{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_54897/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_54897","id":"gutenberg_54897","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/54897","summary":null,"tags":["Astronomy -- History","Category: Philosophy & Ethics","Category: Science - Physics","Physics -- History","Science -- History","Science -- Philosophy"],"text":"_PRELIMINARY DISCOURSE_\n  on the Study of\n  NATURAL PHILOSOPHY\n\n  BY\n  SIR JOHN F.\u00a0W. HERSCHEL, BART. K.H.\n  _M.A.--D.C.L.--F.R.S.L&E.--M.R.I.A.--F.R.A.S.\n  F.G.S.--M.C.U.P.S.--&c. &c._\n\n\n  NEW EDITION.\n  1851.\n\n[Illustration:\n\n  _H. Corbould del._      _E. Finden. sculp._\n\nNATUR\u00c6 MINISTER ET INTERPRES.]\n\n\n  NEW EDITION.\n\n  London:\n  PRINTED FOR LONGMAN, BROWN, GREEN & LONGMANS, PATERNOSTER ROW\n\n\n\n\nCONTENTS.\n\n\n                                                                    Page\n                                PART I.\n\n        OF THE GENERAL NATURE AND ADVANTAGES OF THE STUDY OF THE\n                           PHYSICAL SCIENCES.\n\n\n  CHAP. I.\n\n  Of Man regarded as a Creature of Instinct, of Reason, and\n    Speculation.--General Influence of Scientific Pursuits on\n    the Mind.                                                          1\n\n\n  CHAP. II.\n\n  Of abstract Science as a Preparation for the Study of Physics.--\n    A profound Acquaintance with it not indispensable for a\n    clear Understanding of Physical Laws.--How a Conviction\n    of their Truth may be obtained without it.--Instances.--\n    Further Division of the Subject.                                  18\n\n\n  CHAP. III.\n\n  Of the Nature and Objects, immediate and collateral, of\n    Physical Science, as regarded in itself, and in its\n    Application to the practical Purposes of Life, and its\n    Influence on the Well-being and Progress of Society.              35\n\n\n                                PART II.\n\n  OF THE PRINCIPLES ON WHICH PHYSICAL SCIENCE RELIES FOR ITS\n    SUCCESSFUL PROSECUTION, AND THE RULES BY WHICH A SYSTEMATIC\n    EXAMINATION OF NATURE SHOULD BE CONDUCTED, WITH ILLUSTRATIONS\n    OF THEIR INFLUENCE AS EXEMPLIFIED IN THE HISTORY OF ITS\n    PROGRESS.\n\n\n  CHAP. I.\n\n  Of Experience as the Source of our Knowledge.--Of the\n    Dismissal of Prejudices.--Of the Evidence of our Senses.          75\n\n\n  CHAP. II.\n\n  Of the Analysis of Phenomena.                                       85\n\n\n  CHAP. III.\n\n  Of the State of Physical Science in General, previous to the\n    Age of Galileo and Bacon.                                        104\n\n\n  CHAP. IV.\n\n  Of the Observation of Facts and the Collection of Instances.       118\n\n\n  CHAP. V.\n\n  Of the Classification of Natural Objects and Phenomena, and of\n    Nomenclature.                                                    135\n\n\n  CHAP. VI.\n\n  Of the First Stage of Induction.--The Discovery of Proximate\n    Causes, and Laws of the lowest Degree of Generality, and\n    their Verification.                                              144\n\n\n  CHAP. VII.\n\n  Of the higher Degrees of Inductive Generalization, and of the\n    Formation and Verification of Theories.                          190\n\n\n                               PART III.\n\n    OF THE SUBDIVISION OF PHYSICS INTO DISTINCT BRANCHES, AND THEIR\n                           MUTUAL RELATIONS.\n\n\n  CHAP. I.\n\n  Of the Phenomena of Force, and of the Constitution of Natural\n    Bodies.                                                          221\n\n\n  CHAP. II.\n\n  Of the Communication of Motion through Bodies.--Of Sound and\n    Light.                                                           246\n\n\n  CHAP. III.\n\n  Of Cosmical Phenomena.                                             265\n\n\n  CHAP. IV.\n\n  Of the Examination of the material Constituents of the World.\n                                                                     290\n\n\n  CHAP. V.\n\n  Of the Imponderable Forms of Matter.                               310\n\n\n  CHAP. VI.\n\n  Of the Causes of the actual rapid Advance of the Physical\n    Sciences compared with their Progress at an earlier Period.      347\n\n\n\n\n    \u201cIn primis, hominis est propria VERI inquisitio atque\n    investigatio. Itaque cum sumus negotiis necessariis, curisque\n    vacui, tum avemus aliquid videre, audire, ac dicere,\n    cognitionemque rerum, aut occultarum aut admirabilium, ad ben\u00e8\n    beat\u00e9que vivendum necessariam ducimus;--ex quo intelligitur,\n    quod VERUM, simplex, sincerumque sit, id esse natur\u00e6e hominis\n    aptissimum. Huic veri videndi cupiditati adjuncta est appetitio\n    qu\u00e6dam principat\u00fbs, ut nemini parere animus ben\u00e8 a natur\u00e2\n    informatus velit, nisi pr\u00e6cipienti, aut docenti, aut utilitatis\n    causa just\u00e8 et legitim\u00e8 imperanti: ex quo animi magnitudo\n    existit, et humanararum rerum contemtio.\u201d\n\n                                  CICERO, DE OFFICIIS, Lib. 1. \u00a7 13.\n\n\n    Before all other things, man is distinguished by his pursuit\n    and investigation of TRUTH. And hence, when free from needful\n    business and cares, we delight to see, to hear, and to\n    communicate, and consider a knowledge of many admirable and\n    abstruse things necessary to the good conduct and happiness of\n    our lives: whence it is clear that whatsoever is TRUE, simple,\n    and direct, the same is most congenial to our nature as men.\n    Closely allied with this earnest longing to see and know the\n    truth, is a kind of dignified and princely sentiment which\n    forbids a mind, naturally well constituted, to submit its\n    faculties to any but those who announce it in precept or in\n    doctrine, or to yield obedience to any orders but such as are\n    at once just, lawful, and founded on utility. From this source\n    spring greatness of mind and contempt of worldly advantages and\n    troubles.\n\n\n\n\n                         PRELIMINARY DISCOURSE\n                                   ON\n                               THE STUDY\n                                   OF\n                          NATURAL PHILOSOPHY.\n\n\n\n\n                                PART I.\n\n          OF THE GENERAL NATURE AND ADVANTAGES OF THE STUDY OF\n                         THE PHYSICAL SCIENCES\n\n\n\n\nCHAPTER I.\n\n  OF MAN REGARDED AS A CREATURE OF INSTINCT, OF REASON, AND\n    SPECULATION.--GENERAL INFLUENCE OF SCIENTIFIC PURSUITS ON THE\n    MIND.\n\n\n(1.) The situation of man on the globe he inhabits, and over which he\nhas obtained the control, is in many respects exceedingly remarkable.\nCompared with its other denizens, he seems, if we regard only his\nphysical constitution, in almost every respect their inferior, and\nequally unprovided for the supply of his natural wants and his defence\nagainst the innumerable enemies which surround him. No other animal\npasses so large a portion of its existence in a state of absolute\nhelplessness, or falls in old age into such protracted and lamentable\nimbecility. To no other warm-blooded animal has nature denied that\nindispensable covering without which the vicissitudes of a temperate\nand the rigours of a cold climate are equally insupportable; and to\nscarcely any has she been so sparing in external weapons, whether for\nattack or defence. Destitute alike of speed to avoid and of arms to\nrepel the aggressions of his voracious foes; tenderly susceptible of\natmospheric influences; and unfitted for the coarse aliments which the\nearth affords spontaneously during at least two thirds of the year,\neven in temperate climates,--man, if abandoned to mere instinct, would\nbe of all creatures the most destitute and miserable. Distracted by\nterror and goaded by famine; driven to the most abject expedients\nfor concealment from his enemies, and to the most cowardly devices\nfor the seizure and destruction of his nobler prey, his existence\nwould be one continued subterfuge or stratagem;--his dwelling would\nbe in dens of the earth, in clefts of rocks, or in the hollows of\ntrees; his food worms, and the lower reptiles, or such few and crude\nproductions of the soil as his organs could be brought to assimilate,\nvaried with occasional relics, mangled by more powerful beasts of prey,\nor contemned by their more pampered choice. Remarkable only for the\nabsence of those powers and qualities which obtain for other animals a\ndegree of security and respect, he would be disregarded by some, and\nhunted down by others, till after a few generations his species would\nbecome altogether extinct, or, at best, would be restricted to a few\nislands in tropical regions, where the warmth of the climate, the\npaucity of enemies, and the abundance of vegetable food, might permit\nit to linger.\n\n(2.) Yet man is the undisputed lord of the creation. The strongest\nand fiercest of his fellow-creatures,--the whale, the elephant, the\neagle, and the tiger,--are slaughtered by him to supply his most\ncapricious wants, or tamed to do him service, or imprisoned to make\nhim sport. The spoils of all nature are in daily requisition for his\nmost common uses, yielded with more or less readiness, or wrested with\nreluctance, from the mine, the forest, the ocean, and the air. Such\nare the first fruits of reason. Were they the only or the principal\nones, were the mere acquisition of power over the materials, and the\nless gifted animals which surround us, and the consequent increase\nof our external comforts, and our means of preservation and sensual\nenjoyment, the sum of the privileges which the possession of this\nfaculty conferred, we should after all have little to plume ourselves\nupon. But this is so far from being the case, that every one who passes\nhis life in tolerable ease and comfort, or rather whose whole time\nis not anxiously consumed in providing the absolute necessaries of\nexistence, is conscious of wants and cravings in which the senses have\nno part, of a series of pains and pleasures totally distinct in kind\nfrom any which the infliction of bodily misery or the gratification\nof bodily appetites has ever afforded him; and if he has experienced\nthese pleasures and these pains in any degree of intensity, he will\nreadily admit them to hold a much higher rank, and to deserve much\nmore attention, than the former class. Independent of the pleasures\nof fancy and imagination, and social converse, man is constituted a\nspeculative being; he contemplates the world, and the objects around\nhim, not with a passive, indifferent gaze, as a set of phenomena in\nwhich he has no further interest than as they affect his immediate\nsituation, and can be rendered subservient to his comfort, but as\na system disposed with order and design. He approves and feels the\nhighest admiration for the harmony of its parts, the skill and\nefficiency of its contrivances. Some of these which he can best trace\nand understand he attempts to imitate, and finds that to a certain\nextent, though rudely and imperfectly, he can succeed,--in others, that\nalthough he can comprehend the nature of the contrivance, he is totally\ndestitute of all means of imitation;--while in others, again, and those\nevidently the most important, though he sees the effect produced,\nyet the means by which it is done are alike beyond his knowledge\nand his control. Thus he is led to the conception of a Power and an\nIntelligence superior to his own, and adequate to the production and\nmaintenance of all that he sees in nature,--a Power and Intelligence to\nwhich he may well apply the term infinite, since he not only sees no\nactual limit to the instances in which they are manifested, but finds,\non the contrary, that the farther he enquires, and the wider his sphere\nof observation extends, they continually open upon him in increasing\nabundance; and that as the study of one prepares him to understand and\nappreciate another, refinement follows on refinement, wonder on wonder,\ntill his faculties become bewildered in admiration, and his intellect\nfalls back on itself in utter hopelessness of arriving at an end.\n\n(3.) When from external objects he turns his view upon himself, on his\nown vital and intellectual faculties, he finds that he possesses a\npower of examining and analysing his own nature to a certain extent,\nbut no farther. In his corporeal frame he is sensible of a power to\ncommunicate a certain moderate amount of motion to himself and other\nobjects; that this power depends on his will, and that its exertion\ncan be suspended or increased at pleasure within certain limits; but\n_how_ his will acts on his limbs he has no consciousness: and whence he\nderives the power he thus exercises, there is nothing to assure him,\nhowever he may long to know. His senses, too, inform him of a multitude\nof particulars respecting the external world, and he perceives an\napparatus by which impressions from without may be transmitted, as a\nsort of signals to the interior of his person, and ultimately to his\nbrain, wherein he is obscurely sensible that the thinking, feeling,\nreasoning being he calls _himself_, more especially resides; but by\nwhat means he becomes conscious of these impressions, and what is the\nnature of the immediate communication between that inward sentient\nbeing, and that machinery, his outward man, he has not the slightest\nconception.\n\n(4.) Again, when he contemplates still more attentively the thoughts,\nacts, and passions of this his sentient intelligent self, he finds,\nindeed, that he can remember, and by the aid of memory can compare\nand discriminate, can judge and resolve, and, above all, that he is\nirresistibly impelled, from the perception of any phenomenon without\nor within him, to infer the existence of something prior which stands\nto it in the relation of a _cause_, without which it would not be, and\nthat this knowledge of causes and their consequences is what, in almost\nevery instance, determines his choice and will, in cases where he is\nnevertheless conscious of perfect freedom to act or not to act. He\nfinds, too, that it is in his power to acquire more or less knowledge\nof causes and effects according to the degree of attention he bestows\nupon them, which attention is again in great measure a voluntary act;\nand often when his choice has been decided on imperfect knowledge or\ninsufficient attention, he finds reason to correct his judgment, though\nperhaps too late to influence his decision by after consideration. A\nworld within him is thus opened to his intellectual view, abounding\nwith phenomena and relations, and of the highest immediate interest.\nBut while he cannot help perceiving that the insight he is enabled to\nobtain into this internal sphere of thought and feeling is in reality\nthe source of all his power, the very fountain of his predominance over\nexternal nature, he yet feels himself capable of entering only very\nimperfectly into these recesses of his own bosom, and analysing the\noperations of his mind,--in this as in all other things, in short, \u201c_a\nbeing darkly wise_;\u201d seeing that all the longest life and most vigorous\nintellect can give him power to discover by his own research, or time\nto know by availing himself of that of others, serves only to place\nhim on the very frontier of knowledge, and afford a distant glimpse\nof boundless realms beyond, where no human thought has penetrated,\nbut which yet he is sure must be no less familiarly known to that\nIntelligence which he traces throughout creation than the most obvious\ntruths which he himself daily applies to his most trifling purposes.\nIs it wonderful that a being so constituted should first encourage a\nhope, and by degrees acknowledge an assurance, that his intellectual\nexistence will not terminate with the dissolution of his corporeal\nframe, but rather that in a future state of being, disencumbered of\na thousand obstructions which his present situation throws in his\nway, endowed with acuter senses, and higher faculties, he shall drink\ndeep at that fountain of beneficent wisdom for which the slight taste\nobtained on earth has given him so keen a relish?\n\n(5.) Nothing, then, can be more unfounded than the objection which has\nbeen taken, _in limine_, by persons, well meaning perhaps, certainly\nnarrow-minded, against the study of natural philosophy, and indeed\nagainst all science,--that it fosters in its cultivators an undue and\noverweening self-conceit, leads them to doubt the immortality of the\nsoul, and to scoff at revealed religion. Its natural effect, we may\nconfidently assert, on every well constituted mind is and must be\nthe direct contrary. No doubt, the testimony of natural reason, on\nwhatever exercised, must of necessity stop short of those truths which\nit is the object of revelation to make known; but, while it places\nthe existence and principal attributes of a Deity on such grounds as\nto render doubt impossible, it unquestionably opposes no natural or\nnecessary obstacle to further progress: on the contrary, by cherishing\nas a vital principle an unbounded spirit of enquiry, and ardency of\nexpectation, it unfetters the mind from prejudices of every kind, and\nleaves it open and free to every impression of a higher nature which\nit is susceptible of receiving, guarding only against enthusiasm and\nself-deception by a habit of strict investigation, but encouraging,\nrather than suppressing, every thing that can offer a prospect or a\nhope beyond the present obscure and unsatisfactory state. The character\nof the true philosopher is to hope all things not impossible, and to\nbelieve all things not unreasonable. He who has seen obscurities which\nappeared impenetrable in physical and mathematical science suddenly\ndispelled, and the most barren and unpromising fields of enquiry\nconverted, as if by inspiration, into rich and inexhaustible springs\nof knowledge and power on a simple change of our point of view, or\nby merely bringing to bear on them some principle which it never\noccurred before to try, will surely be the very last to acquiesce in\nany dispiriting prospects of either the present or future destinies of\nmankind; while, on the other hand, the boundless views of intellectual\nand moral as well as material relations which open on him on all hands\nin the course of these pursuits, the knowledge of the trivial place he\noccupies in the scale of creation, and the sense continually pressed\nupon him of his own weakness and incapacity to suspend or modify the\nslightest movement of the machinery he sees in action around him, must\neffectually convince him that humility of pretension, no less than\nconfidence of hope, is what best becomes his character.\n\n(6.) But while we thus vindicate the study of natural philosophy from a\ncharge at one time formidable, owing to the pertinacity and acrimony\nwith which it was urged, and still occasionally brought forward to\nthe distress and disgust of every well constituted mind, we must\ntake care that the testimony afforded by science to religion, be its\nextent or value what it may, shall be at least independent, unbiassed,\nand spontaneous. We do not here allude to such reasoners as would\nmake all nature bend to their narrow interpretations of obscure and\ndifficult passages in the sacred writings: such a course might well\nbecome the persecutors of Galileo and the other bigots of the fifteenth\nand sixteenth centuries, but can only be adopted by dreamers in the\npresent age. But, without going these lengths, it is no uncommon thing\nto find persons, earnestly attached to science and anxious for its\npromotion, who yet manifest a morbid sensibility on points of this\nkind,--who exult and applaud when any fact starts up explanatory (as\nthey suppose) of some scriptural allusion and who feel pained and\ndisappointed when the general course of discovery in any department\nof science runs wide of the notions with which particular passages in\nthe Bible may have impressed themselves. To persons of such a frame of\nmind it ought to suffice to remark, on the one hand, that truth can\nnever be opposed to truth, and, on the other, that error is only to be\neffectually confounded by searching deep and tracing it to its source.\nNevertheless, it were much to be wished that such persons, estimable\nand excellent as many of them are, before they throw the weight of\ntheir applause or discredit into the scale of scientific opinion on\nsuch grounds, would reflect, first, that the credit and respectability\nof _any_ evidence may be destroyed by tampering with its _honesty_;\nand, secondly, that this very disposition of mind implies a lurking\nmistrust in its own principles, since the grand and indeed only\ncharacter of truth is its capability of enduring the test of universal\nexperience, and coming unchanged out of every possible form of _fair_\ndiscussion.\n\n(7.) But if science may be vilified by representing it as opposed to\nreligion, or trammelled by mistaken notions of the danger of free\nenquiry, there is yet another mode by which it may be degraded from\nits native dignity, and that is by placing it in the light of a mere\nappendage to and caterer for our pampered appetites. The question\n\u201c_cui bono_\u201d to what practical end and advantage do your researches\ntend? is one which the speculative philosopher who loves knowledge\nfor its own sake, and enjoys, as a rational being should enjoy, the\nmere contemplation of harmonious and mutually dependent truths, can\nseldom hear without a sense of humiliation. He feels that there is a\nlofty and disinterested pleasure in his speculations which ought to\nexempt them from such questioning; communicating as they do to his own\nmind the purest happiness (after the exercise of the benevolent and\nmoral feelings) of which human nature is susceptible, and tending to\nthe injury of no one, he might surely allege _this_ as a sufficient\nand direct reply to those who, having themselves little capacity, and\nless relish for intellectual pursuits, are constantly repeating upon\nhim this enquiry. But if he can bring himself to descend from this\nhigh but fair ground, and justify himself, his pursuits, and his\npleasures in the eyes of those around him, he has only to point to the\nhistory of all science, where speculations, apparently unprofitable,\nhave, in innumerable instances, been those from which great practical\napplications have emanated. What, for instance, could be more so than\nthe dry speculations of the ancient geometers on the properties of the\nconic sections, or than the dreams of Kepler (as they would naturally\nappear to his contemporaries) about the numerical harmonies of the\nuniverse? Yet these are the steps by which we have risen to a knowledge\nof the elliptic motions of the planets and the law of gravitation,\nwith all its splendid theoretical consequences, and its inestimable\npractical results. The ridicule attached to \u201c_Swing-swangs_\u201d in\nHooke\u2019s time[1] did not prevent him from reviving the proposal of the\n_pendulum_ as a standard of measure, since so effectually wrought into\npractice by the genius and perseverance of Captain Kater;--nor did\nthat which Boyle encountered in his researches on the elasticity and\npressure of the air act as any obstacle to the train of discovery which\nterminated in the steam-engine. The dreams of the alchemists led them\non in the path of experiment, and drew attention to the wonders of\nchemistry, while they brought their advocates (it must be admitted) to\nmerited contempt and ruin. But in this case it was moral dereliction\nwhich gave to ridicule a weight and power not necessarily or naturally\nbelonging to it: but among the alchemists were men of superior minds,\nwho reasoned while they worked, and who, not content to grope always in\nthe dark, and blunder on their object, sought carefully in the observed\nnature of their agents for guides in their pursuit. To these we owe the\ncreation of experimental philosophy.\n\n(8.) Not that it is meant, by any thing above said, to assert\nthat there is no such thing as a great or a little in speculative\nphilosophy, or to place the solution of an enigma on a level with\nthe developement of a law of nature, still less to adopt the homely\ndefinition of Smith[2], that a philosopher is a person whose trade it\nis to do nothing, and speculate on every thing. The speculations of\nthe natural philosopher, however remote they may for a time lead him\nfrom beaten tracks and every-day uses, being grounded in the realities\nof nature, have all, of necessity, a practical application,--nay\nmore, such applications form the very criterions of their truth,\nthey afford the readiest and completest verifications of his\ntheories;--verifications which he will no more neglect to test them by\nthan an arithmetician would omit to _prove_ his sums, or a cautious\ngeometer to try his general theorems by particular cases.[3]\n\n(9.) After all, however, it must be confessed, that to minds\nunacquainted with science, and unused to consider the mutual\ndependencies of its various branches, there is something neither\nunnatural nor altogether blamable in the ready occurrence of this\nquestion of direct advantage. It requires some habit of abstraction,\nsome penetration of the mind with a tincture of scientific enquiry,\nsome conviction of the value of those estimable and treasured\nprinciples which lie concealed in the most common and homely\nfacts,--some experience, in fine, of success in developing and placing\nthem in evidence, announcing them in precise terms, and applying them\nto the explanation of other facts of a less familiar character, or to\nthe accomplishment of some obviously useful purpose:--to cure the mind\nof this tendency to rush at once upon its object, to undervalue the\nmeans in over-estimation of the end, and while gazing too intently at\nthe goal which alone it has been accustomed to desire, to lose sight\nof the richness and variety of the prospects that offer themselves on\neither hand on the road.\n\n(10.) We must never forget that it is principles, not phenomena,--the\ninterpretation, not the mere knowledge of facts,--which are the\nobjects of enquiry to the natural philosopher. As truth is single,\nand consistent with itself, a principle may be as completely and as\nplainly elucidated by the most familiar and simple fact, as by the\nmost imposing and uncommon phenomenon. The colours which glitter on\na soap-bubble are the immediate consequence of a principle the most\nimportant from the variety of phenomena it explains, and the most\nbeautiful, from its simplicity and compendious neatness, in the whole\nscience of optics. If the nature of periodical colours can be made\nintelligible by the contemplation of such a trivial object, from that\nmoment it becomes a noble instrument in the eye of correct judgment;\nand to blow a large, regular, and durable soap-bubble may become the\nserious and praiseworthy endeavour of a sage, while children stand\nround and scoff, or children of a larger growth hold up their hands\nin astonishment at such waste of time and trouble. To the natural\nphilosopher there is no natural object unimportant or trifling. From\nthe least of nature\u2019s works he may learn the greatest lessons. The fall\nof an apple to the ground may raise his thoughts to the laws which\ngovern the revolutions of the planets in their orbits; or the situation\nof a pebble may afford him evidence of the state of the globe he\ninhabits, myriads of ages ago, before his species became its denizens.\n\n(11.) And this is, in fact, one of the great sources of delight\nwhich the study of natural science imparts to its votaries. A mind\nwhich has once imbibed a taste for scientific enquiry, and has\nlearnt the habit of applying its principles readily to the cases\nwhich occur, has within itself an inexhaustible source of pure and\nexciting contemplations:--one would think that Shakspeare had such\na mind in view when he describes a contemplative man as finding all\nnature eloquent--the very trees, the brooks, and the stones reading\nto him lessons of deep and serious import. Accustomed to trace the\noperation of general causes, and the exemplification of general laws,\nin circumstances where the uninformed and unenquiring eye perceives\nneither novelty nor beauty, he walks in the midst of wonders: every\nobject which falls in his way elucidates some principle, affords some\ninstruction, and impresses him with a sense of harmony and order. Nor\nis it a mere passive pleasure which is thus communicated. A thousand\nquestions are continually arising in his mind, a thousand subjects of\nenquiry presenting themselves, which keep his faculties in constant\nexercise, and his thoughts perpetually on the wing, so that lassitude\nis excluded from his life, and that craving after artificial excitement\nand dissipation of mind, which leads so many into frivolous, unworthy,\nand destructive pursuits, is altogether eradicated from his bosom.\n\n(12.) It is not one of the least advantages of these pursuits, which,\nhowever, they possess in common with every class of intellectual\npleasures, that they are altogether independent of external\ncircumstances, and are to be enjoyed in every situation in which a man\ncan be placed in life. The highest degrees of worldly prosperity are so\nfar from being incompatible with them, that they supply inestimable\nadvantages for their pursuit, and that sort of fresh and renewed relish\nwhich arises partly from the sense of contrast, partly from experience\nof the peculiar pre-eminence they possess over the pleasures of sense\nin their capability of unlimited increase and continual repetition\nwithout satiety or distaste. They may be enjoyed, too, in the intervals\nof the most active business; and the calm and dispassionate interest\nwith which they fill the mind renders them a most delightful retreat\nfrom the agitations and dissensions of the world, and from the conflict\nof passions, prejudices, and interests in which the man of business\nfinds himself involved. There is something in the contemplation of\ngeneral laws which powerfully induces and persuades us to merge\nindividual feeling, and to commit ourselves unreservedly to their\ndisposal; while the observation of the calm, energetic regularity of\nnature, the immense scale of her operations, and the certainty with\nwhich her ends are attained, tends, irresistibly, to tranquillize and\nre-assure the mind, and render it less accessible to repining, selfish,\nand turbulent emotions. And this it does, not by debasing our nature\ninto weak compliances and abject submission to circumstances, but by\nfilling us, as from an inward spring, with a sense of nobleness and\npower which enables us to rise superior to them; by showing us our\nstrength and innate dignity, and by calling upon us for the exercise\nof those powers and faculties by which we are susceptible of the\ncomprehension of so much greatness, and which form, as it were, a link\nbetween ourselves and the best and noblest benefactors of our species,\nwith whom we hold communion in thoughts and participate in discoveries\nwhich have raised them above their fellow-mortals, and brought them\nnearer to their Creator.\n\n\n\n\nCHAP. II.\n\n  OF ABSTRACT SCIENCE AS A PREPARATION FOR THE STUDY OF PHYSICS.--A\n    PROFOUND ACQUAINTANCE WITH IT NOT INDISPENSABLE FOR A CLEAR\n    UNDERSTANDING OF PHYSICAL LAWS.--HOW A CONVICTION OF THEIR TRUTH\n    MAY BE OBTAINED WITHOUT IT.--INSTANCES.--FURTHER DIVISION OF THE\n    SUBJECT.\n\n\n(13.) Science is the knowledge of many, orderly and methodically\ndigested and arranged, so as to become attainable by one. The knowledge\nof reasons and their conclusions constitutes _abstract_, that of causes\nand their effects, and of the laws of nature, _natural science_.\n\n(14.) Abstract science is independent of a system of nature,--of a\ncreation,--of every thing, in short, except memory, thought, and\nreason. Its objects are, first, those primary existences and relations\nwhich we cannot even conceive not to _be_, such as space, time,\nnumber, order, &c.; and, secondly, those artificial forms, or symbols,\nwhich thought has the power of creating for itself at pleasure, and\nsubstituting as representatives, by the aid of memory, for combinations\nof those primary objects and of its own conceptions,--either to\nfacilitate the act of reasoning respecting them, or as convenient\ndeposits of its own conclusions, or for their communication to others.\nSuch are, first, _language_, oral or written; its conventional forms,\nwhich constitute grammar, and the rules for its use in argument,\nin which consists the logic of the schools; secondly, _notation_,\nwhich, applied to _number_, is _arithmetic_,--and, to the more general\nrelations of abstract quantity or order, is _algebra_; and, thirdly,\nthat higher kind of logic, which teaches us to use our reason in the\nmost advantageous manner for the discovery of truth; which points\nout the criterions by which we may be sure we have attained it; and\nwhich, by detecting the sources of error, and exposing the haunts where\nfallacies are apt to lurk, at once warns us of their danger, and shows\nus how to avoid them. This greater logic may be termed _rational_[4];\nwhile, to that inferior department which is conversant with words\nalone, the epithet _verbal_[5] may, for distinction, be applied.\n\n(15.) A certain moderate degree of acquaintance with abstract science\nis highly desirable to every one who would make any considerable\nprogress in physics. As the universe exists in time and place; and as\nmotion, velocity, quantity, number, and order, are main elements of\nour knowledge of external things and their changes, an acquaintance\nwith these, abstractedly considered, (that is to say, independent of\nany consideration of the particular things moved, measured, counted,\nor arranged,) must evidently be a useful preparation for the more\ncomplex study of nature. But there is yet another recommendation of\nsuch sciences as a preparation for the study of natural philosophy.\nTheir objects are so definite, and our notions of them so distinct,\nthat we can reason about them with an assurance, that the words and\nsigns used in our reasonings are full and true representatives of the\nthings signified; and, consequently, that when we use language or signs\nin argument, we neither, by their use, introduce extraneous notions,\nnor exclude any part of the case before us from consideration. For\nexample: the words space, square, circle, a hundred, &c., convey to\nthe mind notions so complete in themselves, and so distinct from every\nthing else, that we are sure when we use them we know and have in\nview the whole of our own meaning. It is widely different with words\nexpressing natural objects and mixed relations. Take, for instance,\niron. Different persons attach very different ideas to this word. One\nwho has never heard of magnetism has a widely different notion of\n_iron_ from one in the contrary predicament. The vulgar, who regard\nthis metal as incombustible, and the chemist, who sees it burn with the\nutmost fury, and who has other reasons for regarding it as one of the\nmost combustible bodies in nature;--the poet, who uses it as an emblem\nof rigidity; and the smith and engineer, in whose hands it is plastic,\nand moulded like wax into every form;--the jailer, who prizes it as\nan obstruction, and the electrician, who sees in it only a channel of\nopen communication by which that most impassable of obstacles, the\nair, may be traversed by his imprisoned fluid, have all different, and\nall imperfect, notions of the same word. The meaning of such a term\nis like a rainbow--every body sees a different one, and all maintain\nit to be the same. So it is with nearly all our terms of sense. Some\nare indefinite, as hard or soft, light or heavy (terms which were at\none time the sources of innumerable mistakes and controversies); some\nexcessively complex, as man, life, instinct. But, what is worst of\nall, some, nay most, have two or three meanings; sufficiently distinct\nfrom each other to make a proposition true in one sense and false in\nanother, or even false altogether; yet not distinct enough to keep us\nfrom confounding them in the process by which we arrived at it, or\nto enable us immediately to recognise the fallacy when led to it by\na train of reasoning, each step of which we _think_ we have examined\nand approved. Surely those who thus attach two senses to one word, or\nsuperadd a new meaning to an old one, act as absurdly as colonists who\ndistribute themselves over the world, naming every place they come\nto by the names of those they have left, till all distinctions of\ngeographical nomenclature are confounded, and till we are unable to\ndecide whether an occurrence stated to have happened at Windsor took\nplace in Europe, America, or Australia.[6]\n\n(16.) It is, in fact, in this double or incomplete sense of words that\nwe must look for the origin of a very large portion of the errors\ninto which we fall. Now, the study of the abstract sciences, such as\narithmetic, geometry, algebra, &c., while they afford scope for the\nexercise of reasoning about objects that are, or, at least, may be\nconceived to be, external to us; yet, being free from these sources\nof error and mistake, accustom us to the strict use of language as\nan instrument of reason, and by familiarizing us, in our progress\ntowards truth, to walk uprightly and straight-forward on firm ground,\ngive us that proper and dignified carriage of mind which could never\nbe acquired by having always to pick our steps among obstructions\nand loose fragments, or to steady them in the reeling tempest of\nconflicting meanings.\n\n(17.) But there is yet another point of view under which some\nacquaintance with abstract science may be regarded as highly desirable\nin general education, if not indispensably necessary, to impress on us\nthe distinction between strict and vague reasoning, to show us what\ndemonstration really _is_, and to give us thereby a full and intimate\nsense of the nature and strength of the evidence on which our knowledge\nof the actual system of nature, and the laws of natural phenomena,\nrests. For this purpose, however, a very moderate acquaintance with the\nmore elementary branches of mathematics may suffice. The chain is laid\nbefore us, and every link is submitted to our unreserved examination,\nif we have patience and inclination to enter on such detail. Hundreds\nhave gone through it, and will continue to do so; but, for the\ngenerality of mankind, it is enough to satisfy themselves of the\nsolidity and adamantine texture of its materials, and the unreserved\nexposure of its weakest, as well as its strongest, parts. If, however,\nwe content ourselves with this general view of the matter, we must be\ncontent also to take on trust, that is, on the authority of those who\nhave examined deeper, every conclusion which cannot be made apparent\nto our senses. Now, among these there are many so very surprising,\nindeed apparently so extravagant, that it is quite impossible for any\nenquiring mind to rest contented with a mere hearsay statement of\nthem,--we feel irresistibly impelled to enquire further into their\ntruth. What mere assertion will make any man believe, that in one\nsecond of time, in one beat of the pendulum of a clock, a ray of light\ntravels over 192,000 miles, and would therefore perform the tour of the\nworld in about the same time that it requires to wink with our eyelids,\nand in much less than a swift runner occupies in taking a single\nstride? What mortal can be made to believe, without demonstration, that\nthe sun is almost a million times larger than the earth? and that,\nalthough so remote from us, that a cannon ball shot directly towards\nit, and maintaining its full speed, would be twenty years in reaching\nit, it yet affects the earth by its attraction in an inappreciable\ninstant of time?--a closeness of union of which we can form but a\nfeeble, and totally inadequate, idea, by comparing it to any material\nconnection; since the communication of an impulse to such a distance,\nby any solid intermedium we are acquainted with, would require, not\nmoments, but whole years. And when, with pain and difficulty we have\nstrained our imagination to conceive a distance so vast, a force so\nintense and penetrating, if we are told that the one dwindles to an\ninsensible point, and the other is unfelt at the nearest of the fixed\nstars, from the mere effect of their remoteness, while among those\nvery stars are some whose actual splendour exceeds by many hundred\ntimes that of the sun itself, although we may not deny the truth of the\nassertion, we cannot but feel the keenest curiosity to know _how_ such\nthings were ever made out.\n\n(18.) The foregoing are among those results of scientific research\nwhich, by their magnitude, seem to transcend our powers of conception.\nThere are others, again, which, from their minuteness, would appear\nto elude the grasp of thought, much more of distinct and accurate\nmeasurement. Who would not ask for demonstration, when told that a\ngnat\u2019s wing, in its ordinary flight, beats many hundred times in a\nsecond? or that there exist animated and regularly organized beings,\nmany thousands of whose bodies laid close together would not extend an\ninch? But what are these to the astonishing truths which modern optical\nenquiries have disclosed, which teach us that every point of a medium\nthrough which a ray of light passes is affected with a succession of\nperiodical movements, regularly recurring at equal intervals, no less\nthan five hundred millions of millions of times in a single second!\nthat it is by such movements, communicated to the nerves of our eyes,\nthat we see:--nay more, that it is the _difference_ in the frequency of\ntheir recurrence which affects us with the sense of the diversity of\ncolour; that, for instance, in acquiring the sensation of redness our\neyes are affected four hundred and eighty-two millions of millions of\ntimes; of yellowness, five hundred and forty-two millions of millions\nof times; and of violet, seven hundred and seven millions of millions\nof times per second.[7] Do not such things sound more like the ravings\nof madmen, than the sober conclusions of people in their waking senses?\n\n(19.) They are, nevertheless, conclusions to which any one may most\ncertainly arrive, who will only be at the trouble of examining the\nchain of reasoning by which they have been deduced; but, in order\nto do this, something beyond the mere elements of abstract science\nis required. Waving, however, such instances as these, which, after\nall, are rather calculated to surprise and astound than for any other\npurpose, it must be observed that it is not possible to satisfy\nourselves completely that we _have_ arrived at a true statement of any\nlaw of nature, until, setting out from such statement, and making it\na foundation of reasoning, we can show, by strict argument, that the\nfacts observed must follow from it as necessary logical consequences,\nand _this_, not vaguely and generally, but with all possible precision\nin time, place, weight, and measure.\n\n(20.) To do this, however, as we shall presently see, requires in many\ncases a degree of knowledge of mathematics and geometry altogether\nunattainable by the generality of mankind, who have not the leisure,\neven if they all had the capacity, to enter into such enquiries,\nsome of which are indeed of that degree of difficulty that they can\nbe only successfully prosecuted by persons who devote to them their\nwhole attention, and make them the serious business of their lives.\nBut there is scarcely any person of good ordinary understanding,\nhowever little exercised in abstract enquiries, who may not be readily\nmade to comprehend at least the general train of reasoning by which\nany of the great truths of physics are deduced, and the essential\nbearings and connections of the several parts of natural philosophy.\nThere are whole branches too and very extensive and important ones, to\nwhich mathematical reasoning has never been at all applied; such as\nchemistry, geology, and natural history in general, and many others,\nin which it plays a very subordinate part, and of which the essential\nprinciples, and the grounds of application to useful purposes, may\nbe perfectly well understood by a student who possesses no more\nmathematical knowledge than the rules of arithmetic; so that no one\nneed be deterred from the acquisition of knowledge, or even from\nactive original research in such subjects, by a want of mathematical\ninformation. Even in those branches which, like astronomy, optics, and\ndynamics, are almost exclusively under the dominion of mathematics, and\nin which no effectual progress can be made without _some_ acquaintance\nwith geometry, the principal _results_ may be perfectly understood\nwithout it. To one incapable of following out the intricacies of\nmathematical demonstration, the conviction afforded by verified\npredictions must stand in the place of that purer and more satisfactory\nreliance which a verification of every step in the process of reasoning\ncan alone afford, since every one will acknowledge the validity of\npretensions which he is in the daily habit of seeing brought to the\ntest of practice.\n\n(21.) Among the verifications of this practical kind which abound\nin every department of physics, there are none more imposing than\nthe precise prediction of the greater phenomena of astronomy; none,\ncertainly, which carry a broader conviction home to every mind from\ntheir notoriety and unequivocal character. The prediction of eclipses\nhas accordingly from the earliest ages excited the admiration of\nmankind, and been one grand instrument by which their allegiance (so\nto speak) to natural science, and their respect for its professors,\nhas been maintained; and though strangely abused in unenlightened ages\nby the supernatural pretensions of astrologers, the credence given\neven to their absurdities shows the force of this kind of evidence on\nmen\u2019s minds. The predictions of astronomers are, however, now far too\nfamiliar to endanger the just equipoise of our judgment, since even the\nreturn of comets, true to their paths and exact to the hour of their\nappointment, has ceased to amaze, though it must ever delight all who\nhave souls capable of being penetrated by such beautiful instances of\naccordance between theory and facts. But the age of mere wonder in\nsuch things is past, and men prefer being guided and enlightened, to\nbeing astonished and dazzled. Eclipses, comets, and the like, afford\nbut rare and transient displays of the powers of calculation, and of\nthe certainty of the principles on which it is grounded. A page of\n\u201clunar distances\u201d from the Nautical Almanack is worth all the eclipses\nthat have ever happened for inspiring this necessary confidence in the\nconclusions of science. That a man, by merely measuring the moon\u2019s\napparent distance from a star with a little portable instrument held\nin his hand, and applied to his eye, even with so unstable a footing\nas the deck of a ship, shall say positively, within five miles, where\nhe is, on a boundless ocean, cannot but appear to persons ignorant of\nphysical astronomy an approach to the miraculous. Yet, the alternatives\nof life and death, wealth and ruin, are daily and hourly staked with\nperfect confidence on these marvellous computations, which might\nalmost seem to have been devised on purpose to show how closely the\nextremes of speculative refinement and practical utility can be brought\nto approximate. We have before us an anecdote communicated to us by\na naval officer[8], distinguished for the extent and variety of his\nattainments, which shows how impressive such results may become in\npractice. He sailed from San Blas on the west coast of Mexico, and\nafter a voyage of 8000 miles, occupying 89 days, arrived off Rio de\nJaneiro, having, in this interval, passed through the Pacific Ocean,\nrounded Cape Horn, and crossed the South Atlantic, without making any\nland, or even seeing a single sail, with the exception of an American\nwhaler off Cape Horn. Arrived within a week\u2019s sail of Rio, he set\nseriously about determining, by lunar observations, the precise line\nof the ship\u2019s course and its situation in it at a determinate moment,\nand having ascertained this within from five to ten miles, ran the\nrest of the way by those more ready and compendious methods, known to\nnavigators, which can be safely employed for short trips between one\nknown point and another, but which cannot be trusted in long voyages,\nwhere the moon is the only sure guide. The rest of the tale we are\nenabled by his kindness to state in his own words:--\u201cWe steered towards\nRio de Janeiro for some days after taking the lunars above described,\nand having arrived within fifteen or twenty miles of the coast, I hove\nto at four in the morning till the day should break, and then bore\nup; for although it was very hazy, we could see before us a couple of\nmiles or so. About eight o\u2019clock it became so foggy that I did not\nlike to stand in farther, and was just bringing the ship to the wind\nagain before sending the people to breakfast, when it suddenly cleared\noff, and I had the satisfaction of seeing the great Sugar Loaf Rock,\nwhich stands on one side of the harbour\u2019s mouth, so nearly right ahead\nthat we had not to alter our course above a point in order to hit the\nentrance of Rio. This was the first land we had seen for three months,\nafter crossing so many seas and being set backwards and forwards by\ninnumerable currents and foul winds.\u201d The effect on all on board might\nwell be conceived to have been electric; and it is needless to remark\nhow essentially the authority of a commanding officer over his crew may\nbe strengthened by the occurrence of such incidents, indicative of a\ndegree of knowledge and consequent power beyond their reach.\n\n(22.) But even such results as these, striking as they are, yet fall\nshort of the force with which conviction is urged upon us when,\nthrough the medium of reasoning too abstract for common apprehension,\nwe arrive at conclusions which outrun experience, and describe\nbeforehand what will happen under new combinations, or even correct\nimperfect experiments, and lead us to a knowledge of facts contrary\nto received analogies drawn from an experience wrongly interpreted\nor overhastily generalised. To give an example:--every body knows\nthat objects viewed through a transparent medium, such as water or\nglass, appear distorted or displaced. Thus, a stick in water appears\nbent, and an object seen through a prism or wedge of glass seems to\nbe thrown aside from its true place. This effect is owing to what is\ncalled the _refraction_ of light; and a simple rule discovered by\nWillebrod Snell enables any one to say exactly _how much_ the stick\nwill be bent, and _how far_, and in what _direction_, the apparent\nsituation of an object seen through the glass will deviate from the\nreal one. If a shilling be laid at the bottom of a basin of water\nand viewed obliquely, it will appear to be raised by the water; if\ninstead of water spirits of wine be used it will appear more raised;\nif oil, still more:--but in none of these cases will it appear to be\nthrown _aside_ to the _right_ or _left_ of its true place, however\nthe eye be situated. The _plane_, in which are contained the eye,\nthe object, and the point in the surface of the liquid at which the\nobject is seen, is an upright or _vertical_ plane; and this is one of\nthe principal characters in the _ordinary refraction_ of light, viz.\nthat the ray by which we see an object through a refracting surface,\nalthough it undergoes a bending, and is, as it were, broken at the\nsurface, yet, in pursuing its course to the eye, does not _quit a plane\nperpendicular to the refracting surface_. But there are again other\nsubstances, such as rock-crystal, and especially Iceland spar, which\npossess the singular property of _doubling_ the image or appearance\nof an object seen through them in certain directions; so that instead\nof seeing one object we see two, side by side, when such a crystal or\nspar is interposed between the object and the eye; and if a ray or\nsmall sunbeam be thrown upon a surface of either of these substances,\nit will be split into two, making an angle with each other, and each\npursuing its own separate course,--this is called _double refraction_.\nNow, of these images or doubly refracted rays, one always follows\nthe same rule as if the substance were glass or water: its deviation\ncan be correctly calculated by Snell\u2019s law above mentioned, and it\ndoes not quit the plane perpendicular to the refracting surface. The\nother ray, on the contrary, (which is therefore said to have undergone\n_extraordinary refraction_) _does_ quit that plane, and the amount of\nits deviation from its former course requires for its determination a\nmuch more complicated rule, which cannot be understood or even stated\nwithout a pretty intimate knowledge of geometry. Now, rock-crystal\nand Iceland spar differ from glass in a very remarkable circumstance.\nThey affect naturally certain regular figures, not being found in\nshapeless lumps, but in determinate geometrical forms; and they are\nsusceptible of being cleft or split much easier in certain directions\nthan in others--they have a _grain_ which glass has not. When other\nsubstances having this peculiarity (and which are called _crystallized_\nsubstances) were examined, they were all, or by far the greater part,\nfound to possess this singular property of _double refraction_; and\nit was very natural to conclude, therefore, that the same thing took\nplace in all of them, viz. that of the two rays, into which any beam of\nlight falling on the surface of such a substance was split, or of the\ntwo images of an object seen through it, _one_ only was turned aside\nout of its _plane_ and _extraordinarily_ refracted, while the other\nfollowed the _ordinary_ rule. Accordingly this was supposed to be the\ncase; and not only so, but from some trials and measurements purposely\nmade by a philosopher of great eminence, it was considered to be a fact\nsufficiently established by experiment.\n\n(23.) Perhaps we might have remained long under this impression, for\nthe measurements are delicate, and the subject very difficult. But\nit has lately been demonstrated by an eminent French philosopher and\nmathematician, M. Fresnel, that, granting certain _principles_ or\npostulates, all the phenomena of double refraction, including perhaps\nthe greatest variety of facts that have ever yet been arranged under\none general head, may be satisfactorily explained and deduced from them\nby strict mathematical calculation; and _that_, when applied to the\ncases first mentioned, these principles give a satisfactory account\nof the _want_ of the extraordinary image; _that_ when applied to such\ncases as those of rock-crystal or Iceland spar, they also give a\ncorrect account of both the images, and agree in their conclusions with\nthe rules before ascertained for them: but so far from coinciding with\nthat part of the previous statement, which would make these conclusions\nextend to all crystallised substances, M. Fresnel\u2019s principles lead\nto a conclusion quite opposite, and point to a _fact_ which had never\nbeen observed, viz. that in by far the greater number of crystallized\nsubstances which possess the property of double refraction, _neither_\nof the images follows the ordinary law, but both undergo a deviation\nfrom their original plane. Now this had never been observed to be\nthe case in any previous trial, and all opinion was against it. But\nwhen put to the test of experiment in a great variety of new and\ningenious methods, it was found to be fully verified; and to complete\nthe evidence, the substances on whose imperfect examination the\nfirst erroneous conclusion was founded, having been lately subjected\nto a fresh and more scrupulous examination, the result has shown\nthe insufficiency of the former measurements, and proved in perfect\naccordance with the newly discovered laws. Now it will be observed\nin this case, first, that, so far from the principles assumed by M.\nFresnel being at all obvious, they are extremely remote from ordinary\nobservation; and, secondly, that the chain of reasoning by which they\nare brought to the test is one of such length and complexity, and the\npurely mathematical difficulty of their application so great, that\nno _mere_ good common sense, no general tact or ordinary practical\nreasoning, would afford the slightest chance of threading their\nmazes. Cases like this are the triumph of theories. They show at once\nhow large a part pure reason has to perform in our examination of\nnature, and how implicit our reliance ought to be on that powerful and\nmethodical system of rules and processes which constitute the modern\nmathematical analysis, in all the more difficult applications of exact\ncalculation to her phenomena.\n\n(24.) To take an instance more within ordinary apprehension. An\neminent living geometer had proved by calculations, founded on strict\noptical principles, that in the _centre of the shadow_ of a small\ncircular plate of metal, exposed in a dark room to a beam of light\nemanating from a _very small brilliant point_, there ought to be no\ndarkness,--in fact, _no shadow_ at that place; but, on the contrary, a\ndegree of illumination precisely as bright as if the metal plate were\naway. Strange and even impossible as this conclusion may seem, it has\nbeen put to the trial, and found perfectly correct.[9]\n\n(25.) We shall now proceed to consider more particularly, and in\ndetail,--\n\n    I. The nature and objects immediate and collateral of physical\n         science, as regarded in itself, and in its application to\n         the practical purposes of life, and its influence on the\n         well-being and progress of society.\n\n   II. The principles on which it relies for its successful\n         prosecution, and the rules by which a systematic examination\n         of nature should be conducted, with examples illustrative of\n         their influence.\n\n  III. The subdivision of physical science into distinct branches,\n         and their mutual relations.\n\n\n\n\nCHAP. III.\n\n  OF THE NATURE AND OBJECTS, IMMEDIATE AND COLLATERAL, OF PHYSICAL\n    SCIENCE, AS REGARDED IN ITSELF, AND IN ITS APPLICATION TO THE\n    PRACTICAL PURPOSES OF LIFE, AND ITS INFLUENCE ON THE WELL-BEING\n    AND PROGRESS OF SOCIETY.\n\n\n(26.) The first thing impressed on us from our earliest infancy is,\nthat events do not succeed one another at random, but with a certain\ndegree of order, regularity, and connection;--some constantly, and, as\nwe are apt to think, immutably,--as the alternation of day and night,\nsummer and winter,--others contingently, as the motion of a body from\nits place, if pushed, or the burning of a stick if thrust into the\nfire. The knowledge that the former class of events _has_ gone on,\nuninterruptedly, for ages beyond all memory, impresses us with a strong\nexpectation that it will continue to do so in the same manner; and\nthus our notion of an _order of nature_ is originated and confirmed.\nIf every thing were equally regular and periodical, and the succession\nof events liable to no change depending on our own will, it may be\ndoubted whether we should ever think of looking for causes. No one\nregards the night as the cause of the day, or the day of night. They\nare alternate effects of a common cause, which their regular succession\nalone gives us no sufficient clue for determining. It is chiefly,\nperhaps entirely, from the other or contingent class of events that\nwe gain our notions of cause and effect. From them alone we gather\nthat there are such things as laws of nature. The very idea of a law\nincludes that of contingency. \u201c_Si quis mala carmina condidisset, fuste\nferito_;\u201d if such a case arise, such a course shall be followed,--if\nthe match be applied to the gunpowder, it will explode. Every law is a\nprovision for cases which _may_ occur, and has relation to an infinite\nnumber of cases that never have occurred, and never will. Now, it is\nthis provision, _\u00e0 priori_, for contingencies, this contemplation\nof possible occurrences, and predisposal of what shall happen, that\nimpresses us with the notion of a _law_ and a _cause_. Among all the\npossible combinations of the fifty or sixty elements which chemistry\nshows to exist on the earth, it is likely, nay almost certain, that\n_some_ have never been formed; that some elements, in some proportions,\nand under some circumstances, have never yet been placed in relation\nwith one another. Yet no chemist can doubt that it is _already fixed_\nwhat they will do when the case does occur. They will obey certain\nlaws, of which we know nothing at present, but which must _be_ already\nfixed, or they could not be laws. It is not by habit, or by trial\nand failure, that they will learn what to do. When the contingency\noccurs, there will be no hesitation, no consultation;--their course\nwill at once be decided, and will always be the same if it occur ever\nso often in succession, or in ever so many places at one and the same\ninstant. This is the perfection of a law, that it includes all possible\ncontingencies, and ensures implicit obedience,--and of this kind are\nthe laws of nature.\n\n(27.) This use of the word _law_, however, our readers will of course\nperceive has relation to us as understanding, rather than to the\nmaterials of which the universe consists as obeying, certain rules.\nTo obey a law, to act in _compliance_ with a rule, supposes an\nunderstanding and a will, a power of complying or not, in the being who\nobeys and complies, which we do not admit as belonging to mere matter.\nThe Divine Author of the universe cannot be supposed to have laid down\nparticular laws, enumerating all individual contingencies, which his\nmaterials have understood and obey,--this would be to attribute to\nhim the imperfections of human legislation;--but rather, by creating\nthem, endued with certain fixed qualities and powers, he has impressed\nthem in their origin with the _spirit_, not the _letter_, of his law,\nand made all their subsequent combinations and relations inevitable\nconsequences of this first impression, by which, however, we would no\nway be understood to deny the constant exercise of his direct power in\nmaintaining the system of nature, or the ultimate emanation of every\nenergy which material agents exert from his immediate will, acting in\nconformity with his own laws.\n\n(28.) The discoveries of modern chemistry have gone far to establish\nthe truth of an opinion entertained by some of the ancients, that\nthe universe consists of distinct, separate, indivisible _atoms_,\nor individual beings so minute as to escape our senses, except when\nunited by millions, and by this aggregation making up bodies of even\nthe smallest visible bulk; and we have the strongest evidence that,\nalthough there exist great and essential differences in individuals\namong these atoms, they may yet all be arranged in a very limited\nnumber of groups or classes, all the individuals of each of which\nare, to all intents and purposes, _exactly alike_ in all their\nproperties. Now, when we see a great number of things precisely alike,\nwe do not believe this similarity to have originated except from a\ncommon principle independent of them; and that we recognise this\nlikeness, chiefly by the identity of their deportment under similar\ncircumstances, strengthens rather than weakens the conclusion. A line\nof spinning-jennies[10], or a regiment of soldiers dressed exactly\nalike, and going through precisely the same evolutions, gives us no\nidea of independent existence: we must see them act out of concert\nbefore we can believe them to have independent wills and properties,\nnot impressed on them from without. And this conclusion, which would\nbe strong even were there only two individuals precisely alike in\n_all_ respects and _for ever_, acquires irresistible force when their\nnumber is multiplied beyond the power of imagination to conceive. If\nwe mistake not, then, the discoveries alluded to effectually destroy\nthe idea of an _eternal self-existent matter_, by giving to each of its\natoms the essential characters, at once, of a _manufactured article_,\nand a _subordinate agent_.\n\n(29.) But to ascend to the origin of things, and speculate on the\ncreation, is not the business of the natural philosopher. An humbler\nfield is sufficient for him in the endeavour to discover, as far\nas our faculties will permit, what _are_ these primary qualities\noriginally and unalterably impressed on matter, and to discover the\n_spirit_ of the laws of nature, which includes groups and classes of\nrelations and facts from the _letter_ which, as before observed, is\npresented to us by single phenomena: or if, after all, this should\nprove impossible; if such a step be beyond our faculties; and the\nessential qualities of material agents be really _occult_, or incapable\nof being expressed in any form intelligible to our understandings, at\nleast to approach as near to their comprehension as the nature of the\ncase will allow; and devise such forms of words as shall include and\n_represent_ the greatest possible multitude and variety of phenomena.\n\n(30.) Now, in this research there would seem one great question to\nbe disposed of before our enquiries can even be commenced with any\nthing like a prospect of success, which is, whether the laws of\nnature themselves _have_ that degree of permanence and fixity which\ncan render them subjects of systematic discussion; or whether, on the\nother hand, the qualities of natural agents are subject to mutation\nfrom the lapse of time. To the ancients, who lived in the infancy of\nthe world, or rather, in the infancy of man\u2019s experience, this was a\nvery rational subject of question, and hence their distinctions between\ncorruptible and incorruptible matter. Thus, according to some among\nthem, the matter only of the celestial spaces is pure, immutable, and\nincorruptible, while all sublunary things are in a constant state of\nlapse and change; the world becoming paralysed and effete with age,\nand man himself deteriorating in character, and diminishing at once in\nintellectual and bodily stature. But to us, who have the experience\nof some additional thousands of years, the question of permanence is\nalready, in a great measure, decided in the affirmative. The refined\nspeculations of modern astronomy, grounding their conclusions on\nobservations made at very remote periods, have proved to demonstration,\nthat one at least of the great powers of nature, the force of\ngravitation, the main bond and support of the material universe, has\nundergone no change in intensity from a high antiquity. The stature of\nmankind is just what it was three thousand years ago, as the specimens\nof mummies which have been examined at various times sufficiently\nshow. The intellect of Newton, Laplace, or Lagrange, may stand in\nfair competition with that of Archimedes, Aristotle, or Plato; and the\nvirtues and patriotism of Washington with the brightest examples of\nancient history.\n\n(31.) Again, the researches of chemists have shown that what the\nvulgar call corruption, destruction, &c., is nothing but a change of\narrangement of the same ingredient elements, the disposition of the\nsame materials into other forms, without the loss or actual destruction\nof a single atom; and thus any doubts of the permanence of natural\nlaws are discountenanced, and the whole weight of _appearances_ thrown\ninto the opposite scale. One of the most obvious cases of apparent\ndestruction is, when any thing is ground to dust and scattered to the\nwinds. But it is one thing to grind a fabric to powder, and another to\nannihilate its materials: scattered as they may be, they must fall\nsomewhere, and continue, if only as ingredients of the soil, to perform\ntheir humble but useful part in the economy of nature. The destruction\nproduced by fire is more striking: in many cases, as in the burning\nof a piece of charcoal or a taper, there is no smoke, nothing visibly\ndissipated and carried away; the burning body wastes and disappears,\nwhile nothing _seems_ to be produced but warmth and light, which we\nare not in the habit of considering as substances; and when all has\ndisappeared, except perhaps some trifling ashes, we naturally enough\nsuppose it is gone, lost, destroyed. But when the question is examined\nmore exactly, we detect, in the invisible stream of heated air which\nascends from the glowing coal or flaming wax, the _whole_ ponderable\nmatter, only united in a new combination with the air, and dissolved in\nit. Yet, so far from being thereby destroyed, it is only become again\nwhat it was before it existed in the form of charcoal or wax, an active\nagent in the business of the world, and a main support of vegetable\nand animal life, and is still susceptible of running again and again\nthe same round, as circumstances may determine; so that, for aught we\ncan see to the contrary, the same identical atom may lie concealed for\nthousands of centuries in a limestone rock; may at length be quarried,\nset free in the limekiln, mix with the air, be absorbed from it by\nplants, and, in succession, become a part of the frames of myriads of\nliving beings, till some concurrence of events consigns it once more to\na long repose, which, however, no way unfits it from again resuming its\nformer activity.\n\n(32.) Now, this absolute indestructibility of the ultimate materials\nof the world, in periods commensurate to our experience, and their\nobstinate retention of the same properties, under whatever variety of\ncircumstances we choose to place them, however violent and seemingly\ncontradictory to their natures, is, of itself, enough to render it\nhighly improbable that time alone should have any influence over\nthem. All that age or decay can do seems to be included in a wasting\nof parts which are only dissipated, not destroyed, or in a change of\nsensible properties, which chemistry demonstrates to arise only from\nnew combinations of the same ingredients. But, after all, the question\nis one entirely of experience: we cannot be sure, _\u00e0 priori_, that\nthe laws of nature are _immutable_; but we can ascertain, by enquiry,\n_whether they change or not_; and to this enquiry all experience\nanswers in the negative. It is not, of course, intended here to\ndeny that great operations, productive of extensive changes in the\nvisible state of nature,--such as, for instance, those contemplated\nby the geologists, and embracing for their completion vast periods\nof time,--are constantly going on; but these are consequences and\nfulfilments of the laws of nature, not contradictions or exceptions\nto them. No theorist regards such changes as alterations in the\nfundamental principles of nature; he only endeavours to reconcile them,\nand show how they result from laws already known, and judges of the\ncorrectness of his theory by their ultimate agreement.\n\n(33.) But the laws of nature are not only permanent, but consistent,\nintelligible, and discoverable with such a moderate degree of\nresearch, as is calculated rather to stimulate than to weary curiosity.\nIf we were set down, as creatures of another world, in any existing\nsociety of mankind, and began to speculate on their actions, we should\nfind it difficult at first to ascertain whether they were subject to\nany laws at all: but when, by degrees, we had found out that they did\nconsider themselves to be so; and would then proceed to ascertain, from\ntheir conduct and its consequences, what these laws were, and in what\nspirit conceived; though we might not perhaps have much difficulty\nin discovering single rules applicable to particular cases, yet, the\nmoment we came to generalize, and endeavour from these to ascend, step\nby step, and discover any steady pervading principle, the mass of\nincongruities, absurdities, and contradictions, we should encounter,\nwould either dishearten us from further enquiry or satisfy us that what\nwe were in search of did not exist. It is quite the contrary in nature;\nthere we find no contradictions, no incongruities, but all is harmony.\nWhat once is learnt we never have to unlearn. As rules advance in\ngenerality, apparent exceptions become regular; and equivoque, in her\nsublime legislation, is as unheard of as maladministration.\n\n(34.) Living, then, in a world where such laws obtain, and under their\nimmediate dominion, it is manifestly of the utmost importance to know\nthem, were it for no other reason than to be sure, in all we undertake,\nto have, at least, the law on our side, so as not to struggle in vain\nagainst some insuperable difficulty opposed to us by natural causes.\nWhat pains and expense would not the alchemists, for instance, have\nbeen spared by a knowledge of those simple laws of composition and\ndecomposition, which now preclude all idea of the attainment of their\ndeclared object! what an amount of ingenuity, thrown away on the\npursuit of the perpetual motion, might have been turned to better\nuse, if the simplest laws of mechanics had been known and attended to\nby the inventors of innumerable contrivances destined to that end!\nWhat tortures, inflicted on patients by imaginary cures of incurable\ndiseases, might have been dispensed with, had a few simple principles\nof physiology been earlier recognised!\n\n(35.) But if the laws of nature, on the one hand, are invincible\nopponents, on the other, they are irresistible auxiliaries; and it\nwill not be amiss if we regard them in each of those characters, and\nconsider the great importance of a knowledge of them to mankind,--\n\n    I. _In showing us how to avoid attempting impossibilities._\n\n   II. _In securing us from important mistakes in attempting what\n        is, in itself, possible, by means either inadequate, or\n        actually opposed, to the end in view._\n\n  III. _In enabling us to accomplish our ends in the easiest,\n        shortest, most economical, and most effectual manner._\n\n   IV. _In inducing us to attempt, and enabling us to accomplish,\n        objects which, but for such knowledge, we should never have\n        thought of undertaking._\n\nWe shall therefore proceed to illustrate by examples the effect of\nphysical knowledge under each of these heads:--\n\n(36.) Ex. 1. (35.) I. It is not many years since an attempt was made\nto establish a colliery at Bexhill, in Sussex. The appearance of\nthin seams and sheets of fossil-wood and wood-coal, with some other\nindications similar to what occur in the neighbourhood of the great\ncoal-beds in the north of England, having led to the sinking of a\nshaft, and the erection of machinery on a scale of vast expense, not\nless than eighty thousand pounds are said to have been laid out on\nthis project, which, it is almost needless to add, proved completely\nabortive, as every geologist would have at once declared it must, the\nwhole assemblage of geological facts being adverse to the existence\nof a regular coal-bed _in_ the Hastings\u2019 _sand_; while this, on which\nBexhill is situated, is separated from the _coal-strata_ by a series\nof interposed beds of such enormous thickness as to render all idea of\npenetrating _through_ them absurd. The history of mining operations\nis full of similar cases, where a very moderate acquaintance with the\n_usual order of nature_, to say nothing of theoretical views, would\nhave saved many a sanguine adventurer from utter ruin.\n\n(37.) Ex. 2. (35.) II. The smelting of iron requires the application\nof the most violent heat that can be raised, and is commonly performed\nin tall furnaces, urged by great iron bellows driven by steam-engines.