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diff --git a/old/54897-0.txt b/old/54897-0.txt deleted file mode 100644 index e92fa9e..0000000 --- a/old/54897-0.txt +++ /dev/null @@ -1,10610 +0,0 @@ -The Project Gutenberg EBook of Preliminary Discourse on the Study of -Natural Philosophy, by John F. W. Herschel - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: Preliminary Discourse on the Study of Natural Philosophy - -Author: John F. W. Herschel - -Release Date: June 12, 2017 [EBook #54897] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK PRELIMINARY DISCOURSE--NATURAL PHILOSOPHY *** - - - - -Produced by Sonya Schermann, Charlie Howard, and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - - - - - - - - - _PRELIMINARY DISCOURSE_ - on the Study of - NATURAL PHILOSOPHY - - BY - SIR JOHN F. W. HERSCHEL, BART. K.H. - _M.A.--D.C.L.--F.R.S.L&E.--M.R.I.A.--F.R.A.S. - F.G.S.--M.C.U.P.S.--&c. &c._ - - - NEW EDITION. - 1851. - -[Illustration: - - _H. Corbould del._ _E. Finden. sculp._ - -NATURÆ MINISTER ET INTERPRES.] - - - NEW EDITION. - - London: - PRINTED FOR LONGMAN, BROWN, GREEN & LONGMANS, PATERNOSTER ROW - - - - -CONTENTS. - - - Page - PART I. - - OF THE GENERAL NATURE AND ADVANTAGES OF THE STUDY OF THE - PHYSICAL SCIENCES. - - - CHAP. I. - - Of Man regarded as a Creature of Instinct, of Reason, and - Speculation.--General Influence of Scientific Pursuits on - the Mind. 1 - - - CHAP. II. - - Of abstract Science as a Preparation for the Study of Physics.-- - A profound Acquaintance with it not indispensable for a - clear Understanding of Physical Laws.--How a Conviction - of their Truth may be obtained without it.--Instances.-- - Further Division of the Subject. 18 - - - CHAP. III. - - Of the Nature and Objects, immediate and collateral, of - Physical Science, as regarded in itself, and in its - Application to the practical Purposes of Life, and its - Influence on the Well-being and Progress of Society. 35 - - - PART II. - - OF THE PRINCIPLES ON WHICH PHYSICAL SCIENCE RELIES FOR ITS - SUCCESSFUL PROSECUTION, AND THE RULES BY WHICH A SYSTEMATIC - EXAMINATION OF NATURE SHOULD BE CONDUCTED, WITH ILLUSTRATIONS - OF THEIR INFLUENCE AS EXEMPLIFIED IN THE HISTORY OF ITS - PROGRESS. - - - CHAP. I. - - Of Experience as the Source of our Knowledge.--Of the - Dismissal of Prejudices.--Of the Evidence of our Senses. 75 - - - CHAP. II. - - Of the Analysis of Phenomena. 85 - - - CHAP. III. - - Of the State of Physical Science in General, previous to the - Age of Galileo and Bacon. 104 - - - CHAP. IV. - - Of the Observation of Facts and the Collection of Instances. 118 - - - CHAP. V. - - Of the Classification of Natural Objects and Phenomena, and of - Nomenclature. 135 - - - CHAP. VI. - - Of the First Stage of Induction.--The Discovery of Proximate - Causes, and Laws of the lowest Degree of Generality, and - their Verification. 144 - - - CHAP. VII. - - Of the higher Degrees of Inductive Generalization, and of the - Formation and Verification of Theories. 190 - - - PART III. - - OF THE SUBDIVISION OF PHYSICS INTO DISTINCT BRANCHES, AND THEIR - MUTUAL RELATIONS. - - - CHAP. I. - - Of the Phenomena of Force, and of the Constitution of Natural - Bodies. 221 - - - CHAP. II. - - Of the Communication of Motion through Bodies.--Of Sound and - Light. 246 - - - CHAP. III. - - Of Cosmical Phenomena. 265 - - - CHAP. IV. - - Of the Examination of the material Constituents of the World. - 290 - - - CHAP. V. - - Of the Imponderable Forms of Matter. 310 - - - CHAP. VI. - - Of the Causes of the actual rapid Advance of the Physical - Sciences compared with their Progress at an earlier Period. 347 - - - - - “In primis, hominis est propria VERI inquisitio atque - investigatio. Itaque cum sumus negotiis necessariis, curisque - vacui, tum avemus aliquid videre, audire, ac dicere, - cognitionemque rerum, aut occultarum aut admirabilium, ad benè - beatéque vivendum necessariam ducimus;--ex quo intelligitur, - quod VERUM, simplex, sincerumque sit, id esse naturæe hominis - aptissimum. Huic veri videndi cupiditati adjuncta est appetitio - quædam principatûs, ut nemini parere animus benè a naturâ - informatus velit, nisi præcipienti, aut docenti, aut utilitatis - causa justè et legitimè imperanti: ex quo animi magnitudo - existit, et humanararum rerum contemtio.” - - CICERO, DE OFFICIIS, Lib. 1. § 13. - - - Before all other things, man is distinguished by his pursuit - and investigation of TRUTH. And hence, when free from needful - business and cares, we delight to see, to hear, and to - communicate, and consider a knowledge of many admirable and - abstruse things necessary to the good conduct and happiness of - our lives: whence it is clear that whatsoever is TRUE, simple, - and direct, the same is most congenial to our nature as men. - Closely allied with this earnest longing to see and know the - truth, is a kind of dignified and princely sentiment which - forbids a mind, naturally well constituted, to submit its - faculties to any but those who announce it in precept or in - doctrine, or to yield obedience to any orders but such as are - at once just, lawful, and founded on utility. From this source - spring greatness of mind and contempt of worldly advantages and - troubles. - - - - - PRELIMINARY DISCOURSE - ON - THE STUDY - OF - NATURAL PHILOSOPHY. - - - - - PART I. - - OF THE GENERAL NATURE AND ADVANTAGES OF THE STUDY OF - THE PHYSICAL SCIENCES - - - - -CHAPTER I. - - OF MAN REGARDED AS A CREATURE OF INSTINCT, OF REASON, AND - SPECULATION.--GENERAL INFLUENCE OF SCIENTIFIC PURSUITS ON THE - MIND. - - -(1.) The situation of man on the globe he inhabits, and over which he -has obtained the control, is in many respects exceedingly remarkable. -Compared with its other denizens, he seems, if we regard only his -physical constitution, in almost every respect their inferior, and -equally unprovided for the supply of his natural wants and his defence -against the innumerable enemies which surround him. No other animal -passes so large a portion of its existence in a state of absolute -helplessness, or falls in old age into such protracted and lamentable -imbecility. To no other warm-blooded animal has nature denied that -indispensable covering without which the vicissitudes of a temperate -and the rigours of a cold climate are equally insupportable; and to -scarcely any has she been so sparing in external weapons, whether for -attack or defence. Destitute alike of speed to avoid and of arms to -repel the aggressions of his voracious foes; tenderly susceptible of -atmospheric influences; and unfitted for the coarse aliments which the -earth affords spontaneously during at least two thirds of the year, -even in temperate climates,--man, if abandoned to mere instinct, would -be of all creatures the most destitute and miserable. Distracted by -terror and goaded by famine; driven to the most abject expedients -for concealment from his enemies, and to the most cowardly devices -for the seizure and destruction of his nobler prey, his existence -would be one continued subterfuge or stratagem;--his dwelling would -be in dens of the earth, in clefts of rocks, or in the hollows of -trees; his food worms, and the lower reptiles, or such few and crude -productions of the soil as his organs could be brought to assimilate, -varied with occasional relics, mangled by more powerful beasts of prey, -or contemned by their more pampered choice. Remarkable only for the -absence of those powers and qualities which obtain for other animals a -degree of security and respect, he would be disregarded by some, and -hunted down by others, till after a few generations his species would -become altogether extinct, or, at best, would be restricted to a few -islands in tropical regions, where the warmth of the climate, the -paucity of enemies, and the abundance of vegetable food, might permit -it to linger. - -(2.) Yet man is the undisputed lord of the creation. The strongest -and fiercest of his fellow-creatures,--the whale, the elephant, the -eagle, and the tiger,--are slaughtered by him to supply his most -capricious wants, or tamed to do him service, or imprisoned to make -him sport. The spoils of all nature are in daily requisition for his -most common uses, yielded with more or less readiness, or wrested with -reluctance, from the mine, the forest, the ocean, and the air. Such -are the first fruits of reason. Were they the only or the principal -ones, were the mere acquisition of power over the materials, and the -less gifted animals which surround us, and the consequent increase -of our external comforts, and our means of preservation and sensual -enjoyment, the sum of the privileges which the possession of this -faculty conferred, we should after all have little to plume ourselves -upon. But this is so far from being the case, that every one who passes -his life in tolerable ease and comfort, or rather whose whole time -is not anxiously consumed in providing the absolute necessaries of -existence, is conscious of wants and cravings in which the senses have -no part, of a series of pains and pleasures totally distinct in kind -from any which the infliction of bodily misery or the gratification -of bodily appetites has ever afforded him; and if he has experienced -these pleasures and these pains in any degree of intensity, he will -readily admit them to hold a much higher rank, and to deserve much -more attention, than the former class. Independent of the pleasures -of fancy and imagination, and social converse, man is constituted a -speculative being; he contemplates the world, and the objects around -him, not with a passive, indifferent gaze, as a set of phenomena in -which he has no further interest than as they affect his immediate -situation, and can be rendered subservient to his comfort, but as -a system disposed with order and design. He approves and feels the -highest admiration for the harmony of its parts, the skill and -efficiency of its contrivances. Some of these which he can best trace -and understand he attempts to imitate, and finds that to a certain -extent, though rudely and imperfectly, he can succeed,--in others, that -although he can comprehend the nature of the contrivance, he is totally -destitute of all means of imitation;--while in others, again, and those -evidently the most important, though he sees the effect produced, -yet the means by which it is done are alike beyond his knowledge -and his control. Thus he is led to the conception of a Power and an -Intelligence superior to his own, and adequate to the production and -maintenance of all that he sees in nature,--a Power and Intelligence to -which he may well apply the term infinite, since he not only sees no -actual limit to the instances in which they are manifested, but finds, -on the contrary, that the farther he enquires, and the wider his sphere -of observation extends, they continually open upon him in increasing -abundance; and that as the study of one prepares him to understand and -appreciate another, refinement follows on refinement, wonder on wonder, -till his faculties become bewildered in admiration, and his intellect -falls back on itself in utter hopelessness of arriving at an end. - -(3.) When from external objects he turns his view upon himself, on his -own vital and intellectual faculties, he finds that he possesses a -power of examining and analysing his own nature to a certain extent, -but no farther. In his corporeal frame he is sensible of a power to -communicate a certain moderate amount of motion to himself and other -objects; that this power depends on his will, and that its exertion -can be suspended or increased at pleasure within certain limits; but -_how_ his will acts on his limbs he has no consciousness: and whence he -derives the power he thus exercises, there is nothing to assure him, -however he may long to know. His senses, too, inform him of a multitude -of particulars respecting the external world, and he perceives an -apparatus by which impressions from without may be transmitted, as a -sort of signals to the interior of his person, and ultimately to his -brain, wherein he is obscurely sensible that the thinking, feeling, -reasoning being he calls _himself_, more especially resides; but by -what means he becomes conscious of these impressions, and what is the -nature of the immediate communication between that inward sentient -being, and that machinery, his outward man, he has not the slightest -conception. - -(4.) Again, when he contemplates still more attentively the thoughts, -acts, and passions of this his sentient intelligent self, he finds, -indeed, that he can remember, and by the aid of memory can compare -and discriminate, can judge and resolve, and, above all, that he is -irresistibly impelled, from the perception of any phenomenon without -or within him, to infer the existence of something prior which stands -to it in the relation of a _cause_, without which it would not be, and -that this knowledge of causes and their consequences is what, in almost -every instance, determines his choice and will, in cases where he is -nevertheless conscious of perfect freedom to act or not to act. He -finds, too, that it is in his power to acquire more or less knowledge -of causes and effects according to the degree of attention he bestows -upon them, which attention is again in great measure a voluntary act; -and often when his choice has been decided on imperfect knowledge or -insufficient attention, he finds reason to correct his judgment, though -perhaps too late to influence his decision by after consideration. A -world within him is thus opened to his intellectual view, abounding -with phenomena and relations, and of the highest immediate interest. -But while he cannot help perceiving that the insight he is enabled to -obtain into this internal sphere of thought and feeling is in reality -the source of all his power, the very fountain of his predominance over -external nature, he yet feels himself capable of entering only very -imperfectly into these recesses of his own bosom, and analysing the -operations of his mind,--in this as in all other things, in short, “_a -being darkly wise_;” seeing that all the longest life and most vigorous -intellect can give him power to discover by his own research, or time -to know by availing himself of that of others, serves only to place -him on the very frontier of knowledge, and afford a distant glimpse -of boundless realms beyond, where no human thought has penetrated, -but which yet he is sure must be no less familiarly known to that -Intelligence which he traces throughout creation than the most obvious -truths which he himself daily applies to his most trifling purposes. -Is it wonderful that a being so constituted should first encourage a -hope, and by degrees acknowledge an assurance, that his intellectual -existence will not terminate with the dissolution of his corporeal -frame, but rather that in a future state of being, disencumbered of -a thousand obstructions which his present situation throws in his -way, endowed with acuter senses, and higher faculties, he shall drink -deep at that fountain of beneficent wisdom for which the slight taste -obtained on earth has given him so keen a relish? - -(5.) Nothing, then, can be more unfounded than the objection which has -been taken, _in limine_, by persons, well meaning perhaps, certainly -narrow-minded, against the study of natural philosophy, and indeed -against all science,--that it fosters in its cultivators an undue and -overweening self-conceit, leads them to doubt the immortality of the -soul, and to scoff at revealed religion. Its natural effect, we may -confidently assert, on every well constituted mind is and must be -the direct contrary. No doubt, the testimony of natural reason, on -whatever exercised, must of necessity stop short of those truths which -it is the object of revelation to make known; but, while it places -the existence and principal attributes of a Deity on such grounds as -to render doubt impossible, it unquestionably opposes no natural or -necessary obstacle to further progress: on the contrary, by cherishing -as a vital principle an unbounded spirit of enquiry, and ardency of -expectation, it unfetters the mind from prejudices of every kind, and -leaves it open and free to every impression of a higher nature which -it is susceptible of receiving, guarding only against enthusiasm and -self-deception by a habit of strict investigation, but encouraging, -rather than suppressing, every thing that can offer a prospect or a -hope beyond the present obscure and unsatisfactory state. The character -of the true philosopher is to hope all things not impossible, and to -believe all things not unreasonable. He who has seen obscurities which -appeared impenetrable in physical and mathematical science suddenly -dispelled, and the most barren and unpromising fields of enquiry -converted, as if by inspiration, into rich and inexhaustible springs -of knowledge and power on a simple change of our point of view, or -by merely bringing to bear on them some principle which it never -occurred before to try, will surely be the very last to acquiesce in -any dispiriting prospects of either the present or future destinies of -mankind; while, on the other hand, the boundless views of intellectual -and moral as well as material relations which open on him on all hands -in the course of these pursuits, the knowledge of the trivial place he -occupies in the scale of creation, and the sense continually pressed -upon him of his own weakness and incapacity to suspend or modify the -slightest movement of the machinery he sees in action around him, must -effectually convince him that humility of pretension, no less than -confidence of hope, is what best becomes his character. - -(6.) But while we thus vindicate the study of natural philosophy from a -charge at one time formidable, owing to the pertinacity and acrimony -with which it was urged, and still occasionally brought forward to -the distress and disgust of every well constituted mind, we must -take care that the testimony afforded by science to religion, be its -extent or value what it may, shall be at least independent, unbiassed, -and spontaneous. We do not here allude to such reasoners as would -make all nature bend to their narrow interpretations of obscure and -difficult passages in the sacred writings: such a course might well -become the persecutors of Galileo and the other bigots of the fifteenth -and sixteenth centuries, but can only be adopted by dreamers in the -present age. But, without going these lengths, it is no uncommon thing -to find persons, earnestly attached to science and anxious for its -promotion, who yet manifest a morbid sensibility on points of this -kind,--who exult and applaud when any fact starts up explanatory (as -they suppose) of some scriptural allusion and who feel pained and -disappointed when the general course of discovery in any department -of science runs wide of the notions with which particular passages in -the Bible may have impressed themselves. To persons of such a frame of -mind it ought to suffice to remark, on the one hand, that truth can -never be opposed to truth, and, on the other, that error is only to be -effectually confounded by searching deep and tracing it to its source. -Nevertheless, it were much to be wished that such persons, estimable -and excellent as many of them are, before they throw the weight of -their applause or discredit into the scale of scientific opinion on -such grounds, would reflect, first, that the credit and respectability -of _any_ evidence may be destroyed by tampering with its _honesty_; -and, secondly, that this very disposition of mind implies a lurking -mistrust in its own principles, since the grand and indeed only -character of truth is its capability of enduring the test of universal -experience, and coming unchanged out of every possible form of _fair_ -discussion. - -(7.) But if science may be vilified by representing it as opposed to -religion, or trammelled by mistaken notions of the danger of free -enquiry, there is yet another mode by which it may be degraded from -its native dignity, and that is by placing it in the light of a mere -appendage to and caterer for our pampered appetites. The question -“_cui bono_” to what practical end and advantage do your researches -tend? is one which the speculative philosopher who loves knowledge -for its own sake, and enjoys, as a rational being should enjoy, the -mere contemplation of harmonious and mutually dependent truths, can -seldom hear without a sense of humiliation. He feels that there is a -lofty and disinterested pleasure in his speculations which ought to -exempt them from such questioning; communicating as they do to his own -mind the purest happiness (after the exercise of the benevolent and -moral feelings) of which human nature is susceptible, and tending to -the injury of no one, he might surely allege _this_ as a sufficient -and direct reply to those who, having themselves little capacity, and -less relish for intellectual pursuits, are constantly repeating upon -him this enquiry. But if he can bring himself to descend from this -high but fair ground, and justify himself, his pursuits, and his -pleasures in the eyes of those around him, he has only to point to the -history of all science, where speculations, apparently unprofitable, -have, in innumerable instances, been those from which great practical -applications have emanated. What, for instance, could be more so than -the dry speculations of the ancient geometers on the properties of the -conic sections, or than the dreams of Kepler (as they would naturally -appear to his contemporaries) about the numerical harmonies of the -universe? Yet these are the steps by which we have risen to a knowledge -of the elliptic motions of the planets and the law of gravitation, -with all its splendid theoretical consequences, and its inestimable -practical results. The ridicule attached to “_Swing-swangs_” in -Hooke’s time[1] did not prevent him from reviving the proposal of the -_pendulum_ as a standard of measure, since so effectually wrought into -practice by the genius and perseverance of Captain Kater;--nor did -that which Boyle encountered in his researches on the elasticity and -pressure of the air act as any obstacle to the train of discovery which -terminated in the steam-engine. The dreams of the alchemists led them -on in the path of experiment, and drew attention to the wonders of -chemistry, while they brought their advocates (it must be admitted) to -merited contempt and ruin. But in this case it was moral dereliction -which gave to ridicule a weight and power not necessarily or naturally -belonging to it: but among the alchemists were men of superior minds, -who reasoned while they worked, and who, not content to grope always in -the dark, and blunder on their object, sought carefully in the observed -nature of their agents for guides in their pursuit. To these we owe the -creation of experimental philosophy. - -(8.) Not that it is meant, by any thing above said, to assert -that there is no such thing as a great or a little in speculative -philosophy, or to place the solution of an enigma on a level with -the developement of a law of nature, still less to adopt the homely -definition of Smith[2], that a philosopher is a person whose trade it -is to do nothing, and speculate on every thing. The speculations of -the natural philosopher, however remote they may for a time lead him -from beaten tracks and every-day uses, being grounded in the realities -of nature, have all, of necessity, a practical application,--nay -more, such applications form the very criterions of their truth, -they afford the readiest and completest verifications of his -theories;--verifications which he will no more neglect to test them by -than an arithmetician would omit to _prove_ his sums, or a cautious -geometer to try his general theorems by particular cases.[3] - -(9.) After all, however, it must be confessed, that to minds -unacquainted with science, and unused to consider the mutual -dependencies of its various branches, there is something neither -unnatural nor altogether blamable in the ready occurrence of this -question of direct advantage. It requires some habit of abstraction, -some penetration of the mind with a tincture of scientific enquiry, -some conviction of the value of those estimable and treasured -principles which lie concealed in the most common and homely -facts,--some experience, in fine, of success in developing and placing -them in evidence, announcing them in precise terms, and applying them -to the explanation of other facts of a less familiar character, or to -the accomplishment of some obviously useful purpose:--to cure the mind -of this tendency to rush at once upon its object, to undervalue the -means in over-estimation of the end, and while gazing too intently at -the goal which alone it has been accustomed to desire, to lose sight -of the richness and variety of the prospects that offer themselves on -either hand on the road. - -(10.) We must never forget that it is principles, not phenomena,--the -interpretation, not the mere knowledge of facts,--which are the -objects of enquiry to the natural philosopher. As truth is single, -and consistent with itself, a principle may be as completely and as -plainly elucidated by the most familiar and simple fact, as by the -most imposing and uncommon phenomenon. The colours which glitter on -a soap-bubble are the immediate consequence of a principle the most -important from the variety of phenomena it explains, and the most -beautiful, from its simplicity and compendious neatness, in the whole -science of optics. If the nature of periodical colours can be made -intelligible by the contemplation of such a trivial object, from that -moment it becomes a noble instrument in the eye of correct judgment; -and to blow a large, regular, and durable soap-bubble may become the -serious and praiseworthy