures of the transition from formal to physical science in that\nsubject must not be allowed to limit too narrowly our views of the\nnature of this transition in other cases. We are not, for example,\nto consider that the step which leads us to the knowledge of causes\nin any province of nature must necessarily consist in the discovery\nof centers of forces, and collections of such centers, by which the\neffects are produced. The discovery of the causes of phenomena may\nimply the detection of a fluid by whose undulations, or other\noperations, the results are occasioned. The phenomena of acoustics\nare, we know, produced in this manner by the air; and in the cases\nof light, heat, magnetism, and others, even if we reject all the\ntheories of such fluids which have hitherto been proposed, we still\ncannot deny that such theories are intelligible and possible, as the\ndiscussions concerning them have shown. Nor can it be doubted that\nif the assumption of such a fluid, in any case, were as well\nevidenced as the doctrine of universal gravitation is, it must be\nconsidered as a highly valuable theory.\n\n5. But again; not only must we, in aiming at the formation of a\nCausal Section in each Science of Phenomena, consider Fluids and\ntheir various modes of operation admissible, as well as centers of\nmechanical force; but we must be prepared, if it be necessary, to\nconsider the forces, or powers to which we refer the phenomena,\nunder still more general aspects, and invested with characters\ndifferent from mere mechanical force. For example; the forces by\nwhich the chemical elements of bodies are bound together, and from\nwhich arise, both their sensible texture, their crystalline form,\nand their chemical composition, are certainly forces of a very\ndifferent nature from the mere attraction of matter according to its\nmass. The powers of assimilation and reproduction in plants and\nanimals are obviously still more removed from mere mechanism; yet\n{122} these powers are not on that account less real, nor a less fit\nand worthy subject of scientific inquiry.\n\n6. In fact, these forces--mechanical, chemical and vital,--as we\nadvance from one to the other, each bring into our consideration new\ncharacters; and what these characters are, has appeared in the\nhistorical survey which we made of the Fundamental Ideas of the\nvarious sciences. It was then shown that the forces by which\nchemical effects are produced necessarily involve the Idea of\nPolarity,--they are polar forces; the particles tend together in\nvirtue of opposite properties which in the combination neutralize\neach other. Hence, in attempting to advance to a theory of Causes in\nchemistry, our task is by no means to invent laws of _mechanical_\nforce, and collections of forces, by which the effects may be\nproduced. We know beforehand that no such attempt can succeed. Our\naim must be to conceive such new kinds of force, including Polarity\namong their characters, as may best render the results intelligible.\n\n7. Thus in advancing to a Science of Cause in any subject, the\nlabour and the struggle is, not to analyse the phenomena according\nto any preconceived and already familiar ideas, but to form\ndistinctly new conceptions, such as do really carry us to a more\nintimate view of the processes of nature. Thus in the case of\nastronomy, the obstacle which deferred the discovery of the true\ncauses from the time of Kepler to that of Newton, was the difficulty\nof taking hold of mechanical conceptions and axioms with sufficient\nclearness and steadiness; which, during the whole of that interval,\nmathematicians were learning to do. In the question of causation\nwhich now lies most immediately in the path of science, that of the\ncauses of electrical and chemical phenomena, the business of rightly\nfixing and limiting the conception of polarity, is the proper object\nof the efforts of discoverers. Accordingly a large portion of Mr\nFaraday's recent labours[23\\2] is directed, not to {123} the attempt\nat discovering new laws of phenomena, but to the task of throwing\nlight upon the conception of polarity, and of showing how it must be\nunderstood, so that it shall include electrical induction and other\nphenomena, which have commonly been ascribed to forces acting\nmechanically at a distance. He is by no means content, nor would it\nanswer the ends of science that he should be, with stating the\nresults of his experiments; he is constantly, in every page,\npointing out the interpretation of his experiments, and showing how\nthe conception of Polar Forces enters into this interpretation. 'I\nshall,' he says[24\\2], 'use every opportunity which presents itself\nof returning to that strong test of truth, experiment; but,' he\nadds, 'I shall necessarily have occasion to speak theoretically, and\neven hypothetically.' His hypothesis that electrical inductive\naction always takes place by means of a continuous line of polarized\nparticles, and not by attraction and repulsion at a distance, if\nestablished, cannot fail to be a great step on our way towards a\nknowledge of causes, as well as phenomena, in the subjects under his\nconsideration.\n\n[Note 23\\2: Eleventh, Twelfth, and Thirteenth Series of Researches,\n_Phil. Trans._ 1837 and 8.]\n\n[Note 24\\2: Art. 1318.]\n\n8. The process of obtaining new conceptions is, to most minds, far\nmore unwelcome than any labour in employing old ideas. The effort is\nindeed painful and oppressive; it is feeling in the dark for an\nobject which we cannot find. Hence it is not surprising that we\nshould far more willingly proceed to seek for new causes by applying\nconceptions borrowed from old ones. Men were familiar with solid\nframes, and with whirlpools of fluid, when they had not learnt to\nform any clear conception of attraction at a distance. Hence they at\nfirst imagined the heavenly motions to be caused by Crystalline\nSpheres, and by Vortices. At length they were taught to conceive\nCentral Forces, and then they reduced the solar system to these. But\nhaving done this, they fancied that all the rest of the machinery of\nnature must be central forces. We find Newton {124} expressing this\nconviction[25\\2], and the mathematicians of the last century acted\nupon it very extensively. We may especially remark Laplace's labours\nin this field. Having explained, by such forces, the phenomena of\ncapillary attraction, he attempted to apply the same kind of\nexplanation to the reflection, refraction, and double refraction of\nlight;--to the constitution of gases;--to the operation of heat. It\nwas soon seen that the explanation of refraction was arbitrary, and\nthat of double refraction illusory; while polarization entirely\neluded the grasp of this machinery. Centers of force would no longer\nrepresent the modes of causation which belonged to the phenomena.\nPolarization required some other contrivance, such as the undulatory\ntheory supplied. No theory of light can be of any avail in which the\nfundamental idea of Polarity is not clearly exhibited.\n\n[Note 25\\2: Multa me movent, &c.,--Pref. to the _Principia_, already\nquoted in the _History_.]\n\n9. The sciences of magnetism and electricity have given rise to\ntheories in which this relation of polarity is exhibited by means of\ntwo opposite fluids[26\\2];--a positive and a negative fluid, or a\nvitreous and a resinous, for electricity, and a boreal and an\naustral fluid for magnetism. The hypothesis of such fluids gives\nresults agreeing in a remarkable manner with the facts and their\nmeasures, as Coulomb and others have shown. It may be asked how far\nwe may, in such a case, suppose that we have discovered the true\ncause of the phenomena, and whether it is sufficiently proved that\nthese fluids really exist. The right answer seems to be, that the\nhypothesis certainly represents the truth so far as regards the\npolar relation of the two energies, and the laws of the attractive\nand repulsive forces of the particles in which these energies\nreside; but that we are not entitled to assume that the vehicles of\nthese energies possess other attributes of material fluids, or that\nthe forces thus ascribed to the particles are the primary elementary\nforces from which {125} the action originates. We are the more bound\nto place this cautious limit to our acceptance of the Coulombian\ntheory, since in electricity Faraday has in vain endeavoured to\nbring into view one of the polar fluids without the other: whereas\nsuch a result ought to be possible if there were two separable\nfluids. The impossibility of this separate exhibition of one fluid\nappears to show that the fluids are _real_ only so far as they are\n_polar_. And Faraday's view above mentioned, according to which the\nattractions at a distance are resolved into the action of lines of\npolarized particles of air, appears still further to show that the\nconceptions hitherto entertained of electrical forces, according to\nthe Coulombian theory, do not penetrate to the real and intimate\nnature of the causation belonging to this case.\n\n[Note 26\\2: _Hist. Ind. Sc._ b. xi. c. ii.]\n\n10. Since it is thus difficult to know when we have seized the true\ncause of the phenomena in any department of science, it may appear\nto some persons that physical inquirers are imprudent and\nunphilosophical in undertaking this Research of Causes; and that it\nwould be safer and wiser to confine ourselves to the investigation\nof the laws of phenomena, in which field the knowledge which we\nobtain is definite and certain. Hence there have not been wanting\nthose who have laid it down as a maxim that 'science must study only\nthe laws of phenomena, and never the mode of production[27\\2].' But\nit is easy to see that such a maxim would confine the breadth and\ndepth of scientific inquiries to a most scanty and miserable limit.\nIndeed, such a rule would defeat its own object; for the laws of\nphenomena, in many cases, cannot be even expressed or understood\nwithout some hypothesis respecting their mode of production. How\ncould the phenomena of polarization have been conceived or reasoned\nupon, except by imagining a polar arrangement of particles, or\ntransverse vibrations, or some equivalent hypothesis? The doctrines\nof fits of easy transmission, the doctrine of moveable polarization,\nand the like, even when {126} erroneous as representing the whole of\nthe phenomena, were still useful in combining some of them into\nlaws; and without some such hypotheses the facts could not have been\nfollowed out. The doctrine of a fluid caloric may be false; but\nwithout imagining such a fluid, how could the movement of heat from\none part of a body to another be conceived? It may be replied that\nFourier, Laplace, Poisson, who have principally cultivated the\nTheory of Heat, have not conceived it as a fluid, but have referred\nconduction to the radiation of the molecules of bodies, which they\nsuppose to be separate points. But this molecular constitution of\nbodies is itself an assumption of the mode in which the phenomena\nare produced; and the radiation of heat suggests inquiries\nconcerning a fluid emanation, no less than its conduction does. In\nlike manner, the attempts to connect the laws of phenomena of heat\nand of gases, have led to hypotheses respecting the constitution of\ngases, and the combination of their particles with those of caloric,\nwhich hypotheses may be false, but are probably the best means of\ndiscovering the truth.\n\n[Note 27\\2: Comte, _Philosophie Positive_.]\n\nTo debar science from inquiries like these, on the ground that it is\nher business to inquire into facts, and not to speculate about\ncauses, is a curious example of that barren caution which hopes for\ntruth without daring to venture upon the quest of it. This temper\nwould have stopped with Kepler's discoveries, and would have refused\nto go on with Newton to inquire into the mode in which the phenomena\nare produced. It would have stopped with Newton's optical facts, and\nwould have refused to go on with him and his successors to inquire\ninto the mode in which these phenomena are produced. And, as we have\nabundantly shown, it would, on that very account, have failed in\nseeing what the phenomena really are.\n\nIn many subjects the attempt to study the laws of phenomena,\nindependently of any speculations respecting the causes which have\nproduced them, is neither possible for human intelligence nor for\nhuman temper. Men cannot contemplate the phenomena without clothing\nthem in terms of some hypothesis, and will {127} not be schooled to\nsuppress the questionings which at every moment rise up within them\nconcerning the causes of the phenomena. Who can attend to the\nappearances which come under the notice of the geologist;--strata\nregularly bedded, full of the remains of animals such as now live in\nthe depths of the ocean, raised to the tops of mountains, broken,\ncontorted, mixed with rocks such as still flow from the mouths of\nvolcanos,--who can see phenomena like these, and imagine that he\nbest promotes the progress of our knowledge of the earth's history,\nby noting down the facts, and abstaining from all inquiry whether\nthese are really proof of past states of the earth and of\nsubterraneous forces, or merely an accidental imitation of the\neffects of such causes? In this and similar cases, to proscribe the\ninquiry into causes would be to annihilate the science.\n\nFinally, this caution does not even gain its own single end, the\nescape from hypotheses. For, as we have said, those who will not\nseek for new and appropriate causes of newly-studied phenomena, are\nalmost inevitably led to ascribe the facts to modifications of\ncauses already familiar. They may declare that they will not hear of\nsuch causes as vital powers, elective affinities, electric, or\ncalorific, or luminiferous ethers or fluids; but they will not the\nless on that account assume hypotheses equally unauthorized;--for\ninstance--universal mechanical forces; a molecular constitution of\nbodies; solid, hard, inert matter;--and will apply these hypotheses\nin a manner which is arbitrary in itself as well as quite\ninsufficient for its purpose.\n\n11. It appears, then, to be required, both by the analogy of the\nmost successful efforts of science in past times and by the\nirrepressible speculative powers of the human mind, that we should\nattempt to discover both the _laws of phenomena_, and their\n_causes_. In every department of science, when prosecuted far\nenough, these two great steps of investigation must succeed each\nother. The laws of phenomena must be known before we can speculate\nconcerning causes; the causes must be inquired into when the\nphenomena have been {128} reduced to rule. In both these\nspeculations the suppositions and conceptions which occur must be\nconstantly tested by reference to observation and experiment. In\nboth we must, as far as possible, devise hypotheses which, when we\nthus test them, display those characters of truth of which we have\nalready spoken;--an agreement with facts such as will stand the most\npatient and rigid inquiry; a provision for predicting truly the\nresults of untried cases; a consilience of inductions from various\nclasses of facts; and a progressive tendency of the scheme to\nsimplicity and unity.\n\nWe shall attempt hereafter to give several rules of a more precise\nand detailed kind for the discovery of the causes, and still more,\nof the laws of phenomena. But it will be useful in the first place\nto point out the Classification of the Sciences which results from\nthe principles already established in this **work. And for this\npurpose we must previously decide the question, whether the\npractical Arts, as Medicine and Engineering, must be included in our\nlist of Sciences.\n\n\n\n{{129}}\nCHAPTER VIII.\n\nOF ART AND SCIENCE.\n\n\nAPHORISM XXV.\n\n_Art and Science differ. The object of Science is Knowledge; the\nobjects of Art, are Works. In Art, truth is a means to an end; in\nScience, it is the only end. Hence the Practical Arts are not to be\nclassed among the Sciences._\n\nAPHORISM XXVI.\n\n_Practical Knowledge, such as Art implies, is not Knowledge such as\nScience includes. Brute animals have a practical knowledge of\nrelations of space and force; but they have no knowledge of Geometry\nor Mechanics._\n\n\n1. THE distinction of Arts and Sciences very materially affects all\nclassifications of the departments of Human Knowledge. It is often\nmaintained, expressly or tacitly, that the Arts are a part of our\nknowledge, in the same sense in which the Sciences are so; and that\nArt is the application of Science to the purposes of practical life.\nIt will be found that these views require some correction, when we\nunderstand _Science_ in the exact sense in which we have throughout\nendeavoured to contemplate it, and in which alone our examination of\nits nature can instruct us in the true foundations of our knowledge.\n\nWhen we cast our eyes upon the early stages of the histories of\nnations, we cannot fail to be struck with the consideration, that in\nmany countries the Arts of life already appear, at least in some\nrude form or other, when, as yet, nothing of science exists. A {130}\npractical knowledge of Astronomy, such as enables them to reckon\nmonths and years, is found among all nations except the mere\nsavages. A practical knowledge of Mechanics must have existed in\nthose nations which have left us the gigantic monuments of early\narchitecture. The pyramids and temples of Egypt and Nubia, the\nCyclopean walls of Italy and Greece, the temples of Magna Gr\u00e6cia and\nSicily, the obelisks and edifices of India, the cromlechs and\nDruidical circles of countries formerly Celtic,--must have demanded\nno small practical mechanical skill and power. Yet those modes of\nreckoning time must have preceded the rise of speculative Astronomy;\nthese structures must have been erected before the theory of\nMechanics was known. To suppose, as some have done, a great body of\nscience, now lost, to have existed in the remote ages to which these\nremains belong, is not only quite gratuitous, and contrary to all\nanalogy, but is a supposition which cannot be extended so far as to\nexplain all such cases. For it is impossible to imagine that _every_\nart has been preceded by the science which renders a reason for its\nprocesses. Certainly men formed wine from the grape, before they\npossessed a Science of Fermentation; the first instructor of every\nartificer in brass and iron can hardly be supposed to have taught\nthe Chemistry of metals as a Science; the inventor of the square and\nthe compasses had probably no more knowledge of demonstrated\nGeometry than have the artisans who now use those implements; and\nfinally, the use of speech, the employment of the inflections and\ncombinations of words, must needs be assumed as having been prior to\nany general view of the nature and analogy of Language. Even at this\nmoment, the greater part of the arts which exist in the world are\nnot accompanied by the sciences on which they theoretically depend.\nWho shall state to us the general chemical truths to which the\nmanufactures of glass, and porcelain, and iron, and brass, owe their\nexistence? Do not almost all artisans practise many successful\nartifices long before science explains the ground of the process? Do\nnot arts at this day exist, in a high state {131} of perfection, in\ncountries in which there is no science, as China and India? These\ncountries and many others have no theories of mechanics, of optics,\nof chemistry, of physiology; yet they construct and use mechanical\nand optical instruments, make chemical combinations, take advantage\nof physiological laws. It is too evident to need further\nillustration that Art may exist without Science;--that the former\nhas usually been anterior to the latter, and even now commonly\nadvances independently, leaving science to follow as it can.\n\n2. We here mean by _Science_, that exact, general, speculative\nknowledge, of which we have, throughout this work, been endeavouring\nto exhibit the nature and rules. Between such Science and the\n_practical Arts_ of life, the points of difference are sufficiently\nmanifest. The object of Science is _Knowledge_; the object of Art\nare _Works_. The latter is satisfied with producing its material\nresults; to the former, the operations of matter, whether natural or\nartificial, are interesting only so far as they can be embraced by\nintelligible principles. The End of Art is the Beginning of Science;\nfor when it is seen _what_ is done, then comes the question _why_ it\nis done. Art may have fixed general rules, stated in words; but she\nhas these merely as means to an end: to Science, the propositions\nwhich she obtains are each, in itself, a sufficient end of the\neffort by which it is acquired. When Art has brought forth her\nproduct, her task is finished; Science is constantly led by one step\nof her path to another: each proposition which she obtains impels\nher to go onwards to other propositions more general, more profound,\nmore simple. Art puts elements together, without caring to know what\nthey are, or why they coalesce. Science analyses the compound, and\nat every such step strives not only to perform, but to understand\nthe analysis. Art advances in proportion as she becomes able to\nbring forth products more multiplied, more complex, more various;\nbut Science, straining her eyes to penetrate more and more deeply\ninto the nature of things, reckons her success in proportion as she\nsees, in all the phenomena, however {132} multiplied; complex, and\nvaried, the results of one or two simple and general laws.\n\n3. There are many acts which man, as well as animals, performs by\nthe guidance of nature, without seeing or seeking the reason why he\ndoes so; as, the acts by which he balances himself in standing or\nmoving, and those by which he judges of the form and position of the\nobjects around him. These actions have their reason in the\nprinciples of geometry and mechanics; but of such reasons he who\nthus acts is unaware: he works blindly, under the impulse of an\nunknown principle which we call _Instinct_. When man's speculative\nnature seeks and finds the reasons why he should act thus or\nthus;--why he should stretch out his arm to prevent his falling, or\nassign a certain position to an object in consequence of the angles\nunder which it is seen;--he may perform the same actions as before,\nbut they are then done by the aid of a different faculty, which, for\nthe sake of distinction, we may call _Insight_. Instinct is a purely\nactive principle; it is seen in deeds alone; it has no power of\nlooking inwards; it asks no questions; it has no tendency to\ndiscover reasons or rules; it is the opposite of Insight.\n\n4. Art is not identical with Instinct: on the contrary, there are\nbroad differences. Instinct is stationary; Art is progressive.\nInstinct is mute; it acts, but gives no rules for acting: Art can\nspeak; she can lay down rules. But though Art is thus separate from\nInstinct, she is not essentially combined with Insight. She can see\nwhat to do, but she needs not to see why it is done. She may lay\ndown Rules, but it is not her business to give Reasons. When man\nmakes _that_ his employment, he enters upon the domain of Science.\nArt takes the phenomena and laws of nature as she finds them: that\nthey are multiplied, complex, capricious, incoherent, disturbs her\nnot. She is content that the rules of nature's operations should be\nperfectly arbitrary and unintelligible, provided they are constant,\nso that she can depend upon their effects. But Science is impatient\nof all appearance of caprice, {133} inconsistency, irregularity, in\nnature. She will not believe in the existence of such characters.\nShe resolves one apparent anomaly after another; her task is not\nended till every thing is so plain and simple, that she is tempted\nto believe that she sees that it could by no possibility have been\notherwise than it is.\n\n5. It may be said that, after all, Art does really involve the\nknowledge which Science delivers;--that the artisan who raises large\nweights, practically _knows_ the properties of the mechanical\npowers;--that he who manufactures chemical compounds is virtually\nacquainted with the laws of chemical combination. To this we reply,\nthat it might on the same grounds be asserted, that he who acts upon\nthe principle that two sides of a triangle are greater than the\nthird is really acquainted with geometry; and that he who balances\nhimself on one foot knows the properties of the center of gravity.\nBut this is an acquaintance with geometry and mechanics which even\nbrute animals possess. It is evident that it is not of such\nknowledge as this that we have here to treat. It is plain that this\nmode of possessing principles is altogether different from that\ncontemplation of them on which science is founded. We neglect the\nmost essential and manifest differences, if we confound our\nunconscious assumptions with our demonstrative reasonings.\n\n6. The real state of the case is, that the principles which Art\n_involves_, Science alone _evolves_. The truths on which the success\nof Art depends, lurk in the artist's mind in an undeveloped state;\nguiding his hand, stimulating his invention, balancing his judgment;\nbut not appearing in the form of enunciated Propositions. Principles\nare not to him direct objects of meditation: they are secret Powers\nof Nature, to which the forms which tenant the world owe their\nconstancy, their movements, their changes, their luxuriant and\nvaried growth, but which he can nowhere directly contemplate. That\nthe creative and directive Principles which have their lodgment in\nthe artist's mind, when _unfolded_ by our speculative powers into\n{134} systematic shape, become Science, is true; but it is precisely\nthis process of _development_ which gives to them their character of\nScience. In practical Art, principles are unseen guides, leading us\nby invisible strings through paths where the end alone is looked at:\nit is for Science to direct and purge our vision so that these airy\nties, these principles and laws, generalizations and theories,\nbecome distinct objects of vision. Many may feel the intellectual\nmonitor, but it is only to her favourite heroes that the Goddess of\nWisdom visibly reveals herself.\n\n7. Thus Art, in its earlier stages at least, is widely different\nfrom Science, is independent of it, and is anterior to it. At a\nlater period, no doubt, Art may borrow aid from Science; and the\ndiscoveries of the philosopher may be of great value to the\nmanufacturer and the artist. But even then, this application forms\nno essential part of the science: the interest which belongs to it\nis not an intellectual interest. The augmentation of human power and\nconvenience may impel or reward the physical philosopher; but the\nprocesses by which man's repasts are rendered more delicious, his\njourneys more rapid, his weapons more terrible, are not, therefore,\nScience. They may involve principles which are of the highest\ninterest to science; but as the advantage is not practically more\nprecious because it results from a beautiful theory, so the\ntheoretical principle has no more conspicuous place in science\nbecause it leads to convenient practical consequences. The nature of\nScience is purely intellectual; Knowledge alone,--exact general\nTruth,--is her object; and we cannot mix with such material, as\nmatters of the same kind, the merely Empirical maxims of Art,\nwithout introducing endless confusion into the subject, and making\nit impossible to attain any solid footing in our philosophy.\n\n8. I shall therefore not place, in our Classification of the\nSciences, the Arts, as has generally been done; nor shall I notice\nthe applications of sciences to art, as forming any separate portion\nof each science. The sciences, considered as bodies of general\nspeculative {135} truths, are what we are here concerned with; and\napplications of such truths, whether useful or useless, are\nimportant to us only as illustrations and examples. Whatever place\nin human knowledge the Practical Arts may hold, they are not\nSciences. And it is only by this rigorous separation of the\nPractical from the Theoretical, that we can arrive at any solid\nconclusions respecting the nature of Truth, and the mode of arriving\nat it, such as it is our object to attain.\n\n\n\n{{136}}\nCHAPTER IX.\n\nOF THE CLASSIFICATION OF SCIENCES.\n\n\n1. THE Classification of Sciences has its chief use in pointing out\nto us the extent of our powers of arriving at truth, and the\nanalogies which may obtain between those certain and lucid portions\nof knowledge with which we are here concerned, and those other\nportions, of a very different interest and evidence, which we here\npurposely abstain to touch upon. The classification of human\nknowledge will, therefore, have a more peculiar importance when we\ncan include in it the moral, political, and metaphysical, as well as\nthe physical portions of our knowledge. But such a survey does not\nbelong to our present undertaking: and a general view of the\nconnexion and order of the branches of sciences which our review has\nhitherto included, will even now possess some interest; and may\nserve hereafter as an introduction to a more complete scheme of the\ngeneral body of human knowledge.\n\n2. In this, as in any other case, a sound classification must be the\nresult, not of any assumed principles imperatively applied to the\nsubject, but of an examination of the objects to be classified;--of\nan analysis of them into the principles in which they agree and\ndiffer. The Classification of Sciences must result from the\nconsideration of their nature and contents. Accordingly, that review\nof the Sciences in which the _History_ of the Sciences engaged us,\nled to a Classification, of which the main features are indicated in\nthat work. The Classification thus obtained, depends neither upon\nthe faculties of the mind to which the separate parts of our\nknowledge owe their origin, nor upon the objects which each science\ncontemplates; but upon a more {137} natural and fundamental\nelement;--namely, the _Ideas_ which each science involves. The Ideas\nregulate and connect the facts, and are the foundations of the\nreasoning, in each science: and having in another work more fully\nexamined these _Ideas_, we are now prepared to state here the\nclassification to which they lead. If we have rightly traced each\nscience to the Conceptions which are really fundamental _with regard\nto it_, and which give rise to the first principles on which it\ndepends, it is not necessary for our purpose that we should decide\nwhether these Conceptions are absolutely ultimate principles of\nthought, or whether, on the contrary, they can be further resolved\ninto other Fundamental Ideas. We need not now suppose it determined\nwhether or not _Number_ is a mere modification of the Idea of Time,\nand _Force_ a mere modification of the Idea of Cause: for however\nthis may be, our Conception of Number is the foundation of\nArithmetic, and our Conception of Force is the foundation of\nMechanics. It is to be observed also that in our classification,\neach Science may involve, not only the Ideas or Conceptions which\nare placed opposite to it in the list, but also all which _precede_\nit. Thus Formal Astronomy involves not only the Conception of\nMotion, but also those which are the foundation of Arithmetic and\nGeometry. In like manner. Physical Astronomy employs the Sciences of\nStatics and Dynamics, and thus, rests on their foundations; and\nthey, in turn, depend upon the Ideas of Space and of Time, as well\nas of Cause.\n\n3. We may further observe, that this arrangement of Sciences\naccording to the Fundamental Ideas which they involve, points out\nthe transition from those parts of human knowledge which have been\nincluded in our History and Philosophy, to other regions of\nspeculation into which we have not entered. We have repeatedly found\nourselves upon the borders of inquiries of a psychological, or\nmoral, or theological nature. Thus the History of Physiology[28\\2]\nled us to the consideration {138} of Life, Sensation, and Volition;\nand at these Ideas we stopped, that we might not transgress the\nboundaries of our subject as then predetermined. It is plain that\nthe pursuit of such conceptions and their consequences, would lead\nus to the sciences (if we are allowed to call them sciences) which\ncontemplate not only animal, but human principles of action, to\nAnthropology, and Psychology. In other ways, too, the Ideas which we\nhare examined, although manifestly the foundations of sciences such\nas we have here treated of also plainly pointed to speculations of a\ndifferent order; thus the Idea of a Final Cause is an indispensable\nguide in Biology, as we have seen; but the conception of Design as\ndirecting the order of nature, once admitted, soon carries us to\nhigher contemplations. Again, the Class of Pal\u00e6tiological Sciences\nwhich we were in the _History_ led to construct, although we there\nadmitted only one example of the Class, namely Geology, does in\nreality include many vast lines of research; as the history and\ncauses of the division of plants and animals, the history of\nlanguages, arts, and consequently of civilization. Along with these\nresearches, comes the question how far these histories point\nbackwards to a natural or a supernatural origin; and the Idea of a\nFirst Cause is thus brought under our consideration. Finally, it is\nnot difficult to see that as the Physical Sciences have their\npeculiar governing Ideas, which support and shape them, so the Moral\nand Political Sciences also must similarly have their fundamental\nand formative Ideas, the source of universal and certain truths,\neach of their proper kind. But to follow out the traces of this\nanalogy, and to verify the existence of those Fundamental Ideas in\nMorals and Politics, is a task quite out of the sphere of the work\nin which we are here engaged.\n\n[Note 28\\2: _Hist. Ind. Sc._ b. xvii. c. v. sect. 2.]\n\n4. We may now place before the reader our Classification of the\nSciences. I have added to the list of Sciences, a few not belonging\nto our present subject, that the nature of the transition by which\nwe are to extend our philosophy into a wider and higher region may\nbe in some measure perceived. {139}\n\nThe Classification of the Sciences is given over leaf.\n\nA few remarks upon it offer themselves.\n\nThe _Pure_ Mathematical Sciences can hardly be called _Inductive_\nSciences. Their principles are not obtained by Induction from Facts,\nbut are necessarily assumed in reasoning upon the subject matter\nwhich those sciences involve.\n\nThe Astronomy of the Ancients aimed only at explaining the motions\nof the heavenly bodies, as a _mechanism_. Modern Astronomy, explains\nthese motions on the principles of Mechanics.\n\nThe term _Physics_, when confined to a peculiar class of Sciences,\nis usually understood to exclude the Mechanical Sciences on the one\nside, and Chemistry on the other; and thus embraces the Secondary\nMechanical and Analytico-Mechanical Sciences. But the adjective\n_Physical_ applied to any science and opposed to _Formal_, as in\nAstronomy and Optics, implies those speculations in which we\nconsider not only the Laws of Phenomena but their Causes; and\ngenerally, as in those cases, their Mechanical Causes.\n\nThe term _Metaphysics_ is applied to subjects in which the Facts\nexamined are emotions, thoughts and mental conditions; subjects not\nincluded in our present survey. {140}\n\n Fundamental Ideas or Sciences. Classification.\n Conceptions.\n\nSpace Geometry )\nTime ) Pure Mathematical\n_Number_ Arithmetic }\nSign Algebra ) Sciences.\nLimit Differentials )\n_Motion_ Pure Mechanism } Pure Motional\n Formal Astronomy } Sciences.\n\nCause\n_Force_ Statics )\n_Matter_ Dynamics ) Mechanical\n_Inertia _ Hydrostatics }\n_Fluid Pressure_ Hydrodynamics ) Sciences.\n Physical Astronomy )\n\nOutness\nMedium _of Sensation_ Acoustics )\nIntensity _of Qualities_ Formal Optics ) Secondary\n_Scales of Qualities_ Physical Optics } Mechanical\n Thermotics ) Sciences.\n Atmology ) (_Physics_.)\nPolarity Electricity ) Analytico-Mecha-\n Magnetism } nical Sciences.\n Galvanism ) (_Physics_.)\n\nElement (_Composition_)\n_Chemical_ Affinity\nSubstance (_Atoms_) Chemistry Analytical Science.\nSymmetry Crystallography } Analytico-Classifi-\nLikeness Systematic Mineralogy } catory Sciences.\n_Degrees of Likeness_ Systematic Botany )\n Systematic Zoology } Classificatory\n_Natural_ Affinity Comparative Anatomy ) Sciences.\n(_Vital Powers_)\nAssimilation\nIrritability\n(_Organization_) Biology Organical Sciences.\nFinal Cause\nInstinct\nEmotion Psychology (_Metaphysics_.)\nThought\nHistorical Causation Geology )\n Distribution of ) Pal\u00e6tiological\n Plants and Animals } Sciences.\n Glossology )\n Ethnography )\nFirst Cause Natural Theology.\n\n\n\n\n[*Transcriber's Note: The two following tables were inserted on\nseparate sheets at this point. They were structured as trees, but\nhave here been converted into a diagram to be read from left to\nright, and an associated key. Arrows have replaced the brackets\nWhewell used. In the original, the names of discoverers and comments\nabout inadequate explanations were printed in red.]\n\nINDUCTIVE TABLE OF ASTRONOMY\n\na r ) { )\n ) { )\nb \u2192 j s ) { J )\n ) \u2192 z { )\nc \u2192 k ) { )\n ) )\nd \u2192 l t ) )\n )\ne \u2192 m ) ) { b1 \u2192 c1 \u2192 m1 )\n u ) \u2192 A E \u2192 H ) \u2192 M { N \u2192 Q \u2192 W )\nf \u2192 n ) ) { b1 \u2192 d1 \u2192 n1 ) )\n ) ) )\n ) { R \u2192 X b1 \u2192 e1 ) ) )\ng \u2192 o v \u2192 B F \u2192 I K ) { ) ) )\n ) { O S \u2192 Y b1 \u2192 f1 )\u2192 o1 ) )\n ) { ) ) )\n ) { S \u2192 Z b1 \u2192 g1 ) ) )\u2192 u1\nh \u2192 p w \u2192 C G L ) )\u2192 t1 )\n P T b1 \u2192 h1 \u2192 p1 ) )\n ) )\n q x \u2192 D b1 i1 \u2192 q1 ) )\n ) )\ni y b1 j1 \u2192 r1 ) )\n ) )\n U \u2192 a1 b1 k1 \u2192 s1 ) )\n ) )\n V b1 \u2192 l1 ) )\n\n\na = THE EARTH appears to be immovable.\nb = THE STARS keep their relative places in the vault of the sky,\nand with the Sun and Moon, rise, move, and set.\nc = THE MOON'S bright part is of the shape of a ball enlightened by\nthe Sun.\nd = THE MOON'S ECLIPSES occur when she is full.\ne = ECLIPSES OF THE SUN AND MOON often occur.\nf = THE MOON rises and sets at different times and places. Her\ncourse among the Stars varies.\ng = THE PLANETS are morning and evening Stars: are direct,\nstationary, and retrograde.\nh = THE SUN rises, culminates, and sets in different times and\nplaces at different seasons: different CONSTELLATIONS are visible at\nnight.\ni = THE TIDES ebb and flow.\nj = Chald^ns. _The Sphere of the Heavens appears to make a Diurnal\nRevolution._\nk = Greeks. The Moon receives her light _from the Sun_.\nl = Greeks. The Moon's Eclipses are caused by the _Earth's shadow._\nm = Chald^ns. The Moon's Eclipses follow certain cycles.\nn = Greeks. The Moon appears to revolve monthly in an _oblique\norbit_, which has _Nodes_ and an _Apogee_.\no = Chaldeans. The Planets have proper motions and certain _Cycles_.\np = Pythagoras. The Sun appears to move annually in an _Ecliptic_\noblique to the diurnal motion.\nq = The places of Stars are determined by their Longitude measured\nfrom the Equinox.\nr = The forms and dist^s of known parts of the earth are such as fit\na convex surface.\ns = The visible Pole of the Heavens rises or drops as we travel N.\nor S.\nt = The boundary of the Earth's shadow is always circular.\nu = By observations of Eclipses, the Moon's Nodes and Apogee\nrevolve, and her motion is unequal according to certain laws.\nv = By observations of the Planets, their progressions, stations,\nand retrogradations.\nw = By observations of the Sun, his motion is unequal according to\ncertain laws.\nx = By observations, Longitudes of Stars increase.\ny = By observations, the Tides depend on the Moon and Sun.\nz = Aristotle? The Earth is a _Globe_, about which the Sphere of the\nHeavens performs a _Diurnal Revolution_.\nA = Hipparchus. The Moon appears to move in an _Epicycle_ carried by\na Deferent: the _Velocity of Apogee_ and _Nodes_ determined.\nB = Eudoxus. The Planets appear to move in Epicycles carried by\n_Deferents_.\nC = Hipparchus. The Sun appears to move in an _Eccentric_, his\n_Apogee_ being fixed.\nD = Hippar. There is a _Precession of the Equinoxes_.\nE = By additional observations, the Moon's motion has another\ninequality. Evection.\nF = By additional observations, the Planets' motions in their\nEpicycles are unequal according to certain laws.\nG = By additional observations, the Sun's Apogee moves. Albategnius.\nH = Ptolemy. The Moon appears to move in an _Epicycle_ carried by an\n_Eccentric_.\nI = Ptolemy. The Planets appear to move in _Epicycles_ carried by\n_Eccentrics_.\nJ = * _By the nature of motion_, the apparent motion is the same\nwhether the Heavens or the Earth have a diurnal revolution: the\nlatter is _simpler_.\nK = * _By the nature of motion_, the apparent motion is the same if\nthe Planets revolve about the Sun: this is _simpler_.\nL = * _By the nature of motion_, the apparent motion of the Sun is\nthe same if the Earth revolve round the Sun: this is _simpler_.\nM = * Copernicus. The Earth and Planets revolve about the Sun as a\ncenter in Orbits nearly circular. The Earth revolves about its axis\ninclined to the Ecliptic in a constant position, and the Moon\nrevolves about the Earth. The _Heliocentric Theory_ governs\nsubsequent speculations.\nN = Retaining Moon's Eccentric and Epicycle; By additional\nobservations, the Moon's motion has other inequalities.\nO = Retaining but referring to the Sun as center the Planets'\nEpicycles and Eccentrics and the annual Orbit;\nP = Retaining obs^ns. Earth's Aphelion revolves.\nQ = Tycho. Moon's _Variation_; _Unequal Motion of Node_; _Change of\nInclination_.\nR = By calc^ns. of the periodic times and distances.\nS = By additional observations and calculations.\nT = Planets' Aphelia revolve. Jupiter and Saturn's motions have an\ninequality dep^g. on their mutual positions.\nU = THE WEIGHT of bodies dimin^s in going towards the Equator.\nV = THE SATELLITES of Jupiter and Saturn revolve according to\nKepler's Laws.\nW = Horrox. Halley. The Moon moves in an _Ellipse_ with variable\n_axis_ and _eccentricity_.\nX = Kepler. Distances cubed are as times squared.\nY = Kepler. Areas as described by Planets are as times.\nZ = Kepler. Curves described by Planets are as ellipses.\na1 = Newton. Earth is oblate.\nb1 = * By Mechanics.\nc1 = * Newton. Moon is attracted by the Earth. Fall of heavy bodies.\nd1 = * Newton. Moon's inequalities produced by attraction of Sun.\ne1 = * Newton. Wren. Hooke. Sun's force on different Planets is\ninvers. as square of distance.\nf1 = * Newton. Planets are attracted by the Sun.\ng1 = * Newton. Sun attracts Planets invers. as square of distance.\nh1 = * Newton. These inequalities are produced by mutual attraction\nof the Planets.\ni1 = Precession of Equinoxes is produced by attraction of Moon and\nSun on oblate Earth.\nj1 = Tides are produced by attraction of Moon and Sun on\nSea. Explanation imperfect.\nk1 = Diminution of gravity and oblateness of Earth arise from\nattractions of parts.\nl1 = * Newton. Jupiter and Saturn attract their Satellites inversely\nas the square of the distance, and the Sun attracts Planets and\nSatellites alike.\nm1 = Newton. Earth attracts Moon invers. as square of distance.\nn1 = Newton. Sun attracts Moon.\no1 = Newton. Sun attracts Planets inversely as the square of the\ndistance.\np1 = Newton. Planets attract each other.\nq1 = * Newton. Moon and Sun attract parts of the Earth.\nr1 = * Newton. Moon and Sun attract the Ocean.\ns1 = * Newton. Parts of the Earth attract each other.\nt1 = Newton. All parts of the Earth, Sun, Moon. and Planets\nattract _each other_ with Forces inversely as the square of the\ndistance.\nu1 = Newton. THE THEORY OF UNIVERSAL GRAVITATION. (All bodies\nattract each other with a Force of _Gravity_ which is inversely as\nthe squares of the distances.)\n\n\nINDUCTIVE TABLE OF OPTICS\n\nFirst Facts. The common and obvious Ph\u00e6nomena of Light and Vision.\n\nBy the _Idea of a Medium_ Light and Vision take place by means of\nsomething intermediate.\n\nFirst Law of Ph\u00e6nomena. The effects take place in straight lines\ndenoted by the Term _Rays_.\n\nFacts of\n\na \u2192 m h1 ) ( ) )\n ) ( ) )\nb \u2192 n ) ) i1 ) ( ) )\n )\u2192 r ) ) ( C1 ) )\nc o ) )\u2192 K ) ) ( ) \u2192 F1 )\n ) ) j1 )\u2192 x1 ( ) )\nd p ) L S ) ) ( ) )\n ) ) )\ne s \u2192 M ) T h1 ) D1 ) ) ) \u2192 H1 )\n )\u2192 ) ) ) )\nf t ) U k1 ) ( ) \u2192 G1 ) )\n ( E1 ) ) )\ng ) ( u \u2192 W l1 ) ( ) ) )\n ) ( ) ) )\n ) ( v \u2192 X l1 )\u2192 y1 ) )\n )\u2192 q ( ) ) )\n ) ( w \u2192 Y j1 ) ) )\n ) ( )\n ) ( x \u2192 Z ) ) ) )\n ( ) m1 ) ) )\n ( y \u2192 a1 ) ) ) )\n ( ) ) \u2192 I1 )\n ( z n1 )\u2192 z1 ) )\n ( ) ) ) \u2192 K1\n ( A N b1 o1 ) ) )\n q \u2190( ) ) )\n ( B O p1 ) ) )\n ( )\n ( C ) c1 q1 ) ) )\n ( ) V ) ) )\n ( D ) d1 q1 ) ) )\n ( ) ) )\n ( E j1 )\u2192 A1 ) )\n ( ) ) )\n ( F P e1 ) ) ) )\n ( ) r1 ) ) )\n ( G f1 ) ) ) )\n ( ) \u2192 J1 )\n ( H Q s1 )\n )\nh ( R g1 t1 ) )\n ( ) )\ni ( I u1 ) )\n ( ) )\nj ( v1 )\u2192 B1 )\n ) )\nk ( w1 ) )\n ( J ) )\nl ( w1 ) )\n\n\na = Rays falling on water, specula, &c.\nb = Rays passing through water, glass, &c. Measures. Ptolemy.\nc = Colours seen by prisms, in rainbow, &c.\nd = Colours in diff. transp. Substances. Optical instrum^ts.\ne = Two Images in Rhomb. of Calcspar.\nf = Two Images in other crystals.\ng = Two Rhombs of Calcspar make 4 images alternately appear and\ndisappear.\nh = Fringes of shadows. Grimaldi. Hook. Newton.\ni = Spectra of gratings. Fraunhofer.\nj = Colours of striated surfaces. Coventry's Micromet^r. Barton's\nButtons. Young.\nk = Colours of _thick Plates_. Newton.\nl = Colours of _thin Plates_. Hook. Newton.\nm = Euclid. Ang. Inc. equals Ang. Reflection.\nn = Snell. Sin. Refr. to Sin. Inc. in giv. _Ratio_ in same med.\no = By measures of Refraction.\np = Dispersion of colours is same when Refr. is diff. Measures.\nDollond.\nq = Huyghens. Rays of light have four Sides with regard to which\ntheir properties alternate.\nNewton. Idea of _Polarization_ introduced, which governs subsequent\nobservations. _Dipolarization_ with Colours.\nr = Newt. Refr. R^o. is diff. for diff. colours, but in same med. is\nconst. for each colour.\ns = Measures. Huyghens.\nt = Double Refr. in biaxal crystals. Brewster.\nu = Rays are polarized by Calcspar, Quartz, &c.\nv = Rays are polarized by biaxal crystals.\nw = Rays are polarized by Tourmaline, Agate, &c.\nx = Rays are polarised by Refl. at glass.\ny = Rays are polarized by transmission through glass.\nz = Variable q^y. of pol. refl. light paral. plane of Refl. Arago.\nA = Variable q^y. of pol. refl. light perp. plane of Refl.\nB = Whole light reflected by internal Refl.\nC = Pol. Rays through uniaxal crystals give colours. Rings.\nWollaston.\nD = Pol. Rays through biaxal crystals give colours. Arago.\nE = Pol. Rays. through imperf. crystallized bodies give colours.\n(Glass strained, jellies prest.) Brewster.\nF = Pol. Rays in axis of Quartz give a peculiar set of colours.\nPlane of Pol^n twisted diff^ly. for diff. colours. Biot. Arago.\nG = Pol. Rays oblique in Quartz give peculiar rings, &c.\nH = Pol. Rays through certain liquids give a peculiar set of colours.\nI = The Laws of these Ph\u00e6nomena were never discovered till Theory\nhad indicated them.\nJ = _Newton's Scale of Colours._\n_Fits_ of Rays. Newton.\nK = Dollond.\nL = Prop^n of Ref. R^s is diff. in diff. med. _Achromatism_.\nM = Huygh^s. Law of Double Ref. exp. by a spheroid.\nN = Change of plane of pol. by Refl. Arago\nO = Light is _circularly pol._ by 2 Refl. in _Fresnel's Rhomb._\nFresnel.\nP = + in dir^n of plagihedral faces. J. Herschel.\nQ = Plane of Pol^n. twisted. Biot\nR = Fringes obliterated by stopping light from one edge or\ninterposing a glass. Young. Arago.\nS = Ratios not reconcilable. _Irrationality_. Blair.\nT = Fresnel.\nU = Law exp. by surface of 4 dim^s.\nV = Optical classification of crystals. Brewster.\nW = Newt. Malus. Ray pol. in _principal plane_ of Rhomb.; and perp.\nto it.\nX = Brews. Biot. Ray pol. in plane bisecting ang. at axis; and perp.\nto it.\nY = Brews. Ray pol. paral. to axis.\nZ = Malus. Ray pol. in plane of Refl. for _given angle_.\na1 = Malus. Ray partially pol. in plane perp. to plane of\nReflection.\nb1 = None Refl^d. if tan. ang. equal Refr. R^o. Brewster.\nc1 = Tint is as sq. of sin. Biot.\nd1 = Tint is as sin. \u03b1 sin. \u03b2. Brewster. Biot.\nLemniscates. J. Herschel.\ne1 = * By interf. of resolved undul^ns. of 2 rays circularly pol^d.\nin opp. directions. * Fresnel.\nf1 = * By interf. of resolved undul^ns. of 2 rays elliptically\npol^d. in opp. directions. * Airy.\ng1 = * By interf. of rays from edges. Young.\nh1 = * Refl. produced by spherical undul^ns.\ni1 = * Refr. produced by spherical undul^ns. of diff. vel. for diff.\ncolour.\nj1 = \u2020 Explanation imperfect.\nk1 = * Refr. produced by curved surf. undul^ns.\nl1 = * Pol^n. being prod. by resolution of transv^e undul^ns.\nm1 = * Polarization being produced by resolution of transverse\nundulations.\nn1 = * Undul^ns. being com^d. acc. to laws of elastic bodies.\no1 = * Undul^ns. being com^d. acc. to a certain hypothesis.\np1 = * Impossible formul\u00e6 being interpreted by analogy.\nq1 = * By interf. of resolved parts of transverse undul^ns.\nr1 = * Same hypothesis explains separation of rays in axis and\noblique. \u2020 Explanation imperfect. * Maccullagh.\ns1 = \u2020 Explan. wanting.\nt1 = * By interf. of rays from all parts. * Young. * Fresnel.\nu1 = * By interf. of undul^ns. from all parts. * Fraunhofer.\nv1 = * By interf. of rays from stri\u00e6. * Young.\nw1 = * By interf. of undul^ns. from two surfaces. * Young.\nx1 = * Huyghens. Reflection and Refraction are propagation of\nundulations.\ny1 = * Young. * Fresnel. Polarization in crystals is transverse\nundulations.\nz1 = * Fresnel. Polarization in Reflection and Refraction is\ntransverse undulations.\nA1 = * Fresnel. * Arago. Dipolarized Colours are produced by\ninterference of Rays polarized in same plane; length of undulation\nbeing different for different colours.\nB1 = * Young. * Fresnel. Colours of Fringes, Gratings, Stri\u00e6, thick\nPlates, thin Plates &c. are produced by interference of undulations;\nlength of undulation being different for different colours.\nC1 = * Undulations being propagated by the uniform elasticity of\neach medium.\nD1 = * Undul^ns. prop. by el^y. of medium diff. in 2 diff. dir^ns,\n(_axis of crystal._)\nE1 = * Undul^ns. being prop. by elasticity of med. diff. in 3 diff.\ndirections (_axes_).\nF1 = Young. Reflection and double Refraction are propagation of\nundulations by crystalline elasticity.\nG1 = * Fresnel. Double Refr. and Pol. arise from same cause.\nH1 = Young. Fresnel. Light is transverse undulations propagated in\nmedia by elasticity dependent on axis, when crystalline.\nI1 = Fresnel. Light is transverse undul^ns. transmitted from one\nmed. to another according to probable hypotheses.\nJ1 = Young. Fresnel. Colours result from interferences, the lengths\nof undulation being different for different colours.\nK1 = THE UNDULATORY THEORY OF LIGHT.\n\n\n\n\n{{141}}\nNOVUM ORGANON RENOVATUM.\n\n\nBOOK III.\n\nOF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.\n\nCHAPTER I.\n\nINTRODUCTION.\n\n\nAPHORISM XXVII.\n\n_The Methods by which the construction of Science is promoted are,_\nMethods of Observation, Methods of obtaining clear Ideas, _and_\nMethods of Induction.\n\n\n1. IN the preceding Book, we pointed out certain general Characters\nof scientific knowledge which may often serve to distinguish it from\nopinions of a looser or vaguer kind. In the course of the progress\nof knowledge from the earliest to the present time, men have been\nled to a perception, more or less clear, of these characteristics.\nVarious philosophers, from Plato and Aristotle in the ancient world,\nto Richard de Saint Victor and Roger Bacon in the middle ages,\nGalileo and Gilbert, Francis Bacon and Isaac Newton, in modern\ntimes, were led to offer precepts and maxims, as fitted to guide us\nto a real and fundamental knowledge of nature. It may on another\noccasion be our business to estimate the value of these precepts and\nmaxims. And other contributions of the same kind to the philosophy\nof science might be noticed, and some which {142} contain still more\nvaluable suggestions, and indicate a more practical acquaintance\nwith the subject. Among these, I must especially distinguish Sir\nJohn Herschel's _Discourse on the Study of Natural Philosophy_. But\nmy object at present is not to relate the history, but to present\nthe really valuable results of preceding labours: and I shall\nendeavour to collect, both from them and from my own researches and\nreflections, such views and such rules as seem best adapted to\nassist us in the discovery and recognition of scientific truth; or,\nat least, such as may enable us to understand the process by which\nthis truth is obtained. I would present to the reader the Philosophy\nand, if possible, the Art of Discovery.\n\n2. But, in truth, we must acknowledge, before we proceed with this\nsubject, that, speaking with strictness, an _Art of Discovery_ is\nnot possible;--that we can give no Rules for the pursuit of truth\nwhich shall be universally and peremptorily applicable;--and that\nthe helps which we can offer to the inquirer in such cases are\nlimited and precarious. Still, we trust it will be found that aids\nmay be pointed out which are neither worthless nor uninstructive.\nThe mere classification of examples of successful inquiry, to which\nour rules give occasion, is full of interest for the philosophical\nspeculator. And if our maxims direct the discoverer to no operations\nwhich might not have occurred to his mind of themselves, they may\nstill concentrate our attention on that which is most important and\ncharacteristic in these operations, and may direct us to the best\nmode of insuring their success. I shall, therefore, attempt to\nresolve the Process of Discovery into its parts, and to give an\naccount as distinct as may be of Rules and Methods which belong to\neach portion of the process.\n\n3. In Book II. we considered the three main parts of the process by\nwhich science is constructed: namely, the Decomposition and\nObservation of Complex Facts; the Explication of our Ideal\nConceptions; and the Colligation of Elementary Facts by means of\nthose Conceptions. The first and last of {143} these three steps are\ncapable of receiving additional accuracy by peculiar processes. They\nmay further the advance of science in a more effectual manner, when\ndirected by special technical _Methods_, of which in the present\nBook we must give a brief view. In this more technical form, the\nobservation of facts involves the _Measurement of Phenomena_; and\nthe Colligation of Facts includes all arts and rules by which the\nprocess of Induction can be assisted. Hence we shall have here to\nconsider _Methods of Observation_, and _Methods of Induction_, using\nthese phrases in the widest sense. The second of the three steps\nabove mentioned, the Explication of our Conceptions, does not admit\nof being much assisted by methods, although something may be done by\nEducation and Discussion.\n\n4. The Methods of Induction, of which we have to speak, apply only\nto the first step in our ascent from phenomena to laws of\nnature;--the discovery of _Laws of Phenomena_. A higher and ulterior\nstep remains behind, and follows in natural order the discovery of\nLaws of Phenomena; namely, the _Discovery of Causes_; and this must\nbe stated as a distinct and essential process in a complete view of\nthe course of science. Again, when we have thus ascended to the\ncauses of phenomena and of their laws, we can often reason downwards\nfrom the cause so discovered; and we are thus led to suggestions of\nnew phenomena, or to new explanations of phenomena already known.\nSuch proceedings may be termed _Applications_ of our Discoveries;\nincluding in the phrase, _Verifications_ of our Doctrines by such an\napplication of them to observed facts. Hence we have the following\nseries of processes concerned in the formation of science.\n (1.) Decomposition of Facts;\n (2.) Measurement of Phenomena;\n (3.) Explication of Conceptions;\n (4.) Induction of Laws of Phenomena;\n (5.) Induction of Causes;\n (6.) Application of Inductive Discoveries.\n\n5. Of these six processes, the methods by which the second and\nfourth may be assisted are here our {144} peculiar object of\nattention. The treatment of these subjects in the present work must\nnecessarily be scanty and imperfect, although we may perhaps be able\nto add something to what has hitherto been systematically taught on\nthese heads. Methods of Observation and of Induction might of\nthemselves form an abundant subject for a treatise, and hereafter\nprobably will do so, in the hands of future writers. A few remarks,\noffered as contributions to this subject, may serve to show how\nextensive it is, and how much more ready it now is than it ever\nbefore was, for a systematic discussion.\n\nOf the above steps of the formation of science, the first, the\nDecomposition of Facts, has already been sufficiently explained in\nthe last Book: for if we pursue it into further detail and\nexactitude, we find that we gradually trench upon some of the\nsucceeding parts. I, therefore, proceed to treat of the second step,\nthe Measurement of Phenomena;--of _Methods_ by which this work, in\nits widest sense, is executed, and these I shall term Methods of\nObservation.\n\n\n\n{{145}}\nCHAPTER II.\n\nOF METHODS OF OBSERVATION.\n\n\nAPHORISM XXVIII.\n\n_The Methods of Observation of Quantity in general are_, Numeration,\n_which is precise by the nature of Number; the_ Measurement of Space\n_and_ of Time, _which are easily made precise; the_ Conversion of\nSpace and Time, _by which each aids the measurement of the other;\nthe_ Method of Repetition; _the_ Method of Coincidences _or_\nInterferences. _The measurement of Weight is made precise by the_\nMethod of Double-weighing. _Secondary Qualities are measured by\nmeans of_ Scales of Degrees; _but in order to apply these Scales,\nthe student requires the_ Education of the Senses. _The Education of\nthe Senses is forwarded by the practical study of_ Descriptive\nNatural History, Chemical Manipulation, _and_ Astronomical\nObservation.\n\n\n1. I SHALL speak, in this chapter, of Methods of exact and\nsystematic observation, by which such facts are collected as form\nthe materials of precise scientific propositions. These Methods are\nvery various, according to the nature of the subject inquired into,\nand other circumstances: but a great portion of them agree in being\nprocesses of measurement. These I shall peculiarly consider: and in\nthe first place those referring to Number, Space, and Time, which\nare at the same time objects and instruments of measurement.\n\n2. But though we have to explain how observations may be made as\nperfect as possible, we must not forget that in most cases complete\nperfection is unattainable. _Observations are never perfect._ For we\n{146} observe phenomena by our senses, and measure their relations\nin time and space; but our senses and our measures are all, from\nvarious causes, inaccurate. If we have to observe the exact place of\nthe moon among the stars, how much of instrumental apparatus is\nnecessary! This apparatus has been improved by many successive\ngenerations of astronomers, yet it is still far from being perfect.\nAnd the senses of man, as well as his implements, are limited in\ntheir exactness. Two different observers do not obtain precisely the\nsame measures of the time and place of a phenomenon; as, for\ninstance, of the moment at which the moon occults a star, and the\npoint of her _limb_ at which the occultation takes place. Here,\nthen, is a source of inaccuracy and errour, even in astronomy, where\nthe means of exact observation are incomparably more complete than\nthey are in any other department of human research. In other cases,\nthe task of obtaining accurate measures is far more difficult. If we\nhave to observe the tides of the ocean when rippled with waves, we\ncan see the average level of the water first rise and then fall; but\nhow hard is it to select the exact moment when it is at its greatest\nheight, or the exact highest point which it reaches! It is very\neasy, in such a case, to err by many minutes in time, and by several\ninches in space.\n\nStill, in many cases, good Methods can remove very much of this\ninaccuracy, and to these we now proceed.\n\n3. (I.) _Number_.--Number is the first step of measurement, since it\nmeasures itself, and does not, like space and time, require an\narbitrary standard. Hence the first exact observations, and the\nfirst advances of rigorous knowledge, appear to have been made by\nmeans of number; as for example,--the number of days in a month and\nin a year;--the cycles according to which eclipses occur;--the\nnumber of days in the revolutions of the planets; and the like. All\nthese discoveries, as we have seen in the History of Astronomy, go\nback to the earliest period of the science, anterior to any distinct\ntradition; and these discoveries presuppose a series, probably a\nvery long series, of observations, made {147} principally by means\nof number. Nations so rude as to have no other means of exact\nmeasurement, have still systems of numeration by which they can\nreckon to a considerable extent. Very often, such nations have very\ncomplex systems, which are capable of expressing numbers of great\nmagnitude. Number supplies the means of measuring other quantities,\nby the assumption of a _unit_ of measure of the appropriate kind: but\nwhere nature supplies the unit, number is applicable directly and\nimmediately. Number is an important element in the Classificatory as\nwell as in the Mathematical Sciences. The History of those Sciences\nshows how the formation of botanical systems was effected by the\nadoption of number as a leading element, by C\u00e6salpinus; and how\nafterwards the Reform of Linn\u00e6us in classification depended in a\ngreat degree on his finding, in the pistils and stamens, a better\nnumerical basis than those before employed. In like manner, the\nnumber of rays in the membrane of the gills[1\\3], and the number of\nrays in the fins of fish, were found to be important elements in\nichthyological classification by Artedi and Linn\u00e6us. There are\ninnumerable instances, in all parts of Natural History, of the\nimportance of the observation of number. And in this observation, no\ninstrument, scale or standard is needed, or can be applied; except\nthe scale of natural numbers, expressed either in words or in\nfigures, can be considered as an instrument.\n\n[Note 1\\3: _Hist. Ind. Sc._ b. xvi. c. vii.]\n\n4. (II.) _Measurement of Space._--Of quantities admitting of\n_continuous_ increase and decrease, (for number is discontinuous,)\nspace is the most simple in its mode of measurement, and requires\nmost frequently to be measured. The obvious mode of measuring space\nis by the repeated application of a material measure, as when we\ntake a foot-rule and measure the length of a room. And in this case\nthe foot-rule is the _unit_ of space, and the length of the room is\nexpressed by the number of such units which it contains: or, as it\nmay not contain an exact number, by a number with a _fraction_. But\nbesides this measurement of linear space, {148} there is another\nkind of space which, for purposes of science, it is still more\nimportant to measure, namely, angular space. The visible heavens\nbeing considered as a sphere, the portions and paths of the heavenly\nbodies are determined by drawing circles on the surface of this\nsphere, and are expressed by means of the parts of these circles\nthus intercepted: by such measures the doctrines of astronomy were\nobtained in the very beginning of the science. The arcs of circles\nthus measured, are not like linear spaces, reckoned by means of an\n_arbitrary_ unit, for there is a _natural unit_, the total\ncircumference, to which all arcs may be referred. For the sake of\nconvenience, the whole circumference is divided into 360 parts or\n_degrees_; and by means of these degrees and their parts, all arcs\nare expressed. The _arcs_ are the measures of the _angles at the\ncenter_, and the degrees may be considered indifferently as\nmeasuring the one or the other of these quantities.\n\n5. In the History of Astronomy[2\\3], I have described the method of\nobservation of celestial angles employed by the Greeks. They\ndetermined the lines in which the heavenly bodies were seen, by\nmeans either of Shadows, or of Sights; and measured the angles\nbetween such lines by arcs or rules properly applied to them. The\nArmill, Astrolabe, Dioptra, and Parallactic Instrument of the\nancients, were some of the instruments thus constructed. Tycho Brahe\ngreatly improved the methods of astronomical observation by giving\nsteadiness to the frame of his instruments, (which were large\n_quadrants_,) and accuracy to the divisions of the _limb_[3\\3]. But\nthe application of the _telescope_ to the astronomical quadrant and\nthe fixation of the center of the field by a _cross_ of fine wires\nplaced in the focus, was an immense improvement of the instrument,\nsince it substituted a precise visual ray, pointing to the star,\ninstead of the coarse coincidence of Sights. The accuracy of\nobservation was still further increased {149} by applying to the\ntelescope a _micrometer_ which might subdivide the smaller divisions\nof the arc.