\nInstead of employing this power to force _air_ into the furnace through\nthe intervention of bellows, it was, on one occasion, attempted to\nemploy the steam itself in, apparently, a much less circuitous manner;\nviz. by directing the current of steam in a violent blast, from the\nboiler at once into the fire. From one of the known ingredients of\nsteam being a highly inflammable body, and the other that essential\npart of the air which supports combustion, it was imagined that this\nwould have the effect of increasing the fire to tenfold fury, whereas\nit simply _blew it out_; a result which a slight consideration of the\nlaws of chemical combination, and the state in which the ingredient\nelements exist in steam, would have enabled any one to predict without\na trial.\n\n(38.) Ex. 3. (35.) II. After the invention of the diving-bell, and its\nsuccess in subaqueous processes, it was considered highly desirable\nto devise some means of remaining for any length of time under water,\nand rising at pleasure without assistance, so as either to examine,\nat leisure, the bottom, or perform, at ease, any work that might be\nrequired. Some years ago, an ingenious individual proposed a project\nby which this end was to be accomplished. It consisted in sinking\nthe hull of a ship made quite water-tight, with the decks and sides\nstrongly supported by shores, and the only entry secured by a stout\ntrap-door, in such a manner, that by disengaging, from within, the\nweights employed to sink it, it might rise of itself to the surface. To\nrender the trial more satisfactory, and the result more striking, the\nprojector himself made the first essay. It was agreed that he should\nsink in twenty fathoms water, and rise again without assistance at\nthe expiration of twenty-four hours. Accordingly, making all secure,\nfastening down his trap-door, and provided with all necessaries, as\nwell as with the means of making signals to indicate his situation,\nthis unhappy victim of his own ingenuity entered and was sunk. No\nsignal was made, and the time appointed elapsed. An immense concourse\nof people had assembled to witness his rising, but in vain; for the\nvessel was never seen more. The pressure of the water at so great a\ndepth had, no doubt, been completely under-estimated, and the sides of\nthe vessel being at once crushed in, the unfortunate projector perished\nbefore he could even make the signal concerted to indicate his distress.\n\n(39.) Ex. 4. (35.) III. In the granite quarries near Seringapatam the\nmost enormous blocks are separated from the solid rock by the following\nneat and simple process. The workman having found a portion of the rock\nsufficiently extensive, and situated near the edge of the part already\nquarried, lays bare the upper surface, and marks on it a line in the\ndirection of the intended separation, along which a groove is cut with\na chisel about a couple of inches in depth. Above this groove a narrow\nline of fire is then kindled, and maintained till the rock below is\nthoroughly heated, immediately on which a line of men and women, each\nprovided with a pot full of cold water, suddenly sweep off the ashes,\nand pour the water into the heated groove, when the rock at once\nsplits with a clean fracture. Square blocks of six feet in the side,\nand upwards of eighty feet in length, are sometimes detached by this\nmethod, or by another equally simple and efficacious, but not easily\nexplained without entering into particulars of mineralogical detail.[11]\n\n(40.) Ex. 5. (35.) III. Hardly less simple and efficacious is the\nprocess used in some parts of France, where mill-stones are made. When\na mass of stone sufficiently large is found, it is cut into a cylinder\nseveral feet high, and the question then arises how to subdivide\nthis into horizontal pieces so as to make as many mill-stones. For\nthis purpose horizontal indentations or grooves are chiselled out\nquite round the cylinder, at distances corresponding to the thickness\nintended to be given to the mill-stones, into which wedges of dried\nwood are driven. These are then wetted, or exposed to the night dew,\nand next morning the different pieces are found separated from each\nother by the expansion of the wood, consequent on its absorption of\nmoisture; an irresistible natural power thus accomplishing, almost\nwithout any trouble, and at no expense, an operation which, from\nthe peculiar hardness and texture of the stone, would otherwise\nbe impracticable but by the most powerful machinery or the most\npersevering labour.\n\n(41.) Ex. 6. (35.) III. To accomplish our ends quickly is often of, at\nleast, as much importance as to accomplish them with little labour and\nexpense. There are innumerable processes which, if left to themselves,\n_i.\u00a0e._ to the ordinary operation of natural causes, are done, and well\ndone, but with extreme slowness, and in such cases it is often of\nthe highest practical importance to accelerate them. The bleaching of\nlinen, for instance, performed in the natural way by exposure to sun,\nrain, and wind, requires many weeks or even months for its completion;\nwhereas, by the simple immersion of the cloth in a liquid, chemically\nprepared, the same effect is produced in a few hours. The whole circle\nof the arts, indeed, is nothing but one continued comment upon this\nhead of our subject. The instances above given are selected, not on\naccount of their superior importance, but for the simplicity and\n_directness_ of application of the principles on which they depend, to\nthe objects intended to be attained.\n\n(42.) But so constituted is the mind of man, that his views enlarge,\nand his desires and wants increase, in the full proportion of the\nfacilities afforded to their gratification, and, indeed, with augmented\nrapidity, so that no sooner has the successful exercise of his powers\naccomplished any considerable simplification or improvement of\nprocesses subservient to his use or comfort, than his faculties are\nagain on the stretch to extend the limits of his newly acquired power;\nand having once experienced the advantages which are to be gathered\nby availing himself of some of the powers of nature to accomplish\nhis ends, he is led thenceforward to regard them all as a treasure\nplaced at his disposal, if he have only the art, the industry, or the\ngood fortune, to penetrate those recesses which conceal them from\nimmediate view. Having once learned to look on knowledge as power, and\nto avail himself of it as such, he is no longer content to limit his\nenterprises to the beaten track of former usage, but is constantly\nled onwards to contemplate objects which, in a previous stage of his\nprogress, he would have regarded as unattainable and visionary, had he\neven thought of them at all. It is here that the investigation of the\nhidden powers of nature becomes a mine, every vein of which is pregnant\nwith inexhaustible wealth, and whose ramifications appear to extend in\nall directions wherever human wants or curiosity may lead us to explore.\n\n(43.) Between the physical sciences and the arts of life there subsists\na constant mutual interchange of good offices, and no considerable\nprogress can be made in the one without of necessity giving rise to\ncorresponding steps in the other. On the one hand, every art is in\nsome measure, and many entirely, dependent on those very powers and\nqualities of the material world which it is the object of physical\nenquiry to investigate and explain; and, accordingly, abundant examples\nmight be cited of cases where the remarks of experienced artists, or\neven ordinary workmen, have led to the discovery of natural qualities,\nelements, or combinations which have proved of the highest importance\nin physics. Thus (to give an instance), a soap-manufacturer remarks\nthat the residuum of his ley, when exhausted of the alkali for which\nhe employs it, produces a corrosion of his copper boiler for which he\ncannot account. He puts it into the hands of a scientific chemist for\nanalysis, and the result is the discovery of one of the most singular\nand important chemical elements, iodine. The properties of this,\nbeing studied, are found to occur most appositely in illustration\nand support of a variety of new, curious, and instructive views then\ngaining ground in chemistry, and thus exercise a marked influence\nover the whole body of that science. Curiosity is excited: the origin\nof the new substance is traced to the sea-plants from whose ashes\nthe principal ingredient of soap is obtained, and ultimately to the\nsea-water itself. It is thence hunted through nature, discovered in\nsalt mines and springs, and pursued into all bodies which have a marine\norigin; among the rest, into sponge. A medical practitioner[12] then\ncalls to mind a reputed remedy for the cure of one of the most grievous\nand unsightly disorders to which the human species is subject--the\n_go\u00eetre_--which infests the inhabitants of mountainous districts to\nan extent that in this favoured land we have happily no experience\nof, and which was said to have been originally cured by the ashes of\nburnt sponge. Led by this indication he tries the effect of iodine on\nthat complaint, and the result establishes the extraordinary fact that\nthis singular substance, taken as a medicine, acts with the utmost\npromptitude and energy on _go\u00eetre_, dissipating the largest and most\ninveterate in a short time, and acting (of course, like all medicines,\neven the most approved, with occasional failures,) as a specific, or\nnatural antagonist, against that odious deformity. It is thus that\nany accession to our knowledge of nature is sure, sooner or later, to\nmake itself felt in some practical application, and that a benefit\nconferred on science by the casual observation or shrewd remark of even\nan unscientific or illiterate person infallibly repays itself with\ninterest, though often in a way that could never have been at first\ncontemplated.\n\n(44.) It is to such observation, reflected upon, however, and matured\ninto a rational and scientific form by a mind deeply imbued with the\nbest principles of sound philosophy, that we owe the practice of\nvaccination; a practice which has effectually subdued, in every country\nwhere it has been introduced, one of the most frightful scourges of\nthe human race, and in some extirpated it altogether. Happily for us\nwe know only by tradition the ravages of the small-pox, as it existed\namong us hardly more than a century ago, and as it would in a few\nyears infallibly exist again, were the barriers which this practice,\nand that of inoculation, oppose to its progress abandoned. Hardly\ninferior to this terrible scourge on land was, within the last seventy\nor eighty years, the scurvy at sea. The sufferings and destruction\nproduced by this horrid disorder on board our ships when, as a matter\nof course, it broke out after a few months\u2019 voyage, seem now almost\nincredible. Deaths to the amount of eight or ten a day in a moderate\nship\u2019s company; bodies sewn up in hammocks and washing about the decks\nfor want of strength and spirits on the part of the miserable survivors\nto cast them overboard; and every form of loathsome and excruciating\nmisery of which the human frame is susceptible:--such are the pictures\nwhich the narratives of nautical adventure in those days continually\noffer.[13] At present the scurvy is almost completely eradicated in\nthe navy, partly, no doubt, from increased and increasing attention to\ngeneral cleanliness, comfort, and diet; but mainly from the constant\nuse of a simple and palatable preventive, the acid of the lemon,\nserved out in daily rations. If the gratitude of mankind be allowed on\nall hands to be the just meed of the philosophic physician, to whose\ndiscernment in seizing, and perseverance in forcing it on public notice\nwe owe the great safeguard of infant life, it ought not to be denied to\nthose[14] whose skill and discrimination have thus strengthened the\nsinews of our most powerful arm, and obliterated one of the darkest\nfeatures in the most glorious of all professions.\n\n(45.) These last, however, are instances of simple observation,\nlimited to the point immediately in view, and assuming only so far the\ncharacter of science as a systematic adoption of good and rejection of\nevil, when grounded on experience carefully weighed, justly entitle\nit to do. They are not on that account less appositely cited as\ninstances of the importance of a knowledge of nature and its laws to\nour well-being; though, like the great inventions of the mariner\u2019s\ncompass and of gunpowder, they may have stood, in their origin,\nunconnected with more general views. They are rather to be looked upon\nas the spontaneous produce of a territory essentially fertile, than as\nforming part of the succession of harvests which the same bountiful\nsoil, diligently cultivated, is capable of yielding. The history of\niodine above related affords, however, a perfect specimen of the\nmanner in which a knowledge of natural properties and laws, collected\nfrom facts having no reference to the object to which they have\nbeen subsequently applied, enables us to set in array the resources\nof nature against herself; and deliberately, of afore-thought, to\ndevise remedies against the dangers and inconveniences which beset\nus. In this view we might instance, too, the _conductor_, which, in\ncountries where thunder-storms are more frequent and violent than in\nour own, and at sea (where they are attended with peculiar danger,\nboth from the greater probability of accident, and its more terrible\nconsequences when it does occur,) forms a most real and efficient\npreservative against the effects of lightning[15]:--the _safety-lamp_,\nwhich enables us to walk with light and security while surrounded with\nan atmosphere more explosive than gunpowder:--the _life-boat_, which\ncannot be sunk, and which offers relief in circumstances of all others\nthe most distressing to humanity, and of which a recent invention\npromises to extend the principle to ships of the largest class:--the\n_lighthouse_, with the capital improvements which the lenses of\nBrewster and Fresnel, and the elegant lamp of lieutenant Drummond, have\nconferred, and promise yet to confer by their wonderful powers, the one\nof producing the most intense light yet known, the others of conveying\nit undispersed to great distances:--the discovery of the disinfectant\npowers of chlorine, and its application to the destruction of miasma\nand contagion:--that of _quinine_, the essential principle in which\nreside the febrifuge qualities of the Peruvian bark, a discovery by\nwhich posterity is yet to benefit in its full extent, but which has\nalready begun to diffuse _comparative_ comfort and health through\nregions almost desolated by pestiferous exhalations[16];--and, if we\ndesist, it is not because the list is exhausted, but because a sample,\nnot a catalogue, is intended.\n\n(46.) One instance more, however, we will add, to illustrate the\nmanner in which a most familiar effect, which seemed destined only\nto amuse children, or, at best, to furnish a philosophic toy, may\nbecome a safeguard of human life, and a remedy for a most serious\nand distressing evil. In needle manufactories the workmen who point\nthe needles are constantly exposed to excessively minute particles of\nsteel which fly from the grindstones, and mix, though imperceptible\nto the eye, as the finest dust in the air, and are inhaled with their\nbreath. The effect, though imperceptible on a short exposure, yet,\nbeing constantly repeated from day to day, produces a constitutional\nirritation dependent on the tonic properties of the steel, which is\nsure to terminate in pulmonary consumption; insomuch, that persons\nemployed in this kind of work used scarcely ever to attain the age of\nforty years.[17] In vain was it attempted to purify the air before its\nentry into the lungs by gauzes or linen guards; the dust was too fine\nand penetrating to be obstructed by such coarse expedients, till some\ningenious person bethought him of that wonderful power which every\nchild who searches for its mother\u2019s needle with a magnet, or admires\nthe motions and arrangement of a few steel filings on a sheet of paper\nheld above it, sees in exercise. Masks of magnetized steel wire are now\nconstructed and adapted to the faces of the workmen. By these the air\nis not merely _strained_ but _searched_ in its passage through them,\nand each obnoxious atom arrested and removed.\n\n(47.) Perhaps there is no result which places in a stronger light the\nadvantages which are to be derived from a mere knowledge of the _usual\norder of nature_, without any attempt on our part to modify it, and\napart from all consideration of its causes, than the institution of\nlife-assurances. Nothing is more uncertain than the life of a single\nindividual; and it is the sense of this insecurity which has given\nrise to such institutions. They are, in their nature and objects,\nthe precise reverse of gambling speculations, their object being to\nequalize vicissitude, and to place the pecuniary relations of numerous\nmasses of mankind, in so far as they extend, on a footing independent\nof individual casualty. To do this with the greatest possible\nadvantage, or indeed with any advantage at all, it is necessary to know\nthe _laws of mortality_, or the average numbers of individuals, out\nof a great multitude, who die at every period of life from infancy to\nextreme old age. At first sight this would seem a hopeless enquiry; to\nsome, perhaps, a presumptuous one. But it has been made; and the result\nis, that, abating extraordinary causes, such as wars, pestilence, and\nthe like, a remarkable regularity _does_ obtain, quite sufficient\nto afford grounds not only for general estimations, but for nice\ncalculations of risk and adventure, such as infallibly to insure the\nsuccess of any such institution founded on good computations; and thus\nto confer such stability on the fortunes of families dependent on the\nexertions of one individual as to constitute an important feature in\nmodern civilization. The only thing to be feared in such institutions\nis their too great multiplication and consequent competition, by which\na spirit of gambling and underbidding is liable to be generated among\ntheir conductors, and the very mischief may be produced, on a scale of\nfrightful extent, which they are especially intended to prevent.\n\n(48.) We have hitherto considered only cases in which a knowledge of\nnatural laws enables us to improve our condition, by counteracting\nevils of which, but for its possession, we must have remained forever\nthe helpless victims. Let us now take a similar view of those in which\nwe are enabled to call in nature as an auxiliary to augment our actual\npower, and capacitate us for undertakings, which without such aid might\nseem to be hopeless. Now, to this end, it is necessary that we should\nform a just conception of what those hidden powers of nature _are_,\nwhich we can at pleasure call into action;--how far they transcend\nthe measure of human force, and set at naught the efforts not only of\nindividuals but of whole nations of men.\n\n(49.) It is well known to modern engineers, that _there is virtue_ in a\nbushel of coals properly consumed, to raise seventy millions of pounds\nweight a foot high. This is actually the _average_ effect of an engine\nat this moment working in Cornwall.[18] Let us pause a moment, and\nconsider what this is equivalent to in matters of practice.\n\n(50.) The ascent of Mont Blanc from the valley of Chamouni is\nconsidered, and with justice, as the most toilsome feat that a strong\nman can execute in two days. The combustion of two pounds of coal would\nplace him on the summit.[19]\n\n(51.) The Menai Bridge, one of the most stupendous works of art that\nhas been raised by man in modern ages, consists of a mass of iron, not\nless than four millions of pounds in weight, suspended at a medium\nheight of about 120 feet above the sea. The consumption of seven\nbushels of coal would suffice to raise it to the place where it hangs.\n\n(52.) The great pyramid of Egypt is composed of granite. It is 700 feet\nin the side of its base, and 500 in perpendicular height, and stands on\neleven acres of ground. Its weight is, therefore, 12,760 millions of\npounds, at a medium height of 125 feet; consequently it would be raised\nby the effort of about 630 chaldrons of coal, a quantity consumed in\nsome founderies in a week.\n\n(53.) The annual consumption of coal in London is estimated at\n1,500,000 chaldrons. The effort of this quantity would suffice to raise\na cubical block of marble, 2200 feet in the side, through a space equal\nto its own height, or to pile one such mountain upon another. The Monte\nNuovo, near Pozzuoli, (which was erupted in a single night by volcanic\nfire,) might have been raised by such an effort, from a depth of 40,000\nfeet, or about eight miles.\n\n(54.) It will be observed, that, in the above statement, the inherent\npower of fuel is, of necessity, greatly under-rated. It is not\npretended by engineers that the economy of fuel is yet pushed to its\nutmost limit, or that the whole effective power is obtained in any\napplication of fire yet devised; so that were we to say 100 millions\ninstead of 70, we should probably be nearer the truth.\n\n(55.) The powers of wind and water, which we are constantly impressing\ninto our service, can scarcely be called latent or hidden, yet it\nis not fully considered, in general, what they _do_ effect for us.\nThose who would judge of what advantage may be taken of the wind, for\nexample, even on land (not to speak of navigation), may turn their\neyes on Holland. A great portion of the most valuable and populous\ntract of this country lies much below the level of the sea, and is only\npreserved from inundation by the maintenance of embankments. Though\nthese suffice to keep out the abrupt influx of the ocean, they cannot\noppose that law of nature, by which fluids, in seeking their level,\ninsinuate themselves through the pores and subterraneous channels\nof a loose sandy soil, and keep the country in a constant state of\ninfiltration from below upwards. To counteract this tendency, as well\nas to get rid of the rain water, which has no natural outlet, pumps\nworked by windmills are established in great numbers, on the dams\nand embankments, which pour out the water, as from a leaky ship, and\nin effect preserve the country from submersion, by taking advantage\nof every wind that blows. To drain the Haarlem lake[20] would seem a\nhopeless project to any speculators but those who had the steam-engine\nat their command, or had learnt in Holland what might be accomplished\nby the constant agency of the desultory but unwearied powers of wind.\nBut the Dutch engineer measures his surface, calculates the number of\nhis pumps, and, trusting to time and his experience of the operation of\nthe winds for the success of his undertaking, boldly forms his plans to\nlay dry the bed of an inland sea, of which those who stand on one shore\ncannot see the other.[21]\n\n(56.) To gunpowder, as a source of mechanical power, it seems hardly\nnecessary to call attention; yet it is only when we endeavour to\n_confine_ it, that we get a full conception of the immense energy of\nthat astonishing agent. In count Rumford\u2019s experiments, twenty-eight\ngrains of powder confined in a cylindrical space, _which it just\nfilled_, tore asunder a piece of iron which would have resisted\na strain of 400,000 lbs.[22], applied at no greater mechanical\ndisadvantage.\n\n(57.) But chemistry furnishes us with means of calling into sudden\naction forces of a character infinitely more tremendous than that\nof gunpowder. The terrific violence of the different fulminating\ncompositions is such, that they can only be compared to those\nuntameable animals, whose ferocious strength has hitherto defied all\nuseful management, or rather to spirits evoked by the spells of a\nmagician, manifesting a destructive and unapproachable power, which\nmakes him but too happy to close his book, and break his wand, as the\nprice of escaping: unhurt from the storm he has raised. Such powers are\nnot yet subdued to our purposes, whatever they may hereafter be; but,\nin the expansive force of gases, liberated slowly and manageably from\nchemical mixtures, we have a host of inferior, yet still most powerful,\nenergies, capable of being employed in a variety of useful ways,\naccording to emergencies.[23]\n\n(58.) Such are the forces which nature lends us for the accomplishment\nof our purposes, and which it is the province of practical Mechanics to\nteach us to combine and apply in the most advantageous manner; without\nwhich the mere command of power would amount to nothing. Practical\nMechanics is, in the most pre-eminent sense, a _scientific art_; and\nit may be truly asserted, that almost all the great combinations of\nmodern mechanism, and many of its refinements and nicer improvements,\nare creations of pure intellect, grounding its exertion upon a moderate\nnumber of very elementary propositions in theoretical mechanics and\ngeometry. On this head we might dwell long, and find ample matter,\nboth for reflection and wonder; but it would require not volumes\nmerely, but libraries, to enumerate and describe the prodigies of\ningenuity which have been lavished on every thing connected with\nmachinery and engineering. By these it is that we are enabled to\ndiffuse over the whole earth the productions of any part of it; to fill\nevery corner of it with miracles of art and labour, in exchange for its\npeculiar commodities; and to concentrate around us, in our dwellings,\napparel and utensils, the skill and workmanship not of a few expert\nindividuals, but of all who, in the present and past generations, have\ncontributed their improvements to the processes of our manufactures.\n\n(59.) The transformations of chemistry, by which we are enabled to\nconvert the most apparently useless materials into important objects\nin the arts, are opening up to us every day sources of wealth and\nconvenience of which former ages had no idea, and which have been\npure gifts of science to man. Every department of art has felt their\ninfluence, and new instances are continually starting forth of the\nunlimited resources which this wonderful science developes in the\nmost sterile parts of nature. Not to mention the impulse which its\nprogress has given to a host of other sciences, which will come more\nparticularly under consideration in another part of this discourse,\nwhat strange and unexpected results has it not brought to light in its\napplication to some of the most common objects! Who, for instance,\nwould have conceived that linen rags were capable of producing _more\nthan their own weight_ of sugar, by the simple agency of one of the\ncheapest and most abundant acids?[24]--that dry bones could be a\nmagazine of nutriment, capable of preservation for years, and ready to\nyield up their sustenance in the form best adapted to the support of\nlife, on the application of that powerful agent, steam, which enters\nso largely into all our processes, or of an acid at once cheap and\ndurable?[25]--that sawdust itself is susceptible of conversion into\na substance bearing no remote analogy to bread; and though certainly\nless palatable than that of flour, yet no way disagreeable, and\nboth wholesome and digestible as well as highly nutritive?[26] What\neconomy, in all processes where chemical agents are employed, is\nintroduced by the exact knowledge of the proportions in which natural\nelements unite, and their mutual powers of displacing each other! What\nperfection in all the arts where fire is employed, either in its more\nviolent applications, (as, for instance, in the smelting of metals by\nthe introduction of well adapted fluxes, whereby we obtain the whole\nproduce of the ore in its purest state,) or in its milder forms, as\nin sugar-refining (the whole modern practice of which depends on a\ncurious and delicate remark of a late eminent scientific chemist on the\nnice adjustment of temperature at which the crystallization of syrup\ntakes place); and a thousand other arts which it would be tedious to\nenumerate!\n\n(60.) Armed with such powers and resources, it is no wonder if the\nenterprise of man should lead him to form and execute projects\nwhich, to one uninformed of their grounds, would seem altogether\ndisproportionate. Were they to have been proposed at once, we should,\nno doubt, have rejected them as such: but developed, as they have been,\nin the slow succession of ages, they have only taught us that things\nregarded impossible in one generation may become easy in the next; and\nthat the power of man over nature is limited only by the one condition,\nthat it must be exercised in conformity with the laws of nature. He\nmust study those laws as he would the disposition of a horse he would\nride, or the character of a nation he would govern; and the moment he\npresumes either to thwart her fundamental rules, or ventures to measure\nhis strength with hers, he is at once rendered severely sensible of\nhis imbecility, and meets the deserved punishment of his rashness and\nfolly. But if, on the other hand, he will consent to use, without\nabusing, the resources thus abundantly placed at his disposal, and obey\nthat he may command, there seems scarcely any conceivable limit to the\ndegree in which the _average_ physical condition of great masses of\nmankind may be improved, their wants supplied, and their conveniences\nand comforts increased. Without adopting such an exaggerated view,\nas to assert that the meanest inhabitant of a civilized society is\nsuperior in physical condition to the lordly savage, whose energy and\nuncultivated ability gives him a natural predominance over his fellow\ndenizens of the forest,--at least, if we compare like with like, and\nconsider the multitude of human beings who are enabled, in an advanced\nstate of society, to subsist in a degree of comfort and abundance,\nwhich at best only a few of the most fortunate in a less civilized\nstate could command, we shall not be at a loss to perceive the\nprinciple on which we ought to rest our estimate of the advantages of\ncivilization; and which applies with hardly less force to every degree\nof it, when contrasted with that next inferior, than to the broad\ndistinction between civilized and barbarous life in general.\n\n(61.) The difference of the degrees in which the individuals of a great\ncommunity enjoy the good things of life has been a theme of declamation\nand discontent in all ages; and it is doubtless our paramount duty, in\nevery state of society, to alleviate the pressure of the purely evil\npart of this distribution as much as possible, and, by all the means\nwe can devise, secure the lower links in the chain of society from\ndragging in dishonour and wretchedness: but there is a point of view\nin which the picture is at least materially altered in its expression.\nIn comparing society on its present immense scale, with its infant\nor less developed state, we must at least take care to enlarge every\nfeature in the same proportion. If, on comparing the _very_ lowest\nstates in civilized and savage life, we admit a difficulty in deciding\nto which the preference is due, at least in every superior grade we\ncannot hesitate a moment; and if we institute a similar comparison in\nevery different stage of its progress, we cannot fail to be struck with\nthe rapid _rate of dilatation_ which every degree upward of the scale,\nso to speak, exhibits, and which, in an estimate of averages, gives\nan immense preponderance to the present over every former condition\nof mankind, and, for aught we can see to the contrary, will place\nsucceeding generations in the same degree of superior relation to the\npresent that this holds to those passed away. Or we may put the same\nproposition in other words, and, admitting the existence of every\ninferior grade of advantage in a higher state of civilization which\nsubsisted in the preceding, we shall find, first, that, taking state\nfor state, the proportional numbers of those who enjoy the higher\ndegrees of advantage increases with a constantly accelerated rapidity\nas society advances; and, secondly, that the superior extremity of\nthe scale is constantly enlarging by the addition of new degrees. The\ncondition of a European prince is now as far superior, in the command\nof real comforts and conveniences, to that of one in the middle ages,\nas that to the condition of one of his own dependants.\n\n(62.) The advantages conferred by the augmentation of our physical\nresources through the medium of increased knowledge and improved art\nhave this peculiar and remarkable property,--that they are in their\nnature diffusive, and cannot be enjoyed in any exclusive manner by a\nfew. An eastern despot may extort the riches and monopolize the art\nof his subjects for his own personal use; he may spread around him an\nunnatural splendour and luxury, and stand in strange and preposterous\ncontrast with the general penury and discomfort of his people; he may\nglitter in jewels of gold and raiment of needlework; but the wonders\nof well contrived and executed manufacture which we use daily, and\nthe comforts which have been invented, tried, and improved upon by\nthousands, in every form of domestic convenience, and for every\nordinary purpose of life, can never be enjoyed by him. To produce a\nstate of things in which the physical advantages of civilized life\ncan exist in a high degree, the stimulus of increasing comforts and\nconstantly elevated desires, must have been felt by millions; since it\nis not in the power of a few individuals to create that wide demand\nfor useful and ingenious applications, which alone can lead to great\nand rapid improvements, unless backed by that arising from the speedy\ndiffusion of the same advantages among the mass of mankind.\n\n(63.) If this be true of physical advantages, it applies with still\ngreater force to intellectual. Knowledge can neither be adequately\ncultivated nor adequately enjoyed by a few; and although the conditions\nof our existence on earth may be such as to preclude an abundant\nsupply of the physical necessities of all who may be born, there\nis no such law of nature in force against that of our intellectual\nand moral wants. Knowledge is not, like food, destroyed by use, but\nrather augmented and perfected. It acquires not, perhaps, a greater\ncertainty, but at least a confirmed authority and a probable duration,\nby universal assent; and there is no body of knowledge so complete,\nbut that it may acquire accession, or so free from error but that it\nmay receive correction in passing through the minds of millions. Those\nwho admire and love knowledge for its own sake ought to wish to see\nits elements made accessible to all, were it only that they may be\nthe more thoroughly examined into, and more effectually developed in\ntheir consequences, and receive that ductility and plastic quality\nwhich the pressure of minds of all descriptions, constantly moulding\nthem to their purposes, can alone bestow. But to this end it is\nnecessary that it should be divested, as far as possible, of artificial\ndifficulties, and stripped of all such technicalities as tend to place\nit in the light of a craft and a mystery, inaccessible without a kind\nof apprenticeship. Science, of course, like every thing else, has its\nown peculiar terms, and, so to speak, its idioms of language; and these\nit would be unwise, were it even possible, to relinquish: but every\nthing that tends to clothe it in a strange and repulsive garb, and\nespecially every thing that, to keep up an appearance of superiority\nin its professors over the rest of mankind, assumes an unnecessary\nguise of profundity and obscurity, should be sacrificed without mercy.\nNot to do this, is to deliberately reject the light which the natural\nunencumbered good sense of mankind is capable of throwing on every\nsubject, even in the elucidation of principles: but where principles\nare to be applied to practical uses it becomes absolutely necessary;\nas all mankind have then an interest in their being so familiarly\nunderstood, that no mistakes shall arise in their application.\n\n(64.) The same remark applies to arts. They cannot be perfected till\ntheir whole processes are laid open, and their language simplified and\nrendered universally intelligible. Art is the application of knowledge\nto a practical end. If the knowledge be merely accumulated experience,\nthe art is _empirical_; but if it be experience reasoned upon and\nbrought under general principles, it assumes a higher character, and\nbecomes a _scientific art_. In the progress of mankind from barbarism\nto civilised life, the arts necessarily precede science. The wants and\ncravings of our animal constitution must be satisfied; the comforts,\nand some of the luxuries, of life must exist. Something must be given\nto the vanity of show, and more to the pride of power: the round of\nbaser pleasures must have been tried and found insufficient, before\nintellectual ones can gain a footing; and when they have obtained it,\nthe delights of poetry and its sister arts still take precedence of\ncontemplative enjoyments, and the severer pursuits of thought; and\nwhen these in time begin to charm from their novelty, and sciences\nbegin to arise, they will at first be those of pure speculation. The\nmind delights to escape from the trammels which had bound it to earth,\nand luxuriates in its newly found powers. Hence, the abstractions of\ngeometry--the properties of numbers--the movements of the celestial\nspheres--whatever is abstruse, remote, and extramundane--become the\nfirst objects of infant science. Applications come late: the arts\ncontinue slowly progressive, but their realm remains separated from\nthat of science by a wide gulf which can only be passed by a powerful\nspring. They form their own language and their own conventions, which\nnone but artists can understand. The whole tendency of empirical\nart, is to bury itself in technicalities, and to place its pride in\nparticular short cuts and mysteries known only to adepts; to surprise\nand astonish by results, but conceal processes. The character of\nscience is the direct contrary. It delights to lay itself open to\nenquiry, and is not satisfied with its conclusions, till it can make\nthe road to them broad and beaten: and in its applications it preserves\nthe same character; its whole aim being to strip away all technical\nmystery, to illuminate every dark recess, and to gain free access to\nall processes, with a view to improve them on rational principles.\nIt would seem that a union of two qualities almost opposite to each\nother--a going forth of the thoughts in two directions, and a sudden\ntransfer of ideas from a remote station in one to an equally distant\none in the other--is required to start the first idea of _applying\nscience_. Among the Greeks, this point was attained by Archimedes, but\nattained too late, on the eve of that great eclipse of science which\nwas destined to continue for nearly eighteen centuries, till Galileo in\nItaly, and Bacon in England, at once dispelled the darkness: the one,\nby his inventions and discoveries; the other, by the irresistible force\nof his arguments and eloquence.\n\n(65.) Finally, the improvement effected in the condition of mankind\nby advances in physical science as applied to the useful purposes of\nlife, is very far from being limited to their direct consequences in\nthe more abundant supply of our physical wants, and the increase of our\ncomforts. Great as these benefits are, they are yet but steps to others\nof a still higher kind. The successful results of our experiments and\nreasonings in natural philosophy, and the incalculable advantages which\nexperience, systematically consulted and dispassionately reasoned on,\nhas conferred in matters purely physical, tend of necessity to impress\nsomething of the well weighed and progressive character of science on\nthe more complicated conduct of our social and moral relations. It\nis thus that legislation and politics become gradually regarded as\nexperimental sciences; and history, not, as formerly, the mere record\nof tyrannies and slaughters, which, by immortalizing the execrable\nactions of one age, perpetuates the ambition of committing them in\nevery succeeding one, but as the archive of experiments, successful\nand unsuccessful, gradually accumulating towards the solution of the\ngrand problem--how the advantages of government are to be secured\nwith the least possible inconvenience to the governed. The celebrated\napophthegm, that nations never profit by experience, becomes yearly\nmore and more untrue. Political economy, at least, is found to have\nsound principles, founded in the moral and physical nature of man,\nwhich, however lost sight of in particular measures--however even\ntemporarily controverted and borne down by clamour--have yet a stronger\nand stronger testimony borne to them in each succeeding generation, by\nwhich they must, sooner or later, prevail. The idea once conceived and\nverified, that great and noble ends are to be achieved, by which the\ncondition of the whole human species shall be permanently bettered,\nby bringing into exercise a sufficient quantity of sober thought, and\nby a proper adaptation of means, is of itself sufficient to set us\nearnestly on reflecting what ends _are_ truly great and noble, either\nin themselves, or as conducive to others of a still loftier character;\nbecause we are not now, as heretofore, hopeless of attaining them. It\nis not now equally harmless and insignificant, whether we are right\nor wrong; since we are no longer supinely and helplessly carried down\nthe stream of events, but feel ourselves capable of buffetting at\nleast with its waves, and perhaps of riding triumphantly over them:\nfor why should we despair that the reason which has enabled us to\nsubdue all nature to our purposes, should (if permitted and assisted\nby the providence of God) achieve a far more difficult conquest; and\nultimately find some means of enabling the collective wisdom of mankind\nto bear down those obstacles which individual short-sightedness,\nselfishness, and passion, oppose to all improvements, and by which\nthe highest hopes are continually blighted, and the fairest prospects\nmarred.\n\n\n\n\n                                PART II.\n\n  OF THE PRINCIPLES ON WHICH PHYSICAL SCIENCE RELIES FOR ITS\n    SUCCESSFUL PROSECUTION, AND THE RULES BY WHICH A SYSTEMATIC\n    EXAMINATION OF NATURE SHOULD BE CONDUCTED, WITH ILLUSTRATIONS OF\n    THEIR INFLUENCE AS EXEMPLIFIED IN THE HISTORY OF ITS PROGRESS.\n\n\n\n\nCHAPTER I.\n\n  OF EXPERIENCE AS THE SOURCE OF OUR KNOWLEDGE.--OF THE DISMISSAL OF\n    PREJUDICES.--OF THE EVIDENCE OF OUR SENSES.\n\n\n(66.) Into abstract science, as we have before observed, the notion of\ncause does not enter. The truths it is conversant with are _necessary_\nones, and exist independent of cause. There may be no such real _thing_\nas a right-lined triangle marked out in space; but the moment we\nconceive one in our minds, we cannot refuse to admit the sum of its\nthree angles to be equal to two right angles; and if in addition we\nconceive one of its angles to be a right angle, we cannot thenceforth\nrefuse to admit that the sum of the squares on the two sides, including\nthe right angle, is equal to the square on the side subtending it. To\nmaintain the contrary, would be, in effect, to deny its being right\nangled. No one _causes_ or _makes_ all the diameters of an ellipse\nto be bisected in its centre. To assert the contrary, would not be\nto rebel against a power, but to deny our own words. But in natural\nscience _cause_ and _effect_ are the ultimate relations we contemplate;\nand _laws_, whether imposed or maintained, which, for aught we can\nperceive, might have been other than they are. This distinction is\nvery important. A clever man, shut up alone and allowed unlimited\ntime, might reason out for himself all the truths of mathematics, by\nproceeding from those simple notions of space and number of which he\ncannot divest himself without ceasing to think. But he could never\ntell, by any effort of reasoning, what would become of a lump of sugar\nif immersed in water, or what impression would be produced on his eye\nby mixing the colours yellow and blue.\n\n(67.) We have thus pointed out to us, as the great, and indeed only\nultimate source of our knowledge of nature and its laws, EXPERIENCE;\nby which we mean, not the experience of one man only, or of one\ngeneration, but the accumulated experience of all mankind in all ages,\nregistered in books or recorded by tradition. But experience may be\nacquired in two ways: either, first, by noticing facts as they occur,\nwithout any attempt to influence the frequency of their occurrence, or\nto vary the circumstances under which they occur; this is OBSERVATION:\nor, secondly, by putting in action causes and agents over which we\nhave control, and purposely varying their combinations, and noticing\nwhat effects take place; this is EXPERIMENT. To these two sources we\nmust look as the fountains of all natural science. It is not intended,\nhowever, by thus distinguishing observation from experiment, to\nplace them in any kind of contrast. Essentially they are much alike,\nand differ rather in degree than in kind; so that, perhaps, the\nterms _passive_ and _active observation_ might better express their\ndistinction; but it is, nevertheless, highly important to mark the\ndifferent states of mind in inquiries carried on by their respective\naids, as well as their different effects in promoting the progress of\nscience. In the former, we sit still and listen to a tale, told us,\nperhaps obscurely, piecemeal, and at long intervals of time, with our\nattention more or less awake. It is only by after-rumination that we\ngather its full import; and often, when the opportunity is gone by, we\nhave to regret that our attention was not more particularly directed to\nsome point which, at the time, appeared of little moment, but of which\nwe at length appretiate the importance. In the latter, on the other\nhand, we cross-examine our witness, and by comparing one part of his\nevidence with the other, while he is yet before us, and reasoning upon\nit in his presence, are enabled to put pointed and searching questions,\nthe answer to which may at once enable us to make up our minds.\nAccordingly it has been found invariably, that in those departments\nof physics where the phenomena are beyond our control, or into which\nexperimental enquiry, from other causes, has not been carried, the\nprogress of knowledge has been slow, uncertain, and irregular; while in\nsuch as admit of experiment, and in which mankind have agreed to its\nadoption, it has been rapid, sure, and steady. For example, in our\nknowledge of the nature and causes of volcanoes, earthquakes, the fall\nof stones from the sky, the appearance of new stars and disappearance\nof old ones, and other of those great phenomena of nature which are\naltogether beyond our command, and at the same time are of too rare\noccurrence to permit any one to repeat and rectify his impressions\nrespecting them, we know little more now than in the earliest times.\nHere our tale is told us slowly, and in broken sentences. In astronomy,\nagain, we have at least an uninterrupted narrative; the opportunity\nof observation is constantly present, and makes up in some measure\nfor the impossibility of varying our point of view, and calling for\ninformation at the precise moment it is wanted. Accordingly, astronomy,\nregarded as a science of mere observation, arrived, though by very\nslow degrees, to a state of considerable maturity. But the moment that\nit became a branch of mechanics, a science essentially experimental,\n(that is to say, one in which any principle laid down can be subjected\nto immediate and decisive _trial_, and where experience does not\nrequire to be waited for,) its progress suddenly acquired a tenfold\nacceleration; nay, to such a degree, that it has been asserted, and\nwe believe with truth, that were the records of all observations from\nthe earliest ages annihilated, leaving only those made in a single\nobservatory[27], during a single lifetime[28], the whole of this most\nperfect of sciences might, from those data, and as to the objects\nincluded in them, be at once reconstructed, and appear precisely as\nit stood at their conclusion. To take another instance: mineralogy,\ntill modern times, could hardly be said to exist. The description\nof even the precious stones in Theophrastus and Pliny are, in most\ncases, hardly sufficient to identify them, and in many fall short\neven of that humble object; more recent observers, by attending more\ncarefully to the obvious characters of minerals, had formed a pretty\nextensive catalogue of them, and made various attempts to arrange and\nmethodize the knowledge thus acquired, and even to deduce some general\nconclusions respecting the forms they habitually assume: but from the\nmoment that chemical analysis was applied to resolve them into their\nconstituent elements, and that, led by a happy accident, the genius\nof Bergmann discovered the general fact, that they could be _cloven_\nor split in such directions as to lay bare their peculiar primitive\nor fundamental forms, (which lay concealed within them, as the statue\nmight be conceived encrusted in its marble envelope,)--from that\nmoment, mineralogy ceased to be an unmeaning list of names, a mere\nlaborious cataloguing of stones and rubbish, and became, what it now\nis, a regular, methodical, and most important science, in which every\nyear is bringing to light new relations, new laws, and new practical\napplications.\n\n(68.) Experience once recognized as the fountain of all our knowledge\nof nature, it follows that, in the study of nature and its laws, we\nought at once to make up our minds to dismiss as idle prejudices, or\nat least suspend as premature, any preconceived notion of what might\nor what ought to be the order of nature in any proposed case, and\ncontent ourselves with observing, as a plain matter of fact, what _is_.\nTo experience we refer, as the only ground of all physical enquiry.\nBut before experience itself can be used with advantage, there is one\npreliminary step to make, which depends wholly on ourselves: it is\nthe absolute dismissal and clearing the mind of all prejudice, from\nwhatever source arising, and the determination to stand and fall by\nthe result of a direct appeal to facts in the first instance, and of\nstrict logical deduction from them afterwards. Now, it is necessary\nto distinguish between two kinds of prejudices, which exercise very\ndifferent dominion over the mind, and, moreover, differ extremely\nin the difficulty of dispossessing them, and the process to be gone\nthrough for that purpose. These are,--\n\n  1. Prejudices of opinion.\n  2. Prejudices of sense.\n\n(69.) By prejudices of opinion, we mean opinions hastily taken up,\neither from the assertion of others, from our own superficial views,\nor from vulgar observation, and which, from being constantly admitted\nwithout dispute, have obtained the strong hold of habit on our minds.\nSuch were the opinions once maintained that the earth is the greatest\nbody in the universe, and placed immovable in its centre, and all the\nrest of the universe created for its sole use; that it is the nature\nof fire and of sounds to ascend; that the moonlight is cold; that dews\n_fall_ from the air, &c.\n\n(70.) To combat and destroy such prejudices we may proceed in two ways,\neither by demonstrating the falsehood of the facts alleged in their\nsupport, or by showing how the appearances, which seem to countenance\nthem, are more satisfactorily accounted for without their admission.\nBut it is unfortunately the nature of prejudices of opinion to adhere,\nin a certain degree, to every mind, and to some with pertinacious\nobstinacy, _pigris radicibus_, after all ground for their reasonable\nentertainment is destroyed. Against such a disposition the student of\nnatural science must contend with all his power. Not that we are so\nunreasonable as to demand of him an instant and peremptory dismission\nof all his former opinions and judgments; all we require is, that\nhe will hold them without bigotry, retain till he shall see reason\nto question them, and be ready to resign them when fairly proved\nuntenable, and to doubt them when the weight of probability is shown to\nlie against them. If he refuse this, he is incapable of science.\n\n(71.) Our resistance against the destruction of the other class of\nprejudices, those of sense, is commonly more violent at first, but less\npersistent, than in the case of those of opinion. Not to trust the\nevidence of our senses, seems, indeed, a hard condition, and one which,\nif proposed, none would comply with. But it is not the direct evidence\nof our senses that we are in any case called upon to reject, but only\nthe erroneous judgments we unconsciously form from them, and this only\nwhen they can be shown to be so _by counter evidence of the same sort_;\nwhen one sense is brought to testify against another, for instance; or\nthe same sense against itself, and the obvious conclusions in the two\ncases disagree, so as to compel us to acknowledge that one or other\nmust be wrong. For example, nothing at first can seem a more rational,\nobvious, and incontrovertible conclusion, than that the _colour_ of\nan object is an inherent quality, like its weight, hardness, &c. and\nthat to _see_ the object, and see it _of its own colour_, when nothing\nintervenes between our eyes and it, are one and the same thing. Yet\nthis is only a prejudice; and that it is so, is shown by bringing\nforward the same sense of vision which led to its adoption, as evidence\non the other side; for, when the differently coloured prismatic rays\nare thrown, in a dark room, in succession upon any object, whatever be\nthe colour we are in the habit of calling its own, it will appear of\nthe particular hue of the light which falls upon it: a yellow paper,\nfor instance, will appear scarlet when illuminated by red rays, yellow\nwhen by yellow, green by green, and blue by blue rays; its own (so\ncalled) proper colour _not in the least degree mixing with that it so\nexhibits_.\n\n(72.) To give one or two more examples of the kind of illusion which\nthe senses practise on us, or rather which we practise on ourselves,\nby a misinterpretation of their evidence: the moon at its rising\nand setting appears much larger than when high up in the sky. This\nis, however, a mere erroneous judgment; for when we come to measure\nits diameter, so far from finding our conclusion borne out by fact,\nwe actually find it to measure materially less. Here is eyesight\nopposed to eyesight, with the advantage of deliberate measurement.\nIn ventriloquism we have the hearing at variance with all the other\nsenses, and especially with the sight, which is sometimes contradicted\nby it in a very extraordinary and surprising manner, as when the voice\nis made to seem to issue from an inanimate and motionless object. If\nwe plunge our hands, one into ice-cold water, and the other into water\nas hot as can be borne, and, after letting them stay awhile, suddenly\ntransfer them both to a vessel full of water at a blood heat, the one\nwill feel a sensation of heat, the other of cold. And if we cross the\ntwo first fingers of one hand, and place a pea in the fork between\nthem, moving and rolling it about on a table, we shall (especially if\nwe close our eyes) be fully persuaded we have two peas. If the nose\nbe held while we are eating cinnamon, we shall perceive no difference\nbetween its flavour and that of a deal shaving.\n\n(73.) These, and innumerable instances we might cite, will convince\nus, that though we are never deceived in the _sensible impression_\nmade by external objects on us, yet in forming our judgments of them\nwe are greatly at the mercy of circumstances, which either modify the\nimpressions actually received, or combine them with adjuncts which have\nbecome habitually associated with different judgments; and, therefore,\nthat, in estimating the degree of confidence we are to place in our\nconclusions, we must, of necessity, take into account these modifying\nor accompanying circumstances, whatever they may be. We do not, of\ncourse, here speak of deranged organization; such as, for instance,\na distortion of the eye, producing double vision, and still less of\nmental delusion, which absolutely perverts the meaning of sensible\nimpressions.\n\n(74.) As the mind exists not in the place of sensible objects, and\nis not brought into immediate relation with them, we can only regard\nsensible impressions as signals conveyed from them by a wonderful, and,\nto us, inexplicable mechanism, to our minds, which receives and reviews\nthem, and, by habit and association, connects them with corresponding\nqualities or affections in the objects; just as a person writing down\nand comparing the signals of a telegraph might interpret their meaning.\nAs, for instance, if he had constantly observed that the exhibition of\na certain signal was sure to be followed next day by the announcement\nof the arrival of a ship at Portsmouth, he would connect the two facts\nby a link of the very same nature with that which connects the notion\nof a large wooden building, filled with sailors, with the impression of\nher outline on the retina of a spectator on the beach.\n\n(75.) In captain Head\u2019s amusing and vivid description of his journey\nacross the Pampas of South America occurs an anecdote quite in point.\nHis guide one day suddenly stopped him, and, pointing high into the\nair, cried out, \u201cA lion!\u201d Surprised at such an exclamation, accompanied\nwith such an act, he turned up his eyes, and with difficulty perceived,\nat an immeasurable height, a flight of condors soaring in circles in\na particular spot. Beneath that spot, far out of sight of himself or\nguide, lay the carcass of a horse, and over that carcass stood (as the\nguide well knew) the lion, whom the condors were eyeing with envy from\ntheir airy height. The signal of the birds was to him what the sight of\nthe lion alone could have been to the traveller, a full assurance of\nits existence.\n\n\n\n\nCHAP. II.\n\nOF THE ANALYSIS OF PHENOMENA\n\n\n(76.) _Phenomena_, then, or appearances, as the word is literally\nrendered, are the sensible results of processes and operations carried\non among external objects, or their constituent principles, of which\nthey are only signals, conveyed to our minds as aforesaid. Now, these\nprocesses themselves may be in many instances rendered _sensible_;\nthat is to say, analysed, and shown to consist in the motions or other\naffections of sensible objects themselves. For instance, the phenomenon\nof the sound produced by a musical string, or a bell, when struck,\nmay be shown to be the result of a process consisting in the rapid\nvibratory motion of its parts communicated to the air, and thence to\nour ears; though the immediate effect on our organs of hearing does\nnot excite the least idea of such a motion. On the other hand, there\nare innumerable instances of sensible impressions which (at least\nat present) we are incapable of tracing beyond the mere sensation;\nfor example, in the sensations of bitterness, sweetness, &c. These,\naccordingly, if we were inclined to form hasty decisions, might be\nregarded as ultimate qualities; but the instance of sounds, just\nadduced, alone would teach us caution in such decisions, and incline\nus to believe them mere results of some secret process going on in\nour organs of taste, which is too subtle for us to trace. A simple\nexperiment will serve to set this in a clearer light. A solution of\nthe salt called by chemists _nitrate of silver_, and another of the\n_hyposulphite of soda_, have each of them separately, when taken into\nthe mouth, a disgustingly bitter taste; but if they be mixed, or if\none be tasted before the mouth is thoroughly cleared of the other,\nthe sensible impression is that of intense sweetness. Again, the salt\ncalled _tungstate of soda_ when first tasted is sweet, but speedily\nchanges to an intense and pure bitter, like quassia.[29]\n\n(77.) How far we may ever be enabled to attain a knowledge of the\nultimate and inward processes of nature in the production of phenomena,\nwe have no means of knowing; but, to judge from the degree of obscurity\nwhich hangs about the only case in which we feel within ourselves\na _direct_ power to produce any one, there seems no great hope of\npenetrating so far. The case alluded to is the production of motion by\nthe exertion of force. We are conscious of a power to move our limbs,\nand by their intervention other bodies; and that this effect is the\nresult of a certain inexplicable process which we are aware of, but\ncan no way describe in words, by which we exert _force_. And even when\nsuch exertion produces no visible effect, (as when we press our two\nhands violently together, so as just to oppose each other\u2019s effort,) we\nstill perceive, by the fatigue and exhaustion, and by the impossibility\nof maintaining the effort long, that something is going on within us,\nof which the mind is the agent, and the will the determining cause.\nThis impression which we receive of the nature of force, from our own\neffort and our sense of fatigue, is quite different from that which\nwe obtain of it from seeing the effect of force exerted by others in\nproducing _motion_. Were there no such thing as motion, had we been\nfrom infancy shut up in a dark dungeon, and every limb encrusted with\nplaster, this internal consciousness would give us a complete idea\nof _force_; but when set at liberty, habit alone would enable us to\nrecognize its exertion by its _signal_, motion, and _that_ only by\nfinding that the same action of the mind which in our confined state\nenables us to fatigue and exhaust ourselves by the tension of our\nmuscles, puts it in our power, when at liberty, to move ourselves and\nother bodies. But how obscure is our knowledge of the process going on\nwithin us in the exercise of this important privilege, in virtue of\nwhich alone we act as direct _causes_, we may judge from this, that\nwhen we put any limb in motion, the seat of the exertion seems to us to\nbe _in_ the limb, whereas it is demonstrably no such thing, but either\nin the brain or in the spinal marrow; the proof of which is, that if a\nlittle fibre, called a nerve, which forms a communication between the\nlimb and the brain, or spine, be divided in any part of its course,\nhowever we may make the effort, the limb will not move.\n\n(78.) This one instance of the obscurity which hangs about the only act\nof direct _causation_ of which we have an immediate consciousness, will\nsuffice to show how little prospect there is that, in our investigation\nof nature, we shall ever be able to arrive at a knowledge of ultimate\ncauses, and will teach us to limit our views to that of _laws_, and\nto the analysis of complex phenomena by which they are resolved into\nsimpler ones, which, appearing to us incapable of further analysis, we\nmust consent to regard as causes. Nor let any one complain of this as a\nlimitation of his faculties. We have here \u201cample room and verge enough\u201d\nfor the full exercise of all the powers we possess; and, besides, it\ndoes so happen, that we are actually able to trace up a very large\nportion of the phenomena of the universe to this one _cause_, viz. the\nexertion of mechanical _force_; indeed, so large a portion, that it has\nbeen made a matter of speculation whether this is not the only one that\nis capable of acting on material beings.\n\n(79.) What we mean by the analysis of complex phenomena into simpler\nones, will best be understood by an instance. Let us, therefore,\ntake the phenomenon of sound, and, by considering the various cases\nin which sounds of all kinds are produced, we shall find that they\nall agree in these points:--1st, The excitement of a motion in the\nsounding body. 2dly, The communication of this motion to the air or\nother intermedium which is interposed between the sounding body and our\nears. 3dly, The propagation of such motion from particle to particle\nof such intermedium in due succession. 4thly, Its communication, from\nthe particles of the intermedium adjacent to the ear, to the ear\nitself. 5thly, Its conveyance in the ear, by a certain mechanism, to\nthe auditory nerves. 6thly, The excitement of sensation. Now, in this\nanalysis, we perceive that two principal matters must be understood,\nbefore we can have a true and complete knowledge of sound:--1st,\nThe excitement and propagation of motion. 2dly, The production of\nsensation. These, then, are two other phenomena, of a simpler, or, it\nwould be more correct to say, of a more general or elementary order,\ninto which the complex phenomenon of sound resolves itself. But again,\nif we consider the communication of motion from body to body, or from\none part to another of the same, we shall perceive that it is again\nresolvable into several other phenomena. 1st, The original setting in\nmotion of a material body, or any part of one. 2dly, The behaviour of\na particle set in motion, when it meets another lying in its way, or\nis otherwise impeded or influenced by its connection with surrounding\nparticles. 3dly, The behaviour of the particles so impeding or\ninfluencing it under such circumstances; besides which, the last two\npoint out another phenomenon, which it is necessary also to consider,\nviz. the phenomenon of the connection of the parts of material bodies\nin masses, by which they form aggregates, and are enabled to influence\neach other\u2019s motions.\n\n(80.) Thus, then, we see that an analysis of the phenomenon of sound\nleads to the enquiry, 1st, of two _causes_, viz. the cause of motion,\nand the cause of sensation, these being phenomena which (at least as\nhuman knowledge stands at present) we are unable to analyse further;\nand, therefore, we set them down as simple, elementary, and referable,\nfor any thing we can see to the contrary, to the immediate action of\ntheir causes. 2dly, Of several questions relating to the connection\nbetween the motion of material bodies and its cause, such as, _What\nwill happen_ when a moving body is surrounded on all sides by others\nnot in motion? _What will happen_ when a body not in motion is advanced\nupon by a moving one? It is evident that the answers to such questions\nas these can be no other than _laws of motion_, in the sense we have\nabove attributed to laws of nature, viz. a statement in words of what\nwill happen in such and such proposed general contingencies. Lastly,\nwe are led, by pursuing the analysis, and considering the phenomenon\nof the aggregation of the parts of material bodies, and the way in\nwhich they influence each other, to two other general phenomena, viz.,\nthe cohesion and elasticity of matter; and these we have no means\nof analysing further, and must, therefore, regard them (till we see\nreasons to the contrary) as _ultimate phenomena_, and referable to the\ndirect action of causes, viz. an attractive and a repulsive _force_.\n\n(81.) Of force, as counterbalanced by opposing force, we have, as\nalready said, an internal consciousness; and though it may seem strange\nto us that matter should be capable of exerting on matter the same kind\nof effort, which, judging alone from this consciousness, we might be\nled to regard as a mental one; yet we cannot refuse the direct evidence\nof our senses, which shows us that when we keep a spring stretched with\none hand, we feel our effort opposed exactly in the same way as if we\nhad ourselves opposed it with the other hand, or as it would be by\nthat of another person. The enquiry, therefore, into the aggregation\nof matter resolves itself into the general question, What will be the\nbehaviour of material particles under the mutual action of opposing\nforces capable of counterbalancing each other? and the answer to\nthis question can be no other than the announcement of the _law_ of\nequilibrium, whatever law that may be.\n\n(82.) With regard to the cause of sensation, it must be regarded as\nmuch more obscure than that of motion, inasmuch as we have no conscious\nknowledge of it, _i.\u00a0e._ we have no power, by any act of our minds\nand will, to call up a sensation. It is true, we are not destitute\nof an approach to it, since, by an effort of memory and imagination,\nwe can produce in our minds an impression, or idea, of a sensation\nwhich, in peculiar cases, may even approach in vividness to actual\nreality. In dreams, too, and, in some cases of disordered nerves, we\nhave sensations without objects. But if force, as a cause of motion,\nis obscure to us, even while we are in the act of exercising it, how\nmuch more so is this other cause, whose exercise we can only imitate\nimperfectly by any voluntary act, and of whose purely internal action\nwe are only fully conscious when in a state that incapacitates us from\nreasoning, and almost from observation!\n\n(83.) Dismissing, then, as beyond our reach, the enquiry into causes,\nwe must be content at present to concentrate our attention on the laws\nwhich prevail among phenomena, and which seem to be their immediate\nresults. From the instance we have just given, we may perceive that\nevery enquiry into the intimate nature of a complex phenomenon\nbranches out into as many different and distinct enquiries as there\nare simple or elementary phenomena into which it may be analysed; and\nthat, therefore, it would greatly assist us in our study of nature, if\nwe could, by any means, ascertain what _are_ the ultimate phenomena\ninto which all the composite ones presented by it may be resolved.\nThere is, however, clearly no way by which this can be ascertained _\u00e0\npriori_. We must go to nature itself, and be guided by the same kind\nof rule as the chemist in his analysis, who accounts every ingredient\nan _element_ till it can be decompounded and resolved into others. So,\nin natural philosophy, we must account every phenomenon an elementary\nor simple one till we can analyse it, and show that it is the result\nof others, which in their turn become elementary. Thus, in a modified\nand relative sense, we may still continue to speak of causes, not\nintending thereby those ultimate principles of action on whose exertion\nthe whole frame of nature depends, but of those proximate links which\nconnect phenomena with others of a simpler, higher, and more general or\nelementary kind. For example: we may regard the vibration of a musical\nstring as the proximate cause of the sound it yields, receiving it,\nso far, as an ultimate fact, and waving or deferring enquiry into the\ncause of vibrations, which is of a higher and more general nature.\n\n(84.) Moreover, as in chemistry we are sometimes compelled to\nacknowledge the existence of elements different from those already\nidentified and known, though we cannot insulate them, and to perceive\nthat substances have the characters of compounds, and must therefore\nbe susceptible of analysis, though we do not see how it is to be set\nabout; so, in physics, we may perceive the complexity of a phenomenon,\nwithout being able to perform its analysis. For example: in magnetism,\nthe agency of electricity is clearly made out, and they are shown to\nstand to one another in the relation of effect and cause. But the\nanalysis of magnetism, in its relation to particular metals, is not\nyet quite satisfactorily performed; and we are compelled to admit\nthe existence of some cause, whether proximate or ultimate, whose\npresence in different metals, or in different states of the same metal,\ndetermines that peculiar electric condition which constitutes permanent\nmagnetism. Cases like these, of all which science presents, offer the\nhighest interest. They excite enquiry, like the near approach to the\nsolution of an enigma; they show us that there is light, could only a\ncertain veil be drawn aside.\n\n(85.) In pursuing the analysis of any phenomenon, the moment we find\nourselves stopped by one of which we perceive no analysis, and which,\ntherefore, we are forced to refer (at least provisionally) to the\nclass of ultimate facts, and to regard as elementary, the study of\nthat phenomenon and of its laws becomes a separate branch of science.\nIf we encounter the same elementary phenomenon in the analysis of\nseveral composite ones, it becomes still more interesting, and assumes\nadditional importance; while at the same time we acquire information\nrespecting the phenomenon itself, by observing those with which it\nis habitually associated, that may help us at length to its analysis.\nIt is thus that sciences increase, and acquire a mutual relation and\ndependency. It is thus, too, that we are at length enabled to trace\nparallels and analogies between great branches of science themselves,\nwhich at length terminate in a perception of their dependence on some\ncommon phenomenon of a more general and elementary nature than that\nwhich form the subject of either separately. It was thus, for example,\nthat, previous to O\u00ebrsted\u2019s great discovery of electro-magnetism,\na general resemblance between the two sciences of electricity and\nmagnetism was recognised, and many of the chief phenomena in each were\nascertained to have their parallels, _mutatis mutandis_, in the other.\nIt was thus, too, that an analogy subsisting between sound and light\nhas been gradually traced into a closeness of agreement, which can\nhardly leave any reasonable doubt of their ultimate coincidence in one\ncommon phenomenon, the vibratory motion of an elastic medium. If it be\nallowed to pursue our illustration from chemistry, and to ground its\napplication not on what has been, but on what may one day be, done,\nit is thus that the general family resemblance between certain groups\nof bodies, now regarded as elementary, (as nickel and cobalt, for\ninstance, chlorine, iode, and brome,) will, perhaps, lead us hereafter\nto perceive relations between them of a more intimate kind than we can\nat present trace.\n\n(86.) On those phenomena which are most frequently encountered in\nan analysis of nature and which most decidedly resist further\ndecomposition, it is evident that the greatest pains and attention\nought to be bestowed, not only because they furnish a key to the\ngreatest number of enquiries, and serve to group and classify together\nthe greatest range of phenomena, but by reason of their higher nature,\nand because it is in these that we must look for the direct action of\ncauses, and the most extensive and general enunciation of the laws of\nnature. These, once discovered, place in our power the explanation of\nall particular facts, and become grounds of reasoning, independent of\nparticular trial: thus playing the same part in natural philosophy\nthat axioms do in geometry; containing, in a refined and condensed\nstate, and as it were in a quintessence, all that our reason has\noccasion to draw from experience to enable it to follow out the truths\nof physics by the mere application of logical argument. Indeed, the\naxioms of geometry themselves may be regarded as in some sort an appeal\nto experience, not corporeal, but mental. When we say, the whole is\ngreater than its part, we announce a general fact, which rests, it\nis true, on our ideas of whole and part; but, in abstracting these\nnotions, we begin by considering them as subsisting in space, and time,\nand body, and again, in linear, and superficial, and solid space.\nAgain, when we say, the equals of equals are equal, we mentally make\ncomparisons, in equal spaces, equal times, &c.; so that these axioms,\nhowever self-evident, are still general propositions so far of the\ninductive kind, that, independently of experience, they would not\npresent themselves to the mind.\n\nThe only difference between these and axioms obtained from extensive\ninduction is this, that, in raising the axioms of geometry, the\ninstances offer themselves spontaneously, and without the trouble of\nsearch, and are few and simple; in raising those of nature, they are\ninfinitely numerous, complicated, and remote; so that the most diligent\nresearch and the utmost acuteness are required to unravel their web,\nand place their meaning in evidence.