endeavour of a sage, while children stand -round and scoff, or children of a larger growth hold up their hands -in astonishment at such waste of time and trouble. To the natural -philosopher there is no natural object unimportant or trifling. From -the least of nature’s works he may learn the greatest lessons. The fall -of an apple to the ground may raise his thoughts to the laws which -govern the revolutions of the planets in their orbits; or the situation -of a pebble may afford him evidence of the state of the globe he -inhabits, myriads of ages ago, before his species became its denizens. - -(11.) And this is, in fact, one of the great sources of delight -which the study of natural science imparts to its votaries. A mind -which has once imbibed a taste for scientific enquiry, and has -learnt the habit of applying its principles readily to the cases -which occur, has within itself an inexhaustible source of pure and -exciting contemplations:--one would think that Shakspeare had such -a mind in view when he describes a contemplative man as finding all -nature eloquent--the very trees, the brooks, and the stones reading -to him lessons of deep and serious import. Accustomed to trace the -operation of general causes, and the exemplification of general laws, -in circumstances where the uninformed and unenquiring eye perceives -neither novelty nor beauty, he walks in the midst of wonders: every -object which falls in his way elucidates some principle, affords some -instruction, and impresses him with a sense of harmony and order. Nor -is it a mere passive pleasure which is thus communicated. A thousand -questions are continually arising in his mind, a thousand subjects of -enquiry presenting themselves, which keep his faculties in constant -exercise, and his thoughts perpetually on the wing, so that lassitude -is excluded from his life, and that craving after artificial excitement -and dissipation of mind, which leads so many into frivolous, unworthy, -and destructive pursuits, is altogether eradicated from his bosom. - -(12.) It is not one of the least advantages of these pursuits, which, -however, they possess in common with every class of intellectual -pleasures, that they are altogether independent of external -circumstances, and are to be enjoyed in every situation in which a man -can be placed in life. The highest degrees of worldly prosperity are so -far from being incompatible with them, that they supply inestimable -advantages for their pursuit, and that sort of fresh and renewed relish -which arises partly from the sense of contrast, partly from experience -of the peculiar pre-eminence they possess over the pleasures of sense -in their capability of unlimited increase and continual repetition -without satiety or distaste. They may be enjoyed, too, in the intervals -of the most active business; and the calm and dispassionate interest -with which they fill the mind renders them a most delightful retreat -from the agitations and dissensions of the world, and from the conflict -of passions, prejudices, and interests in which the man of business -finds himself involved. There is something in the contemplation of -general laws which powerfully induces and persuades us to merge -individual feeling, and to commit ourselves unreservedly to their -disposal; while the observation of the calm, energetic regularity of -nature, the immense scale of her operations, and the certainty with -which her ends are attained, tends, irresistibly, to tranquillize and -re-assure the mind, and render it less accessible to repining, selfish, -and turbulent emotions. And this it does, not by debasing our nature -into weak compliances and abject submission to circumstances, but by -filling us, as from an inward spring, with a sense of nobleness and -power which enables us to rise superior to them; by showing us our -strength and innate dignity, and by calling upon us for the exercise -of those powers and faculties by which we are susceptible of the -comprehension of so much greatness, and which form, as it were, a link -between ourselves and the best and noblest benefactors of our species, -with whom we hold communion in thoughts and participate in discoveries -which have raised them above their fellow-mortals, and brought them -nearer to their Creator. - - - - -CHAP. II. - - OF ABSTRACT SCIENCE AS A PREPARATION FOR THE STUDY OF PHYSICS.--A - PROFOUND ACQUAINTANCE WITH IT NOT INDISPENSABLE FOR A CLEAR - UNDERSTANDING OF PHYSICAL LAWS.--HOW A CONVICTION OF THEIR TRUTH - MAY BE OBTAINED WITHOUT IT.--INSTANCES.--FURTHER DIVISION OF THE - SUBJECT. - - -(13.) Science is the knowledge of many, orderly and methodically -digested and arranged, so as to become attainable by one. The knowledge -of reasons and their conclusions constitutes _abstract_, that of causes -and their effects, and of the laws of nature, _natural science_. - -(14.) Abstract science is independent of a system of nature,--of a -creation,--of every thing, in short, except memory, thought, and -reason. Its objects are, first, those primary existences and relations -which we cannot even conceive not to _be_, such as space, time, -number, order, &c.; and, secondly, those artificial forms, or symbols, -which thought has the power of creating for itself at pleasure, and -substituting as representatives, by the aid of memory, for combinations -of those primary objects and of its own conceptions,--either to -facilitate the act of reasoning respecting them, or as convenient -deposits of its own conclusions, or for their communication to others. -Such are, first, _language_, oral or written; its conventional forms, -which constitute grammar, and the rules for its use in argument, -in which consists the logic of the schools; secondly, _notation_, -which, applied to _number_, is _arithmetic_,--and, to the more general -relations of abstract quantity or order, is _algebra_; and, thirdly, -that higher kind of logic, which teaches us to use our reason in the -most advantageous manner for the discovery of truth; which points -out the criterions by which we may be sure we have attained it; and -which, by detecting the sources of error, and exposing the haunts where -fallacies are apt to lurk, at once warns us of their danger, and shows -us how to avoid them. This greater logic may be termed _rational_[4]; -while, to that inferior department which is conversant with words -alone, the epithet _verbal_[5] may, for distinction, be applied. - -(15.) A certain moderate degree of acquaintance with abstract science -is highly desirable to every one who would make any considerable -progress in physics. As the universe exists in time and place; and as -motion, velocity, quantity, number, and order, are main elements of -our knowledge of external things and their changes, an acquaintance -with these, abstractedly considered, (that is to say, independent of -any consideration of the particular things moved, measured, counted, -or arranged,) must evidently be a useful preparation for the more -complex study of nature. But there is yet another recommendation of -such sciences as a preparation for the study of natural philosophy. -Their objects are so definite, and our notions of them so distinct, -that we can reason about them with an assurance, that the words and -signs used in our reasonings are full and true representatives of the -things signified; and, consequently, that when we use language or signs -in argument, we neither, by their use, introduce extraneous notions, -nor exclude any part of the case before us from consideration. For -example: the words space, square, circle, a hundred, &c., convey to -the mind notions so complete in themselves, and so distinct from every -thing else, that we are sure when we use them we know and have in -view the whole of our own meaning. It is widely different with words -expressing natural objects and mixed relations. Take, for instance, -iron. Different persons attach very different ideas to this word. One -who has never heard of magnetism has a widely different notion of -_iron_ from one in the contrary predicament. The vulgar, who regard -this metal as incombustible, and the chemist, who sees it burn with the -utmost fury, and who has other reasons for regarding it as one of the -most combustible bodies in nature;--the poet, who uses it as an emblem -of rigidity; and the smith and engineer, in whose hands it is plastic, -and moulded like wax into every form;--the jailer, who prizes it as -an obstruction, and the electrician, who sees in it only a channel of -open communication by which that most impassable of obstacles, the -air, may be traversed by his imprisoned fluid, have all different, and -all imperfect, notions of the same word. The meaning of such a term -is like a rainbow--every body sees a different one, and all maintain -it to be the same. So it is with nearly all our terms of sense. Some -are indefinite, as hard or soft, light or heavy (terms which were at -one time the sources of innumerable mistakes and controversies); some -excessively complex, as man, life, instinct. But, what is worst of -all, some, nay most, have two or three meanings; sufficiently distinct -from each other to make a proposition true in one sense and false in -another, or even false altogether; yet not distinct enough to keep us -from confounding them in the process by which we arrived at it, or -to enable us immediately to recognise the fallacy when led to it by -a train of reasoning, each step of which we _think_ we have examined -and approved. Surely those who thus attach two senses to one word, or -superadd a new meaning to an old one, act as absurdly as colonists who -distribute themselves over the world, naming every place they come -to by the names of those they have left, till all distinctions of -geographical nomenclature are confounded, and till we are unable to -decide whether an occurrence stated to have happened at Windsor took -place in Europe, America, or Australia.[6] - -(16.) It is, in fact, in this double or incomplete sense of words that -we must look for the origin of a very large portion of the errors -into which we fall. Now, the study of the abstract sciences, such as -arithmetic, geometry, algebra, &c., while they afford scope for the -exercise of reasoning about objects that are, or, at least, may be -conceived to be, external to us; yet, being free from these sources -of error and mistake, accustom us to the strict use of language as -an instrument of reason, and by familiarizing us, in our progress -towards truth, to walk uprightly and straight-forward on firm ground, -give us that proper and dignified carriage of mind which could never -be acquired by having always to pick our steps among obstructions -and loose fragments, or to steady them in the reeling tempest of -conflicting meanings. - -(17.) But there is yet another point of view under which some -acquaintance with abstract science may be regarded as highly desirable -in general education, if not indispensably necessary, to impress on us -the distinction between strict and vague reasoning, to show us what -demonstration really _is_, and to give us thereby a full and intimate -sense of the nature and strength of the evidence on which our knowledge -of the actual system of nature, and the laws of natural phenomena, -rests. For this purpose, however, a very moderate acquaintance with the -more elementary branches of mathematics may suffice. The chain is laid -before us, and every link is submitted to our unreserved examination, -if we have patience and inclination to enter on such detail. Hundreds -have gone through it, and will continue to do so; but, for the -generality of mankind, it is enough to satisfy themselves of the -solidity and adamantine texture of its materials, and the unreserved -exposure of its weakest, as well as its strongest, parts. If, however, -we content ourselves with this general view of the matter, we must be -content also to take on trust, that is, on the authority of those who -have examined deeper, every conclusion which cannot be made apparent -to our senses. Now, among these there are many so very surprising, -indeed apparently so extravagant, that it is quite impossible for any -enquiring mind to rest contented with a mere hearsay statement of -them,--we feel irresistibly impelled to enquire further into their -truth. What mere assertion will make any man believe, that in one -second of time, in one beat of the pendulum of a clock, a ray of light -travels over 192,000 miles, and would therefore perform the tour of the -world in about the same time that it requires to wink with our eyelids, -and in much less than a swift runner occupies in taking a single -stride? What mortal can be made to believe, without demonstration, that -the sun is almost a million times larger than the earth? and that, -although so remote from us, that a cannon ball shot directly towards -it, and maintaining its full speed, would be twenty years in reaching -it, it yet affects the earth by its attraction in an inappreciable -instant of time?