\n\n[Note 2\\3: _Hist. Ind. Sc._ b. iii. c. iv. sect. 3.]\n\n[Note 3\\3: _Ib._ b. vii. c. vi. sect. 1.]\n\n6. By this means, the precision of astronomical observation was made\nso great, that very minute angular spaces could be measured: and it\nthen became a question whether discrepancies which appeared at first\nas defects in the theory, might not arise sometimes from a bending\nor shaking of the instrument, and from the degrees marked on the\nlimb being really somewhat unequal, instead of being rigorously\nequal. Accordingly, the framing and balancing of the instrument, so\nas to avoid all possible tremor or flexure, and the exact division\nof an arc into equal parts, became great objects of those who wished\nto improve astronomical observations. The observer no longer gazed\nat the stars from a lofty tower, but placed his telescope on the\nsolid ground,--and braced and balanced it with various contrivances.\nInstead of a quadrant, an entire circle was introduced (by Ramsden;)\nand various processes were invented for the dividing of instruments.\nAmong these we may notice Troughton's method of dividing; in which\nthe visual ray of a microscope was substituted for the points of a\npair of compasses, and, by _stepping_ round the circle, the partial\narcs were made to bear their exact relation to the whole\ncircumference.\n\n7. Astronomy is not the only science which depends on the\nmeasurement of angles. Crystallography also requires exact measures\nof this kind; and the _goniometer_, especially that devised by\nWollaston, supplies the means of obtaining such measures. The\nscience of Optics also, in many cases, requires the measurement of\nangles.\n\n8. In the measurement of linear space, there is no natural standard\nwhich offers itself. Most of the common measures appear to be taken\nfrom some part of the human body; as a _foot_, a _cubit_, a\n_fathom_; but such measures cannot possess any precision, and are\naltered by convention: thus there were in ancient times many kinds\nof cubits; and in modern Europe, there are a great number of\ndifferent standards of the foot, as the Rhenish foot, the Paris\nfoot, the English foot. It is {150} very desirable that, if\npossible, some permanent standard, founded in nature, should be\nadopted; for the conventional measures are lost in the course of\nages; and thus, dimensions expressed by means of them become\nunintelligible. Two different natural standards have been employed\nin modern times: the French have referred their measures of length\nto the total circumference of a meridian of the earth; a quadrant of\nthis meridian consists of ten million units or _metres_. The English\nhave fixed their linear measure by reference to the length of a\npendulum which employs an exact second of time in its small\noscillation. Both these methods occasion considerable difficulties\nin carrying them into effect; and are to be considered mainly as\nmeans of recovering the standard if it should ever be lost. For\ncommon purposes, some material standard is adopted as authority for\nthe time: for example, the standard which in England possessed legal\nauthority up to the year 1835 was preserved in the House of\nParliament; and was lost in the conflagration which destroyed that\nedifice. The standard of length now generally referred to by men of\nscience in England is that which is in the possession of the\nAstronomical Society of London.\n\n9. A standard of length being established, the artifices for\napplying it, and for subdividing it in the most accurate manner, are\nnearly the same as in the case of measures of arcs: as for instance,\nthe employment of the visual rays of microscopes instead of the legs\nof compasses and the edges of rules; the use of micrometers for\nminute measurements; and the like. Many different modes of avoiding\nerrour in such measurements have been devised by various observers,\naccording to the nature of the cases with which they had to\ndeal[4\\3].\n\n[Note 4\\3: On the precautions employed in astronomical instruments\nfor the measure of space, see Sir J. Herschel's _Astronomy_ (in the\n_Cabinet Cyclop\u00e6dia_,) Arts. 103-110.]\n\n10. (III.) _Measurement of Time_.--The methods of measuring Time are\nnot so obvious as the methods of {151} measuring space; for we\ncannot apply one portion of time to another, so as to test their\nequality. We are obliged to begin by assuming some change as the\nmeasure of time. Thus the motion of the sun in the sky, or the\nlength and position of the shadows of objects, were the first modes\nof measuring the parts of the day. But what assurance had men, or\nwhat assurance could they have, that the motion of the sun or of the\nshadow was uniform? They could have no such assurance, till they had\nadopted some measure of smaller times; which smaller times, making\nup larger times by repetition, they took as the standard of\nuniformity;--for example, an hour-glass, or a clepsydra which\nanswered the same purpose among the ancients. There is no apparent\nreason why the successive periods measured by the emptying of the\nhour-glass should be unequal; they are implicitly accepted as equal;\nand by reference to these, the uniformity of the sun's motion may be\nverified. But the great improvement in the measurement of time was\nthe use of a pendulum for the purpose by Galileo, and the\napplication of this device to clocks by Huyghens in 1656. For the\nsuccessive oscillations of a pendulum are rigorously equal, and a\nclock is only a train of machinery employed for the purpose of\ncounting these oscillations. By means of this invention, the measure\nof time in astronomical observations became as accurate as the\nmeasure of space.\n\n11. What is the _natural unit_ of time? It was assumed from the\nfirst by the Greek astronomers, that the sidereal days, measured by\nthe revolution of a star from any meridian to the same meridian\nagain, are exactly equal; and all improvements in the measure of\ntime tended to confirm this assumption. The sidereal day is\ntherefore the natural standard of time. But the solar day,\ndetermined by the diurnal revolution of the sun, although not\nrigorously invariable, as the sidereal day is, undergoes scarcely\nany perceptible variation; and since the course of daily occurrences\nis regulated by the sun, it is far more convenient to seek the basis\nof our unit of time in _his_ motions. Accordingly the solar day (the\n_mean_ solar day) is divided into 24 hours, {152} and these, into\nminutes and seconds; and this is our scale of time. Of such time,\nthe sidereal day has 23 hours 56 minutes 4\u00b709 seconds. And it is\nplain that by such a statement the length of the hour is fixed, with\nreference to a sidereal day. The _standard_ of time (and the\nstandard of space in like manner) equally answers its purpose,\nwhether or not it coincides with any _whole number_ of units.\n\n12. Since the sidereal day is thus the standard of our measures of\ntime, it becomes desirable to refer to it, constantly and exactly,\nthe instruments by which time is measured, in order that we may\nsecure ourselves against errour. For this purpose, in astronomical\nobservatories, observations are constantly made of the transit of\nstars across the meridian; the _transit instrument_ with which this\nis done being adjusted with all imaginable regard to accuracy[5\\3].\n\n[Note 5\\3: On the precautions employed in the measure of time by\nastronomers, see Herschel's _Astronomy_, Art. 115-127.]\n\n13. When exact measures of time are required in other than\nastronomical observations, the same instruments are still used,\nnamely, clocks and chronometers. In chronometers, the regulating\npart is an oscillating body; not, as in clocks, a pendulum\noscillating by the force of gravity, but a wheel swinging to and fro\non its center, in consequence of the vibrations of a slender coil of\nelastic wire. To divide time into still smaller portions than these\nvibrations, other artifices are used; some of which will be\nmentioned under the next head.\n\n14. (IV.) _Conversion of Space and Time._--Space and time agree in\nbeing extended quantities, which are made up and measured by the\nrepetition of homogeneous parts. If a body move uniformly, whether\nin the way of revolving or otherwise, the _space_ which any point\ndescribes, is _proportional_ to the _time_ of its motion; and the\nspace and the time may each be taken as a measure of the other.\nHence in such cases, by taking space instead of time, or time\ninstead of {153} space, we may often obtain more convenient and\nprecise measures, than we can by measuring directly the element with\nwhich we are concerned.\n\nThe most prominent example of such a conversion, is the measurement\nof the Right Ascension of stars, (that is, their angular distance\nfrom a standard meridian[6\\3] on the celestial sphere,) by means of\nthe time employed in their coming to the meridian of the place of\nobservation. Since, as we have already stated, the visible celestial\nsphere, carrying the fixed stars, revolves with perfect uniformity\nabout the pole; if we observe the stars as they come in succession\nto a fixed circle passing through the poles, the intervals of time\nbetween these observations will be proportional to the angles which\nthe meridian circles passing through these stars make at the poles\nwhere they meet; and hence, if we have the means of measuring time\nwith great accuracy, we can, by watching the _times_ of the transits\nof successive stars across some visible mark in our own meridian,\ndetermine the _angular distances_ of the meridian circles of all the\nstars from one another.\n\n[Note 6\\3: A _meridian_ is a circle passing through the poles about\nwhich the celestial sphere revolves. The meridian _of any place_ on\nthe earth is that meridian which is exactly over the place.]\n\nAccordingly, now that the pendulum clock affords astronomers the\nmeans of determining time exactly, a measurement of the Right\nAscensions of heavenly bodies by means of a clock and a transit\ninstrument, is a part of the regular business of an observatory. If\nthe sidereal clock be so adjusted that it marks the beginning of its\nscale of time when the first point of Right Ascension is upon the\nvisible meridian of our observatory, the point of the scale at which\nthe clock points when any other star is in our meridian, will truly\nrepresent the Right Ascension of the star.\n\nThus as the motion of the stars is our measure of time, we employ\ntime, conversely, as our measure of the places of the stars. The\ncelestial machine and our terrestrial machines correspond to each\nother in their movements; and the star steals silently and steadily\n{154} across our meridian line, just as the pointer of the clock\nsteals past the mark of the hour. We may judge of the scale of this\nmotion by considering that the full moon employs about two minutes\nof time in sailing across any fixed line seen against the sky,\ntransverse to her path: and all the celestial bodies, carried along\nby the revolving sphere, travel at the same rate.\n\n15. In this case, up to a certain degree, we render our measures of\nastronomical angles more exact and convenient by substituting time\nfor space; but when, in the very same kind of observation, we wish\nto proceed to a greater degree of accuracy, we find that it is best\ndone by substituting space for time. In observing the transit of a\nstar across the meridian, if we have the clock within hearing, we\ncan count the beats of the pendulum by the noise which they make,\nand tell exactly at which second of time the passage of the star\nacross the visible thread takes place; and thus we measure Right\nAscension by means of time. But our perception of time does not\nallow us to divide a second into ten parts, and to pronounce whether\nthe transit takes place three-tenths, six-tenths, or seven-tenths of\na second after the preceding beat of the clock. This, however, can\nbe done by the usual mode of observing the transit of a star. The\nobserver, listening to the beat of his clock, fastens his attention\nupon the star at each beat, and especially at the one immediately\nbefore and the one immediately after the passage of the thread: and\nby this means he has these two positions and the position of the\nthread so far present to his intuition at once, that he can judge in\nwhat proportion the thread is nearer to one position than the other,\nand can thus divide the intervening second in its due proportion.\nThus if he observe that at the beginning of the second the star is\non one side of the thread, and at the end of the second on the other\nside; and that the two distances from the thread are as two to\nthree, he knows that the transit took place at two-fifths (or\nfour-tenths) of a second after the former beat. In this way a second\nof time in astronomical observations may, by a skilful observer, be\ndivided into ten equal {155} parts; although when time is observed\nas time, a tenth of a second appears almost to escape our senses.\nFrom the above explanation, it will be seen that the reason why the\nsubdivision is possible in the way thus described, is this:--that\nthe moment of time thus to be divided is so small, that the eye and\nthe mind can retain, to the end of this moment, the impression of\nposition which it received at the beginning. Though the two\npositions of the star, and the intermediate thread, are seen\nsuccessively, they can be contemplated by the mind as if they were\nseen simultaneously: and thus it is precisely the smallness of this\nportion of time which enables us to subdivide it by means of space.\n\n16. There is another case, of somewhat a different kind, in which\ntime is employed in measuring space; namely, when space, or the\nstandard of space, is defined by the length of a pendulum\noscillating in a given time. We might in this way define any space\nby the time which a pendulum of such a length would take in\noscillating; and thus we might speak, as was observed by those who\nsuggested this device, of five minutes of cloth, or a rope half an\nhour long. We may observe, however, that in this case, the space is\n_not proportional_ to the time. And we may add, that though we thus\nappear to avoid the arbitrary standard of space (for as we have\nseen, the standard of measures of time is a natural one,) we do not\ndo so in fact: for we assume the invariableness of gravity, which\nreally varies (though very slightly,) from place to place.\n\n17. (V.) _The Method of Repetition in Measurement._--In many cases\nwe can give great additional accuracy to our measurements by\nrepeatedly adding to itself the quantity which we wish to measure.\nThus if we wished to ascertain the exact breadth of a thread, it\nmight not be easy to determine whether it was one-ninetieth, or\none-ninety-fifth, or one-hundredth part of an inch; but if we find\nthat ninety-six such threads placed side by side occupy exactly an\ninch, we have the precise measure of the breadth of the thread. In\n{156} the same manner, if two clocks are going nearly at the same\nrate, we may not be able to distinguish the excess of an oscillation\nof one of the pendulums over an oscillation of the other: but when\nthe two clocks have gone for an hour, one of them may have gained\nten seconds upon the other; thus showing that the proportion of\ntheir times of oscillation is 3610 to 3600.\n\nIn the latter of these instances, we have the principle of\nrepetition truly exemplified, because (as has been justly observed\nby Sir J. Herschel[7\\3],) there is then 'a juxtaposition of units\nwithout errour,'--'one vibration commences exactly where the last\nterminates, no part of time being lost or gained in the addition of\nthe units so counted.' In space, this juxtaposition of units without\nerrour cannot be rigorously accomplished, since the units must be\nadded together by material contact (as in the above case of the\nthreads,) or in some equivalent manner. Yet the principle of\nrepetition has been applied to angular measurement with considerable\nsuccess in Borda's Repeating Circle. In this instrument, the angle\nbetween two objects which we have to observe, is repeated along the\ngraduated limb of the circle by turning the telescope from one\nobject to the other, alternately fastened to the circle (by its\n_clamp_) and loose from it (by unclamping). In this manner the\nerrours of graduation may (theoretically) be entirely got rid of:\nfor if an angle repeated _nine_ times be found to go twice round the\ncircle, it must be _exactly_ eighty degrees: and where the\nrepetition does not give an exact number of circumferences, it may\nstill be made to subdivide the errour to any required extent.\n\n[Note 7\\3: _Disc. Nat. Phil._ art. 121.]\n\n18. Connected with the principle of repetition, is the _Method of\ncoincidences_ or _interferences_. If we have two Scales, on one of\nwhich an inch is divided into 10, and on the other into 11 equal\nparts; and if, these Scales being placed side by side, it appear\nthat the beginning of the latter Scale is between the 2nd and 3rd\ndivision of the former, it may not be apparent {157} what fraction\nadded to 2 determines the place of beginning of the second Scale as\nmeasured on the first. But if it appear also that the 3rd division\nof the second Scale _coincides_ with a certain division of the\nfirst, (the 5th,) it is certain that 2 and _three-tenths_ is the\n_exact_ place of the beginning of the second Scale, measured on the\nfirst Scale. The 3rd division of the 11 Scale will coincide (or\ninterfere with) a division of the 10 Scale, when the beginning or\n_zero_ of the 11 divisions is three-tenths of a division beyond the\npreceding line of the 10 Scale; as will be plain on a little\nconsideration. And if we have two Scales of equal units, in which\neach unit is divided into nearly, but not quite, the same number of\nequal parts (as 10 and 11, 19 and 20, 29 and 30,) and one sliding on\nthe other, it will always happen that some one or other of the\ndivision lines will coincide, or very nearly coincide; and thus the\nexact position of the beginning of one unit, measured on the other\nscale, is determined. A sliding scale, thus divided for the purpose\nof subdividing the units of that on which it slides, is called a\n_Vernier_, from the name of its inventor.\n\n19. The same Principle of Coincidence or Interference is applied to\nthe exact measurement of the length of time occupied in the\noscillation of a pendulum. If a detached pendulum, of such a length\nas to swing in little less than a second, be placed before the\nseconds' pendulum of a clock, and if the two pendulums begin to move\ntogether, the former will gain upon the latter, and in a little\nwhile their motions will be quite discordant. But if we go on\nwatching, we shall find them, after a time, to agree again exactly;\nnamely, when the detached pendulum has gained one complete\noscillation (back and forwards,) upon the clock pendulum, and again\ncoincides with it in its motion. If this happen after 5 minutes, we\nknow that the times of oscillation of the two pendulums are in the\nproportion of 300 to 302, and therefore the detached pendulum\noscillates in 150/151 of a second. The accuracy which can be\nobtained in the measure of an oscillation by this means is great;\nfor the clock can be compared (by {158} observing transits of the\nstars or otherwise) with the natural standard of time, the sidereal\nday. And the moment of coincidence of the two pendulums may, by\nproper arrangements, be very exactly determined.\n\nWe have hitherto spoken of methods of measuring time and space, but\nother elements also may be very precisely measured by various means.\n\n20. (VI.) _Measurement of Weight._--Weight, like space and time, is\na quantity made up by addition of parts, and may be measured by\nsimilar methods. The principle of repetition is applicable to the\nmeasurement of weight; for if two bodies be simultaneously put in\nthe same pan of a balance, and if they balance pieces in the other\npan, their weights are exactly added.\n\nThere may be difficulties of practiced workmanship in carrying into\neffect the mathematical conditions of a perfect balance; for\nexample, in securing an exact equality of the effective arms of the\nbeam in all positions. These difficulties are evaded by the _Method\nof double weighing_; according to which the standard weights, and\nthe body which is to be weighed, are successively put in the _same_\npan, and made to balance by a third body in the opposite scale. By\nthis means the different lengths of the arms of the beam, and other\nimperfections of the balance, become of no consequence[8\\3].\n\n[Note 8\\3: For other methods of measuring weights accurately, see\nFaraday's _Chemical Manipulation_, p. 25.]\n\n21. There is no natural _Standard_ of weight. The conventional\nweight taken as the standard, is the weight of a given bulk of some\nknown substance; for instance, a _cubic foot of water_. But in order\nthat this may be definite, the water must not contain any portion of\nheterogeneous substance: hence it is required that the water be\n_distilled_ water.\n\n22. (VII.) _Measurement of Secondary Qualities._--We have already\nseen[9\\3] that secondary qualities are estimated by means of\nconventional Scales, which refer {159} them to space, number, or\nsome other definite expression. Thus the Thermometer measures heat;\nthe Musical Scale, with or without the aid of number, expresses the\npitch of a note; and we may have an exact and complete Scale of\nColours, pure and impure. We may remark, however, that with regard\nto sound and colour, the estimates of the ear and the eye are not\nsuperseded, but only assisted: for if we determine what a note is,\nby comparing it with an instrument known to be in tune, we still\nleave the ear to decide when the note is _in unison_ with one of the\nnotes of the instrument. And when we compare a colour with our\nchromatometer, we judge by the eye which division of the\nchromatometer it _matches_. Colour and sound have their Natural\nScales, which the eye and ear habitually apply; what science\nrequires is, that those scales should be systematized. We have seen\nthat several conditions are requisite in such scales of qualities:\nthe observer's skill and ingenuity are mainly shown in devising such\nscales and methods of applying them.\n\n[Note 9\\3: B. iii. c. ii. Of the Measure of Secondary Qualities.]\n\n23. The Method of Coincidences is employed in harmonics: for if two\nnotes are nearly, but not quite, in unison, the coincidences of the\nvibrations produce an audible undulation in the note, which is\ncalled the _howl_; and the exactness of the unison is known by this\nhowl vanishing.\n\n24. (VIII.) _Manipulation._--The process of applying practically\nmethods of experiment and observation, is termed Manipulation; and\nthe value of observations depends much upon the proficiency of the\nobserver in this art. This skill appears, as we have said, not only\nin devising means and modes in measuring results, but also in\ninventing and executing arrangements by which elements are subjected\nto such conditions as the investigation requires: in finding and\nusing some material combination by which nature shall be asked the\nquestion which we have in our minds. To do this in any subject may\nbe considered as a peculiar Art, but especially in Chemistry; where\n'many experiments, and even whole trains of research, are {160}\nessentially dependent for success on mere manipulation[10\\3].' The\nchanges which the chemist has to study,--compositions,\ndecompositions, and mutual actions, affecting the internal structure\nrather than the external form and motion of bodies,--are not\nfamiliarly recognized by common observers, as those actions are\nwhich operate upon the total mass of a body: and hence it is only\nwhen the chemist has become, to a certain degree, familiar with his\nscience, that he has the power of observing. He must learn to\ninterpret the effects of mixture, heat, and other Chemical agencies,\nso as to see in them those facts which chemistry makes the basis of\nher doctrines. And in learning to interpret this language, he must\nalso learn to call it forth;--to place bodies under the requisite\nconditions, by the apparatus of his own laboratory and the\noperations of his own fingers. To do this with readiness and\nprecision, is, as we have said, an Art, both of the mind and of the\nhand, in no small degree recondite and difficult. A person may be\nwell acquainted with all the doctrines of chemistry, and may yet\nfail in the simplest experiment. How many precautions and\nobservances, what resource and invention, what delicacy and\nvigilance, are requisite in _Chemical Manipulation_, may be seen by\nreference to Dr. Faraday's work on that subject.\n\n[Note 10\\3: Faraday's _Chemical Manipulation_, p. 3.]\n\n25. The same qualities in the observer are requisite in some other\ndepartments of science; for example, in the researches of Optics:\nfor in these, after the first broad facts have been noticed, the\nremaining features of the phenomena are both very complex and very\nminute; and require both ingenuity in the invention of experiments,\nand a keen scrutiny of their results. We have instances of the\napplication of these qualities in most of the optical experimenters\nof recent times, and certainly in no one more than Sir David\nBrewster. Omitting here all notice of his succeeding labours, his\n_Treatise on New Philosophical Instruments_, published in 1813, is\nan excellent model of the kind of resource {161} and skill of which\nwe now speak. I may mention as an example of this skill, his mode of\ndetermining the refractive power of an _irregular_ fragment of any\ntransparent substance. At first this might appear an impossible\nproblem; for it would seem that a regular and smooth surface are\nrequisite, in order that we may have any measurable refraction. But\nSir David Brewster overcame the difficulty by immersing the fragment\nin a combination of fluids, so mixed, that they had the same\nrefractive power as the specimen. The question, _when_ they had this\npower, was answered by noticing when the fragment became so\ntransparent that its surface could hardly be seen; for this happened\nwhen, the refractive power within and without the fragment being the\nsame, there was no refraction at the surface. And this condition\nbeing obtained, the refractive power of the fluid, and therefore of\nthe fragment, was easily ascertained.\n\n26. (IX.) _The Education of the Senses._--Colour and Musical Tone\nare, as we have seen, determined by means of the Senses, whether or\nnot Systematical Scales are used in expressing the observed fact.\nSystematical Scales of sensible qualities, however, not only give\nprecision to the record, but to the observation. But for this\npurpose such an Education of the Senses is requisite as may enable\nus to apply the scale immediately. The memory must retain the\nsensation or perception to which the technical term or degree of the\nscale refers. Thus with regard to colour, as we have said\nalready[11\\3], when we find such terms as _tin-white_ or\n_pinchbeck-brown_, the metallic colour so denoted ought to occur at\nonce to our recollection without delay or search. The observer's\nsenses, therefore, must be educated, at first by an actual\nexhibition of the standard, and afterwards by a familiar use of it,\nto understand readily and clearly each phrase and degree of the\nscales which in his observations he has to apply. This is not only\nthe best, but in many cases the only way in which the observation\ncan be expressed. Thus _glassy lustre_, _fatty lustre_, _adamantine\nlustre_, denote certain kinds of {162} shining in minerals, which\nappearances we should endeavour in vain to describe by periphrasis;\nand which the terms, if considered as terms in common language,\nwould by no means clearly discriminate: for who, in common language,\nwould say that coal has a fatty lustre? But these terms, in their\nconventional sense, are perfectly definite; and when the eye is once\nfamiliarized with this application of them, are easily and clearly\nintelligible.\n\n[Note 11\\3: B. viii. c. iii. Terminology.]\n\n27. The education of the senses, which is thus requisite in order to\nunderstand well the terminology of any science, must be acquired by\nan inspection of the objects which the science deals with; and is,\nperhaps, best promoted by the practical study of Natural History. In\nthe different departments of Natural History, the descriptions of\nspecies are given by means of an extensive technical _terminology_:\nand that education of which we now speak, ought to produce the\neffect of making the observer as familiar with each of the terms of\nthis terminology as we are with the words of our common language.\nThe technical terms have a much more precise meaning than other\nterms, since they are defined by express convention, and not learnt\nby common usage merely. Yet though they are thus defined, not the\ndefinition, but the perception itself, is that which the term\nsuggests to the proficient.\n\nIn order to use the terminology to any good purpose, the student\nmust possess it, not as a dictionary, but as a language. The\nterminology of his sciences must be the natural historian's most\nfamiliar tongue. He must learn to think in such language. And when\nthis is achieved, the terminology, as I have elsewhere said, though\nto an uneducated eye cumbrous and pedantical, is felt to be a useful\nimplement, not an oppressive burden[12\\3]. The impatient schoolboy\nlooks upon his grammar and vocabulary as irksome and burdensome; but\nthe accomplished student who has learnt the language by means of\nthem, knows that they have given him the means of expressing what he\nthinks, and {163} even of thinking more precisely. And as the study\nof language thus gives precision to the thoughts, the study of\nNatural History, and especially of the descriptive part of it, gives\nprecision to the senses.\n\n[Note 12\\3: _Hist. Ind. Sc_. b. xvi. c. iv. sect. 2.]\n\nThe Education of the Senses is also greatly promoted by the\npractical pursuit of any science of experiment and observation, as\nchemistry or astronomy. The methods of manipulating, of which we\nhave just spoken, in chemistry, and the methods of measuring\nextremely minute portions of space and time which are employed in\nastronomy, and which are described in the former part of this\nchapter, are among the best modes of educating the senses for\npurposes of scientific observation.\n\n28. By the various Methods of precise observation which we have thus\nvery briefly described, facts are collected, of an exact and\ndefinite kind; they are then bound together in general laws, by the\naid of general ideas and of such methods as we have now to consider.\nIt is true, that the ideas which enable us to combine facts into\ngeneral propositions, do commonly operate in our minds while we are\nstill engaged in the office of observing. Ideas of one kind or other\nare requisite to connect our phenomena into facts, and to give\nmeaning to the terms of our descriptions: and it frequently happens,\nthat long before we have collected all the facts which induction\nrequires, the mind catches the suggestion which some of these ideas\noffer, and leaps forwards to a conjectural law while the labour of\nobservation is yet unfinished. But though this actually occurs, it\nis easy to see that the process of combining and generalizing facts\nis, in the order of nature, posterior to, and distinct from, the\nprocess of observing facts. Not only is this so, but there is an\nintermediate step which, though inseparable from all successful\ngeneralization, may be distinguished from it in our survey; and may,\nin some degree, be assisted by peculiar methods. To the\nconsideration of such methods we now proceed.\n\n\n\n{{164}}\nCHAPTER III.\n\nOF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS; _and first_ OF\nINTELLECTUAL EDUCATION.\n\n\nAPHORISM XXIX.\n\n_The Methods by which the acquisition of clear Scientific Ideas is\npromoted, are mainly two_; Intellectual Education _and_ Discussion\nof Ideas.\n\nAPHORISM XXX.\n\n_The Idea of Space becomes more clear by studying_ Geometry; _the\nIdea of Force, by studying_ Mechanics; _the Ideas of Likeness,\nof Kind, of Subordination of Classes, by studying_ Natural History.\n\nAPHORISM XXXI.\n\nElementary Mechanics _should now form a part of intellectual\neducation, in order that the student may understand the Theory of\nUniversal Gravitation: for an intellectual education should\ncultivate such ideas as enable the student to understand the most\ncomplete and admirable portions of the knowledge which the human\nrace has attained to._\n\nAPHORISM XXXII.\n\nNatural History _ought to form a part of intellectual education, in\norder to correct certain prejudices which arise from cultivating the\nintellect by means of mathematics alone; and in order to lead the\nstudent to see that the division of things into Kinds, and the\nattribution and use of Names, are processes susceptible of great\nprecision._ {165}\n\n\nTHE ways in which men become masters of those clear and yet\ncomprehensive conceptions which the formation and reception of\nscience require, are mainly two; which, although we cannot reduce\nthem to any exact scheme, we may still, in a loose use of the term,\ncall _Methods_ of acquiring clear Ideas. These two ways are\nEducation and Discussion.\n\n1. (I.) _Idea of Space._--It is easily seen that Education may do at\nleast something to render our ideas distinct and precise. To learn\nGeometry in youth, tends, manifestly, to render our idea of space\nclear and exact. By such an education, all the relations, and all\nthe consequences of this idea, come to be readily and steadily\napprehended; and thus it becomes easy for us to understand portions\nof science which otherwise we should by no means be able to\ncomprehend. The conception of _similar triangles_ was to be\nmastered, before the disciples of Thales could see the validity of\nhis method of determining the height of lofty objects by the length\nof their shadows. The conception of _the sphere with its circles_\nhad to become familiar, before the annual motion of the sun and its\ninfluence upon the lengths of days could be rightly traced. The\nproperties of circles, combined with the _pure_[13\\3] _doctrine of\nmotion_, were required as an introduction to the theory of\nEpicycles: the properties of _conic sections_ were needed, as a\npreparation for the discoveries of Kepler. And not only was it\nnecessary that men should possess a _knowledge_ of certain figures\nand their properties; but it was equally necessary that they should\nhave the _habit of reasoning_ with perfect steadiness, precision,\nand conclusiveness concerning the relations of space. No small\ndiscipline of the mind is requisite, in most cases, to accustom it\nto go, with complete insight and security, through the\ndemonstrations respecting intersecting planes and lines, dihedral\nand trihedral angles, which occur in solid geometry. Yet how\nabsolutely necessary is a perfect mastery of such reasonings, to him\nwho is to explain the motions of the moon in {166} latitude and\nlongitude! How necessary, again, is the same faculty to the student\nof crystallography! Without mathematical habits of conception and of\nthinking, these portions of science are perfectly inaccessible. But\nthe early study of plane and solid geometry gives to all tolerably\ngifted persons, the habits which are thus needed. The discipline of\nfollowing the reasonings of didactic works on this subject, till we\nare quite familiar with them, and of devising for ourselves\nreasonings of the same kind, (as, for instance, the solutions of\nproblems proposed,) soon gives the mind the power of _discoursing_\nwith perfect facility concerning the most complex and multiplied\nrelations of space, and enables us to refer to the properties of all\nplane and solid figures as surely as to the visible forms of\nobjects. Thus we have here a signal instance of the efficacy of\neducation in giving to our Conceptions that clearness, which the\nformation and existence of science indispensably require.\n\n[Note 13\\3: See _Hist. Sc. Ideas_, b. ii. c. xiii.]\n\n2. It is not my intention here to enter into the details of the form\nwhich should be given to education, in order that it may answer the\npurposes now contemplated. But I may make a remark, which the above\nexamples naturally suggest, that in a mathematical education,\nconsidered as a preparation for furthering or understanding physical\nscience, Geometry is to be cultivated, far rather than Algebra:--the\nproperties of space are to be studied and reasoned upon as they are\nin themselves, not as they are replaced and disguised by symbolical\nrepresentations. It is true, that when the student is become quite\nfamiliar with elementary geometry, he may often enable himself to\ndeal in a more rapid and comprehensive manner with the relations of\nspace, by using the language of symbols and the principles of\nsymbolical calculation: but this is an ulterior step, which may be\nadded to, but can never be substituted for, the direct cultivation\nof geometry. The method of symbolical reasoning employed upon\nsubjects of geometry and mechanics, has certainly achieved some\nremarkable triumphs in the treatment of the theory of the universe.\nThese successful {167} applications of symbols in the highest\nproblems of physical astronomy appear to have made some teachers of\nmathematics imagine that it is best to _begin_ the pupil's course\nwith such symbolical generalities. But this mode of proceeding will\nbe so far from giving the student clear ideas of mathematical\nrelations, that it will involve him in utter confusion, and probably\nprevent his ever obtaining a firm footing in geometry. To commence\nmathematics in such a way, would be much as if we should begin the\nstudy of a language by reading the highest strains of its lyrical\npoetry.\n\n3. (II.) _Idea of Number, &c._--The study of mathematics, as I need\nhardly observe, developes and renders exact, our conceptions of the\nrelations of number, as well as of space. And although, as we have\nalready noticed, even in their original form the conceptions of\nnumber are for the most part very distinct, they may be still\nfurther improved by such discipline. In complex cases, a methodical\ncultivation of the mind in such subjects is needed: for instance,\nquestions concerning Cycles, and Intercalations, and Epacts, and the\nlike, require very great steadiness of arithmetical apprehension in\norder that the reasoner may deal with them rightly. In the same\nmanner, a mastery of problems belonging to the science of Pure\nMotion, or, as I have termed it, _Mechanism_, requires either great\nnatural aptitude in the student, or a mind properly disciplined by\nsuitable branches of mathematical study.\n\n4. Arithmetic and Geometry have long been standard portions of the\neducation of cultured persons throughout the civilized world; and\nhence all such persons have been able to accept and comprehend those\nportions of science which depend upon the idea of space: for\ninstance, the doctrine of the globular form of the earth, with its\nconsequences, such as the measures of latitude and longitude;--the\nheliocentric system of the universe in modern, or the geocentric in\nancient times;--the explanation of the rainbow; and the like. In\nnations where there is no such education, these portions of science\ncannot exist as a part of the general stock of the knowledge of\nsociety, however intelligently they {168} may be pursued by single\nphilosophers dispersed here and there in the community.\n\n5. (III.) _Idea of Force._--As the idea of Space is brought out in\nits full evidence by the study of Geometry, so the idea of Force is\ncalled up and developed by the study of the science of Mechanics. It\nhas already been shown, in our scrutiny of the Ideas of the\nMechanical Sciences, that Force, the Cause of motion or of\nequilibrium, involves an independent Fundamental Idea, and is quite\nincapable of being resolved into any mere modification of our\nconceptions of space, time, and motion. And in order that the\nstudent may possess this idea in a precise and manifest shape, he\nmust pursue the science of Mechanics in the mode which this view of\nits nature demands;--that is, he must study it as an independent\nscience, resting on solid elementary principles of its own, and not\nbuilt upon some other unmechanical science as its substructure. He\nmust trace the truths of Mechanics from their own axioms and\ndefinitions; these axioms and definitions being considered as merely\nmeans of bringing into play the Idea on which the science depends.\nThe conceptions of force and matter, of action and reaction, of\nmomentum and inertia, with the reasonings in which they are\ninvolved, cannot be evaded by any substitution of lines or symbols\nfor the conceptions. Any attempts at such substitution would render\nthe study of Mechanics useless as a preparation of the mind for\nphysical science; and would, indeed, except counteracted by great\nnatural clearness of thought on such subjects, fill the mind with\nconfused and vague notions, quite unavailing for any purposes of\nsound reasoning. But, on the other hand, the study of Mechanics, in\nits genuine form, as a branch of education, is fitted to give a most\nuseful and valuable precision of thought on such subjects; and is\nthe more to be recommended, since, in the general habits of most\nmen's minds, the mechanical conceptions are tainted with far greater\nobscurity and perplexity than belongs to the conceptions of number,\nspace, and motion.\n\n6. As habitually distinct conceptions of _space_ and {169} _motion_\nwere requisite for the reception of the doctrines of formal\nastronomy, (the Ptolemaic and Copernican system,) so a clear and\nsteady conception of _force_ is indispensably necessary for\nunderstanding the Newtonian system of physical astronomy. It may be\nobjected that the study of Mechanics as a science has not commonly\nformed part of a liberal education in Europe, and yet that educated\npersons have commonly accepted the Newtonian system. But to this we\nreply, that although most persons of good intellectual culture have\nprofessed to assent to the Newtonian system of the universe, yet\nthey have, in fact, entertained it in so vague and perplexed a\nmanner as to show very clearly that a better mental preparation than\nthe usual one is necessary, in order that such persons may really\nunderstand the doctrine of universal attraction. I have elsewhere\nspoken of the prevalent indistinctness of mechanical\nconceptions[14\\3]; and need not here dwell upon the indications,\nconstantly occurring in conversation and in literature, of the utter\ninaccuracy of thought on such subjects which may often be detected;\nfor instance, in the mode in which many men speak of centrifugal and\ncentripetal forces;--of projectile and central forces;--of the\neffect of the moon upon the waters of the ocean; and the like. The\nincoherence of ideas which we frequently witness on such points,\nshows us clearly that, in the minds of a great number of men, well\neducated according to the present standard, the acceptance of the\ndoctrine of Universal Gravitation is a result of traditional\nprejudice, not of rational conviction. And those who are Newtonians\non such grounds, are not at all more intellectually advanced by\nbeing Newtonians in the nineteenth century, than they would have\nbeen by being Ptolemaics in the fifteenth.\n\n[Note 14\\3: _Hist. Sc. Ideas_, b. iii. c. x.]\n\n7. It is undoubtedly in the highest degree desirable that all great\nadvances in science should become the common property of all\ncultivated men. And this can only be done by introducing into the\ncourse of a liberal education such studies as unfold and fix in\nmen's minds {170} the fundamental ideas upon which the\nnew-discovered truths rest. The progress made by the ancients in\ngeography, astronomy, and other sciences, led them to assign, wisely\nand well, a place to arithmetic and geometry among the steps of an\ningenuous education. The discoveries of modern times have rendered\nthese steps still more indispensable; for we cannot consider a man\nas cultivated up to the standard of his times, if he is not only\nignorant of, but incapable of comprehending, the greatest\nachievements of the human intellect. And as innumerable discoveries\nof all ages have thus secured to Geometry her place as a part of\ngood education, so the great discoveries of Newton make it proper to\nintroduce Elementary Mechanics as a part of the same course. If the\neducation deserve to be called _good_, the pupil will not remain\nignorant of those discoveries, the most remarkable extensions of the\nfield of human knowledge which have ever occurred. Yet he cannot by\npossibility comprehend them, except his mind be previously\ndisciplined by mechanical studies. The period appears now to be\narrived when we may venture, or rather when we are bound to\nendeavour, to include a new class of Fundamental Ideas in the\nelementary discipline of the human intellect. This is indispensable,\nif we wish to educe the powers which we know that it possesses, and\nto enrich it with the wealth which lies within its reach[15\\3].\n\n[Note 15\\3: The University of Cambridge has, by a recent law, made\nan examination in Elementary Mechanics requisite for the Degree of\nB.A.]\n\n8. By the view which is thus presented to us of the nature and\nobjects of intellectual education, we are led to consider the mind\nof man as undergoing a progress from age to age. By the discoveries\nwhich are made, and by the clearness and evidence which, after a\ntime, (not suddenly nor soon,) the truths thus discovered acquire,\none portion of knowledge after another becomes _elementary_; and if\nwe would really secure this progress, and make men share in it,\nthese new portions must be treated as elementary in the constitution\nof a {171} liberal education. Even in the rudest forms of\nintelligence, man is immeasurably elevated above the unprogressive\nbrute, for the idea of number is so far developed that he can count\nhis flock or his arrows. But when number is contemplated in a\nspeculative form, he has made a vast additional progress; when he\nsteadily apprehends the relations of space, he has again advanced;\nwhen in thought he carries these relations into the vault of the\nsky, into the expanse of the universe, he reaches a higher\nintellectual position. And when he carries into these wide regions,\nnot only the relations of space and time, but of cause and effect,\nof force and reaction, he has again made an intellectual advance;\nwhich, wide as it is at first, is accessible to all; and with which\nall should acquaint themselves, if they really desire to prosecute\nwith energy the ascending path of truth and knowledge which lies\nbefore them. This should be an object of exertion to all ingenuous\nand hopeful minds. For, that exertion is necessary,--that after all\npossible facilities have been afforded, it is still a matter of toil\nand struggle to appropriate to ourselves the acquisitions of great\ndiscoverers, is not to be denied. Elementary mechanics, like\nelementary geometry, is a study accessible to all: but like that\ntoo, or perhaps more than that, it is a study which requires effort\nand contention of mind,--a forced steadiness of thought. It is long\nsince one complained of this labour in geometry; and was answered\nthat in that region there is no _Royal Road_. The same is true of\nMechanics, and must be true of all branches of solid education. But\nwe should express the truth more appropriately in our days by saying\nthat there is no _Popular Road_ to these sciences. In the mind, as\nin the body, strenuous exercise alone can give strength and\nactivity. The art of exact thought can be acquired only by the\nlabour of close thinking.\n\n9. (IV.) _Chemical Ideas._--We appear then to have arrived at a\npoint of human progress in which a liberal education of the\nscientific intellect should include, besides arithmetic, elementary\ngeometry and mechanics. {172} The question then occurs to us,\nwhether there are any other Fundamental Ideas, among those belonging\nto other sciences, which ought also to be made part of such an\neducation;--whether, for example, we should strive to develope in\nthe minds of all cultured men the ideas of _polarity_, mechanical\nand chemical, of which we spoke in a former part of this work.\n\nThe views to which we have been conducted by the previous inquiry\nlead us to reply that it would not be well at present to make\n_chemical_ Polarities, at any rate, a subject of elementary\ninstruction. For even the most profound and acute philosophers who\nhave speculated upon this subject,--they who are leading the van in\nthe march of discovery,--do not seem yet to have reduced their\nthoughts on this subject to a consistency, or to have taken hold of\nthis idea of Polarity in a manner quite satisfactory to their own\nminds. This part of the subject is, therefore, by no means ready to\nbe introduced into a course of general elementary education; for,\nwith a view to such a purpose, nothing less than the most thoroughly\nluminous and transparent condition of the idea will suffice. Its\nwhole efficacy, as a means and object of disciplinal study, depends\nupon there being no obscurity, perplexity, or indefiniteness with\nregard to it, beyond that transient deficiency which at first exists\nin the learner's mind, and is to be removed by his studies. The idea\nof chemical Polarity is not yet in this condition; and therefore is\nnot yet fit for a place in education. Yet since this idea of\nPolarity is the most general idea which enters into chemistry, and\nappears to be that which includes almost all the others, it would be\nunphilosophical, and inconsistent with all sound views of science,\nto introduce into education some chemical conceptions, and to omit\nthose which depend upon this idea: indeed such a partial adoption of\nthe science could hardly take place without not only omitting, but\nmisrepresenting, a great part of our chemical knowledge. The\nconclusion to which we are necessarily led, therefore, is\nthis:--that at present chemistry {173} cannot with any advantage,\nform a portion of the general intellectual education[16\\3].\n\n[Note 16\\3: I do not here stop to prove that an education (if it be\nso called) in which the memory only retains the verbal expression of\nresults, while the mind does not apprehend the principles of the\nsubject, and therefore cannot even understand the words in which its\ndoctrines are expressed, is of no value whatever to the intellect,\nbut rather, is highly hurtful to the habits of thinking and\nreasoning.]\n\n10. (V.) _Natural-History Ideas._--But there remains still another\nclass of Ideas, with regard to which we may very properly ask\nwhether they may not advantageously form a portion of a liberal\neducation: I mean the Ideas of definite Resemblance and Difference,\nand of one set of resemblances subordinate to another, which form\nthe bases of the classificatory sciences. These Ideas are developed\nby the study of the various branches of Natural History, as Botany,\nand Zoology; and beyond all doubt, those pursuits, if assiduously\nfollowed, very materially affect the mental habits. There is this\nobvious advantage to be looked for from the study of Natural\nHistory, considered as a means of intellectual discipline:--that it\ngives us, in a precise and scientific form, examples of the classing\nand naming of objects; which operations the use of common language\nleads us constantly to perform in a loose and inexact way. In the\nusual habits of our minds and tongues, things are distinguished or\nbrought together, and names are applied, in a manner very\nindefinite, vacillating, and seemingly capricious: and we may\nnaturally be led to doubt whether such defects can be\navoided;--whether exact distinctions of things, and rigorous use of\nwords be possible. Now upon this point we may receive the\ninstruction of Natural History; which proves to us, by the actual\nperformance of the task, that a precise classification and\nnomenclature are attainable, at least for a mass of objects all of\nthe same kind. Further, we also learn from this study, that there\nmay exist, not only an exact distinction of kinds of things, but a\nseries of distinctions, one set subordinate to another, and the more\ngeneral including {174} the more special, so as to form a system of\nclassification. All these are valuable lessons. If by the study of\nNatural History we evolve, in a clear and well defined form, the\nconceptions of _genus_, _species_, and of _higher_ and _lower steps_\nof classification, we communicate precision, clearness, and method\nto the intellect, through a great range of its operations.\n\n11. It must be observed, that in order to attain the disciplinal\nbenefit which the study of Natural History is fitted to bestow, we\nmust teach the _natural_ not the artificial _classifications_; or at\nleast the natural as well as the artificial. For it is important for\nthe student to perceive that there are classifications, not merely\narbitrary, founded upon some _assumed_ character, but natural,\nrecognized by some _discovered_ character: he ought to see that our\nclasses being collected according to one mark, are confirmed by many\nmarks not originally stated in our scheme; and are thus found to be\ngrouped together, not by a single resemblance, but by a mass of\nresemblances, indicating a natural affinity. That objects may be\ncollected into such groups, is a highly important lesson, which\nNatural History alone, pursued as the science of _natural classes_,\ncan teach.\n\n12. Natural History has not unfrequently been made a portion of\neducation: and has in some degree produced such effects as we have\npointed out. It would appear, however, that its lessons have, for\nthe most part, been very imperfectly learnt or understood by persons\nof ordinary education: and that there are perverse intellectual\nhabits very commonly prevalent in the cultivated classes, which\nought ere now to have been corrected by the general teaching of\nNatural History. We may detect among speculative men many prejudices\nrespecting the nature and rules of reasoning, which arise from pure\nmathematics having been so long and so universally the instrument of\nintellectual cultivation. Pure Mathematics reasons from definitions:\nwhatever term is introduced into her pages, as a _circle_, or a\n_square_, its definition comes along with it: and this definition is\nsupposed to supply all that the reasoner needs to know, respecting\nthe term. {175} If there be any doubt concerning the validity of the\nconclusion, the doubt is resolved by recurring to the definitions.\nHence it has come to pass that in other subjects also, men seek for\nand demand definitions as the most secure foundation of reasoning.\nThe definition and the term defined are conceived to be so far\nidentical, that in all cases the one may be substituted for the\nother; and such a substitution is held to be the best mode of\ndetecting fallacies.\n\n13. It has already been shown that even geometry is not founded upon\ndefinitions alone: and we shall not here again analyse the fallacy\nof this belief in the supreme value of definitions. But we may\nremark that the study of Natural History appears to be the proper\nremedy for this erroneous habit of thought. For in every department\nof Natural History the object of our study is _kinds_ of things, not\none of which kinds can be rigorously defined, yet all of them are\nsufficiently definite. In these cases we may indeed give a specific\ndescription of one of the kinds, and may call it a definition; but\nit is clear that such a definition does not contain the essence of\nthe thing. We say[17\\3] that the Rose Tribe are 'Polypetalous\ndicotyledons, with lateral styles, superior simple ovaria, regular\nperigynous stamens, exalbuminous definite seeds, and alternate\nstipulate leaves.' But no one would say that this was our essential\nconception of a rose, to be substituted for it in all cases of doubt\nor obscurity, by way of making our reasonings perfectly clear. Not\nonly so; but as we have already seen[18\\3], the definition does not\neven apply to all the tribe. For the stipul\u00e6 are absent in Lowea:\nthe albumen is present in Neillia: the fruit of Spir\u00e6a sorbifolia is\ncapsular. If, then, we can possess any certain knowledge in Natural\nHistory, (which no cultivator of the subject will doubt,) it is\nevident that our knowledge cannot depend on the possibility of\nlaying down exact definitions and reasoning from them.\n\n[Note 17\\3: Lindley's _Nat. Syst. Bot._ p. 81.]\n\n[Note 18\\3: _Hist. Sc. Ideas,_ b. viii. c. ii. sect. 3.]\n\n14. But it may be asked, if we cannot define a {176} word, or a\nclass of things which a word denotes, how can we distinguish what it\ndoes mean from what it does not mean? How can we say that it\nsignifies one thing rather than another, except we declare what is\nits signification?\n\nThe answer to this question involves the general principle of a\nnatural method of classification, which has already been\nstated[19\\3] and need not here be again dwelt on. It has been shown\nthat names of _kinds_ of things (_genera_) associate them according\nto total resemblances, not partial characters. The principle which\nconnects a group of objects in natural history is not a\n_definition_, but a _type_. Thus we take as the type of the Rose\nfamily, it may be, the common _wild rose_; all species which\nresemble this flower more than they resemble any other group of\nspecies are also _roses_, and form one _genus_. All genera which\nresemble Roses more than they resemble any other group of genera are\nof the same _family_. And thus the Rose family is collected about\nsome one species, which is the type or central point of the group.\n\n[Note 19\\3: _Hist. Sc. Ideas,_ b. viii. c. ii. sect. 3.]\n\nIn such an arrangement, it may readily be conceived that though the\nnucleus of each group may cohere firmly together, the outskirts of\ncontiguous groups may approach, and may even be intermingled, so\nthat some species may doubtfully adhere to one group or another. Yet\nthis uncertainty does not at all affect the truths which we find\nourselves enabled to assert with regard to the general mass of each\ngroup. And thus we are taught that there may be very important\ndifferences between two groups of objects, although we are unable to\ntell where the one group ends and where the other begins; and that\nthere may be propositions of indisputable truth, in which it is\nimpossible to give unexceptionable definitions of the terms\nemployed.\n\n15. These lessons are of the highest value with regard to all\nemployments of the human mind; for the mode in which words in common\nuse acquire their meaning, approaches far more nearly to the _Method\nof_ {177} _Type_ than to the method of definition. The terms which\nbelong to our practical concerns, or to our spontaneous and\nunscientific speculations, are rarely capable of exact definition.\nThey have been devised in order to express assertions, often very\nimportant, yet very vaguely conceived: and the signification of the\nword is extended, as far as the assertion conveyed by it can be\nextended, by apparent connexion or by analogy. And thus, in all the\nattempts of man to grasp at knowledge, we have an exemplification of\nthat which we have stated as the rule of induction, that Definition\nand Proposition are mutually dependent, each adjusted so as to give\nvalue and meaning to the other: and this is so, even when both the\nelements of truth are defective in precision: the Definition being\nreplaced by an incomplete description or a loose reference to a\nType; and the Proposition being in a corresponding degree insecure.\n\n16. Thus the study of Natural History, as a corrective of the belief\nthat definitions are essential to substantial truth, might be of\ngreat use; and the advantage which might thus be obtained is such as\nwell entitles this study to a place in a liberal education. We may\nfurther observe, that in order that Natural History may produce such\nan effect, it must be studied by inspection of the _objects_\nthemselves, and not by the reading of books only. Its lesson is,\nthat we must in all cases of doubt or obscurity refer, not to words\nor definitions, but to things. The Book of Nature is its dictionary:\nit is there that the natural historian looks, to find the meaning of\nthe words which he uses[20\\3]. So {178} long as a plant, in its most\nessential parts, is more _like_ a rose than any thing else, it _is_\na rose. He knows no other definition.\n\n[Note 20\\3: It is a curious example of the influence of the belief\nin definitions, that elementary books have been written in which\nNatural History is taught in the way of question and answer, and\nconsequently by means of words alone. In such a scheme, of course\nall objects are _defined_: and we may easily anticipate the value of\nthe knowledge thus conveyed. Thus, 'Iron is a well-known hard metal,\nof a darkish gray colour, and very elastic:' 'Copper is an\norange-coloured metal, more sonorous than any other, and the most\nelastic of any except iron.' This is to pervert the meaning of\neducation, and to make it a business of mere words.]\n\n17. (VI.) _Well-established Ideas alone to be used._--We may assert\nin general what we have elsewhere, as above, stated specially with\nreference to the fundamental principles of chemistry:--no Ideas are\nsuited to become the elements of elementary education, till they\nhave not only become perfectly distinct and fixed in the minds of\nthe leading cultivators of the science to which they belong; but\ntill they have been so for some considerable period. The entire\nclearness and steadiness of view which is essential to sound\nscience, must have time to extend itself to a wide circle of\ndisciples. The views and principles which are detected by the most\nprofound and acute philosophers, are soon appropriated by all the\nmost intelligent and active minds of their own and of the following\ngenerations; and when this has taken place, (and not till then,) it\nis right, by a proper constitution of our liberal education, to\nextend a general knowledge of such principles to all cultivated\npersons. And it follows, from this view of the matter, that we are\nby no means to be in haste to adopt, into our course of education,\nall new discoveries as soon as they are made. They require some\ntime, in order to settle into their proper place and position in\nmen's minds, and to show themselves under their true aspects; and\ntill this is done, we confuse and disturb, rather than enlighten and\nunfold, the ideas of learners, by introducing the discoveries into\nour elementary instruction. Hence it was perhaps reasonable that a\ncentury should elapse from the time of Galileo, before the rigorous\nteaching of Mechanics became a general element of intellectual\ntraining; and the doctrine of Universal Gravitation was hardly ripe\nfor such an employment till the end of the last century. We must not\ndirect the unformed youthful mind to launch its little bark upon the\nwaters of speculation, till all the agitation of discovery, with its\nconsequent fluctuation and controversy, has well subsided.\n\n18. But it may be asked, How is it that time {179} operates to give\ndistinctness and evidence to scientific ideas? In what way does it\nhappen that views and principles, obscure and wavering at first,\nafter a while become luminous and steady? Can we point out any\nprocess, any intermediate steps, by which this result is produced?\nIf we can, this process must be an important portion of the subject\nnow under our consideration.\n\nTo this we reply, that the transition from the hesitation and\ncontradiction with which true ideas are first received, to the\ngeneral assent and clear apprehension which they afterwards obtain,\ntakes place through the circulation of various arguments for and\nagainst them, and various modes of presenting and testing them, all\nwhich we may include under the term _Discussion_, which we have\nalready mentioned as the second of the two ways by which scientific\nviews are developed into full maturity.\n\n\n\n{{180}}\nCHAPTER IV.\n\nOF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS, _continued._--OF THE\nDISCUSSION OF IDEAS.\n\n\nAPHORISM XXXIII.