\n\n(87.) By far the most general phenomenon with which we are acquainted,\nand that which occurs most constantly, in every enquiry into which we\nenter, is motion, and its communication. Dynamics, then, or the science\nof force and motion, is thus placed at the head of all the sciences;\nand, happily for human knowledge, it is one in which the highest\ncertainty is attainable, a certainty no way inferior to mathematical\ndemonstration. As its axioms are few, simple, and in the highest degree\ndistinct and definite, so they have at the same time an immediate\nrelation to geometrical quantity, space, time, and direction, and\nthus accommodate themselves with remarkable facility to geometrical\nreasoning. Accordingly, their consequences may be pursued, by arguments\npurely mathematical, to any extent, insomuch that the limit of our\nknowledge of dynamics is determined only by that of pure mathematics,\nwhich is the case in no other branch of physical science.\n\n(88.) But, it will now be asked, how we are to proceed to analyse a\ncomposite phenomenon into simpler ones, and whether any general rules\ncan be given for this important process? We answer, None; any more\nthan (to pursue the illustration we have already had recourse to)\ngeneral rules can be laid down by the chemist for the analysis of\nsubstances of which all the ingredients are unknown. Such rules, could\nthey be discovered, would include the whole of natural science; but\nwe are very far, indeed, from being able to propound them. However,\nwe are to recollect that the analysis of phenomena, philosophically\nspeaking, is principally useful, as it enables us to recognize, and\nmark for special investigation, those which appear to us simple; to\nset methodically about determining their laws, and thus to facilitate\nthe work of raising up general axioms, or forms of words, which shall\ninclude the whole of them; which shall, as it were, transplant them\nout of the external into the intellectual world, render them creatures\nof pure thought, and enable us to reason them out _\u00e0 priori_. And what\nrenders the power of doing this so eminently desirable is, that, in\nthus reasoning back from generals to particulars, the propositions\nat which we arrive apply to an immense multitude of combinations and\ncases, which were never individually contemplated in the mental process\nby which our axioms were first discovered; and that, consequently, when\nour reasonings are pushed to the utmost limit of particularity, their\nresults appear in the form of _individual facts_, of which we might\nhave had no knowledge from immediate experience; and thus we are not\nonly furnished with the explanation of all known facts, but with the\nactual discovery of such as were before unknown. A remarkable example\nof this has already been mentioned in Fresnel\u2019s _\u00e0 priori_ discovery\nof the extraordinary refraction of both rays in a doubly refracting\nmedium. To give another example:--The law of gravitation is a physical\naxiom of a very high and universal kind, and has been raised by a\nsuccession of inductions and abstractions drawn from the observation\nof numerous facts and subordinate laws in the planetary system. When\nthis law is taken for granted, and laid down as a basis of reasoning,\nand applied to the actual condition of our own planet, one of the\nconsequences to which it leads is, that the earth, instead of being an\nexact sphere, must be compressed or flattened in the direction of its\npolar diameter, the one diameter being about thirty miles shorter than\nthe other; and this conclusion, deduced at first by mere reasoning, has\nbeen since found to be true in fact. All astronomical predictions are\nexamples of the same thing.\n\n(89.) In the important business of raising these axioms of nature, we\nare not, as in the analysis of phenomena, left wholly without a guide.\nThe nature of abstract or general reasoning points out in a great\nmeasure the course we must pursue. A law of nature, being the statement\nof what will happen in certain general contingencies, may be regarded\nas the announcement, in the same words, of a whole group or class of\nphenomena. Whenever, therefore, we perceive that two or more phenomena\nagree in so many or so remarkable points, as to lead us to regard\nthem as forming a class or group, if we lay out of consideration, or\n_abstract_, all the circumstances in which they disagree, and retain in\nour minds those only in which they agree, and then, under this kind of\nmental convention, frame a definition or statement of one of them, in\nsuch words that it shall apply equally to them all, such statement will\nappear in the form of a general proposition, having so far at least the\ncharacter of a law of nature.\n\n(90.) For example: a great number of transparent substances, when\nexposed, in a certain particular manner, to a beam of light which has\nbeen prepared by undergoing certain reflexions or refractions, (and has\nthereby acquired peculiar properties, and is said to be \u201c_polarized_,\u201d)\nexhibit very vivid and beautiful colours, disposed in streaks, bands,\n&c. of great regularity, which seem to arise within the substance, and\nwhich, from a certain regular succession observed in their appearance,\nare called \u201cperiodical colours.\u201d Among the substances which exhibit\nthese periodical colours occur a great variety of transparent solids,\nbut no fluids and no opake solids. Here, then, there seems to be\nsufficient community of nature to enable us to use a general term, and\nto state the proposition as a law, viz. _transparent solids_ exhibit\nperiodical colours by exposure to polarized light. However, this,\nthough true of many, does not apply to _all_ transparent solids, and\ntherefore we cannot state it as a general truth or law of nature in\nthis form; although the reverse proposition, that all solids which\nexhibit such colours in such circumstances are _transparent_, would\nbe correct and general. It becomes necessary, then, to make a list of\nthose to which it does apply; and thus a great number of substances of\nall kinds become grouped together, in a class linked by this common\nproperty. If we examine the individuals of this group, we find among\nthem the utmost variety of colour, texture, weight, hardness, form and\ncomposition; so that, in these respects, we seem to have fallen upon\nan assemblage of contraries. But when we come to examine them closely,\nin all their properties, we find they have all one point of agreement,\nin the property of double refraction, (see page 30.) and therefore we\nmay describe them all truly as _doubly refracting substances_. We may,\ntherefore, state the fact in the form, \u201cDoubly refracting substances\nexhibit periodical colours by exposure to polarized light;\u201d and in\nthis form it is found, on further examination, to be true, not only\nfor those particular instances which we had in view when we first\npropounded it, but in all cases which have since occurred on further\nenquiry, without a single exception; so that the proposition is\ngeneral, and entitled to be regarded as a law of nature.\n\n(91.) We may therefore regard a law of nature either, 1st, as a general\nproposition, announcing, in abstract terms, a whole group of particular\nfacts relating to the behaviour of natural agents in proposed\ncircumstances; or, 2dly, as a proposition announcing that a whole\nclass of individuals agreeing in one character agree also in another.\nFor example: in the case before us, the law arrived at includes, in\nits general announcement, among others, the particular facts, that\nrock crystal and saltpetre exhibit periodical colours; for these are\nboth of them doubly refracting substances. Or, it may be regarded as\nannouncing a relation between the two phenomena of double refraction,\nand the exhibition of periodical colours; which in the actual case is\none of the most important, viz. the relation of _constant association_,\ninasmuch as it asserts that in whatever individual the one character is\nfound, the other will invariably be found also.\n\n(92.) These two lights, in which the announcement of a general law may\nbe regarded, though at bottom they come to the same thing, yet differ\nwidely in their influence on our minds. The former exhibits a law as\nlittle more than a kind of artificial memory; but in the latter it\nbecomes a step in philosophical investigation, leading directly to\nthe consideration of a proximate, if not an ultimate, cause; inasmuch\nas, whenever two phenomena are observed to be invariably connected\ntogether, we conclude them to be related to each other, either as cause\nand effect, or as common effects of a single cause.\n\n(93.) There is still another light in which we may regard a law of\nthe kind in question, viz. as a proposition asserting the mutual\nconnection, or in some cases the entire identity, of two classes of\nindividuals (whether individual objects or individual facts); and this\nis, perhaps, the simplest and most instructive way in which it can be\nconceived, and that which furnishes the readiest handle to further\ngeneralization in the raising of yet higher axioms. For example: in\nthe case above mentioned, if observation had enabled us to establish\nthe existence of a class of bodies possessing the property of double\nrefraction, and observations of another kind had, independently of the\nformer, led as to recognize a class possessing that of the exhibition\nof periodical colours in polarized light, a mere comparison of lists\nwould at once demonstrate the identity of the two classes, or enable us\nto ascertain whether one was or was not included in the other.\n\n(94.) It is thus we perceive the high importance in physical science of\njust and accurate classifications of particular facts, or individual\nobjects, under general well considered heads or points of agreement\n(for which there are none better adapted than the simple phenomena\nthemselves into which they can be analysed in the first instance); for\nby so doing each of such phenomena, or heads of classification, becomes\nnot a particular but a general fact; and when we have amassed a great\nstore of such _general facts_, they become the objects of another and\nhigher species of classification, and are themselves included in laws\nwhich, as they dispose of groups, not individuals, have a far superior\ndegree of generality, till at length, by continuing the process, we\narrive at _axioms_ of the highest degree of generality of which science\nis capable.\n\n(95.) This process is what we mean by induction; and, from what\nhas been said, it appears that induction may be carried on in two\ndifferent ways,--either by the simple juxta-position and comparison of\nascertained classes, and marking their agreements and disagreements;\nor by considering the individuals of a class, and casting about, as\nit were to find in what particular they all agree, besides that which\nserves as their principle of classification. Either of these methods\nmay be put in practice as one or the other may afford facilities in\nany case; but it will naturally happen that, where facts are numerous,\nwell observed, and methodically arranged, the former will be more\napplicable than in the contrary case: the one is better adapted to the\nmaturity, the other to the infancy, of science: the one employs, as an\nengine, the division of labour; the other mainly relies on individual\npenetration, and requires a union of many branches of knowledge in one\nperson.\n\n\n\n\nCHAP. III.\n\nOF THE STATE OF PHYSICAL SCIENCE IN GENERAL, PREVIOUS TO THE AGE OF\nGALILEO AND BACON.\n\n\n(96.) It is to our immortal countryman Bacon that we owe the broad\nannouncement of this grand and fertile principle; and the developement\nof the idea, that the whole of natural philosophy consists entirely\nof a series of inductive generalizations, commencing with the most\ncircumstantially stated particulars, and carried up to universal laws,\nor axioms, which comprehend in their statements every subordinate\ndegree of generality, and of a corresponding series of inverted\nreasoning from generals to particulars, by which these axioms are\ntraced back into their remotest consequences, and all particular\npropositions deduced from them; as well those by whose immediate\nconsideration we rose to their discovery, as those of which we had\nno previous knowledge. In the course of this descent to particulars,\nwe must of necessity encounter all those facts on which the arts and\nworks that tend to the accommodation of human life depend, and acquire\nthereby the command of an unlimited practice, and a disposal of the\npowers of nature co-extensive with those powers themselves. A noble\npromise, indeed, and one which ought, surely, to animate us to the\nhighest exertion of our faculties; especially since we have already\nsuch convincing proof that it is neither vain nor rash, but, on the\ncontrary, has been, and continues to be, fulfilled, with a promptness\nand liberality which even its illustrious author in his most sanguine\nmood would have hardly ventured to anticipate.\n\n(97.) Previous to the publication of the Novum Organum of Bacon,\nnatural philosophy, in any legitimate and extensive sense of the word,\ncould hardly be said to exist. Among the Greek philosophers, of whose\nattainments in science alone, in the earlier ages of the world, we\nhave any positive knowledge, and that but a very limited one, we are\nstruck with the remarkable contrast between their powers of acute and\nsubtle disputation, their extraordinary success in abstract reasoning,\nand their intimate familiarity with subjects purely intellectual,\non the one hand; and, on the other, with their loose and careless\nconsideration of external nature, their grossly illogical deductions of\nprinciples of sweeping generality from few and ill-observed facts, in\nsome cases; and their reckless assumption of abstract principles having\nno foundation but in their own imaginations, in others; mere forms of\nwords, with nothing corresponding to them in nature, from which, as\nfrom mathematical definitions, postulates, and axioms, they imagined\nthat all phenomena could be derived, all the laws of nature deduced.\nThus, for instance, having settled it in their own minds, that a\ncircle is the most perfect of figures, they concluded, of course, that\nthe movements of the heavenly bodies must all be performed in exact\ncircles, and with uniform motions; and when the plainest observation\ndemonstrated the contrary, instead of doubting the principle, they saw\nno better way of getting out of the difficulty than by having recourse\nto endless combinations of circular motions to preserve their ideal\nperfection.\n\n(98.) Undoubtedly among the Greek philosophers were many men of\ntranscendent talents and virtues, the ornaments of their species,\nand justly entitled to the veneration of all posterity; but regarded\nas a body they can hardly be considered otherwise than as a knot of\ndisputatious candidates for popular favour, too busy in maintaining\ntheir ascendency over their followers and admirers, by an ostentatious\ndisplay of superior knowledge, to have the leisure (had they always the\ninclination) to base their pretensions on a deep and sure foundation,\nand yet too sensible of the disgrace and inconvenience of failure,\nnot to defend their dogmas, however shallow, when once promulgated,\nagainst their keen and sagacious opponents, by every art of sophism\nor appeal to passion. Hence the crudities and chimerical views with\nwhich their systems of philosophy, both natural and moral, were\noverloaded; their endless disputes about verbal subtleties, and, last\nand worst, the proud assumption with which they sheltered ignorance\nand indolence under the screen of unintelligible jargon or dogmatical\nassertion. Perhaps, however, this character applies rather to the\nlater than to the earlier of the Greek philosophers. The spirit of\nrational enquiry into nature seems, if we can judge from the uncertain\nand often contradictory notices handed down to us of their tenets, to\nhave been far more alive, and less warped by this vain and arrogant\nturn, then than at a later period. We know not now what was the\nprecise meaning attached by Thales to his opinion, that water was\nthe origin of all things; but modern geologists will not be at a loss\nto conceive how an observant traveller might become impressed with\nthis notion, without having recourse to the mystic records of Egypt\nor Chaldea. His ideas of eclipses and of the nature of the moon were\nsound; and his prediction of an eclipse of the sun, in particular,\nwas attended with circumstances so remarkable as to have made it a\nmatter of important investigation to modern astronomers. Anaxagoras,\namong a number of crude and imperfectly explained notions, speculated\nrationally enough on the cause of the winds and of the rainbow, and\nless absurdly on earthquakes than many modern geologists have done, and\nappears generally to have had his attention alive to nature, and his\nmind open to just reasoning on its phenomena; while Pythagoras, whether\nhe reasoned it out for himself, or borrowed the notion from Egypt or\nIndia, had attained a just conception of the general disposition of\nthe parts of the solar system, and the place held by the earth in it;\nnay, according to some accounts, had even raised his views so far as to\nspeculate on the attraction of the sun as the bond of its union.\n\n(99.) But the successors of these _bon\u00e2 fide_ enquirers into nature\ndebased the standard of truth; and, taking advantage of the credit\njustly attached to their discoveries, renounced the modest character\nof learners, and erected themselves into teachers, and, to maintain\ntheir pretensions to this character, adopted the tone of men who had\nnothing further to learn. Unfortunately for true science, the national\ncharacter gave every encouragement to pretensions of this kind. That\nrestless craving after novelty, which distinguished the Greeks in their\ncivil and political relations, pursued them into their philosophy.\nWhatever speculations were only ingenious and new had irresistible\ncharms; and the teacher who could embody a clever thought in elegant\nlanguage, or at once save his followers and himself the trouble of\nthinking or reasoning, by bold assertion, was too often induced to\nacquire cheaply the reputation of superior knowledge, snatch a few\nsuperficial notions from the most ordinary and obvious facts, envelope\nthem in a parade of abstruse words, declare them the primary and\nultimate principles of all things, and denounce as absurd and impious\nall opinions opposed to his own.\n\n(100.) In this war of words the study of nature was neglected, and\nan humble and patient enquiry after facts altogether despised, as\nunworthy of the high _priori_ ground a true philosopher ought to take.\nIt was the radical error of the Greek philosophy to imagine that the\nsame method which proved so eminently successful in mathematical,\nwould be equally so in physical, enquiries, and that, by setting out\nfrom a few simple and almost self-evident notions, or _axioms_, every\nthing could be reasoned out. Accordingly, we find them constantly\nstraining their invention to discover these principles, which were to\nprove so pregnant. One makes _fire_ the essential matter and origin\nof the universe; another, _air_; a third, discovers the key to every\ndifficulty, and the explanation of all phenomena, in the \u201c\u03c4\u03bf \u03b1\u03c0\u03b5\u03b9\u03c1\u03bf\u03bd\u201d\nor infinitude of things; a fourth, in the \u03c4\u03bf \u1f41\u03bd and the \u03c4\u03bf \u03bc\u03b7 \u1f41\u03bd, that\nis to say, in entity and nonentity;--till at length an authority,\nwhich was destined to command opinions for nearly two thousand years,\nsettled this important point, by deciding, that _matter_, _form_, and\n_privation_, were to be considered the principles of all things.\n\n(101.) It were to do injustice to Aristotle, however, to judge of him\nby _such_ a sample of his philosophy. He, at least, saw the necessity\nof having recourse to nature for something like principles of physical\nscience; and, as an observer, a collector and recorder of facts and\nphenomena, stood without an equal in his age. It was the fault of that\nage, and of the perverse and flimsy style of verbal disputation which\nhad infected all learning, rather than his own, that he allowed himself\nto be contented with vague and loose notions drawn from general and\nvulgar observation, in place of seeking carefully, in well arranged\nand thoroughly considered instances, for the true laws of nature. His\nvoluminous works, on every department of human knowledge existing in\nhis time, have nearly all perished. From his work on animals, which\nhas descended to us, we are, however, enabled to appreciate his powers\nof observation; and a parallel drawn by an eminent Oxford professor\nbetween his classifications and those of the most illustrious of\nliving naturalists, shows him to have attained a view of animated\nnature in a remarkable degree comprehensive, and which contrasts\nstrikingly with the confusion, vagueness, and assumption of his\nphysical opinions and dogmas. In these it is easy to recognize a mind\nnot at home, and an impression of the necessity of saying something\nlearned and systematic, without knowing what to say. Thus he divides\nmotions into natural and unnatural; the natural motion of fire and\nlight bodies being upwards, those of heavy downwards, each seeking its\nkindred nature in the heavens and the earth. Thus, too, the immediate\nimpressions made on us by external objects, such as hardness, colour,\nheat, &c. are referred at once, in the Aristotelian philosophy, to\noccult qualities, in virtue of which they are as they are, and beyond\nwhich it is useless to enquire.[30] Of course there will occur a limit\nbeyond which it _is_ useless for merely human faculties to enquire; but\nwhere that limit is placed, experience alone can teach us; and at least\nto assert that we _have_ attained it, is now universally recognized as\nthe sure criterion of dogmatism.\n\n(102.) In the early ages of the church the writings of Aristotle were\ncondemned, as allowing too much to reason and sense; and even so late\nas the twelfth century they were sought out and burned, and their\nreaders excommunicated. By degrees, however, the extreme injustice\nof this impeachment of their character was acknowledged: they became\nthe favourite study of the schoolmen, and furnished the keenest\nweapons of their controversy, being appealed to in all disputes as of\nsovereign authority; so that the slightest dissent from any opinion\nof the \u201cgreat master,\u201d however absurd or unintelligible, was at once\ndrowned by clamour, or silenced by the still more effectual argument of\nbitter persecution. If the logic of that gloomy period could be justly\ndescribed as \u201cthe art of talking unintelligibly on matters of which we\nare ignorant,\u201d its physics might, with equal truth, be summed up in a\ndeliberate preference of ignorance to knowledge, in matters of every\nday\u2019s experience and use.\n\n(103.) In \u201cthis opake of nature and of soul,\u201d the perverse activity of\nthe alchemists from time to time struck out a doubtful spark[31]; and\nour illustrious countryman, Roger Bacon, shone out at the obscurest\nmoment, like an early star predicting dawn. It was not, however, till\nthe sixteenth century that the light of nature began to break forth\nwith a regular and progressive increase. The vaunts of Paracelsus\nof the power of his chemical remedies and elixirs, and his open\ncondemnation of the ancient pharmacy, backed as they were by many\nsurprising cures, convinced all rational physicians that chemistry\ncould furnish many excellent remedies, unknown till that time[32], and\na number of valuable experiments began to be made by physicians and\nchemists, desirous of discovering and describing new chemical remedies.\nThe chemical and metallurgic arts, exercised by persons empirically\nacquainted with their secrets, began to be seriously studied with a\nview to the acquisition of rational and useful knowledge, and regular\ntreatises on branches of natural science at length to appear. George\nAgricola, in particular, devoted himself with ardour to the study\nof mineralogy and metallurgy in the mining districts of Bohemia and\nSchemnitz, and published copious and methodical accounts of all\nthe facts within his knowledge: and our countryman, Dr. Gilbert of\nColchester, in 1590, published a treatise on magnetism, full of\nvaluable facts and experiments, ingeniously reasoned on; and he\nlikewise extended his enquiries to a variety of other subjects, in\nparticular to electricity.\n\n(104.) But, as the decisive mark of a great commencing change in the\ndirection of the human faculties, astronomy, the only science in which\nthe ancients had made any real progress, and ascended to any thing like\nlarge and general conceptions, began once more to be studied in the\nbest spirit of a candid philosophy; and the Copernican or Pythagorean\nsystem arose or revived, and rapidly gained advocates. Galileo at\nlength appeared, and openly attacked and refuted the Aristotelian\ndogmas respecting motion, by direct appeal to the evidence of sense,\nand by experiments of the most convincing kind. The persecutions\nwhich such a step drew upon him, the record of his perseverance and\nsufferings, and the ultimate triumph of his opinions and reasonings,\nhave been too lately and too well related[33] to require repetition\nhere.\n\n(105.) By the discoveries of Copernicus, Kepler, and Galileo, the\nerrors of the Aristotelian philosophy were effectually overturned on a\nplain appeal to the facts of nature; but it remained to show on broad\nand general principles, how and why Aristotle was in the wrong; to set\nin evidence the peculiar weakness of his method of philosophizing,\nand to substitute in its place a stronger and better. This important\ntask was executed by Francis Bacon, Lord Verulam, who will, therefore,\njustly be looked upon in all future ages as the great reformer of\nphilosophy, though his own actual contributions to the stock of\nphysical truths were small, and his ideas of particular points strongly\ntinctured with mistakes and errors, which were the fault rather of the\ngeneral want of physical information of the age than of any narrowness\nof view on his own part; and of this he was fully aware. It has been\nattempted by some to lessen the merit of this great achievement, by\nshowing that the inductive method had been practised in many instances,\nboth ancient and modern, by the mere instinct of mankind; but it is not\nthe introduction of inductive reasoning, as a new and hitherto untried\nprocess, which characterizes the Baconian philosophy, but his keen\nperception, and his broad and spirit-stirring, almost enthusiastic,\nannouncement of its paramount importance, as the alpha and omega of\nscience, as the grand and only chain for the linking together of\nphysical truths, and the eventual key to every discovery and every\napplication. Those who would deny him his just glory on such grounds\nwould refuse to Jenner or to Howard their civic crowns, because a few\nfarmers in a remote province had, time out of mind, been acquainted\nwith vaccination, or philanthropists, in all ages, had occasionally\nvisited the prisoner in his dungeon.\n\n(106.) An immense impulse was now given to science, and it seemed as\nif the genius of mankind, long pent up, had at length rushed eagerly\nupon Nature, and commenced, with one accord, the great work of\nturning up her hitherto unbroken soil, and exposing the treasures\nso long concealed. A general sense now prevailed of the poverty and\ninsufficiency of existing knowledge in _matters of fact_; and, as\ninformation flowed fast in, an era of excitement and wonder commenced,\nto which the annals of mankind had furnished nothing similar. It\nseemed, too, as if Nature herself seconded the impulse; and, while\nshe supplied new and extraordinary aids to those senses which were\nhenceforth to be exercised in her investigation,--while the telescope\nand the microscope laid open _the infinite_ in both directions,--as\nif to call attention to her wonders, and signalize the epoch, she\ndisplayed the rarest, the most splendid and mysterious, of all\nastronomical phenomena, the appearance and subsequent total extinction\nof a new and brilliant fixed star twice within the lifetime of Galileo\nhimself.[34]\n\n(107.) The immediate followers of Bacon and Galileo ransacked all\nnature for new and surprising facts, with something of that craving\nfor the marvellous, which might be regarded as a remnant of the age of\nalchemy and natural magic, but which, under proper regulation, is a\nmost powerful and useful stimulus to experimental enquiry. Boyle, in\nparticular, seemed animated by an enthusiasm of ardour, which hurried\nhim from subject to subject, and from experiment to experiment,\nwithout a moment\u2019s intermission, and with a sort of undistinguishing\nappetite; while Hooke (the great contemporary, and almost the worthy\nrival, of Newton) carried a keener eye of scrutinizing reason into a\nrange of research even yet more extensive. As facts multiplied, leading\nphenomena became prominent, laws began to emerge, and generalizations\nto commence; and so rapid was the career of discovery, so signal the\ntriumph of the inductive philosophy, that a single generation and the\nefforts of a single mind sufficed for the establishment of the system\nof the universe, on a basis never after to be shaken.\n\n(108.) We shall now endeavour to enumerate and explain in detail the\nprincipal steps by which legitimate and extensive inductions are\narrived at, and the processes by which the mind, in the investigation\nof natural laws, purges itself by successive degrees of the\nsuperfluities and incumbrances which hang about particulars, and\nobscure the perception of their points of resemblance and connection.\nWe shall state the helps which may be afforded us, in a work of so\nmuch thought and labour, by a methodical course of proceeding, and\nby a careful notice of those means which have at any time been found\nsuccessful, with a view to their better understanding and adaptation\nto other cases: a species of mental induction of no mean utility and\nextent in itself; inasmuch as by pursuing it alone we can attain a more\nintimate knowledge than we actually possess of the laws which regulate\nour discovery of truth, and of the rules, so far as they extend, to\nwhich invention is reducible. In doing this, we shall commence at the\nbeginning, with experience itself, considered as the accumulation of\nthe knowledge of individual objects and facts.\n\n\n\n\nCHAP. IV.\n\nOF THE OBSERVATION OF FACTS AND THE COLLECTION OF INSTANCES.\n\n\n(109.) Nature offers us two sorts of subjects of contemplation in the\nexternal world,--objects, and their mutual actions. But, after what\nhas been said on the subject of sensation, the reader will be at no\nloss to perceive that we know nothing of the objects themselves which\ncompose the universe, except through the medium of the impressions they\nexcite in us, which impressions are the results of certain actions and\nprocesses in which sensible objects and the material parts of ourselves\nare directly concerned. Thus, our observation of external nature is\nlimited to the mutual action of material objects on one another; and\nto facts, that is, the associations of phenomena or appearances. We\ngain no information by perceiving merely that an object is black; but\nif we also perceive it to be fluid, we at least acquire the knowledge\nthat blackness is not incompatible with fluidity, and have thus made\na step, however trifling, to a knowledge of the more intimate nature\nof these two qualities. Whenever, therefore, we would either analyse\na phenomenon into simpler ones, or ascertain what is the course or\nlaw of nature under any proposed general contingency, the first step\nis to accumulate a sufficient quantity of well ascertained facts or\nrecorded instances, bearing on the point in question. Common sense\ndictates this, as affording us the means of examining the same subject\nin several points of view; and it would also dictate, that the more\ndifferent these collected facts are in all other circumstances but that\nwhich forms the subject of enquiry, the better; because they are then\nin some sort brought into contrast with one another in their points of\ndisagreement, and thus tend to render those in which they agree more\nprominent and striking.\n\n(110.) The only facts which can ever become useful as grounds of\nphysical enquiry are those which happen uniformly and invariably\nunder the same circumstances. This is evident: for if they have\nnot this character they cannot be included in laws; they want that\nuniversality which fits them to enter as elementary particles into the\nconstitution of those universal axioms which we aim at discovering.\nIf one and the same result does not constantly happen under a given\ncombination of circumstances, apparently the same, one of two things\nmust be supposed,--caprice (_i.\u00a0e._ the arbitrary intervention of\nmental agency), or differences in the circumstances themselves,\nreally existing, but unobserved by us. In either case, though we may\nrecord such facts as curiosities, or as awaiting explanation when\nthe difference of circumstances shall be understood, we can make\nno use of them in scientific enquiry. Hence, whenever we notice a\nremarkable effect of any kind, our first question ought to be, Can it\nbe reproduced? What are the circumstances under which it has happened?\nAnd will it _always_ happen again if those circumstances, so far as we\nhave been able to collect them, co-exist?\n\n(111.) The circumstances, then, which accompany any observed fact, are\nmain features in its observation, at least until it is ascertained\nby sufficient experience what circumstances have nothing to do with\nit, and might therefore have been left unobserved without sacrificing\n_the fact_. In observing and recording a fact, therefore, altogether\nnew, we ought not to omit any circumstance capable of being noted,\nlest some one of the omitted circumstances should be essentially\nconnected with the fact, and its omission should, therefore, reduce\nthe implied statement of a _law of nature_ to the mere record of an\n_historical event_. For instance, in the fall of meteoric stones,\nflashes of fire are seen proceeding from a cloud, and a loud rattling\nnoise like thunder is heard. These circumstances, and the sudden stroke\nand destruction ensuing, long caused them to be confounded with an\neffect of lightning, and called thunderbolts. But one circumstance is\nenough to mark the difference: the flash and sound have been perceived\noccasionally to emanate from a _very small cloud_ insulated in _a clear\nsky_; a combination of circumstances which never happens in a thunder\nstorm, but which is undoubtedly intimately connected with their real\norigin.\n\n(112.) Recorded observation consists of two distinct parts: 1st, an\nexact notice of the thing observed, and of all the particulars which\nmay be supposed to have any natural connection with it; and, 2dly, a\ntrue and faithful record of them. As our senses are the only inlets\nby which we receive impressions of facts, we must take care, in\nobserving, to have them all in activity, and to let nothing escape\nnotice which affects any one of them. Thus, if lightning were to\nstrike the house we inhabit, we ought to notice what kind of light we\nsaw--whether a sheet of flame, a darting spark, or a broken zig-zag;\nin what direction moving, to what objects adhering, its colour, its\nduration, &c.; what sounds were heard--explosive, crashing, rattling,\nmomentary, or gradually increasing and fading, &c.; whether any smell\nof fire was perceptible, and if sulphureous, metallic, or such as\nwould arise merely from substances scorched by the flash, &c.; whether\nwe felt any shock, stroke, or peculiar sensation, or experienced any\nstrange taste in our mouths. Then, besides detailing the effects of the\nstroke, all the circumstances which might in any degree seem likely to\nattract, produce, or modify it, such as the presence of conductors,\nneighbouring objects, the state of the atmosphere, the barometer,\nthermometer, &c., and the disposition of the clouds, should be noted;\nand after all this particularity, the question _how_ the house _came\nto be struck?_ might ultimately depend on the fact that a flash of\nlightning twenty miles off passed at that particular moment _from\nthe ground to the clouds_, by an effect of what has been termed the\nreturning stroke.\n\n(113.) A writer in the Edinburgh Philosophical Journal[35] states\nhimself to have been led into a series of investigations on the\nchemical nature of a peculiar acid, by noticing, accidentally, a bitter\ntaste in a liquid about to be thrown away. Chemistry is full of such\nincidents.\n\n(114.) In transient phenomena, if the number of particulars be\ngreat, and the time to observe them short, we must consult our\nmemory before they have had time to fade, or refresh it by placing\nourselves as nearly as possible in the same circumstances again; go\nback to the spot, for instance, and try the words of our statement\nby appeal to all remaining indications, &c. This is most especially\nnecessary where we have not observed ourselves, but only collect and\nrecord the observations of others, particularly of illiterate or\nprejudiced persons, on any rare phenomenon, such as the passing of\na great meteor,--the fall of a stone from the sky,--the shock of an\nearthquake,--an extraordinary hailstorm, &c.\n\n(115.) In all cases which admit of numeration or measurement, it is of\nthe utmost consequence to obtain precise numerical statements, whether\nin the measure of time, space, or quantity of any kind. To omit this,\nis, in the first place, to expose ourselves to illusions of sense which\nmay lead to the grossest errors. Thus, in alpine countries, we are\nconstantly deceived in heights and distances; and when we have overcome\nthe first impression which leads us to under-estimate them, we are then\nhardly less apt to run into the opposite extreme. But it is not merely\nin preserving us from exaggerated impressions that numerical precision\nis desirable. It is the very soul of science; and its attainment\naffords the only criterion, or at least the best, of the truth of\ntheories, and the correctness of experiments. Thus, it was entirely\nto the omission of exact numerical determinations of quantity that the\nmistakes and confusion of the Stahlian chemistry were attributable,--a\nconfusion which dissipated like a morning mist as soon as precision,\nin this respect, came to be regarded as essential. Chemistry is in the\nmost pre-eminent degree a science of quantity; and to enumerate the\ndiscoveries which have arisen in it, from the mere determination of\nweights and measures, would be nearly to give a synopsis of this branch\nof knowledge. We need only mention the law of definite proportions,\nwhich fixes the composition of every body in nature in determinate\nproportional weights of its ingredients.\n\n(116.) Indeed, it is a character of all the higher laws of nature to\nassume the form of precise _quantitative_ statement. Thus, the law of\ngravitation, the most universal truth at which human reason has yet\narrived, expresses not merely the general fact of the mutual attraction\nof all matter; not merely the vague statement that its influence\ndecreases as the distance increases, but the exact numerical rate at\nwhich that decrease takes place; so that when its amount is known at\nany one distance it may be calculated exactly for any other. Thus, too,\nthe laws of crystallography, which limit the forms assumed by natural\nsubstances, when left to their own inherent powers of aggregation, to\nprecise geometrical figures, with fixed angles and proportions, have\nthe same essential character of strict mathematical expression, without\nwhich no exact particular conclusions could ever be drawn from them.\n\n(117.) But, to arrive at laws of this description, it is evident that\nevery step of our enquiry must be perfectly free from the slightest\ndegree of looseness and indecision, and carry with it the full force of\nstrict numerical announcement; and that, therefore, the observations\nthemselves on which all laws ultimately rest ought to have the same\nproperty. None of our senses, however, gives us direct information\nfor the exact comparison of quantity. Number, indeed, that is to\nsay, integer number, is an object of sense, because we can count;\nbut we can neither weigh, measure, nor form any precise estimate of\nfractional parts by the unassisted senses. Scarcely any man could tell\nthe difference between twenty pounds and the same weight increased or\ndiminished by a few ounces; still less could he judge of the proportion\nbetween an ounce of gold and a hundred grains of cotton by balancing\nthem in his hands. To take another instance: the eye is no judge of the\nproportion of different degrees of illumination, even when seen side\nby side; and if an interval elapses, and circumstances change, nothing\ncan be more vague than its judgments. When we gaze with admiration\nat the gorgeous spectacle of the golden clouds at sunset, which seem\ndrenched in light and glowing like flames of real fire, it is hardly\nby any effort we can persuade ourselves to regard them as the very\nsame objects which at noonday pass unnoticed as mere white clouds\nbasking in the sun, only participating, from their great horizontal\ndistance, in the ruddy tint which luminaries acquire by shining through\na great extent of the vapours of the atmosphere, and thereby even\nlosing something of their light. So it is with our estimates of time,\nvelocity, and all other matters of quantity; they are absolutely vague,\nand inadequate to form a foundation for any exact conclusion.\n\n(118.) In this emergency we are obliged to have recourse to\ninstrumental aids, that is, to contrivances which shall substitute for\nthe vague impressions of sense the precise one of number, and reduce\nall measurement to counting. As a first preliminary towards effecting\nthis, we fix on convenient _standards_ of weight, dimension, time,\n&c., and invent contrivances for readily and correctly repeating them\nas often as we please, and counting how often such a standard unit is\ncontained in the thing, be it weight, space, time, or angle, we wish to\nmeasure; and if there be a fractional part over, we measure this as a\nnew quantity by aliquot parts of the former standard.\n\n(119.) If every scientific enquirer observed only for his own\nsatisfaction, and reasoned only on his own observations, it would be\nof little importance what standards he used, or what contrivances (if\nonly just ones) he employed for this purpose; but if it be intended\n(as it is most important they should) that observations once made\nshould remain as records to all mankind, and to all posterity, it is\nevidently of the highest consequence that all enquirers should agree on\nthe use of a common standard, and that this should be one not liable\nto change by lapse of time. The selection and verification of such\nstandards, however, will easily be understood to be a matter of extreme\ndifficulty, if only from the mere circumstance that, to verify the\npermanence of one standard, we must compare it with others, which it\nis possible may be themselves inaccurate, or, at least, stand in need\nof verification.\n\n(120.) Here we can only call to our assistance the presumed permanence\nof the great laws of Nature, with all experience in its favour, and the\nstrong impression we have of the general composure and steadiness of\nevery thing relating to the gigantic mass we inhabit--\u201cthe great globe\nitself.\u201d In its uniform rotation on its axis, accordingly, we find a\nstandard of time, which nothing has ever given us reason to regard\nas subject to change, and which, compared with other periods which\nthe revolutions of the planets about the sun afford, has demonstrably\nundergone none since the earliest history. In the dimensions of the\nearth we find a natural unit of the measure of space, which possesses\nin perfection every quality that can be desired; and in its attraction\ncombined with its rotation the researches of dynamical science have\nenabled us, through the medium of the pendulum, to obtain another\ninvariable standard, more refined and less obvious, it is true, in\nits origin, but possessing a great advantage in its capability of\nready verification, and therefore easily made to serve as a check on\nthe other. The former, viz. direct measurement of the dimensions of\nthe earth, is the origin of the _m\u00e8tre_, the French unit of linear\nmeasure; the latter, of the British yard. Theoretically speaking,\nthey are equally eligible; but when we consider that the _quantity\ndirectly measured_, in the case of the m\u00e8tre, is a length a great many\nthousand times the final unit, and in the pendulum or yard very nearly\nthe unit itself, there can be no hesitation in giving the preference\nas an original measure to the former, because any error committed in\nthe process by which that is determined becomes subdivided in the\nfinal result; while, on the other hand, any minute error committed\nin determining the length of the pendulum becomes multiplied by the\nrepetition of the unit in all measurements of considerable lengths\nperformed in yards.\n\n(121.) The same admirable invention of the pendulum affords a means of\nsubdividing time to an almost unlimited nicety. A clock is nothing more\nthan a piece of mechanism for counting the oscillations of a pendulum;\nand by that peculiar property of the pendulum, that one vibration\ncommences exactly where the last terminates, no part of time is lost\nor gained in the juxta-position of the units so counted, so that the\nprecise fractional part of a day can be ascertained which each such\nunit measures.\n\n(122.) It is owing to this peculiar property by which the\n_juxta-position_ of units of time and weight can be performed _without\nerror_, that the whole of the accuracy with which time and weight can\nbe multiplied and subdivided is owing.[36] The same thing cannot be\naccomplished in _space_, by any method we are yet acquainted with, so\nthat our means of subdividing space are much inferior in precision.\nThe beautiful principle of repetition, invented by Borda, offers the\nnearest approach to it, but cannot be said to be absolutely free from\nthe source of error in question. The method of \u201cdouble weighing,\u201d which\nwe owe to the same distinguished observer, affords an instance of the\ndirect comparison of two equal weights independent of almost every\nsource of error which can affect the comparison of one object with\nanother. It has been remarked by Biot, that previous to the invention\nof this elegant method, instruments afforded no perfect means of\nascertaining the weight of a body.\n\n(123.) But it is not enough to possess a standard of this abstract\nkind: a real material measure must be constructed, and exact copies of\nit taken. This, however, is not very difficult; the great difficulty\nis to preserve it unaltered from age to age; for unless we transmit to\nposterity the units of our measurements, _such as we have ourselves\nused them_, we, in fact, only half bequeath to them our observations.\nThis is a point too much lost sight of, and it were much to be wished\nthat some direct provision for so important an object were made.[37]\n\n(124.) But, it may be asked, if our measurement of quantity is thus\nunavoidably liable to error, how is it possible that our observations\ncan possess that quality of numerical veracity which is requisite to\nrender them the foundation of laws, whose distinguishing perfection\nconsists in their strict mathematical expression? To this the reply is\ntwofold. 1st, that though we admit the necessary existence of numerical\nerror in every observation, we can always assign a limit which such\nerror cannot possibly exceed; and the extent of this _latitude of\nerror of observation_ is less in proportion to the perfection of\nthe instrumental means we possess, and the care bestowed on their\nemployment. In the greater part of modern measurements it is, in point\nof fact, extremely minute, and may be still further diminished, almost\nto any required extent, by repeating the measurements a great number of\ntimes, and under a great variety of circumstances, and taking a mean of\nthe results, when errors of opposite kinds will, at length, compensate\neach other. But, 2dly, there exists a much more fundamental reply to\nthis objection. In reasoning upon our observations, the existence and\npossible amount of quantitative error is always to be allowed for; and\nthe extent to which theories may be affected by it is never to be lost\nsight of. In reasoning upwards, from observations confessedly imperfect\nto general laws, we must take care always to regard our conclusions\nas conditional, so far as they may be affected by such unavoidable\nimperfections; and when at length we shall have arrived at our highest\npoint, and attained to axioms which admit of general and deductive\nreasoning, the question, whether they _are_ vitiated by the errors of\nobservation or not, will still remain to be decided, and must become\nthe object of subsequent verification. This point will be made the\nsubject of more distinct consideration hereafter, when we come to speak\nof the verification of theories and the laws of probability.\n\n(125.) With respect to our record of observations, it should be not\nonly circumstantial but _faithful_; by which we mean, that it should\ncontain all we did _observe_, and nothing else. Without any intention\nof falsifying our record, we may do so unperceived by ourselves, owing\nto a mixture of the views and language of an erroneous theory with\nthat of simple fact. Thus, for example, if, in describing the effect\nof lightning, we should say, \u201cThe thunderbolt struck with violence\nagainst the side of the house, and beat in the wall,\u201d a fact would be\nstated which we did not see, and would lead our hearers to believe that\na solid or ponderable projectile was concerned. The \u201cstrong smell of\nsulphur,\u201d which is sometimes said to accompany lightning, is a remnant\nof the theory which made thunder and lightning the explosion of a kind\nof a\u00ebrial gunpowder, composed of sulphureous and nitrous exhalations.\nThere are some subjects particularly infested with this mixture of\ntheory in the statement of observed fact. The older chemistry was\nso overborne by this mischief, as quite to confound and nullify the\ndescriptions of innumerable curious and laborious experiments. And in\ngeology, till a very recent period, it was often extremely difficult,\nfrom this circumstance, to know what _were_ the facts observed. Thus,\nFaujas de St. Fond, in his work on the volcanoes of central France,\ndescribes with every appearance of minute precision craters existing\nno where but in his own imagination. There is no greater fault (direct\nfalsification of fact excepted) which can be committed by an observer.\n\n(126.) When particular branches of science have acquired that degree\nof consistency and generality, which admits of an abstract statement\nof laws, and legitimate deductive reasoning, the principle of the\ndivision of labour tends to separate the province of the observer from\nthat of the theorist. There is no accounting for the difference of\nminds or inclinations, which leads one man to observe with interest\nthe developements of phenomena, another to speculate on their causes;\nbut were it not for this happy disagreement, it may be doubted whether\nthe higher sciences could ever have attained even their present degree\nof perfection. As laws acquire generality, the influence of individual\nobservations becomes less, and a higher and higher degree of\nrefinement in their performance, as well as a great multiplication in\ntheir number, becomes necessary to give them importance. In astronomy,\nfor instance, the superior departments of theory are completely\ndisjoined from the routine of practical observation.\n\n(127.) To make a perfect observer, however, either in astronomy\nor in any other department of science, an extensive acquaintance\nis requisite, not only with the particular science to which his\nobservations relate, but with every branch of knowledge which may\nenable him to appretiate and neutralize the effect of extraneous\ndisturbing causes. Thus furnished, he will be prepared to seize on any\nof those minute indications, which (such is the subtlety of nature)\noften connect phenomena which seem quite remote from each other. He\nwill have his eyes as it were opened, that they may be struck at once\nwith any occurrence which, according to received theories, ought\nnot to happen; for these are the facts which serve as clews to new\ndiscoveries. The deviation of the magnetic needle, by the influence\nof an electrified wire, must have happened a thousand times to a\nperceptible amount, under the eyes of persons engaged in galvanic\nexperiments, with philosophical apparatus of all kinds standing around\nthem; but it required the eye of a philosopher such as O\u00ebrsted to\nseize the indication, refer it to its origin, and thereby connect\ntwo great branches of science. The grand discovery of Malus of the\npolarization of light by reflection originated in his casual remark of\nthe disappearance of one of the images of a window in the Luxembourg\npalace, one evening, when strongly illuminated by the setting sun,\nviewed through a doubly refracting prism.\n\n(128.) To avail ourselves as far as possible of the advantages which\na division of labour may afford for the collection of facts, by the\nindustry and activity which the general diffusion of information,\nin the present age, brings into exercise, is an object of great\nimportance. There is scarcely any well-informed person, who, if he\nhas but the will, has not also the power to add something essential\nto the general stock of knowledge, if he will only observe regularly\nand methodically some particular class of facts which may most excite\nhis attention, or which his situation may best enable him to study\nwith effect. To instance one or two subjects, which can only be\neffectually improved by the united observations of great numbers widely\ndispersed:--Meteorology, one of the most complicated but important\nbranches of science, is at the same time one in which any person\nwho will attend to plain rules, and bestow the necessary degree of\nattention, may do effectual service. What benefits has not Geology\nreaped from the activity of industrious individuals, who, setting\naside all theoretical views, have been content to exercise the useful\nand highly entertaining occupation of collecting specimens from the\ncountries which they visit? In short, there is no branch of science\nwhatever in which, at least, if useful and sensible queries were\ndistinctly proposed, an immense mass of valuable information might not\nbe collected from those who, in their various lines of life, at home\nor abroad, stationary or in travel, would gladly avail themselves of\nopportunities of being useful. Nothing would tend better to attain\nthis end than the circulation of printed skeleton forms, on various\nsubjects, which should be so formed as, 1st, to ask distinct and\npertinent questions, admitting of short and definite answers; 2dly, To\ncall for exact numerical statement on all principal points; 3dly, To\npoint out the attendant circumstances most likely to prove influential,\nand which ought to be observed; 4thly, To call for their transmission\nto a common centre.\n\n\n\n\nCHAP. V.\n\nOF THE CLASSIFICATION OF NATURAL OBJECTS AND PHENOMENA, AND OF\nNOMENCLATURE.\n\n\n(129.) The number and variety of objects and relations which the\nobservation of nature brings before us are so great as to distract\nthe attention, unless assisted and methodized by such judicious\ndistribution of them in classes as shall limit our view to a few at\na time, or to groups so bound together by general resemblances that,\nfor the immediate purpose for which we consider them, they may be\nregarded as individuals. Before we can enter into any thing which\ndeserves to be called a general and systematic view of nature, it is\nnecessary that we should possess an enumeration, if not complete, at\nleast of considerable extent, of her materials and combinations; and\nthat those which appear in any degree important should be distinguished\nby names which may not only tend to fix them in our recollection,\nbut may constitute, as it were, nuclei or centres, about which\ninformation may collect into masses. The imposition of a name on any\nsubject of contemplation, be it a material object, a phenomenon of\nnature, or a group of facts and relations, looked upon in a peculiar\npoint of view, is an epoch in its history of great importance. It not\nonly enables us readily to refer to it in conversation or writing,\nwithout circumlocution, but, what is of more consequence, it gives\nit a recognized existence in our own minds, as a matter for separate\nand peculiar consideration; places it on a list for examination;\nand renders it a head or title, under which information of various\ndescriptions may be arranged; and, in consequence, fits it to perform\nthe office of a connecting link between all the subjects to which such\ninformation may refer.\n\n(130.) For these purposes, however, a temporary or provisional name,\nor one adapted for common parlance, may suffice. But when a very great\nmultitude of objects come to be referred to one class, especially of\nsuch as do not offer very obvious and remarkable distinctions, a more\nsystematic and regular nomenclature becomes necessary, in which the\nnames shall recall the differences as well as the resemblances between\nthe individuals of a class, and in which the direct relation between\nthe name and the object shall materially assist the solution of the\nproblem, \u201c_given the one, to determine the other_.\u201d How necessary\nthis may become, will be at once seen, when we consider the immense\nnumber of individual objects, or rather species, presented by almost\nevery branch of science of any extent; which absolutely require to be\ndistinguished by names. Thus, the botanist is conversant with from\n80,000 to 100,000 species of plants; the entomologist with, perhaps,\nas many, of insects: the chemist has to register the properties of\ncombinations, by twos, threes, fours, and upwards, in various doses\nof upwards of fifty different elements, all distinguished from each\nother by essential differences; and of which though a great many\nthousands are known, by far the greater part have never yet been\nformed, although hundreds of new ones are coming to light, in perpetual\nsuccession, as the science advances; all of which are to be named as\nthey arise. The objects of astronomy are, literally, as numerous as the\nstars of heaven; and although not more than one or two thousand require\nto be expressed by distinct names, yet the number, respecting which\nparticular information is required, is not less than a hundred times\nthat amount; and all these must be registered in lists, (so as to be\nat once referred to, and so that none shall escape,) if not by actual\nnames, at least by some equivalent means.\n\n(131.) Nomenclature, then, is, in itself, undoubtedly an important\npart of science, as it prevents our being lost in a wilderness of\nparticulars, and involved in inextricable confusion. Happily, in those\ngreat branches of science where the objects of classification are most\nnumerous, and the necessity for a clear and convenient nomenclature\nmost pressing, no very great difficulty in its establishment is felt.\nThe very multitude of the objects themselves affords the power of\ngrouping them in subordinate classes, sufficiently well defined to\nadmit of names, and these again into others, whose names may become\nattached to, or compounded with, the former, till at length the\nparticular species is identified. The facility with which the botanist,\nthe entomologist, or the chemist, refers by name to any individual\nobject in his science shows what may be accomplished in this way\nwhen characters are themselves distinct. In other branches, however,\nconsiderable difficulty is experienced. This arises mostly where the\nspecies to be distinguished are separated from each other chiefly by\ndifference in degree, of certain qualities common to all, and where the\ndegrees shade into each other insensibly. Perhaps such subjects can\nhardly be considered ripe for systematic nomenclature; and that the\nattempt to apply it ought only to be partial, embracing such groups\nand parcels of individuals as agree in characters evidently natural\nand generic, and leaving the remainder under trivial or provisional\ndenominations, till they shall be better known, and capable of being\nscientifically grouped.\n\n(132.) Indeed, nomenclature, in a systematic point of view, is as\nmuch, perhaps more, a consequence than a cause of extended knowledge.\nAny one may give an arbitrary name to a thing, merely to be able to\ntalk of it; but, to give a name which shall at once refer it to a\nplace in a system, we must know its properties; and we must _have_ a\nsystem, large enough, and regular enough, to receive it in a place\nwhich belongs to it, and to no other. It appears, therefore, doubtful\nwhether it is desirable, for the essential purposes of science, that\nextreme refinement in systematic nomenclature should be insisted on.\nWere science perfect, indeed, systems of classification might be\nagreed on, which should assign to every object in nature a place in\nsome class, to which it more remarkably and pre-eminently belonged\nthan to any other, and under which it might acquire a name, never\nafterwards subject to change. But, so long as this is not the case,\nand new relations are daily discovered, we must be very cautious how\nwe insist strongly on the establishment and extension of classes\nwhich have in them any thing artificial, as a basis of a rigid\nnomenclature; and especially how we mistake the means for the end, and\nsacrifice convenience and distinctness to a rage for arrangement. Every\nnomenclature dependent on artificial classifications is necessarily\nsubject to fluctuations; and hardly any thing can counterbalance the\nevil of disturbing well-established names, which have once acquired a\ngeneral circulation. In nature, one and the same object makes a part of\nan infinite number of different systems,--an individual in an infinite\nnumber of groups, some of greater, some of less importance, according\nto the different points of view in which they may be considered. Hence,\nas many different systems of nomenclature may be imagined as there can\nbe discovered different heads of classification, while yet it is highly\ndesirable that each object should be universally spoken of under one\nname, _if possible_. Consequently, in all subjects where comprehensive\nheads of classification do not prominently offer themselves, all\nnomenclature must be a balance of difficulties, and a good, short,\n_unmeaning_ name, which has once obtained a footing in usage, is\npreferable to almost any other.\n\n(133.) There is no science in which the evils resulting from a rage for\nnomenclature have been felt to such an extent as in mineralogy. The\nnumber of simple minerals actually recognised by mineralogists does not\nexceed a few hundreds, yet there is scarcely one which has not four or\nfive names in different books. The consequence is most unhappy. No name\nis suffered to endure long enough to take root; and every new writer\non this interesting science begins, as a matter of course, by making a\n_tabula rasa_ of all former nomenclature, and proposing a new one in\nits place. The climax has at length been put to this most inconvenient\nand bewildering state of things by the appearance of a system supported\nby extraordinary merit in other respects, and therefore carrying\nthe highest authority, in which names which had acquired universal\ncirculation, and had hitherto maintained their ground in the midst of\nthe general confusion, and even worked their way into common language,\nas denotive of _species_ too definite to admit of mistake, are actually\nrendered _generic_, and extended to whole groups, comprising objects\nagreeing in nothing but the arbitrary heads of a classification\nfrom which the most important natural relations are professedly and\npurposely rejected.[38]\n\n(134.) The classifications by which science is advanced, however, are\nwidely different from those which serve as bases for artificial systems\nof nomenclature. They cross and intersect one another, as it were, in\nevery possible way, and have for their very aim to interweave all the\nobjects of nature in a close and compact web of mutual relations and\ndependence. As soon, then, as any resemblance or analogy, any point of\nagreement whatever, is perceived between any two or more things,--be\nthey what they will, whether objects, or phenomena, or laws,--they\nimmediately and _ipso facto_ constitute themselves into a group or\nclass, which may become enlarged to any extent by the accession of\nsuch new objects, phenomena, or laws, agreeing in the same point, as\nmay come to be subsequently ascertained. It is thus that the materials\nof the world become grouped in natural families, such as chemistry\nfurnishes examples of, in its various groups of acids, alkalies,\nsulphurets, &c.; or botany, in its euphorbiace\u00e6, umbellifer\u00e6, &c. It is\nthus, too, that phenomena assume their places under general points of\nresemblance; as, in optics, those which refer themselves to the class\nof periodic colours, double refraction, &c.; and that resemblances\nthemselves become traced, which it is the business of induction to\ngeneralize and include in abstract propositions.\n\n(135.) But every class formed on a positive resemblance of characters,\nor on a distinct analogy, draws with it the consideration of a negative\nclass, in which that resemblance either does not subsist at all, or the\ncontrary takes place; and again, there are classes in which a given\nquality is possessed by the different individuals in a descending scale\nof intensity. Now, it is of consequence to distinguish between cases\nin which there is a real opposition of quality, or a mere diminution\nof intensity, in some quality susceptible of degrees, till it becomes\nimperceptible. For example, between transparency and opacity there\nwould at first sight appear a direct opposition; but, on nearer\nconsideration, when we consider the gradations by which transparency\ndiminishes in natural substances, we shall see reason to admit that\nthe latter quality, instead of being the _opposite_ of the former,\nis only its _extreme lowest degree_. Again, in the arrangement of\nnatural objects under the head of weight or specific gravity, the scale\nextends through all nature, and we know of no natural body in which the\nopposite of gravity, or positive _levity_, subsists. On the other hand,\nthe opposite electricities; the north and south magnetic polarities;\nthe alkaline and acid qualities of chemical agents; the positive and\nnegative rotations impressed by plates of rock crystal on the planes\nof polarization of the rays of light, and many other cases, exemplify\nnot merely a negation, but an active opposition of quality. Both these\nmodes of classification have their peculiar importance in the inductive\nprocess: the one, as affording an opportunity of tracing a relation\nbetween phenomena by the observation of a correspondence in their\nscales of intensity; the other, by that of contrast, as we shall show\nmore at large in the next section.\n\n(136.) There is a very wide distinction, too, to be taken between such\nclasses as turn upon a single head of resemblance among individuals\notherwise very different, and such as bind together in natural groups,\nby a great variety of analogies, objects which yet differ in many\nremarkable particulars. For example: if we make colourless transparency\na head of classification, the list of the class will comprise objects\ndiffering most widely in their nature, such as water, air, diamond,\nspirit of wine, glass, &c. On the other hand, the chemical families of\nalkalies, metals, &c. are instances of groups of the other kind; which,\nwith properties in many respects different, still agree in a general\nresemblance of several others, which at once decides us in considering\nthem as having a natural relation. In the former cases, our ingenuity\nis exercised to determine what can be the cause of their resemblance,\nin the latter, of their difference; the former belong to the province\nof inductive generalization, and afford the most instructive cases for\nthe investigation of causes; the latter appertain to the more secret\nrecesses of nature; the very existence of such families being in itself\none of the great and complicated phenomena of the universe, which we\ncannot hope to unriddle without an intimate and extensive acquaintance\nwith the highest laws.[39]\n\n\n\n\nCHAP. VI.\n\n  OF THE FIRST STAGE OF INDUCTION.--THE DISCOVERY OF PROXIMATE\n    CAUSES, AND LAWS OF THE LOWEST DEGREE OF GENERALITY, AND THEIR\n    VERIFICATION.\n\n\n(137.) The first thing that a philosophic mind considers, when any\nnew phenomenon presents itself, is its _explanation_, or reference\nto an immediate producing cause. If that cannot be ascertained, the\nnext is to _generalize_ the phenomenon, and include it, with others\nanalogous to it, in the expression of some law, in the hope that its\nconsideration, in a more advanced state of knowledge, may lead to the\ndiscovery of an adequate proximate cause.\n\n(138.) Experience having shown us the manner in which one phenomenon\ndepends on another in a great variety of cases, we find ourselves\nprovided, as science extends, with a continually increasing stock\nof such antecedent phenomena, or causes (meaning at present merely\nproximate causes), competent, under different modifications, to the\nproduction of a great multitude of effects, besides those which\noriginally led to a knowledge of them. To such causes Newton has\napplied the term _ver\u00e6 caus\u00e6_; that is, causes recognized as having a\nreal existence in nature, and not being mere hypotheses or figments\nof the mind. To exemplify the distinction:--The phenomenon of shells\nfound in rocks, at a great height above the sea, has been attributed\nto several causes. By some it has been ascribed to a plastic virtue in\nthe soil; by some, to fermentation; by some, to the influence of the\ncelestial bodies; by some, to the casual passage of pilgrims with their\nscallops; by some, to birds feeding on shell-fish; and by all modern\ngeologists, with one consent, to the life and death of real mollusca\nat the bottom of the sea, and a subsequent alteration of the relative\nlevel of the land and sea. Of these, the plastic virtue and celestial\ninfluence belong to the class of figments of fancy. Casual transport\nby pilgrims is a real cause, and might account for a few shells here\nand there dropped on frequented passes, but is not extensive enough for\nthe purpose of explanation. Fermentation, generally, is a real cause,\nso far as that there _is such a thing_; but it is not a real cause\nof the production of a shell in a rock, since no such thing was ever\nwitnessed as one of its effects, and rocks and stones do not ferment.\nOn the other hand, for a shell-fish dying at the bottom of the sea to\nleave his shell in the mud, where it becomes silted over and imbedded,\nhappens daily; and the elevation of the bottom of the sea to become dry\nland has really been witnessed so often, and on such a scale, as to\nqualify it for a _vera causa_ available in sound philosophy.\n\n(139.) To take another instance, likewise drawn from the same\ndeservedly popular science:--The fact of a great change in the general\nclimate of large tracts of the globe, if not of the whole earth,\nand of a diminution of general temperature, having been recognised\nby geologists, from their examination of the remains of animals and\nvegetables of former ages enclosed in the strata, various causes for\nsuch diminution of temperature have been assigned. Some consider\nthe whole globe as having gradually cooled from absolute fusion;\nsome regard the immensely superior activity of former volcanoes, and\nconsequent more copious communication of internal heat to the surface,\nin former ages, as the cause. Neither of these can be regarded as\nreal causes in the sense here intended; for we do not _know_ that the\nglobe has so cooled from fusion, nor are we sure that such supposed\ngreater activity of former than of present volcanoes really did exist.\nA cause, possessing the essential requisites of a _vera causa_, has,\nhowever, been brought forward[40] in the varying influence of the\ndistribution of land and sea over the surface of the globe: a change\nof such distribution, in the lapse of ages, by the degradation of the\nold continents, and the elevation of new, being a demonstrated fact;\nand the influence of such a change on the climates of particular\nregions, if not of the whole globe, being a perfectly fair conclusion,\nfrom what we know of continental, insular, and oceanic climates by\nactual observation. Here, then, we have, at least, a cause on which a\nphilosopher may consent to reason; though, whether the changes actually\ngoing on are such as to warrant the whole extent of the conclusion,\nor are even taking place in the right direction, may be considered as\nundecided till the matter has been more thoroughly examined.\n\n(140.) To this we may add another, which has likewise the essential\ncharacters of a _vera causa_, in the astronomical _fact_ of the actual\nslow diminution of the eccentricity of the earth\u2019s orbit round the\nsun; and which, as a general one, affecting the _mean temperature of\nthe whole globe_, and as one of which the effect is both inevitable,\nand susceptible, to a certain degree, of exact estimation, deserves\nconsideration. It is evident that the _mean_ temperature of the\nwhole surface of the globe, in so far as it is maintained by the\naction of the sun at a higher degree than it would have were the sun\nextinguished, must depend on the mean quantity of the sun\u2019s rays which\nit receives, or, which comes to the same thing, on the _total_ quantity\nreceived in a given invariable time: and the length of the year\nbeing unchangeable in all the fluctuations of the planetary system,\nit follows, that the total _annual_ amount of solar radiation will\ndetermine, _c\u00e6teris paribus_, the general climate of the earth. Now,\nit is not difficult to show that this amount is inversely proportional\nto the minor axis of the ellipse described by the earth about the\nsun, regarded as slowly variable; and that, therefore, the major axis\nremaining, as we know it to be, constant, and the orbit being actually\nin a state of approach to a circle, and, consequently, the minor axis\nbeing on the _increase_, the mean annual amount of solar radiation\nreceived by the whole earth must be actually on the _decrease_. We have\nhere, therefore, an evident real cause, of sufficient universality, and\nacting _in the right direction_, to account for the phenomenon. Its\nadequacy is another consideration.[41]\n\n(141.) Whenever, therefore, any phenomenon presents itself for\nexplanation, we naturally seek, in the first instance, to refer it to\nsome one or other of those real causes which experience has shown to\nexist, and to be efficacious in producing similar phenomena. In this\nattempt our probability of success will, of course, mainly depend,\n1st, On the number and variety of causes experience has placed at our\ndisposal; 2dly, On our habit of applying them to the explanation of\nnatural phenomena; and, 3dly, On the number of analogous phenomena\nwe can collect, which have either been explained, or which admit of\nexplanation by some one or other of those causes, and the closeness of\ntheir analogy with that in question.