--a closeness of union of which we can form but a -feeble, and totally inadequate, idea, by comparing it to any material -connection; since the communication of an impulse to such a distance, -by any solid intermedium we are acquainted with, would require, not -moments, but whole years. And when, with pain and difficulty we have -strained our imagination to conceive a distance so vast, a force so -intense and penetrating, if we are told that the one dwindles to an -insensible point, and the other is unfelt at the nearest of the fixed -stars, from the mere effect of their remoteness, while among those -very stars are some whose actual splendour exceeds by many hundred -times that of the sun itself, although we may not deny the truth of the -assertion, we cannot but feel the keenest curiosity to know _how_ such -things were ever made out. - -(18.) The foregoing are among those results of scientific research -which, by their magnitude, seem to transcend our powers of conception. -There are others, again, which, from their minuteness, would appear -to elude the grasp of thought, much more of distinct and accurate -measurement. Who would not ask for demonstration, when told that a -gnat’s wing, in its ordinary flight, beats many hundred times in a -second? or that there exist animated and regularly organized beings, -many thousands of whose bodies laid close together would not extend an -inch? But what are these to the astonishing truths which modern optical -enquiries have disclosed, which teach us that every point of a medium -through which a ray of light passes is affected with a succession of -periodical movements, regularly recurring at equal intervals, no less -than five hundred millions of millions of times in a single second! -that it is by such movements, communicated to the nerves of our eyes, -that we see:--nay more, that it is the _difference_ in the frequency of -their recurrence which affects us with the sense of the diversity of -colour; that, for instance, in acquiring the sensation of redness our -eyes are affected four hundred and eighty-two millions of millions of -times; of yellowness, five hundred and forty-two millions of millions -of times; and of violet, seven hundred and seven millions of millions -of times per second.[7] Do not such things sound more like the ravings -of madmen, than the sober conclusions of people in their waking senses? - -(19.) They are, nevertheless, conclusions to which any one may most -certainly arrive, who will only be at the trouble of examining the -chain of reasoning by which they have been deduced; but, in order -to do this, something beyond the mere elements of abstract science -is required. Waving, however, such instances as these, which, after -all, are rather calculated to surprise and astound than for any other -purpose, it must be observed that it is not possible to satisfy -ourselves completely that we _have_ arrived at a true statement of any -law of nature, until, setting out from such statement, and making it -a foundation of reasoning, we can show, by strict argument, that the -facts observed must follow from it as necessary logical consequences, -and _this_, not vaguely and generally, but with all possible precision -in time, place, weight, and measure. - -(20.) To do this, however, as we shall presently see, requires in many -cases a degree of knowledge of mathematics and geometry altogether -unattainable by the generality of mankind, who have not the leisure, -even if they all had the capacity, to enter into such enquiries, -some of which are indeed of that degree of difficulty that they can -be only successfully prosecuted by persons who devote to them their -whole attention, and make them the serious business of their lives. -But there is scarcely any person of good ordinary understanding, -however little exercised in abstract enquiries, who may not be readily -made to comprehend at least the general train of reasoning by which -any of the great truths of physics are deduced, and the essential -bearings and connections of the several parts of natural philosophy. -There are whole branches too and very extensive and important ones, to -which mathematical reasoning has never been at all applied; such as -chemistry, geology, and natural history in general, and many others, -in which it plays a very subordinate part, and of which the essential -principles, and the grounds of application to useful purposes, may -be perfectly well understood by a student who possesses no more -mathematical knowledge than the rules of arithmetic; so that no one -need be deterred from the acquisition of knowledge, or even from -active original research in such subjects, by a want of mathematical -information. Even in those branches which, like astronomy, optics, and -dynamics, are almost exclusively under the dominion of mathematics, and -in which no effectual progress can be made without _some_ acquaintance -with geometry, the principal _results_ may be perfectly understood -without it. To one incapable of following out the intricacies of -mathematical demonstration, the conviction afforded by verified -predictions must stand in the place of that purer and more satisfactory -reliance which a verification of every step in the process of reasoning -can alone afford, since every one will acknowledge the validity of -pretensions which he is in the daily habit of seeing brought to the -test of practice. - -(21.) Among the verifications of this practical kind which abound -in every department of physics, there are none more imposing than -the precise prediction of the greater phenomena of astronomy; none, -certainly, which carry a broader conviction home to every mind from -their notoriety and unequivocal character. The prediction of eclipses -has accordingly from the earliest ages excited the admiration of -mankind, and been one grand instrument by which their allegiance (so -to speak) to natural science, and their respect for its professors, -has been maintained; and though strangely abused in unenlightened ages -by the supernatural pretensions of astrologers, the credence given -even to their absurdities shows the force of this kind of evidence on -men’s minds. The predictions of astronomers are, however, now far too -familiar to endanger the just equipoise of our judgment, since even the -return of comets, true to their paths and exact to the hour of their -appointment, has ceased to amaze, though it must ever delight all who -have souls capable of being penetrated by such beautiful instances of -accordance between theory and facts. But the age of mere wonder in -such things is past, and men prefer being guided and enlightened, to -being astonished and dazzled. Eclipses, comets, and the like, afford -but rare and transient displays of the powers of calculation, and of -the certainty of the principles on which it is grounded. A page of -“lunar distances” from the Nautical Almanack is worth all the eclipses -that have ever happened for inspiring this necessary confidence in the -conclusions of science. That a man, by merely measuring the moon’s -apparent distance from a star with a little portable instrument held -in his hand, and applied to his eye, even with so unstable a footing -as the deck of a ship, shall say positively, within five miles, where -he is, on a boundless ocean, cannot but appear to persons ignorant of -physical astronomy an approach to the miraculous. Yet, the alternatives -of life and death, wealth and ruin, are daily and hourly staked with -perfect confidence on these marvellous computations, which might -almost seem to have been devised on purpose to show how closely the -extremes of speculative refinement and practical utility can be brought -to approximate. We have before us an anecdote communicated to us by -a naval officer[8], distinguished for the extent and variety of his -attainments, which shows how impressive such results may become in -practice. He sailed from San Blas on the west coast of Mexico, and -after a voyage of 8000 miles, occupying 89 days, arrived off Rio de -Janeiro, having, in this interval, passed through the Pacific Ocean, -rounded Cape Horn, and crossed the South Atlantic, without making any -land, or even seeing a single sail, with the exception of an American -whaler off Cape Horn. Arrived within a week’s sail of Rio, he set -seriously about determining, by lunar observations, the precise line -of the ship’s course and its situation in it at a determinate moment, -and having ascertained this within from five to ten miles, ran the -rest of the way by those more ready and compendious methods, known to -navigators, which can be safely employed for short trips between one -known point and another, but which cannot be trusted in long voyages, -where the moon is the only sure guide. The rest of the tale we are -enabled by his kindness to state in his own words:--“We steered towards -Rio de Janeiro for some days after taking the lunars above described, -and having arrived within fifteen or twenty miles of the coast, I hove -to at four in the morning till the day should break, and then bore -up; for although it was very hazy, we could see before us a couple of -miles or so. About eight o’clock it became so foggy that I did not -like to stand in farther, and was just bringing the ship to the wind -again before sending the people to breakfast, when it suddenly cleared -off, and I had the satisfaction of seeing the great Sugar Loaf Rock, -which stands on one side of the harbour’s mouth, so nearly right ahead -that we had not to alter our course above a point in order to hit the -entrance of Rio. This was the first land we had seen for three months, -after crossing so many seas and being set backwards and forwards by -innumerable currents and foul winds.” The effect on all on board might -well be conceived to have been electric; and it is needless to remark -how essentially the authority of a commanding officer over his crew may -be strengthened by the occurrence of such incidents, indicative of a -degree of knowledge and consequent power beyond their reach. - -(22.) But even such results as these, striking as they are, yet fall -short of the force with which conviction is urged upon us when, -through the medium of reasoning too abstract for common apprehension, -we arrive at conclusions which outrun experience, and describe -beforehand what will happen under new combinations, or even correct -imperfect experiments, and lead us to a knowledge of facts contrary -to received analogies drawn from an experience wrongly interpreted -or overhastily generalised. To give an example:--every body knows -that objects viewed through a transparent medium, such as water or -glass, appear distorted or displaced. Thus, a stick in water appears -bent, and an object seen through a prism or wedge of glass seems to -be thrown aside from its true place. This effect is owing to what is -called the _refraction_ of light; and a simple rule discovered by -Willebrod Snell enables any one to say exactly _how much_ the stick -will be bent, and _how far_, and in what _direction_, the apparent -situation of an object seen through the glass will deviate from the -real one. If a shilling be laid at the bottom of a basin of water -and viewed obliquely, it will appear to be raised by the water; if -instead of water spirits of wine be used it will appear more raised; -if oil, still more:--but in none of these cases will it appear to be -thrown _aside_ to the _right_ or _left_ of its true place, however -the eye be situated. The _plane_, in which are contained the eye, -the object, and the point in the surface of the liquid at which the -object is seen, is an upright or _vertical_ plane; and this is one of -the principal characters in the _ordinary refraction_ of light, viz. -that the ray by which we see an object through a refracting surface, -although it undergoes a bending, and is, as it were, broken at the -surface, yet, in pursuing its course to the eye, does not _quit a plane -perpendicular to the refracting surface_. But there are again other -substances, such as rock-crystal, and especially Iceland spar, which -possess the singular property of _doubling_ the image or appearance -of an object seen through them in certain directions; so that instead -of seeing one object we see two, side by side, when such a crystal or -spar is interposed between the object and the eye; and if a ray or -small sunbeam be thrown upon a surface of either of these substances, -it will be split into two, making an angle with each other, and each -pursuing its own separate course,--this is called _double refraction_. -Now, of these images or doubly refracted rays, one always follows -the same rule as if the substance were glass or water: its deviation -can be correctly calculated by Snell’s law above mentioned, and it -does not quit the plane perpendicular to the refracting surface. The -other ray, on the contrary, (which is therefore said to have undergone -_extraordinary