\n\n_The conception involved in scientific truths have attained the\nrequisite degree of clearness by means of the_ Discussions\n_respecting ideas which have taken place among discoverers and their\nfollowers. Such discussions are very far from being unprofitable to\nscience. They are_ metaphysical, _and must be so: the difference\nbetween discoverers and barren reasoners is, that the former employ\ngood, and the latter bad metaphysics._\n\n\n1. IT is easily seen that in every part of science, the\nestablishment of a new set of ideas has been accompanied with much\nof doubt and dissent. And by means of discussions so occasioned, the\nnew conceptions, and the opinions which involve them, have gradually\nbecome definite and clear. The authors and asserters of the new\nopinions, in order to make them defensible, have been compelled to\nmake them consistent: in order to recommend them to others, they\nhave been obliged to make them more entirely intelligible to\nthemselves. And thus the Terms which formed the main points of the\ncontroversy, although applied in a loose and vacillating manner at\nfirst, have in the end become perfectly definite and exact. The\nopinions discussed have been, in their main features, the same\nthroughout the debate; but they have at first been dimly, and at\nlast clearly apprehended: like the objects of a landscape, at which\nwe look through a telescope ill adjusted, till, by sliding the tube\nbackwards and {181} forwards, we at last bring it into focus, and\nperceive every feature of the prospect sharp and bright.\n\n2. We have in the last Book[21\\3] fully exemplified this gradual\nprogress of conceptions from obscurity to clearness by means of\nDiscussion. We have seen, too, that this mode of treating the\nsubject has never been successful, except when it has been\nassociated with an appeal to facts as well as to reasonings. A\ncombination of experiment with argument, of observation with\ndemonstration, has always been found requisite in order that men\nshould arrive at those distinct conceptions which give them\nsubstantial truths. The arguments used led to the rejection of\nundefined, ambiguous, self-contradictory notions; but the reference\nto facts led to the selection, or at least to the retention, of the\nconceptions which were both true and useful. The two correlative\nprocesses, definition and true assertion, the formation of clear\nideas and the induction of laws, went on together.\n\n[Note 21\\3: B. **ii. c. ii. Of the Explication of Conceptions.]\n\nThus those discussions by which scientific conceptions are rendered\nultimately quite distinct and fixed, include both reasonings from\nPrinciples and illustrations from Facts. At present we turn our\nattention more peculiarly to the former part of the process;\naccording to the distinction already drawn, between the Explication\nof Conceptions and the Colligation of Facts. The Discussions of\nwhich we here speak, are the Method (if they may be called a\n_method_) by which the Explication of Conceptions is carried to the\nrequisite point among philosophers.\n\n3. In the _History_ of the Fundamental Ideas of the Sciences which\nforms the Prelude to this work, and in the _History of the Inductive\nSciences_, I have, in several instances, traced the steps by which,\nhistorically speaking, these Ideas have obtained their ultimate and\npermanent place in the minds of speculative men. I have thus\nexemplified the reasonings and controversies which constitute such\nDiscussion as we now speak of. I have stated, at considerable length,\nthe {182} various attempts, failures, and advances, by which the\nideas which enter into the science of Mechanics were evolved into\ntheir present evidence. In like manner we have seen the conception\nof _refracted rays_ of light, obscure and confused in Seneca,\ngrowing clearer in Roger Bacon, more definite in Descartes,\nperfectly distinct in Newton. The _polarity_ of light, at first\ncontemplated with some perplexity, became very distinct to Malus,\nYoung, and Fresnel; yet the phenomena of _circular polarization_,\nand still more, the _circular polarization of fluids_, leave us,\neven at present, some difficulty in fully mastering this conception.\nThe _related polarities_ of electricity and magnetism are not yet\nfully comprehended, even by our greatest philosophers. One of Mr.\nFaraday's late papers (the Fourteenth Series of his Researches) is\nemployed in an experimental discussion of this subject, which leads\nto no satisfactory result. The controversy between MM. Biot and\nAmp\u00e8re[22\\3], on the nature of the Elementary Forces in\nelectro-dynamic action, is another evidence that the discussion of\nthis subject has not yet reached its termination. With regard to\n_chemical polarity_, I have already stated that this idea is as yet\nvery far from being brought to an ultimate condition of\ndefiniteness; and the subject of Chemical Forces, (for that whole\nsubject must be included in this idea of polarity,) which has\nalready occasioned much perplexity and controversy, may easily\noccasion much more, before it is settled to the satisfaction of the\nphilosophical world. The ideas of the _classificatory_ sciences also\nhave of late been undergoing much, and very instructive discussion,\nin the controversies respecting the relations and offices of the\nnatural and artificial methods. And with regard to _physiological_\nideas, it would hardly be too much to say, that the whole history of\nphysiology up to the present time has consisted of the discussion of\nthe fundamental ideas of the science, such as Vital Forces,\nNutrition, Reproduction, and the like. We had before us at some\nlength, in the _History of Scientific Ideas_, a review {183} of the\nopposite opinions which have been advanced on this subject; and we\nattempted in some degree to estimate the direction in which these\nideas are permanently settling. But without attaching any importance\nto this attempt, the account there given may at least serve to show,\nhow important a share in the past progress of this subject the\n_discussion_ of its Fundamental Ideas has hitherto had.\n\n[Note 22\\3: _Hist. Ind. Sc._ b. xiii. c. 6.]\n\n4. There is one reflexion which is very pointedly suggested by what\nhas been said. The manner in which our scientific ideas acquire\ntheir distinct and ultimate form being such as has been\ndescribed,--always involving much abstract reasoning and analysis of\nour conceptions, often much opposite argumentation and debate;--how\nunphilosophical is it to speak of abstraction and analysis, of\ndispute and controversy, as frivolous and unprofitable processes, by\nwhich true science can never be benefitted; and how erroneous to put\nsuch employments in antithesis with the study of facts!\n\nYet some writers are accustomed to talk with contempt of all past\ncontroversies, and to wonder at the blindness of those who did not\n_at first_ take the view which was established _at last_. Such\npersons forget that it was precisely the controversy, which\nestablished among speculative men that final doctrine which they\nthemselves have quietly accepted. It is true, they have had no\ndifficulty in thoroughly adopting the truth; but that has occurred\nbecause all dissentient doctrines have been suppressed and\nforgotten; and because systems, and books, and language itself, have\nbeen accommodated peculiarly to the expression of the accepted\ntruth. To despise those who have, by their mental struggles and\nconflicts, brought the subject into a condition in which errour is\nalmost out of our reach, is to be ungrateful exactly in proportion\nto the amount of the benefit received. It is as if a child, when its\nteacher had with many trials and much trouble prepared a telescope\nso that the vision through it was distinct, should wonder at his\nstupidity in pushing the tube of the eye-glass out and in so often.\n{184}\n\n5. Again, some persons condemn all that we have here spoken of as\nthe discussion of ideas, terming it _metaphysical_: and in this\nspirit, one writer[23\\3] has spoken of the 'metaphysical period' of\neach science, as preceding the period of 'positive knowledge.' But\nas we have seen, that process which is here termed\n'metaphysical,'--the analysis of our conceptions and the exposure of\ntheir inconsistencies,--(accompanied with the study of facts,)--has\nalways gone on most actively in the most prosperous periods of each\nscience. There is, in Galileo, Kepler, Gassendi, and the other\nfathers of mechanical philosophy, as much of _metaphysics_ as in\ntheir adversaries. The main difference is, that the metaphysics is\nof a better kind; it is more conformable to metaphysical truth. And\nthe same is the case in other sciences. Nor can it be otherwise. For\nall truth, before it can be consistent with _facts_, must be\nconsistent with _itself_: and although this rule is of undeniable\nauthority, its application is often far from easy. The perplexities\nand ambiguities which arise from our having the same idea presented\nto us under different aspects, are often difficult to disentangle:\nand no common acuteness and steadiness of thought must be expended\non the task. It would be easy to adduce, from the works of all great\ndiscoverers, passages more profoundly metaphysical than any which\nare to be found in the pages of barren _\u00e0 priori_ reasoners.\n\n[Note 23\\3: M. Auguste Comte, _Cours de Philosophie Positive_.]\n\n6. As we have said, these metaphysical discussions are not to be put\nin opposition to the study of facts; but are to be stimulated,\nnourished and directed by a constant recourse to experiment and\nobservation. The cultivation of ideas is to be conducted as having\nfor its object the connexion of facts; never to be pursued as a mere\nexercise of the subtilty of the mind, striving to build up a world\nof its own, and neglecting that which exists about us. For although\nman may in this way please himself, and admire the creations of his\nown brain, he can never, by this course, hit upon the {185} real\nscheme of nature. With his ideas unfolded by education, sharpened by\ncontroversy, rectified by metaphysics, he may _understand_ the\nnatural world, but he cannot _invent_ it. At every step, he must try\nthe value of the advances he has made in thought, by applying his\nthoughts to things. The Explication of Conceptions must be carried\non with a perpetual reference to the Colligation of Facts.\n\nHaving here treated of Education and Discussion as the methods by\nwhich the former of these two processes is to be promoted, we have\nnow to explain the methods which science employs in order most\nsuccessfully to execute the latter. But the Colligation of Facts, as\nalready stated, may offer to us two steps of a very different\nkind,--the laws of Phenomena, and their Causes. We shall first\ndescribe some of the methods employed in obtaining truths of the\nformer of these two kinds.\n\n\n\n{{186}}\nCHAPTER V.\n\nANALYSIS OF THE PROCESS OF INDUCTION.\n\n\nAPHORISM XXXIV.\n\n_The Process of Induction may be resolved into three steps; the_\nSelection of the Idea, _the_ Construction of the Conception, _and\nthe_ Determination of the Magnitudes.\n\nAPHORISM XXXV.\n\n_These three steps correspond to the determination of the_\nIndependent Variable, _the_ Formula, _and the_ Coefficients, _in\nmathematical investigations; or to the_ Argument, _the_ Law, _and\nthe_ Numerical Data, _in a Table of an astronomical or other_\nInequality.\n\nAPHORISM XXXVI.\n\n_The Selection of the Idea depends mainly upon inventive sagacity:\nwhich operates by suggesting and trying various hypotheses. Some\ninquirers try erroneous hypotheses; and thus, exhausting the forms\nof errour, form the Prelude to Discovery._\n\nAPHORISM XXXVII.\n\n_The following Rules may be given, in order to the selection of the\nIdea for purposes of Induction:--the Idea and the Facts must be_\nhomogeneous; _and the Rule must be_ tested by the Facts.\n\n\nSECT. I.--_The Three Steps of Induction._\n\n1. WHEN facts have been decomposed and phenomena measured, the\nphilosopher endeavours to combine them into general laws, by the aid\nof {187} Ideas and Conceptions; these being illustrated and\nregulated by such means as we have spoken of in the last two\nchapters. In this task, of gathering laws of nature from observed\nfacts, as we have already said[24\\3], the natural sagacity of gifted\nminds is the power by which the greater part of the successful\nresults have been obtained; and this power will probably always be\nmore efficacious than any Method can be. Still there are certain\nmethods of procedure which may, in such investigations, give us no\ninconsiderable aid, and these I shall endeavour to expound.\n\n[Note 24\\3: B. ii. c. vi.]\n\n2. For this purpose, I remark that the Colligation of ascertained\nFacts into general Propositions may be considered as containing\nthree steps, which I shall term the _Selection of the Idea_, _the\nConstruction of the Conception_, and _the Determination of the\nMagnitudes_. It will be recollected that by the word _Idea_, (or\nFundamental Idea,) used in a peculiar sense, I mean certain wide and\ngeneral fields of intelligible relation, such as Space, Number,\nCause, Likeness; while by _Conception_ I denote more special\nmodifications of these ideas, as a _circle_, a _square number_, a\n_uniform force_, a _like form_ of flower. Now in order to establish\nany law by reference to facts, we must select the _true Idea_ and the\n_true Conception_. For example; when Hipparchus found[25\\3] that the\ndistance of the bright star Spica Virginis from the equinoxial point\nhad increased by two degrees in about two hundred years, and desired\nto reduce this change to a law, he had first to assign, if possible,\nthe _idea_ on which it depended;--whether it was regulated for\ninstance, by _space_, or by _time_; whether it was determined by the\npositions of other stars at each moment, or went on progressively\nwith the lapse of ages. And when there was found reason to select\n_time_ as the regulative _idea_ of this change, it was then to be\ndetermined how the change went on with the time;--whether uniformly,\nor in some other manner: the _conception_, or the rule of the\nprogression, was to be {188} rightly constructed. Finally, it being\nascertained that the change did go on uniformly, the question then\noccurred what was its _amount_:--whether exactly a degree in a\ncentury, or more, or less, and how much: and thus the determination\nof the _magnitude_ completed the discovery of the law of phenomena\nrespecting this star.\n\n[Note 25\\3: _Hist. Ind. Sc._ b. iii. c. iv. sect. 3.]\n\n3. Steps similar to these three may be discerned in all other\ndiscoveries of laws of nature. Thus, in investigating the laws of\nthe motions of the sun, moon or planets, we find that these motions\nmay be resolved, besides a uniform motion, into a series of partial\nmotions, or Inequalities; and for each of these Inequalities, we\nhave to learn upon what it directly depends, whether upon the\nprogress of time only, or upon some configuration of the heavenly\nbodies in space; then, we have to ascertain its law; and finally, we\nhave to determine what is its amount. In the case of such\nInequalities, the fundamental element on which the Inequality\ndepends, is called by mathematicians the _Argument_. And when the\nInequality has been fully reduced to known rules, and expressed in\nthe form of a Table, the Argument is the fundamental Series of\nNumbers which stands in the margin of the Table, and by means of\nwhich we refer to the other Numbers which express the Inequality.\nThus, in order to obtain from a Solar Table the Inequality of the\nsun's annual motion, the Argument is the Number which expresses the\nday of the year; the Inequalities for each day being (in the Table)\nranged in a line corresponding to the days. Moreover, the Argument\nof an Inequality being assumed to be known, we must, in order to\ncalculate the Table, that is, in order to exhibit the law of nature,\nknow also the _Law_ of the Inequality, and its _Amount_. And the\ninvestigation of these three things, the Argument, the Law, and the\nAmount of the Inequality, represents the three steps above\ndescribed, the Selection of the Idea, the Construction of the\nConception, and the Determination of the Magnitude.\n\n4. In a great body of cases, _mathematical_ language and calculation\nare used to express the connexion {189} between the general law and\nthe special facts. And when this is done, the three steps above\ndescribed may be spoken of as the Selection of the _Independent\nVariable_, the Construction of the _Formula_, and the Determination\nof the _Coefficients_. It may be worth our while to attend to an\nexemplification of this. Suppose then, that, in such observations as\nwe have just spoken of, namely, the shifting of a star from its\nplace in the heavens by an unknown law, astronomers had, at the end\nof three successive years, found that the star had removed by 3, by\n8, and by 15 minutes from its original place. Suppose it to be\nascertained also, by methods of which we shall hereafter treat, that\nthis change depends upon the time; we must then take the _time_,\n(which we may denote by the symbol _t_,) for the _independent\nvariable_. But though the star changes its place _with_ the time,\nthe change is not _proportional_ to the time; for its motion which\nis only 3 minutes in the first year, is 5 minutes in the second\nyear, and 7 in the third. But it is not difficult for a person a\nlittle versed in mathematics to perceive that the series 3, 8, 15,\nmay be obtained by means of two terms, one of which is proportional\nto the time, and the other to the square of the time; that is, it is\nexpressed by the _formula at + btt_. The question then occurs, what\nare the values of the _coefficients_ _a_ and _b_; and a little\nexamination of the case shows us that _a_ must be 2, and _b_, 1: so\nthat the formula is 2_t_ + _tt_. Indeed if we add together the series\n2, 4, 6, which expresses a change proportional to the time, and 1,\n4, 9, which is proportional to the square of the time, we obtain the\nseries 3, 8, 15, which is the series of numbers given by\nobservation. And thus the three steps which give us the Idea, the\nConception, and the Magnitudes; or the Argument, the Law, and the\nAmount, of the change; give us the Independent Variable, the\nFormula, and the Coefficients, respectively.\n\nWe now proceed to offer some suggestions of methods by which each of\nthese steps may be in some degree promoted. {190}\n\n\nSECT. II.--_Of the Selection of the Fundamental Idea._\n\n5. When we turn our thoughts upon any assemblage of facts, with a\nview of collecting from them some connexion or law, the most\nimportant step, and at the same time that in which rules can least\naid us, is the Selection of the Idea by which they are to be\ncollected. So long as this idea has not been detected, all seems to\nbe hopeless confusion or insulated facts; when the connecting idea\nhas been caught sight of, we constantly regard the facts with\nreference to their connexion, and wonder that it should be possible\nfor any one to consider them in any other point of view.\n\nThus the different seasons, and the various aspects of the heavenly\nbodies, might at first appear to be direct manifestations from some\nsuperior power, which man could not even understand: but it was soon\nfound that the ideas of time and space, of motion and recurrence,\nwould give coherency to many of the phenomena. Yet this took place\nby successive steps. Eclipses, for a long period, seemed to follow\nno law; and being very remarkable events, continued to be deemed the\nindications of a supernatural will, after the common motions of the\nheavens were seen to be governed by relations of time and space. At\nlength, however, the Chaldeans discovered that, after a period of\neighteen years, similar sets of eclipses recur; and, thus selecting\nthe idea of _time_, simply, as that to which these events were to be\nreferred, they were able to reduce them to rule; and from that time,\neclipses were recognized as parts of a regular order of things. We\nmay, in the same manner, consider any other course of events, and\nmay enquire by what idea they are bound together. For example, if we\ntake the weather, years peculiarly wet or dry, hot and cold,\nproductive and unproductive, follow each other in a manner which, at\nfirst sight at least, seems utterly lawless and irregular. Now can\nwe in any way discover some rule and order in these occurrences? Is\nthere, for example, in these events, as in eclipses, a certain cycle\nof years, after which like {191} seasons come round again? or does\nthe weather depend upon the force of some extraneous body--for\ninstance, the moon--and follow in some way her aspects? or would the\nmost proper way of investigating this subject be to consider the\neffect of the moisture and heat of various tracts of the earth's\nsurface upon the ambient air? It is at our choice to _try_ these and\nother modes of obtaining a science of the weather: that is, we may\nrefer the phenomena to the idea of _time_, introducing the\nconception of a cycle;--or to the idea of external _force_, by the\nconception of the moon's action;--or to the idea of _mutual action_,\nintroducing the conceptions of thermotical and atmological agencies,\noperating between different regions of earth, water, and air.\n\n6. It may be asked, How are we to decide in such alternatives? How\nare we to select the one right idea out of several conceivable ones?\nTo which we can only reply, that this must be done by _trying_ which\nwill succeed. If there really exist a cycle of the weather, as well\nas of eclipses, this must be established by comparing the asserted\ncycle with a good register of the seasons, of sufficient extent. Or\nif the moon really influence the meteorological conditions of the\nair, the asserted influence must be compared with the observed\nfacts, and so accepted or rejected. When Hipparchus had observed the\nincrease of longitude of the stars, the idea of a motion of the\ncelestial sphere suggested itself as the explanation of the change;\nbut this thought was _verified_ only by observing several stars. It\nwas conceivable that each star should have an independent motion,\ngoverned by time only, or by other circumstances, instead of being\nregulated by its place in the sphere; and this possibility could be\nrejected by trial alone. In like manner, the original opinion of the\ncomposition of bodies supposed the compounds to derive their\nproperties from the elements according to the law of _likeness_; but\nthis opinion was overturned by a thousand facts; and thus the really\napplicable Idea of Chemical Composition was introduced in modern\ntimes. In what has already been said on the History of Ideas, we\nhave seen how each science was in a state {192} of confusion and\ndarkness till the right idea was introduced.\n\n7. No general method of evolving such ideas can be given. Such\nevents appear to result from a peculiar sagacity and felicity of\nmind;--never without labour, never without preparation;--yet with no\nconstant dependence upon preparation, or upon labour, or even\nentirely upon personal endowments. Newton explained the colours\nwhich refraction produces, by referring each colour to a peculiar\n_angle of refraction_, thus introducing the right idea. But when the\nsame philosopher tried to explain the colours produced by\ndiffraction, he erred, by attempting to apply the same idea, (_the\ncourse of a single ray_,) instead of applying the truer idea, of the\n_interference of two rays_. Newton gave a wrong rule for the double\nrefraction of Iceland spar, by making the refraction depend on the\n_edges_ of the rhombohedron: Huyghens, more happy, introduced the\nidea of the _axis of symmetry_ of the solid, and thus was able to\ngive the true law of the phenomena.\n\n8. Although the selected idea is proved to be the right one, only\nwhen the true law of nature is established by means of it, yet it\noften happens that there prevails a settled conviction respecting\nthe relation which must afford the key to the phenomena, before the\nselection has been confirmed by the laws to which it leads. Even\nbefore the empirical laws of the tides were made out, it was not\ndoubtful that these laws depended upon the places and motions of the\nsun and moon. We know that the crystalline form of a body must\ndepend upon its chemical composition, though we are as yet unable to\nassign the law of this dependence.\n\nIndeed in most cases of great discoveries, the right idea to which\nthe facts were to be referred, was selected by many philosophers,\nbefore the decisive demonstration that it was the right idea, was\ngiven by the discoverer. Thus Newton showed that the motions of the\nplanets might be explained by means of a central force in the sun:\nbut though he established, he did not first select the idea involved\nin the conception of a {193} central force. The idea had already\nbeen sufficiently pointed out, dimly by Kepler, more clearly by\nBorelli, Huyghens, Wren, and Hooke. Indeed this anticipation of the\ntrue idea is always a principal part of that which, in the _History\nof the Sciences_, we have termed the _Prelude_ of a Discovery. The\ntwo steps of _proposing_ a philosophical problem, and of _solving_\nit, are, as we have elsewhere said, both important, and are often\nperformed by different persons. The former step is, in fact, the\nSelection of the Idea. In explaining any change, we have to discover\nfirst the _Argument_, and then the _Law_ of the change. The\nselection of the Argument is the step of which we here speak; and is\nthat in which inventiveness of mind and justness of thought are\nmainly shown.\n\n9. Although, as we have said, we can give few precise directions for\nthis cardinal process, the Selection of the Idea, in speculating on\nphenomena, yet there is one Rule which may have its use: it is\nthis:--_The idea and the facts must be homogeneous_: the elementary\nConceptions, into which the facts have been decomposed, must be of\nthe same nature as the Idea by which we attempt to collect them into\nlaws. Thus, if facts have been observed and measured by reference to\nspace, they must be bound together by the idea of space: if we would\nobtain a knowledge of mechanical forces in the solar system, we must\nobserve mechanical phenomena. Kepler erred against this rule in his\nattempts at obtaining physical laws of the system; for the facts\nwhich he took were the _velocities_, not the _changes of velocity_,\nwhich are really the mechanical facts. Again, there has been a\ntransgression of this Rule committed by all chemical philosophers\nwho have attempted to assign the relative position of the elementary\nparticles of bodies in their component molecules. For their purpose\nhas been to discover the _relations_ of the particles in _space_;\nand yet they have neglected the only facts in the constitution of\nbodies which have a reference to space--namely, _crystalline form_,\nand _optical properties_. No progress can be made in the theory of\nthe elementary structure of bodies, {194} without making these\nclasses of facts the main basis of our speculations.\n\n10. The only other Rule which I have to offer on this subject, is\nthat which I have already given:--_the Idea must be tested by the\nfacts_. It must be tried by applying to the facts the conceptions\nwhich are derived from the idea, and not accepted till some of these\nsucceed in giving the law of the phenomena. The justice of the\nsuggestion cannot be known otherwise than by making the trial. If we\ncan discover a _true law_ by employing any conceptions, the idea\nfrom which these conceptions are derived is the _right_ one; nor can\nthere be any proof of its rightness so complete and satisfactory, as\nthat we are by it led to a solid and permanent truth.\n\nThis, however, can hardly be termed a Rule; for when we would know,\nto conjecture and to try the truth of our conjecture by a comparison\nwith the facts, is the natural and obvious dictate of common sense.\n\nSupposing the Idea which we adopt, or which we would try, to be now\nfixed upon, we still have before us the range of many Conceptions\nderived from it; many Formul\u00e6 may be devised depending on the same\nIndependent Variable, and we must now consider how our selection\namong these is to be made.\n\n\n\n{{195}}\nCHAPTER VI.\n\nGENERAL RULES FOR THE CONSTRUCTION OF THE CONCEPTION.\n\n\nAPHORISM XXXVIII.\n\n_The Construction of the Conception very often includes, in a great\nmeasure, the Determination of the Magnitudes._\n\nAPHORISM XXXIX.\n\n_When a series of_ progressive _numbers is given as the result of\nobservation, it may generally be reduced to law by combinations of\narithmetical and geometrical progressions._\n\nAPHORISM XL.\n\n_A true formula for a progressive series of numbers cannot commonly\nbe obtained from a_ narrow range _of observations._\n\nAPHORISM XLI.\n\nRecurrent _series of numbers must, in most cases, be expressed by\ncircular formul\u00e6._\n\nAPHORISM XLII.\n\n_The true construction of the conception is frequently suggested by\nsome hypothesis; and in these cases, the hypothesis may be useful,\nthough containing superfluous parts._\n\n\nI. IN speaking of the discovery of laws of nature, those which\ndepend upon _quantity_, as number, space, and the like, are most\nprominent and most easily conceived, and therefore in speaking of\nsuch researches, we shall often use language which applies\npeculiarly to {196} the cases in which quantities numerically\nmeasurable are concerned, leaving it for a subsequent task to extend\nour principles to ideas of other kinds.\n\nHence we may at present consider the Construction of a Conception\nwhich shall include and connect the facts, as being the construction\nof a Mathematical Formula, coinciding with the numerical expression\nof the facts; and we have to consider how this process can be\nfacilitated, it being supposed that we have already before us the\nnumerical measures given by observation.\n\n2. We may remark, however, that the construction of the right\nFormula for any such case, and the determination of the Coefficients\nof such formula, which we have spoken of as two separate steps, are\nin practice almost necessarily simultaneous; for the near\ncoincidence of the results of the theoretical rule with the observed\nfacts confirms at the same time the Formula and its Coefficients. In\nthis case also, the mode of arriving at truth is to try various\nhypotheses;--to modify the hypotheses so as to approximate to the\nfacts, and to multiply the facts so as to test the hypotheses.\n\nThe Independent Variable, and the Formula which we would try, being\nonce selected, mathematicians have devised certain special and\ntechnical processes by which the value of the coefficients may be\ndetermined. These we shall treat of in the next Chapter; but in the\nmean time we may note, in a more general manner, the mode in which,\nin physical researches, the proper formula may be obtained.\n\n3. A person somewhat versed in mathematics, having before him a\nseries of numbers, will generally be able to devise a formula which\napproaches near to those numbers. If, for instance, the series is\nconstantly progressive, he will be able to see whether it more\nnearly resembles an arithmetical or a geometrical progression. For\nexample, MM. Dulong and Petit, in their investigation of the law of\ncooling of bodies, obtained the following series of measures. A\nthermometer, made hot, was placed in an enclosure of which the\ntemperature was 0 degrees, and the rapidity of {197} cooling of the\nthermometer was noted for many temperatures. It was found that\n\n For the temperature 240 the rapidity of cooling was 10\u00b769\n 220 \" 8\u00b781\n 200 \" 7\u00b740\n 180 \" 6\u00b710\n 160 \" 4\u00b789\n 140 \" 3\u00b788\n\nand so on. Now this series of numbers manifestly increases with\ngreater rapidity as we proceed from the lower to the higher parts of\nthe scale. The numbers do not, however, form a geometrical series,\nas we may easily ascertain. But if we were to take the differences\nof the successive terms we should find them to be--\n\n 1\u00b788, 1\u00b741, 1\u00b730, 1\u00b721, 1\u00b701, &c.\n\nand these numbers are very nearly the terms of a geometric series.\nFor if we divide each term by the succeeding one, we find these\nnumbers,\n\n 1\u00b733, 1\u00b709, 1\u00b707, 1\u00b720, 1\u00b727,\n\nin which there does not appear to be any constant tendency to\ndiminish or increase. And we shall find that a geometrical series in\nwhich the ratio is 1\u00b7165, may be made to approach very near to this\nseries, the deviations from it being only such as may be accounted\nfor by conceiving them as errours of observation. In this manner a\ncertain formula[26\\3] is obtained, giving results {198} which very\nnearly coincide with the observed facts, as may be seen in the\nmargin.\n\n[Note 26\\3: The formula is _v_ = 2\u00b7037(_a^t_ - 1) where _v_ is the\nvelocity of cooling, _t_ the temperature of the thermometer\nexpressed in degrees, and _a_ is the quantity, 1\u00b70077.\n\nThe degree of coincidence is as follows:--\n\n Excess of temperature of Observed Calculated\n the thermometer, or values values\n values of _t_. of _v_. of _v_.\n\n 240 10\u00b769 10\u00b768\n 220 8\u00b781 8\u00b789\n 200 7\u00b740 7\u00b734\n 180 6\u00b710 6\u00b703\n 160 4\u00b789 4\u00b787\n 140 3\u00b788 3\u00b789\n 120 3\u00b702 3\u00b705\n 100 2\u00b730 2\u00b733\n 80 1\u00b774 1\u00b772 ]\n\nThe physical law expressed by the formula just spoken of is\nthis:--that when a body is cooling in an empty inclosure which is\nkept at a constant temperature, the quickness of the cooling, for\nexcesses of temperature in arithmetical progression, increases as\nthe terms of a geometrical progression, diminished by a constant\nnumber.\n\n4. In the actual investigation of Dulong and Petit, however, the\nformula was not obtained in precisely the manner just described. For\nthe quickness of cooling depends upon two elements, the temperature\nof the hot body and the temperature of the inclosure; not merely\nupon the _excess_ of one of these over the other. And it was found\nmost convenient, first, to make such experiments as should exhibit\nthe dependence of the velocity of cooling upon the temperature of\nthe enclosure; which dependence is contained in the following\nlaw:--The quickness of cooling of a thermometer in vacuo for a\nconstant excess of temperature, increases in geometric progression,\nwhen the temperature of the inclosure increases in arithmetic\nprogression. From this law the preceding one follows by necessary\nconsequence[27\\3].\n\n[Note 27\\3: For if _\u03b8_ be the temperature of the inclosure, and _t_\nthe excess of temperature of the hot body, it appears, by this law,\nthat the radiation of heat is as _a^\u03b8_. And hence the quickness of\ncooling, which is as the excess of radiation, is as _a^\u03b8+t_ - _a^\u03b8_;\nthat is, as _a^\u03b8_(_a^t_ - 1) which agrees with the formula given in\nthe last note.\n\nThe whole of this series of researches of Dulong and Petit is full\nof the most beautiful and instructive artifices for the construction\nof the proper formul\u00e6 in physical research.]\n\nThis example may serve to show the nature of the artifices which may\nbe used for the construction of formul\u00e6, when we have a constantly\nprogressive series of numbers to represent. We must not only\nendeavour by trial to contrive a formula which will answer the\nconditions, but we must vary our experiments so as to determine,\nfirst one factor or portion of the formula, and then the other; and\nwe must use the most {199} probable hypothesis as means of\nsuggestion for our formul\u00e6.\n\n5. In a _progressive_ series of numbers, unless the formula which we\nadopt be really that which expresses the law of nature, the\ndeviations of the formula from the facts will generally become\nenormous, when the experiments are extended into new parts of the\nscale. True formul\u00e6 for a progressive series of results can hardly\never be obtained from a very limited range of experiments: just as\nthe attempt to guess the general course of a road or a river, by\nknowing two or three points of it in the neighbourhood of one\nanother, would generally fail. In the investigation respecting the\nlaws of the cooling of bodies just noticed, one great advantage of\nthe course pursued by the experimenters was, that their experiments\nincluded so great a range of temperatures. The attempts to assign\nthe law of elasticity of steam deduced from experiments made with\nmoderate temperatures, were found to be enormously wrong, when very\nhigh temperatures were made the subject of experiment. It is easy to\nsee that this must be so: an arithmetical and a geometrical series\nmay nearly coincide for a few terms moderately near each other: but\nif we take remote corresponding terms in the two series, one of\nthese will be very many times the other. And hence, from a narrow\nrange of experiments, we may infer one of these series when we ought\nto infer the other; and thus obtain a law which is widely erroneous.\n\n6. In Astronomy, the series of observations which we have to study\nare, for the most part, not progressive, but _recurrent_. The\nnumbers observed do not go on constantly increasing; but after\nincreasing up to a certain amount they diminish; then, after a\ncertain space, increase again; and so on, changing constantly\nthrough certain _cycles_. In cases in which the observed numbers are\nof this kind, the formula which expresses them must be a _circular\nfunction_, of some sort or other; involving, for instance, sines,\ntangents, and other forms of calculation, which have recurring\nvalues when the angle on which they depend goes on constantly {200}\nincreasing. The main business of formal astronomy consists in\nresolving the celestial phenomena into a series of _terms_ of this\nkind, in detecting their _arguments_, and in determining their\n_coefficients_.\n\n7. In constructing the formul\u00e6 by which laws of nature are\nexpressed, although the first object is to assign the Law of the\nPhenomena, philosophers have, in almost all cases, not proceeded in\na purely empirical manner, to connect the observed numbers by some\nexpression of calculation, but have been guided, in the selection of\ntheir formula, by some _Hypothesis_ respecting the mode of connexion\nof the facts. Thus the formula of Dulong and Petit above given was\nsuggested by the Theory of Exchanges; the first attempts at the\nresolution of the heavenly motions into circular functions were\nclothed in the hypothesis of Epicycles. And this was almost\ninevitable. 'We must confess,' says Copernicus[28\\3], 'that the\ncelestial motions are circular, or compounded of several circles,\nsince their inequalities observe a fixed law, and recur in value at\ncertain intervals, which could not be except they were circular: for\na circle alone can make that quantity which has occurred recur\nagain.' In like manner the first publication of the _Law of the\nSines_, the true formula of optical refraction, was accompanied by\nDescartes with an hypothesis, in which an explanation of the law was\npretended. In such cases, the mere comparison of observations may\nlong fail in suggesting the true formul\u00e6. The fringes of shadows and\nother diffracted colours were studied in vain by Newton, Grimaldi,\nComparetti, the elder Herschel, and Mr. Brougham, so long as these\ninquirers attempted merely to trace the laws of the facts as they\nappeared in themselves; while Young, Fresnel, Fraunhofer, Schwerdt,\nand others, determined these laws in the most rigorous manner, when\nthey applied to the observations the Hypothesis of Interferences.\n\n[Note 28\\3: _De Rev._ l. i. c. iv.]\n\n8. But with all the aid that Hypotheses and Calculation can afford,\nthe construction of true formul\u00e6, in {201} those cardinal\ndiscoveries by which the progress of science has mainly been caused,\nhas been a matter of great labour and difficulty, and of good\nfortune added to sagacity. In the _History of Science_, we have seen\nhow long and how hard Kepler laboured, before he converted the\nformula for the planetary motions, from an _epicyclical_\ncombination, to a simple _ellipse_. The same philosopher, labouring\nwith equal zeal and perseverance to discover the formula of optical\nrefraction, which now appears to us so simple, was utterly foiled.\nMalus sought in vain the formula determining the Angle at which a\ntransparent surface polarizes light: Sir D. Brewster[29\\3], with a\nhappy sagacity, discovered the formula to be simply this, that the\n_index_ of refraction is the _tangent_ of the angle of polarization.\n\n[Note 29\\3: _Hist. Ind. Sc._ b. ix. c. vi.]\n\nThough we cannot give rules which will be of much service when we\nhave thus to divine the general form of the relation by which\nphenomena are connected, there are certain methods by which, in a\nnarrower field, our investigations may be materially\npromoted;--certain special methods of obtaining laws from\nObservations. Of these we shall now proceed to treat.\n\n\n\n{{202}}\nCHAPTER VII.\n\nSPECIAL METHODS OF INDUCTION APPLICABLE TO QUANTITY.\n\n\nAPHORISM XLIII.\n\n_There are special Methods of Induction applicable to Quantity; of\nwhich the principal are, the_ Method of Curves, _the_ Method of\nMeans, _the_ Method of Least Squares, _and the_ Method of Residues.\n\nAPHORISM XLIV.\n\nThe Method of Curves _consists in drawing a curve of which the\nobserved quantities are the Ordinates, the quantity on which the\nchange of these quantities depends being the Abscissa. The efficacy\nof this Method depends upon the faculty which the eye possesses, of\nreadily detecting regularity and irregularity in forms. The Method\nmay be used to detect the Laws which the observed quantities follow:\nand also, when the Observations are inexact, it may be used to\ncorrect these Observations, so as to obtain data more true than the\nobserved facts themselves._\n\nAPHORISM XLV.\n\nThe Method of Means _gets rid of irregularities by taking the\narithmetical mean of a great number of observed quantities. Its\nefficacy depends upon this; that in cases in which observed\nquantities are affected by other inequalities, besides that of which\nwe wish to determine the law, the excesses_ above _and defects_\nbelow _the quantities which the law in question would produce, will,\nin a collection of_ many _observations_, balance _each other._ {203}\n\nAPHORISM XLVI.\n\nThe Method of Least Squares _is a Method of Means, in which the mean\nis taken according to the condition, that the sum of the squares of\nthe errours of observation shall be the least possible which the law\nof the facts allows. It appears, by the Doctrine of Chances, that\nthis is the_ most probable _mean._\n\nAPHORISM XLVII.\n\nThe Method of Residues _consists in subtracting, from the quantities\ngiven by Observation, the quantity given by any Law already\ndiscovered; and then examining the remainder, or_ Residue, _in order\nto discover the leading Law which it follows. When this second Law\nhas been discovered, the quantity given by it may be subtracted from\nthe first Residue; thus giving a_ Second Residue, _which may be\nexamined in the same manner; and so on. The efficacy of this method\ndepends principally upon the circumstance of the Laws of variation\nbeing successively smaller and smaller in amount (or at least in\ntheir mean effect); so that the ulterior undiscovered Laws do not\nprevent the Law in question from being_ prominent _in the\nobservations._\n\nAPHORISM XLVIII.\n\n_The Method of Means and the Method of Least Squares cannot be\napplied without our_ knowing the Arguments _of the Inequalities\nwhich we seek. The Method of Curves and the Method of Residues, when\nthe Arguments of the principal Inequalities are known, often make it\neasy to find the others._\n\n\nIN cases where the phenomena admit of numerical measurement and\nexpression, certain mathematical methods may be employed to\nfacilitate and give accuracy to the determination of the formula by\nwhich the observations are connected into laws. Among the most usual\nand important of these Methods are the following:--{204}\n I. The Method of Curves.\n II. The Method of Means.\nIII. The Method of Least Squares.\n IV. The Method of Residues.\n\n\nSECT. I.--_The Method of Curves._\n\n1. THE Method of Curves proceeds upon this basis; that when one\nquantity undergoes a series of changes depending on the progress of\nanother quantity, (as, for instance, the Deviation of the Moon from\nher equable place depends upon the progress of Time,) this\ndependence may be expressed by means of a _curve_. In the language\nof mathematicians, the variable quantity, whose changes we would\nconsider, is made the _ordinate_ of the curve, and the quantity on\nwhich the changes depend is made the _abscissa_. In this manner, the\ncurve will exhibit in its form a series of undulations, rising and\nfalling so as to correspond with the alternate Increase and\nDiminution of the quantity represented, at intervals of Space which\ncorrespond to the intervals of Time, or other quantity by which the\nchanges are regulated. Thus, to take another example, if we set up,\nat equal intervals, a series of ordinates representing the Height of\nall the successive High Waters brought by the tides at a given\nplace, for a year, the curve which connects the summits of all these\nordinates will exhibit a series of undulations, ascending and\ndescending once in about each Fortnight; since, in that interval, we\nhave, in succession, the high spring tides and the low neap tides.\nThe curve thus drawn offers to the eye a picture of the order and\nmagnitude of the changes to which the quantity under contemplation,\n(the height of high water,) is subject.\n\n2. Now the peculiar facility and efficacy of the Method of Curves\ndepends upon this circumstance;--that order and regularity are more\nreadily and clearly recognized, when thus exhibited to the eye in a\npicture, than they are when presented to the mind in any other\nmanner. To detect the relations of Number considered directly as\nNumber, is not easy: and we might {205} contemplate for a long time\na Table of recorded Numbers without perceiving the order of their\nincrease and diminution, even if the law were moderately simple; as\nany one may satisfy himself by looking at a Tide Table. But if these\nNumbers are expressed by the magnitude of _Lines_, and if these Lines\nare arranged in regular order, the eye readily discovers the rule of\ntheir changes: it follows the curve which runs along their\nextremities, and takes note of the order in which its convexities\nand concavities succeed each other, if any order be readily\ndiscoverable. The separate observations are in this manner compared\nand generalized and reduced to rule by the eye alone. And the eye,\nso employed, detects relations of order and succession with a\npeculiar celerity and evidence. If, for example, we thus arrive as\nordinates the prices of corn in each year for a series of years, we\nshall see the order, rapidity, and amount of the increase and\ndecrease of price, far more clearly than in any other manner. And if\nthere were any recurrence of increase and decrease at stated\nintervals of years, we should in this manner perceive it. The eye,\nconstantly active and busy, and employed in making into shapes the\nhints and traces of form which it contemplates, runs along the curve\nthus offered to it; and as it travels backwards and forwards, is\never on the watch to detect some resemblance or contrast between one\npart and another. And these resemblances and contrasts, when\ndiscovered, are the images of Laws of Phenomena; which are made\nmanifest at once by this artifice, although the mind could not\neasily catch the indications of their existence, if they were not\nthus reflected to her in the clear mirror of Space.\n\nThus when we have a series of good Observations, and know the\nargument upon which their change of magnitude depends, the Method of\nCurves enables us to ascertain, almost at a glance, the law of the\nchange; and by further attention, may be made to give us a formula\nwith great accuracy. The Method enables us to perceive, among our\nobservations, an order, which without the method, is concealed in\nobscurity and perplexity. {206}\n\n3. But the Method of Curves not only enables us to obtain laws of\nnature from _good_ Observations, but also, in a great degree, from\nobservations which are very _imperfect_. For the imperfection of\nobservations may in part be corrected by this consideration;--that\nthough they may appear irregular, the correct facts which they\nimperfectly represent, are really regular. And the Method of Curves\nenables us to remedy this apparent irregularity, at least in part.\nFor when Observations thus imperfect are laid down as Ordinates, and\ntheir extremities connected by a line, we obtain, not a smooth and\nflowing curve, such as we should have if the observations contained\nonly the rigorous results of regular laws; but a broken and\nirregular line, full of sudden and capricious twistings, and bearing\non its face marks of irregularities dependent, not upon law, but\nupon chance. Yet these irregular and abrupt deviations in the curve\nare, in most cases, but small in extent, when compared with those\nbendings which denote the effects of regular law. And this\ncircumstance is one of the great grounds of advantage in the Method\nof Curves. For when the observations thus laid down present to the\neye such a broken and irregular line, we can still see, often with\ngreat ease and certainty, what twistings of the line are probably\ndue to the irregular errours of observation; and can at once reject\nthese, by drawing a more regular curve, cutting off all such small\nand irregular sinuosities, leaving some to the right and some to the\nleft; and then proceeding as if this regular curve, and not the\nirregular one, expressed the observations. In this manner, we\nsuppose the errours of observation to balance each other; some of\nour corrected measures being too great and others too small, but\nwith no great preponderance either way. We draw our main regular\ncurve, not _through_ the points given by our observations, but\n_among_ them: drawing it, as has been said by one of the\nphilosophers[30\\3] who first systematically used this method, 'with\na bold but careful hand.' {207} The regular curve which we thus\nobtain, thus freed from the casual errours of observation, is that\nin which we endeavour to discover the laws of change and succession.\n\n[Note 30\\3: Sir J. Herschel, _Ast. Soc. Trans._ vol. v. p. 1.]\n\n4. By this method, thus getting rid at once, in a great measure, of\nerrours of observation, we obtain data which are _more true than\nthe_ individual _facts themselves_. The philosopher's business is to\ncompare his hypotheses with facts, as we have often said. But if we\nmake the comparison with separate special facts, we are liable to be\nperplexed or misled, to an unknown amount, by the errours of\nobservation; which may cause the hypothetical and the observed\nresult to agree, or to disagree, when otherwise they would not do\nso. If, however, we thus take the _whole mass of the facts_, and\nremove the errours of actual observation[31\\3], by making the curve\nwhich expresses the supposed observation regular and smooth, we have\nthe separate facts corrected by their general tendency. We are put\nin possession, as we have said, of something more true than any fact\nby itself is.\n\n[Note 31\\3: _Ib._ vol. v. p. 4.]\n\nOne of the most admirable examples of the use of this Method of\nCurves is found in Sir John Herschel's _Investigation of the Orbits\nof Double Stars_[32\\3]. The author there shows how far inferior the\ndirect observations of the angle of position are, to the\nobservations corrected by a curve in the manner above stated. 'This\ncurve once drawn,' he says, 'must represent, it is evident, the law\nof variation of the angle of position, with the time, not only for\ninstants intermediate between the dates of observations, but even at\nthe moments of observation themselves, much better than the\nindividual _raw_ observations can possibly (on an average) do. It is\nonly requisite to try a case or two, to be satisfied that by\nsubstituting the curve for the points, we have made a nearer\napproach to nature, and in a great measure eliminated errours of\nobservation.' 'In following the graphical process,' he adds, 'we\nhave a conviction almost approaching to moral certainty that {208}\nwe cannot be greatly misled.' Again, having thus corrected the raw\nobservations, he makes another use of the graphical method, by\ntrying whether an ellipse can be drawn 'if not _through_, at least\n_among_ the points, so as to approach tolerably near them all; and\nthus approaching to the orbit which is the subject of\ninvestigation.'\n\n[Note 32\\3: _Ib._]\n\n5. The _Obstacles_ which principally impede the application of the\nMethod of Curves are (I.) our _ignorance of the arguments_ of the\nchanges, and (II.) the _complication of several laws_ with one\nanother.\n\n(I.) If we do not know on what quantity those changes depend which\nwe are studying, we may fail entirely in detecting the law of the\nchanges, although we throw the observations into curves. For the\ntrue _argument_ of the change should, in fact, be made the\n_abscissa_ of the curve. If we were to express, by a series of\nordinates, the _hour_ of high water on successive days, we should\nnot obtain, or should obtain very imperfectly, the law which these\ntimes follow; for the real argument of this change is not the _solar\nhour_, but the _hour_ at which the _moon_ passes the meridian. But\nif we are supposed to be aware that _this_ is the _argument_, (which\ntheory suggests and trial instantly confirms) we then do immediately\nobtain the primary Rules of the Time of High Water, by throwing a\nseries of observations into a Curve, with the Hour of the Moon's\nTransit for the abscissa.\n\nIn like manner, when we have obtained the first great or\nSemi-mensual Inequality of the tides, if we endeavour to discover\nthe laws of other Inequalities by means of curves, we must take from\ntheory the suggestion that the Arguments of such inequalities will\nprobably be the _parallax_ and the _declination_ of the moon. This\nsuggestion again is confirmed by trial; but if we were supposed to\nbe entirely ignorant of the dependence of the changes of the tide on\nthe Distance and Declination of the moon, the curves would exhibit\nunintelligible and seemingly capricious changes. For by the effect\nof the Inequality arising from the Parallax, the convexities of the\ncurves which belong to the {209} spring tides, are in some years\nmade alternately greater and less all the year through; while in\nother years they are made all nearly equal. This difference does not\nbetray its origin, till we refer it to the Parallax; and the same\ndifficulty in proceeding would arise if we were ignorant that the\nmoon's Declination is one of the Arguments of tidal changes.\n\nIn like manner, if we try to reduce to law any meteorological\nchanges, those of the Height of the Barometer for instance, we find\nthat we can make little progress in the investigation, precisely\nbecause we do not know the Argument on which these changes depend.\nThat there is a certain regular _diurnal_ change of small amount, we\nknow; but when we have abstracted this Inequality, (of which the\nArgument is the _time of day_,) we find far greater Changes left\nbehind, from day to day and from hour to hour; and we express these\nin curves, but we cannot reduce them to Rule, because we cannot\ndiscover on what numerical quantity they depend. The assiduous study\nof barometrical observations, thrown into curves, may perhaps\nhereafter point out to us what are the relations of time and space\nby which these variations are determined; but in the mean time, this\nsubject exemplifies to us our remark, that the method of curves is\nof comparatively small use, so long as we are in ignorance of the\nreal Arguments of the Inequalities.\n\n6. (II.) In the next place, I remark that a difficulty is thrown in\nthe way of the Method of Curves by _the Combination of several laws_\none with another. It will readily be seen that such a cause will\nproduce a complexity in the curves which exhibit the succession of\nfacts. If, for example, we take the case of the Tides, the Height of\nhigh water increases and diminishes with the Approach of the sun to,\nand its Recess from, the syzygies of the moon. Again, this Height\nincreases and diminishes as the moon's Parallax increases and\ndiminishes; and again, the Height diminishes when the Declination\nincreases, and _vice versa_; and all these Arguments of change, the\nDistance from Syzygy, the Parallax, the Declination, complete their\ncircuit and {210} return into themselves in different periods. Hence\nthe curve which represents the Height of high water has not any\nperiodical interval in which it completes its changes and commences\na new cycle. The sinuosity which would arise from each Inequality\nseparately considered, interferes with, disguises, and conceals the\nothers; and when we first cast our eyes on the curve of observation,\nit is very far from offering any obvious regularity in its form. And\nit is to be observed that we have not yet enumerated _all_ the\nelements of this complexity: for there are changes of the tide\ndepending upon the Parallax and Declination of the Sun as well as of\nthe Moon. Again; besides these changes, of which the Arguments are\nobvious, there are others, as those depending upon the Barometer and\nthe Wind, which follow no known regular law, and which constantly\naffect and disturb the results produced by other laws.\n\nIn the Tides, and in like manner in the motions of the Moon, we have\nvery eminent examples of the way in which the discovery of laws may\nbe rendered difficult by the number of laws which operate to affect\nthe same quantity. In such cases, the Inequalities are generally\npicked out in succession, nearly in the order of their magnitudes.\nIn this way there were successively collected, from the study of the\nMoon's motions by a series of astronomers, those Inequalities which\nwe term the _Equation of the Center_, the _Evection_, the\n_Variation_, and the _Annual Equation_. These Inequalities were not,\nin fact, obtained by the application of the Method of Curves; but\nthe Method of Curves might have been applied to such a case with\ngreat advantage. The Method has been applied with great industry and\nwith remarkable success to the investigation of the laws of the\nTides; and by the use of it, a series of Inequalities both of the\nTimes and of the Heights of high water has been detected, which\nexplain all the main features of the observed facts. {211}\n\n\nSECT. II.--_The Method of Means._\n\n7. The Method of Curves, as we have endeavoured to explain above,\nfrees us from the casual and extraneous irregularities which arise\nfrom the imperfection of observation; and thus lays bare the results\nof the laws which really operate, and enables us to proceed in\nsearch of those laws. But the Method of Curves is not the only one\nwhich effects such a purpose. The errours arising from detached\nobservations may be got rid of, and the additional accuracy which\nmultiplied observations give may be obtained, by operations upon the\nobserved numbers, without expressing them by spaces. The process of\ncurves assumes that the errours of observation balance each\nother;--that the accidental excesses and defects are nearly equal in\namount;--that the true quantities which would have been observed if\nall accidental causes of irregularity were removed, are obtained,\nexactly or nearly, by selecting quantities, upon the whole, equally\ndistant from the extremes of great and small, which our imperfect\nobservations offer to us. But when, among a number of unequal\nquantities, we take a quantity equally distant from the greater and\nthe smaller, this quantity is termed the _Mean_ of the unequal\nquantities. Hence the correction of our observations by the method\nof curves consists in taking the Mean of the observations.\n\n8. Now without employing curves, we may proceed arithmetically to\ntake the Mean of all the observed numbers of each class. Thus, if we\nwished to know the Height of the spring tide at a given place, and\nif we found that four different spring tides were measured as being\nof the height of ten, thirteen, eleven, and fourteen feet, we should\nconclude that the true height of the tide was the _Mean_ of these\nnumbers,--namely, twelve feet; and we should suppose that the\ndeviation from this height, in the individual cases, arose from the\naccidents of weather, the imperfections of observation, or the\noperation of other laws, besides the alternation of spring and neap\ntides. {212}\n\nThis process of finding the Mean of an assemblage of observed\nnumbers is much practised in discovering, and still more in\nconfirming and correcting, laws of phenomena. We shall notice a few\nof its peculiarities.\n\n9. The Method of Means requires a knowledge of the _Argument_ of the\nchanges which we would study; for the numbers must be arranged in\ncertain Classes, before we find the Mean of each Class; and the\nprinciple on which this arrangement depends is the Argument. This\nknowledge of the Argument is more indispensably necessary in the\nMethod of Means than in the Method of Curves; for when Curves are\ndrawn, the eye often spontaneously detects the law of recurrence in\ntheir sinuosities; but when we have collections of Numbers, we must\ndivide them into classes by a selection of our own. Thus, in order\nto discover the law which the heights of the tide follow, in the\nprogress from spring to neap, we arrange the observed tides\naccording to the _day of the moon's age_; and we then take the mean\nof all those which thus happen at the _same period_ of the Moon's\nRevolution. In this manner we obtain the law which we seek; and the\nprocess is very nearly the same in all other applications of this\nMethod of Means. In all cases, we begin by assuming the Classes of\nmeasures which we wish to compare, the Law which we could confirm or\ncorrect, the Formula of which we would determine the coefficients.\n\n10. The Argument being thus assumed, the Method of Means is very\nefficacious in ridding our inquiry of errours and irregularities\nwhich would impede and perplex it. Irregularities which are\naltogether accidental, or at least accidental with reference to some\nlaw which we have under consideration, compensate each other in a\nvery remarkable way, when we take the Means of _many_ observations.\nIf we have before us a collection of observed tides, some of them\nmay be elevated, some depressed by the wind, some noted too high and\nsome too low by the observer, some augmented and some diminished by\nuncontemplated changes in the moon's distance or motion: but in the\ncourse of a year or two at the longest, all these causes of\nirregularity balance {213} each other; and the law of succession,\nwhich runs through the observations, comes out as precisely as if\nthose disturbing influences did not exist. In any particular case,\nthere appears to be no possible reason why the deviation should be\nin one way, or of one moderate amount, rather than another. But\ntaking the mass of observations together, the deviations in opposite\nways will be of equal amount, with a degree of exactness very\nstriking. This is found to be the case in all inquiries where we\nhave to deal with observed numbers upon a large scale. In the\nprogress of the population of a country, for instance, what can\nappear more inconstant, in detail, than the causes which produce\nbirths and deaths? yet in each country, and even in each province of\na country, the proportions of the whole numbers of births and deaths\nremain nearly constant. What can be more seemingly beyond the reach\nof rule than the occasions which produce letters that cannot find\ntheir destination? yet it appears that the number of 'dead letters'\nis nearly the same from year to year. And the same is the result\nwhen the deviations arise, not from mere accident, but from laws\nperfectly regular, though not contemplated in our\ninvestigation[33\\3]. Thus the effects of the Moon's Parallax upon\nthe Tides, sometimes operating one way and sometimes another,\naccording to certain rules, are quite eliminated by taking the Means\nof a long series of observations; the excesses and defects\nneutralizing each other, so far as concerns the effect upon any law\nof the tides which we would investigate.\n\n[Note 33\\3: Provided the argument of the law which we neglect have\nno coincidence with the argument of the law which we would\ndetermine.]\n\n11. In order to obtain very great accuracy, very large masses of\nobservations are often employed by philosophers, and the accuracy of\nthe result increases with the multitude of observations. The immense\ncollections of astronomical observations which have in this manner\nbeen employed in order to form and correct the Tables of the\ncelestial motions are perhaps the most signal instances of the\nattempts to obtain {214} accuracy by this accumulation of\nobservations. Delambre's Tables of the Sun are founded upon nearly\n3000 observations; Burg's Tables of the Moon upon above 4000.