\n\n(142.) Here, then, we see the great importance of possessing a stock\nof analogous instances or phenomena which class themselves with that\nunder consideration, the explanation of one among which may naturally\nbe expected to lead to that of all the rest. If the analogy of two\nphenomena be very close and striking, while, at the same time, the\ncause of one is very obvious, it becomes scarcely possible to refuse\nto admit the action of an analogous cause in the other, though not so\nobvious in itself. For instance, when we see a stone whirled round in a\nsling, describing a circular orbit round the hand, keeping the string\nstretched, and flying away the moment it breaks, we never hesitate\nto regard it as retained in its orbit by the tension of the string,\nthat is, by _a force_ directed to the centre; for we feel that we do\nreally exert such a force. We have here _the direct perception_ of the\ncause. When, therefore, we see a great body like the moon circulating\nround the earth and not flying off, we cannot help believing it to\nbe prevented from so doing, not indeed by a material tie, but by\nthat which operates in the other case through the intermedium of the\nstring,--a _force_ directed constantly to the centre. It is thus that\nwe are continually acquiring a knowledge of the existence of causes\nacting under circumstances of such concealment as effectually to\nprevent their direct discovery.\n\n(143.) In general we must observe that motion, wherever produced or\nchanged, invariably points out the existence of _force_ as its cause;\nand thus the forces of nature become known and measured by the\nmotions they produce. Thus, the _force_ of magnetism becomes known by\nthe deviation produced by iron in a compass needle, or by a needle\nleaping up to a magnet held over it, as certainly as by that adhesion\nto it, when in contact and at rest, which requires force to break the\nconnection; and thus the currents produced in the surface of a quantity\nof quicksilver, electrified under a conducting fluid, have pointed out\nthe existence and direction of forces of enormous intensity developed\nby the electric circuit, of which we should not otherwise have had the\nleast suspicion.[42]\n\n(144.) But when the cause of a phenomenon neither presents itself\nobviously on the consideration of the phenomenon itself, nor is as it\nwere forced on our attention by a case of strong analogy, such as above\ndescribed, we have then no resource but in a deliberate assemblage of\nall the parallel instances we can muster; that is, to the formation\nof a class of facts, having the phenomenon in question for a head of\nclassification; and to a search among the individuals of this class\nfor some other common points of agreement, among which the cause will\nof necessity be found. But if more than one cause should appear, we\nmust then endeavour to find, or, if we cannot find, to _produce, new\nfacts_, in which each of these in succession shall be wanting, while\nyet they agree in the general point in question. Here we find the use\nof what Bacon terms \u201c_crucial instances_,\u201d which are phenomena brought\nforward to decide between two causes, each having the same analogies in\nits favour. And here, too, we perceive the utility of _experiment_ as\ndistinguished from mere passive observation. We make an experiment of\nthe crucial kind when we form combinations, and put in action causes\nfrom which some particular one shall be deliberately excluded, and\nsome other purposely admitted; and by the agreement or disagreement of\nthe resulting phenomena with those of the class under examination, we\ndecide our judgment.\n\n(145.) When we would lay down general rules for guiding and\nfacilitating our search, among a great mass of assembled facts, for\ntheir common cause, we must have regard to the characters of that\nrelation which we intend by cause and effect. Now, these are,--\n\n  1st, Invariable connection, and, in particular, invariable\n    antecedence of the cause and consequence of the effect, unless\n    prevented by some counteracting cause. But it must be observed,\n    that, in a great number of natural phenomena, the effect is\n    produced gradually, while the cause often goes on increasing in\n    intensity; so that the antecedence of the one and consequence\n    of the other becomes difficult to trace, though it really\n    exists. On the other hand, the effect often follows the cause\n    so instantaneously, that the interval cannot be perceived. In\n    consequence of this, it is sometimes difficult to decide, of two\n    phenomena constantly accompanying one another, which is cause or\n    which effect.\n\n  2d, Invariable negation of the effect with absence of the cause,\n    unless some other cause be capable of producing the same effect.\n\n  3d, Increase or diminution of the effect, with the increased\n    or diminished intensity of the cause, in cases which admit of\n    increase and diminution.\n\n  4th, Proportionality of the effect to its cause in all cases of\n    _direct unimpeded_ action.\n\n  5th, Reversal of the effect with that of the cause.\n\n(146.) From these characters we are led to the following observations,\nwhich may be considered as so many propositions readily applicable to\nparticular cases, or rules of philosophizing: we conclude, 1st, That if\nin our group of facts there be one in which any assigned peculiarity,\nor attendant circumstance, is wanting or opposite, such peculiarity\ncannot be the cause we seek.\n\n(147.) 2d, That any circumstance in which all the facts without\nexception agree, _may_ be the cause in question, or, if not, at least\na collateral effect of the same cause: if there be but one such point\nof agreement, this possibility becomes a certainty; and, on the other\nhand, if there be more than one, they may be concurrent causes.\n\n(148.) 3d, That we are not to deny the existence of a cause in favour\nof which we have a unanimous agreement of strong analogies, though\nit may not be apparent how such a cause can produce the effect, or\neven though it may be difficult to conceive its existence under the\ncircumstances of the case; in such cases we should rather appeal to\nexperience when possible, than decide _\u00e0 priori_ against the cause, and\ntry whether it cannot be made apparent.\n\n(149.) For instance: seeing the sun vividly luminous, every analogy\nleads us to conclude it intensely hot. How heat can produce light,\nwe know not; and how such a heat can be maintained, we can form no\nconception. Yet we are not, therefore, entitled to deny the inference.\n\n(150.) 4th, That contrary or opposing facts are equally instructive for\nthe discovery of causes with favourable ones.\n\n(151.) For instance: when air is confined with moistened iron filings\nin a close vessel over water, its bulk is diminished, by a certain\nportion of it being abstracted and combining with the iron, producing\n_rust_. And, if the remainder be examined, it is found that it will\n_not_ support flame or animal life. This contrary fact shows that the\ncause of the support of flame and animal life is to be looked for in\nthat part of the air which the iron abstracts, and which rusts it.\n\n(152.) 5th, That causes will very frequently become obvious, by a\nmere arrangement of our facts in the order of intensity in which\nsome peculiar quality subsists; though not of necessity, because\ncounteracting or modifying causes may be at the same time in action.\n\n(153.) For example: sound consists in impulses communicated to our ears\nby the air. If a series of impulses of equal force be communicated\nto it at equal intervals of time, at first in slow succession, and\nby degrees more and more rapidly, we hear at first a rattling noise,\nthen a low murmur, and then a hum, which by degrees acquires the\ncharacter of a musical note, rising higher and higher in acuteness,\ntill its pitch becomes too high for the ear to follow. And from\nthis correspondence between the pitch of the note and the rapidity\nof succession of the impulse, we conclude that our sensation of\nthe different pitches of musical notes originates in the different\nrapidities with which their impulses are communicated to our ears.\n\n(154.) 6th, That such counteracting or modifying causes may subsist\nunperceived, and annul the effects of the cause we seek, in instances\nwhich, but for their action, would have come into our class of\nfavourable facts; and that, therefore, exceptions may often be made\nto disappear by removing or allowing for such counteracting causes.\nThis remark becomes of the greatest importance, when (as is often the\ncase) a single striking exception stands out, as it were, against an\notherwise unanimous array of facts in favour of a certain cause.\n\n(155.) Thus, in chemistry, the _alkaline_ quality of the alkaline\nand earthy bases is found to be due to the presence of oxygen\ncombined with one or other of a peculiar set of metals. Ammonia is,\nhowever, a violent outstanding exception, such as here alluded to,\nbeing a compound of azote and hydrogen: but there are almost certain\nindications that this exception is not a real one, but assumes that\nappearance in consequence of some modifying cause not understood.\n\n(156.) 7th, If we can either find produced by nature, or produce\ndesignedly for ourselves, two instances which agree _exactly_ in all\nbut one particular, and differ in that one, its influence in producing\nthe phenomenon, if it have any, _must_ thereby be rendered sensible.\nIf that particular be present in one instance and wanting altogether\nin the other, the production or non-production of the phenomenon will\ndecide whether it be or be not the only cause: still more evidently,\nif it be present _contrariwise_ in the two cases, and the effect be\nthereby reversed. But if its total presence or absence only produces\na change in the _degree_ or intensity of the phenomenon, we can then\nonly conclude that it acts as a concurrent cause or condition with\nsome other to be sought elsewhere. In nature, it is comparatively\nrare to find instances pointedly differing in one circumstance and\nagreeing in every other; but when we call experiment to our aid, it\nis easy to produce them; and this is, in fact, the grand application\nof _experiments of enquiry_ in physical researches. They become more\nvaluable, and their results clearer, in proportion as they possess this\nquality (of agreeing exactly in all their circumstances but one), since\nthe question put to nature becomes thereby more pointed, and its answer\nmore decisive.\n\n(157.) 8th, If we cannot obtain a complete negative or opposition of\nthe circumstance whose influence we would ascertain, we must endeavour\nto find cases where it varies considerably in degree. If _this_ cannot\nbe done, we may perhaps be able to weaken or exalt its influence by\nthe introduction of some fresh circumstance, which, abstractedly\nconsidered, seems _likely_ to produce this effect, and thus obtain\nindirect evidence of its influence. But then we are always to remember,\nthat the evidence so obtained _is_ indirect, and that the new\ncircumstance introduced _may_ have a direct influence of its own, or\nmay exercise a modifying one on some _other_ circumstance.\n\n(158.) 9th, Complicated phenomena, in which several causes concurring,\nopposing, or quite independent of each other, operate at once, so as to\nproduce a compound effect, may be simplified by subducting the effect\nof all the known causes, as well as the nature of the case permits,\neither by deductive reasoning or by appeal to experience, and thus\nleaving, as it were, a _residual phenomenon_ to be explained. It is by\nthis process, in fact, that science, in its present advanced state, is\nchiefly promoted. Most of the phenomena which nature presents are very\ncomplicated; and when the effects of all known causes are estimated\nwith exactness, and subducted, the residual facts are constantly\nappearing in the form of phenomena altogether new, and leading to the\nmost important conclusions.\n\n(159.) For example: the return of the comet predicted by professor\nEncke, a great many times in succession, and the general good agreement\nof its calculated with its observed place during any one of its periods\nof visibility, would lead us to say that its gravitation towards the\nsun and planets is the sole and sufficient cause of all the phenomena\nof its orbitual motion; but when the effect of this cause is strictly\ncalculated and subducted from the observed motion, there is found to\nremain behind a _residual phenomenon_, which would never have been\notherwise ascertained to exist, which is a small anticipation of the\ntime of its reappearances or a diminution of its periodic time, which\ncannot be accounted for by gravity, and whose cause is therefore to be\nenquired into. Such an anticipation would be caused by the resistance\nof a medium disseminated through the celestial regions; and as there\nare other good reasons for believing this to be a _vera causa_, it has\ntherefore been ascribed to such a resistance.\n\n(160.) This 9th observation is of such importance in science, that\nwe shall exemplify it by another instance or two. M. Arago, having\nsuspended a magnetic needle by a silk thread, and set it in vibration,\nobserved, that it came much sooner to a state of rest when suspended\nover a plate of copper, than when no such plate was beneath it. Now, in\nboth cases there were two _ver\u00e6 caus\u00e6_ why it _should_ come at length\nto rest, viz. the resistance of the air, which opposes, and at length\ndestroys, all motions performed in it; and the want of perfect mobility\nin the silk thread. But the effect of these causes being exactly known\nby the observation made in the absence of the copper, and being thus\nallowed for and subducted, a _residual_ phenomenon appeared, in the\nfact that a retarding influence was exerted by the copper itself;\nand this fact, once ascertained, speedily led to the knowledge of\nan entirely new and unexpected class of relations. To add one more\ninstance. If it be true (as M. Fourrier considers it demonstrated to\nbe) that the celestial regions have a temperature independent of the\nsun, not greatly inferior to that at which quicksilver congeals, and\nmuch superior to some degrees of cold which have been artificially\nproduced, two causes suggest themselves: one is that assigned by the\nauthor above mentioned; the radiation of the stars; another may be\nproposed in the ether or elastic medium mentioned in the last section,\nwhich the phenomena of light and the resistance of comets give us\nreason to believe fills all space, and which, in analogy to all the\nelastic media known, may be supposed to possess a temperature and a\nspecific heat of its own, which it is capable of communicating to\nbodies surrounded by it. Now, if we consider that the heat radiated\nby the sun follows the same proportion as its light, and regard it as\nreasonable to admit with respect to stellar heat what holds good of\nsolar; the effect of stellar radiation in maintaining a temperature in\nspace should be as much inferior to that of the radiation of the sun\nas the light of a moonless midnight is to that of an equatorial noon;\nthat is to say, almost inconceivably smaller. Allowing, then, the full\neffect for this cause, there would still remain a great residuum due to\nthe presence of the ether.\n\n(161.) Many of the new elements of chemistry have been detected in\nthe investigation of _residual phenomena_. Thus, Arfwedson discovered\nlithia by perceiving an _excess of weight_ in the sulphate produced\nfrom a small portion of what he considered as magnesia present in a\nmineral he had analysed. It is on this principle, too, that the _small\nconcentrated residues of great operations_ in the arts are almost\nsure to be the lurking places of new chemical ingredients: witness\niodine, brome, selenium, and the new metals accompanying platina in the\nexperiments of Wollaston and Tennant. It was a happy thought of Glauber\nto examine what every body else threw away.\n\n(162.) Finally, we have to observe, that the detection of a _possible_\ncause, by the comparison of assembled cases, _must_ lead to one of\ntwo things: either, 1st, The detection of a real cause, and of its\nmanner of acting, so as to furnish a complete explanation of the facts;\nor, 2dly, The establishment of an abstract law of nature, pointing\nout two phenomena of a general kind as invariably connected; and\nasserting, that where one is, there the other will always be found.\nSuch invariable connection is itself a phenomenon of a higher order\nthan any particular fact; and when many such are discovered, we may\nagain proceed to classify, combine, and examine them, with a view to\nthe detection of _their_ causes, or the discovery of still more general\nlaws, and so on without end.\n\n(163.) Let us now exemplify this inductive search for a cause by one\ngeneral example: suppose _dew_ were the phenomenon proposed, whose\ncause we would know. In the first place, we must separate dew from rain\nand the moisture of fogs, and limit the application of the term to\nwhat is really meant, which is, the spontaneous appearance of moisture\non substances exposed in the open air when no rain or _visible_ wet\nis falling. Now, here we have analogous phenomena in the moisture\nwhich bedews a cold metal or stone when we breathe upon it; that which\nappears on a glass of water fresh from the well in hot weather; that\nwhich appears on the _inside_ of windows when sudden rain or hail\nchills the external air; that which runs down our walls when, after\na long frost, a warm moist thaw comes on: all these instances agree\nin one point (Rule 2. \u00a7 147.), the coldness of the object dewed, in\ncomparison with the air in contact with it.\n\n(164.) But, in the case of the night dew, is this a _real cause_--is it\na fact that the object dewed _is_ colder than the air? Certainly not,\none would at first be inclined to say; for what is to _make_ it so? But\nthe analogies are cogent and unanimous; and, therefore, (pursuant to\nRule 3. \u00a7 148.) we are not to discard their indications; and, besides,\nthe experiment is easy: we have only to lay a thermometer in contact\nwith the dewed substance, and hang one at a little distance above it\nout of reach of its influence. The experiment has been therefore made;\nthe question has been asked, and the answer has been invariably in the\n_affirmative_. Whenever an object contracts dew, _it is_ colder than\nthe air. Here, then, we have _an invariable concomitant_ circumstance:\nbut is this chill an effect of dew, or its cause? That dews are\naccompanied with a chill is a common remark; but vulgar prejudice would\nmake the cold the _effect_ rather than the cause. We must, therefore,\ncollect more facts, or, which comes to the same thing, vary the\ncircumstances; since every instance in which the circumstances differ\nis a fresh fact; and, especially, we must note the contrary or negative\ncases (Rule 4. \u00a7 150.), _i.\u00a0e._ where no dew is produced.\n\n(165.) Now, 1st, no dew is produced on the surface of _polished\nmetals_, but it is very copiously on glass, both exposed with their\nfaces upwards, and in some cases the under side of a horizontal plate\nof glass is also dewed; which last circumstance (by Rule 1. \u00a7 146.)\nexcludes the _fall_ of moisture from the sky in an invisible form,\nwhich would naturally suggest itself as a cause. In the cases of\npolished metal and polished glass, the contrast shows evidently that\nthe _substance_ has much to do with the phenomenon; therefore, let\nthe substance _alone_ be diversified as much as possible, by exposing\npolished surfaces of various kinds. This done, _a scale of intensity_\nbecomes obvious (Rule 5. \u00a7 152.). Those polished substances are found\nto be most strongly dewed which conduct heat worst; while those which\nconduct well resist dew most effectually. Here we encounter a _law_\nof the first degree of generality. But, if we expose rough surfaces,\ninstead of polished, we sometimes find this law interfered with\n(Rule 5. \u00a7 152.). Thus, roughened iron, especially if painted over\nor blackened, becomes dewed sooner than varnished paper: the kind of\n_surface_ therefore has a great influence. Expose, then, the _same_\nmaterial in very diversified states as to surface (Rule 7. \u00a7 156.), and\nanother scale of intensity becomes at once apparent; those _surfaces_\nwhich _part with their heat_ most readily by radiation are found to\ncontract dew most copiously: and thus we have detected another law of\nthe same generality with the former, by a comparison of two classes of\nfacts, one relating to dew, the other to the radiation of heat from\nsurfaces. Again, the influence ascertained to exist of _substance_ and\n_surface_ leads us to consider that of _texture_: and here, again, we\nare presented on trial with remarkable differences, and with a third\n_scale of intensity_, pointing out substances of a close firm texture,\nsuch as stones, metals, &c. as unfavourable, but those of a loose one,\nas cloth, wool, velvet, eiderdown, cotton, &c. as eminently favourable,\nto the contraction of dew: and these are precisely those which are best\nadapted for clothing, or for impeding the free passage of heat from\nthe skin into the air, so as to allow their outer surfaces to be very\ncold while they remain warm within.\n\n(166.) Lastly, among the negative instances, (\u00a7 150.) it is observed,\nthat dew is never copiously deposited in situations much screened\nfrom the open sky, and not at all in _a cloudy night_; but if the\nclouds withdraw, even for a few minutes, and leave a clear opening,\na deposition of dew presently begins, and goes on increasing. Here,\nthen, a cause is distinctly pointed out by its antecedence to the\neffect in question (\u00a7 145.). A clear view of the cloudless sky, then,\nis an essential condition, or, which comes to the same thing, clouds or\nsurrounding objects act as _opposing causes_. This is so much the case,\nthat dew formed in clear intervals will often even evaporate again when\nthe sky becomes thickly overcast (Rule 4. \u00a7 150.).\n\n(167.) When we now come to assemble these partial inductions so as to\nraise from them a general conclusion, we consider, 1st, That all the\nconclusions we have come to have a reference to that first general\nfact--the cooling of the exposed surface of the body dewed below\nthe temperature of the air. Those surfaces which part with their\nheat outwards most readily, and have it supplied from within most\nslowly, will, of course, become coldest if there be an opportunity\nfor their heat to escape, and not be restored to them from without.\nNow, a clear sky affords such an opportunity. It is a law well known\nto those who are conversant with the nature of heat, that heat is\nconstantly escaping from _all bodies_ in rays, or by _radiation_, but\nis as constantly restored to them by the similar radiation of others\nsurrounding them. Clouds and surrounding objects therefore act as\nopposing causes by replacing the whole or a great part of the heat so\nradiated away, which can escape effectually, without being replaced,\nonly through openings into infinite space. Thus, at length, we arrive\nat the general proximate cause of dew, in the cooling of the dewed\nsurface by radiation faster than its heat can be restored to it, by\ncommunication with the ground, or by counter-radiation; so as to\nbecome colder than the air, and thereby to cause a condensation of its\nmoisture.\n\n(168.) We have purposely selected this theory of dew, first developed\nby the late Dr. Wells, as one of the most beautiful specimens we can\ncall to mind of inductive experimental enquiry lying within a moderate\ncompass. It is not possible in so brief a space to do it justice; but\nwe earnestly recommend his work[43] (a short and very entertaining one)\nfor perusal to the student of natural philosophy, as a model with which\nhe will do well to become familiar.\n\n(169.) In the analysis above given, the formation of dew is referred to\ntwo more general phenomena; the radiation of heat, and the condensation\nof invisible vapour by cold. The cause of the former is a much higher\nenquiry, and may be said, indeed, to be totally unknown; that of the\nlatter actually forms a most important branch of physical enquiry. In\nsuch a case, when we reason upwards till we reach an ultimate fact, we\nregard a phenomenon as fully explained; as we consider the branch of\na tree to terminate when traced to its insertion in the trunk, or a\ntwig to its junction with the branch; or rather, as a rivulet retains\nits importance and its name till lost in some larger tributary, or in\nthe main river which delivers it into the ocean. This, however, always\nsupposes that, on a reconsideration of the case, we see clearly how the\nadmission of such a fact, with all its attendant laws, will perfectly\naccount for _every particular_--as well those which, in the different\nstages of the induction, have led us to a knowledge of it, as those\nwhich we had neglected, or considered less minutely than the rest.\nBut, had we no previous knowledge of the radiation of heat, this same\ninduction would have made it known to us, and, duly considered, might\nhave led to the knowledge of many of its laws.\n\n(170.) In the study of nature, we must not, therefore, be scrupulous\nas to _how_ we reach to a knowledge of such general facts: provided\nonly we verify them carefully when once detected, we must be content\nto seize them wherever they are to be found. And this brings us to\nconsider the _verification_ of inductions.\n\n(171.) If, in our induction, every individual case has actually been\npresent to our minds, we are sure that it will find itself duly\n_represented_ in our final conclusion: but this is impossible for\nsuch cases as were _unknown_ to us, and hardly ever happens even\nwith all the known cases; for such is the tendency of the human mind\nto speculation, that on the least idea of an analogy between a few\nphenomena, it leaps forward, as it were, to a cause or law, to the\ntemporary neglect of all the rest; so that, in fact, almost all our\nprincipal inductions must be regarded as a series of ascents and\ndescents, and of conclusions from a few cases, verified by trial on\nmany.\n\n(172.) Whenever, therefore, we think we have been led by induction to\nthe knowledge of the proximate cause of a phenomenon or of a law of\nnature, our next business is to examine deliberately and _seriatim_\nall the cases we have collected of its occurrence, in order to satisfy\nourselves that they are explicable by our cause, or fairly included in\nthe expression of our law: and in case any exception occurs, it must\nbe carefully noted and set aside for re-examination at a more advanced\nperiod, when, possibly, the cause of exception may appear, and the\nexception itself, by allowing for the effect of that cause, be brought\nover to the side of our induction; but should exceptions prove numerous\nand various in their features, our faith in the conclusion will be\nproportionally shaken, and at all events its importance lessened by the\ndestruction of its universality.\n\n(173.) In the conduct of this verification, we are to consider whether\nthe cause or law to which we are conducted be one already known and\nrecognised as a more general one, whose nature is well understood, and\nof which the phenomenon in question is but one more case in addition\nto those already known, or whether it be one less general, less known,\nor altogether new. In the latter case, our verification will suffice,\nif it merely shows that all the cases considered are plainly cases in\npoint. But in the former, the process of verification is of a much\nmore severe and definite kind. We must trace the action of our cause\nwith distinctness and precision, as modified by all the circumstances\nof each case; we must estimate its effects, and show that nothing\nunexplained remains behind; at least, in so far as the presence of\nunknown modifying causes is not concerned.\n\n(174.) Now, this is precisely the sort of process in which _residual\nphenomena_ (such as spoken of in art. 158.) may be expected to occur.\nIf our induction be really a valid and a comprehensive one, _whatever_\nremains unexplained in the comparison of its conclusion with particular\ncases, under all their circumstances, _is_ such a phenomenon, and comes\nin its turn to be a subject of inductive reasoning to discover its\ncause or laws. It is thus that we may be said to witness facts with\nthe eyes of reason; and it is thus that we are continually attaining a\nknowledge of new phenomena and new laws which lie beneath the surface\nof things, and give rise to the creation of fresh branches of science\nmore and more remote from common observation.\n\n(175.) Physical astronomy affords numerous and splendid instances of\nthis. The law, for example, which asserts that the planets are retained\nin their orbits about the sun, and satellites about their primaries,\nby an attractive force, decreasing as the square of the distances\nincreases, comes to be verified in each particular case by deducing\nfrom it the exact motions which, under the circumstances, ought to take\nplace, and comparing them with fact. This comparison, while it verifies\nin general the existence of the law of gravitation as supposed, and\nits adequacy to explain all the principal motions of every body in the\nsystem, yet leaves some small deviations in those of the planets, and\nsome very considerable ones in that of the moon and other satellites,\nstill unaccounted for; residual phenomena, which still remain to be\ntraced up to causes. By further examining these, their causes have at\nlength been ascertained, and found to consist in the mutual actions of\nthe planets on each other, and the disturbing influence of the sun on\nthe motions of the satellites.\n\n(176.) But a law of nature has not that degree of generality which\nfits it for a stepping-stone to greater inductions, unless it be\n_universal_ in its application. We cannot rely on its enabling us to\nextend our views beyond the circle of instances from which it was\nobtained, unless we have already had experience of its power to do so;\nunless it actually _has_ enabled us before trial to say what will take\nplace in cases analogous to those originally contemplated; unless, in\nshort, we have studiously placed ourselves in the situation of its\nantagonists, and even perversely endeavoured to find exceptions to\nit without success. It is in the precise proportion that a law once\nobtained endures this extreme severity of trial, that its value and\nimportance are to be estimated; and our next step in the verification\nof an induction must therefore consist in _extending_ its application\nto cases not originally contemplated; in studiously varying the\ncircumstances under which our causes act, with a view to ascertain\nwhether their effect is general; and in pushing the application of our\nlaws to extreme cases.\n\n(177.) For example, a fair induction from a great number of facts led\nGalileo to conclude that the accelerating power of gravity is the same\non all sorts of bodies, and on great and small masses indifferently;\nand this he exemplified by letting bodies of very different natures\nand weights fall at the same instant from a high tower, when it was\nobserved that they struck the ground at the same moment, abating a\ncertain trifling difference, due, as he justly believed it to be, to\nthe greater proportional resistance of the air to light than to heavy\nbodies. The experiment could not, at that time, be fairly tried with\nextremely light substances, such as cork, feathers, cotton, &c. because\nof the great resistance experienced by these in their fall; no means\nbeing then known of removing this cause of disturbance. It was not,\ntherefore, till after the invention of the air-pump that this law could\nbe put to the severe test of an extreme case. A guinea and a downy\nfeather were let drop at once from the upper part of a tall exhausted\nglass, and struck the bottom at the same moment. Let any one make the\ntrial _in the air_, and he will perceive the force of an _extreme case_.\n\n(178.) In the verification of a law whose expression is _quantitative_,\nnot only must its generality be established by the trial of it in as\nvarious circumstances as possible, but every such trial must be one of\nprecise measurement. And in such cases the means taken for subjecting\nit to trial ought to be so devised as to repeat and multiply a great\nnumber of times any deviation (if any exist); so that, let it be ever\nso small, it shall at last become sensible.\n\n(179.) For instance, let the law to be verified be, that _the gravity\nof every material body is in the direct proportion of its mass_, which\nis only another mode of expressing Galileo\u2019s law above mentioned.\nThe time of falling from any moderate height cannot be measured with\nprecision enough for our purpose: but if it can be repeated a very\ngreat multitude of times _without any loss or gain_ in the intervals,\nand the whole amount of the times of fall so repeated measured by\na clock; and if at the same time the resistance of the air can be\nrendered _exactly alike_ for all the bodies tried, we have here\nGalileo\u2019s trial in a much more refined state; and it is evident that\nalmost unlimited exactness may be obtained. Now, all this Newton\naccomplished by the simple and elegant contrivance of enclosing in a\nhollow pendulum the same weights of a great number of substances the\nmost different that could be found in all respects, as gold, glass,\nwood, water, wheat, &c.[44], and ascertaining the time required for\nthe pendulum so charged to make a great number of oscillations; in\neach of which it is clear the weights had to fall, and be raised again\nsuccessively, without loss of time, through the same _identical_\nspaces. Thus any difference, however inconsiderable, that might\nexist in the time of one such fall and rise would be multiplied and\naccumulated till they became sensible. And none having been discovered\nby so delicate a process in any case, the law was considered verified\nboth in respect of generality and exactness. This, however, is nothing\nto the verifications afforded by astronomical phenomena, where the\ndeviations, if any, accumulate for thousands of years instead of a few\nhours.\n\n(180.) The surest and best characteristic of a well-founded and\nextensive induction, however, is when verifications of it spring up,\nas it were, spontaneously, into notice, from quarters where they might\nbe least expected, or even among instances of that very kind which\nwere at first considered hostile to them. Evidence of this kind is\nirresistible, and compels assent with a weight which scarcely any other\npossesses. To give an example: M. Mitscherlich had announced a law to\nthis effect--_that_ the chemical elements of which all bodies consist\nare susceptible of being classified in distinct groups, which he termed\n_isomorphous_ groups; and _that_ these groups are so related, that\nwhen similar combinations are formed of individuals belonging to two,\nthree, or more of them, such combinations will crystallize in the same\ngeometrical forms. To this curious and important law there appeared\na remarkable exception. According to professor Mitscherlich, the\narsenic and phosphoric acids _are_ similar combinations coming under\nthe meaning of his law, and their combinations with soda and water,\nforming the salts known to chemists under the names of arseniate and\nphosphate of soda, ought, if the law were general, to crystallize in\nidentical shapes. The fact, however, was understood to be otherwise.\nBut lately, Mr. Clarke, a British chemist, having examined the two\nsalts attentively, ascertained the fact that their compositions\ndeviate essentially from that similarity which M. Mitscherlich\u2019s law\nrequires; and that, therefore, the exception in question disappears.\nThis was something: but, pursuing the subject further, the same\ningenious enquirer happily succeeded in producing a _new_ phosphate of\nsoda, differing from that generally known in containing a different\nproportion of water, and agreeing in composition exactly with the\narseniate. The crystals of this new salt, when examined, were found by\nhim to be precisely identical in form with those of the arseniate: thus\nverifying, in a most striking and totally unexpected manner, the law in\nquestion, or, as it is called, the law of isomorphism.\n\n(181.) Unexpected and peculiarly striking confirmations of inductive\nlaws frequently occur in the form of residual phenomena, in the course\nof investigations of a widely different nature from those which gave\nrise to the inductions themselves. A very elegant example may be cited\nin the unexpected confirmation of the law of the developement of heat\nin elastic fluids by compression, which is afforded by the phenomena\nof sound. The enquiry into the cause of sound had led to conclusions\nrespecting its mode of propagation, from which its velocity in the air\ncould be precisely calculated. The calculations were performed; but,\nwhen compared with fact, though the agreement was quite sufficient\nto show the general correctness of the cause and mode of propagation\nassigned, _yet_ the _whole_ velocity could not be shown to arise from\nthis theory. There was still a _residual_ velocity to be accounted\nfor, which placed dynamical philosophers for a long time in a great\ndilemma. At length Laplace struck on the happy idea, that this might\narise from the _heat_ developed in the act of that condensation which\nnecessarily takes place at every vibration by which sound is conveyed.\nThe matter was subjected to exact calculation, and the result was\nat once the complete explanation of the residual phenomenon, and a\nstriking confirmation of the general law of the developement of heat by\ncompression, under circumstances beyond artificial imitation.\n\n(182.) In extending our inductions to cases not originally\ncontemplated, there is one step which always strikes the mind with\npeculiar force, and with such a sensation of novelty and surprise,\nas often gives it a weight beyond its due philosophic value. It is\nthe transition from the little to the great, and _vice vers\u00e2_, but\nespecially the former. It is so beautiful to see, for instance, an\nexperiment performed in a watch-glass, or before a blowpipe, succeed,\nin a great manufactory, on many tons of matter, or, in the bosom of\na volcano, upon millions of cubic fathoms of lava, that we almost\nforget that these great masses are made up of watch-glassfuls, and\nblowpipe-beads. We see the enormous intervals between the stars and\nplanets of the heavens, which afford room for innumerable processes\nto be carried on, for light and heat to circulate, and for curious\nand complicated motions to go forward among them: we look more\nattentively, and we see sidereal systems, probably not less vast and\ncomplicated than our own, crowded apparently into a small space (from\nthe effect of their distance from us), and forming groups resembling\nbodies of a substantial appearance, having form and outline: yet we\nrecoil with incredulous surprise when we are asked _why_ we cannot\nconceive the atoms of a grain of sand to be as remote from each other\n(proportionally to their sizes) as the stars of the firmament; and\nwhy there may not be going on, in that little microcosm, processes\nas complicated and wonderful as those of the great world around us.\nYet the student who makes any progress in natural philosophy will\nencounter numberless cases in which this transfer of ideas from the one\nextreme of magnitude to the other will be called for: he will find,\nfor instance, the phenomena of the propagation of winds referred to\nthe same laws which regulate the propagation of motions through the\nsmallest masses of air; those of lightning assimilated to the mere\ncommunication of an electric spark, and those of earthquakes to the\ntremors of a stretched wire: in short, he must lay his account to\nfinding the distinction of great and little altogether annihilated in\nnature: and it is well for man that such is the case, and that the same\nlaws, which he can discover and verify in his own circumscribed sphere\nof power, should prove available to him when he comes to apply them on\nthe greatest scale; since it is thus only that he is enabled to become\nan exciting cause in operations of any considerable magnitude, and to\nvindicate his importance in creation.\n\n(183.) But the business of induction does not end here: its final\nresult must be followed out into all its consequences, and applied to\nall those cases which seem even remotely to bear upon the subject of\nenquiry. Every new addition to our stock of causes becomes a means\nof fresh attack with new vantage ground upon all those unexplained\nparts of former phenomena which have resisted previous efforts. It\ncan hardly be pressed forcibly enough on the attention of the student\nof nature, that there is scarcely any natural phenomenon which can be\nfully and completely explained in all its circumstances, without a\nunion of several, perhaps of all, the sciences. The great phenomena of\nastronomy, indeed, may be considered exceptions; but this is merely\nbecause their scale is so vast that one only of the most widely\nextending forces of nature takes the lead, and all those agents whose\nsphere of action is limited to narrower bounds, and which determine\nthe production of phenomena nearer at hand, are thrown into the back\nground, and become merged and lost in comparative insignificance. But\nin the more intimate phenomena which surround us it is far otherwise.\nInto what a complication of different branches of science are we not\nled by the consideration of such a phenomenon as rain, for instance,\nor flame, or a thousand others, which are constantly going on before\nour eyes? Hence, it is hardly possible to arrive at the knowledge of\na law of any degree of generality in any branch of science, but it\nimmediately furnishes us with a means of extending our knowledge of\ninnumerable others, the most remote from the point we set out from; so\nthat, when once embarked in any physical research, it is impossible for\nany one to predict where it may ultimately lead him.\n\n(184.) This remark rather belongs to the inverse or _deductive_\nprocess, by which we pursue laws into their remote consequences.\nBut it is very important to observe, that the successful process of\nscientific enquiry demands continually the alternate use of both\nthe _inductive_ and _deductive_ method. The path by which we rise to\nknowledge must be made smooth and beaten in its lower steps, and often\nascended and descended, before we can scale our way to any eminence,\nmuch less climb to the summit. The achievement is too great for a\nsingle effort; stations must be established, and communications kept\nopen with all below. To quit metaphor; there is nothing so instructive,\nor so likely to lead to the acquisition of general views, as this\npursuit of the consequences of a law once arrived at into every subject\nwhere it may seem likely to have an influence. The discovery of a\nnew law of nature, a new ultimate fact, or one that even temporarily\nputs on that appearance, is like the discovery of a new element in\nchemistry. Thus, selenium was hardly discovered by Berzelius in the\nvitriol works of Fahlun, when it presently made its appearance in the\nsublimates of Stromboli, and the rare and curious products of the\nHungarian mines. And thus it is with every new law, or general fact. It\nis hardly announced before its traces are found every where, and every\none is astonished at its having so long remained concealed. And hence\nit happens that unexpected lights are shed at length over parts of\nscience that had been abandoned in despair, and given over to hopeless\nobscurity.\n\n(185.) The verification of _quantitative_ laws has been already spoken\nof (178.); but their importance in physical science is so very great,\ninasmuch as they alone afford a handle to strict mathematical deductive\napplication, that something ought to be said of the nature of the\ninductions by which they are to be arrived at. In their simplest or\nleast general stages (of which alone we speak at present) they usually\nexpress some numerical relation between two quantities dependent on\neach other, either as collateral effects of a common cause, or as the\namount of its effect under given numerical circumstances or _data_.\nFor example, the law of refraction before noticed (\u00a7 22.) expresses,\nby a very simple relation, the amount of angular deviation of a ray\nof light from its course, when the _angle_ at which it is inclined to\nthe refracting surface is known, viz. that the _sine_ of the angle\nwhich the incident ray makes with a perpendicular to the surface is\nalways to that of the angle made by the refracted ray with the same\nperpendicular, in a constant proportion, so long as the refracting\nsubstance is the same. To arrive inductively at laws of this kind,\nwhere one quantity _depends_ on or _varies with_ another, all that is\nrequired is a series of careful and exact measures in every different\nstate of the _datum_ and _qu\u00e6situm_. Here, however, the mathematical\nform of the law being of the highest importance, the greatest attention\nmust be given to the _extreme cases_ as well as to all those points\nwhere the one quantity changes rapidly with a small change of the\nother.[45] The results must be set down in a table in which the _datum_\ngradually increases in magnitude from the lowest to the highest limit\nof which it is susceptible. It will depend then entirely on our\nhabit of treating mathematical subjects, how far we may be able to\ninclude such a table in the distinct statement of a mathematical law.\nThe discovery of such laws is often remarkably facilitated by the\ncontemplation of a class of phenomena to be noticed further on, under\nthe head of Collective Instances, (see \u00a7 194.) in which the nature of\nthe mathematical expression in which the law sought is comprehended, is\npointed out by the figure of some curve brought under inspection by a\nproper mode of experimenting.\n\n(186.) After all, unless our induction embraces a series of cases which\nabsolutely include the whole scale of variation of which the quantities\nin question admit, the mathematical expression so obtained cannot be\ndepended upon as the true one, and if the scale actually embraced be\nsmall, the extension of laws so derived to extreme cases will in all\nprobability be exceedingly fallacious. For example, air is an elastic\nfluid, and as such, if enclosed in a confined space and squeezed, its\nbulk diminishes: now, from a great number of trials made in cases where\nthe air has been compressed into a half, a third, &c. even as far\nas a fiftieth of its bulk, or less, it has been concluded that \u201cthe\ndensity of air is proportional to the compressing force,\u201d or the bulk\nit occupies _inversely_ as that force; and when the air is rarefied\nby taking off part of its natural pressure, the same is found to be\nthe case, within very extensive limits. Yet it is impossible that this\nshould be, strictly or mathematically speaking, the true law; for, if\nit were so, there could be no limit to the condensation of air, while\nyet we have the strongest analogies to show that long before it had\nreached any very enormous pitch the air would be reduced into a liquid,\nand even, perhaps, if pressed yet more violently, into a solid form.\n\n(187.) Laws thus derived, by the direct process of including in\nmathematical formul\u00e6 the results of a greater or less number of\nmeasurements, are called \u201cempirical laws.\u201d A good example of such a\nlaw is that given by Dr. Young (Phil. Trans. 1826,) for the decrement\nof life, or the law of mortality. Empirical laws in this state are\nevidently _unverified inductions_, and are to be received and reasoned\non with the utmost reserve. No confidence can ever be placed in them\nbeyond the limits of the data from which they are derived; and even\nwithin those limits they require a special and severe scrutiny to\nexamine _how nearly_ they do represent the observed facts; that is to\nsay, whether, in the comparison of their results with the observed\nquantities, the differences are such as may fairly be attributed to\nerror of observation. When so carefully examined, they become, however,\nmost valuable; and frequently, when afterwards verified theoretically\nby a deductive process (as will be explained in our next chapter),\nturn out to be rigorous laws of nature, and afford the noblest and\nmost convincing supports of which theories themselves are susceptible.\nThe finest instances of this kind are the great laws of the planetary\nmotions deduced by Kepler, entirely from a comparison of observations\nwith each other, with no assistance from theory. These laws, viz. that\nthe planets move in ellipses round the sun; that each describes about\nthe sun\u2019s centre equal areas in equal times; and that in the orbits of\ndifferent planets the squares of the periodical times are proportional\nto the cubes of the distances; were the results of inconceivable\nlabour of calculation and comparison: but they amply repaid the\nlabour bestowed on them, by affording afterwards the most conclusive\nand unanswerable proofs of the Newtonian system. On the other hand,\nwhen empirical laws are unduly relied on beyond the limits of the\nobservations from which they were deduced, there is no more fertile\nsource of fatal mistakes. The formul\u00e6 which have been empirically\ndeduced for the elasticity of steam (till very recently), and those\nfor the resistance of fluids, and other similar subjects, have almost\ninvariably failed to support the theoretical structures which have been\nerected on them.\n\n(188.) It is a remarkable and happy fact, that the shortest and most\ndirect of all inductions should be that which has led at once, or by\nvery few steps, to the highest of all natural laws,--we mean those of\nmotion and force. Nothing can be more simple, precise, and general,\nthan the enunciation of these laws; and, as we have once before\nobserved, their application to particular facts in the descending or\ndeductive method is limited by nothing but the limited extent of our\nmathematics. It would seem, then, that dynamical science were taken\nthenceforward out of the pale of induction, and transformed into a\nmatter of absolute _\u00e0 priori_ reasoning, as much as geometry; and so\nit would be, were our mathematics perfect, and all the _data_ known.\nUnhappily, the first is so far from being the case, that in many\nof the most interesting branches of dynamical enquiry they leave\nus completely at a loss. In what relates to the motions of fluids,\nfor instance, this is severely felt. We can include our problems,\nit is true, in algebraical equations, and we can demonstrate that\nthey _contain_ the solutions; but the equations themselves are so\nintractable, and present such insuperable difficulties, that they often\nleave us quite as much in the dark as before. But even were these\ndifficulties overcome, recourse to experience must still be had, to\nestablish the _data_ on which particular applications are to depend;\nand although mathematical analysis affords very powerful means of\n_representing_ in general terms the data of any proposed case, and\n_afterwards_, by comparison of its results with fact, determining\n_what_ those data must be to explain the observed phenomena, still,\nin any mode of considering the matter, an appeal to experience in\nevery particular instance of application is unavoidable, even when\nthe general principles are regarded as sufficiently established\nwithout it. Now, in all such cases of difficulty we must recur to our\ninductive processes, and regard the branches of dynamical science where\nthis takes place as purely experimental. By this we gain an immense\nadvantage, viz. that in all those points of them where the abstract\ndynamical principles _do_ afford distinct conclusions, we obtain\nverifications for our inductions of the highest and finest possible\nkind. When we work our way up inductively to one of these results, we\ncannot help feeling the strongest assurance of the validity of the\ninduction.\n\n(189.) The necessity of this appeal to experiment in every thing\nrelating to the motions of fluids on the large scale has long been\nfelt. Newton himself, who laid the first foundations of hydrodynamical\nscience (so this branch of dynamics is called), distinctly perceived\nit, and set the example of laborious and exact experiments on their\nresistance to motion, and other particulars. Venturi, Bernoulli, and\nmany others, have applied the method of experiment to the motions\nof fluids in pipes and canals; and recently the brothers Weber have\npublished an elaborate and excellent experimental enquiry into the\nphenomena of waves. One of the greatest and most successful attempts,\nhowever, to bring an important, and till then very obscure, branch\nof dynamical enquiry back to the dominion of experiment, has been\nmade by Chladni and Savart in the case of sound and vibratory motion\nin general; and it is greatly to be wished that the example may be\nfollowed in many others hardly less abstruse and impracticable when\ntheoretically treated. In such cases the inductive and deductive\nmethods of enquiry may be said to go hand in hand, the one verifying\nthe conclusions deduced by the other; and the combination of experiment\nand theory, which may thus be brought to bear in such cases, forms\nan engine of discovery infinitely more powerful than either taken\nseparately. This state of any department of science is perhaps of\nall others the most interesting, and that which promises the most to\nresearch.\n\n(190.) It can hardly be expected that we should terminate this division\nof our subject without some mention of the \u201cprerogatives of instances\u201d\nof Bacon, by which he understands characteristic phenomena, selected\nfrom the great miscellaneous mass of facts which occur in nature,\nand which, by their number, indistinctness, and complication, tend\nrather to confuse than to direct the mind in its search for causes\nand general heads of induction. Phenomena so selected on account of\nsome peculiarly forcible way in which they strike the reason, and\nimpress us with a kind of sense of causation, or a particular aptitude\nfor generalization, he considers, and justly, as holding a kind of\nprerogative dignity, and claiming our first and especial attention in\nphysical enquiries.\n\n(191.) We have already observed that, in forming inductions, it will\nmost commonly happen that we are led to our conclusions by the especial\nforce of some two or three strongly impressive facts, rather than by\naffording the whole mass of cases a regular consideration; and hence\nthe need of cautious verification. Indeed, so strong is this propensity\nof the human mind, that there is hardly a more common thing than to\nfind persons ready to assign a cause for every thing they see, and, in\nso doing, to join things the most incongruous, by analogies the most\nfanciful. This being the case, it is evidently of great importance\nthat these first ready impulses of the mind should be made on the\ncontemplation of the cases most likely to lead to good inductions.\nThe misfortune, however, is, in natural philosophy, that the choice\ndoes not rest with us. We must take the instances as nature presents\nthem. Even if we are furnished with a list of them in tabular order,\nwe must understand and compare them with each other, before we can\ntell which _are_ the instances thus deservedly entitled to the highest\nconsideration. And, after all, after much labour in vain, and groping\nin the dark, accident or casual observation will present a case which\nstrikes us at once with a full insight into a subject, before we can\neven have time to determine to what class its _prerogative_ belongs.\nFor example, the laws of crystallography were obscure, and its causes\nstill more so, till Ha\u00fcy fortunately dropped a beautiful crystal of\ncalcareous spar on a stone pavement, and broke it. In piecing together\nthe fragments, he observed their facets not to correspond with those of\nthe crystal in its entire state, but to belong to another form; and,\nfollowing out the hint offered by a \u201c_glaring instance_\u201d thus casually\nobtruded on his notice, he discovered the beautiful laws of the\ncleavage, and the primitive forms of minerals.\n\n(192.) It has always appeared to us, we must confess, that the help\nwhich the classification of instances, under their different titles of\nprerogative, affords to inductions, however just such classification\nmay be in itself, is yet more apparent than real. The force of the\ninstance must be felt in the mind, before it can be referred to\nits place in the system; and, before it can be either referred or\nappretiated, it must be known; and when it _is_ appretiated, we are\nready enough to interweave it in our web of induction, without greatly\ntroubling ourselves with enquiring whence it derives the weight we\nacknowledge it to have in our decisions. However, since much importance\nis usually attached to this part of Bacon\u2019s work, we shall here give a\nfew examples to illustrate the nature of some of his principal cases.\nOne, of what he calls \u201cglaring instances,\u201d has just been mentioned.\nIn these, the _nature_ or cause enquired into, (which in this case\nis the cause of the assumption of a peculiar external form, or the\ninternal _structure_ of a crystal,) \u201cstands naked and alone, and this\nin an eminent manner, or in the highest degree of its power.\u201d No doubt,\nsuch instances as these are highly instructive; but the difficulty in\nphysics is to find such, not to perceive their force when found.\n\n(193.) The contrary of glaring are \u201cclandestine instances,\u201d where\n\u201cthe nature sought is exhibited in its weakest and most imperfect\nstate.\u201d Of this, Bacon himself has given an admirable example in the\ncohesion of fluids, as a _clandestine instance_ of the \u201c_nature_ or\nquality of consistence, or solidity.\u201d Yet here, again, the same acute\ndiscrimination which enabled Bacon to perceive the analogy which\nconnects fluids with solids, through the common property of cohesive\nattraction, would, at the same time, have enabled him to draw from it,\nif properly supported, every consequence necessary to forming just\nnotions of the cohesive force; nor does its reference to the class of\nclandestine instances at all assist in bringing forward and maturing\nthe final results. When, however, the final result is obtained,--when\nour induction is complete, and we would verify it,--this class of\ninstances is of great use, being, in fact, frequently no other than\nthat of _extreme cases_, such as we have already spoken of (in \u00a7\n177.); which, by placing our conclusions, as it were, in violent\ncircumstances, try their temper, and bring their vigour to the test.\n\n(194.) Bacon\u2019s \u201ccollective instances\u201d (_instanti\u00e6 unionis_), are no\nother than general facts, or laws of some degree of generality, and\nare themselves the results of induction. But there is a species of\ncollective instance which Bacon does not seem to have contemplated, of\na peculiarly instructive character; and that is, where particular cases\nare offered to our observation in such numbers at once as to make the\ninduction of their law a matter of ocular inspection. For example, the\nparabolic form assumed by a jet of water spouted from a round hole,\nis a _collective instance_ of the velocities and directions of the\nmotions of all the particles which compose it _seen at once_, and which\nthus leads us, without trouble, to recognize the law of the motion of\na projectile. Again, the beautiful figures exhibited by sand strewed\non regular plates of glass or metal set in vibration, are _collective\ninstances_ of an infinite number of points which remain at rest while\nthe remainder of the plate vibrates; and in consequence afford us,\nas it were, a sight of the law which regulates their arrangement\nand sequence throughout the whole surface. The beautifully coloured\nlemniscates seen around the optic axes of crystals exposed to polarized\nlight afford a superb example of the same kind, pointing at once to\nthe general mathematical expression of the law which regulates their\nproduction.[46] Of such collective instances as these, it is easy to\nsee the importance, and its reason. They lead us to a general law by an\ninduction which offers itself spontaneously, and thus furnish advanced\npoints in our enquiries; and when we start from these, already \u201ca\nthousand steps are lost.\u201d\n\n(195.) A fine example of a collective instance is that of the system\nof Jupiter or Saturn with its satellites. We have here, in miniature,\nand seen at one view, a system similar to that of the planets about\nthe sun; of which, from the circumstance of our being involved in it,\nand unfavourably situated for seeing it otherwise than in detail, we\nare incapacitated from forming a general idea but by slow progressive\nefforts of reason. Accordingly, the contemplation of the _circumjovial\nplanets_ (as they were called) most materially assisted in securing the\nadmission of the Copernican system.\n\n(196.) Of \u201cCrucial instances\u201d we have also already spoken, as affording\nthe readiest and securest means of eliminating extraneous causes, and\ndeciding between rival hypotheses. Owing to the disposition of the\nmind to form hypotheses, and to prejudge cases, it constantly happens\nthat, among all the possible suppositions which may occur, two or three\nprincipal ones occupy us, to the exclusion of the rest; or it may\nbe that, if we have been less precipitate, out of a great multitude\nrejected for obvious inapplicability to some one or other case, two or\nthree of better claims remain for decision; and this such instances\nenable us to do. One of the instances cited by Bacon in illustration of\nhis crucial class is very remarkable, being neither more nor less than\nthe proposal of a direct experiment to determine whether the tendency\nof heavy bodies downwards is a result of some peculiar mechanism in\nthemselves, or of the attraction of the earth \u201cby the corporeal mass\nthereof, as by a collection of bodies of the same nature.\u201d If it be so,\nhe says, \u201cit will follow that the nearer all bodies approach to the\nearth, the stronger and with the greater force and velocity they will\ntend to it; but the farther they are, the weaker and slower:\u201d and his\nexperiment consists in comparing the effect of a spring and a weight\nin keeping up the motions of two \u201cclocks,\u201d regulated together, and\nremoved alternately to the tops of high buildings and into the deepest\nmines. By _clocks_ he could not have meant pendulum clocks, which were\nnot then known, (the first made in England was in 1662,) _fly_-clocks,\nso that the comparison, though too coarse, was not contrary to sound\nmechanical principles. In short, its principle was the comparison of\nthe effect of a spring with that of a weight, in producing certain\nmotions in certain times, on heights and in mines. Now, this is the\nvery same thing that has really been done in the recent experiments\nof professors Airy and Whewell in Dolcoath mine: a pendulum (a weight\nmoved by gravity) has been compared with a chronometer balance, moved\nand regulated by a spring. In his 37th aphorism, Bacon also speaks of\ngravity as an incorporeal power, acting at a distance, and _requiring\ntime for its transmission_; a consideration which occurred at a later\nperiod to Laplace, in one of his most delicate investigations.\n\n(197.) A well chosen and strongly marked crucial instance is,\nsometimes, of the highest importance; when two theories, which run\nparallel to each other (as is sometimes the case) in their explanation\nof great classes of phenomena, at length come to be placed at issue\nupon a single fact. A beautiful instance of this will be cited in the\nnext section. We may add to the examples above given of such instances,\nthat of the application of chemical tests, which are almost universally\ncrucial experiments.\n\n(198.) Bacon\u2019s \u201ctravelling instances\u201d are those in which the _nature_\nor quality under investigation \u201ctravels,\u201d or varies in degree; and thus\n(according to \u00a7 152.) afford an indication of a cause by a gradation\nof intensity in the effect. One of his instances is very happy, being\nthat of \u201cpaper, which is white when dry, but proves less so when wet,\nand comes nearer to the state of transparency upon the exclusion of the\nair, and admission of water.\u201d In reading this, and many other instances\nin the Novum Organum, one would almost suppose (had it been written)\nthat its author had taken them from Newton\u2019s Optics.\n\n(199.) The travelling instances, as well as what Bacon terms \u201cfrontier\ninstances,\u201d are cases in which we are enabled to trace that general\nlaw which seems to pervade all nature--the law, as it is termed, of\ncontinuity, and which is expressed in the well known sentence, \u201cNatura\nnon agit per saltum.\u201d The pursuit of this law into cases where its\napplication is not at first sight obvious, has proved a fertile source\nof physical discovery, and led us to the knowledge of an analogy and\nintimate connection of phenomena between which at first we should never\nhave expected to find any.\n\n(200.) For example, the transparency of gold leaf, which permits a\nbluish-green light to pass through it, is a frontier instance between\nthe transparency of pellucid bodies and the opacity of metals, and it\nprevents a breach of the law of continuity between transparent and\nopake bodies, by exhibiting a body of the class generally regarded\nthe most opake in nature, as still possessed of some slight degree\nof transparency. It thus proves that the quality of opacity is not a\n_contrary_ or _antagonist_ quality to that of transparency, but only\nits extreme lowest degree.\n\n\n\n\nCHAP. VII.\n\n  OF THE HIGHER DEGREES OF INDUCTIVE GENERALIZATION, AND OF THE\n    FORMATION AND VERIFICATION OF THEORIES.\n\n\n(201.) As particular inductions and laws of the first degree of\ngenerality are obtained from the consideration of individual facts,\nso Theories result from a consideration of these laws, and of the\nproximate causes brought into view in the previous process, regarded\nall together as constituting a new set of phenomena, the creatures\nof reason rather than of sense, and each representing under general\nlanguage innumerable particular facts. In raising these higher\ninductions, therefore, more scope is given to the exercise of pure\nreason than in slowly groping out our first results. The mind is more\ndisencumbered of matter, and moves as it were in its own element. What\nis now before it, it perceives more intimately, and less through the\nmedium of sense, or at least not in the same manner as when actually at\nwork on the immediate objects of sense. But it must not be therefore\nsupposed that, in the formation of theories, we are abandoned to\nthe unrestrained exercise of imagination, or at liberty to lay down\narbitrary principles, or assume the existence of mere fanciful causes.\nThe liberty of speculation which we possess in the domains of theory is\nnot like the wild licence of the slave broke loose from his fetters,\nbut rather like that of the freeman who has learned the lessons of\nself-restraint in the school of just subordination. The ultimate\nobjects we pursue in the highest theories are the same as those of the\nlowest inductions; and the means by which we can most securely attain\nthem bear a close analogy to those which we have found successful in\nsuch inferior cases.\n\n(202.) The immediate object we propose to ourselves in physical\ntheories is the analysis of phenomena, and the knowledge of the hidden\nprocesses of nature in their production, so far as they can be traced\nby us. An important part of this knowledge consists in a discovery\nof the actual structure or mechanism of the universe and its parts,\nthrough which, and by which, those processes are executed; and of the\nagents which are concerned in their performance. Now, the mechanism of\nnature is for the most part either on too large or too small a scale\nto be immediately cognizable by our senses; and her agents in like\nmanner elude direct observation, and become known to us only by their\neffects. It is in vain therefore that we desire to become witnesses to\nthe processes carried on with such means, and to be admitted into the\nsecret recesses and laboratories where they are effected. Microscopes\nhave been constructed which magnify more than a thousand times in\n_linear_ dimension, so that the smallest visible grain of sand may\nbe enlarged to the appearance of one a thousand million times more\nbulky; yet the only impression we receive by viewing it through such\na magnifier is, that it reminds us of some vast fragment of a rock,\nwhile the intimate structure on which depend its colour, its hardness,\nand its chemical properties, remains still concealed: we do not seem\nto have made even an approach to a closer analysis of it by any such\nscrutiny.\n\n(203.) On the other hand, the mechanism of the great system of which\nour planet forms a part escapes immediate observation by the immensity\nof its scale, nay, even by the slowness of its evolutions. The motion\nof the minute hand of a watch can hardly be perceived without the\nclosest attention, and that of the hour hand not at all. But what are\nthese, in respect of the impression of slowness they produce in our\nminds, compared with a revolving movement which takes a whole year, or\ntwelve, thirty, or eighty years to complete, as is the case with the\nplanets in their revolutions round the sun. Yet no sooner do we come\nto reflect on the linear dimensions of these orbs, (which however we\ndo not _see_, nor can we measure them but by a long, circuitous, and\ndifficult process,) than we are lost in astonishment at the swiftness\nof the very motions which before seemed so slow.[47] The motion of the\nsails of a windmill offers (on a small scale) an illustrative case. At\na distance the rotation seems slow and steady--but when we stand close\nto one of the sails in its sweep, we are surprised at the swiftness\nwith which it rushes by us.\n\n(204.) Again, the agents employed by nature to act on material\nstructures are invisible, and only to be traced by the effects they\nproduce. Heat dilates matter with an irresistible force; but what heat\nis, remains yet a problem. A current of electricity passing along a\nwire moves a magnetized needle at a distance; but except from this\neffect we perceive no difference between the condition of the wire\nwhen it conveys and when it does not convey the stream: and we apply\nthe terms current, or stream, to the electricity only because in some\nof its relations it reminds us of something we have observed in a\nstream of air or water. In like manner we see that the moon circulates\nabout the earth; and because we believe it to be a solid mass, and\nhave never seen one solid substance revolve round another within our\nreach to handle and examine unless retained by a force or united by a\ntie, we conclude that there _is_ a force, and a mode of connection,\nbetween the moon and the earth; though, what that mode can be, we have\nno conception, nor can imagine _how_ such a force can be exerted at a\ndistance, and with empty space, or at most an invisible fluid, between.\n(See \u00a7 148.)\n\n(205.) Yet are we not to despair, since we see regular and beautiful\nresults brought about in human works by means which nobody would, at\nfirst sight, think could have any thing to do with them. A sheet of\nblank paper is placed upon a frame, and shoved forwards, and after\nwinding its way successively over and under half a dozen rollers, and\nperforming many other strange evolutions, comes out printed on both\nsides. And, after all, the acting cause in this process is nothing\nmore than a few gallons of water boiled in an iron vessel, at a\ndistance from the scene of operations. But _why_ the water so boiled\nshould be capable of producing the active energy which sets the whole\napparatus in motion is, and will probably long remain, a secret to us.\n\n(206.) This, however, does not at all prevent our having a very perfect\ncomprehension of the whole subsequent process. We might frequent\nprinting-houses, and form a theory of printing, and having worked our\nway up to the point where the mechanical action commenced (the boiler\nof the steam-engine), and verified it by taking to pieces, and putting\ntogether again, the train of wheels and the presses, and by sound\ntheoretical examination of all the transfers of motion from one part to\nanother; we should, at length, pronounce our theory good, and declare\nthat we understood printing thoroughly. Nay, we might even go away and\napply the principles of mechanism we had learned in this enquiry to\nother widely different purposes; construct other machines, and put them\nin motion by the same moving power, and all without arriving at any\ncorrect idea as to the ultimate source of the force employed. But, if\nwe were inclined to theorize farther, we might do so; and it is easy\nto imagine how two theorists might form very different _hypotheses_ as\nto the origin of the power which alternately raised and depressed the\npiston-rod of the engine. One, for example, might maintain that the\nboiler (whose contents we will suppose that neither theorist has been\npermitted to examine) was the den of some powerful unknown animal, and\nhe would not be without plausible analogies in the warmth, the supply\nof fuel and water, the breathing noises, the smoke, and above all, the\nmechanical power exerted. He would say (not without a show of reason),\nthat where there is a positive and wonderful effect, and many strong\nanalogies, such as materials consumed, and all the usual signs of life\nmaintained, we are not to deny the existence of animal life because\nwe know no animal that consumes such food. Nay, he might observe with\ntruth, that the fuel actually consists of the chemical ingredients\nwhich constitute the chief food of all animals, &c.; while, on the\nother hand, his brother theorist, who caught a glimpse of the fire,\nand detected the peculiar sounds of ebullition, might acquire a better\nnotion of the case, and form a theory more in consonance with fact.\n\n(207.) Now, nothing is more common in physics than to find two, or even\nmany, _theories_ maintained as to the origin of a natural phenomenon.\nFor instance, in the case of heat itself, one considers it as a really\nexisting material fluid, of such exceeding subtlety as to penetrate\nall bodies, and even to be capable of combining with them chemically;\nwhile another regards it as nothing but a rapid vibratory or rotatory\nmotion in the ultimate particles of the bodies heated; and produces\na singularly ingenious train of mechanical reasoning to show, that\nthere is nothing contradictory to sound dynamical principles in such\na doctrine. Thus, again, with light: one considers it as consisting\nin actual particles darted forth from luminous bodies, and acted\nupon in their progress by forces of extreme intensity residing in the\nsubstances on which they strike; another, in the vibratory motion of\nthe particles of luminous bodies, communicated to a peculiar subtle and\nhighly elastic ethereal medium, filling all space, and conveyed through\nit into our eyes, as sounds are to our ears, by the undulations of the\nair.