refraction_) _does_ quit that plane, and the amount of -its deviation from its former course requires for its determination a -much more complicated rule, which cannot be understood or even stated -without a pretty intimate knowledge of geometry. Now, rock-crystal -and Iceland spar differ from glass in a very remarkable circumstance. -They affect naturally certain regular figures, not being found in -shapeless lumps, but in determinate geometrical forms; and they are -susceptible of being cleft or split much easier in certain directions -than in others--they have a _grain_ which glass has not. When other -substances having this peculiarity (and which are called _crystallized_ -substances) were examined, they were all, or by far the greater part, -found to possess this singular property of _double refraction_; and -it was very natural to conclude, therefore, that the same thing took -place in all of them, viz. that of the two rays, into which any beam of -light falling on the surface of such a substance was split, or of the -two images of an object seen through it, _one_ only was turned aside -out of its _plane_ and _extraordinarily_ refracted, while the other -followed the _ordinary_ rule. Accordingly this was supposed to be the -case; and not only so, but from some trials and measurements purposely -made by a philosopher of great eminence, it was considered to be a fact -sufficiently established by experiment. - -(23.) Perhaps we might have remained long under this impression, for -the measurements are delicate, and the subject very difficult. But -it has lately been demonstrated by an eminent French philosopher and -mathematician, M. Fresnel, that, granting certain _principles_ or -postulates, all the phenomena of double refraction, including perhaps -the greatest variety of facts that have ever yet been arranged under -one general head, may be satisfactorily explained and deduced from them -by strict mathematical calculation; and _that_, when applied to the -cases first mentioned, these principles give a satisfactory account -of the _want_ of the extraordinary image; _that_ when applied to such -cases as those of rock-crystal or Iceland spar, they also give a -correct account of both the images, and agree in their conclusions with -the rules before ascertained for them: but so far from coinciding with -that part of the previous statement, which would make these conclusions -extend to all crystallised substances, M. Fresnel’s principles lead -to a conclusion quite opposite, and point to a _fact_ which had never -been observed, viz. that in by far the greater number of crystallized -substances which possess the property of double refraction, _neither_ -of the images follows the ordinary law, but both undergo a deviation -from their original plane. Now this had never been observed to be -the case in any previous trial, and all opinion was against it. But -when put to the test of experiment in a great variety of new and -ingenious methods, it was found to be fully verified; and to complete -the evidence, the substances on whose imperfect examination the -first erroneous conclusion was founded, having been lately subjected -to a fresh and more scrupulous examination, the result has shown -the insufficiency of the former measurements, and proved in perfect -accordance with the newly discovered laws. Now it will be observed -in this case, first, that, so far from the principles assumed by M. -Fresnel being at all obvious, they are extremely remote from ordinary -observation; and, secondly, that the chain of reasoning by which they -are brought to the test is one of such length and complexity, and the -purely mathematical difficulty of their application so great, that -no _mere_ good common sense, no general tact or ordinary practical -reasoning, would afford the slightest chance of threading their -mazes. Cases like this are the triumph of theories. They show at once -how large a part pure reason has to perform in our examination of -nature, and how implicit our reliance ought to be on that powerful and -methodical system of rules and processes which constitute the modern -mathematical analysis, in all the more difficult applications of exact -calculation to her phenomena. - -(24.) To take an instance more within ordinary apprehension. An -eminent living geometer had proved by calculations, founded on strict -optical principles, that in the _centre of the shadow_ of a small -circular plate of metal, exposed in a dark room to a beam of light -emanating from a _very small brilliant point_, there ought to be no -darkness,--in fact, _no shadow_ at that place; but, on the contrary, a -degree of illumination precisely as bright as if the metal plate were -away. Strange and even impossible as this conclusion may seem, it has -been put to the trial, and found perfectly correct.[9] - -(25.) We shall now proceed to consider more particularly, and in -detail,-- - - I. The nature and objects immediate and collateral of physical - science, as regarded in itself, and in its application to - the practical purposes of life, and its influence on the - well-being and progress of society. - - II. The principles on which it relies for its successful - prosecution, and the rules by which a systematic examination - of nature should be conducted, with examples illustrative of - their influence. - - III. The subdivision of physical science into distinct branches, - and their mutual relations. - - - - -CHAP. III. - - OF THE NATURE AND OBJECTS, IMMEDIATE AND COLLATERAL, OF PHYSICAL - SCIENCE, AS REGARDED IN ITSELF, AND IN ITS APPLICATION TO THE - PRACTICAL PURPOSES OF LIFE, AND ITS INFLUENCE ON THE WELL-BEING - AND PROGRESS OF SOCIETY. - - -(26.) The first thing impressed on us from our earliest infancy is, -that events do not succeed one another at random, but with a certain -degree of order, regularity, and connection;--some constantly, and, as -we are apt to think, immutably,--as the alternation of day and night, -summer and winter,--others contingently, as the motion of a body from -its place, if pushed, or the burning of a stick if thrust into the -fire. The knowledge that the former class of events _has_ gone on, -uninterruptedly, for ages beyond all memory, impresses us with a strong -expectation that it will continue to do so in the same manner; and -thus our notion of an _order of nature_ is originated and confirmed. -If every thing were equally regular and periodical, and the succession -of events liable to no change depending on our own will, it may be -doubted whether we should ever think of looking for causes. No one -regards the night as the cause of the day, or the day of night. They -are alternate effects of a common cause, which their regular succession -alone gives us no sufficient clue for determining. It is chiefly, -perhaps entirely, from the other or contingent class of events that -we gain our notions of cause and effect. From them alone we gather -that there are such things as laws of nature. The very idea of a law -includes that of contingency. “_Si quis mala carmina condidisset, fuste -ferito_;” if such a case arise, such a course shall be followed,--if -the match be applied to the gunpowder, it will explode. Every law is a -provision for cases which _may_ occur, and has relation to an infinite -number of cases that never have occurred, and never will. Now, it is -this provision, _à priori_, for contingencies, this contemplation -of possible occurrences, and predisposal of what shall happen, that -impresses us with the notion of a _law_ and a _cause_. Among all the -possible combinations of the fifty or sixty elements which chemistry -shows to exist on the earth, it is likely, nay almost certain, that -_some_ have never been formed; that some elements, in some proportions, -and under some circumstances, have never yet been placed in relation -with one another. Yet no chemist can doubt that it is _already fixed_ -what they will do when the case does occur. They will obey certain -laws, of which we know nothing at present, but which must _be_ already -fixed, or they could not be laws. It is not by habit, or by trial -and failure, that they will learn what to do. When the contingency -occurs, there will be no hesitation, no consultation;--their course -will at once be decided, and will always be the same if it occur ever -so often in succession, or in ever so many places at one and the same -instant. This is the perfection of a law, that it includes all possible -contingencies, and ensures implicit obedience,--and of this kind are -the laws of nature. - -(27.) This use of the word _law_, however, our readers will of course -perceive has relation to us as understanding, rather than to the -materials of which the universe consists as obeying, certain rules. -To obey a law, to act in _compliance_ with a rule, supposes an -understanding and a will, a power of complying or not, in the being who -obeys and complies, which we do not admit as belonging to mere matter. -The Divine Author of the universe cannot be supposed to have laid down -particular laws, enumerating all individual contingencies, which his -materials have understood and obey,--this would be to attribute to -him the imperfections of human legislation;--but rather, by creating -them, endued with certain fixed qualities and powers, he has impressed -them in their origin with the _spirit_, not the _letter_, of his law, -and made all their subsequent combinations and relations inevitable -consequences of this first impression, by which, however, we would no -way be understood to deny the constant exercise of his direct power in -maintaining the system of nature, or the ultimate emanation of every -energy which material agents exert from his immediate will, acting in -conformity with his own laws. - -(28.) The discoveries of modern chemistry have gone far to establish -the truth of an opinion entertained by some of the ancients, that -the universe consists of distinct, separate, indivisible _atoms_, -or individual beings so minute as to escape our senses, except when -united by millions, and by this aggregation making up bodies of even -the smallest visible bulk; and we have the strongest evidence that, -although there exist great and essential differences in individuals -among these atoms, they may yet all be arranged in a very limited -number of groups or classes, all the individuals of each of which -are, to all intents and purposes, _exactly alike_ in all their -properties. Now, when we see a great number of things precisely alike, -we do not believe this similarity to have originated except from a -common principle independent of them; and that we recognise this -likeness, chiefly by the identity of their deportment under similar -circumstances, strengthens rather than weakens the conclusion. A line -of spinning-jennies[10], or a regiment of soldiers dressed exactly -alike, and going through precisely the same evolutions, gives us no -idea of independent existence: we must see them act out of concert -before we can believe them to have independent wills and properties, -not impressed on them from without. And this conclusion, which would -be strong even were there only two individuals precisely alike in -_all_ respects and _for ever_, acquires irresistible force when their -number is multiplied beyond the power of imagination to conceive. If -we mistake not, then, the discoveries alluded to effectually destroy -the idea of an _eternal self-existent matter_, by giving to each of its -atoms the essential characters, at once, of a _manufactured article_, -and a _subordinate agent_. - -(29.) But to ascend to the origin of things, and speculate on the -creation, is not the business of the natural philosopher. An humbler -field is sufficient for him in the endeavour to discover, as far -as our faculties will permit, what _are_ these primary qualities -originally and unalterably impressed on matter, and to discover the -_spirit_ of the laws of nature, which includes groups and classes of -relations and facts from the _letter_ which, as before observed, is -presented to us by single phenomena: or if, after all, this should -prove impossible; if such a step be beyond our faculties; and the -essential qualities of material agents be really _occult_, or incapable -of being expressed in any form intelligible to our understandings, at -least to approach as near to their comprehension as the nature of the -case will allow; and devise such forms of words as shall include and -_represent_ the greatest possible multitude and variety of phenomena. - -(30.) Now, in this research there would seem one great question to -be disposed of before our enquiries can even be commenced with any -thing like a prospect of success, which is, whether the laws of -nature themselves _have_ that degree of permanence and fixity which -can render them subjects of systematic discussion; or whether, on the -other hand, the qualities of natural agents are subject to mutation -from the lapse of time. To the