\n\nBut there are other instances hardly less remarkable. Mr. Lubbock's\nfirst investigations of the laws of the tides of London[34\\3],\nincluded above 13,000 observations, extending through nineteen\nyears; it being considered that this large number was necessary to\nremove the effects of accidental causes[35\\3]. And the attempts to\ndiscover the laws of change in the barometer have led to the\nperformance of labours of equal amount: Laplace and Bouvard examined\nthis question by means of observations made at the Observatory of\nParis, four times every day for eight years.\n\n[Note 34\\3: _Phil. Trans._ 1831.]\n\n[Note 35\\3: This period of nineteen years was also selected for a\nreason which is alluded to in a former note. It was thought that\nthis period secured the inquirer from the errours which might be\nproduced by the partial coincidence of the Arguments of different\nirregularities; for example, those due to the moon's Parallax and to\nthe moon's Declination. It has since been found (_Phil. Tr._ 1838.\n_On the Determination of the Laws of the Tides from Short Series of\nObservations_), that with regard to Parallax at least, the Means of\none year give sufficient accuracy.]\n\n12. We may remark one striking evidence of the accuracy thus\nobtained by employing large masses of observations. In this way we\nmay often detect inequalities much smaller than the errours by which\nthey are encumbered and concealed. Thus the Diurnal Oscillations of\nthe Barometer were discovered by the comparison of observations of\nmany days, classified according to the hours of the day; and the\nresult was a clear and incontestable proof of the existence of such\noscillations although the differences which these oscillations\nproduce at different hours of the day are far smaller than the\ncasual changes, hitherto reduced to no law, which go on from hour to\nhour and from day to day. The effect of law, operating incessantly\nand steadily, makes itself more and more felt as we give it a longer\nrange; while the effect of accident, followed out in the {215} same\nmanner, is to annihilate itself, and to disappear altogether from\nthe result.\n\n\nSECT. III.--_The Method of Least Squares._\n\n13. The Method of Least Squares is in fact a method of means, but\nwith some peculiar characters. Its object is to determine the _best\nMean_ of a number of observed quantities; or the _most probable Law_\nderived from a number of observations, of which some, or all, are\nallowed to be more or less imperfect. And the method proceeds upon\nthis supposition;--that all errours are not _equally_ probable, but\nthat small errours are more probable than large ones. By reasoning\nmathematically upon this ground, we find that the best result is\nobtained (since we cannot obtain a result in which the errours\nvanish) by making, not the _Errours_ themselves, but the _Sum of\ntheir Squares_, of the _smallest_ possible amount.\n\n14. An example may illustrate this. Let a quantity which is known to\nincrease uniformly, (as the distance of a star from the meridian at\nsuccessive instants,) be measured at equal intervals of time, and be\nfound to be successively 4, 12, 14. It is plain, upon the face of\nthese observations, that they are erroneous; for they ought to form\nan arithmetical progression, but they deviate widely from such a\nprogression. But the question then occurs, what arithmetical\nprogression do they _most probably_ represent: for we may assume\nseveral arithmetical progressions which more or less approach the\nobserved series; as for instance, these three; 4, 9, 14; 6, 10, 14;\n5, 10, 15. Now in order to see the claims of each of these to the\ntruth, we may tabulate them thus.\n\n Sums of Sums of Squares\nObservation 4, 12, 14 Errours Errours. of Errours.\nSeries (1) 4, 9, 14 0, 3, 0 3 9\n \" (2) 6, 10, 14 2, 2, 0 4 8\n \" (3) 5, 10, 15 1, 2, 1 4 6\n\nHere, although the first series gives the sum of the {216} errours\nless than the others, the third series gives the sum of the squares\nof the errours least; and is therefore, by the proposition on which\nthis Method depends, the _most probable_ series of the three.\n\nThis Method, in more extensive and complex cases, is a great aid to\nthe calculator in his inferences from facts, and removes much that\nis arbitrary in the Method of Means.\n\n\nSECT. IV.--_The Method of Residues._\n\n15. By either of the preceding Methods we obtain, from observed\nfacts, such Laws as readily offer themselves; and by the Laws thus\ndiscovered, the most prominent changes of the observed quantities\nare accounted for. But in many cases we have, as we have noticed\nalready, _several_ Laws of nature operating at the same time, and\ncombining their influences to modify those quantities which are the\nsubjects of observation. In these cases we may, by successive\napplications of the Methods already pointed out, detect such Laws\none after another: but this successive process, though only a\nrepetition of what we have already described, offers some peculiar\nfeatures which make it convenient to consider it in a separate\nSection, as the Method of Residues.\n\n16. When we have, in a series of changes of a variable quantity,\ndiscovered _one_ Law which the changes follow, detected its\nArgument, and determined its Magnitude, so as to explain most\nclearly the course of observed facts, we may still find that the\nobserved changes are not fully accounted for. When we compare the\nresults of our Law with the observations, there may be a difference,\nor as we may term it, a _Residue_, still unexplained. But this\nResidue being thus detached from the rest, may be examined and\nscrutinized in the same manner as the whole observed quantity was\ntreated at first: and we may in this way detect in _it_ also a Law\nof change. If we can do this, we must accommodate this new found Law\nas nearly as possible to the Residue to which it belongs; and {217}\nthis being done, the difference of our Rule and of the Residue\nitself, forms a _Second Residue_. This Second Residue we may again\nbring under our consideration; and may perhaps in _it_ also discover\nsome Law of change by which its alterations may be in some measure\naccounted for. If this can be done, so as to account for a large\nportion of this Residue, the remaining unexplained part forms a\n_Third Residue_; and so on.\n\n17. This course has really been followed in various inquiries,\nespecially in those of Astronomy and Tidology. The _Equation of the\nCenter_, for the Moon, was obtained out of the _Residue_ of the\nLongitude, which remained when the _Mean Anomaly_ was taken away.\nThis Equation being applied and disposed of, the _Second Residue_\nthus obtained, gave to Ptolemy the _Evection_. The _Third Residue_,\nleft by the Equation of the Center and the Evection, supplied to\nTycho the _Variation_ and the _Annual Equation_. And the Residue,\nremaining from these, has been exhausted by other Equations, of\nvarious arguments, suggested by theory or by observation. In this\ncase, the successive generations of astronomers have gone on, each\nin its turn executing some step in this Method of Residues. In the\nexamination of the Tides, on the other hand, this method has been\napplied systematically and at once. The observations readily gave\nthe _Semimensual Inequality_; the _Residue_ of this supplied the\ncorrections due to the Moon's _Parallax_ and _Declination_; and when\nthese were determined, the _remaining Residue_ was explored for the\nlaw of the Solar Correction.\n\n18. In a certain degree, the Method of Residues and the Method of\nMeans are _opposite_ to each other. For the Method of Residues\nextricates Laws from their combination, _bringing them into view in\nsuccession_; while the Method of Means discovers each Law, not by\nbringing the others into view, but by _destroying their effect_\nthrough an accumulation of observations. By the Method of Residues\nwe should _first_ extract the Law of the Parallax Correction of the\nTides, and _then_, from the Residue left by this, obtain the\nDeclination Correction. But we might at once employ the Method {218}\nof Means, and put together all the cases in which the Declination\nwas the same; not allowing for the Parallax in each case, but taking\nfor granted that the Parallaxes belonging to the same Declination\nwould neutralize each other; as many falling above as below the mean\nParallax. In cases like this, where the Method of Means is not\nimpeded by a partial coincidence of the Arguments of different\nunknown Inequalities, it may be employed with almost as much success\nas the Method of Residues. But still, when the Arguments of the Laws\nare clearly known, as in this instance, the Method of Residues is\nmore clear and direct, and is the rather to be recommended.\n\n19. If for example, we wish to learn whether the Height of the\nBarometer exerts any sensible influence on the Height of the Sea's\nSurface, it would appear that the most satisfactory mode of\nproceeding, must be to subtract, in the first place, what we know to\nbe the effects of the Moon's Age, Parallax and Declination, and\nother ascertained causes of change; and to search in the\n_unexplained Residue_ for the effects of barometrical pressure. The\ncontrary course has, however, been adopted, and the effect of the\nBarometer on the ocean has been investigated by the direct\napplication of the Method of Means, classing the observed heights of\nthe water according to the corresponding heights of the Barometer\nwithout any previous reduction. In this manner, the suspicion that\nthe tide of the sea is affected by the pressure of the atmosphere,\nhas been confirmed. This investigation must be looked upon as a\nremarkable instance of the efficacy of the Method of Means, since\nthe amount of the barometrical effect is much smaller than the other\nchanges from among which it was by this process extricated. But an\napplication of the Method of Residues would still be desirable on a\nsubject of such extent and difficulty.\n\n20. Sir John Herschel, in his _Discourse on the Study of Natural\nPhilosophy_ (Articles 158-161), has pointed out the mode of making\ndiscoveries by studying Residual Phenomena; and has given several\nillustrations of the process. In some of these, he has also {219}\nconsidered this method in a wider sense than we have done; treating\nit as not applicable to quantity only, but to properties and\nrelations of different kinds.\n\nWe likewise shall proceed to offer a few remarks on Methods of\nInduction applicable to other relations than those of quantity.\n\n\n\n{{220}}\nCHAPTER VIII.\n\nMETHODS OF INDUCTION DEPENDING ON RESEMBLANCE.\n\n\nAPHORISM XLIX.\n\nThe Law of Continuity _is this:--that a quantity cannot pass from\none amount to another by any change of conditions, without passing\nthrough all intermediate magnitudes according to the intermediate\nconditions. This Law may often be employed to disprove distinctions\nwhich have no real foundation._\n\nAPHORISM L.\n\nThe Method of Gradation _consists in taking a number of stages of a\nproperty in question, intermediate between two extreme cases which\nappear to be different. This Method is employed to determine whether\nthe extreme cases are really distinct or not._\n\nAPHORISM LI.\n\n_The Method of Gradation, applied to decide the question, whether the\nexisting_ geological _phenomena arise from existing causes, leads to\nthis result:--That the phenomena do appear to arise from Existing\nCauses, but that the action of existing causes may, in past times,\nhave transgressed, to any extent, their_ recorded _limits of\nintensity._\n\nAPHORISM LII.\n\nThe Method of Natural Classification _consists in classing cases,\nnot according to any_ assumed _Definition, but according to the\nconnexion of the facts themselves, so as to make them the means of\nasserting general truths._ {221}\n\n\nSECT. I.--_The Law of Continuity._\n\n1. THE Law of Continuity is applicable to quantity primarily, and\ntherefore might be associated with the methods treated of in the\nlast chapter: but inasmuch as its inferences are made by a\ntransition from one degree to another among contiguous cases, it\nwill be found to belong more properly to the Methods of Induction of\nwhich we have now to speak.\n\nThe _Law of Continuity_ consists in this proposition,--That a\nquantity cannot pass from one amount to another by any change of\nconditions, without passing through all intermediate degrees of\nmagnitude according to the intermediate conditions. And this law may\noften be employed to correct inaccurate inductions, and to reject\ndistinctions which have no real foundation in nature. For example,\nthe Aristotelians made a distinction between motions according to\nnature, (as that of a body falling vertically downwards,) and\nmotions contrary to nature, (as that of a body moving along a\nhorizontal plane:) the former, they held, became naturally quicker\nand quicker, the latter naturally slower and slower. But to this it\nmight be replied, that a horizontal line may pass, by gradual\nmotion, through various inclined positions, to a vertical position:\nand thus the retarded motion may pass into the accelerated; and\nhence there must be some inclined plane on which the motion\ndownwards is naturally uniform: which is false, and therefore the\ndistinction of such kinds of motion is unfounded. Again, the proof\nof the First Law of Motion depends upon the Law of Continuity: for\nsince, by diminishing the resistance to a body moving on a\nhorizontal plane, we diminish the retardation, and this without\nlimit, the law of continuity will bring us at the same time to the\ncase of no resistance and to the case of no retardation.\n\n2. The Law of Continuity is asserted by Galileo in a particular\napplication; and the assertion which it {222} suggests is by him\nreferred to Plato;--namely[36\\3] that a moveable body cannot pass\nfrom rest to a determinate degree of velocity without passing\nthrough all smaller degrees of velocity. This law, however, was\nfirst asserted in a more general and abstract form by\nLeibnitz[37\\3]: and was employed by him to show that the laws of\nmotion propounded by Descartes must be false. The Third Cartesian\nLaw of Motion was this[38\\3]: that when one moving body meets\nanother, if the first body have a less momentum than the second, it\nwill be reflected with its whole motion: but if the first have a\ngreater momentum than the second, it will lose a part of its motion,\nwhich it will transfer to the second. Now each of these cases leads,\nby the Law of Continuity, to the case in which the two bodies have\n_equal_ momentums: but in this case, by the first part of the law the\nbody would _retain all_ its motion; and by the second part of the law\nit would _lose_ a portion of it: hence the Cartesian Law is false.\n\n[Note 36\\3: _Dialog._ iii. 150. iv. 32.]\n\n[Note 37\\3: _Opera_, i. 366.]\n\n[Note 38\\3: Cartes, _Prin._ p. 35.]\n\n3. I shall take another example of the application of this Law from\nProfessor Playfair's Dissertation on the History of Mathematical and\nPhysical Science[39\\3]. 'The Academy of Sciences at Paris having (in\n1724) proposed, as a Prize Question, the Investigation of the Laws\nof the Communication of Motion, John Bernoulli presented an Essay on\nthe subject very ingenious and profound; in which, however, he\ndenied the existence of hard bodies, because in the collision of\nsuch bodies, a finite change of motion must take place in an\ninstant: an event which, on the principle just explained, he\nmaintained to be impossible.' And this reasoning was justifiable:\nfor we can form a _continuous_ transition from cases in which the\nimpact manifestly occupies a finite time, (as when we strike a large\nsoft body) to cases in which it is apparently instantaneous.\nMaclaurin and others are disposed, in order to avoid the conclusion\nof Bernoulli, to reject the Law of {223} Continuity. This, however,\nwould not only be, as Playfair says, to deprive ourselves of an\nauxiliary, commonly useful though sometimes deceptive; but what is\nmuch worse, to acquiesce in false propositions, from the want of\nclear and patient thinking. For the Law of Continuity, when rightly\ninterpreted, is _never_ violated in actual fact. There are not\nreally any such bodies as have been termed _perfectly hard_: and if\nwe approach towards such cases, we must learn the laws of motion\nwhich rule them by attending to the Law of Continuity, not by\nrejecting it.\n\n[Note 39\\3: In the _Encyc. Brit._ p. 537.]\n\n4. Newton used the Law of Continuity to suggest, but not to prove,\nthe doctrine of universal gravitation. Let, he said, a terrestrial\nbody be carried as high as the moon: will it not still fall to the\nearth? and does not the moon fall by the same force[40\\3]? Again: if\nany one says that there is a material ether which does not\ngravitate[41\\3], this kind of matter, by condensation, may be\ngradually transmuted to the density of the most intensely\ngravitating bodies: and these gravitating bodies, by taking the\ninternal texture of the condensed ether, may cease to gravitate; and\nthus the weight of bodies depends, not on their quantity of matter,\nbut on their texture; which doctrine Newton conceived he had\ndisproved by experiment.\n\n[Note 40\\3: _Principia_, lib. iii. prop. 6.]\n\n[Note 41\\3: _Ib._ cor. 2.]\n\n5. The evidence of the Law of Continuity resides in the universality\nof those Ideas, which enter into our apprehension of Laws of Nature.\nWhen, of two quantities, one depends upon the other, the Law of\nContinuity necessarily governs this dependence. Every philosopher\nhas the power of applying this law, in proportion as he has the\nfaculty of apprehending the Ideas which he employs in his induction,\nwith the same clearness and steadiness which belong to the\nfundamental ideas of Quantity, Space and Number. To those who\npossess this faculty, the Law is a Rule of very wide and decisive\napplication. Its use, as has appeared in the above examples, is seen\nrather in the disproof of erroneous views, and in the correction of\nfalse propositions, {224} than in the invention of new truths. It is\na test of truth, rather than an instrument of discovery.\n\nMethods, however, approaching very near to the Law of Continuity may\nbe employed as positive means of obtaining new truths; and these I\nshall now describe.\n\n\nSECT. II.--_The Method of Gradation._\n\n6. To gather together the cases which resemble each other, and to\nseparate those which are essentially distinct, has often been\ndescribed as the main business of science; and may, in a certain\nloose and vague manner of speaking, pass for a description of some\nof the leading procedures in the acquirement of knowledge. The\nselection of instances which agree, and of instances which differ,\nin some prominent point or property, are important steps in the\nformation of science. But when classes of things and properties have\nbeen established in virtue of such comparisons, it may still be\ndoubtful whether these classes are separated by distinctions of\nopposites, or by differences of degree. And to settle such\nquestions, the _Method of Gradation_ is employed; which consists in\ntaking intermediate stages of the properties in question, so as to\nascertain by experiment whether, in the transition from one class to\nanother, we have to leap over a manifest gap, or to follow a\ncontinuous road.\n\n7. Thus for instance, one of the early _Divisions_ established by\nelectrical philosophers was that of _Electrics_ and _Conductors_.\nBut this division Dr. Faraday has overturned as an essential\nopposition. He takes[42\\3] a _Gradation_ which carries him from\nConductors to Non-conductors. Sulphur, or Lac, he says, are held to\nbe non-conductors, but are not rigorously so. Spermaceti is a bad\nconductor: ice or water better than spermaceti: metals so much\nbetter that they are put in a different class. But even in metals\nthe transit of the electricity is not instantaneous: we have in them\nproof of a retardation of the electric current: 'and what {225}\nreason,\" Mr. Faraday asks, \"why this retardation should not be of\nthe same kind as that in spermaceti, or in lac, or sulphur? But as,\nin them, retardation is insulation, [and insulation is\ninduction[43\\3]] why should we refuse the same relation to the same\nexhibitions of force in the metals?\"\n\n[Note 42\\3: _Researches_, 12th series, art. 1328.]\n\n[Note 43\\3: These words refer to another proposition, also\nestablished by the Method of Gradation.]\n\nThe process employed by the same sagacious philosopher to show the\n_identity_ of Voltaic and Franklinic electricity, is another example\nof the same kind[44\\3]. Machine [Franklinic] electricity was made to\nexhibit the same phenomena as Voltaic electricity, by causing the\ndischarge to pass through a bad conductor, into a very extensive\ndischarging train: and thus it was clearly shown that Franklinic\nelectricity, not so conducted, differs from the other kinds, only in\nbeing in a state of successive tension and explosion instead of a\nstate of continued current.\n\n[Note 44\\3: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 2.]\n\nAgain; to show that the decomposition of bodies in the Voltaic\ncircuit was not due to the _Attraction_ of the Poles[45\\3], Mr.\nFaraday devised a beautiful series of experiments, in which these\nsupposed _Poles_ were made to assume all possible electrical\nconditions:--in some cases the decomposition took place against air,\nwhich according to common language is not a conductor, nor is\ndecomposed;--in others, against the metallic poles, which are\nexcellent conductors but undecomposable;--and so on: and hence he\ninfers that the decomposition cannot justly be considered as due to\nthe Attraction, or Attractive Powers, of the Poles.\n\n[Note 45\\3: _Ibid. Researches_, art. 497.]\n\n8. The reader of the _Novum Organon_ may perhaps, in looking at such\nexamples of the Rule, be reminded of some of Bacon's Classes of\nInstances, as his _instanti\u00e6 absenti\u00e6 in proximo_, and his\n_instanti\u00e6 migrantes_. But we may remark that Instances classed and\ntreated as Bacon recommends in those parts of his work, could hardly\nlead to scientific truth. His {226} processes are vitiated by his\nproposing to himself the _form_ or _cause_ of the property before\nhim, as the object of his inquiry; instead of being content to\nobtain, in the first place, the _law of phenomena_. Thus his\nexample[46\\3] of a Migrating Instance is thus given. \"Let the\n_Nature inquired into_ be that of Whiteness; an Instance Migrating\nto the production of this property is glass, first whole, and then\npulverized; or plain water, and water agitated into a foam; for\nglass and water are transparent, and not white; but glass powder and\nfoam are white, and not transparent. Hence we must inquire what has\nhappened to the glass or water in that Migration. For it is plain\nthat the _Form of Whiteness_ is conveyed and induced by the crushing\nof the glass and shaking of the water.\" No real knowledge has\nresulted from this line of reasoning:--from taking the Natures and\nForms of things and of their qualities for the primary subject of\nour researches.\n\n[Note 46\\3: _Nov. Org._ lib. ii. Aph. 28.]\n\n9. We may easily give examples from other subjects in which the\nMethod of Gradation has been used to establish, or to endeavour to\nestablish, very extensive propositions. Thus Laplace's Nebular\nHypothesis,--that systems like our solar system are formed by\ngradual condensation from diffused masses, such as the nebul\u00e6 among\nthe stars,--is founded by him upon an application of this Method of\nGradation. We see, he conceives, among these nebul\u00e6, instances of\nall degrees of condensation, from the most loosely diffused fluid,\nto that separation and solidification of parts by which suns, and\nsatellites, and planets are formed: and thus we have before us\ninstances of systems in all their stages; as in a forest we see\ntrees in every period of growth. How far the examples in this case\nsatisfy the demands of the Method of Gradation, it remains for\nastronomers and philosophers to examine.\n\nAgain; this method was used with great success by Macculloch and\nothers to refute the opinion, put in currency by the Wernerian\nschool of geologists, that {227} the rocks called _trap rocks_ must\nbe classed with those to which a _sedimentary_ origin is ascribed.\nFor it was shown that a gradual _transition_ might be traced from\nthose examples in which trap rocks most resembled stratified rocks,\nto the lavas which have been recently ejected from volcanoes: and\nthat it was impossible to assign a different origin to one portion,\nand to the other, of this kind of mineral masses; and as the\nvolcanic rocks were certainly not sedimentary, it followed, that the\ntrap rocks were not of that nature.\n\nAgain; we have an attempt of a still larger kind made by Sir C.\nLyell, to apply this Method of Gradation so as to disprove all\ndistinction between the causes by which geological phenomena have\nbeen produced, and the causes which are now acting at the earth's\nsurface. He has collected a very remarkable series of changes which\nhave taken place, and are still taking place, by the action of\nwater, volcanoes, earthquakes, and other terrestrial operations; and\nhe conceives he has shown in these a _gradation_ which leads, with\nno wide chasm or violent leap, to the state of things of which\ngeological researches have supplied the evidence.\n\n10. Of the value of this Method in geological speculations, no doubt\ncan be entertained. Yet it must still require a grave and profound\nconsideration, in so vast an application of the Method as that\nattempted by Sir C. Lyell, to determine what extent we may allow to\nthe steps of our _gradation_; and to decide how far the changes\nwhich have taken place in distant parts of the series may exceed\nthose of which we have historical knowledge, without ceasing to be\nof the _same kind_. Those who, dwelling in a city, see, from time to\ntime, one house built and another pulled down, may say that such\n_existing causes_, operating through past time, sufficiently explain\nthe existing condition of the city. Yet we arrive at important\npolitical and historical truths, by considering the _origin_ of a\ncity as an event of a _different order_ from those daily changes.\nThe causes which are now working to produce geological results, may\nbe supposed to have been, at some former epoch, so far exaggerated\nin their operation, that the changes {228} should be paroxysms, not\ndegrees;--that they should violate, not continue, the gradual\nseries. And we have no kind of evidence whether the duration of our\nhistorical times is sufficient to give us a just measure of the\nlimits of such degrees;--whether the terms which we have under our\nnotice enable us to ascertain the average rate of progression.\n\n11. The result of such considerations seems to be this:--that we may\napply the Method of Gradation in the investigation of geological\ncauses, provided we leave the Limits of the Gradation undefined.\nBut, then, this is equivalent to the admission of the opposite\nhypothesis: for a continuity of which the successive intervals are\nnot limited, is not distinguishable from discontinuity. The\ngeological sects of recent times have been distinguished as\n_uniformitarians_ and _catastrophists_: the Method of Gradation\nseems to prove the doctrine of the uniformitarians; but then, at the\nsame time that it does this, it breaks down the distinction between\nthem and the catastrophists.\n\nThere are other exemplifications of the use of gradations in Science\nwhich well deserve notice: but some of them are of a kind somewhat\ndifferent, and may be considered under a separate head.\n\n\nSECT. III. _The Method of Natural Classification._\n\n12. The Method of Natural Classification consists, as we have seen,\nin grouping together objects, not according to any selected\nproperties, but according to their most important resemblances; and\nin combining such grouping with the assignation of certain marks of\nthe classes thus formed. The examples of the successful application\nof this method are to be found in the Classificatory Sciences\nthrough their whole extent; as, for example, in framing the Genera\nof plants and animals. The same method, however, may often be\nextended to other sciences. Thus the classification of Crystalline\nForms, according to their Degree of Symmetry, (which is really an\nimportant distinction,) as introduced by Mohs and Weiss, was a great\nimprovement {229} upon Ha\u00fcy's arbitrary division according to\ncertain assumed primary forms. Sir David Brewster was led to the\nsame distinction of crystals by the study of their optical\nproperties; and the scientific value of the classification was thus\nstrongly exhibited. Mr. Howard's classification of Clouds appears to\nbe founded in their real nature, since it enables him to express the\nlaws of their changes and successions. As we have elsewhere said,\nthe criterion of a true classification is, that it makes general\npropositions possible. One of the most prominent examples of the\nbeneficial influence of a right classification, is to be seen in the\nimpulse given to geology by the distinction of strata according to\nthe organic fossils which they contain[47\\3]: which, ever since its\ngeneral adoption, has been a leading principle in the speculations\nof geologists.\n\n[Note 47\\3: _Hist. Ind. Sc._ b. xviii. c. ii. sect. 3.]\n\n13. The mode in which, in this and in other cases, the Method of\nNatural Classification directs the researches of the philosopher, is\nthis:--his arrangement being adopted, at least as an instrument of\ninquiry and trial, he follows the course of the different members of\nthe classification, according to the guidance which Nature herself\noffers; not prescribing beforehand the marks of each part, but\ndistributing the facts according to the total resemblances, or\naccording to those resemblances which he finds to be most important.\nThus, in tracing the course of a series of strata from place to\nplace, we identify each stratum, not by any single character, but by\nall taken together;--texture, colour, fossils, position, and any\nother circumstances which offer themselves. And if, by this means,\nwe come to ambiguous cases, where different indications appear to\npoint different ways, we decide so as best to preserve undamaged\nthose general relations and truths which constitute the value of our\nsystem. Thus although we consider the organic fossils in each\nstratum as its most important characteristic, we are not prevented,\nby the disappearance of some fossils, or the addition of others, or\nby the total absence of fossils, {230} from identifying strata in\ndistant countries, if the position and other circumstances authorize\nus to do so. And by this Method of Classification, the doctrine of\n_Geological Equivalents_[48\\3] has been applied to a great part of\nEurope.\n\n[Note 48\\3: _Hist. Ind. Sc._ b. xviii. c. iii. sect. 4.]\n\n14. We may further observe, that the same method of natural\nclassification which thus enables us to identify strata in remote\nsituations, notwithstanding that there may be great differences in\ntheir material and contents, also forbids us to assume the identity\nof the series of rocks which occur in different countries, when this\nidentity has not been verified by such a continuous exploration of\nthe component members of the series. It would be in the highest\ndegree unphilosophical to apply the special names of the English or\nGerman strata to the rocks of India, or America, or even of southern\nEurope, till it has appeared that in those countries the geological\nseries of northern Europe really exists. In each separate country,\nthe divisions of the formations which compose the crust of the earth\nmust be made out, by applying the Method of Natural Arrangement _to\nthat particular case_, and not by arbitrarily extending to it the\nnomenclature belonging to another case. It is only by such\nprecautions, that we can ever succeed in obtaining geological\npropositions, at the same time true and comprehensive; or can obtain\nany sound general views respecting the physical history of the\nearth.\n\n15. The Method of Natural Classification, which we thus recommend,\nfalls in with those mental habits which we formerly described as\nresulting from the study of Natural History. The method was then\ntermed the _Method of Type_, and was put in opposition to the\n_Method of Definition_.\n\nThe Method of Natural Classification is directly opposed to the\nprocess in which we assume and apply _arbitrary_ definitions; for in\nthe former Method, we find our classes in nature, and do not make\nthem by marks of our own imposition. Nor can any advantage {231} to\nthe progress of knowledge be procured, by laying down our characters\nwhen our arrangements are as yet quite loose and unformed. Nothing\nwas gained by the attempts to _define_ Metals by their weight, their\nhardness, their ductility, their colour; for to all these marks, as\nfast as they were proposed, exceptions were found, among bodies\nwhich still could not be excluded from the list of Metals. It was\nonly when elementary substances were divided into _Natural Classes_,\nof which classes Metals were one, that a true view of their\ndistinctive characters was obtained. Definitions in the outset of\nour examination of nature are almost always, not only useless, but\nprejudicial.\n\n16. When we obtain a Law of Nature by induction from phenomena, it\ncommonly happens, as we have already seen, that we introduce, at the\nsame time, a Proposition and a Definition. In this case, the two are\ncorrelative, each giving a real value to the other. In such cases,\nalso, the Definition, as well as the Proposition, may become the\nbasis of rigorous reasoning, and may lead to a series of deductive\ntruths. We have examples of such Definitions and Propositions in the\nLaws of Motion, and in many other cases.\n\n17. When we have established Natural Classes of objects, we seek for\nCharacters of our classes; and these Characters may, to a certain\nextent, be called the _Definitions_ of our classes. This is to be\nunderstood, however, only in a limited sense: for these Definitions\nare not absolute and permanent. They are liable to be modified and\nsuperseded. If we find a case which manifestly belongs to our\nNatural Class, though violating our Definition, we do not shut out\nthe case, but alter our definition. Thus, when we have made it part\nof our Definition of the _Rose_ family, that they have _alternate\nstipulate leaves_, we do not, therefore, exclude from the family the\ngenus _Low\u00e6a_, which has _no stipul\u00e6_. In Natural Classifications,\nour Definitions are to be considered as temporary and provisional\nonly. When Sir C. Lyell established the distinctions of the tertiary\nstrata, which he termed _Eocene_, _Miocene_, and _Pliocene_, he took\na numerical criterion {232} (the proportion of recent species of\nshells contained in those strata) as the basis of his division. But\nnow that those kinds of strata have become, by their application to\na great variety of cases, a series of Natural Classes, we must, in\nour researches, keep in view the natural connexion of the formations\nthemselves in different places; and must by no means allow ourselves\nto be governed by the numerical proportions which were originally\ncontemplated; or even by any amended numerical criterion equally\narbitrary; for however amended, Definitions in natural history are\nnever immortal. The etymologies of _Pliocene_ and _Miocene_ may,\nhereafter, come to have merely an historical interest; and such a\nstate of things will be no more inconvenient, provided the natural\nconnexions of each class are retained, than it is to call a rock\n_oolite_ or _porphyry_, when it has no roelike structure and no\nfiery spots.\n\nThe Methods of Induction which are treated of in this and the\npreceding chapter, and which are specially applicable to causes\ngoverned by relations of Quantity or of Resemblance, commonly lead\nus to _Laws of Phenomena_ only. Inductions founded upon other ideas,\nthose of Substance and Cause for example, appear to conduct us\nsomewhat further into a knowledge of the essential nature and real\nconnexions of things. But before we speak of these, we shall say a\nfew words respecting the way in which inductive propositions, once\nobtained, may be verified and carried into effect by their\napplication.\n\n\n\n{{233}}\nCHAPTER IX.\n\nOF THE APPLICATION OF INDUCTIVE TRUTHS.\n\n\nAPHORISM LIII.\n\n_When the theory of any subject is established, the observations and\nexperiments which are made in applying the science to use and to\ninstruction, supply a perpetual_ verification _of the theory._\n\nAPHORISM LIV.\n\n_Such observations and experiments, when numerous and accurate,\nsupply also_ corrections _of the_ constants _involved in the theory;\nand sometimes_, (_by the Method of Residues_,) additions _to the\ntheory._\n\nAPHORISM LV.\n\n_It is worth considering, whether a continued and connected system\nof observation and calculation, like that of astronomy, might not be\nemployed with advantage in improving our knowledge of other\nsubjects; as Tides, Currents, Winds, Clouds, Rain, Terrestrial\nMagnetism, Aurora Borealis, Composition of Crystals, and many other\nsubjects._\n\nAPHORISM LVI.\n\n_An_ extension _of a well-established theory to the explanation of\nnew facts excites admiration as a discovery; but it is a discovery\nof a lower order than the theory itself._\n\nAPHORISM LVII.\n\n_The practical inventions which are most important in Art may be\neither unimportant parts of Science, or results not explained by\nScience._ {234}\n\nAPHORISM LVIII.\n\n_In modern times, in many departments. Art is constantly guided,\ngoverned and advanced by Science._\n\nAPHORISM LIX.\n\n_Recently several New Arts have been invented, which may be regarded\nas notable verifications of the anticipations of material benefits to\nbe derived to man from the progress of Science._\n\n\n1. BY the application of inductive truths, we here mean, according\nto the arrangement given in chap. I. of this book, those steps,\nwhich in the natural order of science, follow the discovery of each\ntruth. These steps are, the _verification_ of the discovery by\nadditional experiments and reasonings, and its _extension_ to new\ncases, not contemplated by the original discoverer. These processes\noccupy that period, which, in the history of each great discovery,\nwe have termed the _Sequel_ of the epoch; as the collection of\nfacts, and the elucidation of conceptions, form its Prelude.\n\n2. It is not necessary to dwell at length on the processes of the\nVerification of Discoveries. When the Law of Nature is once stated,\nit is far easier to devise and execute experiments which prove it,\nthan it was to discern the evidence before. The truth becomes one of\nthe standard doctrines of the science to which it belongs, and is\nverified by all who study or who teach the science experimentally.\nThe leading doctrines of Chemistry are constantly exemplified by\neach chemist in his _Laboratory_; and an amount of verification is\nthus obtained of which books give no adequate conception. In\nAstronomy, we have a still stronger example of the process of\nverifying discoveries. Ever since the science assumed a systematic\nform, there have been _Observatories_, in which the consequences of\nthe theory were habitually compared with the results of observation.\nAnd to facilitate this comparison, _Tables_ of great extent have\nbeen calculated, with immense labour, from each theory, showing the\nplace which the {235} theory assigned to the heavenly bodies at\nsuccessive times; and thus, as it were, challenging nature to deny\nthe truth of the discovery. In this way, as I have elsewhere stated,\nthe continued prevalence of an errour in the systematic parts of\nastronomy is impossible[49\\3]. An errour, if it arise, makes its way\ninto the tables, into the ephemeris, into the observer's nightly\nlist, or his sheet of reductions; the evidence of sense flies in its\nface in a thousand Observatories; the discrepancy is traced to its\nsource, and soon disappears for ever.\n\n[Note 49\\3: _Hist. Ind. Sc._ b. vii. c. vi. sect. 6.]\n\n3. In these last expressions, we suppose the theory, not only to be\ntested, but also to be _corrected_ when it is found to be imperfect.\nAnd this also is part of the business of the observing astronomer.\nFrom his accumulated observations, he deduces more exact values than\nhad previously been obtained, of the _Constants_ or _Coefficients_\nof these Inequalities of which the _Argument_ is already known. This\nhe is enabled to do by the methods explained in the fifth chapter of\nthis book; the Method of Means, and especially the Method of Least\nSquares. In other cases, he finds, by the Method of Residues, some\nnew Inequality; for if no change of the Coefficients will bring the\nTables and the observation to a coincidence, he knows that a new\nTerm is wanting in his formula. He obtains, as far as he can, the\nlaw of this unknown Term; and when its existence and its law have\nbeen fully established, there remains the task of tracing it to its\ncause.\n\n4. The condition of the science of Astronomy, with regard to its\nsecurity and prospect of progress, is one of singular felicity. It\nis a question well worth our consideration, as regarding the\ninterests of science, whether, in other branches of knowledge also,\n_a continued and corrected system, of observation and calculation_,\nimitating the system employed by astronomers, might not be adopted.\nBut the discussion of this question would involve us in a digression\ntoo wide for the present occasion. {236}\n\n5. There is another mode of application of true theories after their\ndiscovery, of which we must also speak; I mean the process of\nshowing that facts, not included in the original induction, and\napparently of a different kind, are explained by reasonings founded\nupon the theory:--_extensions_ of the theory as we may call them.\nThe history of physical astronomy is full of such events. Thus after\nBradley and Wargentin had observed a certain cycle among the\nperturbations of Jupiter's satellites, Laplace explained this cycle\nby the doctrine of universal gravitation[50\\3]. The long inequality\nof Jupiter and Saturn, the diminution of the obliquity of the\necliptic, the acceleration of the moon's mean motion, were in like\nmanner accounted for by Laplace. The coincidence of the nodes of the\nmoon's equator with those of her orbit was proved to result from\nmechanical principles by Lagrange. The motions of the\nrecently-discovered planets, and of comets, shown by various\nmathematicians to be in exact accordance with the theory, are\nVerifications and Extensions still more obvious.\n\n[Note 50\\3: _Hist. Ind. Sc._ b. vii. c. iv. sect. 3.]\n\n6. In many of the cases just noticed, the consistency between the\ntheory, and the consequences thus proved to result from it, is so\nfar from being evident, that the most consummate command of all the\npowers and aids of mathematical reasoning is needed, to enable the\nphilosopher to arrive at the result. In consequence of this\ncircumstance, the labours just referred to, of Laplace, Lagrange,\nand others, have been the object of very great and very just\nadmiration. Moreover, the necessary connexion of new facts, at first\ndeemed inexplicable, with principles already known to be true;--a\nconnexion utterly invisible at the outset, and yet at last\nestablished with the certainty of demonstration;--strikes us with\nthe delight of a new discovery; and at first sight appears no less\nadmirable than an original induction. Accordingly, men sometimes\nappear tempted to consider Laplace and other great mathematicians as\npersons of a kindred genius to Newton. We must not {237} forget,\nhowever, that there is a great and essential difference between\ninductive and deductive processes of the mind. The discovery of a\n_new_ theory, which is true, is a step widely distinct from any mere\ndevelopment of the consequences of a theory already invented and\nestablished.\n\n7. In the other sciences also, which have been framed by a study of\nnatural phenomena, we may find examples of the explanation of new\nphenomena by applying the principles of the science when once\nestablished. Thus, when the laws of the reflection and refraction of\nlight had been established, a new and poignant exemplification of\nthem was found in the explanation of the Rainbow by the reflection\nand refraction of light in the spherical drops of a shower; and\nagain, another, no less striking, when the intersecting Luminous\nCircles and Mock Suns, which are seen in cold seasons, were\ncompletely explained by the hexagonal crystals of ice which float in\nthe upper regions of the atmosphere. The Darkness of the space\nbetween the primary and secondary rainbow is another appearance\nwhich optical theory completely explains. And when we further\ninclude in our optical theory the doctrine of interferences, we find\nthe explanation of other phenomena; for instance, the Supernumerary\nRainbows which accompany the primary rainbow on its inner side, and\nthe small Halos which often surround the sun and moon. And when we\ncome to optical experiments, we find many instances in which the\ndoctrine of interferences and of undulations have been applied to\nexplain the phenomena by calculations almost as complex as those\nwhich we have mentioned in speaking of astronomy: with results as\nlittle foreseen at first and as entirely satisfactory in the end.\nSuch are Schwerdt's explanation of the diffracted images of a\ntriangular aperture by the doctrine of interferences, and the\nexplanation of the coloured Lemniscates seen by polarized light in\nbiaxal crystals, given by Young and by Herschel: and still more\nmarked is another case, in which the curves are unsymmetrical,\nnamely, the curves seen by passing polarized {238} light through\nplates of quartz, which agree in a wonderful manner with the\ncalculations of Airy. To these we may add the curious phenomena, and\nequally curious mathematical explanation, of Conical Refraction, as\nbrought to view by Professor Lloyd and Sir W. Hamilton. Indeed, the\nwhole history both of Physical Optics and of Physical Astronomy is a\nseries of _felicities_ of this kind, as we have elsewhere observed.\nSuch applications of theory, and unforeseen explanations of new\nfacts by complicated trains of reasoning necessarily flowing from\nthe theory, are strong proof of the truth of the theory, while it is\nin the course of being established; but we are here rather speaking\nof them as applications of the theory after it has been established.\n\nThose who thus apply principles already discovered are not to be\nranked in their intellectual achievements with those who discover\nnew principles; but still, when such applications are masked by the\ncomplex relations of space and number, it is impossible not to\nregard with admiration the clearness and activity of intellect which\nthus discerns in a remote region the rays of a central truth already\nunveiled by some great discoverer.\n\n8. As examples in other fields of the application of a scientific\ndiscovery to the explanation of natural phenomena, we may take the\nidentification of Lightning with electricity by Franklin, and the\nexplanation of Dew by Wells. For Wells's _Inquiry into the Cause of\nDew_, though it has sometimes been praised as an original discovery,\nwas, in fact, only resolving the phenomenon into principles already\ndiscovered. The atmologists of the last century were aware[51\\3]\nthat the vapour which exists in air in an invisible state may be\ncondensed into water by cold; and they had noticed that there is\nalways a certain temperature, lower than that of the atmosphere, to\nwhich if we depress bodies, water forms upon them in fine drops.\nThis temperature is the limit of that which is {239} necessary to\nconstitute vapour, and is hence called the _constituent\ntemperature_. But these principles were not generally familiar in\nEngland till Dr. Wells introduced them into his _Essay on Dew_,\npublished in 1814; having indeed been in a great measure led to them\nby his own experiments and reasonings. His explanation of Dew,--that\nit arises from the coldness of the bodies on which it settles,--was\nestablished with great ingenuity; and is a very elegant confirmation\nof the Theory of Constituent Temperature.\n\n[Note 51\\3:_Hist. Ind. Sc._ b. x. c. iii. sect. 5.]\n\n9. As other examples of such explanations of new phenomena by a\ntheory, we may point out Amp\u00e8re's Theory that Magnetism is\ntransverse voltaic currents, applied to explain the rotation of a\nvoltaic wire round a magnet, and of a magnet round a voltaic wire.\nAnd again, in the same subject, when it had been proved that\nelectricity might be converted into magnetism, it seemed certain\nthat magnetism might be converted into electricity; and accordingly\nFaraday found under what conditions this may be done; though indeed\nhere, the theory rather suggested the experiment than explained it\nwhen it had been independently observed. The production of an\nelectric spark by a magnet was a very striking exemplification of\nthe theory of the identity of these different polar agencies.\n\n10. In Chemistry such applications of the principles of the science\nare very frequent; for it is the chemist's business to account for\nthe innumerable changes which take place in material substances by\nthe effects of mixture, heat, and the like. As a marked instance of\nsuch an application of the science, we may take the explanation of\nthe explosive force of gunpowder[52\\3], from the conversion of its\nmaterials into gases. In Mineralogy also we have to apply the {240}\nprinciples of Chemistry to the analysis of bodies: and I may\nmention, as a case which at the time excited much notice, the\nanalysis of a mineral called Heavy Spar. It was found that different\nspecimens of this mineral differed in their crystalline angles about\nthree degrees and a half; a difference which was at variance with\nthe mineralogical discovery then recently made, of the constancy of\nthe angle of the same substance. Vauquelin solved this difficulty by\ndiscovering that the crystals with the different angles were really\nminerals chemically different; the one kind being sulphate of\nbarytes, and the other, sulphate of strontian.\n\n[Note 52\\3: The explanation is, that the force is due to the sudden\ndevelopment of a large volume of nitrogen and carbonic acid gases,\nwhich at the ordinary temperature of the air would occupy a space\nequal to about 300 times the bulk of the powder used, but from the\nintense heat developed at the moment of the explosion, the\ndilatation amounts to at least 1500 times the volume of the\ngunpowder employed.]\n\n11. In this way a scientific theory, when once established, is\nperpetually finding new applications in the phenomena of nature; and\nthose who make such applications, though, as we have said, they care\nnot to be ranked with the great discoverers who establish theories\nnew and true, often receive a more prompt and general applause than\ngreat discoverers do; because they have not to struggle with the\nperplexity and averseness which often encounter the promulgation of\nnew truths.\n\n12. Along with the verification and extension of scientific truths,\nwe are naturally led to consider the useful application of them. The\nexample of all the best writers who have previously treated of the\nphilosophy of sciences, from Bacon to Herschel, draws our attention\nto those instances of the application of scientific truths, which\nare subservient to the uses of practical life; to the support, the\nsafety, the pleasure of man. It is well known in how large a degree\nthe furtherance of these objects constituted the merit of the _Novum\nOrganon_ in the eyes of its author; and the enthusiasm with which\nmen regard these visible and tangible manifestations of the power\nand advantage which knowledge may bring, has gone on increasing up\nto our own day. And undoubtedly such applications of the discoveries\nof science to promote the preservation, comfort, power and dignity\nof man, must always be objects of great philosophical as well as\npractical interest. Yet we may observe that those {241} practical\ninventions which are of most importance in the Arts, have not\ncommonly, in the past ages of the world, been the results of\ntheoretical knowledge, nor have they tended very greatly to the\npromotion of such knowledge. The use of bread and of wine has\nexisted from the first beginning of man's social history; yet men\nhave not had--we may question whether they yet have--a satisfactory\ntheory of the constitution and fabrication of bread and of wine.\nFrom a very early period there have been workers in metal: yet who\ncould tell upon what principles depended the purifying of gold and\nsilver by the fire, or the difference between iron and steel? In\nsome cases, as in the story of the brass produced by the Corinthian\nconflagration, some particular step in art is ascribed to a special\naccident; but hardly ever to the thoughtful activity of a scientific\nspeculator. The Dyeing of cloths, the fabrication and colouring of\nearthenware and glass vessels was carried to a very high degree of\ncompleteness; yet who had any sound theoretical knowledge respecting\nthese processes? Are not all these arts still practised with a\ndegree of skill which we can hardly or not at all surpass, by\nnations which have, properly speaking, no science? Till lately, at\nleast, if even now the case be different, the operations by which\nman's comforts, luxuries, and instruments were produced, were either\nmere practical processes, which the artist practises, but which the\nscientist cannot account for; or, as in astronomy and optics, they\ndepended upon a small portion only of the theoretical sciences, and\ndid not tend to illustrate, or lead to, any larger truths. Bacon\nmentions as recent discoveries, which gave him courage and hope with\nregard to the future progress of human knowledge, the invention of\ngunpowder, glass, and printing, the introduction of silk, and the\ndiscovery of America. Yet which of these can be said to have been\nthe results of a theoretical enlargement of human knowledge? except\nperhaps the discovery of the New World, which was in some degree the\nresult of Columbus's conviction of the globular form of the earth.\nThis, however, was not a recent, but a very ancient {242} doctrine\nof all sound astronomers. And which of these discoveries has been\nthe cause of a great enlargement of our theoretical\nknowledge?--except any one claims such a merit for the discovery of\nprinting; in which sense the result is brought about in a very\nindirect manner, in the same way in which the progress of freedom\nand of religion may be ascribed as consequences to the same\ndiscovery. However great or striking, then, such discoveries have\nbeen, they have not, generally speaking, produced any marked advance\nof the Inductive Sciences in the sense in which we here speak of\nthem. They have increased man's power, it may be: that is, his power\nof adding to his comforts and communicating with his fellow-men. But\nthey have not necessarily or generally increased his theoretical\nknowledge. And, therefore, with whatever admiration we may look upon\nsuch discoveries as these, we are not to admire them as steps in\nInductive Science.\n\nAnd on the other hand, we are not to ask of Inductive Science, as a\nnecessary result of her progress, such additions as these to man's\nmeans of enjoyment and action. It is said, with a feeling of\ntriumph, that Knowledge is Power: but in whatever sense this may\ntruly be said, we value Knowledge, not because it is Power but\nbecause it is Knowledge; and we estimate wrongly both the nature and\nthe dignity of that kind of science with which we are here\nconcerned, if we expect that every new advance in theory will\nforthwith have a market value:--that science will mark the birth of\na new Truth with some new birthday present, such as a softer stuff\nto wrap our limbs, a brighter vessel to grace our table, a new mode\nof communication with our friends and the world, a new instrument\nfor the destruction of our enemies, or a new region which may be the\nsource of wealth and interest.\n\n13. Yet though, as we have said, many of the most remarkable\nprocesses which we reckon as the triumphs of Art did not result from\na previous progress of Science, we have, at many points of the\nhistory of Science, applications of new views, to enable man to _do_\nas well {243} as to _see_. When Archimedes had obtained clear views\nof the theory of machines, he forthwith expressed them in his bold\npractical boast; 'Give me whereon to stand, and I will move the\nearth.' And his machines with which he is said to have handled the\nRoman ships like toys, and his burning mirrors with which he is\nreported to have set them on fire, are at least possible\napplications of theoretical principles. When he saw the waters\nrising in the bath as his body descended, and rushed out crying, 'I\nhave found the way;' what he had found was the solution of the\npractical question of the quantity of silver mixed with the gold of\nHiero's crown. But the mechanical inventions of Hero of Alexandria,\nwhich moved by the force of air or of steam, probably involved no\nexact theoretical notions of the properties of air or of steam. He\ndevised a toy which revolved by the action of steam; but by the\nforce of steam exerted in issuing from an orifice, not by its\npressure or condensation. And the Romans had no arts derived from\nscience in addition to those which they inherited from the Greeks.\nThey built aqueducts, not indeed through ignorance of the principles\nof hydrostatics, as has sometimes been said; for we, who know our\nhydrostatics, build aqueducts still; but their practice exemplified\nonly Archimedean hydrostatics. Their clepsydras or water-clocks were\nadjusted by trial only. They used arches and vaults more copiously\nthan the Greeks had done, but the principle of the arch appears, by\nthe most recent researches, to have been known to the Greeks. Domes\nand groined arches, such as we have in the Pantheon and in the Baths\nof Caracalla, perhaps they invented; certainly they practised them\non a noble scale. Yet this was rather practical skill than\ntheoretical knowledge; and it was pursued by their successors in the\nmiddle ages in the same manner, as practical skill rather than\ntheoretical knowledge. Thus were produced flying buttresses,\nintersecting pointed vaults, and the other wonders of medi\u00e6val\narchitecture. The engineers of the fifteenth century, as Leonardo da\nVinci, began to convert their practical into theoretical knowledge\nof Mechanics; but still {244} clocks and watches, flying machines\nand printing presses involved no new mechanical principle.\n\n14. But from this time the advances in Science generally produced,\nas their result, new inventions of a practical kind. Thus the\ndoctrine of the weight of air led to such inventions as the\nbarometer used as a Weather-glass, the Air-pump with its train of\ncurious experiments, the Diving-Bell, the Balloon. The telescope was\nperhaps in some degree a discovery due to accident, but its\nprinciples had been taught by Roger Bacon, and still more clearly by\nDescartes. Newton invented a steady thermometer by attending to\nsteady laws of nature. And in the case of the improvements of the\nsteam engine made by Watt, we have an admirable example how superior\nthe method of improving Art by Science is, to the blind gropings of\nmere practical habit.\n\nOf this truth, the history of most of the useful arts in our time\noffers abundant proofs and illustrations. All improvements and\napplications of the forces and agencies which man employs for his\npurposes are now commonly made, not by blind trial but with the\nclearest theoretical as well as practical insight which he can\nobtain, into the properties of the agents which he employs. In this\nway he has constructed, (using theory and calculation at every step\nof his construction,) steam engines, steam boats, screw-propellers,\nlocomotive engines, railroads and bridges and structures of all\nkinds. Lightning-conductors have been improved and applied to the\npreservation of buildings, and especially of ships, with admirable\neffect, by Sir Wm. Snow Harris, an experimenter who has studied with\ngreat care the theory of electricity. The measurement of the\nquantity of oxygen, that is, of vital power, in air, has been taught\nby Cavendish, and by Dr Ure a skilful chemist of our time. Methods\nfor measuring the bleaching power of a substance have been devised\nby eminent chemical philosophers, Gay Lussac and Mr Graham. Davy\nused his discoveries concerning the laws of flame in order to\nconstruct his Safety Lamp:--his discoveries concerning the galvanic\n{245} battery in order to protect ships' bottoms from corrosion. The\nskilled geologist has repeatedly given to those who were about to\ndig for coal where it could have no geological place, advice which\nhas saved them from ruinous expence. Sir Roderick Murchison, from\ngeological evidence, declared the likelihood of gold being found\nabundantly in Australia, many years before the diggings began.\n\nEven the subtle properties of light as shewn in the recent\ndiscoveries of its interference and polarization, have been applied\nto useful purposes. Young invented an _Eriometer_, an instrument\nwhich should measure the fineness of the threads of wool by the\ncoloured fringes which they produce; and substances which it is\nimportant to distinguish in the manufacture of sugar, are\ndiscriminated by their effect in rotating the plane of polarization\nof light. One substance has been termed _Dextrin_, from its\nimpressing a right-handed rotation on the plane of polarization.\n\nAnd in a great number of Arts and Manufactures, the necessity of a\nknowledge of theory to the right conduct of practice is familiarly\nacknowledged and assumed. In the testing and smelting of metals, in\nthe fabrication of soap, of candles, of sugar; in the dyeing and\nprinting of woollen, linen, cotton and silken stuffs; the master\nmanufacturer has always the scientific chemist at his elbow;--either\na 'consulting chemist' to whom he may apply on a special occasion,\n(for such is now a regular profession;) or a chemist who day by day\nsuperintends, controls, and improves the processes which his workmen\ndaily carry on. In these cases, though Art long preceded Science,\nScience now guides, governs and advances Art.\n\n15. Other Arts and manufactures which have arisen in modern times\nhave been new creations produced by Science, and requiring a\ncomplete acquaintance with scientific processes to conduct them\neffectually and securely. Such are the photographic Arts, now so\nvarious in their form; beginning with those which, from their\nauthors, are called Daguerrotype and Talbotype. Such are the Arts of\nElectrotype modelling {246} and Electrotype plating. Such are the\nArts of preparing fulminating substances; gun-cotton; fulminate of\nsilver, and of mercury; and the application of those Arts to use, in\nthe fabrication of percussion-caps for guns. Such is the Art of\nElectric Telegraphy, from its first beginning to its last great\nattempt, the electric cord which connects England and America. Such\nis the Art of imitating by the chemistry of the laboratory the\nvegetable chemistry of nature, and thus producing the flavour of the\npear, the apple, the pine-apple, the melon, the quince. Such is the\nArt of producing in man a temporary insensibility to pain, which was\neffected first through the means of sulphuric ether by Dr Jackson of\nAmerica, and afterwards through the use of chloroform by Dr Simpson\nof Edinburgh. In these cases and many others Science has endowed man\nwith New Arts. And though even in these Arts, which are thus the\nlast results of Science, there is much which Science cannot fully\nunderstand and explain; still, such cases cannot but be looked upon\nas notable verifications of the anticipations of those who In former\ntimes expected from the progress of Science a harvest of material\nadvantages to man.\n\nWe must now conclude our task by a few words on the subject of\ninductions involving Ideas ulterior to those already considered.\n\n\n\n{{247}}\nCHAPTER X.\n\nOF THE INDUCTION OF CAUSES.\n\n\nAPHORISM LX.\n\n_In the_ Induction of Causes _the principal Maxim is, that we must\nbe careful to possess, and to apply, with perfect clearness, the\nFundamental Idea on which the Induction depends._\n\nAPHORISM LXI.\n\n_The Induction of Substance, of Force, of Polarity, go beyond mere\nlaws of phenomena, and may be considered as the Induction of\nCauses._\n\nAPHORISM LXII.\n\n_The Cause of certain phenomena being inferred, we are led to\ninquire into the Cause of this Cause, which inquiry must be\nconducted in the same manner as the previous one; and thus we have\nthe Induction of Ulterior Causes._\n\nAPHORISM LXIII.\n\n_In contemplating the series of Causes which are themselves the\neffects of other causes, we are necessarily led to assume a Supreme\nCause in the Order of Causation, as we assume a First Cause in Order\nof Succession._\n\n\n1. WE formerly[53\\3] stated the objects of the researches of Science\nto be Laws of Phenomena and Causes; and showed the propriety and the\nnecessity of not resting in the former object, but extending our\n{248} inquiries to the latter also. Inductions, in which phenomena\nare connected by relations of Space, Time, Number and Resemblance,\nbelong to the former class; and of the Methods applicable to such\nInductions we have treated already. In proceeding to Inductions\ngoverned by any ulterior Ideas, we can no longer lay down any\nSpecial Methods by which our procedure may be directed. A few\ngeneral remarks are all that we shall offer.