\n\n(208.) Now, are we to be deterred from framing hypotheses and\nconstructing theories, because we meet with such dilemmas, and\nfind ourselves frequently beyond our depth? Undoubtedly not. _Est\nquodam prodire tenus si non datur ultra._ Hypotheses, with respect\nto theories, are what presumed proximate causes are with respect to\nparticular inductions: they afford us motives for searching into\nanalogies; grounds of citation to bring before us all the cases which\nseem to bear upon them, for examination. A well imagined hypothesis,\nif it have been suggested by a fair inductive consideration of general\nlaws, can hardly fail at least of enabling us to generalize a step\nfarther, and group together several such laws under a more universal\nexpression. But this is taking a very limited view of the value and\nimportance of hypotheses: it may happen (and it has happened in the\ncase of the undulatory doctrine of light) that such a weight of analogy\nand probability may become accumulated on the side of an hypothesis,\nthat we are compelled to admit one of two things; either that it is\nan actual statement of what really passes in nature, or that the\nreality, whatever it be, must run so close a parallel with it, as to\nadmit of some mode of expression common to both, at least in so far\nas the phenomena actually known are concerned. Now, this is a very\ngreat step, not only for its own sake, as leading us to a high point in\nphilosophical speculation, but for its applications; because whatever\nconclusions we deduce from an hypothesis so supported must have at\nleast a strong presumption in their favour: and we may be thus led to\nthe trial of many curious experiments, and to the imagining of many\nuseful and important contrivances, which we should never otherwise have\nthought of, and which, at all events, if verified in practice, are real\nadditions to our stock of knowledge and to the arts of life.\n\n(209.) In framing a theory which shall render a rational account of\nany natural phenomenon, we have _first_ to consider the agents on\nwhich it depends, or the causes to which we regard it as ultimately\nreferable. These agents are not to be arbitrarily assumed; they\nmust be such as we have good inductive grounds to believe do exist\nin nature, and do perform a part in phenomena analogous to those we\nwould render an account of; or such, whose presence in the actual\ncase can be demonstrated by unequivocal signs. They must be _ver\u00e6\ncaus\u00e6_, in short, which we can not only show to exist and to act,\nbut the laws of whose action we can derive independently, by direct\ninduction, from experiments purposely instituted; or at least make\nsuch suppositions respecting them as shall not be contrary to our\nexperience, and which will remain to be verified by the coincidence of\nthe conclusions we shall deduce from them, with facts. For example,\nin the theory of gravitation we suppose an agent,--_viz._ force, or\nmechanical power,--to act on _any_ material body which is placed in\nthe presence of _any_ other, and to urge the two mutually towards each\nother. This is a _vera causa_; for heavy bodies (that is, all bodies,\nbut some more, some less,) tend to, or endeavour to reach, the earth,\nand require the exertion of force to counteract this endeavour, or\nto keep them up. Now, that which opposes and neutralizes force _is_\nforce. And again, a plumb-line, which, when allowed to hang freely,\nalways hangs perpendicularly; is found to hang observably aside from\nthe perpendicular when in the neighbourhood of a considerable mountain;\nthereby proving that a force is exerted upon it, which draws it towards\nthe mountain. Moreover, since it is a fact that the moon does circulate\nabout the earth, it must be drawn towards the earth by a force; for if\nthere were no force acting upon it, it would go on in a straight line\nwithout turning aside to circulate in an orbit, and would, therefore,\nsoon go away and be lost in space. This force, then, which we call the\n_force_ of gravity, is a real cause.\n\n(210.) We have next to consider the laws which regulate the action of\nthese our primary agents; and these we can only arrive at in three\nways: 1st, By inductive reasoning; that is, by examining all the\ncases in which we know them to be exercised, inferring, as well as\ncircumstances will permit, its amount or intensity in each particular\ncase, and then piecing together, as it were, these _disjecta membra_,\ngeneralizing from them, and so arriving at the laws desired; 2dly,\nBy forming at once a bold hypothesis, particularizing the law,\nand trying the truth of it by following out its consequences and\ncomparing them with facts; or, 3dly, By a process partaking of both\nthese, and combining the advantages of both without their defects,\nviz. by assuming indeed the laws we would discover, but so generally\nexpressed, that they shall include an unlimited variety of particular\nlaws;--following out the consequences of this assumption, by the\napplication of such general principles as the case admits;--comparing\nthem in succession with all the particular cases within our knowledge;\nand, lastly, _on this comparison_, so modifying and restricting the\ngeneral enunciation of our laws as to _make the results agree_.\n\n(211.) All these three processes for the discovery of those general\nelementary laws on which the higher theories are grounded are\napplicable with different advantage in different circumstances.\nWe might exemplify their successive application to the case of\ngravitation: but as this would rather lead into a disquisition too\nparticular for the objects of this discourse, and carry us too much\ninto the domain of technical mathematics, we shall content ourselves\nwith remarking, that the method last mentioned is that which\nmathematicians (especially such as have a considerable command of\nthose general modes of representing and reasoning on quantity, which\nconstitute the higher analysis,) find the most universally applicable,\nand the most efficacious; and that it is applicable with especial\nadvantage in cases where subordinate inductions of the kind described\nin the last section have already led to laws of a certain generality\nadmitting of mathematical expression. Such a case, for instance,\nis the elliptic motion of a planet, which is a general proposition\nincluding the statement of an infinite number of particular _places_,\nin which the laws of its motion allow it to be some time or other\nfound, and for which, of course, the law of force must be so assumed as\nto account.\n\n(212.) With regard to the first process of the three above enumerated,\nit is in fact an induction of the kind described in \u00a7 185.; and all\nthe remarks we there made on that kind of induction apply to it in\nthis stage. The direct assumption of a particular hypothesis has been\noccasionally practised very successfully. As examples, we may mention\nCoulomb\u2019s and Poisson\u2019s theories of electricity and magnetism, in\nboth which, phenomena of a very complicated and interesting nature\nare referred to the actions of attractive and repulsive forces,\nfollowing a law similar in its expression to the law of gravitation.\nBut the difficulty and labour, which, in the greater theories, always\nattends the pursuit of a fundamental law into its remote consequences,\neffectually precludes this method from being commonly resorted to as\na means of discovery, unless we have some good reason, from analogy\nor otherwise, for believing that the attempt will prove successful,\nor have been first led by partial inductions to particular laws which\nnaturally point it out for trial.\n\n(213.) In this case the law assumes all the characters of a general\nphenomenon resulting from an induction of particulars, but not yet\nverified by comparison with _all_ the particulars, nor extended to all\nthat it is capable of including. (See \u00a7 171.) It is the verification\nof such inductions which constitutes theory in its largest sense, and\nwhich embraces an estimation of the influence of all such circumstances\nas may modify the effect of the cause whose laws of action we have\narrived at and would verify. To return to our example: particular\ninductions drawn from the motions of the several planets about the\nsun, and of the satellites round their primaries, &c. having led us\nto the general conception of an attractive force exerted by every\nparticle of matter in the universe on every other according to the law\nto which we attach the name of gravitation; when we would verify this\ninduction, we must set out with assuming this law, considering the\nwhole system as subjected to its influence and implicitly obeying it,\nand nothing interfering with its action; we then, for the first time,\nperceive a train of modifying circumstances which had not occurred to\nus when reasoning upwards from particulars to obtain the fundamental\nlaw; we perceive that _all the planets_ must attract _each other_,\nmust therefore draw each other out of the orbits which they would\nhave if acted on only by the sun; and as this was never contemplated\nin the inductive process, its validity becomes a question, which can\nonly be determined by ascertaining precisely how great a deviation\nthis new class of mutual actions will produce. To do this is no easy\ntask, or rather, it is the most difficult task which the genius of\nman has ever yet accomplished: still, it _has_ been accomplished by\nthe mere application of the general laws of dynamics; and the result\n(undoubtedly a most beautiful and satisfactory one) is, that all\nthose observed deviations in the motions of our system which stood\nout as exceptions (\u00a7 154.), or were noticed as residual phenomena and\nreserved for further enquiry (\u00a7 158.), in that imperfect view of the\nsubject which we got in the subordinate process by which we rose to\nour general conclusion, prove to be the immediate consequences of the\nabove-mentioned mutual actions. As such, they are neither exceptions\nnor residual facts, but fulfilments of general rules, and essential\nfeatures in the statement of the case, _without_ which our induction\nwould be invalid, and the law of gravitation positively untrue.\n\n(214.) In the theory of gravitation, the law is all in all, applying\nitself at once to the materials, and directly producing the result.\nBut in many other cases we have to consider not merely the laws\nwhich regulate the actions of our ultimate causes, but a system of\nmechanism, or a structure of parts, through the intervention of which\ntheir effects become sensible to us. Thus, in the delicate and curious\nelectro-dynamic theory of Ampere, the mutual attraction or repulsion\nof two magnets is referred to a more universal phenomenon, the mutual\naction of electric currents, according to a certain fundamental law.\nBut, in order to bring the case of a magnet within the range of this\nlaw, he is obliged to make a supposition of a peculiar structure or\nmechanism, which constitutes a body a magnet, viz. that around each\nparticle of the body there shall be constantly circulating, in a\ncertain stated direction, a small current of electric fluid.\n\n(215.) This, we may say, is too complex; it is artificial, and cannot\nbe granted: yet, if the admission of this or any other structure\ntenfold more artificial and complicated will enable any one to present\nin a general point of view a great number of particular facts,--to make\nthem a part of one system, and enable us to reason from the known to\nthe unknown, and actually to _predict facts before trial_,--we would\nask, why should it _not_ be granted? When we examine those instances\nof nature\u2019s workmanship which we can take to pieces and understand,\nwe find them in the highest degree artificial in our own sense of the\nword. Take, for example, the structure of an eye, or of the skeleton of\nan animal,--what complexity and what artifice! In the one, a _pellucid\nmuscle_; a lens formed with elliptical surfaces; a circular aperture\ncapable of enlargement or contraction without loss of form. In the\nother, a framework of the most curious carpentry; in which occurs\nnot a single straight line, nor any known geometrical curve, yet all\nevidently systematic, and constructed by rules which defy our research.\nOr examine a crystallized mineral, which we can in some measure\ndissect, and thus obtain direct evidence of an internal structure.\nNeither artifice nor complication are here wanting; and though it\nis easy to assert that these appearances are, after all, produced\nby something which would be very simple, if we did but know it, it\nis plain that the same might be _said_ of a steam-engine executing\nthe most complicated movements, previous to any investigation of its\nnature, or any knowledge of the source of its power.\n\n(216.) In estimating, however, the value of a theory, we are not to\nlook, _in the first instance_, to the question, whether it establishes\nsatisfactorily, or not, a particular process or mechanism; for of\nthis, after all, we can never obtain more than that indirect evidence\nwhich consists in its leading to the same results. What, in the actual\nstate of science, is far more important for us to know, is whether our\ntheory truly represent _all_ the facts, and include _all_ the laws, to\nwhich observation and induction lead. A theory which did this would,\nno doubt, go a great way to establish any hypothesis of mechanism or\nstructure, which might form an essential part of it: but this is very\nfar from being the case, except in a few limited instances; and, till\nit is so, to lay any great stress on hypotheses of the kind, except in\nas much as they serve as a scaffold for the erection of general laws,\nis to \u201cquite mistake the scaffold for the pile.\u201d Regarded in this\nlight, hypotheses have often an eminent use: and a facility in framing\nthem, if attended with an equal facility in laying them aside when\nthey have served their turn, is one of the most valuable qualities a\nphilosopher can possess; while, on the other hand, a bigoted adherence\nto them, or indeed to peculiar views of any kind, in opposition to the\ntenor of facts as they arise, is the bane of all philosophy.\n\n(217.) There is no doubt, however, that the safest course, when it\ncan be followed, is to rise by inductions carried on among laws, as\namong facts, from law to law, perceiving, as we go on, how laws which\nwe have looked upon as unconnected become particular cases, either\none of the other, or all of one still more general, and, at length,\nblend altogether in the point of view from which we learn to regard\nthem. An example will illustrate what we mean. It is a general law,\nthat all hot bodies throw out or _radiate_ heat in all directions, (by\nwhich we mean, not that heat is an actual substance darted out from hot\nbodies, but only that the laws of the transmission of heat to distant\nobjects are similar to those which would regulate the distribution\nof particles thrown forth in all directions,) and that other colder\nbodies placed in their neighbourhood become hot, _as if_ they received\nthe heat so radiated. Again, all solid bodies which become heated in\none part _conduct_, or diffuse, the heat from that part through their\nwhole substance. Here we have two modes of communicating heat,--by\nradiation, and by conduction; and both these have their peculiar,\nand, to all appearance, very different laws. Now, let us bring a hot\nand a cold body (of the same substance) gradually nearer and nearer\ntogether,--as they approach, the heat will be communicated from the hot\nto the cold one by the _laws of radiation_; and from the nearer to the\nfarther part of the colder one, as it gradually grows warm, by _those\nof conduction_. Let their distance be diminished till they just lightly\ntouch. How does the heat _now_ pass from one to the other? Doubtless,\nby radiation; for it may be proved, that in such a contact there is yet\nan interval. Let them then be _forced_ together, and it will seem clear\nthat it must now be by _conduction_. Yet their _interval_ must diminish\ngradually, as the force by which they are pressed together increases,\ntill they actually cohere, and form one. The law of continuity, then,\nof which we have before spoken (\u00a7 199.), forbids us to suppose that\nthe intimate nature of the process of communication is changed in this\ntransition from light to violent contact, and from that to actual\nunion. If so, we might ask, at what point does the change happen?\nEspecially since it is also demonstrable, that the particles of the\nmost solid body are not, really, in contact. _Therefore_, the laws of\nconduction and radiation have a mutual dependence, and the former are\nonly extreme cases of the latter. If, then, we would rightly understand\nwhat passes, or what is the process of nature in the slow communication\nof heat through the substance of a solid, we must ground our enquiries\nupon what takes place at a distance, and then urge the laws to which we\nhave arrived, up to their extreme case.\n\n(218.) When two theories run parallel to each other, and each explains\na great many facts in common with the other, any experiment which\naffords a crucial instance to decide between them, or by which one or\nother must fall, is of great importance. In thus verifying theories,\nsince they are grounded on general laws, we may appeal, not merely\nto particular cases, but to whole classes of facts; and we therefore\nhave a great range among the individuals of these for the selection\nof some particular effect which ought to take place oppositely in the\nevent of one of the two suppositions at issue being right and the other\nwrong. A curious example is given by M. Fresnel, as decisive, in his\nmind, of the question between the two great opinions on the nature\nof light, which, since the time of Newton and Huyghens, have divided\nphilosophers. (See \u00a7 207.) When two very clean glasses are laid one\non the other, if they be not perfectly flat, but one or both in an\nalmost imperceptible degree convex or prominent, beautiful and vivid\ncolours will be seen between them; and if these be viewed through a\nred glass, their appearance will be that of alternate dark and bright\nstripes. These stripes are formed _between_ the two surfaces in\napparent contact, as any one may satisfy himself by using, instead of\na flat _plate_ of glass for the upper one, a triangular-shaped piece,\ncalled a prism, like a three-cornered stick, and looking through the\ninclined side of it next the eye, by which arrangement the reflection\nof light from the upper surface is prevented from intermixing with that\nfrom the surfaces in contact. Now, the coloured stripes thus produced\nare explicable on both theories, and are appealed to by both as strong\nconfirmatory facts; but there is a difference in one circumstance\naccording as one or the other theory is employed to explain them.\nIn the case of the Huyghenian doctrine, the intervals between the\nbright stripes ought to appear _absolutely black_; in the other,\n_half bright_, when so viewed through a prism. This curious case of\ndifference was tried as soon as the opposing consequences of the two\ntheories were noted by M. Fresnel, and the result is stated by him to\nbe decisive in favour of that theory which makes light to consist in\nthe vibrations of an elastic medium.\n\n(219.) Theories are best arrived at by the consideration of general\nlaws; but most securely verified by comparing them with particular\nfacts, because this serves as a verification of the whole train\nof induction, from the lowest term to the highest. But then, the\ncomparison must be made with facts purposely selected so as to include\nevery variety of case, not omitting extreme ones, and in sufficient\nnumber to afford every reasonable probability of detecting error. A\nsingle numerical coincidence in a final conclusion, however striking\nthe coincidence or important the subject, is not sufficient. Newton\u2019s\ntheory of sound, for example, leads to a numerical expression for the\nactual velocity of sound, differing but little from that afforded by\nthe correct theory afterwards explained by Lagrange, and (when certain\nconsiderations not contemplated by him are allowed for) agreeing with\nfact; yet this coincidence is no verification of Newton\u2019s view of the\ngeneral subject of sound, which is defective in an essential point,\nas the great geometer last named has very satisfactorily shown. This\nexample is sufficient to inspire caution in resting the verification of\ntheories upon any thing but a very extensive comparison with a great\nmass of observed facts.\n\n(220.) But, on the other hand, when a theory will bear the test\nof such extensive comparison, it matters little how it has been\noriginally framed. However strange and, at first sight, inadmissible\nits postulates may appear, or however singular it may seem that\nsuch postulates should have been fixed upon,--if they only lead\nus, by legitimate reasonings, to conclusions in exact accordance\nwith numerous observations purposely made under such a variety of\ncircumstances as fairly to embrace the whole range of the phenomena\nwhich the theory is intended to account for, we cannot refuse to admit\nthem; or if we still hesitate to regard them as demonstrated truths, we\ncannot, at least, object to receive them as temporary substitutes for\nsuch truths, until the latter shall become known. If they suffice to\nexplain all the phenomena known, it becomes highly improbable that they\nwill not explain more; and if all their conclusions we have tried have\nproved correct, it is probable that others yet untried will be found so\ntoo; so that _in rejecting them altogether, we should reject all the\ndiscoveries to which they may lead_.\n\n(221.) In all theories which profess to give a true account of the\nprocess of nature in the production of any class of phenomena, by\nreferring them to general laws, or to the action of general causes,\nthrough a train of modifying circumstances; before we can apply those\nlaws, or trace the action of those causes in any assigned case, we\nrequire to know the circumstances: we must have data whereon to ground\ntheir application. Now, these can be learned only from observation;\nand it may seem to be arguing in a vicious circle to have recourse\nto observation for any part of those theoretical conclusions, by\nwhose comparison with fact the theory itself is to be tried. The\nconsideration of an example will enable us to remove this difficulty.\nThe most general law which has yet been discovered in chemistry is\nthis, that all the elementary substances in nature are susceptible of\nentering into combination with each other only in fixed or _definite\nproportions_ by weight, and not arbitrarily; so that when any two\nsubstances are put together with a view to unite them, if their weights\nare not in some certain determinate proportion, a complete combination\nwill not take place, but some part of one or the other ingredient will\nremain over and above, and uncombined. Suppose, now, we have found a\nsubstance having all the outward characters of a homogeneous or unmixed\nbody, but which, on analysis, we discover to consist of sulphur, and\nlead in the proportion of 20 parts of the former to 130 of the latter\ningredient; and we would know whether this is to be regarded as a\nverification of the law of definite proportions or an exception to\nit. The question is reduced to this, whether the proportion 20 to 130\nbe or be not _that_ fixed and definite proportion, (or one of them,\nif there be more than one proportion possible,) in which, according\nto the law in question, sulphur and lead can combine; now, this can\nnever be decided by merely looking at the law in all its generality.\nIt is clear, that when particularized by restricting its expression\nto sulphur and lead, the law should state _what are_ those particular\nfixed proportions in which these bodies can combine. That is to say,\nthere must be certain data or numbers, by which these are distinguished\nfrom all other bodies in nature, and which require to be known before\nwe can apply the general law to the particular case. To determine such\ndata, observation must be consulted; and if we were to have recourse\nto that of the combination of the two substances in question with each\nother, no doubt there would be ground for the logical objection of\na vicious circle: but this is not done; the determination of these\nnumerical data is derived from experiments purposely made on a great\nvariety of different combinations, among which that under consideration\ndoes not of necessity occur, and all these being found, independently\nof each other, to agree in giving the same results, they are therefore\nsafely assumed as part of the system. Thus, the law of definite\nproportions, when applied to the actual state of nature, requires two\nseparate statements, the one announcing the general law of combination,\nthe other particularizing the numbers appropriate to the several\nelements of which natural bodies consist, or the data of nature. Among\nthese data, if arranged in a list, there will be found opposite to the\nelement sulphur the number 16, and opposite to lead, 104[48]; and since\n20 is to 130 in the exact proportion of 16 to 104, it appears that the\ncombination in question affords a satisfactory verification of the law.\n\n(222.) The great importance of physical data of this description,\nand the advantage of having them well determined, will be obvious,\nif we consider, that a list of them, when taken in combination with\nthe general law, affords the means of determining at once the exact\nproportion of the ingredients of all natural compounds, if we only know\nthe place they hold in the system. In chemistry, the number of admitted\nelements is between fifty and sixty, and new ones are added continually\nas the science advances. Now, the moment the number corresponding to\nany new substance added to the list is determined, we have, in fact,\nascertained all the proportions in which it can enter into combination\nwith all the others, so that a careful experiment made with the object\nof determining this number is, in fact, equivalent to as many different\nexperiments as there are binary, ternary, or yet more complicated\ncombinations capable of existing, into which the new substance may\nenter, as an ingredient.\n\n(223.) The importance of obtaining exact physical data can scarcely\nbe too much insisted on, for without them the most elaborate theories\nare little better than mere inapplicable forms of words. It would be\nof little consequence to be informed, abstractedly, that the sun and\nplanets attract each other, with forces proportional to their masses,\nand inversely as the squares of their distances: but, as soon as we\nknow the data of our system, as soon as we have an accurate statement\n(no matter how obtained) of the distances, masses, and actual motions\nof the several bodies which compose it, we need no more to enable us to\npredict all the movements of its several parts, and the changes that\nwill happen in it for thousands of years to come; and even to extend\nour views backwards into time, and recover from the past, phenomena,\nwhich no observation has noted, and no history recorded, and which yet\n(it is possible) may have left indelible traces of their existence in\ntheir influence on the state of nature in our own globe, and those of\nthe other planets.\n\n(224.) The proof, too, that our data _are_ correctly assumed, is\ninvolved in the general verification of the whole theory, of which,\nwhen once assumed, they form a part; and the same comparison with\nobservation which enables us to decide on the truth of the abstract\nprinciple, enables us, at the same time, to ascertain whether we\nhave fixed the values of our data in accordance with the actual\nstate of nature. If not, it becomes an important question, whether\nthe assumed values can be corrected, so as to bring the results of\ntheory to agree with facts? Thus it happens, that as theories approach\nto their perfection, a more and more exact determination of data\nbecomes requisite. Deviations from observed fact, which, in a first\nor approximative verification, may be disregarded as trifling, become\nimportant when a high degree of precision is attained. A difference\nbetween the calculated and observed places of a planet, which would\nhave been disregarded by Kepler in his verification of the law of\nelliptic motion, would now be considered fatal to the theory of\ngravity, unless it could be shown to arise from an erroneous assumption\nof some of the numerical data of our system.\n\n(225.) The observations most appropriate for the ready and exact\ndetermination of physical data are, therefore, those which it is most\nnecessary to have performed with exactness and perseverance. Hence\nit is, that their performance, in many cases, becomes a national\nconcern, and observatories are erected and maintained, and expeditions\ndespatched to distant regions, at an expense which, to a superficial\nview, would appear most disproportioned to their objects. But it\nmay very reasonably be asked why the direct assistance afforded by\ngovernments to the execution of continued series of observations\nadapted to this especial end should continue to be, as it has hitherto\nalmost exclusively been, confined to astronomy.\n\n(226.) Physical data intended to be employed as elements of calculation\nin extensive theories, require to be known with a much greater degree\nof exactness than any single observation possesses, not only on account\nof their dignity and importance, as affording the means of representing\nan indefinite multitude of facts; but because, in the variety of\ncombinations that may arise, or in the changes that circumstances may\nundergo, cases will occur when any trifling error in one of the data\nmay become enormously magnified in the final result to be compared\nwith observation. Thus, in the case of an eclipse of the sun, when\nthe moon enters very obliquely upon the sun\u2019s disc, a trifling error\nin the diameter of either the sun or moon may make a great one in the\ntime when the eclipse shall be announced to commence. It ought to\nbe remarked, that these are, of all others, the conjunctures where\nobservations are most available for the determination of data; for,\nby the same rule that a small change in the data will, in such cases,\nproduce a great one in the thing to be observed; so, _vice vers\u00e2_, any\nmoderate amount of error, committed in an observation undertaken for\nascertaining its value, can produce but a very trifling one in the\n_reverse_ calculation from which the data come to be determined by\nobservation. This remark extends to every description of physical data\nin every department of science, and is never to be overlooked when the\nobject in view is the determination of data with the last degree of\nprecision.\n\n(227.) But how, it may be asked, are we to ascertain _by_ observation,\ndata more precise than observation itself? How are we to conclude the\nvalue of that which we do not see, with greater certainty than that\nof quantities which we actually see and measure? It is the number of\nobservations which may be brought to bear on the determination of data\nthat enables us to do this. Whatever error we may commit in a single\ndetermination, it is highly improbable that we should always err the\nsame way, so that, when we come to take an average of a great number of\ndeterminations, (unless there be some constant cause which gives a bias\none way or the other,) we cannot fail, at length, to obtain a very near\napproximation to the truth, and, even allowing a bias, to come much\nnearer to it than can fairly be expected from any single observation,\nliable to be influenced by the same bias.\n\n(228.) This useful and valuable property of the average of a great\nmany observations, that it brings us nearer to the truth than any\nsingle observation can be relied on as doing, renders it the most\nconstant resource in all physical enquiries where accuracy is desired.\nAnd it is surprising what a rapid effect, in equalizing fluctuations\nand destroying deviations, a moderate multiplication of individual\nobservations has. A better example can hardly be taken than the average\nheight of the quicksilver in the common barometer, which measures\nthe pressure of the air, and whose fluctuations are proverbial.\nNevertheless, if we only observe it regularly every day, and, at the\nend of each month, take an average of the observed heights, we shall\nfind the fluctuations surprisingly diminished in amount; and if we\ngo on for a whole year, or for many years in succession, the annual\naverages will be found to agree with still greater exactness. This\nequalizing power of averages, by destroying all such fluctuations as\nare irregular or accidental, frequently enables us to obtain evidence\nof fluctuations really regular, periodic in their recurrence, and\nso much smaller in their amount than the accidental ones, that, but\nfor this mode of proceeding, they never would have become apparent.\nThus, if the height of the barometer be observed four times a day,\nconstantly, for a few months, and the averages taken, it will be seen\nthat a regular _daily_ fluctuation, of very small amount, takes place,\nthe quicksilver rising and falling twice in the four-and-twenty hours.\nIt is by such observations that we are enabled to ascertain--what no\nsingle measure (unless by a fortunate coincidence), could give us any\nidea, and never any certain knowledge of--the true _sea level_ at any\npart of the coast, or the height at which the water of the ocean would\nstand, if perfectly undisturbed by winds, waves, or tides: a subject of\nvery great importance, and upon which it would be highly desirable to\npossess an extensive series of observations, at a great many points on\nthe coasts of the principal continents and islands over the whole globe.\n\n(229.) In all cases where there is a direct and simple relation between\nthe phenomenon observed and a single _datum_ on which it depends,\nevery single observation will give a value of this quantity, and the\naverage of all (under certain restrictions) will be its exact value. We\nsay, under certain restrictions; for, if the circumstances under which\nthe observations are made be not alike, they may not all be equally\nfavourable to exactness, and it would be doing injustice to those most\nadvantageous, to class them with the rest. In such cases as these,\nas well as in cases where the _data_ are numerous and complicated\ntogether, so as not to admit of single, separate determination (a\nthing of continual occurrence), we have to enter into very nice, and\noften not a little intricate, considerations respecting the _probable_\naccuracy of our results, or the limits of error within which it is\n_probable_ they lie. In so doing we are obliged to have recourse to\na refined and curious branch of mathematical enquiry, called the\ndoctrine of probabilities, the object of which (as its name imports)\nis to reduce our estimation of the probability of any conclusion to\ncalculation, so as to be able to give more than a mere guess at the\ndegree of reliance which ought to be placed in it.\n\n(230.) To give some general idea of the considerations which such\ncomputations involve, let us imagine a person firing with a pistol\nat a wafer on a wall ten yards distant: we might, in a general way,\ntake it for granted, that he would hit the wall, but not the wafer,\nat the first shot; but if we would form any thing like a probable\nconjecture of _how near_ he would come to it, we must first have an\nidea of his skill. No better way of judging could be devised than\nby letting him fire a hundred shots at it, and marking where they\nall struck. Suppose this done,--suppose the wafer has been hit once\nor twice, that a certain number of balls have hit the wall within an\ninch of it, a certain number between one and two inches, and so on,\nand that one or two have been some feet wide of the mark. Still the\nquestion arises, what estimate are we thence to form of his skill? how\n_near_ (or nearer) may we, after this experience, safely, or at least\nnot unfairly, bet that he will come to the mark the next subsequent\nshot? This the laws of probability enable us on such data to say.\nAgain, suppose, _before_ we were allowed to measure the distances,\nthe wafer were to have been taken away, and we were called upon, on\nthe mere evidence of the marks on the wall, to say where it had been\nplaced; it is clear that no reasoning would enable any one to say with\ncertainty; yet there is assuredly one place which we may fix on with\ngreater probability of being right than any other. Now, this is a very\nsimilar case to that of an observer--an astronomer for example--who\nwould determine the exact place of a heavenly body. He points to it\nhis telescope, and obtains a series of results disagreeing among\nthemselves, but yet all agreeing within certain limits, and only a\ncomparatively small number of them deviating considerably from the mean\nof all; and from these he is called upon to say, definitively, what he\nshall consider to have been the most probable place of his star at the\nmoment. Just so in the calculation of physical _data_; where no two\nresults agree exactly, and where all come within limits, some wide,\nsome close, what have we to guide us when we would make up our minds\nwhat to conclude respecting them? It is evident that any system of\ncalculation that can be shown to lead of necessity to the most probable\nconclusion where certainty is not to be had must be valuable. However,\nas this doctrine is one of the most difficult and delicate among the\napplications of mathematics to natural philosophy, this slight mention\nof it must suffice at present.\n\n(231.) In the foregoing pages we have endeavoured to explain the spirit\nof the methods to which, since the revival of philosophy, natural\nscience has been indebted for the great and splendid advances it has\nmade. What we have all along most earnestly desired to impress on the\nstudent is, that natural philosophy is essentially united in all its\ndepartments, through all which one spirit reigns and one method of\nenquiry applies. It cannot, however, be studied as a whole, without\nsubdivision into parts; and, in the remainder of this discourse, we\nshall therefore take a summary view of the progress which has been made\nin the different branches into which it may be most advantageously\nso subdivided, and endeavour to give a general idea of the nature of\neach, and of its relations to the rest. In the course of this, we shall\nhave frequent opportunity to point out the influence of those general\nprinciples we have above endeavoured to explain, on the progress of\ndiscovery. But this we shall only do as cases arise, without entering\ninto any regular analysis of the history of each department with that\nview. Such an analysis would, indeed, be a most useful and valuable\nwork, but would far exceed our present limits. We are not, however,\nwithout a hope that this great desideratum in science will, ere long,\nbe supplied from a quarter every way calculated to do it justice.\n\n\n\n\n                               PART III.\n\n         OF THE SUBDIVISION OF PHYSICS INTO DISTINCT BRANCHES,\n                      AND THEIR MUTUAL RELATIONS.\n\n\n\n\nCHAPTER I.\n\nOF THE PHENOMENA OF FORCE, AND OF THE CONSTITUTION OF NATURAL BODIES.\n\n\n(232.) Natural History may be considered in two very different lights:\neither, 1st, as a collection of facts and objects presented by nature,\nfrom the examination, analysis, and combination of which we acquire\nwhatever knowledge we are capable of attaining both of the order of\nnature, and of the agents she employs for producing her ends, and from\nwhich, therefore, all sciences arise; or, 2dly, as an assemblage of\nphenomena to be explained; of effects to be deduced from causes; and of\nmaterials prepared to our hands, for the application of our principles\nto useful purposes. Natural history, therefore, considered in the\none or the other of these points of view, is either the beginning or\nthe end of physical science. As it offers to us, in a confused and\ninterwoven mass, the elements of all our knowledge, our business is to\ndisentangle, to arrange, and to present them in a separate and distinct\nstate: and to this end we are called upon to resolve the important but\ncomplicated problem,--Given the effect, or assemblage of effects, to\nfind the causes. The principles on which this enquiry relies are those\nwhich constitute the relation of cause and effect, as it exists with\nreference to our minds; and their rules and mode of application have\nbeen attempted to be sketched out, (though in far less detail than the\nintrinsic interest of the subject, both in a logical and practical\npoint of view, would demand,) in the foregoing pages. It remains\nnow to bring together, in a summary statement, the results of the\ngeneral examination of nature, so far as it has been prosecuted to the\ndiscovery of natural agents, and the mode in which they act.\n\n(233.) The first great agent which the analysis of natural phenomena\noffers to our consideration, more frequently and prominently than\nany other, is force. Its effects are either, 1st, to counteract the\nexertion of opposing force, and thereby to maintain _equilibrium_; or,\n2dly, to produce _motion_ in matter.\n\n(234.) Matter, or that, whatever it be, of which all the objects in\nnature which manifest themselves directly to our senses consist,\npresents us with two general qualities, which at first sight appear\nto stand in contradiction to each other--activity and inertness. Its\nactivity is proved by its power of spontaneously setting other matter\nin motion, and of itself obeying their mutual impulse, and moving\nunder the influence of its own and other force; inertness, in refusing\nto move unless obliged to do so by a force impressed externally, or\nmutually exerted between itself and other matter, and by persisting in\nits state of motion or rest unless disturbed by some external cause.\nYet in reality this contradiction is only apparent. Force being the\ncause, and motion the effect produced by it on matter, to say that\nmatter is inert, or has _inertia_, as it is termed, is only to say\nthat the cause is expended in producing its effect, and that the\nsame cause cannot (without renewal) produce double or triple its own\nproper effect. In this point of view, equilibrium may be conceived as\na continual production of two opposite effects, each undoing at every\ninstant what the other has done.\n\n(235.) However, if this should appear too metaphysical, at all events\nthis difference of effects gives rise to two great divisions of the\nscience of force, which are commonly known by the names of STATICS and\nDYNAMICS; the latter term, which is general, and has been used by us\nbefore in its general sense, being usually confined to the doctrine\nof motion, as produced and modified by force. Each of these great\ndivisions again branches out into distinct subdivisions, according as\nwe consider the equilibrium or motion of matter in the three distinct\nstates in which it is presented to us in nature, the solid, liquid, and\na\u00ebriform state, to which, perhaps, ought to be added the _viscous_,\nas a state intermediate between that of solidity and fluidity, the\nconsideration of which, though very obscure and difficult, offers a\nhigh degree of interest on a variety of accounts.\n\n\n_Statics and Dynamics._\n\n(236.) The principles have been definitively fixed by Galileo and his\nsuccessors, down to Newton, on a basis of sound induction; and as they\nare perfectly general, and apply to every case, they are competent,\nas we have already before observed, to the solution of every problem\nthat can occur in the deductive processes, by which phenomena are\nto be explained, or effects calculated. Hence, they include every\nquestion that can arise respecting the motions and rest of the smallest\nparticles of matter, as well as of the largest masses. But the mode of\nreasoning from these general principles differs materially, whether\nwe consider them as applied to masses of matter of a sensible size,\nor to those excessively minute, and perhaps indivisible, molecules of\nwhich such masses are composed. The investigations which relate to the\nlatter subject are extremely intricate, as they necessarily involve the\nconsideration of the hypotheses we may form respecting the intimate\nconstitution of the several sorts of bodies above enumerated.\n\n(237.) On the other hand, those which respect the equilibrium and\nmotions of sensible masses of matter are happily capable of being\nso managed as to render unnecessary the adoption of any particular\nhypothesis of structure. Thus, in reasoning respecting the application\nof forces to a solid mass, we suppose its parts indissolubly and\nunalterably connected; it matters not by what tie, provided this\ncondition be satisfied, that one point of it cannot be moved without\nsetting all the rest in motion, so that the relative situation of the\nparts one among another be not changed. This is the abstract notion\nof a solid which the mechanician employs in his reasonings. And their\nconclusions will apply to natural bodies, of course, only so far as\nthey conform to such a definition. In strictness of speaking, however,\nthere are no bodies which absolutely conform to it. No substance is\nknown whose parts are absolutely incapable of yielding one among\nanother; but the amount by which they do yield is so excessively\nsmall as to be demonstrably incapable, in most cases, of having any\ninfluence on the results: and in those where it has such influence, an\nespecial investigation of its amount can always be made. This gives\nrise to two subdivisions of the application of mechanical reasonings\nto solid masses. Those which refer to the action of forces on flexible\nor elastic, and on inflexible or rigid, bodies, comprehending under\nthe latter all such whose resistance to flexure or fracture is so\nvery great as to permit our adoption of the language and ideas of the\nextreme case without fear of material error.\n\n(238.) In like manner, when we reason respecting the action of forces\non a fluid mass, all we have occasion to assume is, that its parts\nare freely moveable one among the other. If, besides this, we choose\nto regard a fluid as incompressible, and deduce conclusions on this\nsupposition, they will hold good only so far as there may be found\nsuch fluids in nature. Now, in strictness, there are none such; but,\npractically speaking, in the greater number of cases their resistance\nto compression is so very great that the result of the reasoning so\ncarried on is not sensibly vitiated; and, in the remaining cases,\nthe same general principles enable us to enter on a special enquiry\ndirected to this point: and hence the division of fluids, in mechanical\nlanguage, into compressible and incompressible, the latter being only\nthe extreme or limiting case of the former.\n\n(239.) As we propose here, however, only to consider what is the actual\nconstitution of nature, we shall regard all bodies, as they really\nare, more or less flexible and yielding. We know for certain, that\nthe space which any material body appears to occupy is not entirely\nfilled by it; because there is none which by the application of a\nsufficient force may not be _compressed_ or forced into a smaller\nspace, and which, either wholly, as in air or liquids, or in part, as\nin the greater number of solids, will not recover its former dimensions\nwhen the force is taken off. In the case of air, this condensation\nmay be urged to almost any extent; and not only does a mass of air\nso condensed completely recover its original bulk, when the applied\npressure is removed, but if that ordinary pressure under which it\nexists at the earth\u2019s surface (and which arises from the weight of\nthe atmosphere) be also removed by an air-pump, it will still further\ndilate itself without limit so far as we have yet been able to try\nit. Hence we are led to the conclusion that the particles of air are\nmutually elastic, and have a _tendency to recede from one another_,\nwhich can only be counteracted by _force_, and therefore is itself a\nforce of the repulsive kind. Nevertheless, as air is heavy, and as\ngravitation is a universal property of matter, there is no doubt that\nthis repulsive tendency must have a limit, and that there is a distance\nto which, if the particles of the air could be removed from each other,\ntheir mutual repulsion would cease, and an attraction take its place.\nThis limit is probably attained at some very great height above the\nearth\u2019s surface, beyond which, of course, its atmosphere cannot extend.\n\n(240.) What, however, we can only conclude by this or similar reasoning\nrespecting air, we see distinctly in liquids. They are all, though\nin a small degree, compressible, and recover their former dimensions\ncompletely when the pressure is removed; but they cannot be dilated (by\nmechanical means), and have no tendency, while they remain liquids, to\nenlarge themselves beyond a certain limit, and therefore they assume a\ndeterminate _surface_ while at rest, and their parts actually resist\nfurther separation with a considerable force, thus giving rise to the\nphenomenon of the _cohesion of liquids_.\n\n(241.) Both in air and in liquids, however, the most perfect freedom\nof motion of the parts among each other subsists, which could hardly\nbe the case if they were not separate and independent of each other.\nAnd from this, combined with the foregoing considerations, it has been\nconcluded that they do not actually touch, but are kept asunder at\ndeterminate distances from each other, by the constant action of the\ntwo forces of attraction and repulsion, which are supposed to balance\nand counteract each other at the ordinary distances of the particles,\nbut to prevail, the one, or the other, according as they are forcibly\nurged together or pulled asunder.\n\n(242.) In solids, however, the case is very different. The mutual free\nmotion of their parts _inter se_ is powerfully impeded, and in some\nalmost destroyed. In some, a slow and gradual change of figure may be\nproduced to a great extent, by pressure or blows, as for instance in\nthe metals, clay, butter, &c.; in others, fracture is the consequence\nof any attempt to change the figure by violence beyond a certain very\nsmall limit. In solids, then, it is evident, that the consideration of\ntheir intimate structure has a very great influence in modifying the\ngeneral results of the action of such attractive and repulsive forces\nas may be assumed to account for the phenomena they present; yet the\ngeneral facts that their parts _cohere_ with a certain energy, and that\nthey resist displacement or intrusion on the part of other bodies,\nare sufficient to demonstrate at least the existence of such forces,\nwhatever obscurity may subsist as to their mode of action.\n\n(243.) This division of bodies into airs, liquids, and solids, gives\nrise, then, to three distinct branches of mechanical science, in each\nof which the general principles of equilibrium and motion have their\npeculiar mode of application; viz. pneumatics, hydrostatics, and what\nmight, without impropriety, be termed stereostatics.\n\n\n_Pneumatics._\n\n(244.) Pneumatics relates to the equilibrium or movements of a\u00ebrial\nfluids under all circumstances of pressure, density, and elasticity.\nThe weight of the air, and its pressure on all the bodies on the\nearth\u2019s surface, were quite unknown to the ancients, and only first\nperceived by Galileo, on the occasion of a sucking-pump refusing to\ndraw water above a certain height. Before his time it had always been\nsupposed that water rose by suction in a pipe, in consequence of a\ncertain natural _abhorrence of a vacuum_ or empty space, which obliged\nthe water to enter by way of supplying the place of the air sucked out.\nBut if any such abhorrence existed, and had the force of an _acting\ncause_, which could urge water a single foot into a pipe, there is no\nreason why the same principle should not carry it up two, three, or\nany number of feet; none why it should suddenly stop short at a certain\nheight, and refuse to rise higher, however violent the suction might\nbe, nay, even fall back, if purposely forced up too high.\n\n(245.) Galileo, however, at first contented himself with the\nconclusion, that the natural abhorrence of a vacuum was not strong\nenough to sustain the water more than about thirty-two feet above\nits level; and, although the true cause of the phenomenon at length\noccurred to him, in the pressure of the air on the general surface,\nit was not satisfactorily demonstrated till his pupil, Torricelli,\nconceived the happy idea of instituting an experiment on a small\nscale by the use of a much heavier liquid, mercury, instead of water,\nand, in place of sucking out the air from above, employing the much\nmore effectual method of filling a long glass tube with mercury, and\ninverting it into a basin of the same metal. It was then at once seen,\nas by a _glaring instance_, that the maintenance of the mercury in the\ntube (which is nothing else than the common barometer) was the effect\nof a perfectly definite external cause, while its fluctuations from day\nto day, with the varying state of the atmosphere, strongly corroborated\nthe notion of its being due to the pressure of the external air on the\nsurface of the mercury in the reservoir.\n\n(246.) The discovery of Torricelli was, however, at first much\nmisconceived, and even disputed, till the question was finally decided\nby appeal to a _crucial instance_, one of the first, if not the very\nfirst on record in physics, and for which we are indebted to the\ncelebrated Pascal. His acuteness perceived that if the weight of the\nincumbent air be the direct cause of the elevation of the mercury,\nit must be measured by the amount of that elevation, and therefore\nthat, by carrying a barometer up a high mountain, and so ascending\ninto the atmosphere _above_ a large portion of the incumbent air, the\npressure, as well as the length of the column sustained by it, must\nbe diminished; while, on the other hand, if the phenomenon were due\nto the cause originally assigned, no difference could be expected to\ntake place, whether the observation were made on a mountain or on the\nplain. Perhaps the decisive effect of the experiment which he caused\nto be instituted for the purpose, on the Puy de D\u00f4me, a high mountain\nin Auvergne, while it convinced every one of the truth of Torricelli\u2019s\nviews, tended more powerfully than any thing which had previously been\ndone in science to confirm, in the minds of men, that disposition to\nexperimental verification which had scarcely yet taken full and secure\nroot.\n\n(247.) Immediately on this discovery followed that of the air-pump,\nby Otto von Guericke of Magdeburgh, whose aim seems to have been to\ndecide the question, whether a vacuum could or could not exist, by\nendeavouring to make one. The imperfection of his mechanism enabled\nhim only to diminish the a\u00ebrial contents of his receivers, not\nentirely to empty them; but the curious effects produced by even a\npartial exhaustion of air speedily excited attention, and induced our\nillustrious countryman, Robert Boyle, to the prosecution of those\nexperiments which terminated in his hands, and in those of Hauksbee,\nHooke, Mariotte, and others, in a satisfactory knowledge of the\ngeneral law of the equilibrium of the air under the influence of\ngreater or less pressures. These discoveries have since been extended\nto all the various descriptions of a\u00ebrial fluids which chemistry has\nshown to exist, and to maintain their a\u00ebriform state under artificial\npressure, and even to those which may be produced from liquids reduced\nto a state of vapour by heat, so long as they retain that state.\n\n(248.) The manner in which the observed law of equilibrium of an\nelastic fluid, like air, may be considered to originate in the mutual\nrepulsion of its particles, has been investigated by Newton, and\nthe actual statement of the law itself, as announced by Mariotte,\n\u201cthat the density of the air, or the quantity of it contained in the\nsame space, is, _c\u00e6teris paribus_, proportional to the pressure it\nsupports,\u201d has recently been verified within very extensive limits by\ndirect experiment, by a committee of the Royal Academy of Paris. This\nlaw contains the principle of solution of every dynamical question\nthat can occur relative to the equilibrium of elastic fluids, and is\ntherefore to be regarded as one of the highest _axioms_ in the science\nof pneumatics.\n\n\n_Hydrostatics._\n\n(249.) The principles of the equilibrium of liquids, understanding\nby this word such fluids as do not, though quite at liberty, attempt\nto dilate themselves beyond a certain point, are at once few and\nsimple. The first steps towards a knowledge of them were made by\nArchimedes, who established the general fact, that a solid immersed in\na liquid loses a portion of its weight equal to that of the liquid it\ndisplaces. It seems very astonishing, after this, that it should not\nhave been at once concluded that the weight thus said to be _lost_ is\nonly _counteracted_ by the upward pressure of the liquid, and that,\ntherefore, a portion of any liquid, surrounded on all sides by a liquid\nof the same kind, does really exert its weight in keeping its place.\nYet the prejudice that \u201cliquids do not gravitate in their natural\nplace\u201d kept its ground, and was only dispelled with the mass of error\nand absurdity which the introduction of a rational and experimental\nphilosophy by Galileo swept away.\n\n(250.) The hydrostatical law of _the equal pressure of liquids in all\ndirections_, with its train of curious and important consequences, is\nan immediate conclusion from the perfect mobility of their parts among\none another, in consequence of which each of them tends to recede from\nan excess of pressure on one side, and thus bears upon the rest, and\ndistributes the pressure among its neighbours. In this form it was\nlaid down by Newton, and has proved one of the most useful and fertile\nprinciples of physico-mathematical reasoning on the equilibrium of\nfluid masses, as affording a means of tracing the action of a force\napplied at any point of a liquid through its whole extent. It applies,\ntoo, without any modification, to expansible fluids as well as to\nliquids; and, in the applications of geometry to this subject, enables\nus to dispense with any minute and intricate enquiries as to the mode\nin which individual particles act on each other.\n\n(251.) In a practical point of view, this law is remarkable for the\ndirectness of its application to useful purposes. The immediate and\nperfect distribution of a pressure applied on any one part, however\nsmall, of a fluid surface through the whole mass, enables us to\ncommunicate _at one instant_ the same pressure to any number of such\nparts by merely increasing the surface of the fluid, which may be done\nby enlarging the containing vessel; and if the vessel be so constructed\nthat a large portion of its surface shall be moveable together, the\npressures on all the similar parts of this portion will be united into\none consentient force, which may thus be increased to any extent we\nplease. The hydraulic press, invented by Bramah, (or rather applied by\nhim after a much more ancient inventor, Stevin,) is constructed on this\nprinciple. A small quantity of water is driven by sufficient pressure\ninto a vessel _already full_, and provided with a moveable surface or\npiston of great size. Under such circumstances something must give way;\nthe great surface of the piston accumulates the pressure on it to such\nan extent that nothing can resist its violence. Thus, trees are torn\nup by the roots; piles extracted from the earth; woollen and cotton\ngoods compressed into the most portable dimensions; and even hay, for\nmilitary service, reduced to such a state of coercion as to be easily\npacked on board transports.\n\n(252.) Liquids differ from a\u00ebriform fluids by their _cohesion_, which\nmay be regarded as a kind of approach to a solid state, and was so\nregarded by Bacon (193.). Indeed, there can be little doubt that\nthe solid, liquid, and a\u00ebriform states of bodies are merely stages\nin a progress of gradual transition from one extreme to the other;\nand that, however strongly marked the distinctions between them may\nappear, they will ultimately turn out to be separated by no sudden or\nviolent line of demarcation, but shade into each other by insensible\ngradations. The late experiments of Baron Cagnard de la Tour may be\nregarded as a first step towards the full demonstration of this (199.).\nBut the cohesion of liquids is not, like that of solids, so modified\nby their structure in other respects as to destroy the mobility of\ntheir parts one among another (unless in those cases of nearer approach\nto the solid state which obtain in viscid or gummy liquids). On the\ncontrary, the two qualities co-exist, and give rise to a number of\ncurious and intricate phenomena.\n\n(253.) One of the most remarkable of these is capillary attraction,\nor capillarity as it is sometimes called. Every body has remarked the\nadhesion of water to glass. The elevation of the general surface of\nthe liquid where it is in contact with the containing vessel; the form\nof a drop suspended at the under side of a solid: these are instances\nof capillary attraction. If a small glass tube with a bore as fine as\na hair be immersed in water, the water will be observed to rise in\nit to a certain height, and to assume a concave surface at its upper\nextremity. The attraction of the glass on the water, and the cohesion\nof the parts of the water to each other, are no doubt the joint causes\nof this curious effect; but the mode of action is at once obscure and\ncomplex; and although the researches of Laplace and Young have thrown\ngreat light on it, further investigation seems necessary before we can\nbe said distinctly to understand it.\n\n(254.) As the capillarity and cohesion of the parts of liquids shows\nthem to possess the power of mutual attraction, so their elasticity\ndemonstrates that they also possess that of repulsion when forcibly\nbrought nearer than their natural state. From the extremely small\nextent to which the compression of liquids can be carried by any force\nwe can employ, compared with that of air, we must conclude that this\nrepulsion is much more violent in the former than in the latter, but\ncounteracted also by a more powerful force of attraction. So much more\npowerful, indeed, is the resistance of liquids to compression, that\nthey were usually regarded as incompressible; an opinion corroborated\nby a celebrated experiment made at Florence, in which water was forced\nthrough the pores (as it was said) of a golden ball. More recent\nexperiments by Canton, and since by Perkins, O\u00ebrsted, and others,\nhave demonstrated however the contrary, and assigned the amount of\ncompression.\n\n(255.) The consideration of the motions of fluids, whether liquid\nor expansible, is infinitely more complicated than that of their\nequilibrium. When their motions are slow, it is reasonable to suppose\nthat the law of the equable distribution of pressure obtains; but in\nvery rapid displacements of their parts one among the other, it is not\neasy to see how such an equable distribution can be accomplished, and\nsome phenomena exist which seem to indicate a contrary conclusion.\n\n(256.) Independent of this, there are difficulties of an almost\ninsuperable nature to the regular deductive application of the general\nprinciples of mechanics to this subject, which arise from the excessive\nintricacy of the pure mathematical enquiries to which its investigation\nleads. It was Newton who set the example of a first attempt to draw\nany conclusions respecting the motion of fluid masses by direct\nreasoning from dynamical principles, and thus laid the foundation of\nHYDRODYNAMICS; but it was not till the time of D\u2019Alembert that the\nmethod of reducing any question respecting the motions of fluids under\nthe action of forces to strict mathematical investigation could be said\nto be completely understood. But the cases even now in which this mode\nof treating such questions can be applied with full satisfaction are\nfew in comparison of those in which the experimental method of enquiry\nas already observed (189.) is preferable. Such, for example, is that\nof the resistance of fluids to bodies moving through them; a knowledge\nof which is of great importance in naval architecture and in gunnery,\nwhere the resistance of the air acts to an enormous extent. Such,\ntoo, among the practical subjects which depend mainly on this branch\nof science, are the use of sails in navigation; the construction of\nwindmills, and water-wheels; the transmission of water through pipes\nand channels; the construction of docks and harbours, &c.\n\n\n_Nature of Solids in general._\n\n(257.) The intimate constitution of solids is, in all probability, very\ncomplicated, and we cannot be said to know much of it. By some recent\ndelicate experiments on the dimensions of wires violently strained, it\nhas been shown that they are to a certain small extent capable of being\ndilated by tension, as they are also of being compressed by pressure,\nbut within limits even narrower than those of liquids. Usually, when\nstrained too far, they break, and refuse to re-unite; or, if compressed\ntoo forcibly, take a permanent contraction of dimension. Thus, wood\nmay be indented by a blow, and metals rendered denser and heavier by\nhammering or rolling. There is a certain degree of confusion prevalent\nin ordinary language about the hardness, elasticity, and other similar\nqualities, of solids, which it may be well to remove. Hardness is that\ndisposition of a solid which renders it difficult to displace its\nparts among themselves. Thus, steel is harder than iron; and diamond\nalmost infinitely harder than any other substance in nature: but the\ncompressibility of steel, or the extent to which it will yield to a\ngiven pressure and recover itself, is not much less than that of soft\niron, and that of ice is very nearly the same with that of water.\n\n(258.) Again, we call Indian rubber a very elastic body, and so it is;\nbut in a different sense from steel. Its parts admit of great mutual\ndisplacement without permanent dislocation; however distorted, it\nrecovers its figure readily, but with a small force. Yet, if Indian\nrubber were to be enclosed in a space that it just filled, so as not to\npermit its parts to yield laterally, doubtless it would resist actual\ncompression with great violence. Here, then, we have an instance\nof two kinds of elasticity in one substance; a feebler effort of\nrecovery from distorted figure, and a more violent one from a state\nof altered dimension. Both, however, originate in the same causes,\nand are referable to the same principles; the former being in fact\nonly a modified case of the latter, as the effort of a steel spring,\nwhen bent, to recover its former shape, is referable to the same\nforces which give to steel its hardness and strength to resist actual\ncompression and fracture.\n\n(259.) The toughness of a solid, or that quality by which it will\nendure heavy blows without breaking, is again distinct from hardness\nthough often confounded with it. It consists in a certain yielding of\nparts with a powerful general cohesion, and is compatible with various\ndegrees of elasticity. Malleability is again another quality of solids,\nespecially metals, quite distinct from toughness, and depends on their\ncapability of being deprived of their figure without an effort to\nrecover it and without fracture.\n\n(260.) Tenacity, again, is a property of solids more directly depending\non the cohesion of their parts than toughness. It consists in their\npower of resisting separation by a strain steadily applied, while the\nquality of toughness is materially influenced by their disposition\nto communicate through their substance the jarring effect of a\nblow. Accordingly, the tenacity of a solid is a direct measure of\nthe cohesive attraction of its parts, and is the best proof of the\nexistence of such a power.\n\n\n_Crystallography._\n\n(261.) It cannot be supposed that these and many other tangible\nqualities, as they may be called, should subsist in solids without\na corresponding mechanism in their internal structure. That they\nhave such a mechanism, and that a very curious and intricate one,\nthe phenomena of crystallography sufficiently show. This interesting\nand beautiful department of natural science is of comparatively very\nmodern date. That many natural substances affected certain forms must\nhave been known from the earliest times. Pliny appears to have been\nacquainted with this fact, at least in some instances, as he describes\nthe forms of quartz and diamond. But till the time of Linn\u00e6us no\nmaterial attention seems to have been bestowed on the subject. He,\nhowever, observed, and described with care, the crystalline forms\nof a variety of substances, and even regarded them as so definite a\ncharacter of the solids which assumed them, that he supposed every\nparticular form to be generated by a particular salt. Rom\u00e9 de l\u2019Isle\npursued the study of the crystalline forms of bodies yet farther. He\nfirst ascertained the important fact of the constancy of the angles\nat which their faces meet; and observing further that many of them\nappear in several different shapes, first conceived the idea that these\nshapes might be reducible to one, appropriated in a peculiar manner to\neach _substance_, and modified by strict geometrical laws. Bergmann,\nreasoning on a fact imparted to him by his pupil Gahn, made a yet\ngreater step, and showed how at least one species of crystal might\nbe built up of thin lamin\u00e6 ranged in a certain order, and following\ncertain rules of superposition. He failed, however, in deducing just\nand general conclusions from this remark, which, correctly viewed, is\nthe foundation of the most important law of crystallography, that which\nconnects the primitive form with other forms capable of being exhibited\nby the same substance, by a certain fixed relation. An idea may be\nformed of what is meant by this sort of connection of one form with\nanother, by considering a pointed pyramid built up of cubic stones,\ndisposed in layers, each of which separately is a square plate of the\nthickness of a single stone. These layers, laid horizontally one on the\nother, and decreasing regularly in size from the bottom to the top,\nproduce a pyramidal form with a rough or channeled surface; and if the\nlayers are so extremely thin that the channels cease to be visible to\nthe eye, the pyramid will seem smooth and perfect.\n\n(262.) Very shortly after this, and without knowledge of what had been\ndone by Gahn and Bergmann, the Abb\u00e9 Ha\u00fcy, instructed by the accidental\nfracture of a fine group of crystals, made the remark noticed already\n(in 67.), and reasoning on it with more caution and success, and\npursuing it into all its detail, developed the general laws which\nregulate the superposition of the layers of particles of which he\nsupposes all crystals to be built up, and which enable us, from knowing\ntheir primitive forms, to discover, previous to trial, what other\nforms they are capable of assuming; and which, according to this idea,\nare called derivative or secondary forms. Mohs and others have since\nimagined processes and systems by which the derivation of forms from\neach other is facilitated, and have corrected some errors of over-hasty\ngeneralization into which their predecessors had fallen, as well as\nadvanced, by an extraordinary diligence of research, our knowledge of\nthe forms which the various substances which occur in nature and art\nactually do assume.\n\n(263.) In what manner a variety in point of external form may originate\nin a variety of figures in the ultimate particles of which a solid\nis composed, may very readily be imagined by considering what would\nhappen if the bricks of which an edifice is constructed had all a\ncertain _leaning_ or bias in one direction out of the perpendicular.\nSuppose every brick, for instance, when laid flat on its face, with\nits longer edges north and south, had its eastern and western faces\nupright, but its northern and southern ones leaning southwards at a\ncertain inclination the same for each brick; a house built of such\nbricks would lean the same way, if the bricks fitted well together.\nIf, _besides this_, the eastern and western faces of the bricks,\ninstead of being truly upright, had an inclination eastward, the house\nwould have a similar one, and all its four corners, instead of being\nupright, would lean to the south-east. Suppose, instead of a house, a\npyramid were built of such oblique bricks, with the sides of its base\ndirected to the four points of the compass; then its point, instead\nof being situated vertically over the centre of its base, would stand\nperpendicularly over some point to the south-east of that centre, and\nthe pyramid itself would have its sides facing the south and the east,\nmore highly inclined to the horizon than those towards the north and\nwest.\n\n(264.) Whatever conception we may form of the manner in which the\nparticles of a crystal cohere and form masses, it is next to impossible\nto divest ourselves of the idea of a determinate figure common to them\nall. Any other supposition, indeed, would be incompatible with that\nexact similarity in all other respects which the phenomena of chemistry\nmay be considered as having demonstrated. However, it must be borne in\nmind that this idea, plausible as it may appear, is yet in some degree\nhypothetical, and that the laws of crystallography, as determined from\ninductive observation, are quite independent of any supposition of the\nkind, or even of the existence of such things as ultimate particles or\natoms at all.\n\n(265.) Still, that peculiar internal constitution of solid bodies,\nwhatever it be, which is indicated by the assumption of determinate\nfigures, by their splitting easier in some directions than in others,\nand by their presenting glittering plane surfaces when broken into\nfragments, cannot but have an important influence on all their\nrelations to external agents, as well as to their internal movements\nand the mutual actions of their parts on one another. Accordingly, the\ndivision of bodies into crystallized and uncrystallized, or imperfectly\ncrystallized, is one of the most universal importance; and almost all\nthe phenomena produced by those more intimate natural causes which\nact within small limits, and as it were on the immediate mechanism\nof solid substances, are remarkably modified by their crystalline\nstructure. Thus, in transparent solids, the course taken by the rays\nof light, in traversing them, as well as the properties impressed upon\nthem in so doing, are intimately connected with this structure. The\nrecent experiments of M. Savart, too, have proved that this is also the\ncase with their power of resistance to external force, on which depends\ntheir elasticity. Crystallized substances, according to the results of\nthese experiments, resist compression with different degrees of elastic\nforce, according to the direction in which it is attempted to compress\nthem; and all the phenomena dependent on their elasticity are affected\nby this cause, especially those which relate to their vibratory\nmovements and their conveyance of sound.