ancients, who lived in the infancy of -the world, or rather, in the infancy of man’s experience, this was a -very rational subject of question, and hence their distinctions between -corruptible and incorruptible matter. Thus, according to some among -them, the matter only of the celestial spaces is pure, immutable, and -incorruptible, while all sublunary things are in a constant state of -lapse and change; the world becoming paralysed and effete with age, -and man himself deteriorating in character, and diminishing at once in -intellectual and bodily stature. But to us, who have the experience -of some additional thousands of years, the question of permanence is -already, in a great measure, decided in the affirmative. The refined -speculations of modern astronomy, grounding their conclusions on -observations made at very remote periods, have proved to demonstration, -that one at least of the great powers of nature, the force of -gravitation, the main bond and support of the material universe, has -undergone no change in intensity from a high antiquity. The stature of -mankind is just what it was three thousand years ago, as the specimens -of mummies which have been examined at various times sufficiently -show. The intellect of Newton, Laplace, or Lagrange, may stand in -fair competition with that of Archimedes, Aristotle, or Plato; and the -virtues and patriotism of Washington with the brightest examples of -ancient history. - -(31.) Again, the researches of chemists have shown that what the -vulgar call corruption, destruction, &c., is nothing but a change of -arrangement of the same ingredient elements, the disposition of the -same materials into other forms, without the loss or actual destruction -of a single atom; and thus any doubts of the permanence of natural -laws are discountenanced, and the whole weight of _appearances_ thrown -into the opposite scale. One of the most obvious cases of apparent -destruction is, when any thing is ground to dust and scattered to the -winds. But it is one thing to grind a fabric to powder, and another to -annihilate its materials: scattered as they may be, they must fall -somewhere, and continue, if only as ingredients of the soil, to perform -their humble but useful part in the economy of nature. The destruction -produced by fire is more striking: in many cases, as in the burning -of a piece of charcoal or a taper, there is no smoke, nothing visibly -dissipated and carried away; the burning body wastes and disappears, -while nothing _seems_ to be produced but warmth and light, which we -are not in the habit of considering as substances; and when all has -disappeared, except perhaps some trifling ashes, we naturally enough -suppose it is gone, lost, destroyed. But when the question is examined -more exactly, we detect, in the invisible stream of heated air which -ascends from the glowing coal or flaming wax, the _whole_ ponderable -matter, only united in a new combination with the air, and dissolved in -it. Yet, so far from being thereby destroyed, it is only become again -what it was before it existed in the form of charcoal or wax, an active -agent in the business of the world, and a main support of vegetable -and animal life, and is still susceptible of running again and again -the same round, as circumstances may determine; so that, for aught we -can see to the contrary, the same identical atom may lie concealed for -thousands of centuries in a limestone rock; may at length be quarried, -set free in the limekiln, mix with the air, be absorbed from it by -plants, and, in succession, become a part of the frames of myriads of -living beings, till some concurrence of events consigns it once more to -a long repose, which, however, no way unfits it from again resuming its -former activity. - -(32.) Now, this absolute indestructibility of the ultimate materials -of the world, in periods commensurate to our experience, and their -obstinate retention of the same properties, under whatever variety of -circumstances we choose to place them, however violent and seemingly -contradictory to their natures, is, of itself, enough to render it -highly improbable that time alone should have any influence over -them. All that age or decay can do seems to be included in a wasting -of parts which are only dissipated, not destroyed, or in a change of -sensible properties, which chemistry demonstrates to arise only from -new combinations of the same ingredients. But, after all, the question -is one entirely of experience: we cannot be sure, _à priori_, that -the laws of nature are _immutable_; but we can ascertain, by enquiry, -_whether they change or not_; and to this enquiry all experience -answers in the negative. It is not, of course, intended here to -deny that great operations, productive of extensive changes in the -visible state of nature,--such as, for instance, those contemplated -by the geologists, and embracing for their completion vast periods -of time,--are constantly going on; but these are consequences and -fulfilments of the laws of nature, not contradictions or exceptions -to them. No theorist regards such changes as alterations in the -fundamental principles of nature; he only endeavours to reconcile them, -and show how they result from laws already known, and judges of the -correctness of his theory by their ultimate agreement. - -(33.) But the laws of nature are not only permanent, but consistent, -intelligible, and discoverable with such a moderate degree of -research, as is calculated rather to stimulate than to weary curiosity. -If we were set down, as creatures of another world, in any existing -society of mankind, and began to speculate on their actions, we should -find it difficult at first to ascertain whether they were subject to -any laws at all: but when, by degrees, we had found out that they did -consider themselves to be so; and would then proceed to ascertain, from -their conduct and its consequences, what these laws were, and in what -spirit conceived; though we might not perhaps have much difficulty -in discovering single rules applicable to particular cases, yet, the -moment we came to generalize, and endeavour from these to ascend, step -by step, and discover any steady pervading principle, the mass of -incongruities, absurdities, and contradictions, we should encounter, -would either dishearten us from further enquiry or satisfy us that what -we were in search of did not exist. It is quite the contrary in nature; -there we find no contradictions, no incongruities, but all is harmony. -What once is learnt we never have to unlearn. As rules advance in -generality, apparent exceptions become regular; and equivoque, in her -sublime legislation, is as unheard of as maladministration. - -(34.) Living, then, in a world where such laws obtain, and under their -immediate dominion, it is manifestly of the utmost importance to know -them, were it for no other reason than to be sure, in all we undertake, -to have, at least, the law on our side, so as not to struggle in vain -against some insuperable difficulty opposed to us by natural causes. -What pains and expense would not the alchemists, for instance, have -been spared by a knowledge of those simple laws of composition and -decomposition, which now preclude all idea of the attainment of their -declared object! what an amount of ingenuity, thrown away on the -pursuit of the perpetual motion, might have been turned to better -use, if the simplest laws of mechanics had been known and attended to -by the inventors of innumerable contrivances destined to that end! -What tortures, inflicted on patients by imaginary cures of incurable -diseases, might have been dispensed with, had a few simple principles -of physiology been earlier recognised! - -(35.) But if the laws of nature, on the one hand, are invincible -opponents, on the other, they are irresistible auxiliaries; and it -will not be amiss if we regard them in each of those characters, and -consider the great importance of a knowledge of them to mankind,-- - - I. _In showing us how to avoid attempting impossibilities._ - - II. _In securing us from important mistakes in attempting what - is, in itself, possible, by means either inadequate, or - actually opposed, to the end in view._ - - III. _In enabling us to accomplish our ends in the easiest, - shortest, most economical, and most effectual manner._ - - IV. _In inducing us to attempt, and enabling us to accomplish, - objects which, but for such knowledge, we should never have - thought of undertaking._ - -We shall therefore proceed to illustrate by examples the effect of -physical knowledge under each of these heads:-- - -(36.) Ex. 1. (35.) I. It is not many years since an attempt was made -to establish a colliery at Bexhill, in Sussex. The appearance of -thin seams and sheets of fossil-wood and wood-coal, with some other -indications similar to what occur in the neighbourhood of the great -coal-beds in the north of England, having led to the sinking of a -shaft, and the erection of machinery on a scale of vast expense, not -less than eighty thousand pounds are said to have been laid out on -this project, which, it is almost needless to add, proved completely -abortive, as every geologist would have at once declared it must, the -whole assemblage of geological facts being adverse to the existence -of a regular coal-bed _in_ the Hastings’ _sand_; while this, on which -Bexhill is situated, is separated from the _coal-strata_ by a series -of interposed beds of such enormous thickness as to render all idea of -penetrating _through_ them absurd. The history of mining operations -is full of similar cases, where a very moderate acquaintance with the -_usual order of nature_, to say nothing of theoretical views, would -have saved many a sanguine adventurer from utter ruin. - -(37.) Ex. 2. (35.) II. The smelting of iron requires the application -of the most violent heat that can be raised, and is commonly performed -in tall furnaces, urged by great iron bellows driven by steam-engines. -Instead of employing this power to force _air_ into the furnace through -the intervention of bellows, it was, on one occasion, attempted to -employ the steam itself in, apparently, a much less circuitous manner; -viz. by directing the current of steam in a violent blast, from the -boiler at once into the fire. From one of the known ingredients of -steam being a highly inflammable body, and the other that essential -part of the air which supports combustion, it was imagined that this -would have the effect of increasing the fire to tenfold fury, whereas -it simply _blew it out_; a result which a slight consideration of the -laws of chemical combination, and the state in which the ingredient -elements exist in steam, would have enabled any one to predict without -a trial. - -(38.) Ex. 3. (35.) II. After the invention of the diving-bell, and its -success in subaqueous processes, it was considered highly desirable -to devise some means of remaining for any length of time under water, -and rising at pleasure without assistance, so as either to examine, -at leisure, the bottom, or perform, at ease, any work that might be -required. Some years ago, an ingenious individual proposed a project -by which this end was to be accomplished. It consisted in sinking -the hull of a ship made quite water-tight, with the decks and sides -strongly supported by shores, and the only entry secured by a stout -trap-door, in such a manner, that by disengaging, from within, the -weights employed to sink it, it might rise of itself to the surface. To -render the trial more satisfactory, and the result more striking, the -projector himself made the first essay. It was agreed that he should -sink in twenty fathoms water, and rise again without assistance at -the expiration of twenty-four hours. Accordingly, making all secure, -fastening down his trap-door, and provided with all necessaries, as -well as with the means of making signals to indicate his situation, -this unhappy victim of his own ingenuity entered and was sunk. No -signal was made, and the time appointed elapsed. An immense concourse -of people had assembled to witness his rising, but in vain; for the -vessel was never seen more. The pressure of the water at so great a -depth had, no doubt, been completely under-estimated, and the sides of -the vessel being at once crushed in, the unfortunate projector perished -before he could even make the signal concerted to indicate his distress. - -(39.) Ex. 4. (35.) III. In the granite quarries near Seringapatam the -most enormous blocks are separated from the solid rock by the following -neat and simple process. The workman having found a portion of the rock -sufficiently extensive, and situated near the edge of the part already -quarried, lays bare the upper surface, and marks on it a line in the -direction of the intended separation, along which a groove is cut with -a chisel about a couple of inches in depth. Above this groove a narrow -line of fire is then kindled, and maintained till the rock below is -thoroughly heated, immediately on which a line of men and women, each -provided with a pot full of cold water, suddenly sweep off the ashes, -and pour the water into the heated groove, when the rock at once -splits with a clean fracture. Square blocks of six feet in the side, -and upwards of eighty feet in length, are sometimes detached by this -method, or by another equally simple and efficacious, but not easily -explained without entering into particulars of mineralogical detail.