\n\n[Note 53\\3: B. ii. c. vii.]\n\nThe principal Maxim in such cases of Induction is the obvious\none:--that we must be careful to possess and to apply, with perfect\nclearness and precision, the Fundamental Idea on which the Induction\ndepends.\n\nWe may illustrate this in a few cases.\n\n2. _Induction of Substance._--The Idea of Substance[54\\3] involves\nthis axiom, that the weight of the whole compound must be equal to\nthe weights of the separate elements, whatever changes the\ncomposition or separation of the elements may have occasioned. The\napplication of this Maxim we may term the _Method of the Balance_.\nWe have seen[55\\3] elsewhere how the memorable revolution in\nChemistry, the overthrow of Phlogiston, and the establishment of the\nOxygen Theory, was produced by the application of this Method. We\nhave seen too[56\\3] that the same Idea leads us to this Maxim;--that\n_Imponderable Fluids_ are not to be admitted as _chemical_ elements\nof bodies.\n\n[Note 54\\3: _Hist. Sc. Ideas_, Book vi. c. iii.]\n\n[Note 55\\3: _Ibid._ b. vi. c. iv.]\n\n[Note 56\\3: _Ibid._]\n\nWhether those which have been termed _Imponderable Fluids_,--the\nsupposed fluids which produce the phenomena of Light, Heat,\nElectricity, Galvanism, Magnetism,--really exist or no, is a\nquestion, not merely of the _Laws_, but of the _Causes_ of\nPhenomena. It is, as has already been shown, a question which we\ncannot help discussing, but which is at present involved in great\nobscurity. Nor does it appear at all likely that we shall obtain a\ntrue view of the cause of Light, Heat, and Electricity, till we have\ndiscovered precise and general laws connecting optical, thermotical,\nand {249} electrical _phenomena_ with those chemical doctrines to\nwhich the Idea of Substance is necessarily applied.\n\n3. _Induction of Force._--The inference of _Mechanical Forces_ from\nphenomena has been so abundantly practised, that it is perfectly\nfamiliar among scientific inquirers. From the time of Newton, it has\nbeen the most common aim of mathematicians; and a persuasion has\ngrown up among them, that mechanical forces,--attraction and\nrepulsion,--are the only modes of action of the particles of bodies\nwhich we shall ultimately have to consider. I have attempted to show\nthat this mode of conception is inadequate to the purposes of sound\nphilosophy;--that the Particles of crystals, and the Elements of\nchemical compounds, must be supposed to be combined in some other\nway than by mere mechanical attraction and repulsion. Dr. Faraday\nhas gone further in shaking the usual conceptions of the force\nexerted, in well-known cases. Among the most noted and conspicuous\ninstances of attraction and repulsion exerted at a distance, were\nthose which take place between electrized bodies. But the eminent\nelectrician just mentioned has endeavoured to establish, by\nexperiments of which it is very difficult to elude the weight, that\nthe action in these cases does not take place at a distance, but is\nthe result of a chain of intermediate particles connected at every\npoint by forces of another kind.\n\n4. _Induction of Polarity._--The forces to which Dr. Faraday\nascribes the action in these cases are _Polar Forces_[57\\3]. We have\nalready endeavoured to explain the Idea of Polar Forces; which\nimplies[58\\3] that at every point forces exactly equal act in\nopposite directions; and thus, in the greater part of their course,\nneutralize and conceal each other; while at the extremities of the\nline, being by some cause liberated, they are manifested, still\nequal and opposite. And the criterion by which this polar character\nof forces is recognized, is implied in the reasoning of Faraday, on\nthe question of one or two electricities, of which we {250} formerly\nspoke[59\\3]. The maxim is this:--that in the action of polar forces,\nalong with every manifestation of force or property, there exists a\ncorresponding and simultaneous manifestation of an equal and\nopposite force or property.\n\n[Note 57\\3: _Researches_, 12th series.]\n\n[Note 58\\3: B. v. c. i.]\n\n[Note 59\\3: Book v. c. i.]\n\n5. As it was the habit of the last age to reduce all action to\nmechanical forces, the present race of physical speculators appears\ninclined to reduce all forces to polar forces. Mosotti has\nendeavoured to show that the positive and negative electricities\npervade all bodies, and that gravity is only an apparent excess of\none of the kinds over the other. As we have seen, Faraday has given\nstrong experimental grounds for believing that the supposed remote\nactions of electrized bodies are really the effects of polar forces\namong contiguous particles. If this doctrine were established with\nregard to all electrical, magnetical, and chemical forces, we might\nask, whether, while all other forces are polar, gravity really\naffords a single exception to the universal rule? Is not the\nuniverse pervaded by an omnipresent antagonism, a fundamental\nconjunction of contraries, everywhere opposite, nowhere independent?\nWe are, as yet, far from the position in which Inductive Science can\nenable us to answer such inquiries.\n\n6. _Induction of Ulterior Causes._--The first Induction of a Cause\ndoes not close the business of scientific inquiry. Behind proximate\ncauses, there are ulterior causes, perhaps a succession of such.\nGravity is the cause of the motions of the planets; but what is the\ncause of gravity? This is a question which has occupied men's minds\nfrom the time of Newton to the present day. Earthquakes and\nvolcanoes are the causes of many geological phenomena; but what is\nthe cause of those subterraneous operations? This inquiry after\nulterior causes is an inevitable result from the intellectual\nconstitution of man. He discovers mechanical causes, but he cannot\nrest in them. He must needs ask, whence it is that matter has its\nuniversal power of attracting matter. He discovers polar forces: but\neven {251} if these be universal, he still desires a further insight\ninto the cause of this polarity. He sees, in organic structures,\nconvincing marks of adaptation to an end: whence, he asks, is this\nadaptation? He traces in the history of the earth a chain of causes\nand effects operating through time: but what, he inquires, is the\npower which holds the end of this chain?\n\nThus we are referred back from step to step in the order of\ncausation, in the same, manner as, in the pal\u00e6tiological sciences,\nwe were referred back in the order of time. We make discovery after\ndiscovery in the various regions of science; each, it may be,\nsatisfactory, and in itself complete, but none final. Something\nalways remains undone. The last question answered, the answer\nsuggests still another question. The strain of music from the lyre\nof Science flows on, rich and sweet, full and harmonious, but never\nreaches a close: no cadence is heard with which the intellectual ear\ncan feel satisfied.\n\n_Of the Supreme Cause._--In the utterance of Science, no cadence is\nheard with which the human mind can feel satisfied. Yet we cannot\nbut go on listening for and expecting a satisfactory close. The\nnotion of a cadence appears to be essential to our relish of the\nmusic. The idea of some closing strain seems to lurk among our own\nthoughts, waiting to be articulated in the notes which flow from the\nknowledge of external nature. The idea of something ultimate in our\nphilosophical researches, something in which the mind can acquiesce,\nand which will leave us no further questions to ask, of _whence_,\nand _why_, and _by what power_, seems as if it belongs to us:--as if\nwe could not have it withheld from us by any imperfection or\nincompleteness in the actual performances of science. What is the\nmeaning of this conviction? What is the reality thus anticipated?\nWhither does the developement of this Idea conduct us?\n\nWe have already seen that a difficulty of the same kind, which\narises in the contemplation of causes and effects considered as\nforming an historical series, drives us to the assumption of a First\nCause, as an Axiom {252} to which our Idea of Causation in time\nnecessarily leads. And as we were thus guided to a First Cause, in\norder of Succession, the same kind of necessity directs us to a\nSupreme Cause in order of Causation.\n\nOn this most weighty subject it is difficult to speak fitly; and the\npresent is not the proper occasion, even for most of that which may\nbe said. But there are one or two remarks which flow from the\ngeneral train of the contemplations we have been engaged in, and\nwith which this Work must conclude.\n\nWe have seen how different are the kinds of cause to which we are\nled by scientific researches. _Mechanical Forces_ are insufficient\nwithout _Chemical Affinities_; Chemical Agencies fail us, and we are\ncompelled to have recourse to _Vital Powers_; Vital Powers cannot be\nmerely physical, and we must believe in something hyperphysical,\nsomething of the nature of a _Soul_. Not only do biological\ninquiries lead us to assume an animal soul, but they drive us much\nfurther; they bring before us _Perception_, and _Will_ evoked by\nPerception. Still more, these inquiries disclose to us _Ideas_ as\nthe necessary forms of Perception, in the actions of which we\nourselves are conscious. We are aware, we cannot help being aware,\nof our Ideas and our Volitions as belonging to _us_, and thus we\npass from _things_ to _persons_; we have the idea of _Personality_\nawakened. And the idea of Design and _Purpose_, of which we are\nconscious in our own minds, we find reflected back to us, with a\ndistinctness which we cannot overlook, in all the arrangements which\nconstitute the frame of organized beings.\n\nWe cannot but reflect how widely diverse are the kinds of principles\nthus set before us;--by what vast strides we mount from the lower to\nthe higher, as we proceed through that series of causes which the\nrange of the sciences thus brings under our notice. Yet we know how\nnarrow is the range of these sciences when compared with the whole\nextent of human knowledge. We cannot doubt that on many other\nsubjects, besides those included in physical speculation, man has\nmade out solid and satisfactory trains of {253} connexion;--has\ndiscovered clear and indisputable evidence of causation. It is\nmanifest, therefore, that, if we are to attempt to ascend to the\nSupreme Cause--if we are to try to frame an idea of the Cause of all\nthese subordinate causes;--we must conceive it as more different\nfrom any of them, than the most diverse are from each other;--more\nelevated above the highest, than the highest is above the lowest.\n\nBut further;--though the Supreme Cause must thus be inconceivably\ndifferent from all subordinate causes, and immeasurably elevated\nabove them all, it must still include in itself all that is\nessential to each of them, by virtue of that very circumstance that\nit is the Cause of their Causality. Time and Space,--Infinite Time\nand Infinite Space,--must be among its attributes; for we cannot but\nconceive Infinite Time and Space as attributes of the Infinite Cause\nof the universe. Force and Matter must depend upon it for their\nefficacy; for we cannot conceive the activity of Force, or the\nresistance of Matter, to be independent powers. But these are its\nlower attributes. The Vital Powers, the Animal Soul, which are the\nCauses of the actions of living things, are only the Effects of the\nSupreme Cause of Life. And this Cause, even in the lowest forms of\norganized bodies, and still more in those which stand higher in the\nscale, involves a reference to Ends and Purposes, in short, to\nmanifest Final Causes. Since this is so, and since, even when we\ncontemplate ourselves in a view studiously narrowed, we still find\nthat we have Ideas, and Will and Personality, it would render our\nphilosophy utterly incoherent and inconsistent with itself, to\nsuppose that Personality, and Ideas, and Will, and Purpose, do not\nbelong to the Supreme Cause from which we derive all that we have\nand all that we are.\n\nBut we may go a step further;--though, in our present field of\nspeculation, we confine ourselves to knowledge founded on the facts\nwhich the external world presents to us, we cannot forget, in\nspeaking of such a theme as that to which we have thus been led,\nthat these are but a small, and the least significant {254} portion\nof the facts which bear upon it. We cannot fail to recollect that\nthere are facts belonging to the world within us, which more readily\nand strongly direct our thoughts to the Supreme Cause of all things.\nWe can plainly discern that we have Ideas elevated above the region\nof mechanical causation, of animal existence, even of mere choice\nand will, which still have a clear and definite significance, a\npermanent and indestructible validity. We perceive as a fact, that\nwe have a Conscience, judging of Right and Wrong; that we have Ideas\nof Moral Good and Evil, that we are compelled to conceive the\norganization of the moral world, as well as of the vital frame, to\nbe directed to an end and governed by a purpose. And since the\nSupreme Cause is the cause of these facts, the Origin of these\nIdeas, we cannot refuse to recognize Him as not only the Maker, but\nthe Governor of the World; as not only a Creative, but a\nProvidential Power; as not only a Universal Father, but an Ultimate\nJudge.\n\nWe have already passed beyond the boundary of those speculations\nwhich we proposed to ourselves as the basis of our conclusions. Yet\nwe may be allowed to add one other reflection. If we find in\nourselves Ideas of Good and Evil, manifestly bestowed upon us to be\nthe guides of our conduct, which guides we yet find it impossible\nconsistently to obey;--if we find ourselves directed, even by our\nnatural light, to aim at a perfection of our moral nature from which\nwe are constantly deviating through weakness and perverseness; if,\nwhen we thus lapse and err, we can find, in the region of human\nphilosophy, no power which can efface our aberrations, or reconcile\nour actual with our ideal being, or give us any steady hope and\ntrust with regard to our actions, after we have thus discovered\ntheir incongruity with their genuine standard;--if we discern that\nthis is our condition, how can we fail to see that it is in the\nhighest degree consistent with all the indications supplied by such\na philosophy as that of which we have been attempting to lay the\nfoundations, that the Supreme Cause, through whom man exists as\n{255} a moral being of vast capacities and infinite Hopes, should\nhave Himself provided a teaching for our ignorance, a propitiation\nfor our sin, a support for our weakness, a purification and\nsanctification of our nature?\n\nAnd thus, in concluding our long survey of the grounds and structure\nof science, and of the lessons which the study of it teaches us, we\nfind ourselves brought to a point of view in which we can cordially\nsympathize, and more than sympathize, with all the loftiest\nexpressions of admiration and reverence and hope and trust, which\nhave been uttered by those who in former times have spoken of the\nelevated thoughts to which the contemplation of the nature and\nprogress of human knowledge gives rise. We can not only hold with\nGalen, and Harvey, and all the great physiologists, that the organs\nof animals give evidence of a purpose;--not only assert with Cuvier\nthat this conviction of a purpose can alone enable us to understand\nevery part of every living thing;--not only say with Newton that\n'every true step made in philosophy brings us nearer to the First\nCause, and is on that account highly to be valued;'--and that 'the\nbusiness of natural philosophy is to deduce causes from effects,\ntill we come to the very First Cause, which certainly is not\nmechanical;'--but we can go much farther, and declare, still with\nNewton, that 'this beautiful system could have its origin no other\nway than by the purpose and command of an intelligent and powerful\nBeing, who governs all things, not as the soul of the world, but as\nthe Lord of the Universe; who is not only God, but Lord and\nGovernor.'\n\nWhen we have advanced so far, there yet remains one step. We may\nrecollect the prayer of one, the master in this school of the\nphilosophy of science: 'This also we humbly and earnestly beg;--that\nhuman things may not prejudice such as are divine;--neither that\nfrom the unlocking of the gates of sense, and the kindling of a\ngreater natural light, anything may arise of incredulity or\nintellectual night towards divine mysteries; but rather that by our\nminds thoroughly {256} purged and cleansed from fancy and vanity,\nand yet subject and perfectly given up to the divine oracles, there\nmay be given unto faith the things that are faith's.' When we are\nthus prepared for a higher teaching, we may be ready to listen to a\ngreater than Bacon, when he says to those who have sought their God\nin the material universe, 'Whom ye ignorantly worship, him declare I\nunto you.' And when we recollect how utterly inadequate all human\nlanguage has been shown to be, to express the nature of that Supreme\nCause of the Natural, and Rational, and Moral, and Spiritual world,\nto which our Philosophy points with trembling finger and shaded\neyes, we may receive, with the less wonder but with the more\nreverence, the declaration which has been vouchsafed to us:\n\n \u0395\u039d A\u03a1\u03a7\u0397 \u0397\u039d \u1f49 \u039b\u039f\u0393\u039f\u03a3, \u039a\u0391I \u1f49 \u039b\u039f\u0393\u039f\u03a3 \u0397\u039d \u03a0\u03a1\u039f\u03a3 \u03a4\u039f\u039d \u0398\u0395\u039f\u039d, \u039a\u0391I \u0398\u0395\u039f\u03a3 \u0397\u039d \u1f49\n \u039b\u039f\u0393\u039f\u03a3.\n\n\n\n{{257}}\nNOVUM ORGANON RENOVATUM.\n\n\nBOOK IV.\n\nOF THE LANGUAGE OF SCIENCE.\n\n\nINTRODUCTION.\n\nIT has been shown in the _History of the Sciences_, and has further\nappeared in the course of the _History of Ideas_, that almost every\nstep in the progress of science is marked by the formation or\nappropriation of a technical term. Common language has, in most\ncases, a certain degree of looseness and ambiguity; as common\nknowledge has usually something of vagueness and indistinctness. In\ncommon cases too, knowledge usually does not occupy the intellect\nalone, but more or less interests some affection, or puts in action\nthe fancy; and common language, accommodating itself to the office\nof expressing such knowledge, contains, in every sentence, a tinge\nof emotion or of imagination. But when our knowledge becomes\nperfectly exact and purely intellectual, we require a language which\nshall also be exact and intellectual;--which shall exclude alike\nvagueness and fancy, imperfection and superfluity;--in which each\nterm shall convey a meaning steadily fixed and rigorously limited.\nSuch a language that of science becomes, through the use of\nTechnical Terms. And we must now endeavour to lay down some maxims\nand suggestions, by attention to which Technical Terms may be better\nfitted to answer their purpose. In order to do this, we shall in\n{258} the first place take a rapid survey of the manner in which\nTechnical Terms have been employed from the earliest periods of\nscientific history.\n\nThe progress of the use of technical scientific language offers to\nour notice two different and successive periods; in the first of\nwhich, technical terms were formed casually, as convenience in each\ncase prompted; while in the second period, technical language was\nconstructed intentionally, with set purpose, with a regard to its\nconnexion, and with a view of constructing a system. Though the\ncasual and the systematic formation of technical terms cannot be\nseparated by any precise date of time, (for at all periods some\nterms in some sciences have been framed unsystematically,) we may,\nas a general description, call the former the _Ancient_ and the\nlatter the _Modern_ Period. In illustrating the two following\nAphorisms, I will give examples of the course followed in each of\nthese periods.\n\n\nAPHORISM I.\n\n_In the Ancient Period of Sciences, Technical Terms were formed in\nthree different ways:--by appropriating common words and fixing\ntheir meaning;--by constructing terms containing a description;--by\nconstructing terms containing reference to a theory._\n\n\nTHE earliest sciences offer the earliest examples of technical\nterms. These are Geometry, Arithmetic, and Astronomy; to which we\nhave soon after to add Harmonics, Mechanics, and Optics. In these\nsciences, we may notice the above-mentioned three different modes in\nwhich technical terms were formed.\n\nI. The simplest and first mode of acquiring technical terms, is to\ntake words current in common usage, and by rigorously defining or\notherwise fixing their meaning, to fit them for the expression of\nscientific truths. In this manner almost all the fundamental\ntechnical terms of Geometry were formed. A _sphere_, a _cone_, a\n_cylinder_, had among the Greeks, at first, {259} meanings less\nprecise than those which geometers gave to these words, and besides\nthe mere designation of form, implied some use or application. A\n_sphere_ (\u03c3\u03c6\u03b1\u1fd6\u03c1\u03b1) was a hand-ball used in games; a _cone_ (\u03ba\u1ff6\u03bd\u03bf\u03c2)\nwas a boy's spinning-top, or the crest of a helmet; a _cylinder_\n(\u03ba\u03cd\u03bb\u03b9\u03bd\u03b4\u03c1\u03bf\u03c2) was a roller; a _cube_ (\u03ba\u03cd\u03b2\u03bf\u03c2) was a die: till these\nwords were adopted by the geometers, and made to signify among them\npure modifications of space. So an _angle_ (\u03b3\u03c9\u03bd\u03af\u03b1) was only a\ncorner; a _point_ (\u03c3\u03b7\u03bc\u03b5\u1fd6\u03bf\u03bd) was a signal; a _line_ (\u03b3\u03c1\u03b1\u03bc\u03bc\u1f74) was a\nmark; a _straight_ line (\u03b5\u1f50\u03b8\u03b5\u1fd6\u03b1) was marked by an adjective which at\nfirst meant only _direct_. A _plane_ (\u1f10\u03c0\u03af\u03c0\u03b5\u03b4\u03bf\u03bd) is the neuter form\nof an adjective, which by its derivation means _on the ground_, and\nhence _flat_. In all these cases, the word adopted as a term of\nscience has its sense rigorously fixed; and where the common use of\nthe term is in any degree vague, its meaning may be modified at the\nsame time that it is thus limited. Thus a _rhombus_ (\u1fe5\u03cc\u03bc\u03b2\u03bf\u03c2) by its\nderivation, might mean any figure which is _twisted_ out of a\nregular form; but it is confined by geometers to that figure which\nhas four equal sides, its angles being oblique. In like manner, a\n_trapezium_ (\u03c4\u03c1\u03b1\u03c0\u03ad\u03b6\u03b9\u03bf\u03bd) originally signifies a _table_, and thus\nmight denote any form; but as the tables of the Greeks had one side\nshorter than the opposite one, such a figure was at first called a\n_trapezium_. Afterwards the term was made to signify any figure with\nfour unequal sides; a name being more needful in geometry for this\nkind of figure than for the original form.\n\nThis class of technical terms, namely, words adopted from common\nlanguage, but rendered precise and determinate for purposes of\nscience, may also be exemplified in other sciences. Thus, as was\nobserved in the early portion of the history of astronomy[1\\4], a\n_day_, a _month_, a _year_, described at first portions of time\nmarked by familiar changes, but afterwards portions determined by\nrigorous mathematical definitions. The conception of the heavens as\na revolving sphere, is so obvious, {260} that we may consider the\nterms which involve this conception as parts of common language; as\nthe _pole_ (\u03c0\u03cc\u03bb\u03bf\u03c2); the _arctic circle_, which includes the stars\nthat never set[2\\4]; the _horizon_ (\u1f41\u03c1\u03af\u03b6\u03c9\u03bd) a boundary, applied\ntechnically to the circle bounding the visible earth and sky. The\n_turnings of the sun_ (\u03c4\u03c1\u03bf\u03c0\u03b1\u1f76 \u1f20\u03b5\u03bb\u03af\u03bf\u03b9\u03bf), which are mentioned by\nHesiod, gave occasion to the term _tropics_, the circles at which\nthe sun in his annual motion turns back from his northward or\nsouthward advance. The _zones_ of the earth, (the _torrid_,\n_temperate_, and _frigid_;) the _gnomon_ of a dial; the _limb_ (or\nborder) of the moon, or of a circular instrument, are terms of the\nsame class. An _eclipse_ (\u1f14\u03ba\u03bb\u03b5\u03b9\u03c8\u03b9\u03c2) is originally a deficiency or\ndisappearance, and joined with the name of the luminary, an _eclipse\nof the sun_ or _of the moon_, described the phenomenon; but when the\nterm became technical, it sufficed, without addition, to designate\nthe phenomenon.\n\n[Note 1\\4: _Hist. Ind. Sci._ b. iii. c. i.]\n\n[Note 2\\4: _Hist. Ast._ b. iii. c. i. sect. 8.]\n\nIn Mechanics, the Greeks gave a scientific precision to very few\nwords: we may mention _weights_ (\u03b2\u03ac\u03c1\u03b5\u03b1), the _arms of a lever_\n(\u03bc\u03ae\u03c7\u03b5\u03b1), its _fulcrum_ (\u1f51\u03c0\u03bf\u03bc\u03cc\u03c7\u03bb\u03b9\u03bf\u03bd), and the verb _to balance_\n(\u1f30\u03c3\u03c3\u03bf\u1fe4\u1fe5\u03bf\u03c0\u03b5\u1fd6\u03bd). Other terms which they used, as _momentum_ (\u1fe5\u03bf\u03c0\u1f74) and\n_force_ (\u03b4\u03cd\u03bd\u03b1\u03bc\u03b9\u03c2), did not acquire a distinct and definite meaning\ntill the time of Galileo, or later. We may observe that all abstract\nterms, though in their scientific application expressing mere\nconceptions, were probably at first derived from some word\ndescribing external objects. Thus the Latin word for force, _vis_,\nseems to be connected with a Greek word, \u1f32\u03c2, or \u03dd\u1f76\u03c2, which often has\nnearly the same meaning; but originally, as it would seem, signified\na sinew or muscle, the obvious seat of animal strength.\n\nIn later times, the limitation imposed upon a word by its\nappropriation to scientific purposes, is often more marked than in\nthe cases above described. Thus the _variation_ is made to mean, in\nastronomy, the second inequality of the moon's motion; in magnetism,\nthe _variation_ signifies the angular deviation of the {261}\ncompass-needle from the north; in pure mathematics, the _variation_\nof a quantity is the formula which expresses the result of any small\nchange of the most general kind. In like manner, _parallax_\n(\u03c0\u03b1\u03c1\u03ac\u03bb\u03bb\u03b1\u03be\u03b9\u03c2) denotes a _change_ in general, but is used by\nastronomers to signify the change produced by the spectator's being\nremoved from the center of the earth, his theoretical place, to the\nsurface. _Alkali_ at first denoted the ashes of a particular plant,\nbut afterwards, all bodies having a certain class of chemical\nproperties; and, in like manner, _acid_, the class opposed to\nalkali, was modified in signification by chemists, so as to refer no\nlonger to the taste.\n\nWords thus borrowed from common language, and converted by\nscientific writers into technical terms, have some advantages and\nsome disadvantages. They possess this great convenience, that they\nare understood after a very short explanation, and retained in the\nmemory without effort. On the other hand, they lead to some\ninconvenience; for since they have a meaning in common language, a\ncareless reader is prone to disregard the technical limitation of\nthis meaning, and to attempt to collect their import in scientific\nbooks, in the same vague and conjectural manner in which he collects\nthe purpose of words in common cases. Hence the language of science,\nwhen thus resembling common language, is liable to be employed with\nan absence of that scientific precision which alone gives it value.\nPopular writers and talkers, when they speak of _force_, _momentum_,\n_action and reaction_, and the like, often afford examples of the\ninaccuracy thus arising from the scientific appropriation of common\nterms.\n\nII. Another class of technical terms, which we find occurring as\nsoon as speculative science assumes a distinct shape, consists of\nthose which are intentionally constructed by speculators, and which\ncontain some description or indication distinctive of the conception\nto which they are applied. Such are a _parallelogram_\n(\u03c0\u03b1\u03c1\u03b1\u03bb\u03bb\u03b7\u03bb\u03cc\u03b3\u03c1\u03b1\u03bc\u03bc\u03bf\u03bd), which denotes a plane figure bounded by two\npairs of parallel lines; a _parallelopiped_ {262}\n(\u03c0\u03b1\u03c1\u03b1\u03bb\u03bb\u03b7\u03bb\u03bf\u03c0\u03af\u03c0\u03b5\u03b4\u03bf\u03bd), which signifies a solid figure bounded by three\npairs of parallel planes. A _triangle_ (\u03c4\u03c1\u03af\u03b3\u03c9\u03bd\u03bf\u03c2, _trigon_) and a\n_quadrangle_ (\u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03bf\u03c2, _tetragon_) were perhaps words invented\nindependently of the mathematicians: but such words extended to\nother cases, _pentagon_, _decagon_, _hecc\u00e6decagon_, _polygon_, are\ninventions of scientific men. Such also are _tetrahedron_,\n_hexahedron_, _dodecahedron_, _tesseracontaoctohedron_,\n_polyhedron_, and the like. These words being constructed by\nspeculative writers, explain themselves, or at least require only\nsome conventional limitation, easily adopted. Thus _parallelogram_,\nmight mean a figure bounded by any number of sets of parallel lines,\nbut it is conventionally restricted to a figure of _four_ sides. So\na _great circle_ in a sphere means one which passes through the\ncenter of the sphere; and a _small circle_ is any other. So in\ntrigonometry, we have the hypotenuse (\u1f51\u03c0\u03bf\u03c4\u03b5\u03bd\u03bf\u1fe6\u03c3\u03b1), or _subtending_\nline, to designate the line subtending an angle, and especially a\nright angle. In this branch of mathematics we have many invented\ntechnical terms; as _complement_, _supplement_, _cosine_,\n_cotangent_, a _spherical angle_, the _pole of a circle_, or of a\nsphere. The word _sine_ itself appears to belong to the class of\nterms already described as scientific appropriations of common\nterms, although its origin is somewhat obscure.\n\nMathematicians were naturally led to construct these and many other\nterms by the progress of their speculations. In like manner, when\nastronomy took the form of a speculative science, words were\ninvented to denote distinctly the conceptions thus introduced. Thus\nthe sun's annual path among the stars, in which not only solar, but\nalso all lunar eclipses occur, was termed the _ecliptic_. The circle\nwhich the sun describes in his diurnal motion, when the days and\nnights are equal, the Greeks called the _equidiurnal_ (\u1f30\u03c3\u03b7\u03bc\u03b5\u03c1\u03b9\u03bd\u1f78\u03c2,)\nthe Latin astronomers the _equinoctial_, and the corresponding\ncircle on the earth was the _equator_. The ecliptic intersected the\nequinoctial in the _equinoctial points_. The _solstices_ (in Greek,\n\u03c4\u03c1\u03bf\u03c0\u03b1\u1f76) were the times when the sun arrested his motion northwards\nor {263} southwards; and the _solstitial points_ (\u03c4\u1f70 \u03c4\u03c1\u03bf\u03c0\u03b9\u03ba\u1f70 \u03c3\u03b7\u03bc\u03b5\u1fd6\u03b1)\nwere the places, in the ecliptic where he then was. The name of\n_meridians_ was given to circles passing through the poles of the\nequator; the _solstitial colure_ (\u03ba\u03cc\u03bb\u03bf\u03c5\u03c1\u03bf\u03c2, curtailed), was one of\nthese circles, which passes through the solstitial points, and is\nintercepted by the horizon.\n\nWe have borrowed from the Arabians various astronomical terms, as\n_Zenith_, _Nadir_, _Azimuth_, _Almacantar_. And these words, which\namong the Arabians probably belonged to the first class, of\nappropriated scientific terms, are for us examples of the second\nclass, invented scientific terms; although they differ from most\nthat we have mentioned, in not containing an etymology corresponding\nto their meaning in any language with which European cultivators of\nscience are generally familiar. Indeed, the distinction of our two\nclasses, though convenient, is in a great measure, casual. Thus most\nof the words we formerly mentioned, as _parallax_, _horizon_,\n_eclipse_, though appropriated technical terms among the Greeks, are\nto us invented technical terms.\n\nIn the construction of such terms as we are now considering, those\nlanguages have a great advantage which possess a power of forming\nwords by composition. This was eminently the case with the Greek\nlanguage; and hence most of the ancient terms of science in that\nlanguage, when their origin is once explained, are clearly\nunderstood and easily retained. Of modern European languages, the\nGerman possesses the greatest facility of composition; and hence\nscientific authors in that language are able to invent terms which\nit is impossible to imitate in the other languages of Europe. Thus\nWeiss distinguishes his various systems of crystals as\n_zwei-und-zwei-gliedrig_, _ein-und-zwei-gliedrig_,\n_drey-und-drey-gliedrig,_ _&c._, (two-and-two-membered,\none-and-two-membered, &c.) And Hessel, also a writer on\ncrystallography, speaks of _doubly-one-membered edges_,\n_four-and-three spaced rays_, and the like.\n\nHow far the composition of words, in such cases, may be practised in\nthe English language, and the general question, what are the best\nrules and artifices {264} in such cases, I shall afterwards\nconsider. In the mean time, I may observe that this list of invented\ntechnical terms might easily be much enlarged. Thus in harmonics we\nhave the various intervals, as a _Fourth_, a _Fifth_, an _Octave_,\n(_Diatessaron_, _Diapente_, _Diapason_,) a _Comma_, which is the\ndifference of a _Major_ and _Minor Tone_; we have the various\n_Moods_ or _Keys_, and the notes of various lengths, as _Minims_,\n_Breves_, _Semibreves_, _Quavers_. In chemistry, _Gas_ was at first\na technical term invented by Van Helmont, though it has now been\nalmost adopted into common language. I omit many words which will\nperhaps suggest themselves to the reader, because they belong rather\nto the next class, which I now proceed to notice.\n\nIII. The third class of technical terms consists of such as are\nconstructed by men of science, and involve some theoretical idea in\nthe meaning which their derivation implies. They do not merely\ndescribe, like the class last spoken of, but describe with reference\nto some doctrine or hypothesis which is accepted as a portion of\nscience. Thus _latitude_ and _longitude_, according to their origin,\nsignify breadth and length; they are used, however, to denote\nmeasures of the distance of a place on the earth's surface from the\nequator, and from the first meridian, of which distances, one cannot\nbe called _length_ more properly than the other. But this\nappropriation of these words may be explained by recollecting that\nthe earth, as known to the ancient geographers, was much further\nextended from east to west than from north to south. The\n_Precession_ of the equinoxes is a term which implies that the stars\nare fixed, while the point which is the origin of the measure of\ncelestial longitude moves backward. The _Right Ascension_ of a star\nis a measure of its position corresponding to terrestrial longitude;\nthis quantity is identical with the angular ascent of the\nequinoctial point, when the star is in the horizon in a _right_\nsphere; that is, a sphere which supposes the spectator to be at the\nequator. The _Oblique Ascension_ (a term now little used), is\nderived in like manner from an oblique sphere. The motion of a\nplanet is _direct_ or _retrograde_, _in_ {265} _consequentia_\n(_signa_), or _in antecedentia_, in reference to a certain assumed\nstandard direction for celestial motions, namely, the direction\nopposite to that of the sun's daily motion, and agreeing with his\nannual motion among the stars; or with what is much more evident,\nthe moon's monthly motion. The _equation of time_ is the quantity\nwhich must be added to or subtracted from the time marked by the\nsun, in order to reduce it to a theoretical condition of equable\nprogress. In like manner the _equation of the center_ of the sun or\nof the moon is the angle which must be added to, or subtracted from,\nthe actual advance of the luminary in the heavens, in order to make\nits motion equable. Besides the equation of the center of the moon,\nwhich represents the first and greatest of her deviations from\nequable motion, there are many other _equations_, by the application\nof which her motion is brought nearer and nearer to perfect\nuniformity. The second of these equations is called the _evection_,\nthe third the _variation_, the fourth the _annual equation_, The\nmotion of the sun as affected by its inequalities is called his\n_anomaly_, which term denotes inequality. In the History of\nAstronomy, we find that the inequable motions of the sun, moon, and\nplanets were, in a great measure, reduced to rule and system by the\nGreeks, by the aid of an hypothesis of circles, revolving, and\ncarrying in their motion other circles which also revolved. This\nhypothesis introduced many technical terms, as _deferent_,\n_epicycle_, _eccentric_. In like manner, the theories which have\nmore recently taken the place of the theory of epicycles have\nintroduced other technical terms, as the _elliptical orbit_, the\n_radius vector_, and the _equable description of areas_ by this\nradius, which phrases express the true laws of the planetary\nmotions.\n\nThere is no subject on which theoretical views have been so long and\nso extensively prevalent as astronomy, and therefore no other\nscience in which there are so many technical terms of the kind we\nare now considering. But in other subjects also, so far as theories\nhave been established, they have been accompanied by the\nintroduction or fixation of technical terms. Thus, as {266} we have\nseen in the examination of the foundations of mechanics, the terms\n_force_ and _inertia_ derive their precise meaning from a\nrecognition of the first law of motion; _accelerating force_ and\n_composition of motion_ involve the second law; _moving force_,\n_momentum_, _action_ and _reaction_, are expressions which imply the\nthird law. The term _vis viva_ was introduced to express a general\nproperty of moving bodies; and other terms have been introduced for\nlike purposes, as _impetus_ by Smeaton, and _work done_, by other\nengineers. In the recent writings of several French engineers, the\nterm _travail_ is much employed, to express the work done and the\nforce which does it: this term has been rendered by _labouring\nforce_. The proposition which was termed the _hydrostatic paradox_\nhad this name in reference to its violating a supposed law of the\naction of forces. The verb to _gravitate_, and the abstract term\n_gravitation_, sealed the establishment of Newton's theory of the\nsolar system.\n\nIn some of the sciences, opinions, either false, or disguised in\nvery fantastical imagery, have prevailed; and the terms which have\nbeen introduced during the reign of such opinions, bear the impress\nof the time. Thus in the days of alchemy, the substances with which\nthe operator dealt were personified; and a metal when exhibited pure\nand free from all admixture was considered as a little king, and was\nhence called a _regulus_, a term not yet quite obsolete. In like\nmanner, a substance from which nothing more of any value could be\nextracted, was dead, and was called a _caput mortuum_. Quick silver,\nthat is, live silver (_argentum vivum_), was killed by certain\nadmixtures, and was _revived_ when restored to its pure state.\n\nWe find a great number of medical terms which bear the mark of\nopinions formerly prevalent among physicians; and though these\nopinions hardly form a part of the progress of science, and were not\npresented in our History, we may notice some of these terms as\nexamples of the mode in which words involve in their derivation\nobsolete opinions. Such words as _hysterics_, _hypochondriac_,\n_melancholy_, _cholera_, _colic_, _quinsey_ {267} (_squinantia_,\n\u03c3\u03c5\u03bd\u03ac\u03b3\u03c7\u03b7, a suffocation), _megrim_, _migrane_ (_hemicranium_, the\nmiddle of the skull), _rickets_, (_rachitis_, from \u1fe5\u03ac\u03c7\u03b9\u03c2, the\nbackbone), _palsy_, (_paralysis_, \u03c0\u03b1\u03c1\u03ac\u03bb\u03c5\u03c3\u03b9\u03c2,) _apoplexy_ (\u1f00\u03c0\u03bf\u03c0\u03bb\u03b7\u03be\u03af\u03b1,\na stroke), _emrods_, (\u03b1\u1f31\u03bc\u03bf\u1fe4\u1fe5\u03bf\u0390\u03b4\u03b5\u03c2, _hemorrhoids_, a flux of blood),\n_imposthume_, (corrupted from _aposteme_, \u1f00\u03c0\u03cc\u03c3\u03c4\u03b7\u03bc\u03b1, an abscess),\n_phthisis_ (\u03c6\u03b8\u03af\u03c3\u03b9\u03c2, consumption), _tympanum_ (\u03c4\u03c5\u03bc\u03c0\u03b1\u03bd\u03af\u03b1, swelling),\n_dropsy_ (_hydropsy_, \u1f55\u03b4\u03c1\u03c9\u03c8,) _sciatica_, isciatica (\u1f30\u03c3\u03ba\u03b9\u03b1\u03b4\u03b9\u03ba\u1f74,\nfrom \u1f30\u03c3\u03ba\u03af\u03bf\u03bd, the hip), _catarrh_ (\u03ba\u03b1\u03c4\u03ac\u1fe4\u1fe5\u03bf\u03c5\u03c2, a flowing down),\n_diarrh\u0153a_ (\u03b4\u03b9\u03b1\u1fe4\u1fe5\u03bf\u03af\u03b1, a flowing through), _diabetes_ (\u03b4\u03b9\u03b1\u03b2\u03ae\u03c4\u03b7\u03c2, a\npassing through), _dysentery_ (\u03b4\u03c5\u03c3\u03b5\u03bd\u03c4\u03b5\u03c1\u03af\u03b1, a disorder of the\nentrails), _arthritic_ pains (from \u1f04\u03c1\u03b8\u03c1\u03b1, the joints), are names\nderived from the supposed or real seat and circumstances of the\ndiseases. The word from which the first of the above names is\nderived (\u1f51\u03c3\u03c4\u03ad\u03c1\u03b1, the last place,) signifies the womb, according to\nits order in a certain systematic enumeration of parts. The second\nword, _hypochondriac_, means something affecting the viscera below\nthe cartilage of the breastbone, which cartilage is called \u03c7\u03cc\u03bd\u03b4\u03c1\u03bf\u03c2;\n_melancholy_ and _cholera_ derive their names from supposed\naffections of \u03c7\u03bf\u03bb\u1f74, the bile. _Colic_ is that which affects the\n_colon_ (\u03ba\u1ff6\u03bb\u03bf\u03bd), the largest member of the bowels. A disorder of the\neye is called _gutta serena_ (the 'drop serene' of Milton), in\ncontradistinction to _gutta turbida_, in which the impediment to\nvision is perceptibly opake. Other terms also record the opinions of\nthe ancient anatomists, as _duodenum_, a certain portion of the\nintestines, which they estimated as twelve inches long. We might add\nother allusions, as the _tendon of Achilles_.\n\nAstrology also supplied a number of words founded upon fanciful\nopinions; but this study having been expelled from the list of\nsciences, such words now survive, only so far as they have found a\nplace in common language. Thus men were termed _mercurial_,\n_martial_, _jovial_, or _saturnine_, accordingly as their characters\nwere supposed to be determined by the influence of the planets,\nMercury, Mars, Jupiter, or Saturn. Other expressions, such as\n_disastrous_, _ill-starred_, _exorbitant_, _lord of the ascendant_,\nand hence _ascendancy_, _influence_, {268} a _sphere of action_, and\nthe like, may serve to show how extensively astrological opinions\nhave affected language, though the doctrine is no longer a\nrecognized science.\n\nThe preceding examples will make it manifest that opinions, even of\na recondite and complex kind, are often implied in the derivation of\nwords; and thus will show how scientific terms, framed by the\ncultivators of science, may involve received hypotheses and\ntheories. When terms are thus constructed, they serve not only to\nconvey with ease, but to preserve steadily and to diffuse widely,\nthe opinions which they thus assume. Moreover, they enable the\nspeculator to employ these complex conceptions, the creations of\nscience, and the results of much labour and thought, as readily and\nfamiliarly as if they were convictions borrowed at once from the\nsenses. They are thus powerful instruments in enabling philosophers\nto ascend from one step of induction and generalization to another;\nand hereby contribute powerfully to the advance of knowledge and\ntruth.\n\nIt should be noticed, before we proceed, that the names of natural\nobjects, when they come to be considered as the objects of a\nscience, are selected according to the processes already enumerated.\nFor the most part, the natural historian adopts the common names of\nanimals, plants, minerals, gems, and the like, and only endeavours\nto secure their steady and consistent application. But many of these\nnames imply some peculiar, often fanciful, belief respecting the\nobject.\n\nVarious plants derive their names from their supposed virtues, as\n_herniaria_, _rupture-wort_; or from legends, as _herba Sancti\nJohannis_, _St. John's wort_. The same is the case with minerals:\nthus the _topaz_ was asserted to come from an island so shrouded in\nmists that navigators could only _conjecture_ (\u03c4\u03bf\u03c0\u03ac\u03b6\u03b5\u03b9\u03bd) where it\nwas. In these latter cases, however, the legend is often not the\ntrue origin of the name, but is suggested by it.\n\nThe privilege of constructing names where they are wanted, belongs\nto natural historians no less than to {269} the cultivators of\nphysical science; yet in the ancient world, writers of the former\nclass appear rarely to have exercised this privilege, even when they\nfelt the imperfections of the current language. Thus Aristotle\nrepeatedly mentions classes of animals which have no name, as\nco-ordinate with classes that have names; but he hardly ventures to\npropose names which may supply these defects[3\\4]. The vast\nimportance of nomenclature in natural history was not recognized\ntill the modern period.\n\n[Note 3\\4: In his _History of Animals_, (b. i. c. vi.), he says,\nthat the great classes of animals are Quadrupeds, Birds, Fishes,\nWhales (_Cetaceans_), Oysters (_Testaceans_), animals like crabs\nwhich have no general name (_Crustaceans_), soft animals (_Mollusks_\nand _Insects_). He does, however, call the Crustaces by a name\n(_Malacostraca_, soft-shelled) which has since been adopted by\nNaturalists.]\n\nWe have, however, hitherto considered only the formation or\nappropriation of single terms in science; except so far as several\nterms may in some instances be connected by reference to a common\ntheory. But when the value of technical terms began to be fully\nappreciated, philosophers proceeded to introduce them into their\nsciences more copiously and in a more systematic manner. In this\nway, the modern history of technical language has some features of a\ndifferent aspect from the ancient; and must give rise to a separate\nAphorism.\n\n\nAPHORISM II.\n\n_In the Modern Period of Science, besides the three processes\nanciently employed in the formation of technical terms, there have\nbeen introduced Systematic Nomenclature, Systematic Terminology, and\nthe Systematic Modification of Terms to express theoretical\nrelations_[4\\4].\n\n[Note 4\\4: On the subject of Terminology and Nomenclature, see also\nAphorisms LXXXVIII and XCVIII concerning Ideas, and b. viii. c. ii.\nof the _History of Scientific Ideas_. In those places I have spoken\nof the distinction of _Terminology_ and _Nomenclature_.]\n\n\nWRITERS upon science have gone on up to modern times forming such\ntechnical terms as they had occasion for, by the three processes\nabove {270} described;--namely, appropriating and limiting words in\ncommon use;--constructing for themselves words descriptive of the\nconception which they wished to convey;--or framing terms which by\ntheir signification imply the adoption of a theory. Thus among the\nterms introduced by the study of the connexion between magnetism and\nelectricity, the word _pole_ is an example of the first kind; the\nname of the subject, _electro-magnetism_, of the second; and the\nterm _current_, involving an hypothesis of the motion of a fluid, is\nan instance of the third class. In chemistry, the term _salt_ was\nadopted from common language, and its meaning extended to denote any\ncompound of a certain kind; the term _neutral_ salt implied the\nnotion of a balanced opposition in the two elements of the compound;\nand such words as _subacid_ and _superacid_, invented on purpose,\nwere introduced to indicate the cases in which this balance was not\nattained. Again, when the phlogistic theory of chemistry was\nestablished, the term _phlogiston_ was introduced to express the\ntheory, and from this such terms as _phlogisticated_ and\n_dephlogisticated_ were derived, exclusively words of science. But\nin such instances as have just been given, we approach towards a\nsystematic modification of terms, which is a peculiar process of\nmodern times. Of this, modern chemistry forms a prominent example,\nwhich we shall soon consider, but we shall first notice the other\nprocesses mentioned in the Aphorism.\n\nI. In ancient times, no attempt was made to invent or select a\nNomenclature of the objects of Natural History which should be\nprecise and permanent. The omission of this step by the ancient\nnaturalists gave rise to enormous difficulty and loss of time when\nthe sciences resumed their activity. We have seen in the history of\nthe sciences of classification, and of botany in especial[5\\4], that\nthe early cultivators of that study in modern times endeavoured to\nidentify all the plants described by Greek and Roman writers with\nthose which grow in the north of Europe; and were involved {271} in\nendless confusion[6\\4], by the multiplication of names of plants, at\nthe same time superfluous and ambiguous. The _Synonymies_ which\nbotanists (Bauhin and others) found it necessary to publish, were\nthe evidences of these inconveniences. In consequence of the\ndefectiveness of the ancient botanical nomenclature, we are even yet\nuncertain with respect to the identification of some of the most\ncommon trees mentioned by classical writers[7\\4]. The ignorance of\nbotanists respecting the importance of nomenclature operated in\nanother manner to impede the progress of science. As a good\nnomenclature presupposes a good system of classification, so, on the\nother hand, a system of classification cannot become permanent\nwithout a corresponding nomenclature. C\u00e6salpinus, in the sixteenth\ncentury[8\\4], published an excellent system of arrangement for\nplants; but this, not being connected with any system of names, was\nnever extensively accepted, and soon fell into oblivion. The\nbusiness of framing a scientific botanical classification was in\nthis way delayed for about a century. In the same manner,\nWilloughby's classification of fishes, though, as Cuvier says, far\nbetter than any which preceded it, was never extensively adopted, in\nconsequence of having no nomenclature connected with it.\n\n[Note 5\\4: _Hist. Ind. Sc._ b. xvi. c. ii.]\n\n[Note 6\\4: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 3.]\n\n[Note 7\\4: For instance, whether the _fagus_ of the Latins be the\nbeech or the chestnut.]\n\n[Note 8\\4: _Ib._ b. xvi. c. iii. sect. 2.]\n\nII. Probably one main cause which so long retarded the work of\nfixing at the same time the arrangement and the names of plants, was\nthe great number of minute and diversified particulars in the\nstructure of each plant which such a process implied. The stalks,\nleaves, flowers, and fruits of vegetables, with their appendages,\nmay vary in so many ways, that common language is quite insufficient\nto express clearly and precisely their resemblances and differences.\nHence botany required not only a fixed system of _names_ of plants,\nbut also an artificial system of phrases fitted to _describe_ their\nparts: not only a _Nomenclature_, but also {272} a _Terminology_.\nThe Terminology was, in fact, an instrument indispensably requisite\nin giving fixity to the Nomenclature. The recognition of the kinds\nof plants must depend upon the exact comparison of their\nresemblances and differences; and to become a part of permanent\nscience, this comparison must be recorded in words.\n\nThe formation of an exact descriptive language for botany was thus\nthe first step in that systematic construction of the technical\nlanguage of science, which is one of the main features in the\nintellectual history of modern times. The ancient botanists, as De\nCandolle[9\\4] says, did not make any attempt to select terms of\nwhich the sense was rigorously determined; and each of them employed\nin his descriptions the words, metaphors, or periphrases which his\nown genius suggested. In the History of Botany[10\\4], I have noticed\nsome of the persons who contributed to this improvement. 'Clusius,'\nit is there stated, 'first taught botanists to describe well. He\nintroduced exactitude, precision, neatness, elegance, method: he\nsays nothing superfluous; he omits nothing necessary.' This task was\nfurther carried on by Jung and Ray[11\\4]. In these authors we see\nthe importance which began to be attached to the exact definition of\ndescriptive terms; for example, Ray quotes Jung's definition of\n_Caulis_, a stalk.\n\n[Note 9\\4: _Theor. Elem. de Bot._ p. 327.]\n\n[Note 10\\4: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 3.]\n\n[Note 11\\4: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 3 (about A.D.\n1660).]\n\nThe improvement of descriptive language, and the formation of\nschemes of classification of plants, went on gradually for some\ntime, and was much advanced by Tournefort. But at last Linn\u00e6us\nembodied and followed out the convictions which had gradually been\naccumulating in the breasts of botanists; and by remodelling\nthroughout both the terminology and the nomenclature of botany,\nproduced one of the greatest reforms which ever took place in any\nscience. He thus supplied a conspicuous example of such a reform,\nand a most admirable model of a language, from which {273} other\nsciences may gather great instruction. I shall not here give any\naccount of the terms and words introduced by Linn\u00e6us. They have been\nexemplified in the _History of Science_[12\\4]; and the principles\nwhich they involve I shall consider separately hereafter. I will\nonly remind the reader that the great simplification in\n_nomenclature_ which was the result of his labours, consisted in\ndesignating each kind of plant by a _binary_ term consisting of the\nname of the _genus_ combined with that of the _species_: an artifice\nseemingly obvious, but more convenient in its results than could\npossibly have been anticipated.\n\n[Note 12\\4: _Ib._ c. iv. sect. 1-3.]\n\nSince Linn\u00e6us, the progress of Botanical Anatomy and of Descriptive\nBotany have led to the rejection of several inexact expressions, and\nto the adoption of several new terms, especially in describing the\nstructure of the fruit and the parts of cryptogamous plants. Hedwig,\nMedikus, Necker, Desvaux, Mirbel, and especially G\u00e6rtner, Link, and\nRichard, have proposed several useful innovations, in these as in\nother parts of the subject; but the general mass of the words now\ncurrent consists still, and will probably continue to consist, of\nthe terms established by the Swedish Botanist[13\\4].\n\n[Note 13\\4: De Candolle, _Th. Elem._ p. 307.]\n\nWhen it was seen that botany derived so great advantages from a\nsystematic improvement of its language, it was natural that other\nsciences, and especially classificatory sciences, should endeavour\nto follow its example. This attempt was made in Mineralogy by\nWerner, and afterwards further pursued by Mohs. Werner's innovations\nin the descriptive language of Mineralogy were the result of great\nacuteness, an intimate acquaintance with minerals, and a most\nmethodical spirit: and were in most respects great improvements upon\nprevious practices. Yet the introduction of them into Mineralogy was\nfar from regenerating that science, as Botany had been regenerated\nby the Linn\u00e6an reform. It would seem that the perpetual {274}\nscrupulous attention to most minute differences, (as of lustre,\ncolour, fracture,) the greater part of which are not really\nimportant, fetters the mind, rather than disciplines it or arms it\nfor generalization. Cuvier has remarked[14\\4] that Werner, after his\nfirst _Essay on the Characters of Minerals_, wrote little; as if he\nhad been afraid of using the system which he had created, and\ndesirous of escaping from the chains which he had imposed upon\nothers. And he justly adds, that Werner dwelt least, in his\ndescriptions, upon that which is really the most important feature\nof all, the crystalline structure. This, which is truly a definite\ncharacter, like those of Botany, does, when it can be clearly\ndiscerned, determine the place of the mineral in a system. This,\ntherefore, is the character which, of all others, ought to be most\ncarefully expressed by an appropriate language. This task, hardly\nbegun by Werner, has since been fully executed by others, especially\nby Rom\u00e9 de l'Isle, Ha\u00fcy, and Mohs. All the forms of crystals can be\ndescribed in the most precise manner by the aid of the labours of\nthese writers and their successors. But there is one circumstance\nwell worthy our notice in these descriptions. It is found that the\nlanguage in which they can best be conveyed is not that of words,\nbut of _symbols_. The relations of space which are involved in the\nforms of crystalline bodies, though perfectly definite, are so\ncomplex and numerous, that they cannot be expressed, except in the\nlanguage of mathematics: and thus we have an extensive and recondite\nbranch of mathematical science, which is, in fact, only a part of\nthe Terminology of the mineralogist.\n\n[Note 14\\4: _\u00c9loges_, ii. 134.]\n\nThe Terminology of Mineralogy being thus reformed, an attempt was\nmade to improve its Nomenclature also, by following the example of\nBotany. Professor Mohs was the proposer of this innovation. The\nnames framed by him were, however, not composed of two but of three\nelements, designating respectively the Species, the Genus, and the\nOrder[15\\4]: thus he has such species as {275} _Rhombohedral Lime\nHaloide_, _Octahedral Fluor Haloide_, _Prismatic Hal Baryte_. These\nnames have not been generally adopted; nor is it likely that any\nnames constructed on such a scheme will find acceptance among\nmineralogists, till the higher divisions of the system are found to\nhave some definite character. We see no real mineralogical\nsignificance in Mohs's Genera and Orders, and hence we do not expect\nthem to retain a permanent place in the science.\n\n[Note 15\\4: _Hist. Ind. Sc._ b. xv. c. ix.]\n\nThe only systematic names which have hitherto been generally\nadmitted in Mineralogy, are those expressing the chemical\nconstitution of the substance; and these belong to a system of\ntechnical terms different from any we have yet spoken of, namely to\nterms formed by systematic modification.\n\nIII. The language of Chemistry was already, as we have seen, tending\nto assume a systematic character, even under the reign of the\nphlogiston theory. But when oxygen succeeded to the throne, it very\nfortunately happened that its supporters had the courage and the\nforesight to undertake a completely new and systematic recoinage of\nthe terms belonging to the science. The new nomenclature was\nconstructed upon a principle hitherto hardly applied in science, but\neminently commodious and fertile; namely, the principle of\nindicating a modification of relations of elements, by a change in\nthe termination of the word. Thus the new chemical school spoke of\nsulph_uric_ and sulph_urous_ acids; of sulph_ates_ and sulph_ites_\nof bases; and of sulph_urets_ of metals; and in like manner, of\nphos_phoric_ and phos_phorous_ acids, of phos_phates_, phos_phites_,\nphos_phurets_. In this manner a nomenclature was produced, in which\nthe very name of a substance indicated at once its constitution and\nplace in the system.\n\nThe introduction of this chemical language can never cease to be\nconsidered one of the most important steps ever made in the\nimprovement of technical terms; and as a signal instance of the\nadvantages which may result from artifices apparently trivial, if\nemployed in a manner conformable to the laws of phenomena, and\nsystematically pursued. It was, however, proved that {276} this\nlanguage, with all its merits, had some defects. The relations of\nelements in composition were discovered to be more numerous than the\nmodes of expression which the terminations supplied. Besides the\nsulphurous and sulphuric acids, it appeared there were others; these\nwere called the _hyposulphurous_ and _hyposulphuric_: but these\nnames, though convenient, no longer implied, by their form, any\ndefinite relation. The compounds of Nitrogen and Oxygen are, in\norder, the _Protoxide_, the _Deutoxide_ or _Binoxide_; _Hyponitrous_\nAcid, _Nitrous_ Acid, and _Nitric_ Acid. The nomenclature here\nceases to be systematic. We have three oxides of Iron, of which we\nmay call the first the _Protoxide_, but we cannot call the others\nthe _Deutoxide_ and _Trioxide_, for by doing so we should convey a\nperfectly erroneous notion of the proportions of the elements. They\nare called the _Protoxide_, the _Black_ Oxide, and the _Peroxide_.\nWe are here thrown back upon terms quite unconnected with the\nsystem.\n\nOther defects in the nomenclature arose from errours in the theory;\nas for example the names of the muriatic, oxymuriatic, and\nhyperoxymuriatic acids; which, after the establishment of the new\ntheory of chlorine, were changed to _hydrochloric_ acid, _chlorine_,\nand _chloric_ acid.\n\nThus the chemical system of nomenclature, founded upon the oxygen\ntheory, while it shows how much may be effected by a good and\nconsistent scheme of terms, framed according to the real relations\nof objects, proves also that such a scheme can hardly be permanent\nin its original form, but will almost inevitably become imperfect\nand anomalous, in consequence of the accumulation of new facts, and\nthe introduction of new generalizations. Still, we may venture to\nsay that such a scheme does not, on this account, become worthless;\nfor it not only answers its purpose in the stage of scientific\nprogress to which it belongs:--so far as it is not erroneous, or\nmerely conventional, but really systematic and significant of truth,\nits terms can be translated at once into the language of any higher\ngeneralization which is afterwards arrived at. If terms express\n{277} relations really ascertained to be true, they can never lose\ntheir value by any change of the received theory. They are like\ncoins of pure metal, which, even when carried into a country which\ndoes not recognize the sovereign whose impress they bear, are still\ngladly received, and may, by the addition of an explanatory mark,\ncontinue part of the common currency of the country.\n\nThese two great instances of the reform of scientific language, in\nBotany and in Chemistry, are much the most important and instructive\nevents of this kind which the history of science offers. It is not\nnecessary to pursue our historical survey further. Our remaining\nAphorisms respecting the Language of Science will be collected and\nillustrated indiscriminately, from the precepts and the examples of\npreceding philosophers of all periods[16\\4].\n\n[Note 16\\4: See at the end of these Aphorisms, further illustrations\nof them from the recent history of Comparative Anatomy and\nChemistry.]\n\nWe may, however, remark that Aphorisms III., IV., V., VI., VII.,\nrespect peculiarly the Formation of Technical Terms by the\nAppropriation of Common Words, while the remaining ones apply to the\nFormation of New Terms.\n\nIt does not appear possible to lay down a system of rules which may\ndetermine and regulate the construction of all technical terms, on\nall the occasions on which the progress of science makes them\nnecessary or convenient. But if we can collect a few maxims such as\nhave already offered themselves to the minds of philosophers, or\nsuch as may be justified by the instances by which we shall\nillustrate them, these maxims may avail to guide us in doubtful\ncases, and to prevent our aiming at advantages which are\nunattainable, or being disturbed by seeming imperfections which are\nreally no evils. I shall therefore state such maxims of this kind as\nseem most sound and useful. {278}\n\n\nAPHORISM III.\n\n_In framing scientific terms, the appropriation of old words is\npreferable to the invention of new ones._\n\n\nTHIS maxim is stated by Bacon in his usual striking manner. After\nmentioning _Metaphysic_, as one of the divisions of Natural\nPhilosophy, he adds[17\\4]: 'Wherein I desire it may be conceived\nthat I use the word _metaphysic_ in a different sense from that that\nis received: and in like manner I doubt not but it will easily\nappear to men of judgment that in this and other particulars,\nwheresoever my conception and notion may differ from the ancient,\nyet I am studious to keep the ancient terms. For, hoping well to\ndeliver myself from mistaking by the order and perspicuous\nexpressing of that I do propound; I am otherwise zealous and\naffectionate to recede as little from antiquity, either in terms or\nopinions, as may stand with truth, and the proficience of knowledge,\n. . . To me, that do desire, as much as lieth in my pen, to ground a\nsociable intercourse between antiquity and proficience, it seemeth\nbest to keep a way with antiquity _usque ad aras_; and therefore to\nretain the ancient terms, though I sometimes alter the uses and\ndefinitions; according to the moderate proceeding in civil\ngovernments, when, although there be some alteration, yet that\nholdeth which Tacitus wisely noteth, _eadem magistratuum vocabula_.'