\n\n(266.) There can be little doubt that modifications, similarly\ndepending on the internal structure of crystals, will be traced through\nevery department of physics. In that interesting one which relates\nto the action of heat in expanding the dimensions of substances, a\nbeginning has already been made by Professor Mitscherlich. It had long\nbeen known that all substances are dilated by heat, and no exception\nto this law has been found, so long as we regard the _bulk_ of the\nheated body. Thus, an iron rod when hot is both longer and thicker than\nwhen cold; and the difference of dimension, though but trifling in\nitself, is yet capable of being made sensible, and is of considerable\nconsequence in engineering. Thus, too, the quicksilver in a common\nthermometer occupies a larger space when hot than when cold; and being\nconfined by the glass ball, (which also expands, but _not so much in\nproportion_,) it is forced to rise in the tube. These and similar facts\nhad long been known; and accurate measures of the total amount of\ndilatation of a variety of different bodies, under similar accessions\nof heat, had been obtained and registered in tables. But no one had\nsuspected the important fact, that this expansion in crystallized\nbodies takes place under totally different circumstances from what\nobtains in uncrystallized ones. M. Mitscherlich has lately shown that\nsuch substances expand differently in different directions, and has\neven produced a case in which expansion in one direction is actually\naccompanied with contraction in another. This step, the most important\nbeyond a doubt which has yet been made in pyrometry, can however only\nbe regarded as the first in a series of researches which will occupy\nthe next generation, and which promises to afford an abundant harvest\nof new facts, as well as the elucidation of some of the most obscure\nand interesting points in the doctrine of heat.\n\n(267.) From what has been said, it is clear that if we look upon solid\nbodies as collections of particles or atoms, held together and kept\nin their places by the perpetual action of attractive and repulsive\nforces, we cannot suppose these forces, at least in crystallized\nsubstances, to act alike in all directions. Hence arises the conception\nof _polarity_, of which we see an instance, on a great scale, in the\nmagnetic needle, but which, under modified forms, there is nothing to\nprevent us from conceiving to act among the ultimate atoms of solid\nor even fluid bodies, and to produce all the phenomena which they\nexhibit in their crystallized state, either when acting on each other,\nor on light, heat, &c. It is not difficult, if we give the reins to\nimagination, to conceive how attractive and repulsive atoms, bound\ntogether by some unknown tie, may form little machines or compound\nparticles, which shall have many of the properties which we refer to\npolarity; and accordingly many ingenious suppositions have been made to\nthat effect: but in the actual state of science it is certainly safest\nto wave these hypotheses, without however absolutely rejecting them,\nand regard the _polarity of matter_ as one of the ultimate phenomena to\nwhich the analysis of nature leads us, and of which it is our business\nfully to investigate the laws, before we endeavour to ascertain its\ncauses, or trace the mechanism by which it is produced.\n\n(268.) The mutual attractions and repulsions of the particles of\nmatter, then, and their polarity, whether regarded as an original or a\nderivative property, are the forces which, acting with great energy,\nand within very confined limits, we must look to as the principles on\nwhich the intimate constitution of all bodies and many of their mutual\nactions depend. These are what are understood by the general term of\n_molecular forces_. Molecular attraction has been attempted to be\nconfounded by some with the general attraction of gravity, which all\nmatter exerts on all other matter; but this idea is refuted by the\nplainest facts.\n\n\n\n\nCHAP. II.\n\nOF THE COMMUNICATION OF MOTION THROUGH BODIES.--OF SOUND AND LIGHT.\n\n\n(269.) The propagation of motion through all substances, whether of a\nsingle impulse, as a blow or thrust, or of one frequently and regularly\nrepeated, such as a jarring or vibratory movement, depends wholly on\nthese molecular forces; and it is on such propagation that sound and\nvery probably light depend. To conceive the manner in which a motion\nmay be conveyed from one part of a substance to another, whether solid\nor fluid, we may attend to what takes place when a wave is made to\nrun along a stretched string, or the surface of still water. Every\npart of the string, or water, is in succession moved from its place,\nand agitated with a motion similar to that of the original impulse,\nleaving its place and returning to it, and when one part ceases to move\nthe next receives as it were the impression, and forwards it onward.\nThis may seem a slow and circuitous process in description; but when\nsound, for example, is conveyed through the air, we are to consider,\n1st, that the air, the substance actually in motion, is extremely light\nand acted upon by a very powerful elasticity, so that the force which\npropagates the motion, or by which the particles adjacent act on, and\nurge forward, each other, is very great, compared with the quantity of\nmaterials set in motion by it: and the same is true, even in a greater\ndegree, in liquids and solids; for in these the elastic forces are even\ngreater, in proportion to the weight, than in air.\n\n(270.) A general notion of the mode in which sounds are conveyed\nthrough the air was not altogether deficient among the ancients; but\nit is to Newton that we owe the first attempt to analyze the process,\nand show correctly what takes place in the communication of motion\nfrom particle to particle. Reasoning on the properties of the air as\nan elastic body, he showed the effect of an impulse on any portion of\nit to consist in a condensation of the air immediately adjacent in the\ndirection of the impulse, which then, re-acting by its spring, drives\nback the portion which had advanced to its original place, and at the\nsame time urges forward the portion before it, in the direction of the\nimpulse, so that every particle alternately advances and retreats.\nBut, in pursuing this idea into its details, Newton fell into some\nerrors which were pointed out by Cramer, though their origin was not\ntraced, nor the reasoning corrected, till the subject was resumed by\nLagrange and Euler; nor is this any impeachment of the penetration of\nour immortal countryman. The mathematical theory of the propagation\nof sound, and of vibratory and undulatory motions in general, is\none of the utmost intricacy; and, in spite of every exertion on the\npart of the most expert geometers, continues to this day to give\ncontinual occasion for fresh researches; while phenomena are constantly\npresenting themselves, which show how far we are from being able to\ndeduce all the particulars, even of cases comparatively simple, by any\ndirect reasoning from first principles.\n\n(271.) Whenever an impulse of any kind is conveyed by the air, to our\nears, it produces the impression of sound; but when such an impulse\nis regularly and uniformly repeated in extremely rapid succession, it\ngives us that of a musical note, the pitch of the note depending on\nthe rapidity of the succession (see art. 153.). The sense of harmony,\ntoo, depends on the periodical recurrence of coincident impulses on the\near, and affords, perhaps, the only instance of a sensation for whose\npleasing impression a distinct and intelligible reason can be assigned.\n\n(272.) Acoustics, then, or the science of sound, is a very considerable\nbranch of physics, and one which has been cultivated from the earliest\nages. Even Pythagoras and Aristotle were not ignorant of the general\nmode of its transmission through the air, and of the nature of harmony;\nbut as a branch of science, independent of its delightful application\nin the art of music, it could be hardly said to exist, till its nature\nand laws became a matter of experimental enquiry to Bacon and Galileo,\nMersenne and Wallis; and of mathematical investigation to Newton, and\nhis illustrious successors, Lagrange and Euler. From that time its\nprogress, as a branch both of mathematical and experimental science,\nhas been constant and accelerated. A curious and beautiful method of\nobservation, due to Chladni, consists in the happy device of strewing\nsand over the surfaces of bodies in a state of sonorous vibration,\nand marking the figures it assumes. This has made their motions\nsusceptible of ocular examination, and has been lately much improved\non, and varied in its application, by M. Savart, to whom we also owe a\nsuccession of instructive researches on every point connected with the\nsubject of sound, which may rank among the finest specimens of modern\nexperimental enquiry. But the subject is far from being exhausted; and,\nindeed, there are few branches of physics which promise at once so much\namusing interest, and such important consequences, in its bearings on\nother subjects, and especially, through the medium of strong analogies,\non that of light.\n\n\n_Light and Vision._\n\n(273.) The nature of light has always been involved in considerable\ndoubt and mystery. The ancients could scarcely be said to have any\nopinion on the subject, unless, indeed, it could be considered such\nto affirm that distant bodies could not be put into communication\nwithout an intermedium; and that, therefore, there must be _something_\nbetween the eye and the thing seen. What that something is, however,\nthey could only form crude and vague conjectures. One supposed that\nthe eyes themselves emit rays or emanations of some unknown kind, by\nwhich distant objects are as it were felt; a singularly unfortunate\nidea, since it gives no reason why objects should not be equally\nwell seen in the dark--no account, in short, of the part performed\nby _light_ in vision. Others imagined that all visible objects are\nconstantly throwing out from them, in all directions, some sort of\nresemblances or spectral forms of themselves, which, when received by\nthe eyes, produce an impression of the objects. Vague and clumsy as\nthis hypothesis obviously is, it assigns to the object a power, and to\nlight a diffusive propagation in all directions, which are, the one and\nthe other, independent of our eyes, and therefore goes to separate the\nphenomena of _light_ from those of _vision_.\n\n(274.) The hypothesis of Newton is a refinement and improvement on\nthis idea. Instead of spectra or resemblances, he supposes luminous\nobjects actually to dart out from them in all directions, particles,\nof inconceivable minuteness (as indeed they must be, having such\nan enormous velocity (see 17.), not to dash in pieces every thing\nthey strike upon). These particles he supposes to be acted upon by\nattractive and repulsive forces, residing in all material bodies, the\nlatter extending to some very small distance beyond their surfaces; and\nby the action of these forces to be turned aside from their natural\nstraight-lined course, without ever coming in actual contact with the\nparticles themselves of the bodies on which they fall, but either being\nturned back and _reflected_ by the repulsive forces before they reach\nthem, or penetrating between their intervals, as a bird may be supposed\nto fly through the branches of a forest, and undergoing all their\nactions, to take at quitting them a direction finally determined by\nthe position of the surface at which they emerge with respect to their\ncourse.\n\n(275.) This hypothesis, which was discussed and reasoned upon by Newton\nin a manner worthy of himself, affords, by the application of the\nsame dynamical laws which he had applied with so much success to the\nexplanation of the planetary motions, not merely a plausible, but a\nperfectly reasonable and fair explanation of all the _usual_ phenomena\nof light known in his time. His own beautiful discoveries, too, of\nthe different refrangibilities of the differently coloured rays,\nwere perfectly well represented in this theory, by simply admitting\na difference of velocity in the particles, which produce in the eye\nthe sensations of different colours. And had the properties of light\nremained confined to these, there would have been no occasion to have\nresorted to any other mode of conceiving it.\n\n(276.) A very different hypothesis had, however, been suggested about\nthe same period by Huyghens, who supposed light to be produced in the\nsame manner with sound, by the communication of a vibratory motion\nfrom the luminous body to a highly elastic fluid, which he imagined\nas filling all space, and as being less condensed within the limits\nof space occupied by matter, and that to a greater or less extent,\naccording to the nature of the occupying substance. Thus, in place of\nany thing actually thrown off, he substituted waves, or vibrations,\npropagated in all directions from luminous bodies, through this medium,\nor ether, as he called it. Huyghens, being himself a consummate\nmathematician, was enabled to trace many of the consequences of this\nhypothesis, and to show that the ordinary laws of reflection and\nrefraction were represented or accounted for by it, as well as by\nNewton\u2019s. But the hypothesis of Huyghens has not been fully successful\nin accounting for what may be considered the chief of all optical\nfacts, the production of colours in the ordinary refraction of\nlight by a prism, of which the theory of Newton gives a complete and\nelegant explanation; and the discovery of which by him marks one of\nthe greatest epochs in the annals of experimental science. This, which\nhas been often urged in objection to it, remains still, if not quite\nunanswered, at least only imperfectly removed.\n\n(277.) Other phenomena, however, were not wanting to afford a further\ntrial of the _explanatory powers_ of either hypothesis. The diffraction\nor inflection of light, discovered by Grimaldi, a Jesuit of Bologna,\nseemed to indicate that the rays of light were turned aside from their\nstraight course by merely passing near bodies of every description.\nThese phenomena, which are very curious and beautiful, were minutely\nexamined by Newton, and referred by him to the action of repulsive\nforces extending to a sensible distance from the surfaces of bodies;\nand his explanation, so far as the facts known to him are concerned,\nappears as satisfactory as could reasonably be then expected; and much\nmore so than any thing which could at that time be produced on the side\nof the hypothesis of Huyghens, which, in fact, seemed incapable of\ngiving any account whatever of them.\n\n(278.) Another class of delicate and splendid optical phenomena, which\nhad begun to attract attention somewhat previous to Newton\u2019s time,\nseemed to leave both hypotheses equally at a loss. These were the\ncolours exhibited by very thin films, either of a liquid (such as a\nsoap-bubble), or of air, as when two glasses are laid together with\nonly air between them. These colours were examined by Newton with a\nminuteness and care altogether unexampled in experimental philosophy\nat that time, and with which few researches undertaken since will bear\nto stand in competition. Their result was a theory of a very singular\nnature, which he grounded on an hypothesis of what he termed _fits of\neasy transmission and reflection_; and which supposed each ray of light\nto pass in its progress periodically through a succession of states\nsuch as would alternately dispose it to penetrate or be reflected back\nfrom the surface of a body on which it might fall. The simplest way\nin which the reader may conceive this hypothesis, is to regard every\nparticle of light as a sort of little magnet revolving rapidly about\nits own centre while it advances in its course, and thus alternately\npresenting its attractive and repulsive pole, so that when it arrives\nat the surface of a body with its repulsive pole foremost, it is\nrepelled and reflected; and when the contrary, attracted, so as to\nenter the surface. Newton, however, very cautiously avoided announcing\nhis theory in this or any similar form, confining himself entirely to\ngeneral language. In consequence, it has been confidently asserted\nby all his followers, that the doctrine of fits of easy reflection\nand transmission, as laid down by him, is substantially nothing more\nthan a statement of facts. Were it so, it is clear that any other\ntheory which should offer a just account of the same phenomena must\nultimately involve and coincide with that of Newton. But this, as we\nshall presently see, is not the case; and this instance ought to serve\nto make us extremely cautious how we employ, in stating physical laws\nderived from experiment, language which involves any thing in the\nslightest degree theoretical, if we would present the laws themselves\nin a form which no future research shall modify or subvert.\n\n(279.) A third class of optical phenomena, which were likewise\ndiscovered while Newton was yet engaged in his optical researches, was\nthat exhibited by doubly refracting crystals. In what the phenomenon of\ndouble refraction consists, we have already had occasion to explain.\nThe fact itself was first noticed by Erasmus Bartolin in the crystal\ncalled Iceland spar; and was studied with attention by Huyghens, who\nascertained its laws, and referred it with remarkable ingenuity and\nsuccess to his theory of light, by the additional hypothesis of such\na constitution of his ethereal medium within the crystal as should\nenable it to convey an impulse faster in one direction than another:\nas if, for example\u2019s sake, we should suppose a sound conveyed through\nthe air with different degrees of rapidity in a vertical and horizontal\ndirection.\n\n(280.) Some remarkable facts accompanying the double refraction\nproduced by Iceland spar, which Bartolin, Huyghens, and Newton, had\nobserved, led the latter to conceive the singular idea that a ray of\nlight after its emergence from such a crystal acquires _sides_, that\nis to say, distinct relations to surrounding space, which it carries\nwith it through its whole subsequent course, and which give rise to all\nthose curious and complicated phenomena which are now known under the\nname of the _polarization of light_. These results, however, appeared\nso extraordinary, and offered so little handle for further enquiry,\nthat their examination dropped, as if by common consent; Newton himself\nresting content with urging strongly the apparent incompatibility of\nthese properties with the Huyghenian doctrine, but without making any\nattempt to explain them by his own.\n\n(281.) From the period of Newton\u2019s optical discoveries to the\ncommencement of the present century, no great accession to our\nknowledge of the nature of light was made, if we except one, which,\nfrom its invaluable practical application, must ever hold a prominent\nplace in the annals both of art and science: we mean, the discovery\nof the principle of the achromatic telescope, which originated in a\ndiscussion between the celebrated geometer Euler, Klingenstierna, an\neminent Swedish philosopher, and our own countryman, the admirable\noptician Dollond, on the occasion of certain abstract theoretical\ninvestigations of the former, which led him to speculate on its\n_possibility_, and which ultimately terminated in its complete and\nhappy _execution_ by the latter; a memorable case in science, though\nnot a singular one, where the speculative geometer in his chamber,\napart from the world, and existing among abstractions, has originated\nviews of the noblest practical application.[49]\n\n(282.) The explanation which our knowledge of optical laws affords of\nthe mechanism of the eye, and the process by which vision is performed,\nis as complete and satisfactory as that of hearing by the propagation\nof motion through the air. The camera obscura, invented by Baptista\nPorta in 1560, gave the first idea how the actual images of external\nobjects might be conveyed into the eye, but it was not till after a\nconsiderable interval that Kepler, the immortal discoverer of those\ngreat laws which regulate the periods and motions of the planets,\npointed out distinctly the offices performed by the several parts\nof the eye in the act of vision. From this to the invention of the\ntelescope and microscope there would seem but a small step, but it is\nto accident rather than design that it is due; and its re-invention\nby Galileo, on a mere description of its effects, may serve, among\na thousand similar instances, to show that inestimable practical\napplications lie open to us, if we can only once bring ourselves\nto conceive their possibility, a lesson which the invention of the\nachromatic telescope itself, as we have above related it, not less\nstrongly exemplifies.\n\n(283.) The little instrument with which Galileo\u2019s splendid discoveries\nwere made was hardly superior in power to an ordinary finder of the\npresent day; but it was rapidly improved on, and in the hands of\nHuyghens attained to gigantic dimensions and very great power. It was\nto obviate the necessity of the enormous length required for these\ntelescopes, and yet secure the same power, that Gregory and Newton\ndevised the reflecting telescope, which has since become a much\nmore powerful instrument than its original inventors probably ever\ncontemplated.\n\n(284.) The telescope, as it exists at present, with the improvements\nin its structure and execution which modern artists have effected, must\nassuredly be ranked among the highest and most refined productions of\nhuman art; that in which man has been able to approximate most closely\nto the workmanship of nature, and which has conferred upon him, if\nnot another sense, at least an exaltation of one already possessed\nby him that merits almost to be regarded as a new one. Nor does it\nappear yet to have reached its ultimate perfection, to which indeed\nit is difficult to assign any bounds, when we take into consideration\nthe wonderful progress which workmanship of every kind is making,\nand the delicacy, far superior to that of former times, with which\nmaterials may now be wrought, as well as the ingenious inventions and\ncombinations which every year is bringing forth for accomplishing the\nsame ends by means hitherto unattempted.[50]\n\n(285.) After a long torpor, the knowledge of the properties of light\nbegan to make fresh progress about the end of the last century,\nadvancing with an accelerated rapidity, which has continued unabated\nto the present time. The example was set by our late admirable and\nlamented countryman, Dr. Wollaston, who re-examined and verified\nthe laws of double refraction in Iceland spar announced by Huyghens.\nAttention being thus drawn to the subject, the geometry of Laplace\nsoon found a means of explaining at least one portion of the mystery\nof this singular phenomenon, by the Newtonian theory of light, applied\nunder certain supposed conditions; and the reasoning which led him to\nthe result (at that time quite unexpected), may justly be regarded as\none of his happiest efforts. The prosecution of the subject, which had\nnow acquired a high degree of interest, was encouraged by the offer\nof a prize on the part of the French Academy of Sciences; and it was\nin a memoir which received this honourable reward on that occasion,\nin 1810, that Malus, a retired officer of engineers in the French\narmy, announced the great discovery of the _polarization of light_ by\nordinary reflection at the surface of a transparent body.\n\n(286.) Malus found that when a beam of light is reflected from the\nsurface of such a body at a certain angle, it acquires precisely the\nsame singular property which is impressed upon it in the act of double\nrefraction, and which Newton had before expressed by saying that it\npossessed _sides_. This was the first circumstance which pointed out a\nconnection between that hitherto mysterious phenomenon and any of the\nordinary modifications of light; and it proved ultimately the means of\nbringing the whole within the limits, if not of a complete explanation,\nat least of a highly plausible theoretical representation. So true is,\nin science, the remark of Bacon, that no natural phenomenon can be\nadequately studied _in itself alone_, but, to be understood, must be\nconsidered _as it stands connected with all nature_.\n\n(287.) The new class of phenomena thus disclosed were immediately\nstudied with diligence and success, both abroad by Malus and Arago, and\nat home by our countryman Dr. Brewster, and their laws investigated\nwith a care proportioned to their importance; when another and\napparently still more extraordinary class of phenomena presented\nitself in the production of the most vivid and beautiful colours\n(every way resembling those observed by Newton in thin films of air\nor liquids, only infinitely more developed and striking,) in certain\ntransparent crystallized substances, when divided into flat plates in\nparticular directions, and exposed in a beam of polarized light. The\nattentive examination of these colours by Wollaston, Biot, and Arago,\nbut more especially by Brewster, speedily led to the disclosure of a\nseries of optical phenomena so various, so brilliant, and evidently\nso closely connected with the most important points relating to the\nintimate structure of crystallized bodies, as to excite the highest\ninterest,--that sort of interest which is raised when we feel we are\non the eve of some extraordinary discovery, and expect every moment\nthat some leading fact will turn up, which will throw light on all that\nappears obscure, and reduce into order all that seems anomalous.\n\n(288.) This expectation was not disappointed. So long before the time\nwe are speaking of as the first year of the present century, our\nillustrious countryman, the late Dr. Thomas Young, had established a\nprinciple in optics, which, regarded as a physical law, has hardly its\nequal for beauty, simplicity, and extent of application, in the whole\ncircle of science. Considering the manner in which the vibrations of\ntwo musical sounds arriving at once at the ear affect the sense with\nan impression of sound or silence according as they conspire or oppose\neach other\u2019s effects, he was led to the idea that the same ought to\nhold good with light as with sound, if the theory which makes light\nanalogous to sound be the true one; and that, therefore, two rays of\nlight, setting off from the same origin, at the same instant, and\narriving at the same place by different routes, ought to strengthen\nor wholly or partially destroy each other\u2019s effects according to\nthe difference in length of the routes described by them. That two\nlights should in any circumstances combine to produce darkness may\nbe considered strange, but is _literally true_; and it had even been\nnoticed long ago as a singular and unaccountable fact by Grimaldi, in\nhis experiments on the inflection of light. The experimental means by\nwhich Dr. Young confirmed this principle, which is known in optics\nby the name of the _interference_ of the rays of light, were as\nsimple and satisfactory as the principle itself is beautiful; but the\nverifications of it, drawn from the explanation it affords of phenomena\napparently the most remote, are still more so. Newton\u2019s colours of thin\nfilms were the first phenomena to which its author applied it with full\nsuccess. Its next remarkable application was to those of diffraction,\nof which, in the hands of M. Fresnel, a late eminent French geometer,\nit also furnished a complete explanation, and that, too, in cases to\nwhich Newton\u2019s hypothesis could not apparently be made to apply, and\nthrough a complication of circumstances which might afford a very\nsevere test of any hypothesis.\n\n(289.) A simple and beautiful experiment on the interferences of\npolarized light due to Fresnel and Arago enabled them to bring Dr.\nYoung\u2019s law to bear on the colours produced by crystallized plates in a\npolarized beam, and by so doing afforded a key to all the intricacies\nof these magnificent but complex phenomena. Nothing now was wanting to\na rational theory of double refraction but to frame an hypothesis of\nsome mode in which light might be conceived to be propagated through\nthe elastic medium supposed to convey it in such a way as not to be\ncontradictory to any of the facts, nor to the general laws of dynamics.\nThis essential idea, without which every thing that had been before\ndone would have been incomplete, was also furnished by Dr. Young, who,\nwith a sagacity which would have done honour to Newton himself, had\ndeclared, that to accommodate the doctrine of Huyghens to the phenomena\nof polarized light it is necessary to conceive the mode of propagation\nof a luminous impulse through the ether, differently from that of a\nsonorous one through the air. In the latter, the particles of the air\n_advance_ and _recede_; in the former, those of the ether must be\nsupposed to _tremble laterally_.\n\n(290.) Taking this as the groundwork of his reasoning, Fresnel\nsucceeded in erecting on it a theory of polarization and double\nrefraction, so happy in its adaptation to facts, and in the coincidence\nwith experience of results deduced from it by the most intricate\nanalysis, that it is difficult to conceive it unfounded. If it be\nso, it is at least the most curiously artificial system that science\nhas yet witnessed; and whether it be so or not, so long as it serves\nto group together in one comprehensive point of view a mass of facts\nalmost infinite in number and variety, to reason from one to another,\nand to establish analogies and relations between them; on whatever\nhypothesis it may be founded, or whatever arbitrary assumptions it\nmay make respecting structures and modes of action, it can never be\nregarded as other than a most real and important accession to our\nknowledge.\n\n(291.) Still, it is by no means impossible that the Newtonian theory of\nlight, if cultivated with equal diligence with the Huyghenian, might\nlead to an equally plausible explanation of phenomena now regarded\nas beyond its reach. M. Biot is the author of the hypothesis we have\nalready mentioned of a rotatory motion of the particles of light about\ntheir axes. He has employed it only for a very limited purpose; but\nit might doubtless be carried much farther; and by admitting only the\nregular emission of the luminous particles at equal intervals of time,\nand in similar states of motion from the shining body, which does not\nseem a very forced supposition, all the phenomena of interference at\nleast would be readily enough explained without the admission of an\nether.\n\n(292.) The optical examination of crystallized substances affords\none among many fine examples of the elucidation which every branch\nof science is capable of affording to every other. The indefatigable\nresearches of Dr. Brewster and others have shown that the phenomena\nexhibited by polarized light in its transmission through crystals\nafford a certain indication of the most important points relating to\nthe structure of the crystals themselves, and thus become most valuable\ncharacters by which to recognise their internal constitution. It was\nNewton who first showed of what importance as a physical character,--as\nthe indication of other properties,--the action of a body on light\nmight become; but the characters afforded by the use of polarized light\nas an instrument of experimental enquiry are so marked and intimate,\nthat they may almost be said to have furnished us with a kind of\nintellectual sense, by which we are enabled to scrutinize the internal\narrangement of those wonderful structures which Nature builds up by\nher refined and invisible architecture, with a delicacy eluding our\nconception, yet with a symmetry and beauty which we are never weary\nof admiring. In this point of view the science of optics has rendered\nto mineralogy and crystallography services not less important than to\nastronomy by the invention of the telescope, or to natural history by\nthat of the microscope; while the relations which have been discovered\nto exist between the optical properties of bodies and their crystalline\nforms, and even their chemical habitudes, have afforded numerous\nand beautiful instances of general laws concluded from laborious and\npainful induction, and curiously exemplifying the simplicity of nature\nas it emerges slowly from an entangled mass of particulars in which, at\nfirst, neither order nor connection can be traced.\n\n\n\n\nCHAP. III.\n\nOF COSMICAL PHENOMENA.\n\n\n_Astronomy and Celestial Mechanics._\n\n(293.) Astronomy, as has been observed in the former part of this\ndiscourse, as a science of observation, had made considerable progress\namong the ancients: indeed, it was the only branch of physical science\nwhich could be regarded as having been cultivated by them with any\ndegree of assiduity or real success. The Chaldean and Egyptian records\nhad furnished materials from which the motions of the sun and moon\ncould be calculated with sufficient exactness for the prediction of\neclipses; and some remarkable cycles, or periods of years in which\nthe lunar eclipses return in very nearly the same order, had been\nascertained by observation. Considering the extreme imperfection of\ntheir means of measuring time and space, this was, perhaps, as much\nas could have been expected at that early period, and it was followed\nup for a while in a philosophical spirit of just speculation, which,\nif continued, could hardly have failed to lead to sound and important\nconclusions.\n\n(294.) Unfortunately, however, the philosophy of Aristotle laid it\ndown as a principle, that the celestial motions were regulated by laws\nproper to themselves, and bearing no affinity to those which prevail\non earth. By thus drawing a broad and impassable line of separation\nbetween celestial and terrestrial mechanics, it placed the former\naltogether out of the pale of experimental research, while it at the\nsame time impeded the progress of the latter by the assumption of\nprinciples respecting natural and unnatural motions, hastily adopted\nfrom the most superficial and cursory remark, undeserving even the\nname of observation. Astronomy, therefore, continued for ages a\nscience of mere record, in which theory had no part, except in so\nfar as it attempted to conciliate the inequalities of the celestial\nmotions with that assumed law of uniform circular revolution which\nwas alone considered consistent with the perfection of the heavenly\nmechanism. Hence arose an unwieldy, if not self-contradictory, mass\nof hypothetical motions of sun, moon, and planets, in circles, whose\ncentres were carried round in other circles, and these again in others\nwithout end,--\u201ccycle on epicycle, orb on orb,\u201d--till at length, as\nobservation grew more exact, and fresh epicycles were continually\nadded, the absurdity of so cumbrous a mechanism became too palpable to\nbe borne. Doubts were expressed, to which the sarcasm of a monarch[51]\ngave a currency they might not have obtained in a period when men\nscarcely dared trust themselves to think; and at length Copernicus,\npromulgating his own, or reviving the Pythagorean doctrine, which\nplaces the sun in the centre of our system, gave to astronomy a\nsimplicity which, contrasted with the complication of the preceding\nviews, at once commanded assent.\n\n(295.) An elegant writer[52], whom we have before had occasion to\nquote, has briefly and neatly accounted for the confused notions which\nso long prevailed respecting the constitution of our system, and the\ndifficulty experienced in acquiring a true notion of the disposition\nof its parts. \u201cWe see it,\u201d he observes, \u201cnot in _plan_, but in\n_section_.\u201d The reason of this is, that our point of observation lies\nin its general plane, but the notion we aim at forming of it is not\nthat of its section, but of its plan. This is as if we should attempt\nto read a book, or make out the countries on a map, with the eye on a\nlevel with the paper. We can only judge directly of the distances of\nobjects by their sizes, or rather of their change of distance by their\nchange of size; neither have we any means of ascertaining, otherwise\nthan indirectly, even their positions, one among the other, from their\napparent places as seen by us. Now, the variations in apparent size\nof the sun and moon are too small to admit of exact measure without\nthe use of the telescope, and the bodies of the planets cannot even be\ndistinguished as having any distinct size with the naked eye.\n\n(296.) The Copernican system once admitted, however, this difficulty\nof conception, at least, is effectually got over, and it becomes\na mere problem of geometry and calculation to determine, from the\nobserved places of a planet, its real orbit about the sun, and the\nother circumstances of its motion. This Kepler accomplished for the\norbit of Mars, which he ascertained to be an ellipse having the sun\nin one of its foci; and the same law, being extended by inductive\nanalogy to all the planets, was found to be verified in the case of\neach. This with the other remarkable laws which are usually cited in\nphysical astronomy by the name of Kepler\u2019s laws, constitute undoubtedly\nthe most important and beautiful system of geometrical relations which\nhave ever been discovered by a mere inductive process, independent of\nany consideration of a theoretical kind. They comprise within them a\ncompendium of the motions of all the planets, and enable us to assign\ntheir places in their orbits at any instant of time past or to come\n(disregarding their mutual perturbations), provided certain purely\ngeometrical problems can be numerically resolved.\n\n(297.) It was not, however, till long after Kepler\u2019s time that the\nreal importance of these laws could be felt. Regarded in themselves,\nthey offered, it is true, a fine example of regular and harmonious\ndisposition in the greatest of all the works of creation, and a\nstriking contrast to the cumbersome mechanism of the cycles and\nepicycles which preceded them; but there their utility seemed to\nterminate, and, indeed, Kepler was reproached, and not without a\nsemblance of reason, with having rendered the actual calculation of\nthe places of the planets more difficult than before, the resources of\ngeometry being then inadequate to resolve the problems to which the\nstrict application of his laws gave rise.\n\n(298.) The first result of the invention of the telescope and its\napplication to astronomical purposes, by Galileo, was the discovery\nof Jupiter\u2019s disc and satellites,--of a system offering a beautiful\nminiature of that greater one of which it forms a portion, and\npresenting to the eye of sense, at a single glance, that disposition of\nparts which in the planetary system itself is discerned only by the eye\nof reason and imagination (see 195.). Kepler had the satisfaction of\nseeing it ascertained, that the law which he had discovered to connect\nthe times of revolution of the planets with their distances from the\nsun, holds good also when applied to the periods of circulation of\nthese little attendants round the centre of their principal; thus\ndemonstrating it to be something more than a mere empirical rule, and\nto depend on the intimate nature of planetary motion itself.\n\n(299.) It had been objected to the doctrine of Copernicus, that, were\nit true, Venus should appear sometimes horned like the moon. To this\nhe answered by admitting the conclusion, and averring that, should we\never be able to see its actual shape, it _would_ appear so. It is easy\nto imagine with what force the application would strike every mind when\nthe telescope confirmed this prediction, and showed the planet just as\nboth the philosopher and his objectors had agreed it ought to appear.\nThe history of science affords perhaps only one instance analogous to\nthis. When Dr. Hutton expounded his theory of the consolidation of\nrocks by the application of heat, at a great depth below the bed of\nthe ocean, and especially of that of marble by actual fusion; it was\nobjected that, whatever might be the case with others, with calcareous\nor marble rocks, at least, it was impossible to grant such a cause\nof consolidation, since heat decomposes their substance and converts\nit into quicklime, by driving off the carbonic acid, and leaving a\nsubstance perfectly infusible, and incapable even of agglutination\nby heat. To this he replied, that the pressure under which the heat\nwas applied would prevent the escape of the carbonic acid; and that\nbeing retained, it might be expected to give that fusibility to the\ncompound which the simple quicklime wanted. The next generation saw\nthis anticipation converted into an observed fact, and verified by the\ndirect experiments of Sir James Hall, who actually succeeded in melting\nmarble, by retaining its carbonic acid under violent pressure.\n\n(300.) Kepler, among a number of vague and even wild speculations on\nthe causes of the motions whose laws he had developed so beautifully\nand with so much patient labour, had obtained a glimpse of the general\nlaw of the inertia of matter, as applicable to the great masses of the\nheavenly bodies as well as to those with which we are conversant on\nthe earth. After Kepler, Galileo, while he gave the finishing blow to\nthe Aristotelian dogmas which erected a barrier between the laws of\ncelestial and terrestrial motion, by his powerful argument and caustic\nridicule, contributed, by his investigations of the laws of falling\nbodies and the motions of projectiles, to lay the foundation of a\ntrue system of dynamics, by which motions could be determined from a\nknowledge of the forces producing them, and forces from the motions\nthey produce. Hooke went yet farther, and obtained a view so distinct\nof the mode in which the planets might be retained in their orbits\nby the sun\u2019s attraction, that, had his mathematical attainments been\nequal to his philosophical acumen, and his scientific pursuits been\nless various and desultory, it can hardly be doubted that he would have\narrived at a knowledge of the law of gravitation.\n\n(301.) But every thing which had been done towards this great end,\nbefore Newton, could only be regarded as smoothing some first\nobstacles, and preparing a state of knowledge, in which powers like his\ncould be effectually exerted. His wonderful combination of mathematical\nskill with physical research enabled him to invent, at pleasure, new\nand unheard-of methods of investigating the effects of those causes\nwhich his clear and penetrating mind detected in operation. Whatever\ndepartment of science he touched, he may be said to have formed afresh.\nAscending by a series of close-compacted inductive arguments to the\nhighest axioms of dynamical science, he succeeded in applying them\nto the complete explanation of all the great astronomical phenomena,\nand many of the minuter and more enigmatical ones. In doing this, he\nhad every thing to create: the mathematics of his age proved totally\ninadequate to grapple with the numerous difficulties which were to\nbe overcome; but this, so far from discouraging him, served only to\nafford new opportunities for the exertion of his genius, which, in the\ninvention of the method of fluxions, or, as it is now more generally\ncalled, the differential calculus, has supplied a means of discovery,\nbearing the same proportion to the methods previously in use, that\nthe steam-engine does to the mechanical powers employed before its\ninvention. Of the optical discoveries of Newton we have already spoken;\nand if the magnitude of the objects of his astronomical discoveries\nexcite our admiration of the mental powers which could so familiarly\ngrasp them, the minuteness of the researches into which he there set\nthe first example of entering, is no less calculated to produce a\ncorresponding impression. Whichever way we turn our view, we find\nourselves compelled to bow before his genius, and to assign to the\nname of NEWTON a place in our veneration which belongs to no other in\nthe annals of science. His era marks the accomplished maturity of the\nhuman reason as applied to such objects. Every thing which went before\nmight be more properly compared to the first imperfect attempts of\nchildhood, or the essays of inexpert, though promising, adolescence.\nWhatever has been since performed, however great in itself, and worthy\nof so splendid and auspicious a beginning, has never, in point of\nintellectual effort, surpassed that astonishing one which produced the\nPrincipia.\n\n(302.) In this great work, Newton shows all the celestial motions known\nin his time to be consequences of the simple law, that every particle\nof matter attracts every other particle in the universe with a force\nproportional to the product of their masses directly, and the square\nof their mutual distance inversely, and is itself attracted with an\nequal force. Setting out from this, he explains how an attraction\narises between the great spherical masses of which our system consists,\nregulated by a law precisely similar in its expression; how the\nelliptic motions of planets about the sun, and of satellites about\ntheir primaries, according to the exact rules inductively arrived at\nby Kepler, result as necessary consequences from the same general law\nof force; and how the orbits of comets themselves are only particular\ncases of planetary movements. Thence proceeding to applications of\ngreater difficulty, he explains how the perplexing inequalities of\nthe moon\u2019s motion result from the sun\u2019s disturbing action; how tides\narise from the unequal attraction of the sun as well as of the moon\non the earth, and the ocean which surrounds it; and, lastly, how the\nprecession of the equinoxes is a necessary consequence of the very same\nlaw.\n\n(303.) The immediate successors of Newton found full occupation\nin verifying his discoveries, and in extending and improving the\nmathematical methods which it had now become manifest were to prove\nthe keys to an inexhaustible treasure of knowledge. The simultaneous\nbut independent discovery of a method of mathematical investigation in\nevery respect similar to that of Newton, by Leibnitz, while it created\na degree of national jealousy which can now only be regretted, had the\neffect of stimulating the continental geometers to its cultivation, and\nimpressing on it a character more entirely independent of the ancient\ngeometry, to which Newton was peculiarly attached. It was fortunate\nfor science that it did so; for it was speedily found that (with one\nfine exception on the part of our countryman Maclaurin, followed up,\nafter a long interval, by the late Professor Robison of Edinburgh, with\nequal elegance,) the geometry of Newton was like the bow of Ulysses,\nwhich none but its master could bend; and that, to render his methods\navailable beyond the points to which he himself carried them, it was\nnecessary to strip them of every vestige of that antique dress in which\nhe had delighted to clothe them. This, however, the countrymen of\nNewton were very unwilling to do; and they paid the penalty in finding\nthemselves condemned to the situation of lookers on, while their\ncontinental neighbours both in Germany and France were pushing forward\nin the career of mathematico-physical discovery with emulous rapidity.\n\n(304.) The legacy of research which Newton may be said to have left\nto his successors was truly immense. To pursue, through all its\nintricacies, the consequences of the law of gravitation; to account for\nall the inequalities of the planetary movements, and the infinitely\nmore complicated, and to us more important ones, of the moon; and to\ngive, what Newton himself certainly never entertained a conception\nof, a demonstration of the stability and permanence of the system,\nunder all the accumulating influence of its internal perturbations;\nthis labour, and this triumph, were reserved for the succeeding\nage, and have been shared in succession by Clairaut, D\u2019Alembert,\nEuler, Lagrange and Laplace. Yet so extensive is the subject, and so\ndifficult and intricate the purely mathematical enquiries to which it\nleads, that another century may yet be required to go through with\nthe task. The recent discoveries of astronomers have supplied matter\nfor investigation, to the geometers of this and the next generation,\nof a difficulty far surpassing any thing that had before occurred.\nFive primary planets have been added to our system; four of them\nsince the commencement of the present century, and these, singularly\ndeviating from the general analogy of the others, and offering _cases\nof difficulty_ in theory, which no one had before contemplated. Yet\neven the intricate questions to which these bodies have given rise\nseem likely to be surpassed by those which have come into view, with\nthe discovery of several comets revolving in elliptic orbits, like the\nplanets, round the sun, in very moderate periods. But the resources of\nmodern geometry seem, so far from being exhausted, to increase with the\ndifficulties they have to encounter, and already, among the successors\nof Lagrange and Laplace, the present generation has to enumerate a\npowerful array of names, which promise to render it not less celebrated\nin the annals of physico-mathematical research than that which has just\npassed away.\n\n(305.) Meanwhile the positions, figures, and dimensions of all the\nplanetary orbits, are now well known, and their variations from century\nto century in great measure determined; and it has been generally\ndemonstrated, that all the changes which the mutual actions of the\nplanets on each other can produce in the course of indefinite ages,\nare _periodical_, that is to say, increasing to a certain extent (and\nthat never a very great one), and then again decreasing; so that the\nsystem can never be destroyed or subverted by the mutual action of its\nparts, but keeps constantly oscillating, as it were, round a certain\nmean state, from which it can never deviate to any ruinous extent. In\nparticular the researches of Laplace, Lagrange, and Poisson, have shown\nthe ultimate invariability of the mean distance of each planet from the\nsun, and consequently of its periodic time. Relying on these grand\ndiscoveries, we are enabled to look forward, from the point of time\nwhich we now occupy, many thousands of years into futurity, and predict\nthe state of our system without fear of material error, but such as\nmay arise from causes whose existence at present we have no reason to\nsuppose, or from interference which we have no right to anticipate.\n\n(306.) A correct enumeration and description of the fixed stars in\ncatalogues, and an exact knowledge of their position, supply the\nonly effectual means we can have of ascertaining what changes they\nare liable to, and what motions, too slow to deprive them of their\nusual epithet, _fixed_, yet sufficient to produce a sensible change\nin the lapse of ages, may exist among them. Previous to the invention\nof the compass, they served as guides to the navigator by night; but\nfor this purpose, a very moderate knowledge of a few of the principal\nones sufficed. Hipparchus was the first astronomer, who, excited\nby the appearance of a new star, conceived the idea of forming a\ncatalogue of the stars, with a view to its use as an astronomical\nrecord, \u201cby which,\u201d says Pliny, \u201cposterity will be able to discover,\nnot only whether they are born and die, but also whether they change\ntheir places, and whether they increase or decrease.\u201d His catalogue,\ncontaining more than 1000 stars, was constructed about 128 years before\nChrist. It was in the course of the laborious discussion of his own and\nformer observations of them, undertaken with a view to the formation of\nthis catalogue, that he first recognised the fact of that slow, general\nadvance of all the stars eastward, when compared with the place of\nthe equinox, which is known under the name of the precession of the\nequinoxes, and which Newton succeeded in referring to a motion in the\nearth\u2019s axis, produced by the attraction of the sun and moon.\n\n(307.) Since Hipparchus, at various periods in the history of\nastronomy, catalogues of stars have been formed, among which that\nof Ulugh Begh, comprising about 1000 stars, constructed in 1437, is\nremarkable as the production of a sovereign prince, working personally\nin conjunction with his astronomers; and that of Tycho Brahe,\ncontaining 777 stars, constructed in 1600, as having originated in a\nphenomenon similar to that which drew the attention of Hipparchus. In\nmore recent times, astronomers provided with the finest instruments\ntheir respective eras could supply, and established in observatories,\nmunificently endowed by the sovereigns and governments of different\nEuropean nations, have vied and are still vying with each other,\nin extending the number of registered stars, and giving the utmost\npossible degree of accuracy to the determination of their places.\nAmong these, it would be ungrateful not to claim especial notice\nfor the superb series of observations which, under a succession of\nindefatigable and meritorious astronomers, has, for a very long period,\ncontinued to emanate from our own national observatory of Greenwich.\n\n(308.) The distance of the fixed stars is so immense, that every\nattempt to assign a limit, _within which_ it _must_ fall, has hitherto\nfailed. The enquiries of astronomers of all ages have been directed\nto ascertain this distance, by taking the dimensions of our own\nparticular system of sun and planets, or of the earth itself, as the\nunit of a scale on which it might be measured. But although many have\nimagined that their observations afforded grounds for the decision\nof this interesting point, it has uniformly happened either that the\nphenomena on which they relied have proved to be referable to other\ncauses not previously known, and which the superior accuracy of their\nresearches has for the first time brought to light; or to errors\narising from instrumental imperfections and unavoidable defects of the\nobservations themselves.\n\n(309.) The only indication we can expect to obtain of the actual\ndistance of a star, would consist in an annual change in its apparent\nplace corresponding to the motion of the earth round the sun, called\nits _annual parallax_, and which is nothing more than the measure\nof the apparent size of the earth\u2019s orbit as seen from the star.\nMany observers have thought they have detected a measurable amount\nof this parallax; but as astronomical instruments have advanced in\nperfection, the quantity which they have successively assigned to it\nhas been continually reduced within narrower and narrower limits,\nand has invariably been commensurate with the errors to which the\ninstruments used might fairly be considered liable. The conclusion this\nstrongly presses on us is, that it is really a quantity too small to\nadmit of distinct measurement in the present state of our means for\nthat purpose; and that, therefore, the distance of the stars must be\na magnitude of such an order as the imagination almost shrinks from\ncontemplating. But this increase in our scale of dimension calls for\na corresponding enlargement of conception in all other respects. The\nsame reasoning which places the stars at such immeasurable remoteness,\nexalts them at the same time into glorious bodies, similar to, and even\nfar surpassing, our own sun, the centres perhaps of other planetary\nsystems, or fulfilling purposes of which we can have no idea, from any\nanalogy in what passes immediately around us.\n\n(310.) The comparison of catalogues, published at different periods,\nhas given occasion to many curious remarks, respecting changes both\nof place and brightness among the stars, to the discovery of variable\nones which lose and recover their lustre periodically, and to that of\nthe disappearance of several from the heavens so completely as to have\nleft no vestige discernible even by powerful telescopes. In proportion\nas the construction of astronomical and optical instruments has gone on\nimproving, our knowledge of the contents of the heavens has undergone\na corresponding extension, and, at the same time, attained a degree of\nprecision which could not have been anticipated in former ages. The\nplaces of all the principal stars in the northern hemisphere, and of a\ngreat many in the southern, are now known to a degree of nicety which\nmust infallibly detect any real motions that may exist among them,\nand has in fact done so, in a great many instances, some of them very\nremarkable ones.\n\n(311.) It is only since a comparatively recent date, however, that\nany great attention has been bestowed on the smaller stars, among\nwhich there can be no doubt of the most interesting and instructive\nphenomena being sooner or later brought to light. The minute\nexamination of them with powerful telescopes, and with delicate\ninstruments for the determination of their places, has, indeed, already\nproduced immense catalogues and masses of observations, in which\nthousands of stars invisible to the naked eye are registered; and has\nled to the discovery of innumerable important and curious facts, and\ndisclosed the existence of whole classes of celestial objects, of a\nnature so wonderful as to give room for unbounded speculation on the\nextent and construction of the universe.\n\n(312.) Among these, perhaps the most remarkable are the revolving\ndouble stars, or stars which, to the naked eye or to inferior\ntelescopes, appear single; but, if examined with high magnifying\npowers, are found to consist of two individuals placed almost close\ntogether, and which, when carefully watched, are (many of them) found\nto revolve in regular elliptic orbits about each other; and so far\nas we have yet been able to ascertain, to obey the same laws which\nregulate the planetary movements. There is nothing calculated to give a\ngrander idea of the scale on which the sidereal heavens are constructed\nthan these beautiful systems. When we see such magnificent bodies\nunited in pairs, undoubtedly by the same bond of mutual gravitation\nwhich holds together our own system, and sweeping over their enormous\norbits, in periods comprehending many centuries, we admit at once that\nthey must be accomplishing ends in creation which will remain for ever\nunknown to man; and that we have here attained a point in science\nwhere the human intellect is compelled to acknowledge its weakness, and\nto feel that no conception the wildest imagination can form will bear\nthe least comparison with the intrinsic greatness of the subject.\n\n\n_Geology._\n\n(313.) The researches of physical astronomy are confessedly incompetent\nto carry us back to the origin of our system, or to a period when\nits state was, in any great essential, different from what it is\nat present. So far as the causes now in action go, and so far as\nour calculations will enable us to estimate their effects, we are\nequally unable to perceive in the general phenomena of the planetary\nsystem either the evidence of a beginning, or the prospect of an end.\nGeometers, as already stated, have demonstrated that, in the midst of\nall the fluctuations which can possibly take place in the elements of\nthe orbits of the planets, by reason of their mutual attraction, the\ngeneral balance of the parts of the system will always be preserved,\nand every departure from a mean state periodically compensated. But\nneither the researches of the physical astronomer, nor those of\nthe geologist, give us any ground for regarding our system, or the\nglobe we inhabit, as of eternal duration. On the contrary, there are\ncircumstances in the physical constitution of our own planet which at\nleast obscurely point to an origin and a formation, however remote,\nsince it has been found that the figure of the earth is not globular\nbut elliptical, and that its attraction is such as requires us to admit\nthe interior to be more dense than the exterior, and the density to\nincrease with some degree of regularity from the surface towards the\ncentre, and _that_, in layers arranged elliptically round the centre,\ncircumstances which could scarcely happen without some such successive\ndeposition of materials as would enable pressure to be propagated with\na certain degree of freedom from one part of the mass to another, even\nif we should hesitate to admit a state of primitive fluidity.\n\n(314.) But from such indications nothing distinct can be concluded;\nand if we would speculate to any purpose on a former state of our\nglobe and on the succession of events which from time to time may have\nchanged the condition and form of its surface, we must confine our\nviews within limits far more restricted, and to subjects much more\nwithin the reach of our capacity, than either the creation of the world\nor its assumption of its present figure. These, indeed, were favourite\nspeculations with a race of geologists now extinct; but the science\nitself has undergone a total change of character, even within the last\nhalf century, and is brought, at length, effectually within the list\nof the inductive sciences. Geologists now no longer bewilder their\nimaginations with wild theories of the formation of the globe from\nchaos, or its passage through a series of hypothetical transformations,\nbut rather aim at a careful and accurate examination of the records\nof its former state, which they find indelibly impressed on the great\nfeatures of its actual surface, and to the evidences of former life\nand habitation which organised remains imbedded and preserved in its\nstrata indisputably afford.\n\n(315.) Records of this kind are neither few nor vague; and though the\nobsoleteness of their language when we endeavour to interpret it too\nminutely, may, and no doubt often does, lead to misapprehension, still\nits general meaning is, on the whole, unequivocal and satisfactory.\nSuch records teach us, in terms too plain to be misunderstood, that\nthe whole or nearly the whole of our present lands and continents\nwere formerly at the bottom of the sea, where they received deposits\nof materials from the wearing and degradation of other lands not now\nexisting, and furnished receptacles for the remains of marine animals\nand plants inhabiting the ocean above them, as well as for similar\nspoils of the land washed down into its bosom.\n\n(316.) These remains are occasionally brought to light; and their\nexamination has afforded indubitable evidence of the former existence\nof a state of animated nature widely different from what now obtains\non the globe, and of a period anterior to that in which it has been\nthe habitation of man, or rather, indeed, of a series of periods, of\nunknown duration, in which both land and sea teemed with forms of\nanimal and vegetable life, which have successively disappeared and\ngiven place to others, and these again to new races approximating\ngradually more and more nearly to those which now inhabit them, and at\nlength comprehending species which have their counterparts existing.\n\n(317.) These wrecks of a former state of nature, thus wonderfully\npreserved (like ancient medals and inscriptions in the ruins of an\nempire), afford a sort of rude chronology, by whose aid the successive\ndepositions of the strata in which they are found may be marked out\nin epochs more or less definitely terminated, and each characterized\nby some peculiarity which enables us to recognise the deposits of any\nperiod, in whatever part of the world they may be found. And, so far\nas has been hitherto investigated, the _order_ of succession in which\nthese deposits have been formed appears to have been the same in every\npart of the globe.\n\n(318.) Many of the strata which thus bear evident marks of having been\ndeposited at the bottom of the sea, and of course in a horizontal\nstate, are now found in a position highly inclined to the horizon, and\neven occasionally vertical. And they often bear no less evident marks\nof violence, in their bending and fracture, the dislocation of parts\nwhich were once contiguous, and the existence of vast collections of\nbroken fragments which afford every proof of great violence having been\nused in accomplishing some at least of the changes which have taken\nplace.\n\n(319.) Besides the rocks which carry this internal evidence of\nsubmarine deposition, are many which exhibit no such proofs, but on the\ncontrary hold out every appearance of owing their origin to volcanoes\nor to some other mode of igneous action; and in every part of the\nworld, and among strata of all ages, there occur evidences of such\naction so abundant, and on such a scale, as to point out the volcano\nand the earthquake as agents which may have been instrumental in the\nproduction of those changes of level, and those violent dislocations\nwhich we perceive to have taken place.\n\n(320.) At all events, in accounting for those changes, geologists\nhave no longer recourse, as formerly, to causes purely hypothetical,\nsuch as a shifting of the earth\u2019s axis of rotation, bringing the sea\nto overflow the land, by a change in the place of the longer and\nshorter diameters of the spheroidal figure, nor to tides produced by\nthe attraction of comets suddenly approaching very near the earth,\nnor to any other fanciful and arbitrarily assumed hypotheses; but\nrather endeavour to confine themselves to a careful consideration\nof causes evidently in action at present, with a view to ascertain\nhow far they, in the first instance, are capable of accounting for\nthe facts observed, and thus legitimately bringing into view, as\nresidual phenomena, those effects which cannot be so accounted for.\nWhen this shall have been in some measure accomplished, we shall be\nable to pronounce with greater security than at present respecting the\nnecessity of admitting a long succession of tremendous and ravaging\ncatastrophes and cataclysms,--epochs of terrific confusion and violence\nwhich many geologists (perhaps with justice) regard as indispensable to\nthe explanation of the existing features of the world. We shall learn\nto distinguish between the effects which require for their production\nthe sudden application of convulsive and fracturing efforts, and those,\nprobably not less extensive, changes which may have been produced by\nforces equally or more powerful, but acting with less irregularity,\nand so distributed over time as to produce none of those _interregnums_\nof chaotic anarchy which we are apt to think (perhaps erroneously)\ngreat disfigurements of an order so beautiful and harmonious as that of\nnature.\n\n(321.) But to estimate justly the effects of causes now in action in\ngeology is no easy task. There is no _\u00e0 priori_ or deductive process by\nwhich we can estimate the amount of the annual erosion, for instance,\nof a continent by the action of meteoric agents, rain, wind, frost,\n&c., nor the quantity of destruction produced on its coasts by the\ndirect violence of the sea, nor the quantity of lava thrown up _per\nannum_ by volcanoes over the whole surface of the earth, nor any\nsimilar effect. And to consult experience on all such points is a\nslow and painful process if rightly gone into, and a very fallible\none if only partially executed. Much, then, at present must be left\nto opinion, and to that sort of clear-judging tact which sometimes\nanticipates experience; but this ought not to stand in the way of our\nmaking every possible effort to obtain accurate information on such\npoints, by which alone geology can be rendered, if not an experimental\nscience, at least a science of that kind of active observation which\nforms the nearest approach to it, where actual experiment is impossible.\n\n(322.) Let us take, for example, the question, \u201cWhat is the actual\ndirection in which changes of relative level are taking place between\nthe existing continents and seas?\u201d If we consult partial experience,\nthat is, _all_ the information that we possess respecting ancient\nsea-marks, soundings, &c., we shall only find ourselves bewildered in\na mass of conflicting, because imperfect, evidence. It is obvious that\nthe only way to decide the point is to ascertain, by very precise and\ncareful observations at proper stations on coasts, selected at points\nwhere there exist natural marks not liable to change in the course of\nat least a century, the true elevation of such marks above the _mean_\nlevel of the sea, and to multiply these stations sufficiently over the\nwhole globe to be capable of affording real available knowledge. Now,\nthis is not a very easy operation (considering the accuracy required);\nfor the _mean_ level of the sea can be determined by no single\nobservation, any more than the mean height of the barometer at a given\nstation, being affected both by periodical and accidental fluctuations\ndue to tides, winds, waves, and currents. Yet if an instrument adapted\nfor the purpose were constructed, and rendered easily attainable, and\nrules for its use carefully drawn up, there is little doubt we should\nsoon (by the industry of observers scattered over the world) be in\npossession of a most valuable mass of information, which could not fail\nto afford a point of departure for the next generation, and furnish\nground for the only kind of argument which ever can be conclusive on\nsuch subjects.\n\n(323.) Geology, in the magnitude and sublimity of the objects of\nwhich it treats, undoubtedly ranks, in the scale of the sciences,\nnext to astronomy; like astronomy, too, its progress depends on the\ncontinual accumulation of observations carried on for ages. But, unlike\nastronomy, the observations on which it depends, when the whole extent\nof the subject to be explored is taken into consideration, can hardly\nyet be said to be more than commenced. Yet, to make up for this, there\nis another important difference, that while in the latter science it is\nimpossible to recall the past or anticipate the future, and observation\nis in consequence limited to a single fact in a single moment; in\nthe former, the records of the past are always present;--they may be\nexamined and re-examined as often as we please, and require nothing\nbut diligence and judgment to put us in possession of their whole\ncontents. Only a very small part of the surface of our globe has,\nhowever, been accurately examined in detail, and of that small portion\nwe are only able to scratch the mere exterior, for so we must consider\nthose excavations which we are apt to regard as searching the bowels\nof the earth; since the deepest mines which have been sunk penetrate\nto a depth hardly surpassing the ten thousandth part of the distance\nbetween its surface and its centre. Of course inductions founded on\nsuch limited examination can only be regarded as provisional, except\nin those remarkable cases where the same great formations in the same\norder have been recognised in very distant quarters, and without\nexception. This, however, cannot long be the case. The spirit with\nwhich the subject has been prosecuted for many years in our own country\nhas been rewarded with so rich a harvest of surprising and unexpected\ndiscoveries, and has carried the investigation of our island into such\ndetail, as to have excited a corresponding spirit among our continental\nneighbours; while the same zeal which animates our countrymen on their\nnative shore accompanies them in their sojourns abroad, and has\nalready begun to supply a fund of information respecting the geology of\nour Indian possessions, as well as of every other point where English\nintellect and research can penetrate.\n\n(324.) Nothing can be more desirable than that every possible facility\nand encouragement should be afforded for such researches, and indeed\nto the pursuits of the enlightened resident or traveller in every\ndepartment of science, by the representatives of our national authority\nwherever our power extends. By these only can our knowledge of the\nactual state of the surface of the globe, and that of the animals\nand vegetables of the ancient continents and seas, be extended and\nperfected, while more complete information than we at present possess\nof the habits of those actually existing, and the influence of changes\nof climate, food, and circumstances, on them, may be expected to render\nmaterial assistance to our speculations respecting those which have\nbecome extinct.\n\n\n\n\nCHAP. IV.\n\nOF THE EXAMINATION OF THE MATERIAL CONSTITUENTS OF THE WORLD.\n\n\n_Mineralogy._\n\n(325.) The consideration of the history and structure of our globe, and\nthe examination of the fossil contents of its strata, lead us naturally\nto consider the materials of which it consists. The history of these\nmaterials, their properties as objects of philosophical enquiry, and\ntheir application to the useful arts and the embellishments of life,\nwith the characters by which they can be certainly distinguished one\nfrom another, form the object of mineralogy, taken in its most extended\nsense.\n\n(326.) There is no branch of science which presents so many points\nof contact with other departments of physical research, and serves\nas a connecting link between so many distant points of philosophical\nspeculation, as this. To the geologist, the chemist, the optician, the\ncrystallographer, the physician, it offers especially the very elements\nof their knowledge, and a field for many of their most curious and\nimportant enquiries. Nor, with the exception of chemistry, is there any\nwhich has undergone more revolutions, or been exhibited in a greater\nvariety of forms. To the ancients it could scarcely be said to be at\nall known, and up to a comparatively recent period, nothing could\nbe more imperfect than its descriptions, or more inartificial and\nunnatural than its classification. The more important minerals in the\narts, indeed, those used for economical purposes and those from which\nmetals were extracted, had a certain degree of attention paid to them,\nfor the sake of their utility and commercial value, and the precious\nstones for that of ornament. But until their crystalline forms were\nattentively observed and shown to be determinate characters on which\ndependence could be placed, no mineralogist could give any correct\naccount of the real distinction between one mineral and another.\n\n(327.) It was only, however, when chemical analysis had acquired\na certain degree of precision and universal applicability that\nthe importance of mineralogy as a science began to be recognized,\nand the connection between the external characters of a stone and\nits ingredient constituents brought into distinct notice. Among\nthese characters, however, none were found to possess that eminent\ndistinctness which the crystalline form offers; a character, in the\nhighest degree geometrical, and affording, as might be naturally\nsupposed, the strongest evidence of its necessary connection with the\nintimate constitution of the substance. The full importance of this\ncharacter was, however, not felt until its connection with the texture\nor cleavage of a mineral was pointed out, and even then it required\nnumerous and striking instances of the critical discernment of Ha\u00fcy\nand other eminent mineralogists in predicting from the measurements\nof the angles of crystals which had been confounded together that\ndifferences would be found to exist in their chemical composition, all\nwhich proved fully justified in their result before the essential value\nof this character was acknowledged. This was no doubt in great measure\nowing to the high importance set by the German mineralogists on those\nexternal characters of touch, sight, weight, colour, and other sensible\nqualities, which are little susceptible, with the exception of weight,\nof exact determination, and which are subject to material variations\nin different specimens of the same mineral. By degrees, however, the\nnecessity of ascribing great weight to a character so definite was\nadmitted, especially when it was considered that the same step which\npointed out the intimate connection of external form with internal\nstructure furnished the mineralogist with the means of reducing all\nthe forms of which a mineral is susceptible under one general type, or\nprimitive form, and afforded grounds for an elegant theoretical account\nof the assumption of definite figures _ab initio_.