[11] - -(40.) Ex. 5. (35.) III. Hardly less simple and efficacious is the -process used in some parts of France, where mill-stones are made. When -a mass of stone sufficiently large is found, it is cut into a cylinder -several feet high, and the question then arises how to subdivide -this into horizontal pieces so as to make as many mill-stones. For -this purpose horizontal indentations or grooves are chiselled out -quite round the cylinder, at distances corresponding to the thickness -intended to be given to the mill-stones, into which wedges of dried -wood are driven. These are then wetted, or exposed to the night dew, -and next morning the different pieces are found separated from each -other by the expansion of the wood, consequent on its absorption of -moisture; an irresistible natural power thus accomplishing, almost -without any trouble, and at no expense, an operation which, from -the peculiar hardness and texture of the stone, would otherwise -be impracticable but by the most powerful machinery or the most -persevering labour. - -(41.) Ex. 6. (35.) III. To accomplish our ends quickly is often of, at -least, as much importance as to accomplish them with little labour and -expense. There are innumerable processes which, if left to themselves, -_i. e._ to the ordinary operation of natural causes, are done, and well -done, but with extreme slowness, and in such cases it is often of -the highest practical importance to accelerate them. The bleaching of -linen, for instance, performed in the natural way by exposure to sun, -rain, and wind, requires many weeks or even months for its completion; -whereas, by the simple immersion of the cloth in a liquid, chemically -prepared, the same effect is produced in a few hours. The whole circle -of the arts, indeed, is nothing but one continued comment upon this -head of our subject. The instances above given are selected, not on -account of their superior importance, but for the simplicity and -_directness_ of application of the principles on which they depend, to -the objects intended to be attained. - -(42.) But so constituted is the mind of man, that his views enlarge, -and his desires and wants increase, in the full proportion of the -facilities afforded to their gratification, and, indeed, with augmented -rapidity, so that no sooner has the successful exercise of his powers -accomplished any considerable simplification or improvement of -processes subservient to his use or comfort, than his faculties are -again on the stretch to extend the limits of his newly acquired power; -and having once experienced the advantages which are to be gathered -by availing himself of some of the powers of nature to accomplish -his ends, he is led thenceforward to regard them all as a treasure -placed at his disposal, if he have only the art, the industry, or the -good fortune, to penetrate those recesses which conceal them from -immediate view. Having once learned to look on knowledge as power, and -to avail himself of it as such, he is no longer content to limit his -enterprises to the beaten track of former usage, but is constantly -led onwards to contemplate objects which, in a previous stage of his -progress, he would have regarded as unattainable and visionary, had he -even thought of them at all. It is here that the investigation of the -hidden powers of nature becomes a mine, every vein of which is pregnant -with inexhaustible wealth, and whose ramifications appear to extend in -all directions wherever human wants or curiosity may lead us to explore. - -(43.) Between the physical sciences and the arts of life there subsists -a constant mutual interchange of good offices, and no considerable -progress can be made in the one without of necessity giving rise to -corresponding steps in the other. On the one hand, every art is in -some measure, and many entirely, dependent on those very powers and -qualities of the material world which it is the object of physical -enquiry to investigate and explain; and, accordingly, abundant examples -might be cited of cases where the remarks of experienced artists, or -even ordinary workmen, have led to the discovery of natural qualities, -elements, or combinations which have proved of the highest importance -in physics. Thus (to give an instance), a soap-manufacturer remarks -that the residuum of his ley, when exhausted of the alkali for which -he employs it, produces a corrosion of his copper boiler for which he -cannot account. He puts it into the hands of a scientific chemist for -analysis, and the result is the discovery of one of the most singular -and important chemical elements, iodine. The properties of this, -being studied, are found to occur most appositely in illustration -and support of a variety of new, curious, and instructive views then -gaining ground in chemistry, and thus exercise a marked influence -over the whole body of that science. Curiosity is excited: the origin -of the new substance is traced to the sea-plants from whose ashes -the principal ingredient of soap is obtained, and ultimately to the -sea-water itself. It is thence hunted through nature, discovered in -salt mines and springs, and pursued into all bodies which have a marine -origin; among the rest, into sponge. A medical practitioner[12] then -calls to mind a reputed remedy for the cure of one of the most grievous -and unsightly disorders to which the human species is subject--the -_goître_--which infests the inhabitants of mountainous districts to -an extent that in this favoured land we have happily no experience -of, and which was said to have been originally cured by the ashes of -burnt sponge. Led by this indication he tries the effect of iodine on -that complaint, and the result establishes the extraordinary fact that -this singular substance, taken as a medicine, acts with the utmost -promptitude and energy on _goître_, dissipating the largest and most -inveterate in a short time, and acting (of course, like all medicines, -even the most approved, with occasional failures,) as a specific, or -natural antagonist, against that odious deformity. It is thus that -any accession to our knowledge of nature is sure, sooner or later, to -make itself felt in some practical application, and that a benefit -conferred on science by the casual observation or shrewd remark of even -an unscientific or illiterate person infallibly repays itself with -interest, though often in a way that could never have been at first -contemplated. - -(44.) It is to such observation, reflected upon, however, and matured -into a rational and scientific form by a mind deeply imbued with the -best principles of sound philosophy, that we owe the practice of -vaccination; a practice which has effectually subdued, in every country -where it has been introduced, one of the most frightful scourges of -the human race, and in some extirpated it altogether. Happily for us -we know only by tradition the ravages of the small-pox, as it existed -among us hardly more than a century ago, and as it would in a few -years infallibly exist again, were the barriers which this practice, -and that of inoculation, oppose to its progress abandoned. Hardly -inferior to this terrible scourge on land was, within the last seventy -or eighty years, the scurvy at sea. The sufferings and destruction -produced by this horrid disorder on board our ships when, as a matter -of course, it broke out after a few months’ voyage, seem now almost -incredible. Deaths to the amount of eight or ten a day in a moderate -ship’s company; bodies sewn up in hammocks and washing about the decks -for want of strength and spirits on the part of the miserable survivors -to cast them overboard; and every form of loathsome and excruciating -misery of which the human frame is susceptible:--such are the pictures -which the narratives of nautical adventure in those days continually -offer.[13] At present the scurvy is almost completely eradicated in -the navy, partly, no doubt, from increased and increasing attention to -general cleanliness, comfort, and diet; but mainly from the constant -use of a simple and palatable preventive, the acid of the lemon, -served out in daily rations. If the gratitude of mankind be allowed on -all hands to be the just meed of the philosophic physician, to whose -discernment in seizing, and perseverance in forcing it on public notice -we owe the great safeguard of infant life, it ought not to be denied to -those[14] whose skill and discrimination have thus strengthened the -sinews of our most powerful arm, and obliterated one of the darkest -features in the most glorious of all professions. - -(45.) These last, however, are instances of simple observation, -limited to the point immediately in view, and assuming only so far the -character of science as a systematic adoption of good and rejection of -evil, when grounded on experience carefully weighed, justly entitle -it to do. They are not on that account less appositely cited as -instances of the importance of a knowledge of nature and its laws to -our well-being; though, like the great inventions of the mariner’s -compass and of gunpowder, they may have stood, in their origin, -unconnected with more general views. They are rather to be looked upon -as the spontaneous produce of a territory essentially fertile, than as -forming part of the succession of harvests which the same bountiful -soil, diligently cultivated, is capable of yielding. The history of -iodine above related affords, however, a perfect specimen of the -manner in which a knowledge of natural properties and laws, collected -from facts having no reference to the object to which they have -been subsequently applied, enables us to set in array the resources -of nature against herself; and deliberately, of afore-thought, to -devise remedies against the dangers and inconveniences which beset -us. In this view we might instance, too, the _conductor_, which, in -countries where thunder-storms are more frequent and violent than in -our own, and at sea (where they are attended with peculiar danger, -both from the greater probability of accident, and its more terrible -consequences when it does occur,) forms a most real and efficient -preservative against the effects of lightning[15]:--the _safety-lamp_, -which enables us to walk with light and security while surrounded with -an atmosphere more explosive than gunpowder:--the _life-boat_, which -cannot be sunk, and which offers relief in circumstances of all others -the most distressing to humanity, and of which a recent invention -promises to extend the principle to ships of the largest class:--the -_lighthouse_, with the capital improvements which the lenses of -Brewster and Fresnel, and the elegant lamp of lieutenant Drummond, have -conferred, and promise yet to confer by their wonderful powers, the one -of producing the most intense light yet known, the others of conveying -it undispersed to great distances:--the discovery of the disinfectant -powers of chlorine, and its application to the destruction of miasma -and contagion:--that of _quinine_, the essential principle in which -reside the febrifuge qualities of the Peruvian bark, a discovery by -which posterity is yet to benefit in its full extent, but which has -already begun to diffuse _comparative_ comfort and health through -regions almost desolated by pestiferous exhalations[16];--and, if we -desist, it is not because the list is exhausted, but because a sample, -not a catalogue, is intended. - -(46.) One instance more, however, we will add, to illustrate the -manner in which a most familiar effect, which seemed destined only -to amuse children, or, at best, to furnish a philosophic toy, may -become a safeguard of human life, and a remedy for a most serious -and distressing evil. In needle manufactories the workmen who point -the needles are constantly exposed to excessively minute particles of -steel which fly from the grindstones, and mix, though imperceptible -to the eye, as the finest dust in the air, and are inhaled with their -breath. The effect, though imperceptible on a short exposure, yet, -being constantly repeated from day to day, produces a constitutional -irritation dependent on the tonic properties of the steel, which is -sure to terminate in pulmonary consumption; insomuch, that persons -employed in this kind of work used scarcely ever to attain the age of -forty years.