\n\n[Note 17\\4: _De Augm._ lib. iii. c. iv.]\n\nWe have had before us a sufficient number of examples of scientific\nterms thus framed; for they formed the first of three classes which\nwe described in the First Aphorism. And we may again remark, that\nscience, when she thus adopts terms which are in common use, always\nlimits and fixes their meaning in a technical manner. We may also\nrepeat here the warning already given respecting terms of this kind,\nthat they are peculiarly liable to mislead readers who {279} do not\ntake care to understand them in their technical instead of their\ncommon signification. _Force_, _momentum_, _inertia_, _impetus_,\n_vis viva_, are terms which are very useful, if we rigorously bear\nin mind the import which belongs to each of them in the best\ntreatises on Mechanics; but if the reader content himself with\nconjecturing their meaning from the context, his knowledge will be\nconfused and worthless.\n\nIn the application of this Third Aphorism, other rules are to be\nattended to, which I add.\n\n\nAPHORISM IV.\n\n_When common words are appropriated as technical terms, their\nmeaning and relations in common use should be retained as far as can\nconveniently be done._\n\n\nI WILL state an example in which this rule seems to be applicable.\nMr Davies Gilbert[18\\4] has recently proposed the term _efficiency_\nto designate the work which a machine, according to the force\nexerted upon it, is capable of doing; the work being measured by the\nweight raised, and the space through which it is raised, jointly.\nThe usual term employed among engineers for the work which a machine\nactually does, measured in the way just stated, is _duty_. But as\nthere appears to be a little incongruity in calling that work\n_efficiency_ which the machine _ought_ to do, when we call that work\n_duty_ which it really does, I have proposed to term these two\nquantities _theoretical efficiency_ and _practical efficiency_, or\n_theoretical duty_ and _practical duty_[19\\4].\n\n[Note 18\\4: _Phil. Trans._ 1827, p. 25.]\n\n[Note 19\\4: The term _travail_ is used by French engineers, to\nexpress _efficiency_ or _theoretical duty_. This term has been\nrendered in English by _labouring force_.]\n\nSince common words are often vague in their meaning, I add as a\nnecessary accompaniment to the Third Aphorism the following:-- {280}\n\n\nAPHORISM V.\n\n_When common words are appropriated as technical terms, their\nmeaning may be modified, and must be rigorously fixed._\n\n\nTHIS is stated by Bacon in the above extract: 'to retain the ancient\nterms, though I sometimes _alter the uses and definitions_.' The\nscientific use of the term is in all cases much more precise than\nthe common use. The loose notions of _velocity_ and _force_ for\ninstance, which are sufficient for the usual purposes of language,\nrequire to be fixed by exact measures when these are made terms in\nthe science of Mechanics.\n\nThis scientific fixation of the meaning of words is to be looked\nupon as a matter of convention, although it is in reality often an\ninevitable result of the progress of science. _Momentum_ is\nconventionally defined to be the product of the numbers expressing\nthe weight and the velocity; but then, it could be of no use in\nexpressing the laws of motion if it were defined otherwise.\n\nHence it is no valid objection to a scientific term that the word in\ncommon language does not mean exactly the same as in its common use.\nIt is no sufficient reason against the use of the term _acid_ for a\nclass of bodies, that all the substances belonging to this class are\nnot sour. We have seen that a _trapezium_ is used in geometry for\nany four-sided figure, though originally it meant a figure with two\nopposite sides parallel and the two others equal. A certain stratum\nwhich lies below the chalk is termed by English geologists _the\ngreen sand_. It has sometimes been objected to this denomination\nthat the stratum has very frequently no tinge of green, and that it\nis often composed of lime with little or no sand. Yet the term is a\ngood technical term in spite of these apparent improprieties; so\nlong as it is carefully applied to that stratum which is\ngeologically equivalent to the greenish sandy bed to which the\nappellation was originally applied.\n\nWhen it appeared that _geometry_ would have to be employed as much\nat least about the heavens as the earth, Plato exclaimed against the\nfolly of calling the {281} science by such a name; since the word\nsignifies 'earth-measuring;' yet the word _geometry_ has retained\nits place and answered its purpose perfectly well up to the present\nday.\n\nBut though the meaning of the term may be modified or extended, it\nmust be rigorously fixed when it is appropriated to science. This\nprocess is most abundantly exemplified by the terminology of Natural\nHistory, and especially of Botany, in which each term has a most\nprecise meaning assigned to it. Thus Linn\u00e6us established exact\ndistinctions between _fasciculus_, _capitulum_, _racemus_,\n_thyrsus_, _paniculus_, _spica_, _amentum_, _corymbus_, _umbella_,\n_cyma_, _verticillus_; or, in the language of English Botanists, _a\ntuft_, _a head_, _a cluster_, _a bunch_, _a panicle_, _a spike_, _a\ncatkin_, _a corymb_, _an umbel_, _a cyme_, _a whorl_. And it has\nsince been laid down as a rule[20\\4], that each organ ought to have\na separate and appropriate name; so that the term _leaf_, for\ninstance, shall never be applied to _a leaflet_, _a bractea_, or _a\nsepal_ of the calyx.\n\n[Note 20\\4: De Candolle, _Theor. El._ 328.]\n\nBotanists have not been content with fixing the meaning of their\nterms by verbal definition, but have also illustrated them by\nfigures, which address the eye. Of these, as excellent modern\nexamples, may be mentioned those which occur in the works of\nMirbel[21\\4], and Lindley[22\\4].\n\n[Note 21\\4: _\u00c9l\u00e9mens de Botanique_.]\n\n[Note 22\\4: _Elements of Botany_.]\n\n\nAPHORISM VI.\n\n_When common words are appropriated as technical terms, this must be\ndone so that they are not ambiguous in their application._\n\n\nAN example will explain this maxim. The conditions of a body, as a\nsolid, a liquid, and an air, have been distinguished as different\n_forms_ of the body. But the word _form_, as applied to bodies, has\nother meanings; so that if we were to inquire in _what form_ water\nexists in a snow-cloud, it might be doubted whether the forms of\ncrystallization were meant, or {282} the different forms of ice,\nwater, and vapour. Hence I have proposed[23\\4] to reject the term\n_form_ in such cases, and to speak of the different _consistence_ of\na body in these conditions. The term _consistence_ is usually\napplied to conditions between solid and fluid; and may without\neffort be extended to those limiting conditions. And though it may\nappear more harsh to extend the term _consistence_ to the state of\nair, it may be justified by what has been said in speaking of\nAphorism V.\n\n[Note 23\\4: _Hist. Ind. Sc._ b. x. c. ii. sect. 2.]\n\nI may notice another example of the necessity of avoiding ambiguous\nwords. A philosopher who makes method his study, would naturally be\ntermed a _methodist_; but unluckily this word is already\nappropriated to a religious sect: and hence we could hardly venture\nto speak of C\u00e6salpinus, Ray, Morison, Rivinus, Tournefort, Linn\u00e6us,\nand their successors, as _botanical methodists_. Again, by this\nmaxim, we are almost debarred from using the term _physician_ for a\ncultivator of the science of physics, because it already signifies a\npractiser of physic. We might, perhaps, still use _physician_ as the\nequivalent of the French _physicien_, in virtue of Aphorism V.; but\nprobably it would be better to form a new word. Thus we may say,\nthat while the Naturalist employs principally the ideas of\nresemblance and life, the _Physicist_ proceeds upon the ideas of\nforce, matter, and the properties of matter.\n\nWhatever may be thought of this proposal, the maxim which it implies\nis frequently useful. It is this.\n\n\nAPHORISM VII.\n\n_It is better to form new words as technical terms, than to employ\nold ones in which the last three Aphorisms cannot be complied with._\n\n\nTHE principal inconvenience attending the employment of new words\nconstructed expressly for the use of science, is the difficulty of\neffectually introducing them. Readers will not readily take the\ntrouble to learn the meaning of a word, in which the memory is {283}\nnot assisted by some obvious suggestion connected with the common\nuse of language. When this difficulty is overcome, the new word is\nbetter than one merely appropriated; since it is more secure from\nvagueness and confusion. And in cases where the inconveniences\nbelonging to a scientific use of common words become great and\ninevitable, a new word must be framed and introduced.\n\nThe Maxims which belong to the construction of such words will be\nstated hereafter; but I may notice an instance or two tending to\nshow the necessity of the Maxim now before us.\n\nThe word _Force_ has been appropriated in the science of Mechanics\nin two senses: as indicating the cause of motion; and again, as\nexpressing certain measures of the effects of this cause, in the\nphrases _accelerating force_ and _moving force_. Hence we might have\noccasion to speak of the accelerating or moving force _of_ a certain\n_force_; for instance, if we were to say that the force which\ngoverns the motions of the planets resides in the sun; and that the\naccelerating force _of_ this _force_ varies only with the distance,\nbut its moving force varies as the product of the mass of the sun\nand the planet. This is a harsh and incongruous mode of expression;\nand might have been avoided, if, instead of _accelerating force_ and\n_moving force_, single abstract terms had been introduced by Newton:\nif, for instance, he had said that the velocity generated in a\nsecond measures the _accelerativity_ of the force which produces it,\nand the momentum produced in a second measures the _motivity_ of the\nforce.\n\nThe science which treats of heat has hitherto had no special\ndesignation: treatises upon it have generally been termed treatises\n_On Heat_. But this practice of employing the same term to denote\nthe property and the science which treats of it, is awkward, and\noften ambiguous. And it is further attended with this inconvenience,\nthat we have no adjective derived from the name of the science, as\nwe have in other cases, when we speak of _acoustical_ experiments\nand _optical_ theories. This inconvenience has led various persons\nto suggest names for the Science of Heat. M. Comte {284} terms it\n_Thermology_. In the _History of the Sciences_, I have named it\n_Thermotics_, which appears to me to agree better with the analogy\nof the names of other corresponding sciences, _Acoustics_ and\n_Optics_.\n\n_Electricity_ is in the same condition as Heat; having only one word\nto express the property and the science. M. Le Comte proposes\n_Electrology_: for the same reason as before, I should conceive\n_Electrics_ more agreeable to analogy. The coincidence of the word\nwith the plural of Electric would not give rise to ambiguity; for\n_Electrics_, taken as the name of a science, would be singular, like\n_Optics_ and _Mechanics_. But a term offers itself to express\n_common_ or _machine Electrics_, which appears worthy of admission,\nthough involving a theoretical view. The received doctrine of the\ndifference between Voltaic and Common Electricity is, that in the\nformer case the fluid must be considered as in motion, in the latter\nas at rest. The science which treats of the former class of subjects\nis commonly termed _Electrodynamics_, which obviously suggests the\nname _Electrostatics_ for the latter.\n\nThe subject of the Tides is, in like manner, destitute of any name\nwhich designates the science concerned about it. I have ventured to\nemploy the term _Tidology_, having been much engaged in tidological\nresearches.\n\nMany persons possess a peculiarity of vision, which disables them\nfrom distinguishing certain colours. On examining many such cases,\nwe find that in all such persons the peculiarities are the same; all\nof them confounding scarlet with green, and pink with blue. Hence\nthey form a class, which, for the convenience of physiologists and\nothers, ought to have a fixed designation. Instead of calling them,\nas has usually been done, 'persons having a peculiarity of vision,'\nwe might take a Greek term implying this meaning, and term them\n_Idiopts_.\n\nBut my business at present is not to speak of the selection of new\nterms when they are introduced, but to illustrate the maxim that the\nnecessity for their introduction often arises. The construction of\nnew terms will be treated of subsequently. {285}\n\n\nAPHORISM VIII.\n\n_Terms must be constructed and appropriated so as to be fitted to\nenunciate simply and clearly true general propositions._\n\n\nTHIS Aphorism may be considered as the fundamental principle and\nsupreme rule of all scientific terminology. It is asserted by\nCuvier, speaking of a particular case. Thus he says[24\\4] of Gmelin,\nthat by placing the lamantin in the genus of morses, and the siren\nin the genus of eels, he had rendered every general proposition\nrespecting the organization of those genera impossible.\n\n[Note 24\\4: _R\u00e8gne Animal_, Introd. viii.]\n\nThe maxim is true of words appropriated as well as invented, and\napplies equally to the mathematical, chemical, and classificatory\nsciences. With regard to most of these, and especially the two\nformer classes, it has been abundantly exemplified already, in what\nhas previously been said, and in the _History of the Sciences_. For\nwe have there had to notice many technical terms, with the occasions\nof their introduction; and all these occasions have involved the\nintention of expressing in a convenient manner some truth or\nsupposed truth. The terms of Astronomy were adopted for the purpose\nof stating and reasoning upon the relations of the celestial\nmotions, according to the doctrine of the sphere, and the other laws\nwhich were discovered by astronomers. The few technical terms which\nbelong to Mechanics, _force_, _velocity_, _momentum_, _inertia_,\n&c., were employed from the first with a view to the expression of\nthe laws of motion and of rest; and were, in the end, limited so as\ntruly and simply to express those laws when they were fully\nascertained. In Chemistry, the term _phlogiston_ was useful, as has\nbeen shown in the _History_, in classing together processes which\nreally are of the same nature; and the nomenclature of the _oxygen_\ntheory was still preferable, because it enabled the chemist to\nexpress a still greater number of general truths. {286}\n\nTo the connexion here asserted, of theory and nomenclature, we have\nthe testimony of the author of the oxygen theory. In the Preface to\nhis _Chemistry_, Lavoisier says:--'Thus while I thought myself\nemployed only in forming a Nomenclature, and while I proposed to\nmyself nothing more than to improve the chemical language, my work\ntransformed itself by degrees, without my being able to prevent it,\ninto a Treatise on the Elements of Chemistry.' And he then proceeds\nto show how this happened.\n\nIt is, however, mainly through the progress of Natural History in\nmodern times, that philosophers have been led to see the importance\nand necessity of new terms in expressing new truths. Thus Harvey, in\nthe Preface to his work on Generation, says:--'Be not offended if in\nsetting out the History of the Egg I make use of a new method, and\nsometimes of unusual terms. For as they which find out a new\nplantation and new shores call them by names of their own coining,\nwhich posterity afterwards accepts and receives, so those that find\nout new secrets have good title to their compellation. And here,\nmethinks, I hear Galen advising: If we consent in the things,\ncontend not about the words.'\n\nThe Nomenclature which answers the purposes of Natural History is a\nSystematic Nomenclature, and will be further considered under the\nnext Aphorism. But we may remark, that the Aphorism now before us\ngoverns the use of words, not in science only, but in common\nlanguage also. Are we to apply the name _fish_ to animals of the\nwhale kind? The answer is determined by our present rule: we are to\ndo so, or not, accordingly as we can best express true propositions.\nIf we are speaking of the internal structure and physiology of the\nanimal, we must not call them _fish_; for in these respects they\ndeviate widely from fishes: they have warm blood, and produce and\nsuckle their young as land quadrupeds do. But this would not prevent\nour speaking of the _whale-fishery_, and calling such animals _fish_\non all occasions connected with this employment; for the relations\nthus arising depend upon the animal's living in the water, and being\ncaught in a {287} manner similar to other fishes. A plea that human\nlaws which mention fish do not apply to whales, would be rejected at\nonce by an intelligent judge.\n\n[A bituminiferous deposit which occurs amongst the coal measures in\nthe neighbourhood of Edinburgh was used as coal, and called 'Boghead\nCannel Coal.' But a lawsuit arose upon the question whether this,\nwhich geologically was not _the coal_, should be regarded in law as\n_coal_. The opinions of chemists and geologists, as well as of\nlawyers, were discrepant, and a direct decision of the case was\nevaded.[25\\4]]\n\n[Note 25\\4: Miller's _Chemistry_, iii. 98.]\n\n\nAPHORISM IX.\n\n_In the Classificatory Sciences, a Systematic Nomenclature is\nnecessary; and the System and the Nomenclature are each essential to\nthe utility of the other._\n\n\nTHE inconveniences arising from the want of a good Nomenclature were\nlong felt in Botany, and are still felt in Mineralogy. The attempts\nto remedy them by _Synonymies_ are very ineffective, for such\ncomparisons of synonyms do not supply a systematic nomenclature; and\nsuch a one alone can enable us to state general truths respecting\nthe objects of which the classificatory sciences treat. The _System_\nand the _Names_ ought to be introduced together; for the former is a\ncollection of asserted analogies and resemblances, for which the\nlatter provide simple and permanent expressions. Hence it has\nrepeatedly occurred in the progress of Natural History, that good\nSystems did not take root, or produce any lasting effect among\nnaturalists, because they were not accompanied by a corresponding\nNomenclature. In this way, as we have already noticed, the excellent\nbotanical System of C\u00e6salpinus was without immediate effect upon the\nscience. The work of Willoughby, as Cuvier says[26\\4], forms an\nepoch, and {288} a happy epoch in Ichthyology; yet because Willoughby\nhad no Nomenclature of his own, and no fixed names for his genera,\nhis immediate influence was not great. Again, in speaking of\nSchlotheim's work containing representations of fossil vegetables,\nM. Adolphe Brongniart observes[27\\4] that the figures and\ndescriptions are so good, that if the author had established a\nnomenclature for the objects he describes, his work would have\nbecome the basis of all succeeding labours on the subject.\n\n[Note 26\\4: _Hist. des Poissons_, Pref.]\n\n[Note 27\\4: _Prodrom. Veg. Foss._ p. 3.]\n\nAs additional examples of cases in which the improvement of\nclassification, in recent times, has led philosophers to propose new\nnames, I may mention the term _P\u0153cilite_, proposed by Mr. Conybeare\nto designate the group of strata which lies below the oolites and\nlias, including the new red or variegated sandstone, with the keuper\nabove, and the magnesian limestone below it. Again, the transition\ndistricts of our island have recently been reduced to system by\nProfessor Sedgwick and Mr. Murchison; and this step has been marked\nby the terms _Cambrian_ system, and _Silurian_ system, applied to\nthe two great groups of formations which they have respectively\nexamined, and by several other names of the subordinate members of\nthese formations.\n\nThus System and Nomenclature are each essential to the other.\nWithout Nomenclature, the system is not permanently incorporated\ninto the general body of knowledge, and made an instrument of future\nprogress. Without System, the names cannot express general truths,\nand contain no reason why they should be employed in preference to\nany other names.\n\nThis has been generally acknowledged by the most philosophical\nnaturalists of modern times. Thus Linn\u00e6us begins that part of his\nBotanical Philosophy in which names are treated of, by stating that\nthe foundation of botany is twofold, _Disposition_ and\n_Denomination_; and he adds this Latin line,\n Nomina si nescis perit et cognitio rerum. {289}\nAnd Cuvier, in the Preface to his _Animal\nKingdom_, explains, in a very striking manner, how the attempt to\nconnect zoology with anatomy led him, at the same time, to reform\nthe classifications, and to correct the nomenclature of preceding\nzoologists.\n\nI have stated that in Mineralogy we are still destitute of a good\nnomenclature generally current. From what has now been said, it will\nbe seen that it may be very far from easy to supply this defect,\nsince we have, as yet, no generally received system of mineralogical\nclassification. Till we know what are really different species of\nminerals, and in what larger groups these species can be arranged,\nso as to have common properties, we shall never obtain a permanent\nmineralogical nomenclature. Thus _Leucocyclite_ and _Tesselite_ are\nminerals previously confounded with Apophyllite, which Sir John\nHerschel and Sir David Brewster distinguished by those names, in\nconsequence of certain optical properties which they exhibit. But\nare these properties definite distinctions? and are there any\nexternal differences corresponding to them? If not, can we consider\nthem as separate species? and if not separate species, ought they to\nhave separate names? In like manner, we might ask if _Augite_ and\n_Hornblende_ are really the same species, as Gustavus Rose has\nmaintained? if _Diallage_ and _Hypersthene_ are not definitely\ndistinguished, which has been asserted by Kobell? Till such\nquestions are settled, we cannot have a fixed nomenclature in\nmineralogy. What appears the best course to follow in the present\nstate of the science, I shall consider when we come to speak of the\nform of technical terms.\n\nI may, however, notice here that the main Forms of systematic\nnomenclature are two:--terms which are produced by combining words\nof higher and lower generality, as the binary names, consisting of\nthe name of the genus and the species, generally employed by natural\nhistorians since the time of Linn\u00e6us;--and terms in which some\nrelation of things is indicated by a change in the form of the word,\nfor example, an alteration of its termination, of which kind of\n{290} nomenclature we have a conspicuous example in the modern\nchemistry.\n\n\nAPHORISM X.\n\n_New terms and changes of terms, which are not needed in order to\nexpress truth, are to be avoided._\n\n\nAS the Seventh Aphorism asserted that novelties in language may be\nand ought to be introduced, when they aid the enunciation of truths,\nwe now declare that they are not admissible in any other case. New\nterms and new systems of terms are not to be introduced, for\nexample, in virtue of their own neatness or symmetry, or other\nmerits, if there is no occasion for their use.\n\nI may mention, as an old example of a superfluous attempt of this\nkind, an occurrence in the history of Astronomy. In 1628 John Bayer\nand Julius Schiller devised a _C\u0153lum Christianum_, in which the\ncommon names of the planets, &c., were replaced by those of Adam,\nMoses, and the Patriarchs. The twelve Signs became the twelve\nApostles, and the constellations became sacred places and things.\nPeireskius, who had to pronounce upon the value of this proposal,\npraised the piety of the inventors, but did not approve, he\nsaid[28\\4], the design of perverting and confounding whatever of\ncelestial information from the period of the earliest memory is\nfound in books.\n\n[Note 28\\4: Gassendi, _Vita Peireskii_, 300.]\n\nNor are slight anomalies in the existing language of science\nsufficient ground for a change, if they do not seriously interfere\nwith the expression of our knowledge. Thus Linn\u00e6us says[29\\4] that a\nfair generic name is not to be exchanged for another though apter\none: and[30\\4] if we separate an old genus into several, we must try\nto find names for them among the synonyms which describe the old\ngenus. This maxim excludes the restoration of ancient names long\ndisused, no less than the needless invention of new ones. Linn\u00e6us\n{291} lays down this rule[31\\4]; and adds, that the botanists of the\nsixteenth century well nigh ruined botany by their anxiety to\nrecover the ancient names of plants. In like manner Cuvier[32\\4]\nlaments it as a misfortune, that he has had to introduce many new\nnames; and declares earnestly that he has taken great pains to\npreserve those of his predecessors.\n\n[Note 29\\4: _Phil. Bot._ 246.]\n\n[Note 30\\4: _Ib._ 247.]\n\n[Note 31\\4: _Phil. Bot._ 248.]\n\n[Note 32\\4: _R\u00e8gne Anim._ Pref. xvi.]\n\nThe great bulk which the Synonymy of botany and of mineralogy have\nattained, shows us that this maxim has not been universally attended\nto. In these cases, however, the multiplication of different names\nfor the same kind of object has arisen in general from ignorance of\nthe identity of it under different circumstances, or from the want\nof a system which might assign to it its proper place. But there are\nother instances, in which the multiplication of names has arisen not\nfrom defect, but from excess, of the spirit of system. The love\nwhich speculative men bear towards symmetry and completeness is\nconstantly at work, to make them create systems of classification\nmore regular and more perfect than can be verified by the facts: and\nas good systems are closely connected with a good nomenclature,\nsystems thus erroneous and superfluous lead to a nomenclature which\nis prejudicial to science. For although such a nomenclature is\nfinally expelled, when it is found not to aid us in expressing the\ntrue laws of nature, it may obtain some temporary sway, during\nwhich, and even afterwards, it may be a source of much confusion.\n\nWe have a conspicuous example of such a result in the geological\nnomenclature of Werner and his school. Thus it was assumed, in\nWerner's system, that his _First_, _Second_, and _Third Fl\u00f6tz\nLimestone_, his _Old_ and _New Red Sandstone_, were universal\nformations; and geologists looked upon it as their business to\ndetect these strata in other countries. Names were thus assigned to\nthe rocks of various parts of Europe, which created immense\nperplexity before they were again ejected. The geological terms\nwhich now prevail, for {292} instance, those of Smith, are for the\nmost part not systematic, but are borrowed from accidents, as\nlocalities, or popular names; as _Oxford Clay_ and _Cornbrash_; and\nhence they are not liable to be thrust out on a change of system. On\nthe other hand we do not find sufficient reason to accept the system\nof names of strata proposed by Mr. Conybeare in the _Introduction to\nthe Geology of England and Wales_, according to which the\n_Carboniferous Rocks_ are the _Medial Order_,--having above them the\n_Supermedial Order_ (_New Red Sand_, _Oolites_ and _Chalk_), and\nabove these the _Superior Order_ (_Tertiary Rocks_); and\nagain,--having below, the _Submedial Order_ (the _Transition\nRocks_), and the _Inferior Order_ (_Mica Slate_, _Gneiss_,\n_Granite_). For though these names have long been proposed, it does\nnot appear that they are useful in enunciating geological truths. We\nmay, it would seem, pronounce the same judgment respecting the\nsystem of geological names proposed by M. Alexander Brongniart, in\nhis _Tableau des Terrains qui composent l'\u00e9corce du Globe_. He\ndivides these strata into nine classes, which he terms _Terrains\nAlluviens_, _Lysiens_, _Pyrogenes_, _Clysmiens_, _Yzemiens_,\n_Hemilysiens_, _Agalysiens_, _Plutoniques_, _Vulcaniques_. These\nclasses are again variously subdivided: thus the Terrains Yzemiens\nare _Thalassiques_, _Pelagiques_, and _Abyssiques_; and the\nAbyssiques are subdivided into _Lias_, _Keuper_, _Conchiliens_,\n_P\u0153ciliens_, _Peneens_, _Rudimentaires_, _Entritiques_, _Houillers_,\n_Carbonifers_ and _Gres Rouge Ancien_. Scarcely any amount of new\ntruths would induce geologists to burthen themselves at once with\nthis enormous system of new names: but in fact, it is evident that\nany portion of truth, which any author can have brought to light,\nmay be conveyed by means of a much simpler apparatus. Such a\nnomenclature carries its condemnation on its own face.\n\nNearly the same may be said of the systematic nomenclature proposed\nfor mineralogy by Professor Mohs. Even if all his Genera be really\nnatural groups, (a doctrine which we can have no confidence in till\nthey are confirmed by the evidence of chemistry,) there is no {293}\nnecessity to make so great a change in the received names of\nminerals. His proceeding in this respect, so different from the\ntemperance of Linn\u00e6us and Cuvier, has probably ensured a speedy\noblivion to this part of his system. In crystallography, on the\nother hand, in which Mohs's improvements have been very valuable,\nthere are several terms introduced by him, as _rhombohedron_,\n_scalenohedron_, _hemihedral_, _systems_ of crystallization, which\nwill probably be a permanent portion of the language of science.\n\nI may remark, in general, that the only persons who succeed in\nmaking great alterations in the language of science, are not those\nwho make names arbitrarily and as an exercise of ingenuity, but\nthose who have much new knowledge to communicate; so that the\nvehicle is commended to general reception by the value of what it\ncontains. It is only eminent discoverers to whom the authority is\nconceded of introducing a new system of names; just as it is only\nthe highest authority in the state which has the power of putting a\nnew coinage in circulation.\n\nI will here quote some judicious remarks of Mr. Howard, which fall\npartly under this Aphorism, and partly under some which follow. He\nhad proposed, as names for the kinds of clouds, the following:\n_Cirrus_, _Cirrocumulus_, _Cirrostratus_, _Cumulostratus_,\n_Cumulus_, _Nimbus_, _Stratus_. In an abridgment of his views, given\nin the Supplement to the _Encyclop\u00e6dia Britannica_, English names\nwere proposed as the equivalents of these; _Curlcloud_,\n_Sondercloud_, _Wanecloud_, _Twaincloud_, _Stackencloud_,\n_Raincloud_, _Fallcloud_. Upon these Mr. Howard observes: 'I mention\nthese, in order to have the opportunity of saying that I do not\nadopt them. The names for the clouds which I deduced from the Latin,\nare but seven in number, and very easy to remember. They were\nintended as _arbitrary terms_ for the _structure_ of clouds, and the\nmeaning of them was carefully fixed by a definition. The observer\nhaving once made himself master of this, was able to apply the term\nwith correctness, after a little experience, to the subject under\nall its varieties of form, colour, or position. The {294} new names,\nif meant to be another set of arbitrary terms, are superfluous; if\nintended to convey in themselves an explanation in English, they\nfail in this, by applying to some part or circumstance only of the\ndefinition; the _whole_ of which must be kept in view to study the\nsubject with success. To take for an example the first of the\nmodifications. The term _cirrus_ very readily takes an abstract\nmeaning, equally applicable to the rectilinear as to the flexuous\nforms of the subject. But the name of _curl-cloud_ will not, without\nsome violence to its _obvious sense_, acquire this more extensive\none: and will therefore be apt to mislead the reader rather than\nfurther his progress. Others of these names are as devoid of a\nmeaning obvious to the English reader, as the Latin terms\nthemselves. But the principal objection to English or any other\nlocal terms, remains to be stated. They take away from the\nnomenclature its general advantage of constituting, as far as it\ngoes, an universal language, by means of which the intelligent of\nevery country may convey to each other their ideas without the\nnecessity of translation.'\n\nI here adduce these as examples of the arguments against changing an\nestablished nomenclature. As grounds of selecting a new one, they\nmay be taken into account hereafter.\n\n\nAPHORISM XI.\n\n_Terms which imply theoretical views are admissible, as far as the\ntheory is proved._\n\n\nIT is not unfrequently stated that the circumstances from which the\nnames employed in science borrow their meaning, ought to be facts\nand not theories. But such a recommendation implies a belief that\nfacts are rigorously distinguished from theories and directly\nopposed to them; which belief, we have repeatedly seen, is\nunfounded. When theories are firmly established, they become facts;\nand names founded on such theoretical views are unexceptionable. If\nwe speak of the _minor_ {295} _axis_ of Jupiter's _orbit_, or of his\n_density_, or of _the angle of refraction_, or _the length of an\nundulation_ of red light, we assume certain theories; but inasmuch\nas the theories are now the inevitable interpretation of ascertained\nfacts, we can have no better terms to designate the conceptions thus\nreferred to. And hence the rule which we must follow is, not that\nour terms must involve no theory, but that they imply the theory\nonly in that sense in which it is the interpretation of the facts.\n\nFor example, the term _polarization_ of light was objected to, as\ninvolving a theory. Perhaps the term was at first suggested by\nconceiving light to consist of particles having poles turned in a\nparticular manner. But among intelligent speculators, the notion of\npolarization soon reduced itself to the simple conception of\nopposite properties in opposite positions, which is a bare statement\nof the fact: and the term being understood to have this meaning, is\na perfectly good term, and indeed the best which we can imagine for\ndesignating what is intended.\n\nI need hardly add the caution, that names involving theoretical\nviews not in accordance with facts are to be rejected. The following\ninstances exemplify both the positive and the negative application\nof this maxim.\n\nThe distinction of _primary_ and _secondary_ rocks in geology was\nfounded upon a theory; namely, that those which do not contain any\norganic remains were first deposited, and afterwards, those which\ncontain plants and animals. But this theory was insecure from the\nfirst. The difficulty of making the separation which it implied, led\nto the introduction of a class of _transition_ rocks. And the recent\nresearches of geologists lead them to the conclusion, that those\nrocks which are termed _primary_, may be the newest, not the oldest,\nproductions of nature.\n\nIn order to avoid this incongruity, other terms have been proposed\nas substitutes for these. Sir C. Lyell remarks[33\\4], that granite,\ngneiss, and the like, form a class {296} which should be designated\nby a common name; which name should not be of chronological import.\nHe proposes _hypogene_, signifying 'nether-formed;' and thus he\nadopts the theory that they have not assumed their present form and\nstructure at the surface, but determines nothing of the period when\nthey were produced.\n\n[Note 33\\4: _Princ. Geol._ iv. 386.]\n\nThese hypogene rocks, again, he divides into unstratified or\n_plutonic_, and altered stratified, or _metamorphic_; the latter\nterm implying the hypothesis that the stratified rocks to which it\nis applied have been altered, by the effect of fire or otherwise,\nsince they were deposited. That fossiliferous strata, in some cases\nat least, have undergone such a change, is demonstrable from\nfacts[34\\4].\n\n[Note 34\\4: _Elem. Geol._ p. 17.]\n\nThe modern nomenclature of chemistry implies the oxygen theory of\nchemistry. Hence it has sometimes been objected to. Thus Davy, in\nspeaking of the Lavoisierian nomenclature, makes the following\nremarks, which, however plausible they may sound, will be found to\nbe utterly erroneous[35\\4]. 'Simplicity and precision ought to be\nthe characteristics of a scientific nomenclature: words should\nsignify _things_, or the _analogies_ of things, and not _opinions_.\n. . . A substance in one age supposed to be simple, in another is\nproved to be compound, and _vice vers\u00e2_. A theoretical nomenclature\nis liable to continual alterations: _oxygenated muriatic acid_ is as\nimproper a term as _dephlogisticated marine acid_. Every school\nbelieves itself to be in the right: and if every school assumes to\nitself the liberty of altering the names of chemical substances in\nconsequence of _new ideas_ of their composition, there can be no\npermanency in the language of the science; it must always be\nconfused and uncertain. Bodies which are _similar_ to each other\nshould always be classed together; and there is a presumption that\ntheir composition is _analogous_. _Metals_, _earths_, _alkalis_, are\nappropriate names for the bodies they represent, and independent of\nall speculation: whereas _oxides_, _sulphurets_, and _muriates_ are\nterms founded upon opinions of the composition of bodies, some of\nwhich have been already found erroneous. {297} The least dangerous\nmode of giving a systematic form to a language seems to be to\nsignify the analogies of substances by some common sign affixed to\nthe beginning or the termination of the word. Thus as the metals\nhave been distinguished by a termination in _um_, as _aurum_, so\ntheir calciform or oxidated state might have been denoted by a\ntermination in _a_, as _aura_: and no progress, however great, in\nthe science could render it necessary that such a mode of\nappellation should be changed.'\n\n[Note 35\\4: _Elements of Chem. Phil._ p. 46.]\n\nThese remarks are founded upon distinctions which have no real\nexistence. We cannot separate _things_ from their _properties_, nor\ncan we consider their properties and analogies in any other way than\nby having _opinions_ about them. By contrasting _analogies_ with\n_opinions_, it might appear as if the author maintained that there\nwere certain analogies about which there was no room for erroneous\nopinions. Yet the analogies of chemical compounds, are, in fact,\nthose points which have been most the subject of difference of\nopinion, and on which the revolutions of theories have most changed\nmen's views. As an example of analogies which are still recognized\nunder alterations of theory, the writer gives the relation of a\nmetal to its oxide or calciform state. But this analogy of metallic\noxides, as Red Copper or Iron Ore, to Calx, or burnt lime, is very\nfar from being self-evident;--so far indeed, that the recognition of\nthe analogy was a great step in chemical _theory_. The terms which\nhe quotes, _oxygenated muriatic acid_ (and the same may be said of\n_dephlogisticated marine acid_,) if improper, are so not because\nthey involve theory, but because they involve false theory;--not\nbecause those who framed them did not endeavour to express\nanalogies, but because they expressed analogies about which they\nwere mistaken. Unconnected names, as _metals_, _earths_, _alkalis_,\nare good as the _basis_ of a systematic nomenclature, but they are\nnot substitutes for such a nomenclature. A systematic nomenclature\nis an instrument of great utility and power, as the modern history\nof chemistry has shown. It would be highly unphilosophical to reject\n{298} the use of such an instrument, because, in the course of the\nrevolutions of science, we may have to modify, or even to remodel it\naltogether. Its utility is not by that means destroyed. It has\nretained, transmitted, and enabled us to reason upon, the doctrines\nof the earlier theory, so far as they are true; and when this theory\nis absorbed into a more comprehensive one, (for this, and not its\nrefutation, is the end of a theory _so far as_ it is true,) the\nnomenclature is easily translated into that which the new theory\nintroduces. We have seen, in the history of astronomy, how valuable\nthe theory of _epicycles_ was, in its time: the nomenclature of the\nrelations of a planet's orbit, which that theory introduced, was one\nof Kepler's resources in discovering the _elliptical_ theory; and,\nthough now superseded, is still readily intelligible to astronomers.\n\nThis is not the place to discuss the reasons for the _form_ of\nscientific terms; otherwise we might ask, in reference to the\nobjections to the Lavoisierian nomenclature, if such forms as\n_aurum_ and _aura_ are good to represent the absence or presence of\noxygen, why such forms as _sulphite_ and _sulphate_ are not equally\ngood to represent the presence of what we may call a smaller or\nlarger dose of oxygen, so long as the oxygen theory is admitted in\nits present form; and to indicate still the difference of the same\nsubstances, if under any change of theory it should come to be\ninterpreted in a new manner.\n\nBut I do not now dwell upon such arguments, my object in this place\nbeing to show that terms involving theory are not only allowable, if\nunderstood so far as the theory is proved, but of great value, and\nindeed of indispensable use, in science. The objection to them is\ninconsistent with the objects of science. If, after all that has\nbeen done in chemistry or any other science, we have arrived at no\nsolid knowledge, no permanent truth;--if all that we believe now may\nbe proved to be false to-morrow;--then indeed our opinions and\ntheories are corruptible elements, on which it would be unwise to\nrest any thing important, and which we might wish to exclude, even\nfrom our names. But if {299} our knowledge has no more security than\nthis, we can find no reason why we should wish at all to have names\nof things, since the names are needed mainly that we may reason upon\nand increase our knowledge such as it is. If we are condemned to\nendless alternations of varying opinions, then, no doubt, our\ntheoretical terms may be a source of confusion; but then, where\nwould be the advantage of their being otherwise? what would be the\nvalue of words which should express in a more precise manner\nopinions equally fleeting? It will perhaps be said, our terms must\nexpress facts, not theories: but of this distinction so applied we\nhave repeatedly shown the futility. Theories firmly established are\nfacts. Is it not a fact that the rusting of iron arises from the\nmetal combining with the oxygen of the atmosphere? Is it not a fact\nthat a combination of oxygen and hydrogen produces water? That our\nterms should express _such_ facts, is precisely what we are here\ninculcating.\n\nOur examination of the history of science has led us to a view very\ndifferent from that which represents it as consisting in the\nsuccession of hostile opinions. It is, on the contrary, a progress,\nin which each step is recognized and employed in the succeeding one.\nEvery theory, so far as it is true, (and all that have prevailed\nextensively and long, contain a large portion of truth,) is taken up\ninto the theory which succeeds and seems to expel it. All the\nnarrower inductions of the first are included in the more\ncomprehensive generalizations of the second. And this is performed\nmainly by means of such terms as we are now considering;--terms\ninvolving the previous theory. It is by means of such terms, that\nthe truths at first ascertained become so familiar and manageable,\nthat they can be employed as elementary facts in the formation of\nhigher inductions.\n\nThese principles must be applied also, though with great caution,\nand in a temperate manner, even to descriptive language. Thus the\nmode of describing the forms of crystals adopted by Werner and Rom\u00e9\nde l'Isle was to consider an original form, from which other forms\nare derived by _truncations_ of the edges and the {300} angles.\nHa\u00fcy's method of describing the same forms, was to consider them as\nbuilt up of rows of small solids, the angles being determined by the\n_decrements_ of these rows. Both these methods of description\ninvolve hypothetical views; and the last was intended to rest on a\ntrue physical theory of the constitution of crystals. Both\nhypotheses are doubtful or false: yet both these methods are good as\nmodes of description: nor is Ha\u00fcy's terminology vitiated, if we\nsuppose (as in fact we must suppose in many instances,) that\ncrystalline bodies are not really made up of such small solids. The\nmode of describing an octahedron of fluor spar, as derived from the\ncube, by decrements of one row on all the edges, would still be\nproper and useful as a description, whatever judgment we should form\nof the material structure of the body. But then, we must consider\nthe solids which are thus introduced into the description as merely\nhypothetical geometrical forms, serving to determine the angles of\nthe faces. It is in this way alone that Ha\u00fcy's nomenclature can now\nbe retained.\n\nIn like manner we may admit theoretical views into the descriptive\nphraseology of other parts of Natural History: and the theoretical\nterms will replace the obvious images, in proportion as the theory\nis generally accepted and familiarly applied. For example, in\nspeaking of the Honeysuckle, we may say that the upper leaves are\n_perfoliate_, meaning that a single round leaf is perforated by the\nstalk, or threaded upon it. Here is an image which sufficiently\nconveys the notion of the form. But it is now generally recognized\nthat this apparent single leaf is, in fact, two opposite leaves\njoined together at their bases. If this were doubted, it may be\nproved by comparing the upper leaves with the lower, which are\nreally separate and opposite. Hence the term _connate_ is applied to\nthese conjoined opposite leaves, implying that they grow together;\nor they are called _connato-perfoliate_. Again; formerly the corolla\nwas called _monopetalous_ or _polypetalous_, as it consisted of one\npart or of several: but it is now agreed among botanists that those\ncorollas which {301} appear to consist of a single part, are, in\nfact, composed of several soldered together; hence the term\n_gamopetalous_ is now employed (by De Candolle and his followers)\ninstead of monopetalous[36\\4].\n\n[Note 36\\4: On this subject, see Illiger, _Versuch einer\nSystematischen Vollst\u00e4ndigen Terminologie f\u00fcr das Thierreich und\nPflanzenreich_ (1810). De Candolle, _Th\u00e9orie \u00c9l\u00e9mentaire de la\nBotanique_.]\n\nIn this way the language of Natural History not only expresses, but\ninevitably implies, general laws of nature; and words are thus\nfitted to aid the progress of knowledge in this, as in other\nprovinces of science.\n\n\nAPHORISM XII.\n\n_If terms are systematically good, they are not to be rejected\nbecause they are etymologically inaccurate._\n\n\nTERMS belonging to a system are defined, not by the meaning of their\nradical words, but by their place in the system. That they should be\nappropriate in their signification, aids the processes of\nintroducing and remembering them, and should therefore be carefully\nattended to by those who invent and establish them; but this once\ndone, no objections founded upon their etymological import are of\nany material weight. We find no inconvenience in the circumstance\nthat _geometry_ means the measuring of the earth, that the name\n_porphyry_ is applied to many rocks which have no fiery spots, as\nthe word implies, and _oolite_ to strata which have no roelike\nstructure. In like manner, if the term _p\u0153cilite_ were already\ngenerally received, as the name of a certain group of strata, it\nwould be no valid ground for quarrelling with it, that this group\nwas not always variegated in colour, or that other groups were\nequally variegated: although undoubtedly in _introducing_ such a\nterm, care should be taken to make it as distinctive as possible. It\noften happens, as we have seen, that by the natural progress of\nchanges in language, a word is steadily confirmed in a sense quite\ndifferent from its etymological import. But though {302} we may\naccept such instances, we must not wantonly attempt to imitate them.\nI say, not wantonly: for if the progress of scientific\nidentification compel us to follow any class of objects into\ncircumstances where the derivation of the term is inapplicable, we\nmay still consider the term as an unmeaning sound, or rather an\nhistorical symbol, expressing a certain member of our system. Thus\nif, in following the course of the _mountain_ or _carboniferous_\nlimestone, we find that in Ireland it does not form mountains nor\ncontain coal, we should act unwisely in breaking down the\nnomenclature in which our systematic relations are already\nexpressed, in order to gain, in a particular case, a propriety of\nlanguage which has no scientific value.\n\nAll attempts to act upon the maxim opposite to this, and to make our\nscientific names properly descriptive of the objects, have failed\nand must fail. For the marks which really distinguish the natural\nclasses of objects, are by no means obvious. The discovery of them\nis one of the most important steps in science; and when they are\ndiscovered, they are constantly liable to exceptions, because they\ndo not contain the essential differences of the classes. The natural\norder _Umbellat\u00e6_, in order to be a natural order, must contain some\nplants which have not umbels, as _Eryngium_[37\\4]. 'In such cases,'\nsaid Linn\u00e6us, 'it is of small import what you call the order, if you\ntake a proper series of plants, and give it some name which is\nclearly understood to apply to the plants you have associated.' 'I\nhave,' he adds, 'followed the rule of borrowing the name _\u00e0\nfortiori_, from the principal feature.'\n\n[Note 37\\4: See _Hist. Ind. Sc._ b. xvi. c. iv. sect. 5.]\n\nThe distinction of crystals into systems according to the degree of\nsymmetry which obtains in them, has been explained elsewhere. Two of\nthese systems, of which the relation as to symmetry might be\nexpressed by saying that one is _square pyramidal_ and the other\n_oblong pyramidal_, or the first _square prismatic_ and the second\n_oblong prismatic_, are termed by Mohs, the first, _Pyramidal_, and\nthe second _Prismatic_. And it may {303} be doubted whether it is\nworth while to invent other terms, though these are thus defective\nin characteristic significance. As an example of a needless\nrejection of old terms in virtue of a supposed impropriety in their\nmeaning, I may mention the attempt made in the last edition of\nHa\u00fcy's _Mineralogy_, to substitute _autopside_ and _heteropside_ for\n_metallic_ and _unmetallic_. It was supposed to be proved that all\nbodies have a metal for their basis; and hence it was wished to\navoid the term _unmetallic_. But the words _metallic_ and\n_unmetallic_ may mean that minerals _seem_ metallic and unmetallic,\njust as well as if they contained the element _opside_ to imply this\nseeming. The old names express all that the new express, and with\nmore simplicity, and therefore should not be disturbed.\n\nThe maxim on which we are now insisting, that we are not to be too\nscrupulous about the etymology of scientific terms, may, at first\nsight, appear to be at variance with our Fourth Aphorism, that words\nused technically are to retain their common meaning as far as\npossible. But it must be recollected, that in the Fourth Aphorism we\nspoke of _common_ words _appropriated_ as technical terms; we here\nspeak of words _constructed_ for scientific purposes. And although\nit is, perhaps, impossible to draw a broad line between these two\nclasses of terms, still the rule of propriety may be stated thus: In\ntechnical terms, deviations from the usual meaning of words are bad\nin proportion as the words are more familiar in our own language.\nThus we may apply the term _Cirrus_ to a cloud composed of\nfilaments, even if these filaments are straight; but to call such a\ncloud a _Curl cloud_ would be much more harsh.\n\nSince the names of things, and of classes of things, when\nconstructed so as to involve a description, are constantly liable to\nbecome bad, the natural classes shifting away from the descriptive\nmarks thus prematurely and casually adopted, I venture to lay down\nthe following maxim. {304}\n\n\nAPHORISM XIII.\n\n_The fundamental terms of a system of Nomenclature may be\nconveniently borrowed from casual or arbitrary circumstances._\n\n\nFOR instance, the names of plants, of minerals, and of geological\nstrata, may be taken from the places where they occur conspicuously\nor in a distinct form; as _Parietaria_, _Parnassia_, _Chalcedony_,\n_Arragonite_, _Silurian_ system, _Purbeck_ limestone. These names\nmay be considered as at first supplying standards of reference; for\nin order to ascertain whether any rock be _Purbeck_ limestone, we\nmight compare it with the rocks in the Isle of Purbeck. But this\nreference to a local standard is of authority only till the place of\nthe object in the system, and its distinctive marks, are\nascertained. It would not vitiate the above names, if it were found\nthat the _Parnassia_ does not grow on Parnassus; that _Chalcedony_\nis not found in Chalcedon; or even that _Arragonite_ no longer\noccurs in Arragon; for it is now firmly established as a mineral\nspecies. Even in geology such a reference is arbitrary, and may be\nsuperseded, or at least modified, by a more systematic\ndetermination. _Alpine_ limestone is no longer accepted as a\nsatisfactory designation of a rock, now that we know the limestone\nof the Alps to be of various ages.\n\nAgain, names of persons, either casually connected with the object,\nor arbitrarily applied to it, may be employed as designations. This\nhas been done most copiously in botany, as for example, _Nicotiana_,\n_Dahlia_, _Fuchsia_, _Jungermannia_, _Lonicera_. And Linn\u00e6us has\nlaid down rules for restricting this mode of perpetuating the memory\nof men, in the names of plants. Those generic names, he says[38\\4],\nwhich have been constructed to preserve the memory of persons who\nhave deserved well of botany, are to be religiously retained. This,\nhe adds, is the sole and supreme reward of the botanist's labours,\nand must be carefully guarded and {305} scrupulously bestowed, as an\nencouragement and an honour. Still more arbitrary are the terms\nborrowed from the names of the gods and goddesses, heroes and\nheroines of antiquity, to designate new genera in those departments\nof natural history in which so many have been discovered in recent\ntimes as to weary out all attempts at descriptive nomenclature.\nCuvier has countenanced this method. 'I have had to frame many new\nnames of genera and sub-genera,' he says[39\\4], 'for the sub-genera\nwhich I have established were so numerous and various, that the\nmemory is not satisfied with numerical indications. These I have\nchosen either so as to indicate some character, or among the usual\ndenominations, which I have latinized, or finally, after the example\nof Linn\u00e6us, among the names of mythology, which are in general\nagreeable to the ear, and which are far from being exhausted.'\n\n[Note 38\\4: _Phil. Bot._ 241.]\n\n[Note 39\\4: _R\u00e8gne An._ p. 16.]\n\nThis mode of framing names from the names of persons to whom it was\nintended to do honour, has been employed also in the mathematical\nand chemical sciences; but such names have rarely obtained any\npermanence, except when they recorded an inventor or discoverer.\nSome of the constellations, indeed, have retained such appellations,\nas _Berenice's Hair_; and the new star which shone out in the time\nof C\u00e6sar, would probably have retained the name given to it, of the\n_Julian Star_, if it had not disappeared again soon after. In the\nmap of the Moon, almost all the parts have had such names imposed\nupon them by those who have constructed such maps, and these names\nhave very properly been retained. But the names of new planets and\nsatellites thus suggested have not been generally accepted; as the\n_Medicean_ stars, the name employed by Galileo for the satellites of\nJupiter; the _Georgium Sidus_, the appellation proposed by Herschel\nfor Uranus when first discovered[40\\4]; Ceres _Ferdinandea_, {306}\nthe name which Piazzi wished to impose on the small planet Ceres.\nThe names given to astronomical Tables by the astronomers who\nconstructed them have been most steadily adhered to, being indeed\nnames of books, and not of natural objects. Thus there were the\n_Ilchanic_, the _Alphonsine_, the _Rudolphine_, the _Carolinian_\nTables. Comets which have been ascertained to be periodical, have\nvery properly had assigned to them the name of the person who\nestablished this point; and of these we have thus, _Halley's_,\n_Encke's Comet_, and _Biela's_ or _Gambart's Comet_.\n\n[Note 40\\4: In this case, the name _Uranus_, selected with a view to\nsymmetry according to the mythological order of descent of the\npersons (_Uranus_, _Saturn_, _Jupiter_, _Mars_) was adopted by\nastronomers in general, though not proposed or sanctioned by the\ndiscoverer of the new planet. In the cases of the smaller planets,\n_Ceres_, _Pallas_, _Juno_, and _Vesta_, the names were given either\nby the discoverer, or with his sanction. Following this rule, Bessel\ngave the name of _Astr\u00e6a_ to a new planet discovered in the same\nregion by Mr. Hencke, as mentioned in the additions to book vii. of\nthe _History_ (2nd Ed.). Following the same rule, and adhering as\nmuch as possible to mythological connexion, the astronomers of\nEurope have with the sanction of M. Le Verrier, given the name of\n_Neptune_ to the planet revolving beyond Uranus, and discovered in\nconsequence of his announcement of its probable existence, which had\nbeen inferred by Mr. Adams and him (calculating in ignorance of each\nother's purpose) from the perturbations of Uranus; as I have stated\nin the Additions to the Third Edition of the _History_.]\n\nIn the case of discoveries in science or inventions of apparatus,\nthe name of the inventor is very properly employed as the\ndesignation. Thus we have the _Torricellian_ Vacuum, the _Voltaic_\nPile, _Fahrenheit's_ Thermometer. And in the same manner with regard\nto laws of nature, we have _Kepler's_ Laws, _Boyle_ or _Mariotte's_\nlaw of the elasticity of air, _Huyghens's_ law of double refraction,\n_Newton's_ scale of colours. _Descartes'_ law of refraction is an\nunjust appellation; for the discovery of the law of sines was made\nby Snell. In deductive mathematics, where the invention of a theorem\nis generally a more definite step than an induction, this mode of\ndesignation is more common, as _Demoivre's_ Theorem, _Maclaurin's_\nTheorem, _Lagrange's_ Theorem, _Eulerian_ Integrals.\n\nIn the _History of Science_[41\\4] I have remarked that in the\ndiscovery of what is termed galvanism, Volta's {307} office was of a\nhigher and more philosophical kind than that of Galvani; and I have,\non this account, urged the propriety of employing the term\n_voltaic_, rather than _galvanic_ electricity. I may add that the\nelectricity of the common machine is often placed in contrast with\nthis, and appears to require an express name. Mr. Faraday calls it\n_common_ or _machine_ electricity; but I think that _franklinic_\nelectricity would form a more natural correspondence with _voltaic_,\nand would be well justified by Franklin's place in the history of\nthat part of the subject.\n\n[Note 41\\4: b. xiii. c. 1.]\n\n\nAPHORISM XIV.\n\n_The Binary Method of Nomenclature_ (_Names by Genus and Species_) _is\nthe most convenient hitherto employed in Classification._\n\n\nTHE number of species in every province of Natural History is so\nvast that we cannot distinguish them and record the distinctions\nwithout some artifice. The known species of plants, for instance,\nwere 10,000 in the time of Linn\u00e6us, and are now probably 60,000. It\nwould be useless to endeavour to frame and employ separate names for\neach of these species.\n\nThe division of the objects into a subordinated system of\nclassification enables us to introduce a Nomenclature which does not\nrequire this enormous number of names. The artifice employed is, to\nname a specimen by means of two (or it might be more) steps of the\nsuccessive division. Thus in Botany, each of the Genera has its\nname, and the species are marked by the addition of some epithet to\nthe name of the genus. In this manner about 1,700 Generic Names,\nwith a moderate number of Specific Names, were found by Linn\u00e6us\nsufficient to designate with precision all the species of vegetables\nknown at his time. And this _Binary Method_ of Nomenclature has been\nfound so convenient, that it has been universally adopted in every\nother department of the Natural History of organized beings. {308}\n\nMany other modes of Nomenclature have been tried, but no other has\nat all taken root. Linn\u00e6us himself appears at first to have intended\nmarking each species by the Generic Name, accompanied by a\ncharacteristic Descriptive Phrase; and to have proposed the\nemployment of a _Trivial_ Specific Name, as he termed it, only as a\nmethod of occasional convenience. The use of these trivial names,\nhowever, has become universal, as we have said; and is by many\npersons considered the greatest improvement introduced at the\nLinn\u00e6an reform.\n\n\nAPHORISM XV.\n\n_The Maxims of Linn\u00e6us concerning the Names to be used in Botany_,\n(Philosophia Botanica, Nomina. Sections 210 to 255) _are good\nexamples of Aphorisms on this subject._\n\n\nBOTH Linn\u00e6us and other writers (as Adanson) have given many maxims\nwith a view of regulating the selection of generic and specific\nnames. The maxims of Linn\u00e6us were intended as much as possible to\nexclude barbarism and confusion, and have, upon the whole, been\ngenerally adopted.\n\nThese canons, and the sagacious modesty of great botanists, like\nRobert Brown, in conforming to them, have kept the majority of good\nbotanists within salutary limits; though many of these canons were\nobjected to by the contemporaries of Linn\u00e6us (Adanson and\nothers[42\\4]) as capricious and unnecessary restrictions.\n\n[Note 42\\4: Pref. cxxix. clxxii.]\n\nMany of the names introduced by Linn\u00e6us certainly appear fanciful\nenough. Thus he gives the name _Bauhinia_ to a plant which has\nleaves in pairs, because the Bauhins were a pair of brothers.\n_Banisteria_ is the name of a climbing plant in honour of Banister,\nwho travelled among mountains. But such names once established by\nadequate authority lose all their inconvenience and easily become\npermanent, and hence the reasonableness of one of the Linn\u00e6an\nrules[43\\4]:--\nThat as such a perpetuation of the names of persons\n{309} by the names of plants is the only honour that botanists have\nto bestow, it ought to be used with care and caution, and\nreligiously respected.\n\n[Note 43\\4: _Phil. Bot._ s. 239.]\n\n[3rd ed. It may serve to show how sensitive botanists are to the\nallusions contained in such names, that it has been charged against\nLinn\u00e6us, as a proof of malignity towards Buffon, that he changed the\nname of the genus _Buffonia_, established by Sauvages, into\n_Bufonia_, which suggested a derivation from _Bufo_, a toad. It\nappears to be proved that the spelling was not Linn\u00e6us's doing.]\n\nAnother Linn\u00e6an maxim is (Art. 219), that the generic name must be\nfixed before we attempt to form a specific name; 'the latter without\nthe former is like the clapper without the bell.'\n\nThe name of the genus being fixed, the species may be marked (Art.\n257) by adding to it 'a single word taken at will from any quarter;'\nthat is, it need not involve a description or any essential property\nof the plant, but may be a casual or arbitrary appellation. Thus the\nvarious species of _Hieracium_[44\\4] are _Hieracium Alpinum_, _H.\nHalleri_, _H. Pilosella_, _H. dubium_, _H. murorum_, &c., where we\nsee how different may be the kind of origin of the words.\n\n[Note 44\\4: Hooker, _Fl. Scot._ 228.]\n\nAttempts have been made at various times to form the names of\nspecies from those of genera in some more symmetrical manner. But\nthese have not been successful, nor are they likely to be so; and we\nshall venture to propound an axiom in condemnation of such names.\n\n\nAPHORISM XVI.\n\n_Numerical names in Classification are bad; and the same may be said\nof other names of kinds, depending upon any fixed series of notes of\norder._\n\n\nWITH regard to numerical names of kinds, of species for instance,\nthe objections are of this nature. Besides that such names offer\nnothing for the imagination to take hold of, new discoveries will\nprobably alter the {310} numeration, and make the names erroneous.