\n\n(328.) A simple and elegant invention of Dr. Wollaston, the reflecting\ngoniometer, gave a fresh impulse to that view of mineralogy which makes\nthe crystalline form the essential or leading character, by putting\nit in the power of every one, by the examination of even the smallest\nportion of a broken crystal, to ascertain and verify that essential\ncharacter on which the identity of a mineral in the system of Ha\u00fcy\nwas made to depend. The application of so ready and exact a method\nspeedily led to important results, and to a still nicer discrimination\nof mineral species than could before be attained; and the confirmation\ngiven to these results by chemical analysis stamped them with a\nscientific and decided character which they have retained ever since.\n\n(329.) Meanwhile the progress made in chemical analysis had led to\nthe important conclusion that every chemical compound susceptible of\nassuming the solid state assumed with it a determinate crystalline\nform; and the progress of optical science had shown that the\nfundamental crystalline form, in the case at least of transparent\nbodies, drew with it a series of optical properties no less curious\nthan important in relation to the affections of light in its passage\nthrough such substances. Thus, in every point of view, additional\nimportance became added to this character; and the study of the\ncrystalline forms of bodies in general assumed the form of a separate\nand independent branch of science, of which the geometrical forms of\nthe mineral world constituted only a particular case. Mineralogy,\nhowever, as a branch of natural history, remains still distinct either\nfrom optics or crystallography. The mineralogist is content, and thinks\nhe has performed his task, if not as a natural historian at least as\na classifier and arranger, if he only gives such a characteristic\ndescription of a mineral as shall effectually distinguish it from every\nother, and shall enable any one who may encounter such a body in any\npart of the world to impose on it its name, assign it a place in his\nsystem, and turn to his books for a further description of all that\nthe chemist, the optician, the lapidary, or the artist, may require to\nknow. Still this is no easy matter: the laborious researches of the\nmost eminent mineralogists can hardly yet be said to have effectually\naccomplished it; and its difficulty may be appreciated by the small\nnumber of simple minerals, or minerals of perfectly definite and\nwell-marked characters, which have been hitherto made out. Nor can\nthis indeed be wondered at, when we consider that by far the greater\nportion of the rocks and stones which compose the external crust of the\nglobe consists of nothing more than the accumulated _detritus_ of older\nrocks, in which the fragments and powder of an infinite variety of\nsubstances are mingled together, in all sorts of varying proportions,\nand in such a way as to defy separation. Many of these rocks, however,\nso compounded, occur with sufficient frequency and uniformity of\ncharacter to have acquired names and to have been usefully applied;\nindeed, in the latter respect, minerals of this description far surpass\nall the others. As objects of natural history, therefore, they are well\nworthy of attention, however difficult it may be to assign them a place\nin any artificial arrangement.\n\n(330.) This paucity of simple minerals, however, is probably rather\napparent than real, and in proportion as the researches of the chemist\nand crystallographer shall be extended throughout nature, they will\nno doubt become much more numerous. Indeed, in the great laboratories\nof nature it can hardly be doubted that almost every kind of chemical\nprocess is going forwards, by which compounds of every description are\ncontinually forming. Accordingly, it is remarked, that the lavas and\nejected scori\u00e6 of volcanoes are receptacles in which mineral products\npreviously unknown are constantly discovered, and that the primitive\nformations, as they are called in geology, which bear no marks of\nhaving been produced by the destruction of others, are also remarkable\nfor the beauty and distinctness of character of their minerals.\n\n(331.) The great difficulty which has been experienced in attempts to\nclassify mineral substances by their chemical constituents has arisen\nfrom the observed presence, in some specimens of minerals bearing\nthat general resemblance in other respects as well as agreement in\nform which would seem to entitle them to be considered as alike, of\ningredients foreign to the usual composition of the species, and that\noccasionally in so large a proportion as to render it unjustifiable\nto refer their occurrence to accidental impurities. These cases, as\nwell as some anomalies observed in the classification of minerals by\ntheir crystalline forms, which seemed to show that the same substance\nmight occasionally appear under two distinct forms, as well as some\nremarkable coincidences between the forms of substances quite distinct\nfrom each other in a chemical point of view, have within a recent\nperiod given rise to a branch of the science of crystallography of a\nvery curious and important nature. The _isomorphism_ of certain groups\nof chemical elements has already afforded us an example illustrative\nof the manner in which inductions sometimes receive unexpected\nverifications (see 180.). The laws and relations thus brought to light\nare among the most curious and interesting parts of modern science,\nand seem likely in their further developement to afford ample scope\nfor the exercise of chemical and mineralogical research. They have\nalready afforded innumerable fine examples of that important step in\nscience by which anomalies disappear, and occasional incongruities\nbecome reconciled under more general expressions of physical laws,\nand thus unite in affording support to those very views which they\npromised, when first observed, to overset. Nothing, indeed, can be\nmore striking than to see the very ingredient which every previous\nchemist and mineralogist would agree to disregard and reject as a\nmere casual impurity brought forward and appealed to in support of a\ntheory expressly directed to the object of rescuing science from the\nimputation of disregarding, under any circumstances, the plain results\nof direct experiment.\n\n\n_Chemistry._\n\n(332.) The laws which concern the intimate constitution of bodies,\nnot as respects their _structure_ or the manner in which their parts\nare put together, but as regards their _materials_ or the ingredients\nof which those parts are composed, form the objects of chemistry. A\nsolid body may be regarded as a fabric, more or less regularly and\nartificially constructed, in which the materials and the workmanship\nmay be separately considered, and in which, though the latter be\nruined and confounded by violence, the former remain unchanged in\ntheir nature, though differently arranged. In liquid or a\u00ebrial bodies,\ntoo, though there prevails a less degree of difference in point of\nstructure, and a greater facility of dispersion and dissipation, than\nin solids, yet an equal diversity of _materials_ subsists, giving to\nthem properties differing extremely from each other.\n\n(333.) The inherent activity of matter is proved not only by the\nproduction of motion by the mutual attractions and repulsions of\ndistant or contiguous masses, but by the changes and apparent\ntransformations which different substances undergo in their sensible\nqualities by mere mixture. If water be added to water, or salt to salt,\nthe effect is an increase of quantity, but no change of quality. In\nthis case, the mutual action of the particles is entirely mechanical.\nAgain, if a blue powder and a yellow one, each perfectly dry, be mixed\nand well shaken together, a green powder will be produced; but this\nis a mere effect arising in the eye from the intimate mixture of the\nyellow and blue light separately and independently reflected from\nthe minute particles of each; and the proof is had by examining the\nmixture with a microscope, when the yellow and blue grains will be seen\nseparate and each quite unaltered. If the same experiment be tried with\ncoloured liquids, which are susceptible of mixing without chemical\naction, a compound colour is likewise produced, but no examination\nwith magnifiers is in that case sufficient to detect the ingredients;\nthe reason obviously being, the excessive minuteness of the parts, and\ntheir perfect intermixture, produced by agitating two liquids together.\nFrom the mixture of two powders, extreme patience would enable any one,\nby picking out with a magnifier grain after grain, to separate the\ningredients. But when liquids are mixed, no mechanical separation is\nany longer practicable; the particles are so minute as to elude all\nsearch. Yet this does not hinder us from regarding such a compound as\nstill a mere mixture, and its properties are accordingly intermediate\nbetween those of the liquids mixed. But this is far from being the\ncase with all liquids. When a solution of potash, for example, and\nanother of tartaric acid, each perfectly liquid, are mixed together in\nproper proportions, a great quantity of a solid saline substance falls\nto the bottom of the containing vessel, which is quite different from\neither potash or tartaric acid, and the liquid from which it subsided\noffers no indications by its taste or other sensible qualities of the\ningredients mixed, but of something totally different from either.\nIt is evident that this is a phenomenon widely different from that\nof mere mixture; there has taken place a great and radical change in\nthe intimate nature of the ingredients, by which a new substance is\nproduced which had no existence before. And it has been produced by the\n_union_ of the ingredients presented to each other; for when examined\nit is found that nothing has been _lost_, the weight of the whole\nmixture being the sum of the weights mixed. Yet the potash and tartaric\nacid have disappeared entirely, and the weight of the new product is\nfound to be exactly equal to that of the tartaric acid and potash\nemployed, taken together, abating a small portion held in solution in\nthe liquid, which may be obtained however by evaporation. They have\ntherefore combined, and adhere to one another with a cohesive force\nsufficient to form a solid out of a liquid; a force which has thus been\ncalled into action by merely presenting them to each other in a state\nof solution.\n\n(334.) It is the business of chemistry to investigate these and similar\nchanges, or the reverse of such changes, where a single substance is\nresolved into two or more others, having different properties from it,\nand from each other, and to enquire into all the circumstances which\ncan influence them; and either determine, modify, or suspend their\naccomplishment, whether such influence be exercised by heat or cold, by\ntime and rest, or by agitation or pressure, or by any of those agents\nof which we have acquired a knowledge, such as electricity, light,\nmagnetism, &c.\n\n(335.) The wonderful and sudden transformations with which chemistry is\nconversant, the violent activity often assumed by substances usually\nconsidered the most inert and sluggish, and, above all, the insight\nit gives into the nature of innumerable operations which we see daily\ncarried on around us, have contributed to render it the most popular,\nas it is one of the most extensively useful, of the sciences; and\nwe shall, accordingly, find none which have sprung forward, during\nthe last century, with such extraordinary vigour, and have had such\nextensive influence in promoting corresponding progress in others. One\nof the chief causes of its popularity is, perhaps, to be sought for in\nthis, that it is, of all the sciences, perhaps, the most completely an\nexperimental one; and even its theories are, for the most part, of that\ngenerally intelligible and readily applicable kind, which demand no\nintense concentration of thought, and lead to no profound mathematical\nresearches. The simple process of inductive generalization, grounded on\nthe examination of numerous facts, all of them presenting considerable\nintrinsic interest, has sufficed, in most instances, to lead, by a\nclear and direct road, to its highest laws yet known. But, on the other\nhand, these laws, when stated, are not yet fully sufficient to lead us,\nexcept in very limited cases, to a deductive knowledge of particulars\nnever before examined, at least, not without great caution, and\nconstant appeal to experiment as a check on our reasoning; so that we\nare justified in regarding the _axioms_ of chemistry, the true handles\nof deductive reasoning, as still unknown, and, perhaps, likely long\nto remain so. This is no fault of its cultivators, who have comprised\nin their list the highest and most varied talents and industry, but\nof the inherent complexity of the subject, and the infinite multitude\nof causes which are concerned in the production of every, even the\nsimplest, chemical phenomenon.\n\n(336.) The history of chemistry (on which, however, we are not about\nto enlarge,) is one of great interest to those who delight to trace\nthe steps by which mankind advance to the discovery of truth through\na series of mistakes and failures. It may be divided, 1st, into\nthe period of the alchemists, a lamentable epoch in the annals of\nintellectual wandering; 2dly, that of the phlogistic doctrines of\nBeccher and Stahl, in which, as if to prove the perversity of the human\nmind, of two possible roads the wrong was chosen; and a theory obtained\nuniversal credence on the strength of an induction, valid as such, but\nwrongly interpreted, which is negatived, _in every instance_, by an\nappeal to the balance. This, too, happened, not by reason of unlucky\ncoincidences, or individual oversights, but of necessity, and from an\ninherent defect of the theory itself, which thus impeded the progress\nof the science, as far as a science of experiment can be impeded by\na false theory, by perplexing its cultivators with the appearance of\ncontradictions in their experiments where none really subsisted, by\ndestroying all their confidence in the numerical exactness of their\nown results, and by involving the subject in a mist of visionary and\nhypothetical causes in place of the true acting principles. Thus, in\nthe combustion of any substance which is incapable of flying away in\nfumes, an increase of weight takes place,--the ashes are heavier than\nthe fuel. Whenever this was observed, however, it was passed carelessly\nover as arising from the escape of phlogiston, or the principle of\ninflammability, which was considered as being either the element of\nfire itself, or in some way combined with it, and thus essentially\n_light_. It is now known that the increase of weight is owing to\nthe absorption of, and combination with, a quantity of a peculiar\ningredient called _oxygen_, from the air, a principle essentially\n_heavy_. So far as weight is concerned, it makes no difference whether\na body having weight enters, or one having levity escapes; but there\nis this plain difference in a philosophical point of view, that oxygen\nis a real producible substance, and phlogiston is no such thing: the\nformer is a _vera causa_, the latter an hypothetical being, introduced\nto account for what the other accounts for much better.\n\n(337.) The third age of chemistry--that which may be called\nemphatically modern chemistry--commenced (in 1786) when Lavoisier, by\na series of memorable experiments, extinguished for ever this error,\nand placed chemistry in the rank of one of the exact sciences,--a\nscience of number, weight, and measure. From that epoch to the\npresent day it has constantly advanced with an accelerated progress,\nand at this moment may be regarded as more progressive than ever.\nThe principal features in this progress may be comprised under the\nfollowing general heads:--\n\n   1. The discovery of the proximate, if not the ultimate, elements\n        of all bodies, and the enlargement of the list of known\n        elements to its present extent of between fifty and sixty\n        substances.\n\n   2. The developement of the doctrine of latent heat by Black,\n        with its train of important consequences, including the\n        scientific theory of the steam-engine.\n\n   3. The establishment of Wenzel\u2019s law of definite proportions on\n        his own experiments, and those of Richter, a discovery\n        subsequently merged in the more general wording and better\n        development of Dalton\u2019s atomic theory.\n\n   4. The precise determination of the atomic weights of the\n        different chemical elements, mainly due to the astonishing\n        industry of Berzelius, and his unrivalled command of chemical\n        resources, as well as to the researches of the other chemists\n        of the Swedish and German school.\n\n   5. The assimilation of gases and vapours, by which we are led\n        to regard the former, universally, as particular cases of\n        the latter, a generalization resulting chiefly from the\n        experiments of Faraday on the condensation of the gases,\n        and those of Gay-Lussac and Dalton, on the laws of their\n        expansion by heat compared with that of vapours.\n\n   6. The establishment of the laws of the combination of gases and\n        vapours by definite volumes, by Gay-Lussac.\n\n   7. The discovery of the chemical effects of electricity, and\n        the decomposing agency of the Voltaic pile, by Nicholson\n        and Carlisle; the investigation of the laws of such\n        decompositions, by Berzelius and Hisinger: the decomposition\n        of the alkalies by Davy, and the consequent introduction into\n        chemistry of new and powerful agents in their metallic bases.\n\n   8. The application of chemical analysis to all the objects of\n        organized and unorganized nature, and the discovery of\n        the ultimate constituents of all, and the proximate ones\n        of organic matter, and the recognisance of the important\n        distinctions which appear to divide these great classes of\n        bodies from each other.\n\n   9. The applications of chemistry to innumerable processes in the\n        arts, and among other useful purposes to the discovery of the\n        essential medical principles in vegetables, and to important\n        medicaments in the mineral kingdom.\n\n  10. The establishment of the intimate connection between\n        chemical composition and crystalline form, by Ha\u00fcy\n        and Vauquelin, with the successive rectifications the\n        statement of that connection has undergone in the hands of\n        Mitscherlich, Rose, and others, with the progress of chemical\n        and crystallographical knowledge.\n\n(338.) To pursue these several heads into detail would lead us into\na treatise on chemistry; but a few remarks on one or two of them, as\nthey bear upon the general principles of all scientific enquiry, will\nnot be irrelevant. And first, then, with reference to the discovery\nof new elements, it will be observed, that philosophical chemistry no\nmore aims at determining the one essential element out of which all\nmatter is framed--the one ultimate principle of the universe--than\nastronomy at discovering the origin of the planetary movements in\nthe application of a determinate projectile force in a determinate\ndirection, or geology at ascending to the creation of the earth. There\nmay be such an element. Some singular relations which have been pointed\nout in the atomic weights of bodies seem to suggest to minds fond of\nspeculation that there is; but philosophical chemistry is content to\nwait for some striking fact, which may either occur unexpectedly or\nbe led to by the slow progress of enlarged views, to disclose to us\nits existence. Still, the multiplication of so-considered elementary\nbodies has been considered by some as an inconvenience. We confess\nwe do not coincide with this view. Whatever they be, the obstinacy\nwith which they resist decomposition shows that they are ingredients\nof a very high and primary importance in the economy of nature; and\nsuch as, in any state of science, it would be indispensably necessary\nto be perfectly familiar with. Like particular theorems in geometry,\nwhich, though not rising to the highest point of generality, have yet\ntheir several scopes and ranges of extensive application, they must be\nwell and perfectly understood in all their bearings. Should we ever\narrive at an analysis of these bodies, the chemical properties of the\nnew elements which will then come into view will be known only by our\nknowledge of these, or of other compounds of the same class, which they\nmay be capable of forming. Not but that such an analysis would be a\nmost important and indeed triumphant achievement, and change the face\nof chemistry; but it would undo nothing that has been done, and render\nuseless no point of knowledge which we have yet arrived at.\n\n(339.) The atomic theory, or the law of definite proportions, which\nis the same thing presented in a form divested of all hypothesis,\nafter the laws of mechanics, is, perhaps, the most important which\nthe study of nature has yet disclosed. The extreme simplicity which\ncharacterizes it, and which is itself an indication, not unequivocal,\nof its elevated rank in the scale of physical truths, had the effect\nof causing it to be announced at once by Mr. Dalton, in its most\ngeneral terms, on the contemplation of a few instances[53], without\npassing through subordinate stages of painful inductive ascent by the\nintermedium of subordinate laws, such as, had the contrary course been\npursued by him, would have been naturally preparatory to it, and such\nas would have led others to it by the prosecution of Wenzel\u2019s and\nRichter\u2019s researches, had they been duly attended to. This is, in fact,\nan example, and a most remarkable one, of the effect of that natural\npropensity to generalize and simplify (noticed in 171.), which, if it\noccasionally leads to over-hasty conclusions, limited or disproved by\nfurther experience, is yet the legitimate parent of many of our most\nvaluable and soundest results. Instances like this, where great and,\nindeed, immeasurable steps in our knowledge of nature are made at once,\nand almost without intellectual effort, are well calculated to raise\nour hopes of the future progress of science, and, by pointing out the\nsimplest and most obvious combinations as those which are actually\nfound to be agreeable to the harmony of creation, to hold out the\ncheering prospect of difficulties diminishing as we advance, instead of\nthickening around us in increasing complexity.\n\n(340.) A consequence of this immediate presentation of the law of\ndefinite proportions in its most general form is, that its subordinate\nlaws--those which limit its generality in particular cases, which\ndiminish the number of combinations abstractly possible, and restrain\nthe indiscriminate mixture of elements,--remain to be discovered. Some\nsuch limitations have, in fact, been traced to a certain extent, but by\nno means so far as the importance of the subject requires; and we have\nhere abundant occupation for chemists for some time.\n\n(341.) The determination of the atomic weights of the chemical\nelements, like that of other standard physical data, with the utmost\nexactness, is in itself a branch of enquiry not only of the greatest\nimportance, but of extreme difficulty. Independent of the general\nreasons for desiring accuracy in this respect, there is one peculiar\nto the subject. It has been suggested (by Dr. Prout), and strongly\ninsisted on (by Dr. Thomson), that all the numbers representing these\nweights, constituting a scale of great extent, in which the extremes\nalready known are in proportion to each other, as 1 to upwards of 200,\nare simple even multiples of the least of them. If this be really the\ncase, it opens views of such importance as to justify any degree of\nlabour and pains in the verification of the law as a purely inductive\none. But in the actual state of chemical analysis, with all deference\nto such high authority, we confess it appears to us to stand in great\nneed of further confirmation, since it seems doubtful whether such\naccuracy has yet been attained as to enable us to answer positively\nfor a fraction not exceeding the three or four hundredth part of the\nwhole quantity to be determined: at least the results of the first\nexperimenters, obtained with the greatest care, differ often by a\ngreater amount; and this degree of exactness, at least, would be\nrequired to verify the law satisfactorily in the higher parts of the\nscale.\n\n(342.) The mere agitation of such a question, however, points out\na class of phenomena in physical science of a remote and singular\nkind, and of a very high and refined order, which could never become\nknown but in an advanced state of science, not only practical, but\ntheoretical,--we mean, such as consist in observed relations among the\n_data_ of physics, which show them to be quantities not _arbitrarily_\nassumed, but depending on laws and causes which they may be the means\nof at length disclosing. A remarkable instance of such a relation is\nthe curious law which Bode observed to obtain in the progression of the\nmagnitudes of the several planetary orbits. This law was interrupted\nbetween Mars and Jupiter, so as to induce him to consider a planet\nas wanting in that interval;--a deficiency long afterwards strangely\nsupplied by the discovery of _four_ new planets in that very interval,\nall of whose orbits conform in dimension to the law in question, within\nsuch moderate limits of error as may be due to causes independent of\nthose on which the law itself ultimately rests.[54]\n\n(343.) Neither is it irrelevant to our subject to remark, that the\nprogress which has been made in this department of chemistry, and\nthe considerable exactness actually attainable in chemical analysis,\nhave been owing, in great measure, to a circumstance which might at\nfirst have been hardly considered likely to exercise much influence\non the progress of a science,--the discovery of platina. Without the\nresources placed at the ready disposal of chemists by this invaluable\nmetal, it is difficult to conceive that the multitude of delicate\nanalytical experiments which have been required to construct the fabric\nof existing knowledge could have ever been performed. This, among many\nsuch lessons, will teach us that the most important uses of natural\nobjects are not those which offer themselves to us most obviously. The\nchief use of the moon for man\u2019s immediate purposes remained unknown to\nhim for five thousand years from his creation. And, since it cannot but\nbe that innumerable and most important uses remain to be discovered\namong the materials and objects already known to us, as well as among\nthose which the progress of science must hereafter disclose, we may\nhence conceive a well-grounded expectation, not only of constant\nincrease in the physical resources of mankind, and the consequent\nimprovement of their condition, but of continual accessions to our\npower of penetrating into the arcana of nature, and becoming acquainted\nwith her highest laws.\n\n\n\n\nCHAP. V.\n\nOF THE IMPONDERABLE FORMS OF MATTER.\n\n\n_Heat._\n\n(344.) One of the chief agents in chemistry, on whose proper\napplication and management the success of a great number of its\nenquiries depends, and many of whose most important laws are disclosed\nto us by phenomena of a chemical nature, is HEAT. Although some of\nits effects are continually before our eyes as matters of the most\ncommon occurrence, insomuch that there is scarcely any process in the\nuseful arts and manufactures which does not call for its intervention,\nand although, independent of this high utility, and the proportionate\nimportance of a knowledge of its nature and laws, it presents in itself\na subject of the most curious speculation; yet there is scarcely\nany physical agent of which we have so imperfect a knowledge, whose\nintimate nature is more hidden, or whose laws are of such delicate and\ndifficult investigation.\n\n(345.) The word heat generally implies the sensation which we\nexperience on approaching a fire; but, in the sense it carries in\nphysics, it denotes the cause, whatever it be, of that sensation, and\nof all the other phenomena which arise on the application of fire,\nor of any other heating cause. We should be greatly deceived if we\nreferred only to sensation as an indication of the presence of this\ncause. Many of those things which excite in our organs, and especially\nof those of taste, a sensation of heat, owe this property to chemical\nstimulants, and not at all to their being actually _hot_. This error\nof judgment has produced a corresponding confusion of language, and\nhence had actually at one period[55] crept into physical philosophy\na great many illogical and absurd conclusions. Again, there are a\nnumber of chemical agents, which, from their corroding, blackening, and\ndissolving, or drying up the parts of some descriptions of bodies, and\nproducing on them effects not generally unlike (though intrinsically\nvery different from) those produced by heat, are said, in loose and\nvulgar language, to burn them; and this error has even become rooted\ninto a prejudice, by the fact that some of these agents are capable\nof becoming actually and truly _hot_ during their action on moist\nsubstances, by reason of their combination with the water the latter\ncontain. Thus, quicklime and oil of vitriol both exercise a powerful\ncorrosive action on animal and vegetable substances, and both become\nviolently hot by their combination with water. They are, therefore,\nset down in vulgar parlance as substances of a hot nature; whereas,\nin their relations to the physical cause of heat, they agree with the\ngenerality of bodies similarly constituted.\n\n(346.) The nature of heat has hitherto been chiefly studied under the\ngeneral heads of--\n\n  1st, Its sources, or the phenomena which it usually accompanies.\n\n  2d, Its communication from its sources to substances capable of\n        receiving it, and from these to others, with a view to\n        discover the laws which regulate its distribution through\n        space or through the bodies which occupy it.\n\n  3d, Its effects, on our senses, and on the bodies to which it is\n        communicated in its various degrees of intensity, by which,\n        means are afforded us of measuring these degrees.\n\n  4th, Its intimate relations to the atoms of matter, as exhibited\n        in its capability of acquiring a latent state under certain\n        circumstances, and of entering into something like chemical\n        combinations.\n\n(347.) The most obvious sources of heat are, the sun, fire, animal\nlife, fermentations, violent chemical actions of all kinds, friction,\npercussion, lightning, or the electric discharge, in whatever manner\nproduced, the sudden condensation of air, and others, so numerous,\nand so varied, as to show the extensive and important part it has\nto perform in the economy of nature. The discoveries of chemists,\nhowever, have referred most of these to the general head of chemical\ncombination. Thus, fire, or the combustion of inflammable bodies, is\nnothing more than a violent chemical action attending the combination\nof their ingredients with the oxygen of the air. Animal heat is, in\nlike manner, referable to a process bearing no remote analogy to\na slow combustion, by which a portion of carbon, an inflammable\nprinciple existing in the blood, is united with the oxygen of the air\nin respiration; and thus carried off from the system: fermentation\nis nothing more than a decomposition of chemical elements loosely\nunited, and their re-union in a more permanent state of combination.\nThe analogy between the sun and terrestrial fire is so natural as to\nhave been chosen by Newton to exemplify the irresistible force of an\ninference derived from that principle. But the nature of the sun and\nthe mode in which its wonderful supply of light and heat is maintained\nare involved in a mystery which every discovery that has been made\neither in chemistry or optics, so far from elucidating, seems only to\nrender more profound. Friction as a source of heat is well known: we\nrub our hands to warm them, and we grease the axles of carriage-wheels\nto prevent their setting fire to the wood; an accident which, in\nspite of this precaution, does sometimes happen. But the effect of\nfriction, as a means of producing heat with little or no consumption\nof materials, was not fully understood till made the subject of direct\nexperiment by count Rumford, whose results appear to have established\nthe extraordinary fact, that an unlimited supply of heat may be derived\nby friction from the same materials. Condensation, whether of air by\npressure, or of metals by percussion, is another powerful source of\nheat. Thus, iron may be so dexterously hammered as to become red-hot,\nand the rapid condensation of a confined portion of air will set tinder\non fire.\n\n(348.) The most violent heats known are produced by the concentration\nof the solar rays by burning glasses,--by the combustion of oxygen and\nhydrogen gases mixed in the exact proportion in which they combine to\nproduce water,--and by the discharge of a continued and copious current\nof electricity through a small conductor. As these three sources of\nheat are independent of each other, and each capable of being brought\ninto action in a very confined space, there seems no reason why they\nmight not all three be applied at once at the same point, by which\nmeans, probably, effects would be produced infinitely surpassing any\nhitherto witnessed.\n\n(349.) Heat is communicated either by _radiation_ between bodies at a\ndistance, or by _conduction_ between bodies in contact, or between the\ncontiguous parts of one and the same body. The laws of the radiation\nof heat have been studied with great attention, and have been found\nto present strong analogies with that of light in some points, and\nsingular differences in others. Thus, the heat which accompanies the\nsun\u2019s rays comports itself, in all respects, like light; being subject\nto similar laws of reflection, refraction, and even of polarization, as\nhas been shown by Berard. Yet they are not identical with each other;\nSir William Herschel having shown, by decisive experiments, verified by\nthose of Sir H. Englefield, that there exist in a solar beam both rays\nof heat which are not luminous, and rays of light which have no heating\npower.\n\n(350.) The heat, radiated by terrestrial fires, and by bodies\n_obscurely_ hot, by whatever means they have acquired their heat\n(even by exposure to the sun\u2019s rays), differs very materially from\nsolar heat in their power of penetrating transparent substances. This\nsingular and important difference was first noticed by Mariotte, and\nafterwards made the subject of many curious and interesting experiments\nby Scheele, who found that terrestrial heat, or that radiated from\nfires or heated bodies, is intercepted and detained by glass or\nother transparent bodies, while solar heat is not; and that, being\nso detained, it heats them: which the latter, as it passes freely\nthrough them, is incapable of doing. The more recent researches of\nDelaroche, however, have shown that this detention is complete only\nwhen the temperature of the source of heat is low; but that, as that\ntemperature is higher, a portion of the heat radiated acquires a\npower of penetrating glass; and that the quantity which does so bears\ncontinually a larger and larger proportion to the whole, as the heat\nof the radiant body is more intense. This discovery is very important,\nas it establishes a community of nature between solar and terrestrial\nheat; while at the same time it leads us to regard the actual\ntemperature of the sun as far exceeding that of any earthly flame.\n\n(351.) A variety of theories have been framed to account for these\ncurious phenomena; but the subject stands rather in need of further\nelucidation from experiment, and is one which merits, and will probably\namply repay, the labours of those who may hereafter devote their\nattention to it. The theory of the radiation of heat, in general, which\nseems to agree best with the known phenomena, is that of M. Prevost,\nwho considers all bodies as constantly radiating out heat in all\ndirections, and receiving it by a similar means of communication from\nothers, and thus tending, in any space filled, wholly or in part, with\nbodies at various temperatures, to establish an equilibrium or equality\nof heat in all parts. The application of this idea to the explanation\nof the phenomenon of dew we have already seen (see 167.). The laws\nof such radiation, under various circumstances, have been lately\ninvestigated in a beautiful series of experiments on the cooling of\nbodies by their own radiation in vacuo, by Messrs. Dulong and Petit,\nwhich offer some of the best examples in science of the inductive\ninvestigation of quantitative laws.\n\n(352.) The communication of heat between bodies in contact, or between\nthe different parts of the same body, is performed by a process called\nconduction. It is, in fact, only a particular case of radiation, as\nhas been explained above (217.); but a case _so_ particular as to\nrequire a separate and independent investigation of its laws. The most\nimportant consideration introduced into the enquiry by this peculiarity\nis that of time. The communication of heat by conduction is performed,\nfor the most part, with extreme slowness, while that performed by\ndirect radiation is probably not less rapid than the propagation\nof light itself. The analysis of the delicate and difficult points\nwhich arise in the investigation of this subject in its reduction\nto direct geometrical treatment has been executed with admirable\nsuccess by the late Baron Fourrier, whose recent lamented death has\ndeprived science of an ornament it could ill spare, thinned as its\nranks have been within the last few years. This acute philosopher and\nprofound mathematician has developed, in a series of elaborate memoirs\npresented to the French Institute, the laws of the communication of\nheat through the interior of solid masses, placed under the influence\nof any external heating and cooling causes, and has in particular\napplied his results to the conditions on which the maintenance of the\nactual observed temperature on the earth\u2019s surface depends; to the\npossible influence of a supposed central heat on our climates; and to\nthe determination of the actual amount of the heat, derived to us from\nthe sun, or at least that portion of it on which the difference of the\nseasons depends.\n\n(353.) The principal effects of heat are the sensations of warmth or\ncold consequent on its entry or egress into or out of our bodies; the\ndilatation it causes in the dimensions of all substances in which it is\naccumulated; the changes of state it produces in the melting of solids,\nand the conversion of them and of liquids into vapour; and the chemical\nchanges it performs by actual decompositions effected in the intimate\nmolecules of various substances, especially those of which vegetables\nand animals are composed; to which we may add, the production of\nelectric phenomena under certain circumstances in the contact of\nmetals, and the developement of electric polarity in crystallised\nsubstances.\n\n(354.) Cold has been considered by some as a positive quality, the\neffect of a cause antagonist to that of heat; but this idea seems\nnow (with perhaps a single exception) to be universally abandoned.\nThe sensation of cold is as easily explicable by the passage of heat\noutwards through the surface of the body as that of heat by its ingress\nfrom without; and the experiments cited in proof of a radiation of\ncold are all perfectly explained by Prevost\u2019s theory of reciprocal\ninterchange. It is remarkable, however, how very limited our means\nof producing intense cold are, compared with those we possess of\neffecting the accumulation of heat in bodies. This is one of the\nstrongest arguments adducible in favour of the doctrines of those who\nmaintain the possibility of exhausting the heat of a body altogether,\nand leaving it in a state absolutely devoid of it. But we ought to\nconsider, that the known methods of generating heat chiefly turn on the\nproduction of chemical combinations: we may easily conceive, therefore,\nthat, to obtain equally powerful corresponding frigorific effects, we\nought to possess the means of effecting a disunion equally extensive\nand rapid between such elements, actually combined, as have already\nproduced heat by their union. This, however, we can only accomplish by\nengaging them in combinations still more energetic, that is to say,\nin which we may reasonably expect more heat to be produced by the new\ncombination than would be destroyed or abstracted by the proposed\ndecomposition. Chemistry, however, (unaided by electric agency,)\naffords no means of suddenly breaking the union of two elements, and\npresenting _both_ in an uncombined state. A certain analogy to such\ndisunion, however, and its consequences, may be traced in the sudden\nexpansion of condensed gases from a liquid state into vapour, which is\nthe most powerful source of cold known.\n\n(355.) The dilatation of bodies by heat forms the subject of that\nbranch of science called pyrometry. There is no body but is capable\nof being penetrated by heat, though some with greater, others with\nless rapidity; and being so penetrated, all bodies (with a very few\nexceptions, and those depending on very peculiar circumstances,) are\ndilated by it in bulk, though with a great diversity in the amount\nof dilatation produced by the same degree of heat. Of the several\nforms of natural bodies, gases and vapours are observed to be most\ndilatable; liquids next, and solids least of all. The dilatation of\nsolids has been made a subject of repeated and careful measurement by\nseveral experimenters; among whom, Smeaton, Lavoisier, and Laplace, are\nthe principal. The remarkable discovery of the unequal dilatation of\ncrystallised bodies by Mitscherlich has already been spoken of. (266.)\nThat of gases and vapours was examined about the same time by Dalton\nand Gay-Lussac, who both arrived independently at the conclusion of an\nequal dilatability subsisting in them all, which constitutes one of the\nmost remarkable points in their history.\n\n(356.) The dilatation of air by heat affords, perhaps, the most\nunexceptionable means known of measuring degrees of heat. The\nthermometer, as originally constructed by Cornelius Drebell, was an\nair thermometer. Those now in common use measure accessions of heat\nnot by the degree of dilatation of air but of mercury. It has been\nshown, by the researches of Dulong and Petit, that its indications\ncoincide exactly with that of the air-thermometer in moderate\ntemperatures; though at very elevated ones they exhibit a sensible,\nand even considerable, deviation. By this instrument, which owes its\npresent convenience and utility to the happy idea of Newton, who first\nthought of fixing determinate points on its scale, we are enabled\nto estimate, or at least identify, the degrees of heat; and thereby\nto investigate with accuracy the laws of its communication and its\nother properties. Were we sure that equal additions of heat produced\nequal increments of dimension in any substance, the indications of a\nthermometer would afford a true and secure _measure_ of the quantity\npresent; but this is so far from being the case, that we are nearly in\ntotal ignorance on this important point; a circumstance which throws\nthe greatest difficulty in the way of all theoretical reasoning, and\neven of experimental enquiry. The laws of the dilatation of liquids, in\nconsequence of this deficiency of necessary preliminary knowledge, are\nstill involved in great obscurity, notwithstanding the pains which have\nbeen bestowed on them by the elaborate experiments and calculations of\nGilpin, Blagden, Deluc, Dalton, Gay-Lussac, and Biot.\n\n(357.) The most striking and important of the effects of heat consist,\nhowever, in the liquefaction of solid substances, and the conversion of\nthe liquids so produced into vapour. There is no solid substance known\nwhich, by a sufficiently intense heat, may not be melted, and finally\ndissipated in vapour; and this analogy is so extensive and cogent,\nthat we cannot but suppose that all those bodies which are liquid\nunder ordinary circumstances, owe their liquidity to heat, and would\nfreeze or become solid if their heat could be sufficiently reduced.\nIn many we see this to be the case in ordinary winters; for some,\nsevere frosts are requisite; others freeze only with the most intense\nartificial colds; and some have hitherto resisted all our endeavours;\nyet the number of these last is few, and they will probably cease to be\nexceptions as our means of producing cold become enlarged.\n\n(358.) A similar analogy leads us to conclude that all a\u00ebriform\nfluids are merely liquids kept in the state of vapour by heat. Many\nof them have been actually condensed into the liquid state by cold\naccompanied with violent pressure; and as our means of applying these\ncauses of condensation have improved, more and more refractory ones\nhave successively yielded. Hence we are fairly entitled to extend our\nconclusion to those which we have not yet been able to succeed with;\nand thus we are led to regard it as a general fact, that the liquid and\na\u00ebriform or vaporous states are entirely dependent on _heat_; that were\nit not for this cause, there would be nothing but solids in nature; and\nthat, on the other hand, nothing but a sufficient intensity of heat is\nrequisite to destroy the cohesion of every substance, and reduce all\nbodies, first to liquids, and then into vapour.\n\n(359.) But solids, themselves, by the abstraction of heat shrink in\ndimension, and at the same time become harder, and more brittle;\nyielding less to pressure, and permitting less separation between\ntheir parts by tension. These facts, coupled with the greater\ncompressibility of liquids, and the still greater of gases, strongly\ninduce us to believe that it is heat, and heat alone, which holds\nthe particles of all bodies at that distance from each other which\nis necessary to allow of compression; which in fact gives them\ntheir elasticity, and acts as the antagonist force to their mutual\nattraction, which would otherwise draw them into actual contact, and\nretain them in a state of absolute immobility and impenetrability.\nThus we learn to regard heat as one of the great maintaining powers of\nthe universe, and to attach to all its laws and relations a degree of\nimportance which may justly entitle them to the most assiduous enquiry.\n\n(360.) It was first ascertained by Dr. Black that when heat produces\nthe liquefaction of a solid, or the conversion of a liquid into vapour,\nthe liquid or the vapour resulting is no _hotter_ than the solid or\nliquid from which it was produced, though a great deal of heat has been\nexpended in producing this effect, and has actually entered into the\nsubstance.\n\n(361.) Hence he drew the conclusion that it has become _latent_, and\ncontinues to exist in the product, maintaining it in its new state,\nwithout increasing its temperature. He further proved, that when the\nvapour condenses, or the liquid freezes, this latent heat is again\ngiven out from it. This great discovery, with its natural and hardly\nless important concomitant, that of the difference of specific heats in\ndifferent bodies, or the different quantities of heat they require to\nraise their temperature equally, are the chief reasons for regarding\nheat as a material substance in a more decided manner than light, with\nwhich in its radiant state it holds so close an analogy.\n\n(362.) The subject of latent heat has been far less attentively\nstudied than its great practical importance would appear to demand,\nwhen we consider that it is to this part of physical science that the\ntheory of the steam-engine is mainly referable, and that material\nimprovements may not unreasonably be expected in that wonderful\ninstrument, from a more extended knowledge than we possess of the\nlatent heats of different vapours. This is not the case, however,\nwith the subject of specific heat, which was followed up immediately\nafter its first promulgation with diligence by Irvine; and, after a\nbrief interval, by Lavoisier and Laplace, as well as by our countryman\nCrawfurd, who determined the specific heats of many substances, both\nsolid and liquid. After a considerable period of inactivity, the\nsubject was again resumed by Delaroche and Berard, and subsequently\nby Dulong and Petit: the result of whose investigations has been the\ninductive establishment of one of those simple and elegant physical\nlaws which carry with them, if not their own evidence, at least their\nown recommendation to our belief, as being in unison with every thing\nwe know of the harmony of nature. The law to which we allude is\nthis:--that the atoms of all the simple chemical elements have exactly\nthe same capacity for heat, or are all equally heated or cooled by\nequal accessions or abstractions of heat. It is only among laws like\nthis that we can expect to find a clew capable of guiding us to a\nknowledge of the true nature of heat, and its relations to ponderable\nmatter.\n\n\n_Magnetism and Electricity._\n\n(363.) These two subjects, which had long maintained a distinct\nexistence, and been studied as separate branches of science, are at\nlength effectually blended. This is, perhaps, the most satisfactory\nresult which the experimental sciences have ever yet attained. All\nthe phenomena of magnetic polarity, attraction, and repulsion, have\nat length been resolved into one general fact, that two currents of\nelectricity, moving in the same direction repel, and in contrary\ndirections attract, each other. The phenomena of the communication\nof magnetism and what is called its induced state, alone remain\nunaccounted for; but the interesting theory which has been developed\nby M. Ampere, under the name of Electro-dynamics, holds out a hope\nthat this difficulty will also in its turn give way, and the whole\nsubject be at length completely merged, as far as the consideration of\nthe acting causes goes, in the more general one of electricity. This,\nhowever, does not prevent magnetism from maintaining its separate\nimportance as a department of physical enquiry, having its own peculiar\nlaws and relations of the highest practical interest, which are capable\nof being studied quite apart from all consideration of its electrical\norigin. And not only so, but to study them with advantage, we must\nproceed as if that origin were totally unknown, and, at least up to\na certain point, and that a considerably advanced one, conduct our\nenquiries into the subject on the same inductive principles as if this\nbranch of physics were absolutely independent of all others.\n\n(364.) Iron, and its oxides and alloys, were for a long time the only\nsubstances considered susceptible of magnetism. The loadstone was\neven one of the examples produced by Bacon of that class of physical\ninstances to which he applies the term \u201cInstanti\u00e6 monodic\u00e6\u201d--_singular\ninstances_. And the history of magnetism affords a beautiful comment\non his remark on instances of this sort. \u201cNor should our enquiries,\u201d\nhe observes, \u201cinto their nature be broken off, till the properties and\nqualities found in such things as may be esteemed wonders in nature\nare reduced and comprehended under some certain law; so that all\nirregularity or singularity may be found to depend upon some common\nform, and the wonder only rest in the exact differences, degrees,\nor extraordinary concurrence, and not in the species itself.\u201d The\ndiscovery of the magnetism of nickel, which though inferior to that\nof iron, is still considerable; that of cobalt, yet feebler, and\nthat of titanium, which is only barely perceptible, have effectually\nbroken down the imaginary limit between iron and the other materials\nof the world, and established the existence of that general law of\ncontinuity which it is one chief business of philosophy to trace\nthroughout nature. The more recent discoveries of M. Arago (mentioned\nin 160.) have completed this generalization, by showing that there\nis no substance but which, under proper circumstances, is capable of\nexhibiting unequivocal signs of the magnetic virtue. And to obliterate\nall traces of that line of separation which was once so broad, we are\nnow enabled, by the great discovery of O\u00ebrsted, to communicate at and\nduring pleasure to a coiled wire of any metal indifferently all the\nproperties of a magnet;--its attraction, repulsion, and polarity; and\n_that_ even in a more intense degree than was previously thought to\nbe possible in the best natural magnets. In short, in this case, and\nin this case only, perhaps, in science, have we arrived at that point\nwhich Bacon seems to have understood by the discovery of \u201cforms.\u201d \u201cThe\n_form_ of any nature,\u201d says he, \u201cis such, that where it is, the given\nnature must infallibly be. The form, therefore, is perpetually present\nwhen that nature is present; ascertains it universally, and accompanies\nit every where. Again, this form is such, that when removed, the given\nnature infallibly vanishes. Lastly, a true form is such as can deduce\na given nature from some essential property, which resides in many\nthings.\u201d\n\n(365.) Magnetism is remarkable in another important point of view. It\noffers a prominent, or \u201c_glaring instance_\u201d of that quality in nature\nwhich is termed _polarity_ (267.), and that under circumstances which\npeculiarly adapt it for the study of this quality. It does not appear\nthat the ancients had any knowledge of this property of the magnet,\nthough its attraction of iron was well known to them. The first mention\nof it in modern times cannot be traced earlier than 1180, though it\nwas probably known to the Chinese before that time. The polarity of\nthe magnet consists in this, that if suspended freely, one part of it\nwill invariably direct itself towards a certain point in the horizon,\nthe other towards the opposite point; and that, if two magnets, so\nsuspended, be brought near each other, there will take place a mutual\naction, in consequence of which, the positions of both will be\ndisturbed, in the same manner as would happen if the corresponding\nparts of each repelled, and those oppositely directed attracted, each\nother; and by properly varying the experiment, it is found that they\nreally do so. If a small magnet, freely suspended, be brought into\nthe neighbourhood of a larger one, it will take a position depending\non the position of the _poles_ of the larger one, with respect to its\npoint of suspension. And it has been ascertained that these and all\nother phenomena exhibited by magnets in their mutual attractions and\nrepulsions are explicable on the supposition of two forces or virtues\nlodged in the particles of the magnets, the one predominating at one\nend, the other at the other; and such that each particle shall attract\nthose in which the _opposite_ virtue to its own prevails, and repel\nthose in which a _similar_ one resides with a force proportional to the\ninverse square of their mutual distance.\n\n(366.) The direction in which a magnetic bar, or needle of steel,\nfreely suspended, places itself, has been ascertained to be different\nat different points of the earth\u2019s surface. In some places it points\nexactly north and south, in others it deviates from this direction\nmore or less, and at some actually stands at right angles to it. This\nremarkable phenomenon, which is called the variation of the needle,\nand which was discovered by Sebastian Cabot in the year 1500, is\naccompanied with another called the dip, noticed by Robert Norman in\n1576. It consists in a tendency of a needle, nicely balanced on its\ncentre, when unmagnetized, to _dip_ or point downwards when rendered\nmagnetic, towards a point below the horizon, and situated within the\nearth. By tracing the variation and dip over the whole surface of the\nglobe, it has been found that these phenomena take place as they would\ndo if the earth itself were a great magnet, having its poles deeply\nsituated below the surface,--and, what is very remarkable, possessing\na slow motion within it, in consequence of which neither the variation\nnor dip remain constantly the same at the same place. The laws of this\nmotion are at present unknown; but the discovery of electro-magnetism,\nby rendering it almost certain that the earth\u2019s magnetism is merely an\neffect of the continual circulation of great quantities of electricity\nround it, in a direction generally corresponding with that of its\nrotation, have dissipated the greater part of the mystery which hung\nover these phenomena; since a variety of causes, both geological and\nothers, may be imagined which may produce considerable deviations in\nthe intensity, and partial ones in the direction, of such electric\ncurrents. The unequal distribution of land and sea in the two\nhemispheres, by affecting the operation of the sun\u2019s heat in producing\nevaporation from the latter, which is probably one of the great sources\nof terrestrial electricity, may easily be conceived to modify the\ngeneral tendency of such currents, and to produce irregularities in\nthem, which may render a satisfactory account of whatever still appears\nanomalous in the phenomena of terrestrial magnetism. This branch\nof science thus becomes connected, on a great scale, with that of\nmeteorology, one of the most complicated and difficult, but at the same\ntime interesting, subjects of physical research; one, however, which\nhas of late begun to be studied with a diligence which promises the\nspeedy disclosure of relations and laws of which at present we can form\nbut a very imperfect notion.\n\n(367.) The communication of magnetism from the earth to a magnetic\nbody, or from one magnetic body to another, is performed by a process\nto which the name of induction has been given, and the laws and\nproperties of such induced magnetism have been studied with much\nperseverance and success,--practically, by Gilbert, Boyle, Knight,\nWhiston, Cavallo, Canton, Duhamel, Rittenhouse, Scoresby, and others;\nand theoretically, by \u00c6pinus, Coulomb, and Poisson, and in our own\ncountry by Messrs. Barlow and Christie, who have investigated with\ngreat care the curious phenomena which take place when masses of iron\nare presented successively, in different positions, by rotation on\nan axis, to the influence of the earth\u2019s magnetism. The magnetism of\ncrystallized bodies (partly from the extreme rarity of such as are\nsusceptible of any considerable magnetic virtue) has not hitherto been\nat all examined, but would probably afford very curious results.\n\n(368.) To electricity the views of the physical enquirer now turn\nfrom almost every quarter, as to one of those universal powers which\nNature seems to employ in her most important and secret operations.\nThis wonderful agent, which we see in intense activity in lightning,\nand in a feebler and more diffused form traversing the upper regions\nof the atmosphere in the northern lights, is present, probably in\nimmense abundance, in every form of matter which surrounds us, but\nbecomes sensible only when disturbed by excitements of peculiar\nkinds. The most effectual of these is friction, which we have already\nobserved to be a powerful source of heat. Everybody is familiar\nwith the crackling sparks which fly from a cat\u2019s back when stroked.\nThese, by proper management, may be accumulated in bodies suitably\ndisposed to receive them, and, although then no longer visible, give\nevidence of their existence by the exhibition of a vast variety of\nextraordinary phenomena,--producing attractions and repulsions in\nbodies at a distance,--admitting of being transferred by contact, or\nby sudden and violent transilience of the interval of separation, from\none body to another, under the form of sparks and flashes;--traversing\nwith perfect facility the substance of the densest metals, and a\nvariety of other bodies called conductors, but being detained by\nothers, such as glass, and especially _air_, which are thence called\nnon-conductors,--producing painful shocks and convulsive motions, and\neven death itself if in sufficient quantity, in animals through which\nthey pass, and finally imitating, on a small scale, all the effects of\nlightning.\n\n(369.) The study of these phenomena and their laws until a\ncomparatively recent period occupied the entire attention of\nelectricians, and constituted the whole of the science of electricity.\nIt appears, as the result of their enquiries, that all the phenomena in\nquestion are explicable on the supposition that electricity consists\nin a rare, subtle, and highly elastic fluid, which in its tendency\nto expand and diffuse itself pervades with more or less facility\nthe substance of conductors, but is obstructed and detained from\nexpansion more or less completely by non-conductors. It is supposed,\nmoreover, that this electric fluid possesses a power of attraction\nfor the particles of all ponderable matter, together with that of a\nrepulsion for particles of its own kind. Whether it has weight, or is\nrather to be regarded as a species of matter distinct from that of\nwhich ponderable bodies consist, is a question of such delicacy, that\nno direct experiments have yet enabled us to decide it; but at all\nevents its _inertia_ compared with its elastic force must be conceived\nexcessively small, so that it is to be regarded as a fluid in the\nhighest degree _active_, obeying every impulse, internal or external,\nwith the greatest promptitude; in short, a fluid whose energies can\nonly be compared with those of the ethereal medium by which, in the\nundulatory doctrine, light is supposed to be conveyed. The properties\nof hydrogen gas compared with those of the denser a\u00ebriform fluids will,\nin some slight degree, aid our conception of the excessive mobility and\npenetrating activity of a fluid so constituted. Electricity, however,\nmust be regarded as differing in some remarkable points from all those\nfluids to which we have hitherto been accustomed to apply the epithet\nelastic, such as air, gases, and vapours. In these, the repulsive force\nof the particles on which their elasticity depends is considered as\nextending only to very small distances, so as to affect only those in\nthe immediate vicinity of each other, while their attractive power, by\nwhich they obey the general gravitation of all matter, extends to any\ndistance. In electricity, on the other hand, the very reverse must be\nadmitted. The force by which its particles repel each other extends to\ngreat distances, while its force of adhesion to ponderable matter must\nbe regarded as limited in its extent to such minute intervals as escape\nobservation.\n\n(370.) The conception of a single fluid of this kind, which when\naccumulated in excess in bodies tends constantly to escape, and seek\na restoration of equilibrium by communicating itself to any others\nwhere there may be a deficiency, is that which occurs most naturally\nto the mind, and was accordingly maintained by Franklin, to whom the\nscience of electricity is under great obligations for those decisive\nexperiments which informed us respecting the true nature of lightning.\nThe same theory was afterwards advocated by \u00c6pinus, who first showed\nhow the laws of equilibrium of such a fluid might be reduced to strict\nmathematical investigation. But there are phenomena accompanying its\ntransfer from body to body and the state of equilibrium it affects\nunder various circumstances, which appear to require the admission of\n_two distinct fluids_ antagonist to each other, each attracting the\nother, and repelling itself; but each, alike, susceptible of adhesion\nto material substances, and of transfer more or less rapid from\nparticle to particle of them. These fluids in the natural undisturbed\nstate are conceived to exist in a state of combination and mutual\nsaturation; but this combination may be broken, and either of them\nseparately accumulated in a body to any amount without the other,\nprovided its escape be properly obstructed by surrounding it with\nnon-conductors. When so accumulated, its repulsion for its own kind\nand attraction of the opposite species in neighbouring bodies tends\nto disturb the natural equilibrium of the two fluids present in them,\nand to produce phenomena of a peculiar description, which are termed\n_induced_ electricity. Curious and artificial as this theory may\nappear, there has hitherto been produced no phenomenon of which it\nwill not afford at least a plausible, and in by far the majority of\ncases a very satisfactory, explanation. It has one character which is\nextremely valuable in any theory, that of admitting the application of\nstrict mathematical reasoning to the conclusions we would draw from\nit. Without this, indeed, it is scarcely possible that any theory\nshould ever be fairly brought to the test by a comparison with facts.\nAccordingly, the mathematical theory of electrical equilibrium,\nand the laws of the distribution of the electric fluids over the\nsurfaces of bodies in which they are accumulated, have been made the\nsubject of elaborate geometrical investigation by the most expert\nmathematicians, and have attained a degree of extent and elegance\nwhich places this branch of science in a very high rank in the scale\nof mathematico-physical enquiry. These researches are grounded on\nthe assumption of a law of attraction and repulsion similar to those\nof gravity and magnetism, and which by the general accordance of the\nresults with facts, as well as by experiments instituted for the\nexpress purpose of ascertaining the laws in question, are regarded as\nsufficiently demonstrated.\n\n(371.) The most obscure part of the subject is no doubt the original\nmode of disturbance of electrical equilibrium, by which electricity is\nexcited in the first instance, either by friction or by any other of\nthose causes which have been ascertained to produce such an effect:\nanalogies, it is true, are not wanting[56]; but it must be allowed that\nhitherto nothing decisive has been offered on the subject; and that\nconjectural modes of action have in this instance too often usurped the\nplace of those to which a careful examination of facts alone can lead\nus.\n\n(372.) Philosophers had long been familiar with the effects of\nelectricity above referred to, and with those which it produces in\nits sudden and violent transfer from one body to another, in rending\nand shattering the parts of the substances through which it passes,\nand where in great quantity, producing all the effect of intense\nheat, igniting, fusing, and volatilizing metals, and setting fire to\ninflammable bodies; even its occasional influence in destroying or\naltering the polarity of the magnetic needle had been noticed: but as\nheat was known to be produced by mechanical violence, and as magnetism\nwas also known to be greatly affected by the same cause, these effects\nwere referred rather to that cause than to any thing in the peculiar\nnature of the electric matter, and regarded rather as an indirect\nconsequence of its mode of action than as connected with its intimate\nnature. In short, electricity seemed destined to furnish another in\naddition to many instances of subjects insulated from the rest of\nphilosophy, and capable of being studied only in its own internal\nrelations, when the great discoveries of Galvani and Volta placed a new\npower at the command of the experimenter, by whose means those effects\nwhich had before been crowded within an inappreciable instant could\nbe developed in detail and studied at leisure; and those forces which\nhad previously exhibited themselves only in a state of uncontrollable\nintensity were tamed down, as it were, and made to distribute their\nefficacy over an indefinite time, and to regulate their action at the\nwill of the operator. It was then soon ascertained that electricity\nin the act of its passage along conductors, produces a variety of\nwonderful effects, which had never been previously suspected; and these\nof such a nature, as to afford points of contact with several other\nbranches of physical enquiry, and to throw new and unexpected lights on\nsome of the most obscure operations of nature.\n\n(373.) The history of this grand discovery affords a fine illustration\nof the advantage to be derived in physical enquiry from a close and\ncareful attention to any phenomenon, however apparently trifling,\nwhich may at the moment of observation appear inexplicable on received\nprinciples. The convulsive motions of a dead frog in the neighbourhood\nof an electric discharge, which originally drew Galvani\u2019s attention to\nthe subject, had been noticed by others nearly a century before his\ntime, but attracted no further remark than as indicating a peculiar\nsensibility to electrical excitement depending on that remnant of\nvitality which is not extinguished in the organic frame of an animal\nby the deprivation of actual life. Galvani was not so satisfied. He\nanalysed the phenomenon; and in investigating all the circumstances\nconnected with it was led to the observation of a peculiar electrical\nexcitement which took place when a circuit was formed of three distinct\nparts, a muscle, a nerve, and a metallic conductor, each placed in\ncontact with the other two, and which was manifested by a convulsive\nmotion produced in the muscle. To this phenomenon he gave the name of\nanimal electricity, an unfortunate epithet, since it tended to restrict\nenquiry into its nature to the class of phenomena in which it first\nbecame apparent. But this circumstance, which in a less enquiring age\nof science might have exercised a fatal influence on the progress of\nknowledge, proved happily no obstacle to the further developement of\nits principles, the subject being immediately taken up with a kind\nof prophetic ardour by Volta, who at once generalized the phenomena,\nrejecting the physiological considerations introduced by Galvani, as\nforeign to the enquiry, and regarding the contraction of the muscles\nas merely a delicate means of detecting the production of electrical\nexcitements too feeble to be rendered sensible by any other means.\nIt was thus that he arrived at the knowledge of a general fact, that\nof the disturbance of electrical equilibrium by the mere contact of\ndifferent bodies, and the circulation of a current of electricity in\none constant direction, through a circuit composed of three different\nconductors. To increase the intensity of the very minute and delicate\neffect thus observed became his next aim, nor did his enquiry terminate\ntill it had placed him in possession of that most wonderful of all\nhuman inventions, the pile which bears his name, through the medium of\na series of well conducted and logically combined experiments, which\nhas rarely, if ever, been surpassed in the annals of physical research.\n\n(374.) Though the original pile of Volta was feeble compared to those\ngigantic combinations which were afterwards produced, it sufficed,\nhowever, to exhibit electricity under a very different aspect from any\nthing which had gone before, and to bring into view those peculiar\nmodifications in its action which Dr. Wollaston was the first to\nrender a satisfactory account of, by referring them to an increase\nof _quantity_, accompanied with a diminution of _intensity_ in the\nsupply afforded. The discovery had not long been made public, and\nthe instrument in the hands of chemists and electricians, before it\nwas ascertained that the electric current, transmitted by it through\nconducting liquids, produces in them chemical decompositions. This\ncapital discovery appears to have been made, in the first instance, by\nMessrs. Nicholson and Carlisle, who observed the decomposition of water\nso produced. It was speedily followed up by the still more important\none of Berzelius and Hisinger, who ascertained it as a general law,\nthat, in all the decompositions so effected, the acids and oxygen\nbecome transferred to, and accumulated around, the positive,--and\nhydrogen, metals, and alkalies round the negative, pole of a Voltaic\ncircuit; being transferred in an invisible, and, as it were, a latent\nor torpid state, by the action of the electric current, through\nconsiderable spaces, and even through large quantities of water or\nother liquids, again to re-appear with all their properties at their\nappropriate resting-places.\n\n(375.) It was in this state of things that the subject was taken up\nby Davy, who, seeing that the strongest chemical affinities were thus\nreadily subverted by the decomposing action of the pile, conceived\nthe happy idea of bringing to bear the intense power of the enormous\nbatteries of the Royal Institution on those substances which, though\nstrongly suspected to be compounds, had resisted all attempts to\ndecompose them--the alkalies and earths. They yielded to the force\napplied, and a total revolution was thus effected in chemistry; not so\nmuch by the introduction of the new elements thus brought to light, as\nby the mode of conceiving the nature of chemical affinity, which from\nthat time has been regarded (as Davy broadly laid it down, in a theory\nwhich was readily adopted by the most eminent chemists, and by none\nmore readily than by Berzelius himself,) as entirely due to electric\nattractions and repulsions, those bodies combining most intimately\nwhose particles are habitually in a state of the most powerful\nelectrical antagonism, and dispossessing each other, according to the\namount of their difference in this respect.\n\n(376.) The connection of magnetism and electricity had long been\nsuspected, and innumerable fruitless trials had been made to determine,\nin the affirmative or negative, the question of such connection. The\nphenomena of many crystallized minerals which become electric by heat,\nand develope opposite electric poles at their two extremities, offered\nan analogy so striking to the polarity of the magnet, that it seemed\nhardly possible to doubt a closer connection of the two powers. The\ndevelopement of a similar polarity in the Voltaic pile pointed strongly\nto the same conclusion; and experiments had even been made with a\nview to ascertain whether a pile in a state of excitement might not\nmanifest a disposition to place itself in the magnetic meridian; but\nthe essential condition had been omitted, that of allowing the pile to\ndischarge itself freely, a condition which assuredly never would have\noccurred of itself to any experimenter. Of all the philosophers who\nhad speculated on this subject, none had so pertinaciously adhered to\nthe idea of a necessary connection between the phenomena as O\u00ebrsted.\nBaffled often, he returned to the attack; and his perseverance was at\nlength rewarded by the complete disclosure of the wonderful phenomena\nof electro-magnetism. There is something in this which reminds us of\nthe obstinate adherence of Columbus to his notion of the necessary\nexistence of the New World; and the whole history of this beautiful\ndiscovery may serve to teach us reliance on those general analogies\nand parallels between great branches of science by which one strongly\nreminds us of another, though no direct connection appears; as an\nindication not to be neglected of a community of origin.\n\n(377.) It is highly probable that we are still ignorant of many\ninteresting features in electrical science, which the study of the\nVoltaic circuit will one day disclose. The violent mechanical effects\nproduced by it on mercury, placed under conducting liquids which have\nbeen referred by Professor Erman to a modified form of capillary\nattraction, but which a careful and extended view of the phenomena\nhave led others[57] to regard in a very different light, as pointing\nout a primary action of a dynamical rather than a statical character,\ndeserve, in this point of view, a further investigation; and the\ncurious relations of electricity to heat, as exhibited in the phenomena\nof what has been called thermo-electricity, promise an ample supply of\nnew information.\n\n(378.) Among the remarkable effects of electricity disclosed by the\nresearches of Galvani and Volta, perhaps the most so consisted in its\ninfluence on the nervous system of animals. The origin of muscular\nmotion is one of those profound mysteries of nature which we can\nscarcely venture to hope will ever be fully explained. Physiologists,\nhowever, had long entertained a general conception of the conveyance\nof some subtle fluid or spirit from the brain to the muscles of\nanimals along the nerves; and the discovery of the rapid transmission\nof electricity along conductors, with the violent effects produced by\nshocks, transmitted through the body, on the nervous system, would\nvery naturally lead to the idea that this nervous fluid, if it had\nany real existence, might be no other than the electrical. But until\nthe discoveries of Galvani and Volta, this could only be looked upon\nas a vague conjecture. The character of a _vera causa_ was wanting to\ngive it any degree of rational plausibility, since no reason could\nbe imagined for the disturbance of the electrical equilibrium in the\nanimal frame, composed as it is entirely of conductors, or rather, it\nseemed contrary to the then known laws of electrical communication\nto suppose any such. Yet one strange and surprising phenomenon might\nbe adduced indicative of the possibility of such disturbance, viz.\nthe powerful shock given by the torpedo and other fishes of the same\nkind, which presented so many analogies with those arising from\nelectricity, that they could hardly be referred to a different source,\nthough _besides_ the shock neither spark nor any other indication of\nelectrical tension could be detected in them.\n\n(379.) The benumbing effect of the torpedo had been ascertained to\ndepend on certain singularly constructed organs composed of membranous\ncolumns, filled from end to end with lamin\u00e6, separated from each other\nby a fluid: but of its mode of action no satisfactory account could be\ngiven; nor was there any thing in its construction, and still less in\nthe nature of its materials, to give the least ground for supposing\nit an electrical apparatus. But the pile of Volta supplied at once\nthe analogies both of structure and of effect, so as to leave little\ndoubt of the electrical nature of the apparatus, or of the power, a\nmost wonderful one certainly, of the animal, to determine, by an effort\nof its will, that concurrence of conditions on which its activity\ndepends. This remained, as it probably ever will remain, mysterious\nand inexplicable; but the principle once established, that there\nexists in the animal economy a power of determining the developement\nof electric excitement, capable of being transmitted along the nerves,\nand it being ascertained, by numerous and decisive experiments, that\nthe transmission of Voltaic electricity along the nerves of even\na dead animal is sufficient to produce the most violent muscular\naction, it became an easy step to refer the origin of muscular motion\nin the living frame to a similar cause; and to look to the brain, a\nwonderfully constituted organ, for which no mode of action possessing\nthe least plausibility had ever been devised, as the source of the\nrequired electrical power.[58]\n\n(380.) It is not our intention, however, to enter into any further\nconsideration of physiological subjects. They form, it is true, a\nmost important and deeply interesting province of philosophical\nenquiry; but the view that we have taken of physical science has\nrather been directed to the study of inanimate nature, than to that of\nthe mysterious phenomena of organization and life, which constitute\nthe object of physiology. The history of the animal and vegetable\nproductions of the globe, as affording objects and materials for the\nconvenience and use of man, and as dependent on and indicative of the\ngeneral laws which determine the distribution of heat, moisture, and\nother natural agents, over its surface, and the revolutions it has\nundergone, are of course intimately connected with our subject, and\nwill, therefore, naturally afford room for some remarks, but not such\nas will long detain the reader\u2019s attention.\n\n(381.) In _zoology_, the connection of peculiar modes of life and\nfood, with peculiarities of structure, has given rise to systems of\nclassification at once obvious and natural; and the great progress\nwhich has been made in comparative anatomy has enabled us to trace\na graduated scale of organization almost through the whole chain of\nanimal being; a scale not without its intervals, but which every\nsuccessive discovery of animals heretofore unknown has tended to fill\nup. The wonders disclosed by microscopic observation have opened to\nus a new world, in which we discover, with astonishment, the extremes\nof minuteness and complexity of structure united; while, on the other\nhand, the examination of the fossil remains of a former state of\ncreation has demonstrated the existence of animals far surpassing in\nmagnitude those now living, and brought to light many forms of being\nwhich have nothing analogous to them at present, and many others\nwhich afford important connecting links between existing genera. And,\non the other hand, the researches of the comparative anatomist and\nconchologist have thrown the greatest light on the studies of the\ngeologist, and enabled him to discern, through the obscure medium of a\nfew relics, scattered here and there through a stratum, circumstances\nconnected with the formation of the stratum itself which he could have\nrecognised by no other indication. This is one among many striking\ninstances of the unexpected lights which sciences, however apparently\nremote, may throw upon each other.\n\n(382.) To _botany_ many of the same remarks apply. Its artificial\nsystems of classification, however convenient, have not prevented\nbotanists from endeavouring to group together the objects of their\nscience in natural classes having a community of character more\nintimate than those which determine their place in the Linnean or any\nsimilar system; a community of character extending over the whole\nhabit and properties of the individuals compared. The important\nchemical discoveries which have been lately made of peculiar proximate\nprinciples which, in an especial manner, characterize certain\nfamilies of plants, hold out the prospect of a greatly increased\nfield of interesting knowledge in this direction, and not only\ninteresting, but in a high degree important, when it is considered\nthat the principles thus brought into view are, for the most part,\nvery powerful medicines, and are, in fact, the essential ingredients\non which the medical virtues of the plants depend. The law of the\ndistribution of the generic forms of plants over the globe, too, has,\nwithin a comparatively recent period, become an object of study to the\nnaturalist; and its connection with the laws of climate constitutes one\nof the most interesting and important branches of natural-historical\nenquiry, and one on which great light remains to be thrown by future\nresearches. It is this which constitutes the chief connecting link\nbetween botany and geology, and renders a knowledge of the vegetable\nfossils, of any portion of the earth\u2019s surface, indispensable to the\nformation of a correct judgment of the circumstances under which it\nexisted in its ancient state. Fossil botany is accordingly cultivated\nwith great and increasing ardour; and the subterraneous \u201cFlora\u201d of a\ngeological formation is, in many instances, studied with a degree of\ncare and precision little inferior to that which its surface exhibits.\n\n\n\n\nCHAP. VI.\n\n  OF THE CAUSES OF THE ACTUAL RAPID ADVANCE OF THE PHYSICAL SCIENCES\n    COMPARED WITH THEIR PROGRESS AT AN EARLIER PERIOD.\n\n\n(383.) There is no more extraordinary contrast than that presented by\nthe slow progress of the physical sciences, from the earliest ages\nof the world to the close of the sixteenth century, and the rapid\ndevelopement they have since experienced. In the former period of\ntheir history, we find only small additions to the stock of knowledge,\nmade at long intervals of time; during which a total indifference\non the part of the mass of mankind to the study of nature operated\nto effect an almost complete oblivion of former discoveries, or,\nat best, permitted them to linger on record, rather as literary\ncuriosities, than as possessing, in themselves, any intrinsic interest\nand importance. A few enquiring individuals, from age to age, might\nperceive their value, and might feel that irrepressible thirst after\nknowledge which, in minds of the highest order, supplies the absence\nboth of external stimulus and opportunity. But the total want of a\nright direction given to enquiry, and of a clear perception of the\nobjects to be aimed at, and the advantages to be gained by systematic\nand connected research, together with the general apathy of society\nto speculations remote from the ordinary affairs of life, and\nstudiously kept involved in learned mystery, effectually prevented\nthese occasional impulses from overcoming the inertia of ignorance, and\nimpressing any regular and steady progress on science. Its objects,\nindeed, were confined in a region too sublime for vulgar comprehension.\nAn earthquake, a comet, or a fiery meteor, would now and then call the\nattention of the whole world, and produce from all quarters a plentiful\nsupply of crude and fanciful conjectures on their causes; but it was\nnever supposed that sciences could exist among common objects, have a\nplace among mechanical arts, or find worthy matter of speculation in\nthe mine or the laboratory. Yet it cannot be supposed, that all the\nindications of nature continually passed unremarked, or that much good\nobservation and shrewd reasoning on it failed to perish unrecorded,\nbefore the invention of printing enabled every one to make his ideas\nknown to all the world. The moment this took place, however, the sparks\nof information from time to time struck out, instead of glimmering\nfor a moment, and dying away in oblivion, began to accumulate into a\ngenial glow, and the flame was at length kindled which was speedily to\nacquire the strength and rapid spread of a conflagration. The universal\nexcitement in the minds of men throughout Europe, which the first\nout-break of modern science produced, has been already spoken of. But\neven the most sanguine anticipators could scarcely have looked forward\nto that steady, unintermitted progress which it has since maintained,\nnor to that rapid succession of great discoveries which has kept up\nthe interest of the first impulse still vigorous and undiminished. It\nmay truly, indeed, be said, that there is scarcely a single branch of\nphysical enquiry which is either stationary, or which has not been,\nfor many years past, in a constant state of advance, and in which the\nprogress is not, at this moment, going on with accelerated rapidity.\n\n(384.) Among the causes of this happy and desirable state of things,\nno doubt we are to look, in the first instance, to that great\nincrease in wealth and civilization which has at once afforded the\nnecessary leisure and diffused the taste for intellectual pursuits\namong numbers of mankind, which have long been and still continue\nsteadily progressive in every principal European state, and which the\nincrease and fresh establishment of civilized communities in every\ndistant region are rapidly spreading over the whole globe. It is not,\nhowever, merely the increased number of cultivators of science, but\ntheir enlarged opportunities, that we have here to consider, which, in\nall those numerous departments of natural research that require local\ninformation, is in fact the most important consideration of all. To\nthis cause we must trace the great extension which has of late years\nbeen conferred on every branch of natural history, and the immense\ncontributions which have been made, and are daily making, to the\ndepartments of zoology and botany, in all their ramifications. It is\nobvious, too, that all the information that can possibly be procured,\nand reported, by the most enlightened and active travellers, must fall\ninfinitely short of what is to be obtained by individuals actually\nresident upon the spot. Travellers, indeed, may make collections,\nmay snatch a few hasty observations, may note, for instance, the\ndistribution of geological formations in a few detached points, and now\nand then witness remarkable local phenomena; but the resident alone can\nmake continued series of regular observations, such as the scientific\ndetermination of climates, tides, magnetic variations, and innumerable\nother objects of that kind, requires; can alone mark all the details\nof geological structure, and refer each stratum, by a careful and long\ncontinued observation of its fossil contents, to its true epoch; can\nalone note the habits of the animals of his country, and the limits\nof its vegetation, or obtain a satisfactory knowledge of its mineral\ncontents, with a thousand other particulars essential to that complete\nacquaintance with our globe as a whole, which is beginning to be\nunderstood by the extensive designation of physical geography. Besides\nwhich, ought not to be omitted multiplied opportunities of observing\nand recording those extraordinary phenomena of nature which offer an\nintense interest, from the rarity of their occurrence as well as the\ninstruction they are calculated to afford. To what, then, may we not\nlook forward, when a spirit of scientific enquiry shall have spread\nthrough those vast regions in which the process of civilization, its\nsure precursor, is actually commenced and in active progress? And what\nmay we not expect from the exertions of powerful minds called into\naction under circumstances totally different from any which have yet\nexisted in the world, and over an extent of territory far surpassing\nthat which has hitherto produced the whole harvest of human intellect?\nIn proportion as the number of those who are engaged on each department\nof physical enquiry increases, and the geographical extent over which\nthey are spread is enlarged, a proportionately increased facility\nof communication and interchange of knowledge becomes essential to\nthe prosecution of their researches with full advantage. Not only\nis this desirable, to prevent a number of individuals from making\nthe same discoveries at the same moment, which (besides the waste of\nvaluable time) has always been a fertile source of jealousies and\nmisunderstandings, by which great evils have been entailed on science;\nbut because methods of observation are continually undergoing new\nimprovements, or acquiring new facilities, a knowledge of which, it is\nfor the general interest of science, should be diffused as widely and\nas rapidly as possible. By this means, too, a sense of common interest,\nof mutual assistance, and a feeling of sympathy in a common pursuit,\nare generated, which proves a powerful stimulus to exertion; and, on\nthe other hand, means are thereby afforded of detecting and pointing\nout mistakes before it is too late for their rectification.\n\n(385.) Perhaps it may be truly remarked, that, next to the\nestablishment of institutions having either the promotion of science\nin general, or, what is still more practically efficacious in its\npresent advanced state, that of particular departments of physical\nenquiry, for their express objects, nothing has exercised so powerful\nan influence on the progress of modern science as the publication\nof monthly and quarterly scientific journals, of which there is now\nscarcely a nation in Europe which does not produce several. The quick\nand universal circulation of these, places observers of all countries\non the same level of perfect intimacy with each other\u2019s objects and\nmethods, while the abstracts they from time to time (if well conducted)\ncontain of the most important researches of the day consigned to the\nmore ponderous tomes of academical collections, serve to direct the\ncourse of general observation, as well as to hold out, in the most\nconspicuous manner, models for emulative imitation. In looking forward\nto what may hereafter be expected from this cause of improvement, we\nare not to forget the powerful effect which must in future be produced\nby the spread of elementary works and digests of what is actually known\nin each particular branch of science. Nothing can be more discouraging\nto one engaged in active research, than the impression that all he\nis doing may, very likely, be labour taken in vain; that it may,\nperhaps, have been already done, and much better done, than, with his\nopportunities, or his resources, he can hope to perform it; and, on the\nother hand, nothing can be more exciting than the contrary impression.\nThus, by giving a connected view of what has been done, and what\nremains to be accomplished in every branch, those digests and bodies\nof science, which from time to time appear, have, in fact, a very\nimportant weight in determining its future progress, quite independent\nof the quantity of information they communicate. With respect to\nelementary treatises, it is needless to point out their utility, or\nto dwell on the influence which their actual abundance, contrasted\nwith their past remarkable deficiency, is likely to exercise over the\nfuture. It is only by condensing, simplifying, and arranging, in the\nmost lucid possible manner, the acquired knowledge of past generations,\nthat those to come can be enabled to avail themselves to the full of\nthe advanced point from which they will start.\n\n(386.) One of the means by which an advanced state of physical science\ncontributes greatly to accelerate and secure its further progress,\nis the exact knowledge acquired of physical data, or those normal\nquantities which we have more than once spoken of in the preceding\npages (222.); a knowledge which enables us not only to appretiate\nthe accuracy of experiments, but even to correct their results. As\nthere is no surer criterion of the state of science in any age than\nthe degree of care bestowed, and discernment exhibited, in the choice\nof such data, so as to afford the simplest possible grounds for the\napplication of theories, and the degree of accuracy attained in their\ndetermination, so there is scarcely any thing by which science can be\nmore truly benefited than by researches directed expressly to this\nobject, and to the construction of tables exhibiting the true numerical\nrelations of the elements of theories, and the actual state of nature,\nin all its different branches. It is only by such determinations that\nwe can ascertain what changes are slowly and imperceptibly taking place\nin the existing order of things; and the more accurate they are, the\n_sooner_ will this knowledge be acquired. What might we not now have\nknown of the motions of the (so-called) fixed stars, had the ancients\npossessed the means of observation we now possess, and employed them\nas we employ them now?\n\n(387.) In any enumeration of causes which have contributed to\nthe recent rapid advancement of science, we must not forget the\nvery important one of improved and constantly improving means of\nobservation, both in instruments adapted for the exact measurement of\nquantity, and in the general convenience and well-judged adaptation\nto its purposes, of every description of scientific apparatus. In\nthe actual state of science there are few observations which can\nbe productive of any great advantage but such as afford accurate\nmeasurement; and an increased refinement in this respect is constantly\ncalled for. The degree of delicacy actually attained, we will not say\nin the most elaborate works of the highest art, but in such ordinary\napparatus as every observer may now command, is such as could not have\nbeen arrived at unless in a state of the mechanical arts, which in\nits turn (such is the mutual re-action of cause and effect) requires\nfor its existence a very advanced state of science. What an important\ninfluence may be exercised over the progress of a single branch of\nscience by the invention of a ready and convenient mode of executing a\ndefinite measurement, and the construction and common introduction of\nan instrument adapted for it cannot be better exemplified than by the\ninstance of the reflecting goniometer. This simple, cheap, and portable\nlittle instrument, has changed the face of mineralogy, and given it all\nthe characters of one of the exact sciences.\n\n(388.) Our means of perceiving and measuring minute quantities, in the\nimportant relations of weight, space, and time, seem already to have\nbeen carried to a point which it is hardly conceivable they should\nsurpass. Balances have been constructed which have rendered sensible\nthe millionth part of the whole quantity weighed; and to turn with the\nthousandth part of a grain is the performance of balances pretending\nto no very extraordinary degree of merit. The elegant invention of\nthe sph\u00e6rometer, by substituting the sense of touch for that of sight\nin the measurement of minute objects, permits the determination of\ntheir dimensions with a degree of precision which is fully adequate\nto the nicest purposes of scientific enquiry. By its aid an inch may\nbe readily subdivided into ten or even twenty thousand parts; and the\nlever of contact, an instrument in use among the German opticians,\nenables us to appretiate quantities of space even yet smaller. For\nthe subdivision of time, too, the perfection of modern mechanism has\nfurnished resources which leave very little to be desired. By the\naid of clocks and chronometers, as they are now constructed, a few\ntenths of a second is all the error that need be apprehended in the\nsubdivision of a day; and for the further subdivision of smaller\nportions of time, instruments have been imagined which admit of\nalmost unlimited precision, and permit us to appreciate intervals to\nthe nicety of the hundredth, or even the thousandth part of a single\nsecond.[59] When the precision attainable by such means is contrasted\nwith what could be procured a few generations ago, by the rude and\nclumsy workmanship of even the early part of the last century, it will\nbe no matter of astonishment that the sciences which depend on exact\nmeasurements should have made a proportional progress. Nor will any\ndegree of nicety in physical determinations appear beyond our reach, if\nwe consider the inexhaustible resources which science itself furnishes,\nin rendering the quantities actually to be determined by measure great\nmultiples of the elements required for the purposes of theory, so as to\ndiminish in the same proportion the influence of any errors which may\nbe committed on the final results.\n\n(389.) Great, indeed, as have been of late the improvements in the\nconstruction of instruments, both as to what regards convenience and\naccuracy, it is to the discovery of improved _methods_ of observation\nthat the chief progress of those parts of science which depend on\nexact determinations is owing. The balance of torsion, the ingenious\ninvention of Cavendish and Coulomb, may be cited as an example of what\nwe mean. By its aid we are enabled not merely to render sensible,\nbut to subject to precise measurement and subdivision, degrees of\nforce infinitely too feeble to affect the nicest balance of the usual\nconstruction, even were it possible to bring them to act on it. The\ngalvanometer, too, affords another example of the same kind, in an\ninstrument whose range of utility lies among electric forces which we\nhave no other means of rendering sensible, much less of estimating\nwith exactness. In determinations of quantities less minute in\nthemselves, the methods devised by Messrs. Arago and Fresnel, for the\nmeasurement of the refractive powers of transparent media by means of\nthe phenomenon of diffraction, may be cited as affording a degree of\nprecision limited only by the wishes of the observer, and the time and\npatience he is willing to devote to his observation. And in respect of\nthe direction of observations to points from which real information\nis to be obtained, and positive conclusions drawn, the hygrometer of\nDaniell may be cited as an elegant example of the introduction into\ngeneral use of an instrument substituting an indication founded on\nstrict principles for one perfectly arbitrary.\n\n(390.) In speculating on the future prospects of physical science,\nwe should not be justified in leaving out of consideration the\nprobability, or rather certainty, of the occasional occurrence of those\nhappy accidents which have had so powerful an influence on the past;\noccasions, where a fortunate combination opportunely noticed may admit\nus in an instant to the knowledge of principles of which no suspicion\nmight occur but for some such casual notice. Boyle has entitled one of\nhis essays thus remarkably,--\u201c_Of Man\u2019s great Ignorance of the Uses\nof natural Things; or that there is no one Thing in Nature whereof\nthe Uses to human Life are yet thoroughly understood_.\u201d[60] The whole\nhistory of the arts since Boyle\u2019s time has been one continued comment\non this text; and if we regard among the uses of the works of nature,\n_that_, assuredly the noblest of all, which leads us to a knowledge\nof the Author of nature through the contemplation of the wonderful\nmeans by which he has wrought out his purposes in his works, the\nsciences have not been behind hand in affording their testimony to its\ntruth. Nor are we to suppose that the field is in the slightest degree\nnarrowed, or the chances in favour of such fortunate discoveries at all\ndecreased, by those which have already taken place: on the contrary,\nthey have been incalculably extended. It is true that the ordinary\nphenomena which pass before our eyes have been minutely examined, and\nthose more striking and obvious principles which occur to superficial\nobservation have been noticed and embodied in our systems of science;\nbut, not to mention that by far the greater part of natural phenomena\nremain yet unexplained, every new discovery in science brings into\nview whole classes of facts which would never otherwise have fallen\nunder our notice at all, and establishes relations which afford to\nthe philosophic mind a constantly extending field of speculation,\nin ranging over which it is next to impossible that he should not\nencounter new and unexpected principles. How infinitely greater, for\ninstance, are the mere chances of discovery in chemistry among the\ninnumerable combinations with which the modern chemist is familiar,\nthan at a period when two or three imaginary elements, and some ten\nor twenty substances, whose properties were known with an approach to\ndistinctness, formed the narrow circle within which his ideas had to\nrevolve? How many are the instances where a new substance, or a new\nproperty, introduced into familiar use, by being thus brought into\nrelation with all our actual elements of knowledge, has become the\nmeans of developing properties and principles among the most common\nobjects, which could never have otherwise been discovered? Had not\nplatina (to take an instance) been an object of the most ordinary\noccurrence in a laboratory, would a suspicion have ever occurred that\na lamp could be constructed to burn without flame; and should we have\never arrived at a knowledge of those curious phenomena and products of\nsemi-combustion which this beautiful experiment discloses?\n\n(391.) Finally, when we look back on what has been accomplished in\nscience, and compare it with what remains to be done, it is hardly\npossible to avoid being strongly impressed with the idea that we have\nbeen and are still executing the labour by which succeeding generations\nare to profit.[61] In a few instances only have we arrived at those\ngeneral axiomatic laws which admit of direct deductive inference,\nand place the solutions of physical phenomena before us as so many\nproblems, whose principles of solution we fully possess, and which\nrequire nothing but acuteness of reasoning to pursue even into their\nfarthest recesses. In fewer still have we reached that command of\nabstract reasoning itself which is necessary for the accomplishment of\nso arduous a task. Science, therefore, in relation to our faculties,\nstill remains boundless and unexplored, and, after the lapse of a\ncentury and a half from the \u00e6ra of Newton\u2019s discoveries, during which\nevery department of it has been cultivated with a zeal and energy which\nhave assuredly met their full return, we remain in the situation in\nwhich he figured himself,--standing on the shore of a wide ocean, from\nwhose beach we may have culled some of those innumerable beautiful\nproductions it casts up with lavish prodigality, but whose acquisition\ncan be regarded as no diminution of the treasures that remain.\n\n(392.) But this consideration, so far from repressing our efforts, or\nrendering us hopeless of attaining any thing intrinsically great, ought\nrather to excite us to fresh enterprise, by the prospect of assured\nand ample recompense from that inexhaustible store which only awaits\nour continued endeavours. \u201cIt is no detraction from human capacity to\nsuppose it incapable of infinite exertion, or of exhausting an infinite\nsubject.\u201d[62] In whatever state of knowledge we may conceive man to\nbe placed, his progress towards a yet higher state need never fear a\ncheck, but must continue till the last existence of society.\n\n(393.) It is in this respect an advantageous view of science, which\nrefers all its advances to the discovery of general laws, and to\nthe inclusion of what is already known in generalizations of still\nhigher orders; inasmuch as this view of the subject represents it, as\nit really is, essentially incomplete, and incapable of being fully\nembodied in any system, or embraced by any single mind. Yet it must be\nrecollected that, so far as our experience has hitherto gone, every\nadvance towards generality has at the same time been a step towards\nsimplification. It is only when we are wandering and lost in the mazes\nof particulars, or entangled in fruitless attempts to work our way\ndownwards in the thorny paths of applications, to which our reasoning\npowers are incompetent, that nature appears complicated:--the moment we\ncontemplate it as it is, and attain a position from which we can take a\ncommanding view, though but of a small part of its plan, we never fail\nto recognise that sublime simplicity on which the mind rests satisfied\nthat it has attained the truth.\n\n\n\n\nINDEX.\n\n\n  Acoustics cultivated by Pythagoras and Aristotle, page 248.\n\n  \u00c6pinus, his laws of equilibrium of electricity, 332.\n\n  A\u00ebriform fluids, liquids kept in a state of vapour, 321.\n\n  Agricola, George, his knowledge of mineralogy and metallurgy, 112.\n\n  Air, compressibility and elasticity of; limitation to the repulsive\n        tendency of, 226.\n    Weight of, unknown to the ancients, 228.\n    First perceived by Galileo, 228.\n    Proved by a crucial instance, 229.\n    Equilibrium of, established, 231.\n    Dilatation of, by heat, 319.\n\n  Air-pump, discovery of, 230.\n\n  Airy, his experiments in Dolcoath mine, 187.\n\n  Alchemists, advantages derived from, 11.\n\n  Algebra, 19.\n\n  Ampere, his electro-dynamic theory, 202.\n    Utility of, 203, 324.\n\n  Analysis of force, 86.\n    Of motion, 87.\n    Of complex phenomena, 88.\n\n  Anaxagoras, philosophy of, 107.\n\n  Animal electricity, 337.\n\n  Arago, M., his experiment with a magnetic needle and a plate of\n        copper, 157.\n\n  Archimedes, his practical application of science, 72.\n    His knowledge of hydrostatics, 231.\n\n  Arfwedson, his discovery of lithia, 158.\n\n  Aristotle, his knowledge of natural history, 109.\n    His works condemned, and subsequently studied with avidity, 111.\n    His philosophy overturned by the discoveries of Copernicus, Kepler,\n        and Galileo, 113.\n\n  Arithmetic, 19.\n\n  Art, empirical and scientific, differences between, 71.\n    Remarks on the language, terms, or signs, used in treating of\n        it, 70.\n\n  Assurances, life, utility and abuses of, 58.\n\n  Astronomy, cause of the slow progress of our knowledge of, 78.\n    Theory and practical observations distinct in, 132.\n    An extensive acquaintance with science and every branch of knowledge\n        necessary to make a perfect observer in, 132.\n    Five primary planets added to our system, 274.\n    Positions, figures, and dimensions of all the planetary orbits now\n        well known, 275.\n\n  Atomic theory, 305.\n    Advantage of, 306.\n\n  Atomic weights of chemical elements, 306.\n\n  Attraction, capillary, or capillarity, investigated by Laplace and\n        Young, 234.\n\n\n  Bacon, celebrated in England for his knowledge of science, 72.\n    Benefits conferred on Natural Philosophy by him, 104.\n    His Novum Organum, 105.\n    His reform in philosophy proves the paramount importance of\n        induction, 114.\n    His prerogative of facts, 181.\n    Illustrated by the fracture of a crystallized substance, 183.\n    His collective instances, 184.\n    Importance of, 185.\n    His experiment on the weight of bodies, 186.\n    Travelling instances of, frontier instances of, 188.\n    His difference between liquids and a\u00ebriform fluids, 233.\n\n  Bartolin, Erasmus, first discovers the phenomena exhibited by doubly\n        refracting crystals, 254.\n\n  Beccher, phlogistic doctrines of, 300.\n\n  Bergmann, his advancement in crystallography, 239.\n\n  Bernoulli, experiments of, in hydrodynamical science, 181.\n\n  Biot, his hypothesis of a rotatory motion of the particles of light\n        about their axes, 262.\n\n  Black, Dr., his discovery of latent heat, 322.\n\n  Bode, his curious law observed in the progression of the magnitudes of\n        the several planetary orbits, 308.\n\n  Bodies, natural constitution of, 221.\n    Division of, into crystallized and uncrystallized, 242.\n\n  Bones, dry, a magazine of nutriment, 65.\n\n  Borda, his invention for subdivision, 128.\n\n  Botany, general utility of, 345.\n\n  Boyle, Robert, his enthusiasm in the pursuit of science, 115.\n    His improvement on the air-pump, 230.\n\n  Brain, hypothesis of its being an electric pile, 343.\n\n  Bramah\u2019s press, principle and utility of, 233.\n\n  Brewster, Dr., his improvement on lenses for lighthouses, 56.\n    His researches prove that the phenomena exhibited by polarized\n        light, in its transmission through crystals, afford a certain\n        indication of the most important points relating to the\n        structure of crystals themselves, 263.\n\n\n  Cabot, Sebastian, his discovery of the variation of the needle, 327.\n\n  Cagnard, Baron de la Tour, utility of his experiments, 234.\n\n  Causes and consequences directors of the will of man, 6.\n\n  Causes, proximate, discovery of, called by Newton _ver\u00e6 caus\u00e6_, 144.\n\n  Celestial mechanics, 265.\n\n  Chaldean records, 265.\n\n  Chemistry furnishes causes of sudden action, also fulminating\n        compositions, 62.\n    Analogy of the complex phenomena of, with those of physics, 92.\n    Benefits arising from the analysis of, 94.\n    Axioms of, analogous to those of geometry, 95.\n    Many of the new elements of, detected in the investigation of\n        residual phenomena, 158.\n    The most general law of, 209.\n    Illustration of, 210.\n    Between fifty and sixty elements in, 211.\n    Objects of, 296.\n    General heads of the principal improvements in, 302.\n    Remarks on those general heads, 304.\n\n  Chemistry, Stahlian, cause of the mistakes and confusions of, 123.\n\n  Chladni, experiments of, in dynamical science, 181.\n\n  Chlorine, disinfectant powers of, 56.\n\n  Clarke, Dr., his experiments on the arseniate and phosphate\n        of soda, 170.\n    His success in producing a new phosphate of soda, 171.\n\n  Climate, change of, in large tracts of the globe, alleged\n        cause of, 145.\n\n  Coals, power of a bushel of, properly consumed, 59.\n    Quantity consumed in London, 60.\n\n  Cohesion, an ultimate phenomenon, 90.\n\n  Cold, qualities of, 318.\n\n  Compass, mariner\u2019s, 55.\n\n  Condensation, a source of heat, 313.\n\n  Conduction of heat, laws of, 205.\n\n  Copernicus, effect of his discoveries on the Aristotelian\n        philosophy, 113.\n    Objections to his astronomical doctrines, 269.\n\n  Crystallography, laws of, 123, 239.\n    A determinate figure supposed to be common to all the particles of a\n        crystal, 242.\n\n\n  D\u2019Alembert, his improvements in hydrodynamics, 236.\n\n  Dalton, his announcement of the atomic theory, 305.\n    His examination of gases and vapours, 319.\n\n  Davy, Sir H., brings the voltaic pile to bear upon the earths and\n        alkalies, 339.\n\n  Deduction, utility of, 174.\n\n  De l\u2019Isle, Rom\u00e9, his study of crystalline bodies, 239.\n\n  Dew, causes of, investigated, 159.\n    Effects of, on different substances, 160.\n    Objects capable of contracting it, 161.\n    A cloudless sky favourable to its production, 162.\n    General proximate cause of, 163.\n\n  Drummond, lieutenant, his improvement on lenses for lamps of\n        lighthouses, 56.\n\n  Dynamics, importance of, 96, 223.\n\n\n  Earth, the orbit of,--diminution of its eccentricity round\n        the sun, 147.\n\n  Economy, political, 73.\n\n  Egypt, great pyramid of, height, weight, and ground occupied by\n        it, 60.\n    Accuracy of the astronomical records of, 265.\n\n  Elasticity, an ultimate phenomenon, 90.\n\n  Electricity may be the cause of magnetism, 93.\n    Universality of, 329.\n    Effects of, 330.\n    Activity of, 331.\n    Equilibrium of, 332.\n    Productive of chemical decomposition, 338.\n\n  Empirical laws, 178.\n    Evils resulting from, 179.\n\n  Encke, professor, his prediction of the return of the comet so many\n        times in succession, 156.\n\n  Englefield, sir H., his analysis of a solar beam, 314.\n\n  Equilibrium maintained by force, 222.\n\n  Erman, professor, his opinion of the effects of the voltaic\n        circuit, 340.\n\n  Euler, his improvement on Newton\u2019s theory of sound, 247.\n\n  Experience, source of our knowledge of nature\u2019s laws, 76.\n\n  Experiment, a means of acquiring experience, 76.\n    Utility of, 151.\n\n\n  Facts, the observation of, 118.\n\n  Faujas de St. Fond, imaginary craters of, 131.\n\n  Fluids, laws of the motion of, 181.\n    Compressibility of, 225.\n    Consideration of the motions of, more complicated than that of\n        equilibrium, 235.\n\n  Force, analysis of, 86.\n    The cause of motion, 149.\n    Phenomena of, 221.\n    Molecular forces, 245.\n\n  Fourier, baron, his opinion that the celestial regions have a\n        temperature, independent of the sun, not greatly inferior\n        to that at which quicksilver congeals, 157.\n    His analysis of the laws of conduction and radiation of heat, 317.\n\n  Franklin, Dr., his experiments on electricity, 332.\n\n  Fresnel, M., his mathematical explanation of the phenomena of double\n        refraction, 32.\n    His improvement on lenses for lamps of lighthouses, 56.\n    His opinions on the nature of light, 207.\n    His experiments on the interference of polarized light, 261.\n    His theory of polarization, 262.\n\n  Friction, a source of heat, 313.\n\n\n  Galileo, celebrity of, for his knowledge of science, 72.\n    His exposition of the Aristotelian philosophy, 110.\n    His refutation of Aristotle\u2019s dogmas respecting motion, his\n        persecution in consequence of it, 113.\n    His knowledge of the accelerating power of gravity, 168.\n    His knowledge of the weight of the atmosphere, 228.\n\n  Galvani, utility of his discoveries in electricity, 335.\n    His application of it to animals, 336.\n\n  Gay-Lussac, his examination of gases and vapours, 319.\n\n  Generalization, inductive, 1, 90.\n\n  Geology, 281.\n    Its rank as a science, 287.\n\n  Geometry, axioms of, an appeal to experience, not corporeal, but\n        mental, 95.\n\n  Gilbert, Dr., of Colchester, his knowledge of magnetism and\n        electricity, 112.\n\n  Gravitation, law of, a physical axiom of a very high and universal\n        kind, 98.\n    Influence of, decreases in the inverse ratio of the square of the\n        distance, 123.\n\n  Greece, philosophers of, their extraordinary success in abstract\n        reasoning, and their careless consideration of external\n        nature, 105.\n    Their general character, 106.\n    Philosophy of, 108.\n\n  Grimaldi, a jesuit of Bologna, his discovery of diffraction, or\n        inflection of light, 252.\n\n  Guinea and feather experiment, 168.\n\n  Gunpowder, invention of, 55.\n    A mechanical agent, 62.\n\n\n  Haarlem lake, draining of, 61.\n\n  Harmony, sense of, 248.\n\n  Head, captain, anecdote of, 84.\n\n  Heat, 193.\n    Radiation and conduction of, 205.\n    One of the chief agents in chemistry, 310.\n    Our ignorance of the nature of, 310.\n    Abuse of the sense of the term, 311.\n    The general heads under which it is studied, 312.\n    Its most obvious sources, 312.\n    Animal heat, to what process referable, 313.\n    Radiation and conduction of, 314.\n    Solar heat differs from terrestrial fires, or hot bodies, 315.\n    Principal effects of, 317.\n    The antagonist to mutual attraction, 322.\n    Latent heat, 322.\n    Specific heat, 323.\n\n  Herschel, sir William, his analysis of a solar beam, 314.\n\n  Hipparchus, his catalogue of stars, 276.\n\n  Holland drained of water by windmills, 61.\n\n  Hooke almost the rival of Newton, 116.\n\n  Huel Towan, steam-engine at, 59.\n\n  Huyghens, his doctrine of light, 207.\n    Ascertains the laws of double refraction, 254.\n\n  Hydrostatics, first step towards a knowledge of, made by\n        Archimedes, 231.\n    Law of the equal pressure of liquids, 232.\n    General applicability of, 232.\n\n  Hypothesis, not to be deterred from framing them, 196.\n    Conditions on which they should be framed, 197.\n    Illustrated by the laws of gravitation, 198.\n    Use and abuse of, 204.\n\n\n  Induction, different ways of carrying it on, 102.\n    Steps by which it is arrived at on a legitimate and extensive\n        scale, 118.\n    First stage of, 144.\n    Verification of, 164.\n    Instanced in astronomy, 166.\n    Must be followed into all its consequences, and applied to all those\n        cases which seem even remotely to bear upon the subject of\n        enquiry, 173.\n    Nature of the inductions by which quantitative laws are arrived\n        at, 176.\n    Necessity of induction embracing a series of cases which absolutely\n        include the whole scale of variation of which the quantities\n        in question admit, 177.\n\n  Induced electricity, 333.\n\n  Inertia, 223.\n\n  Iodine, discovery of, 50.\n    Efficacy of, in curing go\u00eetre, 51.\n\n  Isomorphism, law of, 170.\n\n\n  Kepler, effect of his discoveries on the Aristotelian philosophy, 113.\n    Nature of his laws of the planetary system, 178.\n    Proofs of the Newtonian system, 179.\n\n  Knowledge, physical facts illustrative of the utility of, 45.\n    Diffusion of, how to take advantage of in the investigation of\n        nature, 138.\n\n\n  Lagrange, his improvements on Newton\u2019s theory of sound, 247.\n    His astronomical researches, 275.\n\n  Lamp, safety, 55.\n\n  Laplace, his explanation of the residual velocity of sound and\n        confirmation of the general law of the developement of heat\n        by compression, 172.\n    His astronomical research, 275.\n    His experiments on the dilatation of bodies by heat, 319.\n    His study of specific heat, 323.\n    Latent heat, 323.\n\n  Laws, inductive, 171.\n    General, 198.\n    How applicable, 199.\n    Illustrated by the planetary system, 201.\n    Empirical laws, 178.\n\n  Lavoisier, his improvements in chemical science, 302.\n    Experiments on dilatation of bodies by heat, 319.\n    His investigation on specific heat, 323.\n\n  Light, refraction of, 30.\n    Double refraction of, 31.\n    Polarization of, 254.\n\n  Light and vision, ignorance of the ancients respecting, 249.\n\n  Lighthouse, 56.\n\n  Lightning, how to judge philosophically of it, 120.\n    Returning stroke of, 121.\n\n  Liquids, cohesion, attraction and repulsion of the particles of, 227.\n    Differ from a\u00ebriform fluids by their cohesion, 233.\n    The Florentine experiment on; experiments by Canton, Perkins,\n        O\u00ebrsted, and others on, 235.\n    Obscurity of the laws of dilatation of, 320.\n\n  Linn\u00e6us, his knowledge of crystalline substances, 239.\n\n  Logic, 19.\n\n  Lyell\u2019s Principles of Geology, extract from, 146.\n\n\n  Magnetism may be caused by electricity, 93.\n    Offers a \u201cglaring instance\u201d of polarity, 326.\n    Experiments illustrative of, 327.\n\n  Malus, a French officer of engineers, discovers the polarization of\n        light, 132, 258.\n\n  Man, regarded as a creature of instinct, 1.\n    Of reason and speculation, 3.\n    His will determined by causes and consequences, 6.\n    Advantages to, from the study of science, 7.\n    His necessity to study the laws of nature illustrated, 66.\n    Happiness and the opposite state of man in the aggregate, 67.\n    Advantages conferred on, by the augmentation of physical\n        resources, 68.\n    Advantages from intellectual resources, 69.\n\n  Mariotte, his law of equilibrium of an elastic fluid recently verified\n        by the Royal Academy of Paris, 231.\n    His difference between solar and other heat, 315.\n\n  Matter, indestructibility of; Divided by grinding, 40.\n    By fire, 41.\n    Dilated by heat, 193.\n    Inertia of, 202.\n    Polarity of, one of the ultimate phenomena to which the analysis of\n        nature leads us, 245.\n    Inherent activity of, 297.\n    Causes of the polarity of, 299.\n    Imponderable forms of, 310.\n\n  Measure, the standard, difficulty of preserving it unaltered, 128.\n    How to be assisted in measurement, 129.\n    Our conclusions from, should be conditional, 130.\n\n  Menai Bridge, weight and height of, 60.\n\n  Mechanics, practical, 63.\n\n  M\u00e8tre, the French, 126.\n\n  Microscopes, power of, 191.\n\n  Millstones, method of making in France, 48.\n\n  Mind, its transition from the little to the great, and _vice vers\u00e2_,\n        illustrated, 172.\n\n  Mineralogy unknown to the ancients, 79.\n    Prejudiced by the rage for nomenclature, 139.\n    Benefited by the progress of chemical analysis, 293.\n\n  Minerals, simple, apparent paucity of, 294.\n    Difficulty in classing them, 295.\n\n  Mitscherlich, his law of isomorphism, 170.\n    His experiments on the expansion of substances by heat, 243.\n\n  Motion, 87.\n    Simplicity and precision of the laws of, 179.\n\n\n  Nature, laws of, 37.\n    Immutability of, 42.\n    Harmony of, and advantage of studying them, 43.\n    Prove the impossibility of attaining the declared object of the\n        alchemist. How they serve mankind generally, 44.\n    Illustrated by mining, 45.\n    Economy derived from a knowledge of, 65.\n    How to be regarded, 100, 101.\n\n  Nature, objects of, an enumeration and nomenclature of, useful in the\n        study of, 135.\n    Mechanism of, on too large or too small a scale to be immediately\n        cognisable by our senses, 191.\n\n  Newton, his proof of Galileo\u2019s laws of gravitation by an experiment\n        with a hollow glass pendulum, 160.\n    His foundation to hydrodynamical science, 181.\n    Fixes the division between statics and dynamics, 223.\n    His investigation of the law of equilibrium of elastic fluids, 231.\n    His law of hydrostatics, 232.\n    His foundation of hydrodynamics 236.\n    His analysis of sound, 247.\n    Hypothesis of light, 250.\n    Examination of a soap-bubble, 252.\n    His hypothesis of fits of easy transmission and reflection, 253.\n    His combination of mathematical skill with physical research, 271.\n    His Principia, 272.\n    His successors; his geometry, 273.\n\n  Nomenclature, importance of, to science, 136.\n    More a consequence than a cause of extended knowledge, 138.\n    Prejudicial to mineralogy, 139.\n\n  Norman, Robert, his discovery of the dip of the needle, 327.\n\n  Numerical precision, necessity of, in science, 122.\n\n\n  Objects, and their mutual actions, subjects of contemplation, 118.\n\n  Observation, a means of acquiring experience, 76.\n    Passive and active, 77.\n    Recorded observation, 120.\n    Necessity of, to acquire precise physical data, 215.\n    Illustrated by the barometer, 216.\n\n  O\u00ebrsted, his discoveries in electricity and magnetism, 132.\n    Of electro-magnetism, 340.\n\n  Opacity, 189.\n\n  Otto von Guericke of Magdeburgh, his invention of the air-pump, 230.\n\n\n  Paracelsus, power of his chemical remedies; his use of mercury,\n        opium, and tartar, 112.\n\n  Pascal, his crucial instances proving the weight of air, 229.\n\n  Pendulum, 126.\n\n  Phenomena, analysis of, illustrated by musical sounds, the sensation\n        of taste, 85.\n    The ultimate and inward process of nature in the production of, 86.\n    Analysis of complex phenomena, 88.\n    Ultimate phenomena, 90.\n    How the analysis of, is useful, 97.\n    A transient phenomenon, how to judge of, 122.\n    Method of explaining one when it presents itself, 148.\n    How to discover the cause of one, 150.\n    Two, or many, theories, maintained as the origin of, in\n        physics, 195.\n    Cosmical phenomena, 265.\n\n  Philosophy, natural, unfounded objections to the study of, 7.\n    Advantages derivable from the study of, 10.\n    Pleasure and happiness, the consequences of the study of, 15.\n\n  Phlogistic doctrines of Beccher and Stahl, 300.\n\n  Physical data, necessity of, 209.\n    Great importance of, 211.\n    Illustrated by the erection of observatories, 213.\n    Necessity of an exact knowledge of, 214.\n    More precise than the observations by which we acquire them, 215.\n\n  Physics, axioms of; analysis of, 102.\n\n  Planets, circumjovial, 186.\n\n  Platina, discovery of, 308.\n\n  Pliny, his knowledge of quartz and diamond, 239.\n\n  Pneumatics, 228.\n\n  Political economy, 73.\n\n  Prejudices of opinion and sense, 80.\n    Conditions on which such are injurious, 81.\n    Illustrated by the division of the rays of light, by the moon at the\n        horizon, and by ventriloquism, 82.\n    By the transition of the hand from heat to cold, 83.\n\n  Prevost, M., his theory of heat, 316.\n    His theory of reciprocal interchanges, a proof of the radiation\n        of cold, 318.\n\n  Printing, the art of, 193.\n    Performed by steam, 194.\n\n  Probabilities, doctrine of, 217.\n    Illustrated by shooting at a wafer, 218.\n\n  Prout, Dr., his opinion of the atomic weights, 307.\n\n  Pyrometry, 319.\n\n  Pythagoras, philosophy of, 107.\n\n\n  Quinine, sulphate of, comparative comfort and health resulting from\n        the use of, 56.\n\n\n  Radiation of heat, laws of, 205.\n\n  Repulsion in fluids and solids, 227.\n\n  Rules, general, for guiding and facilitating our search among a great\n        mass of assembled facts, 151.\n\n  Rumford, count, experiments of, on gunpowder, 62.\n\n\n  Savart, M., his experiments on solids, 243.\n    His researches on sound, 249.\n\n  Science, abstract, a preparation for the study of physics, 19.\n    Not indispensable to the study of physical laws, 25.\n    Instances illustrative of, 27.\n\n  Science, physical, nature and objects, immediate and collateral, as\n        regarded in itself and in its application to the practical\n        purposes of life, and its influence on society, 35.\n    State of, previous to the age of Galileo and Bacon, 104.\n    Causes of the rapid advance of, compared with the progress at an\n        earlier period, 347.\n\n  Science, natural, cause and effect, the ultimate relations of, 76.\n\n  Sciences and Arts, remarks on the language, terms, or signs used in\n        treating of them, 70.\n    Receive an impulse by the Baconian philosophy, 114.\n\n  Sensation, cause of, 91.\n\n  Senses, inadequate to give us direct information for the exact\n        comparison of quantity, 124.\n    Substitutes for the inefficiency of, 125.\n\n  Seringapatam, method of breaking blocks from the quarries of, 47.\n\n  Shells found in rocks at a great height above the sea, supposed\n        cause of, 145.\n\n  Smeaton, his experiments on bodies dilated by heat, 319.\n\n  Solids, transparent, exhibit periodical colours when exposed to\n        polarized light, 99.\n    Influence of, on the Mind, 101.\n\n  Solids in general, nature of, 236.\n    Constitution of, complicated, 237.\n    Toughness of, distinct from hardness; tenacity of, 238.\n    Become liquefied by the addition of heat, 321.\n\n  Sounds, musical, illustrative of the analysis of phenomena, 85.\n    Means of having a knowledge of, 89.\n    Propagation of, through the air, 246.\n    Newton\u2019s analysis of, 247.\n\n  Standard measurement, necessity of, 125.\n    Laws of nature used as such, illustrated by the rotation of the\n        earth, 126.\n\n  Substances all subject to dilatation by the addition of heat, 243.\n\n  Sun, the character of the heat of, 315.\n\n\n  Thales, philosophy of, 107.\n\n  Theories, how to estimate the value of, 204.\n    Best arrived at by the consideration of general laws, 208.\n    Explanatory of the phenomena of nature; on what their application\n        ought to be grounded, 209.\n\n  Thomson, Dr., his opinion of the atomic weights, 307.\n\n  Thermometer, air, 319.\n\n  Thermo-electricity, 341.\n\n  Time, division of, 126, 127.\n\n  Torricelli, pupil of Galileo, his experiments proving the weight of\n        atmosphere, 229.\n\n  Torpedo, shock of, 341, 342.\n\n\n  Ulugh Begh, his catalogue of stars, 277.\n\n\n  Vaccination, success of, as a preventive to small-pox, 52.\n\n  Vision and light, ignorance of the ancients respecting, 249.\n\n  Volta, his discoveries in electricity, 335.\n    Electric pile of, 337.\n\n  Voltaic circuit, 338.\n\n\n  Water, effects of the power of, 61.\n\n  Whewell, his experiments, 187.\n\n  Wells, Dr., his theory of dew, 163.\n\n  Wind, effects of the power of, 61.\n\n  Wire steel, magnetized masks of, used by needle-makers, 57.\n\n  Wollaston, Dr., his verification of the laws of double refraction in\n        Iceland spar, 258.\n    His invention of the goniometer, 292.\n\n  World, the materials of the, 290.\n\n\n  Young, Dr., his experiments on the interference of the rays of\n        light, 260.\n\n\n  Zoology, fossil, 344.\n\n\nTHE END.\n\n\n  LONDON\n  PRINTED BY SPOTTISWOODE AND CO.\n  NEW-STREET SQUARE.\n\n\n\n\nFOOTNOTES\n\n\n[1] Hooke\u2019s Posthumous Works. Lond. 1705.--p. 472 and p. 458.\n\n[2] Wealth of Nations, book i. chap. i. p. 15.\n\n[3] On this subject, we cannot forbear citing a passage from one of\nthe most profound but at the same time popular writers of our time, on\na subject unconnected it is true with our own, but bearing strongly\non the point before us. \u201cBut, if science be manifestly incomplete,\nand yet of the highest importance, it would surely be most unwise\nto restrain enquiry, conducted on just principles, even where the\nimmediate practical utility of it was not visible. In mathematics,\nchemistry, and every branch of natural philosophy, how many are the\nenquiries necessary for their improvement and completion, which, taken\nseparately, do not appear to lead to any specifically advantageous\npurpose! how many useful inventions, and how much valuable and\nimproving knowledge, would have been lost, if a rational curiosity,\nand a mere love of information, had not generally been allowed to be a\nsufficient motive for the search after truth!\u201d--Malthus\u2019s Principles of\nPolitical Economy, p. 16.\n\n[4] \u039b\u03bf\u03b3\u03bf\u03c2, _ratio_, reason.\n\n[5] \u039b\u03bf\u03b3\u03bf\u03c2, _verbum_, a word.\n\n[6] It were much to be wished that navigators would be more cautious in\nlaying themselves open to a similar censure. On looking hastily over\na map of the world we see three Melville Islands, two King George\u2019s\nSounds, and Cape Blancos innumerable.\n\n[7] Young. Lectures on Nat. Phil. ii. 627. See also Phil. Trans. 1801-2.\n\n[8] Captain Basil Hall, R.\u00a0N.\n\n[9] We must caution our readers who would assure themselves of it by\ntrial, that it is an experiment of some delicacy, and not to be made\nwithout several precautions to ensure success. For these we must refer\nto our original authority (Fresnel. M\u00e9moire sur la Diffraction de la\nLumiere, p. 124.); and the principles on which they depend will of\ncourse be detailed in that volume of the Cabinet Cyclop\u00e6dia which is\ndevoted to the subject of LIGHT.\n\n[10] Little reels used in cotton mills to twist the thread.\n\n[11] Such a block would weigh between four and five hundred thousand\npounds. See Dr. Kennedy\u2019s \u201cAccount of the Erection of a Granite Obelisk\nof a Single Stone about Seventy Feet high, at Seringapatam.\u201d--_Ed.\nPhil. Trans._ vol. ix, p. 312.\n\n[12] Dr. Coindet of Geneva.\n\n[13] Journal of a Voyage to the South Seas, &c. &c. under the Command\nof Commodore George Anson, in 1740-1744, by Pascoe Thomas, Lond. 1745,\nSo tremendous were the ravages of scurvy, that, in the year 1726,\nadmiral Hosier sailed with seven ships of the line to the West Indies,\nand buried his ships\u2019 companies twice, and died himself in consequence\nof a broken heart. Dr. Johnson, in the year 1778, could describe a\nsea-life in such terms as these:--\u201cAs to the sailor, when you look down\nfrom the quarter deck to the space below, you see the utmost extremity\nof human misery, such crowding, such filth, such stench!\u201d--\u201cA ship is\na prison with the chance of being drowned--it is worse--worse in every\nrespect--worse room, worse air, worse food--worse company!\u201d Smollet,\nwho had personal experience of the horrors of a seafaring life in those\ndays, gives a lively picture of them in his Roderick Random.\n\n[14] Lemon juice was known to be a remedy for scurvy far superior\nto all others 200 years ago, as appears by the writings of Woodall.\nHis work is entitled \u201cThe Surgeon\u2019s Mate, or Military and Domestic\nMedicine. By John Woodall, Master in Surgery London, 1636,\u201d p. 165. In\n1600, Commodore Lancaster sailed from England with three other ships\nfor the Cape of Good Hope, on the 2d of April, and arrived in Saldanha\nBay on the 1st of August, the commodore\u2019s own ship being in perfect\nhealth, from the administration of three table-spoonsfull of lemon\njuice every morning to each of his men, whereas the other ships were so\nsickly as to be unmanageable for want of hands, and the commander was\nobliged to send men on board to take in their sails and hoist out their\nboats. (Purchas\u2019s Pilgrim, vol. i. p. 149.) A Fellow of the college,\nand an eminent practitioner, in 1753 published a tract on sea scurvy,\nin which he adverts to the superior virtue of this medicine; and Mr. A.\nBaird, surgeon of the Hector sloop of war, states, that from what he\nhad seen of its effects on board of that ship, he \u201cthinks he shall not\nbe accused of presumption in pronouncing it, if properly administered,\na _most infallible remedy_, both in the cure and prevention of\nscurvy.\u201d (Vide Trotter\u2019s Medicina Nautica.) The precautions adopted\nby captain Cook in his celebrated voyages, had fully demonstrated by\ntheir complete success the practicability of keeping scurvy under in\nthe longest voyages, but a uniform system of prevention throughout the\nservice was still deficient.\n\nIt is to the representations of Dr. Blair and sir Gilbert Blane, in\ntheir capacity of commissioners of the board for sick and wounded\nseamen, in 1795, we believe, that its _systematic introduction into\nnautical diet_, by a general order of the admiralty, is owing. The\neffect of this wise measure (taken, of course, in conjunction with the\ngeneral causes of improved health,) may be estimated from the following\nfacts:--In 1780, the number of cases of scurvy received into Haslar\nhospital was 1457; in 1806 _one_ only, and in 1807 _one_. There are now\nmany surgeons in the navy who have never seen the disease.\n\n[15] Throughout France the conductor is recognised as a most\nvaluable and useful instrument; and in those parts of Germany where\nthunder-storms are still more common and tremendous they are become\nnearly universal. In Munich there is hardly a modern house unprovided\nwith them, and of a much better construction than ours--several copper\nwires twisted into a rope.\n\n[16] We have been informed by an eminent physician in Rome, (Dr.\nMorichini) that a vast quantity of the sulphate of quinine is\nmanufactured there and consumed in the Campagna, with an evident effect\nin mitigating the severity of the malarious complaints which affect its\ninhabitants.\n\n[17] Dr. Johnson, Memoirs of the Medical Society, vol. v.\n\n[18] The engine at Huel Towan. See Mr. Henwood\u2019s Statement \u201cof the\nperformance of steam-engines in Cornwall for April, May, and June,\n1829.\u201d Brewster\u2019s Journal, Oct. 1829.--The _highest_ monthly average of\nthis engine extends to 79 millions of pounds.\n\n[19] However, this is not quite a fair statement; a man\u2019s daily labour\nis about 4 lbs. of coals. The extreme toil of this ascent arises from\nother obvious causes than the mere height.\n\n[20] Its surface is about 40,000 acres, and medium depth about 20 feet.\nIt was proposed to drain it by running embankments across it, and thus\ncutting it up into more manageable portions to be drained by windmills.\n\n[21] No one doubts the _practicability_ of the undertaking. Eight or\nnine thousand chaldrons of coals duly burnt would evacuate the whole\ncontents. But many doubt whether it would be profitable, and some,\nconsidering that a few hundreds of fishermen who gain their livelihood\non its waters would be dispossessed, deny that it would be _desirable_.\n\n[22] \u201cExperiments to determine the Force of fired Gunpowder.\u201d Phil.\nTrans. vol. lxxxvii. p. 254. et seq.\n\n[23] See a very ingenious application of this kind in Mr. Babbage\u2019s\narticle on Diving in the Encyc. Metrop.--Others will readily suggest\nthemselves. For instance, the ballast in reserve of a balloon might\nconsist of materials capable of evolving great quantities of hydrogen\ngas in proportion to their weight, should such be found.\n\n[24] The sulphuric. Bracconot, Annales de Chimie, vol. xii. p. 184.\n\n[25] D\u2019Arcet, Annales de l\u2019Industrie, Fevrier, 1829.\n\n[26] See Dr. Prout\u2019s account of the experiments of professor Autenrieth\nof Tubingen. Phil. Trans. 1827, p. 381. This discovery, which renders\nfamine next to _impossible_, deserves a higher degree of celebrity than\nit has obtained.\n\n[27] Greenwich.\n\n[28] Maskelyne\u2019s.\n\n[29] Thomson\u2019s First Principles of Chemistry, vol. ii. p. 68.\n\n[30] Galileo exposes unsparingly the Aristotelian style of reasoning.\nThe reader may take the following from him as a specimen of its\nquality. The object is to prove the immutability and incorruptibility\nof the heavens; and thus it is done:--\n\n    I. Mutation is either generation or corruption.\n\n   II. Generation and corruption only happen between contraries.\n\n  III. The motions of contraries are contrary.\n\n   IV. The celestial motions are circular.\n\n    V. Circular motions have no contraries.\n\n      \u03b1. Because there can be but three simple motions.\n             1. To a centre.\n             2. Round a centre.\n             3. From a centre.\n\n      \u03b2. Of three things, one only can be contrary to one.\n\n      \u03b3. But a motion to a centre is manifestly the contrary to a\n          motion from a centre.\n\n      \u03b4. Therefore a motion _round_ a centre (_i.\u00a0e._ a circular\n          motion) remains without a contrary.\n\n   VI. _Therefore_ celestial motions have no contraries--_therefore_\n         among celestial _things_ there are no contraries--_therefore_\n         the heavens are eternal, immutable, incorruptible, and so forth.\n\nIt is evident that all this string of nonsense depends on the excessive\nvagueness of the notions of generation, corruption, contrariety, &c. on\nwhich the changes are rung.--_See_ GALILEO, _Systema Cosmicum_, Dial.\ni. p. 30.\n\n[31] Macquer justly observes, that the alchemists would have rendered\nessential service to chemistry had they only related their unsuccessful\nexperiments as clearly as they have obscurely related those which they\npretend to have been successful.--_Macquer\u2019s Dictionary of Chemistry_,\ni. x.\n\n[32] Paracelsus performed most of these cures by mercury and opium,\nthe use of which latter drug he had learned in Turkey. Of mercurial\npreparations the physicians of his time were ignorant, and of opium\nthey were afraid, as being \u201ccold in the fourth degree.\u201d Tartar was\nlikewise a great favourite of Paracelsus, who imposed on it that name,\n\u201cbecause it contains the water, the salt, the oil, and the acid, which\nburn the patient as hell does:\u201d in short, a kind of counterbalance to\nhis opium.\n\n[33] See the Life of Galileo Galilei, by Mr. Drinkwater, with\nIllustrations of the Advancement of Experimental Philosophy.\n\n[34] The temporary star in Cassiopeia observed by Cornelius Gemma, in\n1572, was so bright as to be seen at noon-day. That in Serpentarius,\nfirst seen by Kepler in 1604, exceeded in brilliancy all the other\nstars and planets.\n\n[35] Edinburgh Phil. Journ. 1819, vol. i. p. 8.\n\n[36] The abstract principle of repetition in matters of measurement\n(viz. juxta-position of units without error) is applicable to a great\nvariety of cases in which quantities are required to be determined to\nminute nicety. In chemistry, in determining the standard atomic weights\nof bodies, it seems easily and completely applicable, by a process\nwhich will suggest itself at once to every chemist, and seems the only\nthing wanting to place the exactness of chemical determinations on a\npar with astronomical measurements.\n\n[37] Accurate and _perfectly_ authentic copies of the yard and pound,\nexecuted in platina, and hermetically sealed in glass, should be\ndeposited deep in the interior of the massive stone-work of some great\npublic building, whence they could only be rescued with a degree\nof difficulty sufficient to preclude their being disturbed unless\non some very high and urgent occasion. The fact should be publicly\nrecorded, and its memory preserved by an inscription. Indeed, how much\nvaluable and useful information of the actual existing state of arts\nand knowledge at any period might be transmitted to posterity in a\ndistinct, tangible, and imperishable form, if, instead of the absurd\nand useless deposition of a few coins and medals under the foundations\nof buildings, specimens of ingenious implements or condensed statements\nof scientific truths, or processes in arts and manufactures, were\nsubstituted. Will books infallibly preserve to a remote posterity all\nthat we may desire should be hereafter known of ourselves and our\ndiscoveries, or all that posterity would wish to know? and may not a\nuseless ceremony be thus transformed into an act of enrolment in a\nperpetual archive of what we most prize, and acknowledge to be most\nvaluable?\n\n[38] In the system alluded to, the name of quartz is assigned to\niolite and obsidian; that of mica to plumbago, chlorite, and uranite;\nsulphur, to orpiment and realgar, &c. See Mohs\u2019s System of Mineralogy,\ntranslated by Haidinger.\n\n[39] The following passage, from Lindley\u2019s Synopsis of the British\nFlora, characterises justly the respective merits, in a philosophical\npoint of view, of natural and artificial systems of classification\nin general, though limited in its expression to his own immediate\nscience:--\u201cAfter all that has been effected, or is likely to be\naccomplished hereafter, there will always be more difficulty in\nacquiring a knowledge of the natural system of botany than of the\nLinn\u00e6an. The latter skims only the surface of things, and leaves the\nstudent in the fancied possession of a sort of information which it is\neasy enough to obtain, but which is of little value when acquired: the\nformer requires a minute investigation of every part and every property\nknown to exist in plants; but when understood has conveyed to the mind\na store of real information, of the utmost use to man in every station\nof life. Whatever the difficulties may be of becoming acquainted with\nplants according to this method, they are inseparable from botany,\nwhich cannot be usefully studied without encountering them.\u201d Schiller\nhas some beautiful lines on this, entitled \u201cMenschliches Wissen\u201d (or\nHuman Knowledge); Gedichte, vol. i. p. 72. Leipzig, 1800.\n\n[40] Lyell\u2019s Principles of Geology, vol. i. Fourrier, M\u00e9m. de l\u2019Acad.\ndes Sciences, tom. vii. p. 592. \u201cL\u2019\u00e9tablissement et le progr\u00e8s des\nsoci\u00e9t\u00e9s humaines, l\u2019action des forces naturelles, peuvent changer\nnotablement, et dans de vastes contr\u00e9es, l\u2019\u00e9tat de la surface du sol,\nla distribution des eaux, et les grands mouvemens de l\u2019air. De tels\neffets sont propres \u00e0 faire varier, dans le cours de plusieurs si\u00e8cles,\nle d\u00e9gr\u00e9 de la chaleur moyenne; car les expressions analytiques\ncomprennent des coefficiens qui se rapportent \u00e0 l\u2019\u00e9tat superficiel,\net qui influent beaucoup sur la valeur de la temp\u00e9rature.\u201d In this\nenumeration, by M. Fourrier, of causes which may vary the general\nrelation of the surface of extensive continents to heat, it is but\njustice to Mr. Lyell to observe, that the gradual shifting of the\n_places_ of the continents themselves on the surface of the globe,\nby the abrading action of the sea on the one hand, and the elevating\nagency of subterranean forces on the other, does not expressly occur\nand cannot be fairly included in the general sense of the passage,\nwhich confines itself to the consideration of such changes as may take\nplace on the existing surface of the land.\n\n[41] The reader will find this subject further developed in a paper\nlately communicated to the Geological Society.\n\n[42] Phil. Trans. 1824.\n\n[43] Wells on Dew.\n\n[44] Principia, book iii. prop. 6.\n\n[45] A very curious instance of the pursuit of a law completely\nempirical into an extreme case is to be found in Newton\u2019s rule for\nthe dilatation of his coloured rings seen between glasses at great\nobliquities. Optics, book ii. part i. obs. 7.\n\n[46] See Phil. Trans. 1819.\n\n[47] \u201cWhen we are told that Saturn moves in his orbit more than 22,000\nmiles an hour, we fancy the motion to be swift; but when we find that\nhe is more than three hours moving his own diameter, we must then think\nit, as it really is, slow.\u201d Thirty Letters on various Subjects, by\nWilliam Jackson, 1795.\n\n[48] Thomson\u2019s First Principles of Chemistry.\n\n[49] There seems no doubt, however, that an achromatic telescope had\nbeen constructed by a private amateur, a Mr. Hall, some time before\neither Euler or Dollond ever thought of it.\n\n[50] We allude to the recently invented achromatic combinations of\nMessrs. Barlow and Rogers, and the dense glasses of which Mr. Faraday\nhas recently explained the manufacture in a memoir full of the most\nbeautiful examples of delicate and successful chemical manipulation,\nand which promise to give rise to a new era in optical practice, by\nwhich the next generation at least may benefit. See Phil. Trans. 1830.\n\n[51] Alphonso of Castile, 1252.\n\n[52] Jackson, Letters on Various Subjects, &c.\n\n[53] Thomson\u2019s First Principles of Chemistry, Introduction.\n\n[54] The progress of astronomical discovery has since shown that this\nlaw cannot be relied on (1851).\n\n[55] Novum Organum, part ii. table 2. (24), (30), &c. on the form or\nnature of heat.\n\n[56] We will mention one which we do not remember to have seen\nnoticed elsewhere in the case of a disturbance of the equilibrium of\nheat produced by means purely mechanical, and by a process depending\nentirely on a certain order and sequence of events, and the operation\nof known causes. Suppose a quantity of air enclosed in a metallic\nreservoir, of some good conductor of heat, and suddenly compressed by\na piston. After giving time for the heat developed by the condensation\nto be communicated from the air to the metal which will be thereby\nmore or less raised in temperature _above_ the surrounding atmosphere,\nlet the piston be suddenly retracted and the air restored to its\noriginal volume in an instant. The whole apparatus is now precisely in\nits initial situation, as to the disposition of its material parts,\nand the whole quantity of heat it contains remains unchanged. But it\nis evident that the distribution of this heat within it is now very\ndifferent from what it was before; for the air in its sudden expansion\ncannot re-absorb in an instant of time all the heat it had parted with\nto the metal: it will, therefore, have a temperature _below_ that of\nthe general atmosphere, while the metal yet retains one above it. Thus,\na subversion of the equilibrium of temperature has been _bon\u00e2 fide_\neffected. Heat has been driven from the air into the metal, while every\nthing else remains unchanged.\n\nWe have here a means by which, it is evident, heat may be obtained, to\nany extent, from the air, without fuel. For if, in place of withdrawing\nthe piston and letting the _same_ air expand, within the reservoir, it\nbe allowed to escape so suddenly as not to re-absorb the heat given\noff, and fresh air be then admitted and the process repeated, any\nquantity of air may thus be _drained_ of its heat.\n\n[57] See Phil. Trans. 1824.\n\n[58] If the brain be an electric pile, constantly in action, it may be\nconceived to discharge itself at regular intervals, when the tension\nof the electricity developed reaches a certain point, along the nerves\nwhich communicate with the heart, and thus to excite the pulsations of\nthat organ. This idea is forcibly suggested by a view of that elegant\napparatus, the dry pile of Deluc; in which the successive accumulations\nof electricity are carried off by a suspended ball, which is kept by\nthe discharges in a state of regular pulsation for any length of time.\nWe have witnessed the action of such a pile maintained in this way for\nwhole years in the study of the above-named eminent philosopher. The\nsame idea of the cause of the pulsation of the heart appears to have\noccurred to Dr. Arnott; and is mentioned in his useful and excellent\nwork on physics, to which however, we are not indebted for the\nsuggestion, it having occurred to us independently many years ago.\n\n[59] See a description of a contrivance of this kind by Dr. Young,\nLectures, vol. i. p. 191.\n\n[60] Boyle\u2019s Works, folio, vol. iii. Essay x. p. 185.\n\n[61] Jackson, The Four Ages, p. 52. London: Cadell and Davies, 1798.\n8vo.\n\n[62] Jackson, The Four Ages, p. 90.\n\n\n\n\nTranscriber\u2019s Notes\n\n\nCover created by Transcriber and placed in the Public Domain.\n\nPunctuation, hyphenation, and spelling were made consistent when a\npredominant preference was found in this book; otherwise they were not\nchanged.\n\nSimple typographical errors were corrected; occasional unbalanced\nquotation marks retained.\n\nAmbiguous hyphens at the ends of lines were retained.\n\nSpelling of non-English words was not reviewed.\n\nText uses both \u201cappreciate\u201d and \u201cappretiate\u201d; both retained.\n\nIndex not checked for proper alphabetization or correct page references.","title":"Preliminary Discourse on the Study of Natural Philosophy","tradition":"philosophy-ethics","translated_text":null,"word_count":99710}