\nThus, if we call the species of a genus 1, 2, 3, a new species\nintermediate between 1 and 2, 2 and 3, &c. cannot be put in its\nplace without damaging the numbers.\n\nThe geological term _Trias_, lately introduced to designate the\ngroup consisting of the _three_ members (Bunter Sandstein,\nMuschelkalk, and Keuper) becomes improper if, as some geologists\nhold, two of these members cannot be separated.\n\nObjections resembling those which apply to numerical designations of\nspecies, apply to other cases of fixed series: for instance, when it\nhas been proposed to mark the species by altering the termination of\nthe genus. Thus Adanson[45\\4], denoting a genus by the name _Fonna_\n(_Lychnidea_), conceived he might mark five of its species by\naltering the last syllable, _Fonna_, _Fonna-e_, _Fonna-i_,\n_Fonna-o_, _Fonna-u_; then others by _Fonna-ba_, _Fonna-ka_, and so\non. This would be liable to the same evils which have been noticed\nas belonging to the numerical method[46\\4].\n\n[Note 45\\4: Pref. clxxvi.]\n\n[Note 46\\4: In like manner the names assigned by Mr. Rickman to the\nsuccessive of styles of Gothic architecture in England,--_Early\nEnglish_, _Decorated_, and _Perpendicular_,--cannot be replaced by\nnumerical designations, _First Pointed_, _Second Pointed_, _Third\nPointed_. For--besides that he who first distinctly establishes\nclasses has the right of naming them, and that Mr. Rickman's names\nare really appropriate and significant--these new names would\nconfound all meaning of language. We should not be able to divide\nEarly English, or Decorated, or Perpendicular into sub-styles;--for\nwho could talk of _First Second Pointed_ and _Second Second\nPointed_; and what should we call that pointed style--the\n_Transition_ from the Norman--which precedes the _First Pointed_?]\n\n\nAPHORISM XVII.\n\n_In any classificatory science names including more than two steps\nof the classification may be employed if it be found convenient._\n\n\nLINN\u00c6US, in his canons for botanical nomenclature (Art. 212), says\nthat the names of the class and the order are to be _mute_, while\nthe names of the Genus and Species are _sonorous_. And accordingly\nthe names {311} of plants (and the same is true of animals) have in\ncommon practice been binary only, consisting of a generic and a\nspecific name. The class and the order have not been admitted to\nform part of the appellation of the species. Indeed it is easy to\nsee that a name, which must be identical in so many instances as\nthat of an Order would be, would be felt as superfluous and\nburthensome. Accordingly, Linn\u00e6us makes it one of his maxims[47\\4],\nthat the name of the Class and Order must not be expressed but\nunderstood, and hence, he says, Royen, who took _Lilium_ for the\nname of a Class, rightly rejected this word as a generic name, and\nsubstituted _Lirium_ with the Greek termination.\n\n[Note 47\\4: _Phil. Bot._ s. 215.]\n\nYet we must not too peremptorily assume such maxims as these to be\nuniversal for all classificatory sciences. It is very possible that\nit may be found advisable to use _three_ terms, that of Order,\nGenus, and Species in designating minerals, as is done in Mohs's\nnomenclature, for example, _Rhombohedral Calc Haloide_, _Paratomous\nHal Baryte_.\n\nIt is possible also that it may be found useful in the same science\n(Mineralogy) to mark some of the steps of classification by the\ntermination. Thus it has been proposed to confine the termination\n_ite_ to the Order _Silicides_ of Naumann, as Apophyll_ite_,\nStilb_ite_, Leuc_ite_, &c., and to use names of different form in\nother orders, as Talc _Spar_ for Brennerite, Pyramidal Titanium\n_Oxide_ for Octahedrite. Some such method appears to be the most\nlikely to give us a tolerable mineralogical nomenclature.\n\n\nAPHORISM XVIII.\n\n_In forming a Terminology, words may be invented when necessary, but\nthey cannot be conveniently borrowed from casual or arbitrary\ncircumstances_[48\\4].\n\n[Note 48\\4: I may also refer to _Hist. Sc. Id._ b. viii. c. ii. sec.\n2, for some remarks on Terminology.]\n\nIT will be recollected that Terminology is a language employed for\ndescribing objects, Nomenclature, a body {312} of names of the\nobjects themselves. The _names_, as was stated in the last maxim,\nmay be arbitrary; but the _descriptive_ terms must be borrowed from\nwords of suitable meaning in the modern or the classical languages.\nThus the whole terminology which Linn\u00e6us introduced into botany, is\nfounded upon the received use of Latin words, although he defined\ntheir meaning so as to make it precise when it was not so, according\nto Aphorism V. But many of the terms were invented by him and other\nbotanists, as _Perianth_, _Nectary_, _Pericarp_; so many, indeed, as\nto form, along with the others, a considerable language. Many of the\nterms which are now become familiar were originally invented by\nwriters on botany. Thus the word _Petal_, for one division of the\ncorolla, was introduced by Fabius Columna. The term _Sepal_ was\ndevised by Necker to express each of the divisions of the calyx. And\nup to the most recent times, new denominations of parts and\nconditions of parts have been devised by botanists, when they found\nthem necessary, in order to mark important differences or\nresemblances. Thus the general _Receptacle_ of the flower, as it is\ntermed by Linn\u00e6us, or _Torus_ by Salisbury, is continued into organs\nwhich carry the stamina and pistil, or the pistil alone, or the\nwhole flower; this organ has hence been termed[49\\4] _Gonophore_,\n_Carpophore_, and _Anthophore_, in these cases.\n\n[Note 49\\4: De Candolle's _Th. El._ 405.]\n\nIn like manner when Cuvier had ascertained that the lower jaws of\nSaurians consisted always of six pieces having definite relations of\nform and position, he gave names to them, and termed them\nrespectively the _Dental_, the _Angular_, the _Coronoid_, the\n_Articular_, the _Complementary_, and the _Opercular_ Bones.\n\nIn all these cases, the descriptive terms thus introduced have been\nsignificant in their derivation. An attempt to circulate a perfectly\narbitrary word as a means of description would probably be\nunsuccessful. We have, indeed, some examples approaching to\narbitrary designations, in the Wernerian names of colours, {313}\nwhich are a part of the terminology of Natural History. Many of\nthese names are borrowed from natural resemblances, as _Auricula\npurple_, _Apple green_, _Straw yellow_; but the names of others are\ntaken from casual occurrences, mostly, however, such as were already\nrecognized in common language, as _Prussian blue_, _Dutch orange_,\n_King's yellow_.\n\nThe extension of arbitrary names in scientific terminology is by no\nmeans to be encouraged. I may mention a case in which it was very\nproperly avoided. When Mr. Faraday's researches on Voltaic\nelectricity had led him to perceive the great impropriety of the\nterm _poles_, as applied to the apparatus, since the processes have\nnot reference to any opposed points, but to two opposite directions\nof a path, he very suitably wished to substitute for the phrases\n_positive pole_ and _negative pole_, two words ending in _ode_, from\n\u1f45\u03b4\u03bf\u03c2, a way. A person who did not see the value of our present\nmaxim, that descriptive terms should be descriptive in their origin,\nmight have proposed words perfectly arbitrary, as _Alphode_, and\n_Betode_: or, if he wished to pay a tribute of respect to the\ndiscoverers in this department of science, _Galvanode_ and\n_Voltaode_, But such words would very justly have been rejected by\nMr. Faraday, and would hardly have obtained any general currency\namong men of science. _Zincode_ and _Platinode_, terms derived from\nthe metal which, in one modification of the apparatus, forms what\nwas previously termed the pole, are to be avoided, because in their\norigin too much is casual; and they are not a good basis for\nderivative terms. The pole at which the zinc is, is the Anode or\nCathode, according as it is associated with different metals. Either\nthe _Zincode_ must sometimes mean the pole at which the Zinc is, and\nat other times that at which the Zinc is not, or else we must have\nas many names for poles as there are metals. _Anode_ and _Cathode_,\nthe terms which Mr. Faraday adopted, were free from these\nobjections; for they refer to a natural standard of the direction of\nthe voltaic current, in a manner which, though perhaps not obvious\nat first sight, is easily understood and {314} retained. _An_ode and\n_Cath_ode, the _rising_ and the _setting_ way, are the directions\nwhich correspond to east and west in that voltaic current to which\nwe must ascribe terrestrial magnetism. And with these words it was\neasy to connect _An\u00efon_ and _Cath\u00efon_, to designate the opposite\nelements which are separated and liberated at the two _Electrodes_.\n\n\nAPHORISM XIX.\n\n_The meaning of Technical Terms must be fixed by convention, not by\ncasual reference to the ordinary meaning of words._\n\n\nIN fixing the meaning of the Technical Terms which form the\nTerminology of any science, at least of the descriptive Terms, we\nnecessarily fix, at the same time, the perceptions and notions which\nthe Terms are to convey to a hearer. What do we mean by\n_apple-green_ or _French grey_? It might, perhaps, be supposed that,\nin the first example, the term _apple_, referring to so familiar an\nobject, sufficiently suggests the colour intended. But it may easily\nbe seen that this is not true; for apples are of many different hues\nof green, and it is only by a conventional selection that we can\nappropriate the term to one special shade. When this appropriation\nis once made, the term refers to the sensation, and not to the parts\nof this term; for these enter into the compound merely as a help to\nthe memory, whether the suggestion be a natural connexion as in\n'apple-green,' or a casual one as in 'French grey.' In order to\nderive due advantage from technical terms of this kind, they must be\nassociated _immediately_ with the perception to which they belong;\nand not connected with it through the vague usages of common\nlanguage. The memory must retain the sensation; and the technical\nword must be understood as directly as the most familiar word, and\nmore distinctly. When we find such terms as _tin-white_ or\n_pinchbeck-brown_, the metallic colour so denoted ought to start up\nin our memory without delay or search. {315}\n\nThis, which it is most important to recollect with respect to the\nsimpler properties of bodies, as colour and form, is no less true\nwith respect to more compound notions. In all cases the term is\nfixed to a peculiar meaning by convention; and the student, in order\nto use the word, must be completely familiar with the convention, so\nthat he has no need to frame conjectures from the word itself. Such\nconjectures would always be insecure, and often erroneous. Thus the\nterm _papilionaceous_, applied to a flower, is employed to indicate,\nnot only a resemblance to a butterfly, but a resemblance arising\nfrom five petals of a certain peculiar shape and arrangement; and\neven if the resemblance to a butterfly were much stronger than it is\nin such cases, yet if it were produced in a different way, as, for\nexample, by one petal, or two only, instead of a 'standard,' two\n'wings,' and a 'keel' consisting of two parts more or less united\ninto one, we should no longer be justified in speaking of it as a\n'papilionaceous' flower.\n\nThe formation of an exact and extensive descriptive language for\nbotany has been executed with a degree of skill and felicity, which,\nbefore it was attained, could hardly have been dreamt of as\nattainable. Every part of a plant has been named; and the form of\nevery part, even the most minute, has had a large assemblage of\ndescriptive terms appropriated to it, by means of which the botanist\ncan convey and receive knowledge of form and structure, as exactly\nas if each minute part were presented to him vastly magnified. This\nacquisition was part of the Linn\u00e6an Reform, of which we have spoken\nin the _History_. 'Tournefort,' says De Candolle[50\\4], 'appears to\nhave been the first who really perceived the utility of fixing the\nsense of terms in such a way as always to employ the same word in\nthe same sense, and always to express the same idea by the same\nword; but it was Linn\u00e6us who really created and fixed this botanical\nlanguage, and this is his fairest claim to glory, for by this\nfixation of language he has shed clearness and precision over all\nparts of the science.'\n\n[Note 50\\4: _Th\u00e9or. \u00c9l\u00e9m._ p. 327.]\n\n{316} It 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 minutely\nexamined. Thus the flower was successively distinguished into the\n_calyx_, the _corolla_, the _stamens_, and the _pistils_: the\nsections of the corolla were termed _petals_ by Columna; those of\nthe calyx were called _sepals_ by Necker[51\\4]. Sometimes terms of\ngreater generality were devised; as _perianth_ to include the calyx\nand corolla, whether one or both of these were present[52\\4];\n_pericarp_ for the part inclosing the grain, of whatever kind it be,\nfruit, nut, pod, &c. And it may easily be imagined that descriptive\nterms may, by definition and combination, become very numerous and\ndistinct. Thus leaves may be called _pinnatifid_[53\\4],\n_pinnnatipartite_, _pinnatisect_, _pinnatilobate_, _palmatifid_,\n_palmatipartite_, &c., and each of these words designates different\ncombinations of the modes and extent of the divisions of the leaf\nwith the divisions of its outline. In some cases arbitrary numerical\nrelations are introduced into the definition: thus a leaf is called\n_bilobate_[54\\4] when it is divided into two parts by a notch; but\nif the notch go to the middle of its length, it is _bifid_; if it go\nnear the base of the leaf, it is _bipartite_; if to the base, it is\n_bisect_. Thus, too, a pod of a cruciferous plant is a\n_silica_[55\\4] if it be four times as long as it is broad, but if it\nbe shorter than this it is a _silicula_. Such terms being\nestablished, the form of the very complex leaf or frond of a fern is\nexactly conveyed, for example, by the following phrase: 'fronds\nrigid pinnate, pinn\u00e6 recurved subunilateral pinnatifid, the segments\nlinear undivided or bifid spinuloso-serrate[56\\4].'\n\n[Note 51\\4: De Candolle, 329.]\n\n[Note 52\\4: For this Erhart and De Candolle use _Perigone_.]\n\n[Note 53\\4: De Candolle, 318.]\n\n[Note 54\\4: _Ibid._ 493.]\n\n[Note 55\\4: _Ibid._ 422.]\n\n[Note 56\\4: Hooker, _Brit. Flo._ p. 450. _Hymenophyllum Wilsoni_,\nScottish filmy fern, abundant in the highlands of Scotland and about\nKillarney.]\n\nOther characters, as well as form, are conveyed with the like\nprecision: Colour by means of a classified scale of colours, as we\nhave seen in speaking of the Measures {317} of Secondary Qualities;\nto which, however, we must add, that the naturalist employs\narbitrary names, (such as we have already quoted,) and not mere\nnumerical exponents, to indicate a certain number of selected\ncolours. This was done with most precision by Werner, and his scale\nof colours is still the most usual standard of naturalists. Werner\nalso introduced a more exact terminology with regard to other\ncharacters which are important in mineralogy, as lustre, hardness.\nBut Mohs improved upon this step by giving a numerical scale of\nhardness, in which _talc_ is 1, _gypsum_, 2, _calc spar_ 3, and so\non, as we have already explained in the History of Mineralogy. Some\nproperties, as specific gravity, by their definition give at once a\nnumerical measure; and others, as crystalline form, require a very\nconsiderable array of mathematical calculation and reasoning, to\npoint out their relations and gradations. In all cases the features\nof likeness in the objects must be rightly apprehended, in order to\ntheir being expressed by a distinct terminology. Thus no terms could\ndescribe crystals for any purpose of natural history, till it was\ndiscovered that in a class of minerals the proportion of the faces\nmight vary, while the angle remained the same. Nor could crystals be\ndescribed so as to distinguish species, till it was found that the\nderived and primitive forms are connected by very simple relations\nof space and number. The discovery of the mode in which characters\nmust be apprehended so that they may be considered as _fixed_ for a\nclass, is an important step in the progress of each branch of\nNatural History; and hence we have had, in the History of Mineralogy\nand Botany, to distinguish as important and eminent persons those\nwho made such discoveries, Rom\u00e9 de Lisle and Ha\u00fcy, C\u00e6salpinus and\nGesner.\n\nBy the continued progress of that knowledge of minerals, plants, and\nother natural objects, in which such persons made the most distinct\nand marked steps, but which has been constantly advancing in a more\ngradual and imperceptible manner, the most important and essential\nfeatures of similarity and dissimilarity in such objects have been\nselected, arranged, and fitted with {318} names; and we have thus in\nsuch departments, systems of Terminology which fix our attention\nupon the resemblances which it is proper to consider, and enable us\nto convey them in words.\n\nThe following Aphorisms respect the Form of Technical Terms.\n\nBy the _Form_ of terms, I mean their philological conditions; as,\nfor example, from what languages they may be borrowed, by what modes\nof inflexion they must be compounded, how their derivatives are to\nbe formed, and the like. In this, as in other parts of the subject,\nI shall not lay down a system of rules, but shall propose a few\nmaxims.\n\n\nAPHORISM XX.\n\n_The two main conditions of the Form of technical terms are, that\nthey must be generally intelligible, and susceptible of such\ngrammatical relations as their scientific use requires._\n\n\nTHESE conditions may at first appear somewhat vague, but it will be\nfound that they are as definite as we could make them, without\ninjuriously restricting ourselves. It will appear, moreover, that\nthey have an important bearing upon most of the questions respecting\nthe form of the words which come before us; and that if we can\nsucceed in any case in reconciling the two conditions, we obtain\nterms which are practically good, whatever objections may be urged\nagainst them from other considerations.\n\n1. The former condition, for instance, bears upon the question\nwhether scientific terms are to be taken from the learned languages,\nGreek and Latin, or from our own. And the latter condition very\nmaterially affects the same question, since in English we have\nscarcely any power of inflecting our words; and therefore must have\nrecourse to Greek or Latin in order to obtain terms which admit of\ngrammatical modification. If we were content with the term _Heat_,\nto express the _science_ of heat, still it would be a bad technical\nterm, for we cannot derive from it an adjective like {319}\n_thermotical_. If _bed_ or _layer_ were an equally good term with\n_stratum_, we must still retain the latter, in order that we may use\nthe derivative _Stratification_, for which the English words cannot\nproduce an equivalent substitute. We may retain the words _lime_ and\n_flint_, but their adjectives for scientific purposes are not _limy_\nand _flinty_, but _calcareous_ and _siliceous_; and hence we are\nable to form a compound, as _calcareo-siliceous_, which we could not\ndo with indigenous words. We might fix the phrases _bent back_ and\n_broken_ to mean (of optical rays) that they are reflected and\nrefracted; but then we should have no means of speaking of the\nangles of _Reflection_ and _Refraction_, of the _Refractive_\nIndices, and the like.\n\nIn like manner, so long as anatomists described certain parts of a\nvertebra as _vertebral lamin\u00e6_, or _vertebral plates_, they had no\nadjective whereby to signify the properties of these parts; the term\n_Neurapophysis_, given to them by Mr. Owen, supplies the\ncorresponding expression _neurapophysial_. So again, the term\n_Basisphenoid_, employed by the same anatomist, is better than\n_basilar_ or _basial process of the sphenoid_, because it gives us\nthe adjective _basisphenoidal_. And the like remark applies to other\nchanges recently proposed in the names of portions of the skeleton.\n\nThus one of the advantages of going to the Greek and Latin languages\nfor the origin of our scientific terms is, that in this way we\nobtain words which admit of the formation of adjectives and abstract\nterms, and of composition, and of other inflexions. Another\nadvantage of such an origin is, that such terms, if well selected,\nare readily understood over the whole lettered world. For this\nreason, the descriptive language of science, of botany for instance,\nhas been, for the most part, taken from the Latin; many of the terms\nof the mathematical and chemical sciences have been derived from the\nGreek; and when occasion occurs to construct a new term, it is\ngenerally to that language that recourse is had. The advantage of\nsuch terms is, as has already been intimated, that they constitute\nan universal language, by means of which {320} cultivated persons in\nevery country may convey to each other their ideas without the need\nof translation.\n\nOn the other hand, the advantage of indigenous terms is, that so far\nas the language extends, they are intelligible much more clearly and\nvividly than those borrowed from any other source, as well as more\neasily manageable in the construction of sentences. In the\ndescriptive language of botany, for example, in an English work, the\nterms _drooping_, _nodding_, _one-sided_, _twining_, _straggling_,\nappear better than _cernuous_, _nutant_, _secund_, _volubile_,\n_divaricate_. For though the latter terms may by habit become as\nintelligible as the former, they cannot become more so to any\nreaders; and to most English readers they will give a far less\ndistinct impression.\n\n2. Since the advantage of indigenous over learned terms, or the\ncontrary, depends upon the balance of the capacity of inflexion and\ncomposition on the one hand, against a ready and clear significance\non the other, it is evident that the employment of scientific terms\nof the one class or of the other may very properly be extremely\ndifferent in different languages. The German possesses in a very\neminent degree that power of composition and derivation, which in\nEnglish can hardly be exercised at all, in a formal manner. Hence\nGerman scientific writers use native terms to a far greater extent\nthan do our own authors. The descriptive terminology of botany, and\neven the systematic nomenclature of chemistry, are represented by\nthe Germans by means of German roots and inflexions. Thus the\ndescription of _Potentilla anserina_, in English botanists, is that\nit has _Leaves interruptedly pinnate_, _serrate_, _silky_, _stem\ncreeping_, _stalks axilllar_, _one-flowered_. Here we have words of\nSaxon and Latin origin mingled pretty equally. But the German\ndescription is entirely Teutonic. _Die Blume in Achsel_; _die\nBl\u00e4tter unterbrochen gefiedert_, _die Bl\u00e4ttchen scharf gesagt_, _die\nSt\u00e4mme kriechend_, _die Bluthenstiele einblumig_. We could imitate\nthis in our own language, by saying _brokenly-feathered_,\n_sharp-sawed_; by using _threed_ for _ternate_, as the Germans\nemploy _gedreit_; by saying {321} _fingered-feathered_ for\n_digitato-pinnate_, and the like. But the habit which we have, in\ncommon as well as scientific language, of borrowing words from the\nLatin for new cases, would make such usages seem very harsh and\npedantic.\n\nWe may add that, in consequence of these different practices in the\ntwo languages, it is a common habit of the German reader to impose a\nscientific definiteness upon a common word, such as our Fifth\nAphorism requires; whereas the English reader expects rather that a\nword which is to have a technical sense shall be derived from the\nlearned languages. _Die Kelch_ and _die Blume_ (the cup and the\nflower) easily assume the technical meaning of _calyx_ and\n_corolla_; _die Griffel_ (the pencil) becomes _the pistil_; and a\nname is easily found for the _pollen_, the _anthers_, and the\n_stamens_, by calling them the dust, the dust-cases, and the\ndust-threads (_der Staub_, _die Staub-beutel_, or _Staub-f\u00e4cher_,\nand _die Staub-f\u00e4den_), This was formerly done in English to a\ngreater extent than is now possible without confusion and pedantry.\nThus, in Grew's book on the _Anatomy of Plants_, the calyx is called\nthe _impalement_, and the sepals the _impalers_; the petals are\ncalled the _leaves of the flower_; the stamens with their anthers\nare the _seminiform attire_. But the English language, as to such\nmatters, is now less flexible than it was; partly in consequence of\nits having adopted the Linn\u00e6an terminology almost entire, without\nany endeavour to naturalize it. Any attempt at idiomatic description\nwould interfere with the scientific language now generally received\nin this country. In Germany, on the other hand, those who first\nwrote upon science in their own language imitated the Latin words\nwhich they found in foreign writers, instead of transferring new\nroots into their own language. Thus the _Numerator_ and\n_Denominator_ of a fraction they call the _Namer_ and the _Counter_\n(_Nenner_ and _Z\u00e4hler_). This course they pursued even where the\nexpression was erroneous. Thus that portion of the intestines which\nancient anatomists called _Duodenum_, because they falsely estimated\nits length at twelve inches, the {322} Germans also term\n_Zw\u00f6lffingerdarm_ (twelve-inch-gut), though this intestine in a\nwhale is twenty feet long, and in a frog not above twenty lines. As\nanother example of this process in German, we may take the word\n_Muttersackbauchblatte_, the _uterine periton\u00e6um_.\n\nIt is a remarkable evidence of this formative power of the German\nlanguage, that it should have been able to produce an imitation of\nthe systematic chemical nomenclature of the French school, so\ncomplete, that it is used in Germany as familiarly as the original\nsystem is in France and England. Thus Oxygen and Hydrogen are\n_Sauerstoff_ and _**Wasserstoff_; Azote is _Stickstoff_ (suffocating\nmatter); Sulphuric and Sulphurous Acid are _Schwefel-s\u00e4ure_ and\n_Schwefelichte-s\u00e4ure_. The Sulphate and Sulphite of Baryta, and\nSulphuret of Baryum, are _Schwefel-s\u00e4ure Baryterde_,\n_Schwefelichte-s\u00e4ure Baryterde_, and _Schwefel-baryum_. Carbonate of\nIron is _Kohlen-s\u00e4ures Eisenoxydul_; and we may observe that, in\nsuch cases, the German name is much more agreeable to analogy than\nthe English one; for the Protoxide of Iron, (_Eisenoxydul_,) and not\nthe Iron itself, is the base of the salt. And the German language\nhas not only thus imitated the established nomenclature of\nchemistry, but has shown itself capable of supplying new forms to\nmeet the demands which the progress of theory occasions. Thus the\nHydracids are _Wasserstoff-s\u00e4uren_; and of these, the Hydriodic Acid\nis _Iodwasserstoff-s\u00e4ure_, and so of the rest. In like manner, the\ntranslator of Berzelius has found German names for the sulpho-salts\nof that chemist; thus he has _Wasserstoffschwefliges\nSchewefellithium_, which would be (if we were to adopt his\ntheoretical view) hydro-sulphuret of sulphuret of lithium: and a\nlike nomenclature for all other similar cases.\n\n3. In English we have no power of imitating this process, and must\ntake our technical phrases from some more flexible language, and\ngenerally from the Latin or Greek. We are indeed so much accustomed\nto do this, that except a word has its origin in one of these\nlanguages, it hardly seems to us a technical {323} term; and thus by\nemploying indigenous terms, even descriptive ones, we may, perhaps,\nlose in precision more than we gain in the vividness of the\nimpression. Perhaps it may be better to say _cuneate_, _lunate_,\n_hastate_, _sagittate_, _reniform_, than _wedge-shaped_,\n_crescent-shaped_, _halbert-headed_, _arrow-headed_,\n_kidney-shaped_. _Ringent_ and _personate_ are better than any\nEnglish words which we could substitute for them; _labiate_ is more\nprecise than _lipped_ would readily become. _Urceolate_,\n_trochlear_, are more compact than _pitcher-shaped_,\n_pulley-shaped_; and _infundibuliform_, _hypocrateriform_, though\nlong words, are not more inconvenient than _funnel-shaped_ and\n_salver-shaped_. In the same way it is better to speak (with Dr.\nPrichard[57\\4],) of _repent_ and _progressive_ animals, than of\n_creeping_ and progressive: the two Latin terms make a better pair\nof correlatives.\n\n[Note 57\\4: _Researches_, p. 69.]\n\n4. But wherever we may draw the line between the proper use of\nEnglish and Latin terms in descriptive phraseology, we shall find it\nadvisable to borrow almost all other technical terms from the\nlearned languages. We have seen this in considering the new terms\nintroduced into various sciences in virtue of our Ninth Maxim. We\nmay add, as further examples, the names of the various animals of\nwhich a knowledge has been acquired from the remains of them which\nexist in various strata, and which have been reconstructed by Cuvier\nand his successors. Such are the _Pal\u00e6otherium_, the\n_Anoplotherium_, the _Megatherium_, the _Dinotherium_, the\n_Chirotherium_, the _Megalichthys_, the _Mastodon_, the\n_Ichthyosaurus_, the _Plesiosaurus_, the _Pterodactylus_. To these\nothers are every year added; as, for instance, very recently, the\n_Toxodon_, _Zeuglodon_, and _Phascolotherium_ of Mr. Owen, and the\n_Thylacotherium_ of M. Valenciennes. Still more recently the terms\n_Glyptodon_, _Mylodon_, _Dicynodon_, _Paloplotherium_,\n_Rhynchosaurus_, have been added by Mr. Owen to designate fossil\nanimals newly determined by him. {324}\n\nThe names of species, as well as of genera, are thus formed from the\nGreek: as the Plesiosaurus _dolichodeirus_ (long-necked),\nIchthyosaurus _platyodon_ (broad-toothed), the Irish elk, termed\nCervus _megaceros_ (large-horned). But the descriptive specific\nnames are also taken from the Latin, as Plesiosaurus _brevirostris_,\n_longirostris_, _crassirostris_; besides which there are arbitrary\nspecific names, which we do not here consider.\n\nThese names being all constructed at a period when naturalists were\nfamiliar with an artificial system, the standard language of which\nis Latin, have not been taken from modern language. But the names of\nliving animals, and even of their classes, long ago formed in the\ncommon language of men, have been in part adopted in the systems of\nnaturalists, agreeably to Aphorism Third. Hence the language of\nsystems in natural history is mixed of ancient and modern languages.\nThus Cuvier's divisions of the vertebrated animals are _Mammif\u00e8res_\n(Latin), _Oiseaux_, _Reptiles_, _Poissons_; _Bimanes_,\n_Quadrumanes_, _Carnassi\u00e8res_, _Rongeurs_, _Pachydermes_ (Greek),\n_Ruminans_ (Latin), _C\u00e9tac\u00e9s_ (Latin). In the subordinate divisions\nthe distribution being more novel, the names are less idiomatic:\nthus the kinds of Reptiles are _Cheloniens_, _Sauriens_,\n_Ophidiens_, _Batraciens_, all which are of Greek origin. In like\nmanner. Fish are divided into _Chondropterygiens_,\n_Malacopterygiens_, _Acanthopterygiens_. The unvertebrated animals\nare _Mollusques_, _Animaux articul\u00e9s_, and _Animaux rayonn\u00e9s_; and\nthe Mollusques are divided into six classes, chiefly according to\nthe position or form of their foot; namely, _Cephalopodes_,\n_Pteropodes_, _Gasteropodes_, _Acephales_, _Brachiopodes_,\n_Cirrhopodes_.\n\nIn transferring these terms into English, when the term is new in\nFrench as well as English, we have little difficulty; for we may\ntake nearly the same liberties in English which are taken in French;\nand hence we may say _mammifers_ (rather _mammals_), _cetaceans_ or\n_cetaces_, _batracians_ (rather _batrachians_), using the words as\nsubstantives. But in other cases we must go back to the Latin: thus\nwe say _radiate_ {325} animals, or _radiata_ (rather _radials_), for\n_rayonn\u00e9s_. These changes, however, rather refer to another\nAphorism.\n\n(Mr. Kirby has proposed _radiary_, _radiaries_, for _radiata_.)\n\n5. When new Mineral Species have been established in recent times,\nthey have generally had arbitrary names assigned to them, derived\nfrom some person or places. In some instances, however, descriptive\nnames have been selected; and then these have been generally taken\nfrom the Greek, as _Augite_, _Stilbite_, _Diaspore_, _Dichroite_,\n_Dioptase_. Several of these Greek names imposed by Ha\u00fcy, refer to\nsome circumstances, often fancifully selected, in his view of the\ncrystallization of the substance, as _Epidote_, _Peridote_,\n_Pleonast_. Similar terms of Greek origin have been introduced by\nothers, as _Orthite_, _Anorthite_, _Periklin_. Greek names founded\non casual circumstances are less to be commended. Berzelius has\ntermed a mineral _Eschynite_ from \u03b1\u1f30\u03c3\u03c7\u03c5\u03bd\u1f74, _shame_, because it is,\nhe conceives, a shame for chemists not to have separated its\nelements more distinctly than they did at first.\n\n6. In Botany, the old names of genera of Greek origin are very\nnumerous, and many of them are descriptive, as _Glycyrhiza_ (\u03b3\u03bb\u03c5\u03ba\u1f7a\u03c2\nand \u1fe5\u03b9\u03b6\u03b1, sweet root) liquorice, _Rhododendron_ (rose-tree),\n_H\u00e6matoxylon_ (bloody wood), _Chrysocoma_ (golden hair),\n_Alopecurus_ (fox-tail), and many more. In like manner there are\nnames which derive a descriptive significance from the Latin, either\nadjectives, as _Impatiens_, _Gloriosa_, _Sagittaria_, or\nsubstantives irregularly formed, as _Tussilago_ (\u00e0 tussis\ndomatione), _Urtica_ (ab urendo tactu), _Salsola_ (\u00e0 salsedine). But\nthese, though good names when they are established by tradition, are\nhardly to be imitated in naming new plants. In most instances, when\nthis is to be done, arbitrary or local names have been selected, as\n_Strelitzia_.\n\n7. In Chemistry, new substances have of late had names assigned them\nfrom Greek roots, as _Iodine_, from its violet colour, _Chlorine_\nfrom its green colour. In like manner fluorine has by the French\nchemists been called _Phthor_, from its destructive properties. So\nthe {326} new metals, _Chrome_, _Rhodium_, _Iridium_, _Osmium_, had\nnames of Greek derivation descriptive of their properties. Some such\nterms, however, were borrowed from localities, as _Strontia_,\n_Yttria_, the names of new earths. Others have a mixed origin, as\n_Pyrogallic_, _Pyroacetic_, and _Pyroligneous_ Spirit. In some cases\nthe derivation has been extravagantly capricious. Thus in the\nprocess for making Pyrogallic Acid, a certain substance is left\nbehind, from which M. Braconnot extracted an acid which he called\n_Ellagic_ Acid, framing the root of the name by reading the word\n_Galle_ backwards.\n\nThe new laws which the study of Electro-chemistry brought into view,\nrequired a new terminology to express their conditions: and in this\ncase, as we have observed in speaking of the Twelfth Maxim,\narbitrary words are less suitable. Mr. Faraday very properly\nborrowed from the Greek his terms _Electrolyte_, _Electrode_,\n_Anode_, _Cathode_, _An\u00efon_, _Cath\u00efon_, _Dielectric_. In the\nmechanico-chemical and mechanical sciences, however, new terms are\nless copiously required than in the sciences of classification, and\nwhen they are needed, they are generally determined by analogy from\nexisting terms. _Thermo-electricity_ and _Electro-dynamics_ were\nterms which very naturally offered themselves; Nobili's\n_thermo-multiplier_, Snow Harris's _unit-jar_, were almost equally\nobvious names. In such cases, it is generally possible to construct\nterms both compendious and descriptive, without introducing any new\nradical words.\n\n8. The subject of Crystallography has inevitably given rise to many\nnew terms, since it brings under our notice a great number of new\nrelations of a very definite but very complex form. Ha\u00fcy attempted\nto find names for all the leading varieties of crystals, and for\nthis purpose introduced a great number of new terms, founded on\nvarious analogies and allusions. Thus the forms of calc-spar are\ntermed by him _primitive_, _equiaxe_, _inverse_, _metastatique_,\n_contrastante_, _imitable_, _birhomboidale_, _prismatique_,\n_apophane_, _uniternaire_, _bisunitaire_, _dod\u00e9ca\u00e8dre_,\n_contract\u00e9e_, _dilat\u00e9e_, _sexduodecimale_, _bisalterne_,\n_binoternaire_, and many others. The {327} want of uniformity in the\norigin and scheme of these denominations would be no valid objection\nto them, if any general truth could be expressed by means of them:\nbut the fact is, that there is no definite distinction of these\nforms. They pass into each other by insensible gradations, and the\noptical and physical properties which they possess are common to all\nof them. And as a mere enunciation of laws of form, this terminology\nis insufficient. Thus it does not at all convey the relation between\nthe _bisalterne_ and the _binoternaire_, the former being a\ncombination of the _metastatique_ with the _prismatique_, the\nlatter, of the _metastatique_ with the _contrastante_: again, the\n_contrastante_, the _mixte_, the _cuboide_, the _contract\u00e9e_, the\n_dilat\u00e9e_, all contain faces generated by a common law, the index\nbeing respectively altered so as to be in these cases, 3, 3/2, 4/5,\n9/4, 5/9; and this, which is the most important geometrical relation\nof these forms, is not at all recorded or indicated by the\nnomenclature. The fact is, that it is probably impossible, the\nsubject of crystallography having become so complex as it now is, to\ndevise a system of names which shall express the relations of form.\nNumerical symbols, such as those of Weiss or Naumann, or Professor\nMiller, are the proper ways of expressing these relations, and are\nthe only good crystallographic terminology for cases in detail.\n\nThe terms used in expressing crystallographic laws have been for the\nmost part taken from the Greek by all writers except some of the\nGermans. These, we have already stated, have constructed terms in\ntheir own language, as _zwei-und-ein gliedrig_, and the like.\n\nIn Optics we have some new terms connected with crystalline laws, as\n_uniaxal_ and _biaxal_ crystals, _optical axes_, which offered\nthemselves without any effort on the part of the discoverers. In the\nwhole history of the undulatory theory, very few innovations in\nlanguage were found necessary, except to fix the sense of a few\nphrases, as _plane-polarized_ light in opposition to\n_circularly-polarized_, and the like.\n\nThis is still more the case in Mechanics, Astronomy, {328} and pure\nmathematics. In these sciences, several of the primary stages of\ngeneralization being already passed over, when any new steps are\nmade, we have before us some analogy by which we may frame our new\nterms. Thus when the _plane of maximum areas_ was discovered, it had\nnot some new arbitrary denomination assigned it, but the name which\nobviously described it was fixed as a technical name.\n\nThe result of this survey of the scientific terms of recent\nformation seems to be this;--that indigenous terms may be employed\nin the descriptions of facts and phenomena as they at first present\nthemselves; and in the first induction from these; but that when we\ncome to generalize and theorize, terms borrowed from the learned\nlanguages are more readily fixed and made definite, and are also\nmore easily connected with derivatives. Our native terms are more\nimpressive, and at first more intelligible; but they may wander from\ntheir scientific meaning, and are capable of little inflexion. Words\nof classical origin are precise to the careful student, and capable\nof expressing, by their inflexions, the relations of general ideas;\nbut they are unintelligible, even to the learned man, without\nexpress definition, and convey instruction only through an\nartificial and rare habit of thought.\n\nSince in the balance between words of domestic and of foreign origin\nso much depends upon the possibility of inflexion and derivation, I\nshall consider a little more closely what are the limits and\nconsiderations which we have to take into account in reference to\nthat subject.\n\n\nAPHORISM XXI.\n\n_In the composition and inflexion of technical terms, philological\nanalogies are to be preserved if possible, but modified according to\nscientific convenience._\n\n\nIN the language employed or proposed by writers upon subjects of\nscience, many combinations and forms of derivation occur, which\nwould be rejected and condemned by those who are careful of the\npurity and {329} correctness of language. Such anomalies are to be\navoided as much as possible; but it is impossible to escape them\naltogether, if we are to have a scientific language which has any\nchance of being received into general use. It is better to admit\ncompounds which are not philologically correct, than to invent many\nnew words, all strange to the readers for whom they are intended:\nand in writing on science in our own language, it is not possible to\navoid making additions to the vocabulary of common life; since\nscience requires exact names for many things which common language\nhas not named. And although these new names should, as much as\npossible, be constructed in conformity with the analogies of the\nlanguage, such extensions of analogy can hardly sound, to the\ngrammarian's ear, otherwise than as solecisms. But, as our maxim\nindicates, the analogy of science is of more weight with us than the\nanalogy of language: and although anomalies in our phraseology\nshould be avoided as much as possible, innovations must be permitted\nwherever a scientific language, easy to acquire, and convenient to\nuse, is unattainable without them.\n\nI shall proceed to mention some of the transgressions of strict\nphilological rules, and some of the extensions of grammatical forms,\nwhich the above conditions appear to render necessary.\n\n1. The combination of different languages in the derivation of\nwords, though to be avoided in general, is in some cases admissible.\n\nSuch words are condemned by Quintilian and other grammarians, under\nthe name of hybrids, or things of a mixed race; as _biclinium_ from\n_bis_ and \u03ba\u03bb\u03af\u03bd\u03b7; _epitogium_, from \u1f10\u03c0\u1f76 and _toga_. Nor are such\nterms to be unnecessarily introduced in science. Whenever a\nhomogeneous word can be formed and adopted with the same ease and\nconvenience as a hybrid, it is to be preferred. Hence we must have\n_ichthyology_, not _piscology_, _entomology_, not _insectology_,\n_insectivorous_, not _insectophagous_. In like manner, it would be\nbetter to say _unoculus_ than _monoculus_, though the latter has the\nsanction of Linn\u00e6us, who was a purist in such matters. {330} Dr.\nTurner, in his _Chemistry_, speaks of _protoxides_ and _binoxides_,\nwhich combination violates the rule for making the materials of our\nterms as homogeneous as possible; _protoxide_ and _deutoxide_ would\nbe preferable, both on this and on other accounts.\n\nYet this rule admits of exceptions. _Mineralogy_, with its Greek\ntermination, has for its root _minera_, a medieval Latin word of\nTeutonic origin, and is preferable to _Oryctology_. _Terminology_\nappears to be better than _Glossology_: which according to its\nderivation would be rather the science of language in general than\nof technical terms; and _Horology_, from \u1f45\u03c1\u03bf\u03c2, a term, would not be\nimmediately intelligible, even to Greek scholars; and is already\nemployed to indicate the science which treats of horologes, or\ntime-pieces.\n\nIndeed, the English reader is become quite familiar with the\ntermination _ology_, the names of a large number of branches of\nscience and learning having that form. This termination is at\npresent rather apprehended as a formative affix in our own language,\nindicating a science, than as an element borrowed from foreign\nlanguage. Hence, when it is difficult or impossible to find a Greek\nterm which clearly designates the subject of a science, it is\nallowable to employ some other, as in _Tidology_, the doctrine of\nthe Tides.\n\nThe same remark applies to some other Greek elements of scientific\nwords: they are so familiar to us that in composition they are\nalmost used as part of our own language. This naturalization has\ntaken place very decidedly in the element _arch_, (\u1f00\u03c1\u03c7\u1f78\u03c2 a leader,)\nas we see in _archbishop_, _archduke_. It is effected in a great\ndegree for the preposition _anti_: thus we speak of _anti-slavery_\nsocieties, _anti-reformers_, _anti-bilious_, or _anti-acid_\nmedicines, without being conscious of any anomaly. The same is the\ncase with the Latin preposition _pr\u00e6_ or _pre_, as appears from such\nwords as _pre-engage_, _pre-arrange_, _pre-judge_, _pre-paid_; and\nin some measure with _pro_, for in colloquial language we speak of\n_pro-catholics_ and _anti-catholics_. Also the preposition _ante_ is\nsimilarly used, as _ante-nicene_ fathers. The preposition _co_,\nabbreviated from _con_, and {331} implying things to be simultaneous\nor connected, is firmly established as part of the language, as we\nsee in _coexist_, _coheir_, _coordinate_; hence I have called those\nlines _cotidal_ lines which pass through places where the high water\nof the tide occurs simultaneously.\n\n2. As in the course of the mixture by which our language has been\nformed, we have thus lost all habitual consciousness of the\ndifference of its ingredients, (Greek, Latin, Norman-French, and\nAnglo-Saxon): we have also ceased to confine to each ingredient the\nmode of grammatical inflexion which originally belonged to it. Thus\nthe termination _ive_ belongs peculiarly to Latin adjectives, yet we\nsay _sportive_, _talkative_. In like manner, _able_ is added to\nwords which are not Latin, as _eatable_, _drinkable_, _pitiable_,\n_enviable_. Also the termination _al_ and _ical_ are used with\nvarious roots, as _loyal_, _royal_, _farcical_, _whimsical_; hence\nwe may make the adjective _tidal_ from _tide_. This ending, _al_, is\nalso added to abstract terms in _ion_, as _occasional_,\n_provisional_, _intentional_, _national_; hence we may, if\nnecessary, use such words as _educational_, _terminational_. The\nending _ic_ appears to be suited to proper names, as _Pindaric_,\n_Socratic_, _Platonic_; hence it may be used when scientific words\nare derived from proper names, as _Voltaic_ or _Galvanic_\nelectricity: to which I have proposed to add _Franklinic_.\n\nIn adopting scientific adjectives from the Latin, we have not much\nroom for hesitation; for, in such cases, the habits of derivation\nfrom that language into our own are very constant; _ivus_ becomes\n_ive_, as _decursive_; _inus_ becomes _ine_, as in _ferine_; _atus_\nbecomes _ate_, as _hastate_; and _us_ often becomes _ous_, as\n_rufous_; _aris_ becomes _ary_, as _axillary_; _ens_ becomes _ent_,\nas _ringent_. And in adopting into our language, as scientific\nterms, words which in another language, the French for instance,\nhave a Latin origin familiar to us, we cannot do better than form\nthem as if they were derived directly from the Latin. Hence the\nFrench adjectives _c\u00e9tac\u00e9_, _crustac\u00e9_, _testac\u00e9_, may become either\n_cetaceous_, _crustaceous_, _testaceous_, according to the analogy\nof _farinaceous_, _predaceous_, or else _cetacean_, _crustacean_,\n{332} _testacean_, imitating the form of _patrician_. Since, as I\nshall soon have to notice, we require substantives as well as\nadjectives from these words, we must, at least for that use, take\nthe forms last suggested.\n\nIn pursuance of the same remark, _rongeur_ becomes _rodent_; and\n_edent\u00e9_ would become _edentate_, but that this word is rejected on\nanother account: the adjectives _bimane_ and _quadrumane_ are\n_bimanous_ and _quadrumanous_.\n\n3. There is not much difficulty in thus forming adjectives: but the\npurposes of Natural History require that we should have substantives\ncorresponding to these adjectives; and these cannot be obtained\nwithout some extension of the analogies of our language. We cannot\nin general use adjectives or participles as singular substantives.\n_The happy_ or _the doomed_ would, according to good English usage,\nsignify those who are happy and those who are doomed in the plural.\nHence we could not speak of a particular scaled animal as _the\nsquamate_, and still less could we call any such animal _a\nsquamate_, or speak of _squamates_ in the plural. Some of the forms\nof our adjectives, however, do admit of this substantive use. Thus\nwe talk of _Europeans_, _plebeians_, _republicans_; of _divines_ and\n_masculines_; of the _ultramontanes_; of _mordants_ and\n_brilliants_; of _abstergents_ and _emollients_; of _mercenaries_\nand _tributaries_; of _animals_, _mammals_, and _officials_; of\n_dissuasives_ and _motives_. We cannot generally use in this way\nadjectives in _ous_, nor in _ate_ (though _reprobates_ is an\nexception), nor English participles, nor adjectives in which there\nis no termination imitating the Latin, as _happy_, _good_. Hence, if\nwe have, for purposes of science, to convert adjectives into\nsubstantives, we ought to follow the form of examples like these, in\nwhich it has already appeared in fact, that such usage, though an\ninnovation at first, may ultimately become a received part of the\nlanguage.\n\nBy attention to this rule we may judge what expressions to select in\ncases where substantives are needed. I will take as an example the\ndivision of the mammalian animals into Orders. These Orders, {333}\naccording to Cuvier, are _Bimanes_, _Quadrumanes_, _Carnassiers_,\n_Rongeurs_, _Edent\u00e9s_, _Ruminants_, _Pachydermes_, _C\u00e9tac\u00e9s_; and of\nthese, _Bimanes_, _Quadrumanes_, _Rodents_, _Ruminants_,\n_Pachyderms_ are admissible as English substantives on the grounds\njust stated. _Cetaceous_ could not be used substantively; but\n_Cetacean_ in such a usage is sufficiently countenanced by such\ncases as we have mentioned, _patrician_, &c.; hence we adopt this\nform. We have no English word equivalent to the French\n_Carnassiers_: the English translator of Cuvier has not provided\nEnglish words for his technical terms; but has formed a Latin word,\n_Carnaria_, to represent the French terms. From this we might\nreadily form _Carnaries_; but it appears much better to take the\nLinn\u00e6an name _Fer\u00e6_ as our root, from which we may take _Ferine_,\nsubstantive as well as adjective; and hence we call this order\n_Ferines_. The word for which it is most difficult to provide a\nproper representation is _Edent\u00e9_, _Edentata_: for, as we have said,\nit would be very harsh to speak of the order as the _Edentates_; and\nif we were to abbreviate the word into _edent_, we should suggest a\nfalse analogy with _rodent_, for as _rodent_ is _quod rodit_, that\nwhich gnaws, _edent_ would be _quod edit_, that which eats. And even\nif we were to take _edent_ as a substantive, we could hardly use it\nas an adjective: we should still have to say, for example, the\n_edentate_ form of head. For these reasons it appears best to alter\nthe form of the word, and to call the Order the _Edentals_, which is\nquite allowable, both as adjective and substantive.\n\n[An objection might be made to this term, both in its Latin, French\nand English form: namely, that the natural group to which it is\napplied includes many species, both existing and extinct, well\nprovided with teeth. Thus the armadillo is remarkable for the number\nof its teeth; the megatherium, for their complex structure. But the\nanalogy of scientific language readily permits us to fix, upon the\nword _edentata_, a special meaning, implying the absence of one\nparticular kind of teeth, namely, incisive teeth. Linn\u00e6us called the\nequivalent order _Bruta_. We could not {334} apply in this case the\nterm _Brutes_; for common language has already attached to the word\na wider meaning, too fixedly for scientific use to trifle with it.]\n\nThere are several other words in _ate_ about which there is the same\ndifficulty in providing substantive forms. Are we to speak of\n_Vertebrates_? or would it not be better, in agreement with what has\nbeen said above, to call these _Vertebrals_, and the opposite class\n_Invertebrals_?\n\nThere are similar difficulties with regard to the names of\nsubordinate portions of zoological classification; thus the Ferines\nare divided by Cuvier into _Cheiropt\u00e9res_, _Insectivores_,\n_Carnivores_; and these latter into _Plantigrades_, _Digitigrades_,\n_Amphibies_, _Marsupiaux_. There is not any great harshness in\nnaturalizing these substantives as _Chiropters_, _Insectivores_,\n_Carnivores_, _Plantigrades_, _Digitigrades_, _Amphibians_, and\n_Marsupials_. These words _Carnivores_ and _Insectivores_ are\nbetter, because of more familiar origin, than Greek terms; otherwise\nwe might, if necessary, speak of _Zoophagans_ and _Entomophagans_.\n\nIt is only with certain familiar adjectival terminations, as _ous_\nand _ate_, that there is a difficulty in using the word as\nsubstantive. When this can be avoided, we readily accept the new\nword, as _Pachyderms_, and in like manner _Mollusks_.\n\nIf we examine the names of the Orders of Birds, we find that they\nare in Latin, _Predatores_ or _Accipitres_, _Passeres_, _Scansores_,\n_Rasores_ or _Gallin\u00e6_, _Grallatores_, _Palmipedes_ and _Anseres_:\nCuvier's Orders are, _Oiseaux de Proie_, _Passereaux_, _Grimpeurs_,\n_Gallinac\u00e9s_, _\u00c9chassiers_, _Palmipedes_. These may be englished\nconveniently as _Predators_, _Passerines_, _Scansors_,\n_Gallinaceans_, (rather than _Rasors_,) _Grallators_, _Palmipedans_,\n[or rather _Palmipeds_, like _Bipeds_]. _Scansors_, _Grallators_,\nand _Rasors_, are better, as technical terms, than _Climbers_,\n_Waders,_ and _Scratchers_. We might venture to anglicize the\nterminations of the names which Cuvier gives to the divisions of\nthese Orders: thus the Predators are the _Diurnals_ and the\n_Nocturnals_; the Passerines are the _Dentirostres_, the\n_Fissirostres_, the {335} _Conirostres_, the _Tenuirostres_, and the\n_Syndactyls_: the word _lustre_ showing that the former termination\nis allowable. The Scansors are not sub-divided, nor are the\nGallinaceans. The Grallators are _Pressirostres_, _Cultrirostres_,\n_Macrodactyls_. The Palmipeds are the _Plungers_, the _Longipens_,\nthe _Totipalmes_ and the _Lamellirostres_.\n\nThe next class of Vertebrals is the _Reptiles_, and these are either\n_Chelonians_, _Saurians_, _Ophidians_, or _Batrachians_. Cuvier\nwrites _Batraciens_, but we prefer the spelling to which the Greek\nword directs us.\n\nThe last or lowest class is the _Fishes_, in which province Cuvier has\nhimself been the great systematist, and has therefore had to devise\nmany new terms. Many of these are of Greek or Latin origin, and can\nbe anglicized by the analogies already pointed out, as\n_Chondropterygians_, _Malacopterygians_, _Lophobranchs_,\n_Plectognaths_, _Gymnodonts_, _Scleroderms_. _Discoboles_ and\n_Apodes_ may be English as well as French. There are other cases in\nwhich the author has formed the names of Families, either by forming\na word in _ides_ from the name of a genus, as _Gadoides_,\n_Gobi\u00f6ides_, or by gallicizing the Latin name of the genus, as\n_Salmones_ from _Salmo_, _Clupes_ from _Clupea_, _\u00c9soces_ from\n_Esox_, _Cyprins_ from _Cyprinus_. In these cases Agassiz's\nfavourite form of names for families of fishes has led English\nwriters to use the words _Gadoids_, _Gobioids_, _Salmonoids_,\n_Clupeoids_, _Lucioids_ (for _\u00c9soces_), _Cyprinoids_, &c. There is a\ntaint of hybridism in this termination, but it is attended with this\nadvantage, that it has begun to be characteristic of the\nnomenclature of family groups in the class _Pisces_. One of the\norders of fishes, co-ordinate with the Chondropterygians and the\nLophobranchs, is termed _Osseux_ by Cuvier. It appears hardly worth\nwhile to invent a substantive word for this, when _Bony Fishes_ is\nso simple a phrase, and may readily be understood as a technical\nname of a systematic order.\n\nThe Mollusks are the next Class; and these are divided into\n_Cephallopods_, _Gasteropods_, and the like. The Gasteropods are\n_Nudibranchs_, _Inferobranchs_, {336} _Tectibranchs,_\n_Pectinibranchs_, _Scutibranchs_, and _Cyclobranchs_. In framing\nmost of these terms Cuvier has made hybrids by a combination of a\nLatin word with _branchi\u00e6_ which is the Greek name for the gills of\na fish; and has thus avoided loading the memory with words of an\norigin not obvious to most naturalists, as terms derived from the\nGreek would have been. Another division of the Gasteropods is\n_Pulmon\u00e9s_, which we must make _Pulmonians_. In like manner the\nsubdivisions of the Pectinibranchs are the _Trochoidans_ and\n_Buccinoidans_, (_Trocho\u00efdes_, _Buccino\u00efdes)_. The _Ac\u00e9phales_,\nanother order of Mollusks, may be _Acephals_ in English.\n\nAfter these comes the third grand division, _Articulated Animals_,\nand these are _Annelidans_, _Crustaceans,_ _Arachnidans_, and\n_Insects_. I shall not dwell upon the names of these, as the form of\nEnglish words which is to be selected must be sufficiently obvious\nfrom the preceding examples.\n\nFinally, we have the fourth grand division of animals, the\n_Rayonn\u00e9s_, or _Radiata_; which, for reasons already given, we may\ncall _Radials_, or _Radiaries_. These are _Echinoderms_,\n_Intestinals_, (or rather _Entozoans_,) _Acalephes_, and _Polyps_.\nThe Polyps, which are composite animals in which many gelatinous\nindividuals are connected so as to have a common life, have, in many\ncases, a more solid framework belonging to the common part of the\nanimal. This framework, of which coral is a special example, is\ntermed in French _Polypier_; the word has been anglicized by the\nword _polypary_, after the analogy of _aviary_ and _apiary_. Thus\nPolyps are either _Polyps with Polyparies_ or _Naked Polyps_.\n\nAny common kind of Polyps has usually in the English language been\ncalled _Polypus_, the Greek termination being retained. This\ntermination in _us_, however, whether Latin or Greek, is to be\nexcluded from the English as much as possible, on account of the\nembarrassment which it occasions in the formation of the plural. For\nif we say _Polypi_ the word ceases to be English, while _Polypuses_\nis harsh: and there is the additional inconvenience, that both these\nforms would indicate the plural of individuals rather than of\nclasses. {337} If we were to say, 'The Corallines are a Family of\nthe _Polypuses with Polyparies_,' it would not at once occur to the\nreader that the last three words formed a technical phrase.\n\nThis termination _us_ which must thus be excluded from the names of\nfamilies, may be admitted in the designation of genera; of animals,\nas _Nautilus_, _Echinus_, _Hippopotamus_; and of plants, as\n_Crocus_, _Asparagus_, _Narcissus_, _Acanthus_, _Ranunculus_,\n_Fungus_. The same form occurs in other technical words, as _Fucus_,\n_Mucus_, _\u0152sophagus_, _Hydrocephalus_, _Callus_, _Calculus_,\n_Uterus_, _F\u0153tus_, _Radius_, _Focus_, _Apparatus_. It is, however,\nadvisable to retain this form only in cases where it is already\nfirmly established in the language; for a more genuine English form\nis preferable. Hence we say, with Mr. Lyell, _Ichthyosaur_,\n_Plesiosaur_, _Pterodactyl_. In like manner Mr. Owen anglicizes the\ntermination _erium_, and speaks of the _Anoplothere_ and\n_Paleothere_.\n\nSince the wants of science thus demand adjectives which can be used\nalso as substantive names of classes, this consideration may\nsometimes serve to determine our selection of new terms. Thus Mr.\nLyell's names for the subdivisions of the tertiary strata,\n_Miocene_, _Pliocene,_ can be used as substantives; but if such\nwords as _Mioneous_, _Plioneous_, had suggested themselves, they\nmust have been rejected, though of equivalent signification, as not\nfulfilling this condition.\n\n4. (_a._) Abstract substantives can easily be formed from\nadjectives: from electric we have _electricity_; from galvanic,\n_galvanism_; from organic, _organization_; _velocity_, _levity_,\n_gravity_, are borrowed from Latin adjectives. _Caloric_ is\nfamiliarly used for the matter of heat, though the form of the word\nis not supported by any obvious analogy.\n\n(_b._) It is intolerable to have words regularly formed, in\nopposition to the analogy which their meaning offers; as when bodies\nare said to have conduct_ibility_ or conduc_ibility_ with regard to\nheat. The bodies are conduct_ive_, and their property is\nconduct_ivity_.\n\n(_c._) The terminations _ize_ (rather than _ise_), _ism_, and _ist_,\nare applied to words of all origins: thus we have to {338}\n_pulverize_, to _colonize_, _Witticism_, _Heathenism_, _Journalist_,\n_Tobacconist_. Hence we may make such words when they are wanted. As\nwe cannot use _physician_ for a cultivator of physics, I have called\nhim a _Physicist_. We need very much a name to describe a cultivator\nof science in general. I should incline to call him a _Scientist_.\nThus we might say, that as an Artist is a Musician, Painter, or\nPoet, a Scientist is a Mathematician, Physicist, or Naturalist.\n\n(_d._) Connected with verbs in _ize_, we have abstract nouns in\n_ization_, as _polarization_, _crystallization_. These it appears\nproper to spell in English with _z_ rather than _s_; governing our\npractice by the Greek verbal termination \u03af\u03b6\u03c9 which we imitate. But\nwe must observe that verbs and substantives in _yse_, (_analyse_),\nbelong to a different analogy, giving an abstract noun in _ysis_ and\nan adjective _ytic_ or _ytical_; (_analysis_, _analytic_,\n_analytical_). Hence _electrolyse_ is more proper than\n_electrolyze_.\n\n(_e._) The names of many sciences end in _ics_ after the analogy of\n_Mathematics_, _Metaphysics_; as _Optics_, _Mechanics_. But these,\nin most other languages, as in our own formerly, have the singular\nform _Optice_, _l'Optique_, _Optik_, _Optick_: and though we now write\n_Optics_, we make such words of the singular number: 'Newton's\nOpticks is an example.' As, however, this connexion in new words is\nstartling, as when we say 'Thermo-electrics is now much cultivated,'\nit appears better to employ the singular form, after the analogy of\n_Logic_ and _Rhetoric_, when we have words to construct. Hence we\nmay call the science of languages _Linguistic_, as it is called by\nthe best German writers, for instance, William Von Humboldt.\n\n5. In the derivation of English from Latin or Greek words, the\nchanges of letters are to be governed by the rules which have\ngenerally prevailed in such cases. The Greek \u03bf\u03b9 and \u03b1\u03b9, the Latin\n_oe_ and _ae_, are all converted into a simple _e_, as in _E_conomy,\nGeod_e_sy, p_e_nal, C_e_sar. Hence, according to common usage, we\nshould write ph_e_nomena, not ph_\u00e6_nomena, pal_e_ontology, not\npal_\u00e6_ontology, mioc_e_ne not mioc_\u00e6_ne, p_e_kilite not {339}\np_\u0153_kilite. But in order to keep more clearly in view the origin of\nour terms, it may be allowable to deviate from these rules of\nchange, especially so long as the words are new and unfamiliar. Dr.\nBuckland speaks of the _poikilitic_, not _pecilitic_, group of\nstrata: _pal\u00e6ontology_ is the spelling commonly adopted; and in\nimitation of this I have written _pal\u00e6tiology_. The diphthong \u03b5\u03b9 was\nby the Latins changed into _i_, as in Arist_i_des; and hence this\nhas been the usual form in English. Some recent authors indeed (Mr.\nMitford for instance) write Arist_eid_es; but the former appears to\nbe the more legitimate. Hence we write m_i_ocene, pl_i_ocene, not\nm_ei_ocene, pl_ei_ocene. The Greek \u03c5 becomes _y_, and \u03bf\u03c5 becomes\n_u_, in English as in Latin, as cr_y_stal, col_u_re. The consonants\n\u03ba and \u03c7 become _c_ and _ch_ according to common usage. Hence we\nwrite _crystal_, not _chrystal_, batra_ch_ian, not batra_c_ian,\n_c_ryolite, not _ch_ryolite. As, however, the letter _c_ before _e_\nand _i_ differs from _k_, which is the sound we assign to the Greek\n\u03ba, it may be allowable to use _k_ in order to avoid this confusion.\nThus, as we have seen, poi_k_ilite has been used, as well as\npe_c_ilite. Even in common language some authors write s_k_eptic,\nwhich appears to be better than s_c_eptic with our pronunciation,\nand is preferred by Dr. Johnson. For the same reason, namely, to\navoid confusion in the pronunciation, and also, in order to keep in\nview the connexion with _cathode_, the elements of an electrolyte\nwhich go to the anode and cathode respectively may be termed the\nanion and cat_h_ion; although the Greek would suggest cat\u00efon,\n(\u03ba\u03b1\u03c4\u03af\u03bf\u03bd).\n\n6. The example of chemistry has shown that we have in the\nterminations of words a resource of which great use may be made in\nindicating the relations of certain classes of objects: as\nsulphur_ous_ and sulphur_ic_ acids; sulph_ates_, sulph_ites_, and\nsulph_urets_. Since the introduction of the artifice by the\nLavoisierian school, it has been extended to some new cases. The\nChlor_ine_, Fluor_ine_, Brom_ine_, Iod_ine_, had their names put\ninto that shape in consequence of their supposed analogy: and for\nthe same reason have been termed Chlore, {340} Phlore, Brome, Iode,\nby French chemists. In like manner, the names of metals in their\nLatin form have been made to end in _um_, as Osmium, Palladium; and\nhence it is better to say Platin_um_, Molybden_um_, than Platin_a_,\nMolybden_a_. It has been proposed to term the basis of Boracic acid\nBor_on_; and those who conceive that the basis of Silica has an\nanalogy with Boron have proposed to term it Silic_on_, while those\nwho look upon it as a metal would name it Silic_ium_. Seleni_um_ was\nso named when it was supposed to be a metal: as its analogies are\nnow acknowledged to be of another kind, it would be desirable, if\nthe change were not too startling, to term it Sel_en_, as it is in\nGerman. Phosph_orus_ in like manner might be Phosph_ur_, which would\nindicate its analogy with Sulph_ur_.\n\nThe resource which terminations offer has been applied in other\ncases. The names of many species of minerals end in _lite_, or\n_ite_, as Stauro_lite_, Aug_ite_. Hence Adolphe Brongniart, in order\nto form a name for a genus of fossil plants, has given this\ntermination to the name of the recent genus which they nearly\nresemble, as Zam_ites_, from Zamia, Lycopod_ites_ from Lycopodium.\n\nNames of different genera which differ in termination only are\nproperly condemned by Linn\u00e6us[58\\4]; as _Alsine_, _Alsinoides_,\n_Alsinella_, _Alsinastrum_; for there is no definite relation marked\nby those terminations. Linn\u00e6us gives to such genera distinct names,\n_Alsine_, _Bufonia_, _Sagina_, _Elatine_.\n\n[Note 58\\4: _Phil. Bot._ 231.]\n\nTerminations are well adapted to express definite systematic\nrelations, such as those of chemistry, but they must be employed\nwith a due regard to all the bearings of the system. Davy proposed\nto denote the combinations of other substances with chlorine by\npeculiar terminations; using _ane_ for the smallest proportion of\nChlorine, and _anea_ for the larger, as Cupr_ane_, Cupr_anea_. In\nthis nomenclature, common salt would be _Sodane_, and Chloride of\nNitrogen would be _Azotane_. This suggestion never found favour. It\nwas {341} objected that it was contrary to the Linn\u00e6an precept, that\na specific name must not be united to a generic termination. But\nthis was not putting the matter exactly on its right ground; for the\nrules of nomenclature of natural history do not apply to chemistry;\nand the Linn\u00e6an rule might with equal propriety have been adduced as\na condemnation of such terms as Sulphur_ous_, Sulphur_ic_. But\nDavy's terms were bad; for it does not appear that Chlorine enters,\nas Oxygen does, into so large a portion of chemical compounds, that\nits relations afford a key to their nature, and may properly be made\nan element in their names.\n\nThis resource, of terminations, has been abused, wherever it has\nbeen used wantonly, or without a definite significance in the\nvariety. This is the case in M. Beudant's Mineralogy. Among the\nnames which he has given to new species, we find the following\n(besides many in _ite_), Scolexer_ose_, Opsim_ose_, Exanthel_ose_,\n&c.; Diacr_ase_, Panab_ase_, Neopl_ase_; Neocl_ese_; Rhodo_ise_,\nStibicon_ise_, &c.; Marcel_ine_, Wilhelm_ine_, &c.; Exit_ele_, and\nmany others. In addition to other objections which might be made to\nthese names, their variety is a material defect: for to make this\nvariety depend on caprice alone, as in those cases it does, is to\nthrow away a resource of which chemical nomenclature may teach us\nthe value.\n\n\nAPHORISM XXII.\n\n_When alterations in technical terms become necessary, it is\ndesirable that the new term should contain in its form some memorial\nof the old one._\n\n\nWE have excellent examples of the advantageous use of this maxim in\nLinn\u00e6us's reform of botanical nomenclature. His innovations were\nvery extensive, but they were still moderated as much as possible,\nand connected in many ways with the names of plants then in use. He\nhas himself given several rules of nomenclature, which tend to\nestablish this connexion of the {342} old and new in a reform. Thus\nhe says, 'Generic names which are current, and are not accompanied\nwith harm to botany, should be tolerated[59\\4].' 'A passable generic\nname is not to be changed for another, though more apt[60\\4]'. 'New\ngeneric names are not to be framed so long as passable synonyms are\nat hand[61\\4].' 'A generic name of one genus, except it be\nsuperfluous, is not to be transferred to another genus, though it\nsuit the other better[62\\4].' 'If a received genus requires to be\ndivided into several, the name which before included the whole,\nshall be applied to the most common and familiar kind[63\\4].' And\nthough he rejects all _generic_ names which have not a Greek or\nLatin root[64\\4], he is willing to make an exception in favour of\nthose which from their form might be supposed to have such a root,\nthough they are really borrowed from other languages, as _Thea_,\nwhich is the Greek for goddess; _Coffea_, which might seem to come\nfrom a Greek word denoting silence (\u03ba\u03c9\u03c6\u03cc\u03c2); _Cheiranthus_, which\nappears to mean hand-flower, but is really derived from the Arabic\n_Keiri_: and many others.\n\n[Note 59\\4: _Philosophia Botanica_, Art. 242.]\n\n[Note 60\\4: Art. 246.]\n\n[Note 61\\4: Art. 247.]\n\n[Note 62\\4: Art. 249.]\n\n[Note 63\\4: Art. 249.]\n\n[Note 64\\4: Art. 232.]\n\nAs we have already said, the attempt at a reformation of the\nnomenclature of Mineralogy made by Professor Mohs will probably not\nproduce any permanent effect, on this account amongst others, that\nit has not been conducted in this temperate mode; the innovations\nbear too large a proportion to the whole of the names, and contain\ntoo little to remind us of the known appellations. Yet in some\nrespects Professor Mohs has acted upon this maxim. Thus he has\ncalled one of his classes _Spar_, because _Felspar_ belongs to it. I\nshall venture to offer a few suggestions on this subject of\nMineralogical Nomenclature.\n\nIt has already been remarked that the confusion and complexity which\nprevail in this subject render a reform very desirable. But it will\nbe seen, from the reasons assigned under the Ninth Aphorism, that no\npermanent system of names can be looked for, till a {343} sound\nsystem of classification be established. The best mineralogical\nsystems recently published, however, appear to converge to a common\npoint; and certain classes have been formed which have both a\nnatural-historical and a chemical significance. These Classes,\naccording to Naumann, whose arrangement appears the best, are\nHydrolytes, Haloids, Silicides, Oxides of Metals, Metals,\nSulphurides (Pyrites, Glances, and Blendes), and Anthracides. Now we\nfind;--that the Hydrolytes are all compounds, such as are commonly\ntermed _Salts_;--that the Haloids are, many of them, already called\n_Spars_, as _Calc Spar_, _Heavy Spar_, _Iron Spar_, _Zinc\nSpar_;--that the _Silicides_, the most numerous and difficult class,\nare denoted for the most part, by single words, many of which end in\n_ite_;--that the other classes, or subclasses, _Oxides_, _Pyrites_,\n_Glances_, and _Blendes_, have commonly been so termed; as _Red Iron\nOxide_, _Iron Pyrites_, _Zinc Blende_;--while pure metals have\nusually had the adjective _native_ prefixed, as _Native Gold_,\n_Native Copper_. These obvious features of the current names appear\nto afford us a basis for a systematic nomenclature. The Salts and\nSpars might all have the word _salt_ or _spar_ included in their\nname, as _Natron Salt_, _Glauber Salt_, _Mock Salt_; _Calc Spar_,\n_Bitter Spar_, (Carbonate of Lime and Magnesia), _Fluor Spar_,\n_Phosphor Spar_ (Phosphate of Lime), _Heavy Spar_, _Celestine Spar_\n(Sulphate of Strontian), _Chromic Lead Spar_ (Chromate of Lead); the\n_Silicides_ might all have the name constructed so as to be a single\nword ending in _ite_, as _Chabasite_ (Chabasie), _Natrolite_\n(Mesotype), _Sommite_ (Nepheline), _Pistacite_ (Epidote); from this\nrule might be excepted the _Gems_, as _Topaz_, _Emerald_,\n_Corundum_, which might retain their old names. The Oxides, Pyrites,\nGlances, and Blendes, might be so termed; thus we should have\n_Tungstic Iron Oxide_ (usually called Tungstate of Iron), _Arsenical\nIron Pyrites_ (Mispickel), _Tetrahedral Copper Glance_ (Fahlerz),\n_Quicksilver Blende_ (Cinnabar), and the metals might be termed\n_native_, as _Native Copper_, _Native Silver_.\n\nSuch a nomenclature would take in a very large {344} proportion of\ncommonly received appellations, especially if we were to select\namong the synonyms, as is proposed above in the case of _Glauber\nSalt_, _Bitter Spar_, _Sommite_, _Pistacite_, _Natrolite_. Hence it\nmight be adopted without serious inconvenience. It would make the\nname convey information respecting the place of the mineral in the\nsystem; and by imposing this condition, would limit the extreme\ncaprice, both as to origin and form, which has hitherto been\nindulged in imposing mineralogical names.\n\nThe principle of a mineralogical nomenclature determined by the\nplace of the species in the system, has been recognized by Mr.\nBeudant as well as Mr. Mohs. The former writer has proposed that we\nshould say _Carbonate Calcaire_, _Carbonate Witherite_, _Sulphate\nCouperose_, _Silicate Stilbite_, _Silicate Chabasie_, and so on. But\nthese are names in which the part added for the sake of the system,\nis not incorporated with the common name, and would hardly make its\nway into common use.\n\nWe have already noticed Mr. Mohs's designations for two of the\nSystems of Crystallization, the _Pyramidal_ and the _Prismatic_, as\nnot characteristic. If it were thought advisable to reform such a\ndefect, this might be done by calling them the _Square Pyramidal_\nand the _Oblong Prismatic_, which terms, while they expressed the\nreal distinction of the systems, would be intelligible at once to\nthose acquainted with the Mohsian terminology.\n\nI will mention another suggestion respecting the introduction of an\nimprovement in scientific language. The term _Depolarization_ was\nintroduced, because it was believed that the effect of certain\ncrystals, when polarized light was incident upon them in certain\npositions, was to destroy the peculiarity which polarization had\nproduced. But it is now well known, that the effect of the second\ncrystal in general is to divide the polarized ray of light into two\nrays, polarized in different planes. Still this effect is often\nspoken of as _Depolarization_, no better term having been yet\ndevised. I have proposed and used the term _Dipolarization_, {345}\nwhich well expresses what takes place, and so nearly resembles the\nelder word, that it must sound familiar to those already acquainted\nwith writings on this subject.\n\nI may mention one term in another department of literature which it\nappears desirable to reform in the same manner. The theory of the\nFine Arts, or the philosophy which speculates concerning what is\nbeautiful in painting, sculpture or architecture, and other arts,\noften requires to be spoken of in a single word. Baumgarten and\nother German writers have termed this province of speculation\n_\u00c6sthetics_; \u03b1\u1f30\u03c3\u03b8\u03ac\u03bd\u03b5\u03c3\u03b8\u03b1\u03b9, _to perceive_, being a word which appeared\nto them fit to designate the perception of beauty in particular.\nSince, however, _\u00e6sthetics_ would naturally denote the Doctrine of\nPerception in general; since this Doctrine requires a name; since\nthe term _\u00e6sthetics_ has actually been applied to it by other German\nwriters (as Kant); and since the essential point in the philosophy\nnow spoken of is that it attends to Beauty;--it appears desirable to\nchange this name. In pursuance of the maxim now before us, I should\npropose the term _Call\u00e6sthetics_, or rather (in agreement with what\nwas said in page 338) _Call\u00e6sthetic_, the science of the perception\nof beauty.\n\n\n\n{{346}}\nFURTHER ILLUSTRATIONS OF THE APHORISMS\n ON SCIENTIFIC LANGUAGE, FROM THE\n RECENT COURSE OF SCIENCES.\n\n\n1. BOTANY.\n\nTHE nomenclature of Botany as rescued from confusion by Linn\u00e6us, has\nin modern times been in some danger of relapsing into disorder or\nbecoming intolerably extensive, in consequence of the multiplication\nof genera by the separation of one old genus into several new ones,\nand the like subdivisions of the higher groups, as subclasses and\nclasses. This inconvenience, and the origin of it, have been so well\npointed out by Mr. G. Bentham[65\\4], that I shall venture to adopt\nhis judgment as an Aphorism, and give his reasons for it.\n\n[Note 65\\4: _Linn\u00e6an Society's Proceedings_, vol. ii. p. 30 (June,\n1857).]\n\n\nAPHORISM XXIII.\n\n_It is of the greatest importance that the Groups which give their\nsubstantive names to every included species should remain large._\n\n\nIT will be recollected that according to the Linn\u00e6an nomenclature,\nthe genus is marked by a substantive, (as _Rosa_), and the species\ndesignated by an adjective added to this substantive, (as _Rosa\nAlpina_); while the natural orders are described by adjectives taken\nsubstantively, (as _Rosace\u00e6_), But this rule, though it has been\nuniversally assented to in theory, has often been deviated from in\npractice. The number of known species having much increased, and the\nlanguage of Linn\u00e6us and the principles of Jussieu having much\naugmented the facilities for the study of affinities, botanists have\nbecome aware that the species of a genus and the genera of an order\ncan be collected into intermediate groups {347} as natural and as\nwell defined as the genera and orders themselves, and names are\nrequired for these subordinate groups as much as for the genera and\norders.\n\nNow two courses have been followed in providing names for these\nsubordinate groups.\n\n1. The original genera (considering the case of genera in the first\nplace) have been preserved, (if well founded); and the lower groups\nhave been called _subgenera_, _sections_, _subsections_,\n_divisions_, &c.: and the original names of the genera have been\nmaintained for the purpose of nomenclature, in order to retain a\nconvenient and stable language. But when these subordinate groups\nare so well defined and so natural, that except for the convenience\nof language, they might be made good genera, there are given also to\nthese subordinate groups, substantive or substantively-taken\nadjective names. When these subordinate groups are less defined or\nless natural, either no names at all are given, and they are\ndistinguished by figures or signs such as *, **, or \u00a7 1, \u00a7 2, &c. or\nthere are given them mere adjective names.\n\nOr, 2, To regard these intermediate groups between species and the\noriginal genera, as so many independent genera; and to give them\nsubstantive names, to be used in ordinary botanical nomenclature.\n\nNow the second course is that which has produced the intolerable\nmultiplication of genera in modern times; and the first course is\nthe only one which can save botanical nomenclature from replunging\ninto the chaos in which Linn\u00e6us found it. It was strongly advocated\nby the elder De Candolle; although in the latter years of his life,\nseeing how general was the disposition to convert his subgenera and\nsections into genera, he himself more or less gave in to the general\npractice. The same principle was adopted by Endlichen, but he again\nwas disposed to go far in giving substantive names to purely\ntechnical or ill-defined subsections of genera.\n\nThe multiplication of genera has been much too common. Botanists\nhave a natural pride in establishing new genera (or orders); and\nbesides this, it is felt how useful it is, in the study of\naffinities, to define and {348} name all natural groups in every\ngrade, however numerous they may be: and in the immense variety of\nlanguage it is found easy to coin names indefinitely.\n\nBut the arguments on the other side much preponderate. In attempting\nto introduce all these new names into ordinary botanical language,\nthe memory is taxed beyond the capabilities of any mind, and the\noriginal and legitimate object of the Linn\u00e6an nomenclature is wholly\nlost sight of. In a purely scientific view it matters little if the\nOrders are converted into Classes or Alliances, the Genera into\nOrders, and the Sections or Subsections into Genera: their relative\nimportance does not depend on the names given to them, but on their\nheight in the scale of comprehensiveness. But for language, the\ngreat implement without which science cannot work, it is of the\ngreatest importance, as our Aphorism declares, That the groups which\ngive their substantive names to every species which they include,\nshould remain large. If, independently of the inevitable increase of\nGenera by new discoveries, such old ones as _Ficus_, _Begonia_,\n_Arum_, _Erica_, &c. are divided into 10, 20, 30, or 40 independent\nGenera, with names and characters which are to be recollected before\nany one species can be spoken of;--if Genera are to be reckoned by\ntens of thousands instead of by thousands;--the range of any\nindividual botanist will be limited to a small portion of the whole\nfield of the sciences.\n\nAnd in like manner with regard to Orders, so long as the number of\nOrders can be kept within, or not much beyond a couple of hundred,\nit may reasonably be expected that a botanist of ordinary capacity\nshall obtain a sufficient general idea of their nature and\ncharacters to call them at any time individually to his mind for the\npurpose of comparison: but if we double the number of Orders, all is\nconfusion.\n\nThe inevitable confusion and the necessity of maintaining in some\nway the larger groups, have been perceived by those even who have\ngone the furthest in lowering the scale of Orders and Genera. As a\nremedy for this confusion, they propose to erect the old genera into\nindependent orders, and the old orders into classes {349} or\ndivisions. But this is but an incomplete resumption of the old\nprinciples, without the advantage of the old nomenclature.\n\nAnd it will not be asserted, with regard to these new genera, formed\nby cutting up the old ones, that the new group is better defined\nthan the group above it: on the contrary, it is frequently less so.\nIt is not pretended that _Urostigma_ or _Phannacosyce_, new genera\nformed out of the old genus _Ficus_, are better defined than the\ngenus _Ficus_: or that the new genera which have lately been cut out\nof the old genus _Begonia_, form more natural groups than _Begonia_\nitself does. The principle which seems to be adopted in such\nsubdivisions of old genera is this: that the lowest definable group\nabove a species is a genus. If we were to go a step further, every\nspecies becomes a genus with a substantive name.\n\nIt ought always to be recollected that though the analytical process\ncarried to the uttermost, and separating groups by observation of\ndifferences, is necessary for the purpose of ascertaining the facts\nupon which botany or any other classificatory science is based, it\nis a judicious synthesis alone, associating individuals by the ties\nof language, which can enable the human mind to take a comprehensive\nview of these facts, to deduce from them the principles of the\nscience, or to communicate to others either facts or principles.\n\n\n2. COMPARATIVE ANATOMY.\n\nThe Language of Botany, as framed by Linn\u00e6us, and regulated by his\nCanons, is still the most notable and successful example of\nscientific terminology which has obtained general reception among\nnaturalists. But the Language of Anatomy, and especially of the\nComparative Anatomy of the skeleton, has of late been an object of\ngreat attention to physiologists; and especially to Mr. Owen; and\nthe collection of terms which he has proposed are selected with so\nmuch thought and care, that they may minister valuable lessons to us\nin this part of our subject.\n\nThere is, at first sight, this broad difference between the\ndescriptive language of Botany and of Comparative {350} Anatomy;\nthat in the former science, we have comparatively few parts to\ndescribe, (_calyx_, _corolla_, _stamen_, _pistil_, _pericarp_,\n_seed_, &c.): while each of these parts is susceptible of many\nforms, for describing which with precision many terms must be\nprovided: in Comparative Anatomy, on the other hand, the skeletons\nof many animals are to be regarded as modifications of a common\ntype, and the terms by which their parts are described are to mark\nthis community of type. The terminology of Botany has for its object\n_description_; the language of Comparative Anatomy must have for its\nbasis _morphology_. Accordingly, Mr. Owen's terms are selected so as\nto express the analogies, or, as he calls them, the _homologies_ of\nthe skeleton; those parts of the skeleton being termed _homologues_,\nwhich have the same place in the general type, and therefore ought\nto have the same name.\n\nYet this distinction of the basis of botanical and anatomical\nterminology is not to be pushed too far. The primary definitions in\nbotany, as given by Linn\u00e6us, are founded on morphological views; and\nimply a general type of the structure of plants. These are his\ndefinitions (_Phil. Bot._ Art. 86).\nCALYX, _Cortex_ plant\u00e6 in Fructificatione pr\u00e6sens.\nCOROLLA, _Liber_ plant\u00e6 in Flora pr\u00e6sens.\nSTAMEN, Viscus pro Pollinis pr\u00e6paratione.\nPISTILLUM, Viscus fructui adherens pro Pollinis receptione.\nPERICARPIUM, Viscus gravidum seminibus, qu\u00e6 matura dimittit.\n\nBut in what follows these leading definitions, the terms are\ndescriptive merely. Now in Comparative Anatomy, an important object\nof terms is, to express what part of the type each bone\nrepresents--to answer the question, _what_ is it? before we proceed,\nassuming that we know what it is, to describe its shape. The\ndifficulty of this previous question is very great when we come to\nthe bones of the head; and when we assume, as morphology leads us to\ndo, that the heads of all vertebrated animals, including even\nfishes, are composed of homologous bones. And, as I have already\n{351} said in the History (b. xvii. c. 7), speaking of Animal\nMorphology, the best physiologists are now agreed that the heads of\nvertebrates may be resolved into a series of vertebr\u00e6, homologically\nrepeated and modified in different animals. This doctrine has been\ngradually making its way among anatomists, through a great variety\nof views respecting details; and hence, with great discrepancies in\nthe language by which it has been expressed. Mr. Owen has proposed a\ncomplete series of terms for the bones of the head of all\nvertebrates; and these names are supported by reasons which are full\nof interest and instruction to the physiologist, on account of the\ncomprehensive and precise knowledge of comparative osteology which\nthey involve; but they are also, as I have said, interesting and\ninstructive to us, as exemplifying the reasons which may be given\nfor the adoption of words in scientific language. The reasons thus\ngiven agree with several of the aphorisms which I have laid down,\nand may perhaps suggest a few others. Mr. Owen has done me the great\nhonour to quote with approval some of these aphorisms. The terms\nwhich he has proposed belong, as I have already said, to the\n_Terminology_, not to the _Nomenclature_ of Zoology. In the latter\nsubject, the Nomenclature (the names of species) the binary\nnomenclature established by Linn\u00e6us remains, in its principle,\nunshaken, simple and sufficient.\n\nI shall best derive from Mr. Owen's labours and reflexions some of\nthe instruction which they supply with reference to the Language of\nScience, by making remarks on his terminology with reference to such\naphorisms as I have propounded on the subject, and others of a like\nkind.\n\nMr. Owen, in his _Homologies of the Vertebrate Skeleton_, has given\nin a Tabular Form his views of the homology of the bones of the head\nof vertebrates, and the names which he consequently proposes for\neach bone, with the synonyms as they occur in the writings of some\nof the most celebrated anatomical philosophers, Cuvier, Geoffroy,\nHallmann, Meckel and Wagner, Agassiz and Soemmering. And he has\nadded to this Table his reasons for dissenting from his predecessors\n{352} to the extent to which he has done so. He has done this, he\nsays, only where nature seemed clearly to refuse her sanction to\nthem; acting upon the maxim (our Aphorism X.) that new terms and\nchanges of terms which are not needed in order to express truth, are\nto be avoided. The illustrations which I have there given, however,\nof this maxim, apply rather to the changes in nomenclature than in\nterminology; and though many considerations apply equally to these\ntwo subjects, there are some points in which the reasons differ in\nthe two cases: especially in this point:--the names, both of genera\nand of species, in a system of nomenclature, may be derived from\ncasual or arbitrary circumstances, as I have said in Aphorism XIII.\nBut the terms of a scientific terminology ought to cohere as a\nsystem, and therefore should not commonly be derived from anything\ncasual or arbitrary, but from some analogy or connexion. Hence it\nseems unadvisable to apply to bones terms derived from the names of\npersons, as _ossa wormiana_; or even from an accident in anatomical\nhistory, as _os innominatum_.\n\nIt is further desirable that in establishing such a terminology,\neach bone should be designated by a single word, and not by a\ndescriptive phrase, consisting of substantive and adjective. On this\nground Mr. Owen proposes _presphenoid_ for _sphen\u00f6ide anterieur_. So\nalso _prefrontal_ is preferred to _anterior frontal_, and\n_postfrontal_ to _posterior frontal_. And the reason which he gives\nfor this is worthy of being stated as an Aphorism, among those which\nshould regulate this subject. I shall therefore state it thus:\n\n\nAPHORISM XXIV.\n\n_It is advisable to substitute definite single names for descriptive\nphrases as better instruments of thought._\n\n\nIT will be recollected by the reader that in the case of the Linn\u00e6an\nreform of the botanical nomenclature of species, this was one of the\ngreat improvements which was introduced.\n\nAgain: some of the first of the terms which Mr. Owen proposes\nillustrate, and confirm by their manifest claim {353} to acceptance,\na maxim which we stated as Aphorism XXII.: namely,\nWhen alterations in technical terms become necessary, it is desirable\nthat the new term should contain in its form some memorial of the old\none.\n\nThus for 'basilaire,' which Cuvier exclusively applies to the 'pars\nbasilaris' of the occiput, and which Geoffroy as exclusively applies\n(in birds) to the 'pars basilaris' of the sphenoid, Mr. Owen\nsubstitutes the term _basioccipital_.\n\nAgain: for the term 'suroccipital' of Geoffroy, Mr. Owen proposes\n_paroccipital_, to avoid confusion and false suggestion: and with\nreference to this word, he makes a remark in agreement with what we\nhave said in the discussion of Aphorism XXI.: namely, that the\ncombination of different languages in the derivation of words,\nthough to be avoided in general, is in some cases admissible. He\nsays, 'If the purists who are distressed by such harmless hybrids as\n\"mineralogy,\" \"terminology,\" and \"mammalogy,\" should protest against\nthe combination of the Greek prefix to the Latin noun, I can only\nplead that servility to a particular source of the fluctuating\nsounds of vocal language is a matter of taste: and that it seems no\nunreasonable privilege to use such elements as the servants of\nthought; and in the interests of science to combine them, even\nthough they come from different countries, when the required duty is\nbest and most expeditiously performed by their combination.'\n\nSo again we have illustrations of our Aphorism XII., that if terms\nare systematically good they are not to be rejected because they are\netymologically inaccurate. In reference to that bone of the skull\nwhich has commonly been called _vomer_, the ploughshare: a term\nwhich Geoffroy rejected, but which Mr. Owen retains, he says, 'When\nGeoffrey was induced to reject the term _vomer_ as being applicable\nonly to the peculiar form of the bone in a small portion of the\nvertebrata, he appears not to have considered that the old term, in\nits wider application, would be used without reference to its\nprimary allusion to the ploughshare, and that becoming, as it {354}\nhas, a purely arbitrary term, it is superior and preferable to any\npartially descriptive one.'\n\nAnother condition which I have mentioned in Aphorism XX., as\nvaluable in technical terms is, that they should be susceptible of\nsuch grammatical relations as their scientific use requires.\n\nThis is, in fact, one of the grounds of the Aphorism which we have\nalready borrowed from Mr. Owen, that we are to prefer single\nsubstantives to descriptive phrases. For from such substantives we\ncan derive adjectives, and other forms; and thus the term becomes,\nas Mr. Owen says, _a better instrument of thought_. Hence, he most\nconsistently mentions it as a recommendation of his system of names,\nthat by them the results of a long series of investigations into the\nspecial homologies of the bones of the head are expressed in simple\nand definite terms, _capable of every requisite inflection_ to\nexpress the proportion of the parts.\n\nI may also, in reference to this same passage in Mr. Owen's appeal\nin behalf of his terminology, repeat what I have said under Aphorism\nX.: that the persons who may most properly propose new scientific\nterms, are those who have much new knowledge to communicate: so that\nthe vehicle is commended to general reception by the value of what\nit contains. It is only to eminent discoverers and profound\nphilosophers that the authority is conceded of introducing a new\nsystem of terms; just as it is only the highest authority in the\nstate which has the power of putting a new coinage into circulation.\nThe long series of investigations of which the results are contained\nin Mr. Owen's table of synonyms, and the philosophical spirit of his\ngeneralizations, entitles him to a most respectful hearing when he\nappeals to the Professors and Demonstrators of Human Anatomy for an\nunbiassed consideration of the advantages of the terms proposed by\nhim, as likely to remedy the conflicting and unsettled synonymy\nwhich has hitherto pervaded the subject.\n\nThere is another remark which is suggested by the works on\nComparative Anatomy, which I am now considering. I have said in\nvarious places that Technical {355} Terms are a necessary condition\nof the progress of a science. But we may say much more than this:\nand the remark is so important, that it deserves to be stated as one\nof our Aphorisms, as follows:\n\n\nAPHORISM XXV.\n\n_In an advanced Science, the history of the Language of the Science\nis the history of the Science itself._\n\n\nI HAVE already stated in previous Aphorisms (VIII. and XI.) that\nTerms must be constructed so as to be fitted to enunciate general\npropositions, and that Terms which imply theoretical views are\nadmissible for this purpose. And hence it happens that the history\nof Terms in any science which has gone through several speculative\nstages, is really the history of the generalizations and theories\nwhich have had currency among the cultivators of the science.\n\nThis appears in Comparative Anatomy from what we have been saying.\nThe recent progress of that science is involved in the rise and\ncurrency of the Terms which have been used by the anatomists whose\nsynonyms Mr. Owen has to discuss; and the reasons for selecting\namong these, or inventing others, include those truths and\ngeneralizations which are the important recent steps of the science.\nThe terms which are given by Mr. Owen in his table to denote the\nbones of the head are good terms, _if_ they _are_ good terms,\nbecause their adoption and use is the only complete way of\nexpressing the truths of homology: namely, of that Special Homology,\naccording to which all vertebrate skeletons are referred to the\nhuman skeleton as their type, and have their parts designated\naccordingly.\n\nBut further: there is another kind of homology which Mr. Owen calls\n_General_ Homology, according to which the primary type of a\nvertebrate animal is merely a series of vertebr\u00e6; and all limbs and\nother appendages are only developements of the parts of one or\nanother of the vertebr\u00e6. And in order to express this view, and in\nproportion as the doctrine has become current amongst {356}\nanatomists, the parts of vertebr\u00e6 have been described by terms of a\ndegree of generality which admit of such an interpretation. And\nhere, also, Mr. Owen has proposed a terminology for the parts of the\nvertebr\u00e6, which seems to convey more systematically and\ncomprehensively than those of preceding writers the truths to which\nthey have been tending. Each vertebra is composed of a _centrum_,\n_neurapophysis_, _parapophysis_, _pleurapophysis_, _h\u00e6maphysis_,\n_neural spine_ and _h\u00e6mal spine_, with certain exogenous parts.\n\nThe opinion that the head, as well as the other parts of the frame\nof vertebrates, is composed of vertebr\u00e6, is now generally accepted\namong philosophical anatomists. In the _History_ (_Hist. I. S._ b.\nxvii. c. 7, sect. 1), I have mentioned this opinion as proposed by\nsome writers; and I have stated that Oken, in 1807 published a\n'Program' _On the signification of the bones of the Skull_, in which\nhe maintained, that these bones are equivalent to four vertebr\u00e6:\nwhile Meckel, Spix, and Geoffroy took views somewhat different.\nCuvier and Agassiz opposed this doctrine, but Mr. Owen has in his\n_Archetype and Homologies of the Vertebrate Skeleton_ (1848),\naccepted the views of Oken, and argued at length against the\nobjections of Cuvier, and also those of Mr. Agassiz. As I have noted\nin the last edition of the _History of the Inductive Sciences_ (b.\nxvii. c. 7), he gives a Table in which the Bones of the Head are\nresolved into four vertebr\u00e6, which he terms the Occipital, Parietal,\nFrontal and Nasal Vertebr\u00e6 respectively: the neural arches of which\nagree with what Oken called the Ear-vertebra, the Jaw-vertebra, the\nEye-vertebra, and the Nose-vertebra.\n\nBesides these doctrines of _Special Homology_ by which the bones of\nall vertebrates are referred to their corresponding bones in the\nhuman skeleton, and of _General Homology_, by which the bones are\nreferred to the parts of vertebr\u00e6 which they represent, Mr. Owen\ntreats of _Serial Homology_, the recognition of the same elements\nthroughout the series of segments of the same skeleton; as when we\nshew in what manner the arms correspond to the legs. And thus, he\nsays, in the head also, the _basioccipital_, _basisphenoid_,\n_presphenoid_ and _vomer_ are {357} homotypes with the _centrums_ of\nall succeeding vertebr\u00e6. The _excoccipitals_,_ alisphenoids_,\n_orbitosphenoids_, and _prefrontals_, are homotypes with the\n_neurapophyses_ of all the succeeding vertebr\u00e6. The _paroccipitals_,\n_mactoids_ and _postfrontals_, with the _transverse processes_ of\nall the succeeding vertebr\u00e6: and so on. Perhaps these examples may\nexemplify sufficiently for the general reader both Mr. Owen's\nterminology, and the intimate manner in which it is connected with\nthe widest generalizations to which anatomical philosophy has yet\nbeen led.\n\nThe same doctrine, that the history of the Language of a Science is\nthe history of the Science, appears also in the recent progress of\nChemistry; but we shall be better able to illustrate our Aphorism in\nthis case by putting forward previously one or two other Aphorisms\nbearing upon the history of that Science.\n\n\nAPHORISM XXVI.\n\n_In the Terminology of Science it may be necessary to employ\nletters, numbers, and algebraical symbols._\n\n\n1. MINERALOGY.\n\nI HAVE already said, in Aphorism XV., that symbols have been found\nrequisite as a part of the terminology of Mineralogy. The _names_\nproposed by Ha\u00fcy, borrowed from the crystalline laws, were so\ninadequate and unsystematic that they could not be retained. He\nhimself proposed a _notation_ for crystalline forms, founded upon\nhis principle of the derivation of such forms from a _primitive_\nform, by _decrements_, on its _edges_ or its _angles_. To denote\nthis derivation he took the first letters of the three syllables to\nmark the faces of the _PriMiTive_ form, _P_, _M_, _T_; the vowels\n_A_, _E_, _I_, _O_ to mark the angles; the consonants _B_, _C_, _D_,\n&c. to mark the edges; and numerical exponents, annexed in various\npositions to these letters, represented the law and manner of\nderivation. Thus when the primitive form was a cube,\n 1\n _B_\nrepresented the result of a derivation by a decrement of one row\n{358} on an edge; that is, a rhombic octahedron; and\n 1\n_BP_ represented the combination of this octahedron with the\nprimitive cube. In this way the pentagonal dodecahedron, produced by\ndecrements of 2 to 1 on half the edges of the cube, was represented by\n \u00bd\n_B_\u00b2 _C G_\u00b2 \u00b2_G_.\n\nNot only, however, was the hypothesis of primitive forms and\ndecrements untenable, but this notation was too unsystematic to\nstand long. And when Weiss and Mohs established the distinction of\nSystems of Crystallography[66\\4], they naturally founded upon that\ndistinction a notation for crystalline forms. Mohs had several\nfollowers; but his algebraical notation so barbarously violated all\nalgebraical meaning, that it was not likely to last. Thus, from a\nprimitive rhombohedron which he designated by _R_, he derived, by a\ncertain process, a series of other rhombohedrons, which he denoted\nby _R_ + 1, _R_ + 2, _R_ \u2212 1, &c.; and then, by another mode of\nderivation from them, he obtained forms which he marked as\n(_R_ + 2)\u00b2, (_R_ + 2)\u00b3, &c. In doing this he used the algebraical\nmarks of addition and involution without the smallest ground;\nbesides many other proposals no less transgressing mathematical\nanalogy and simplicity.\n\n[Note 66\\4: _Hist. Ind. Sc._ b. xv. c. 4.]\n\nBut this notation might easily suggest a better. If we take a\nprimitive form, we can generally, by two steps of derivation, each\ncapable of numerical measure, obtain any possible face; and\ntherefore any crystalline form bounded by such faces. Hence all that\nwe need indicate in our crystalline laws is the primitive form, and\ntwo numerical exponents; and rejecting all superfluity in our\nsymbols, instead of (_R_ + 2)\u00b3 we might write 2 _R_ 3. Nearly of\nthis kind is the notation of Naumann. The systems of\ncrystallization, the octahedral or tessular, the rhombic, and the\nprismatic, are marked by the letters _O_, _R_, _P_; and from these\nare derived, by certain laws, such symbols as\n 3 _O_ \u00bd, \u221e _R_ 2, \u00bd _P_ 2, {359}\nwhich have their definite signification flowing from the rules of\nthe notation.\n\nBut Professor Miller, who has treated the subject of Crystallography\nin the most general and symmetrical manner, adopts the plan of\nmarking each crystalline plane by _three_ numerical indices. Thus in\nthe Octahedral System, the cube is {100}; the octahedron is {111};\nthe rhombic dodecahedron is {011}; the pentagonal dodecahedron is \u03c0\n{012}; where \u03c0 indicates that the form is not _holohedral_ but\n_hemihedral_, only half the number of faces being taken which the\nlaw of derivation would give. This system is the most mathematically\nconsistent, and affords the best means of calculation, as Professor\nMiller has shown; but there appears to be in it this defect, that\nthough an essential part of the scheme is the division of\ncrystalline forms into Systems,--the Octahedral, Pyramidal,\nRhombohedral and Prismatic,--this division does not at all appear in\nthe notation.\n\nBut whatever be the notation which the crystallographer adopts, it\nis evident that he must employ some notation; and that, without it,\nhe will be unable to express the forms and relations of forms with\nwhich he has to deal.\n\n2. CHEMISTRY.\n\nThe same has long been the case in Chemistry. As I have stated\nelsewhere[67\\4], the chemical nomenclature of the oxygen theory was\nfor a time very useful and effective. But yet it had defects which\ncould not be overlooked, as I have already stated under Aphorism II.\nThe relations of elements were too numerous, and their numerical\nproperties too important, to be expressed by terminations and other\nmodifications of words. Thus the compounds of Nitrogen and Oxygen\nare the Protoxide, the Deutoxide, Nitrous Acid, Peroxide of\nNitrogen, Nitric Acid. The systematic nomenclature here, even thus\nloosely extended, does not express our knowledge. And the Atomic\nTheory, when established, brought to view numerical {360} relations\nwhich it was very important to keep in sight. If _N_ represents\nNitrogen and _O_ Oxygen, the compounds of the two elements just\nmentioned might be denoted by _N_ + _O_, _N_ + 2_O_, _N_ + 3_O_,\n_N_ + 4_O_, _N_ + 5_O_. And by adopting a letter for each of the\nelementary substances, all the combinations of them might be\nexpressed in this manner.\n\n[Note 67\\4: _Hist. Ind. Sc._ b. xiv. c. 6.]\n\nBut in chemistry there are different orders of combination. A salt,\nfor instance, is a compound of a base and an acid, each of which is\nalready compound. If _Fe_ be iron and _C_ be carbon, _Fe_ + _O_ will\nbe the protoxide of iron, and _C_ + 2_O_ will be carbonic acid; and\nthe carbonate of iron (more properly carbonate of protoxide of\niron), may be represented by\n (_Fe_ + _O_) + (_C_ + 2_O_)\nwhere the brackets indicate the first stage of composition.\n\nBut these brackets and signs of addition, in complex cases, would\ncumber the page in an inconvenient degree; and oxygen is of such\nvery wide occurrence, that it seems desirable to abridge the\nnotation so far as it is concerned. Hence Berzelius proposed[68\\4]\nthat in the first stage of composition the oxygen should be\nexpressed by dots over the letter; and thus the carbonate of iron\nwould be [.]_Fe_ + [..]_C_. But Berzelius further introduced into\nhis notation indexes such as in algebra denote involution to the\nsquare, cube, &c. Thus _Cu_ being copper, the sulphate of copper is\nrepresented by [...]_S_\u00b2[..]_Cu_. This notation, when first\nproposed, was strongly condemned by English chemists, and\nBerzelius's reply to them may be taken as stating the reasons in\nfavour of such notation. He says[69\\4], 'We answer to the opponents,\nthat undoubtedly the matter may be looked at in various lights. The\nuse of Formul\u00e6 has always, for a person who has not accustomed\nhimself to them, something repulsive; but this is easy to overcome.\nI agree with my opponent, {361} who says that nothing can be\nunderstood in a Formula which cannot be expressed in words; and that\nif the words express it as easily as the Formula, the use of the\nlatter would be a folly. But there are cases in which this is not\nso; in which the Formula says in a glance what it would take many\nlines to express in words; and in which the expression of the\nFormula is clearer and more easily apprehended by the reader than\nthe longer description in words. Let us examine such a Formula, and\ncompare it with the equivalent description in words. Take, for\nexample, crystallized sulphate of copper, of which the Formula is\n [..]_Cu_[...]_S_\u00b2 + 10_H_\u00b2_O_.\nNow this Formula expresses the following propositions:\n'That the salt consists of one atom of copper-oxide combined with 2\natoms of sulphuric acid and with 10 atoms of water; that the\ncopper-oxide contains two atoms of oxygen; and that the sulphuric\nacid contains 3 atoms of oxygen for one atom of sulphur; that its\noxygen is three times as much as that of the oxide; and that the\nnumber of atoms of oxygen in the acid is 6; and that the number of\natoms of oxygen in the water is 10; that is, 5 times the number in\nthe oxide; and that finally the salt contains, of simple atoms, 1\ncopper, 2 sulphur, 20 hydrogen, and 18 oxygen.\n\n[Note 68\\4: _System of Mineralogy_, 1816.]\n\n[Note 69\\4: _Jahresbericht_, 1824, p. 119.]\n\n'Since so much is expressed in this brief Formula, how very long\nwould the explanation be for a more composite body, for example,\nAlum; for which the Formula is\n [..]_K_[...]_S_\u00b2 + 2[...]_Al_[...]_S_\u00b3 + 48_H_\u00b2_O_.\nIt would take half a page to express all which this Formula contains.\n\n'Perhaps it may be objected that it is seldom that any one wants to\nknow all this at once. But it might reasonably be said in reply,\nthat the peculiar value of the Formula consists in this, that it\ncontains answers to all the questions which can be asked with regard\nto the composition of the body. {362}\n\n'But these Formul\u00e6 have also another application, of which I have\nsometimes had occasion to make use. Experiments sometimes bring\nbefore us combinations which cannot be foreseen from the\nnomenclature, and for which it is not always easy to find a\nconsistent and appropriate name. In writing, the Formula may be\napplied instead of a Name: and the reader understands it better than\nif one made a new name. In my treatise upon the sulphuretted\nalkalies I found Degrees of Sulphur-combination, for which\nNomenclature has no name. I expressed them, for example, by _KS_^6,\n_KS_^8, _KS_^10 and I believed that every one understood what was\nthereby meant. Moreover, I found another class of bodies in which an\nelectro-negative sulphuretted metal played the part of an Acid with\nrespect to an electro-positive sulphuretted metal, for which a whole\nnew nomenclature was needed; while yet it were not prudent to\nconstruct such a nomenclature, till more is known on the subject.\nInstead of new names I used formulas; for example,\n _KS_\u00b2 + 2_As S_\u00b3,\ninstead of saying the combination of 2 atoms of Sulphuret of Arsenic\ncontaining 3 atoms of Sulphur, with one atom of Sulphuret of\nPotassium (Kali) with the least dose of sulphur.'\n\nBerzelius goes on to say that the English chemists had found\nthemselves unable to find any substitutes for his formul\u00e6 when they\ntranslated his papers.\n\nOur English chemists have not generally adopted the notation of\noxygen by dots; but have employed commas or full stops and symbols\n(, or . and +), to denote various degrees of union, and numerical\nindices. Thus the double sulphate of copper and potash is\n_Cu O_, _SO__3 + _KO_, _SO__3.\n\nWhat has been said is applicable mainly to inorganic bodies (as\nsalts and minerals)[70\\4]. In these bodies there is (at least\naccording to the views of many intelligent chemists) a _binary_ plan\nof combination, union taking {363} place between _pairs_ of elements,\nand the compounds so produced again uniting themselves to other\ncompound bodies in the same manner. Thus, in the above example,\ncopper and oxygen combine into oxide of copper, potassium and oxygen\ninto potash, sulphur and oxygen into sulphuric acid; sulphuric acid\nin its turn combines both with oxide of copper and oxide of\npotassium, generating a pair of salts which are capable of uniting\nto form the double compound _Cu O_, _SO__3 + _KO_, _SO__3.\n\n[Note 70\\4: Fownes's _Chemistry_. Part iii.]\n\nThe most complicated products of inorganic chemistry may be thus\nshown to be built up by this repeated _pairing_ on the part of their\nconstituents. But with organic bodies the case is remarkably\ndifferent; no such arrangement can here be traced. In sugar, which\nis _C__12 _H__11 _O__11, or morphia[71\\4], which is\n_C__35 _H__20 _NO__6, the elements are as it were bound together\ninto a single whole, which can enter into combination with other\nsubstances, and be thence discharged with properties unaltered;\nthe elements not being obviously arranged in any subordinate groups.\nHence the symbols for those substances are such as I have given above,\nno marks of combination being used.\n\n[Note 71\\4: Fownes's _Chemistry_, p. 354.]\n\nIt is perhaps a consequence of this peculiarity that organic\ncompounds are _unstable_ in comparison with inorganic. In unorganic\nsubstances generally the elements are combined in such a way that\nthe most powerful affinities are satisfied[72\\4], and hence arises a\nstate of very considerable permanence and durability. But in an\norganic substance containing three or four elements, there are often\nopposing affinities nearly balanced, and when one of these\ntendencies by some accident obtains a preponderance and the\nequilibrium is destroyed, then the organic body breaks up into two\nor more new bodies of simpler and more permanent constitution.\n\n[Note 72\\4: See _Hist. Ind. Sc._ b. xiv. c. 3.]\n\nThere is another property of many organic substances which is called\nthe _Law of Substitution_. The {364} Hydrogen of the organic\nsubstance may often be replaced by Chlorine, Bromine, Iodine, or\nsome other elements, without the destruction of the primitive type\nor constitution of the compound so modified. And this substitution\nmay take place by several successive steps, giving rise to a series\nof substitution-compounds, which depart more and more in properties\nfrom the original substance. This Law also gives rise to a special\nnotation. Thus a certain compound called _Dutch liquid_ has the\nelements _C__4 _H__4 _Cl__2: but this substance is affected by\nchlorine (_Cl_) in obedience to the law of substitution; one and two\nequivalents of hydrogen being successively removed by the prolonged\naction of chlorine gas aided by sunshine. The successive products\nmay be thus written\n _H__3 _H__2\n _C__4 _H__4 _Cl__2; _C__4 { } _Cl__2; _C_4 { } _Cl__2.\n _Cl_ _Cl_2\n\nPerhaps at a future period, chemical symbols, and especially those\nof organic bodies, may be made more systematic and more significant\nthan they at present are.\n\n\nAPHORISM XXVII.\n\n_In using algebraical symbols as a part of scientific language,\nviolations of algebraical analogy are to be avoided, but may be\nadmitted when necessary._\n\n\nAS we must in scientific language conform to etymology, so must we\nto algebra; and as we are not to make ourselves the slaves of the\nformer, so also, not to the latter. Hence we reject such\ncrystallographical notation as that of Mohs; and in chemistry we use\n_C__2, _O__3 rather than _C_\u00b2, _O_\u00b3, which signify the square of _C_\nand the cube of _O_. But we may use, as we have said, both the comma\nand the sign of addition, for chemical combination, for the sake of\nbrevity, though both steps of combination are really addition. {365}\n\n\nAPHORISM XXVIII.\n\n_In a complex science, which is in a state of transition, capricious\nand detached derivations of terms are common; but are not\nsatisfactory._\n\n\nIN this remark I have especial reference to Chemistry; in which the\ndiscoveries made, especially in organic chemistry, and the\ndifficulty of reducing them to a system, have broken up in several\ninstances the old nomenclature, without its being possible at\npresent to construct a new set of terms systematically connected.\nHence it has come to pass that chemists have constructed words in a\ncapricious and detached way: as by taking fragments of words, and\nthe like. I shall give some examples of such derivations, and also\nof some attempts which have more of a systematic character.\n\nI have mentioned (Aph. **XX. sect. 7) the word _Ellagic_ (acid), made\nby inverting the word _Galle_. Several words have recently been\nformed by chemists by taking syllables from two or more different\nwords. Thus Chevreul discovered a substance to which he gave the\nname **_Ethal_, from the first syllables of the words _ether_ and\n_alcohol_, because of its analogy to those liquids in point of\ncomposition[73\\4]. So Liebig has the word _chloral_[74\\4].\n\n[Note: 73\\4: Turner's _Chemistry_, 1834, p. 955]\n\n[Note: 74\\4: Berzelius' _Jahresbericht_, xv. p. 372.]\n\nLiebig, examining the product of distillation of alcohol, sulphuric\nacid and amber, found a substance which he termed _Aldehyd_, from\nthe words _Al_cohol _dehyd_rogenated[75\\4]. This mode of making\nWords has been strongly objected to by Mr. Dumas[76\\4]. Still more\nhas he objected to the word _Mercaptan_ (of Zeise), which {366} he\nsays rests upon a mere play of words; for it means both _mercurium\ncaptans_ and _mercurio aptum_.\n\n[Note 75\\4: _Ibid._ xvi. p. 308.]\n\n[Note 76\\4: _Le\u00e7ons de Chimie_, p. 354.]\n\nDumas and Peligot, working on pyroligneous acids, found reason to\nbelieve the existence of a substance[77\\4] which they called\n_methylene_, deriving the name from _methy_, a spirituous fluid, and\n_hyle_, wood. Berzelius remarks that the name should rather be\n_methyl_, and that \u1f55\u03bb\u03b7 may be taken in its signification of matter,\nto imply the Radical of Wine: and he proposes that the older\n\u00c6ther-Radical, _C__4 _H__10 shall be called _\u00c6thyl_, the newer,\n_C__2 _H__6, _Methyl_.\n\n[Note 77\\4: Berzelius' _Jahresbericht_, xv. (1836).]\n\nThis notion of marking by the termination _yl_ the hypothetical\ncompound radical of a series of chemical compounds has been\ngenerally adopted; and, as we see from the above reference, it must\nbe regarded as representing the Greek word \u1f55\u03bb\u03b7: and such\nhypothetical radicals of bases have been termed in general _basyls_.\n\nBunsen obtained from Cadet's fuming liquid a substance which he\ncalled _Alkarsin_ (_alk_ali-_ars_enic?): and the substance produced\nfrom this by oxidation he called _Alkargen_[78\\4]. Berzelius was of\nopinion, that the true view of its composition was that it contained\na compound ternary radical = _C_^6 _H_^12 _As_^2, after the manner of\norganic bodies; and he proposed for this the name[79\\4] _Kakodyl_.\nAlkarsin is Kakodyl-oxyd, [.]Kd, Alkargen is Kakodyl-acid, [\u2234]Kd.\n\n[Note 78\\4: _Ibid._ xviii. p. 497.]\n\n[Note 79\\4: _Ibid._ xx. p. 527.]\n\nThe discovery of Kakodyl was the first instance of the insulation of\nan organic metallic _basyl_[80\\4].\n\n[Note 80\\4: Miller's _Chemistry_, iii. 220.]\n\nThe first of the Hydrocarbon Radicals of the Alcohols was the\nradical of Tetrylic alcohol obtained by Kolbe from Valerate of\nPotash, and hence called _Valyl_ _C__16 _H__18.\n\n_Chloroform_ is per_chloride_ of _formyl_, the hypothetical radical\nof formic acid[81\\4].\n\n[Note 81\\4: Dumas, _Le\u00e7ons sur la Phil. Chim._ p. 356.]\n\n{367} The discovery of such bases goes back to 1815. The substance\nformerly called _Prussiate of Mercury_, being treated in a\nparticular manner, was resolved into metallic mercury and\n_Cyanogen_. This substance, _Cyanogen_, is, according to the older\nnomenclature, _Bicarburet of Nitrogen_; but chemists are agreed that\nits most convenient name is _Cyanogen_, proposed by its discoverer,\nGay-Lussac, in 1815[82\\4]. The importance of the discovery consists\nin this; that this substance was the first compound body which was\ndistinctly proved to enter into combination with elementary\nsubstances in a manner similar to that in which they combine with\neach other.\n\n[Note 82\\4: Turner's _Chemistry_ (1834), p. 420. Miller's\n_Chemistry_, ii. 66.]\n\nThe truth of our Aphorism (XXV.) that in such a science as\nchemistry, the history of the scientific nomenclature is the history\nof the science, appears from this; that the controversies with\nrespect to chemical theories and their application take the form of\nobjections to the common systematic names and proposals of new names\ninstead. Thus a certain compound of potassa, sulphur, hydrogen, and\noxygen, may be regarded either as _Hydrosulphate of Potassa_, or as\n_Sulphide of Potassium in solution_, according to different\nviews[83\\4]. In some cases indeed, changes are made merely for the\nsake of clearness. Instead of _Hydrochloric_ and _Hydrocyanic_ acid,\nmany French writers, following Thenard, transpose the elements of\nthese terms; they speak of _Chlorhydric_ and _Cyanhydric_ acid; by\nthis means they avoid any ambiguity which might arise from the use\nof the prefix _Hydro_, which has sometimes been applied to compounds\nwhich contain water[84\\4].\n\n[Note 83\\4: Miller's _Chemistry_, vol. ii. p. 583.]\n\n[Note 84\\4: _Ibid._ ii. 433.]\n\nAn incompleteness in chemical nomenclature was further felt, when it\nappeared, from the properties of various substances, that mere\nidentity in chemical composition is not sufficient to produce\nidentity of chemical character or properties[85\\4]. The doctrine of\n{368} the existence of compounds identical in ultimate composition,\nbut different in chemical properties, was termed _Isomerism_. Thus\nchemists enumerate the following compounds, all of which contain\ncarbon and hydrogen in the proportion of single equivalents of\neach[86\\4];--_Methylene_, _Olefiant gas_, _Propylene_, _Oil gas_,\n_Amylene_, _Caproylene_, _Naphthene_, _Eleene_, _Peramylene_,\n_Cetylene_, _Cerotylene_, _Melissine_.\n\n[Note 85\\4: _Ibid._ ii. 653.]\n\n[Note 86\\4: Miller's _Chemistry_, ii. p. 654.]\n\nI will, in the last place, propound an Aphorism which has already\noffered itself in considering the history of Chemistry[87\\4] as\nhaving a special bearing upon that Science, but which may be\nregarded as the supreme and ultimate rule with regard to the\nlanguage of Science.\n\n[Note 87\\4: _Hist. Ind. Sc._ b. xiv. c. 1.]\n\n\nAPHORISM XXIX.\n\n_In learning the meaning of Scientific Terms, the history of science\nis our Dictionary: the steps of scientific induction are our\nDefinitions._\n\n\nIT is usual for unscientific readers to complain that the technical\nterms which they meet with in books of science are not accompanied\nby plain definitions such as they can understand. But such\ndefinitions cannot be given. For definitions must consist of words;\nand, in the case of scientific terms, must consist of words which\nrequire again to be defined: and so on, without limit. _Elementary\nsubstances_ in chemistry, for instance, what are they? The\nsubstances into which bodies can be _analysed_, and by the junction\nof which they are _composed_. But what is _analysis_? what is\n_composition_? We have seen that it required long and laborious\ncourses of experiment to answer these questions; and that finally\nthe balance decided among rival answers. And so it is in other\ncases. In entering upon each science, we come upon a new set of\nwords. And how are we to learn {369} the meaning of this collection\nof words? In what other language shall it be explained? In what\nterms shall we define these new expressions? To this we are\ncompelled to reply, that we cannot translate these terms into any\nordinary or familiar language. Here, as in all other branches of\nknowledge, the meaning of words is to be sought in the progress of\nthought. It is only by going back through the successful researches\nof men respecting the _composition_ and _elements_ of bodies, that\nwe can learn in what sense such terms can be understood, so as to\nconvey real knowledge. In order that they may have a meaning for us,\nwe must inquire what meaning they had in the minds of the authors of\nour discoveries. And the same is the case in other subjects. To take\nthe instance of Morphology. When the beginner is told that every\ngroup of animals may be reduced to an _Archetype_, he will seek for\na definition of Archetype. Such a definition has been offered, to\nthis effect: the Archetype of a group of animals is a diagram\nembodying all the organs and parts which are found in the group in\nsuch a relative position as they would have had if none had attained\nan excessive development. But, then, we are led further to ask, How\nare we in each case to become acquainted with the diagram; to know\nof what parts it consists, and how they are related; and further;\nWhat is the standard of _excess_? It is by a wide examination of\nparticular species, and by several successive generalizations of\nobserved facts, that we are led to a diagram of an animal form of a\ncertain kind, (for example, a vertebrate;) and of the various ways,\nexcessive and defective, in which the parts may be developed.\n\nThis craving for definitions, as we have already said, arises in a\ngreat degree from the acquaintance with geometry which most persons\nacquire at an early age. The definitions of geometry are easily\nintelligible by a beginner, because the idea of space, of which they\nare modifications, is clearly possessed without any special culture.\nBut this is not and cannot be the case in other sciences founded\nupon a wide and exact observation of facts. {370}\n\nIt was formerly said that there was no Royal Road to Geometry: in\nmodern times we have occasion often to repeat that there is no\nPopular Road--no road easy, pleasant, offering no difficulty and\ndemanding no toil,--to Comparative Anatomy, Chemistry or any other\nof the Inductive Sciences.\n\n\n\nTHE END.\n\n\n\n\n\n\nCAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.\n\n\n\nTranscriber's Notes\n\nWhewell published the first edition of the _Philosophy of the\nInductive Sciences_ in 1840 in two volumes, as a companion to the\n1837 _History of the Inductive Sciences_. Revised second editions of\nboth works appeared in 1847. The third editions saw a major\nreshaping of the _Philosophy_: a two volume _History of Scientific\nIdeas_ (1858; in Project Gutenberg as #69093), _Novum Organon\nRenovatum_ (1858; the present text, relying upon resources kindly\nprovided by the Internet Archive), and _On the Philosophy of\nDiscovery: chapters historical and critical_ (1860; long since in\nProject Gutenberg's collection as #5155). (The third edition of the\n_History of the Inductive Sciences_ is available in PG as #68693.)\n\nAdaptations in this text\n\nIn the present text footnotes are numbered by Book and are placed\nafter the paragraph to which they attach; in the original, notes\nwere numbered by chapter. Page numbers appear in { }, or {{ }} when\nthe number is not printed. Where a word was hyphenated across pages\nthe number has been placed before the word. Fractions have been\ntranscribed as numerator \u2044 denominator; the original usually has\nnumerator over a line with denominator below.\n\nSome unusual symbols occur. On pages 357 and 358, there are italic\nletters with a number written above them. On two occasions B has a\n1 above it, and once C has \u00bd above it. On page 364 a formula is\nwritten with two entries containing H on a line above Cl. These\nsuperpositions have been preserved at the cost of some short lines.\nThe other oddities have been captured by using [ ] to indicate items\nabove the following character. (They should not be confused with the\nuse of [ ] for footnote anchors.) For superscripts ^ has been used\nexcept for expressions using only the superscripted numbers\navailable in Unicode. Subscripts are indicated by a _ preceding the\ncharacter. (This unfortunately results in double __ when the\npreceding characters are in italics.)\n\nOn pages 152 and 197 Whewell uses a raised dot as a decimal point\nand in footnote 26\\3 a comma. These have been replaced by a mid dot.\n\nInductive Charts\n\nAt the end of Book II., Whewell included two very large inserts,\ndescribed in some detail in the Book itself. They were not captured\nby the scans available in the Internet Archive. I was kindly\nprovided with photographs of them. Those charts were four times as\nwide as the normal page and a quarter as long. In the html version\nthey have been fairly accurately represented via tables; but with up\nto 25 columns these tables will be very difficult to decipher on\nsmall screens. In the text version, coded structure diagrams have\nbeen used, which again utilise the full 70 spaces Project Gutenberg\nallows. Rather than the tree shape Whewell used, the diagrams have\nbeen made to flow from left to right.\n\nCorrections\n\nCorrections are comparatively few. Apart from the silent ones, they\nhave been marked by ** and are listed below.\n\n Page Printed text Corrected text\n{{xiii}} v iii\n LXX. LXXIII.\n LXXXV. LXXXII.\np. 12 of and\np. 128 word work\nnote 21\\3 i. ii.\np. 322 Wafferstoff Wasserstoff\np. 365 XV. XX.\n Ethol Ethal\n\nGiven the various editions, some of the internal cross-references\nturn out to be obsolete or erroneous:\nnote 11\\3 reads B. viii. c. iii. but it refers actually to Book viii.\nc. ii. article 3 in earlier editions and in the _History of Scientific\nIdeas_, cf. Aphorism 88 in Book I. of the present volume. Compare also\nAphorism 19 in this volume's Book IV.\nnotes 58\\3 and 59\\3 refer to Book v. c. i. For the present third\nedition they should have been aimed at that chapter of the _History\nof Scientific Ideas_.\n\nThere are some inconsistencies, notably in spelling, which have in\ngeneral not been adjusted; nor have Whewell's unbalanced quotation\nmarks and positioning of footnote anchors been modernized.","title":"Novum organon renovatum: Being the second part of the philosophy of the inductive sciences","tradition":"philosophy-ethics","translated_text":null,"word_count":126126}