[17] In vain was it attempted to purify the air before its -entry into the lungs by gauzes or linen guards; the dust was too fine -and penetrating to be obstructed by such coarse expedients, till some -ingenious person bethought him of that wonderful power which every -child who searches for its mother’s needle with a magnet, or admires -the motions and arrangement of a few steel filings on a sheet of paper -held above it, sees in exercise. Masks of magnetized steel wire are now -constructed and adapted to the faces of the workmen. By these the air -is not merely _strained_ but _searched_ in its passage through them, -and each obnoxious atom arrested and removed. - -(47.) Perhaps there is no result which places in a stronger light the -advantages which are to be derived from a mere knowledge of the _usual -order of nature_, without any attempt on our part to modify it, and -apart from all consideration of its causes, than the institution of -life-assurances. Nothing is more uncertain than the life of a single -individual; and it is the sense of this insecurity which has given -rise to such institutions. They are, in their nature and objects, -the precise reverse of gambling speculations, their object being to -equalize vicissitude, and to place the pecuniary relations of numerous -masses of mankind, in so far as they extend, on a footing independent -of individual casualty. To do this with the greatest possible -advantage, or indeed with any advantage at all, it is necessary to know -the _laws of mortality_, or the average numbers of individuals, out -of a great multitude, who die at every period of life from infancy to -extreme old age. At first sight this would seem a hopeless enquiry; to -some, perhaps, a presumptuous one. But it has been made; and the result -is, that, abating extraordinary causes, such as wars, pestilence, and -the like, a remarkable regularity _does_ obtain, quite sufficient -to afford grounds not only for general estimations, but for nice -calculations of risk and adventure, such as infallibly to insure the -success of any such institution founded on good computations; and thus -to confer such stability on the fortunes of families dependent on the -exertions of one individual as to constitute an important feature in -modern civilization. The only thing to be feared in such institutions -is their too great multiplication and consequent competition, by which -a spirit of gambling and underbidding is liable to be generated among -their conductors, and the very mischief may be produced, on a scale of -frightful extent, which they are especially intended to prevent. - -(48.) We have hitherto considered only cases in which a knowledge of -natural laws enables us to improve our condition, by counteracting -evils of which, but for its possession, we must have remained forever -the helpless victims. Let us now take a similar view of those in which -we are enabled to call in nature as an auxiliary to augment our actual -power, and capacitate us for undertakings, which without such aid might -seem to be hopeless. Now, to this end, it is necessary that we should -form a just conception of what those hidden powers of nature _are_, -which we can at pleasure call into action;--how far they transcend -the measure of human force, and set at naught the efforts not only of -individuals but of whole nations of men. - -(49.) It is well known to modern engineers, that _there is virtue_ in a -bushel of coals properly consumed, to raise seventy millions of pounds -weight a foot high. This is actually the _average_ effect of an engine -at this moment working in Cornwall.[18] Let us pause a moment, and -consider what this is equivalent to in matters of practice. - -(50.) The ascent of Mont Blanc from the valley of Chamouni is -considered, and with justice, as the most toilsome feat that a strong -man can execute in two days. The combustion of two pounds of coal would -place him on the summit.[19] - -(51.) The Menai Bridge, one of the most stupendous works of art that -has been raised by man in modern ages, consists of a mass of iron, not -less than four millions of pounds in weight, suspended at a medium -height of about 120 feet above the sea. The consumption of seven -bushels of coal would suffice to raise it to the place where it hangs. - -(52.) The great pyramid of Egypt is composed of granite. It is 700 feet -in the side of its base, and 500 in perpendicular height, and stands on -eleven acres of ground. Its weight is, therefore, 12,760 millions of -pounds, at a medium height of 125 feet; consequently it would be raised -by the effort of about 630 chaldrons of coal, a quantity consumed in -some founderies in a week. - -(53.) The annual consumption of coal in London is estimated at -1,500,000 chaldrons. The effort of this quantity would suffice to raise -a cubical block of marble, 2200 feet in the side, through a space equal -to its own height, or to pile one such mountain upon another. The Monte -Nuovo, near Pozzuoli, (which was erupted in a single night by volcanic -fire,) might have been raised by such an effort, from a depth of 40,000 -feet, or about eight miles. - -(54.) It will be observed, that, in the above statement, the inherent -power of fuel is, of necessity, greatly under-rated. It is not -pretended by engineers that the economy of fuel is yet pushed to its -utmost limit, or that the whole effective power is obtained in any -application of fire yet devised; so that were we to say 100 millions -instead of 70, we should probably be nearer the truth. - -(55.) The powers of wind and water, which we are constantly impressing -into our service, can scarcely be called latent or hidden, yet it -is not fully considered, in general, what they _do_ effect for us. -Those who would judge of what advantage may be taken of the wind, for -example, even on land (not to speak of navigation), may turn their -eyes on Holland. A great portion of the most valuable and populous -tract of this country lies much below the level of the sea, and is only -preserved from inundation by the maintenance of embankments. Though -these suffice to keep out the abrupt influx of the ocean, they cannot -oppose that law of nature, by which fluids, in seeking their level, -insinuate themselves through the pores and subterraneous channels -of a loose sandy soil, and keep the country in a constant state of -infiltration from below upwards. To counteract this tendency, as well -as to get rid of the rain water, which has no natural outlet, pumps -worked by windmills are established in great numbers, on the dams -and embankments, which pour out the water, as from a leaky ship, and -in effect preserve the country from submersion, by taking advantage -of every wind that blows. To drain the Haarlem lake[20] would seem a -hopeless project to any speculators but those who had the steam-engine -at their command, or had learnt in Holland what might be accomplished -by the constant agency of the desultory but unwearied powers of wind. -But the Dutch engineer measures his surface, calculates the number of -his pumps, and, trusting to time and his experience of the operation of -the winds for the success of his undertaking, boldly forms his plans to -lay dry the bed of an inland sea, of which those who stand on one shore -cannot see the other.[21] - -(56.) To gunpowder, as a source of mechanical power, it seems hardly -necessary to call attention; yet it is only when we endeavour to -_confine_ it, that we get a full conception of the immense energy of -that astonishing agent. In count Rumford’s experiments, twenty-eight -grains of powder confined in a cylindrical space, _which it just -filled_, tore asunder a piece of iron which would have resisted -a strain of 400,000 lbs.[22], applied at no greater mechanical -disadvantage. - -(57.) But chemistry furnishes us with means of calling into sudden -action forces of a character infinitely more tremendous than that -of gunpowder. The terrific violence of the different fulminating -compositions is such, that they can only be compared to those -untameable animals, whose ferocious strength has hitherto defied all -useful management, or rather to spirits evoked by the spells of a -magician, manifesting a destructive and unapproachable power, which -makes him but too happy to close his book, and break his wand, as the -price of escaping: unhurt from the storm he has raised. Such powers are -not yet subdued to our purposes, whatever they may hereafter be; but, -in the expansive force of gases, liberated slowly and manageably from -chemical mixtures, we have a host of inferior, yet still most powerful, -energies, capable of being employed in a variety of useful ways, -according to emergencies.[23] - -(58.) Such are the forces which nature lends us for the accomplishment -of our purposes, and which it is the province of practical Mechanics to -teach us to combine and apply in the most advantageous manner; without -which the mere command of power would amount to nothing. Practical -Mechanics is, in the most pre-eminent sense, a _scientific art_; and -it may be truly asserted, that almost all the great combinations of -modern mechanism, and many of its refinements and nicer improvements, -are creations of pure intellect, grounding its exertion upon a moderate -number of very elementary propositions in theoretical mechanics and -geometry. On this head we might dwell long, and find ample matter, -both for reflection and wonder; but it would require not volumes -merely, but libraries, to enumerate and describe the prodigies of -ingenuity which have been lavished on every thing connected with -machinery and engineering. By these it is that we are enabled to -diffuse over the whole earth the productions of any part of it; to fill -every corner of it with miracles of art and labour, in exchange for its -peculiar commodities; and to concentrate around us, in our dwellings, -apparel and utensils, the skill and workmanship not of a few expert -individuals, but of all who, in the present and past generations, have -contributed their improvements to the processes of our manufactures. - -(59.) The transformations of chemistry, by which we are enabled to -convert the most apparently useless materials into important objects -in the arts, are opening up to us every day sources of wealth and -convenience of which former ages had no idea, and which have been -pure gifts of science to man. Every department of art has felt their -influence, and new instances are continually starting forth of the -unlimited resources which this wonderful science developes in the -most sterile parts of nature. Not to mention the impulse which its -progress has given to a host of other sciences, which will come more -particularly under consideration in another part of this discourse, -what strange and unexpected results has it not brought to light in its -application to some of the most common objects! Who, for instance, -would have conceived that linen rags were capable of producing _more -than their own weight_ of sugar, by the simple agency of one of the -cheapest and most abundant acids?[24]--that dry bones could be a -magazine of nutriment, capable of preservation for years, and ready to -yield up their sustenance in the form best adapted to the support of -life, on the application of that powerful agent, steam, which enters -so largely into all our processes, or of an acid at once cheap and -durable?[25]--that sawdust itself is susceptible of conversion into -a substance bearing no remote analogy to bread; and though certainly -less palatable than that of flour, yet no way disagreeable, and -both wholesome and digestible as well as highly nutritive?[26] What -economy, in all processes where chemical agents are employed, is -introduced by the exact knowledge of the proportions in which natural -elements unite, and their mutual powers of displacing each other! What -perfection in all the arts where fire is employed, either in its more -violent applications, (as, for instance, in the smelting of metals by -the introduction of well adapted fluxes, whereby we obtain the whole -produce of the ore in its purest state,) or in its milder forms, as -in sugar-refining (the whole modern practice of which depends on a -curious and delicate remark of a late eminent scientific chemist on the -nice adjustment of temperature at which the crystallization of syrup -takes place); and a thousand other arts which it would be tedious to -enumerate! - -(60.) Armed with such powers and resources, it is no wonder if the -enterprise of man should lead him to form and execute projects -which, to one uninformed of their grounds, would seem altogether -disproportionate. Were they to have been proposed at once, we should, -no doubt, have rejected them as such: but developed, as they have been, -in the slow succession of ages, they have only taught us that things -regarded impossible in one generation may become easy in the next; and -that the power of man over nature is limited only by the one condition, -that it must be exercised in conformity with the laws of nature. He -must study those laws as he would the disposition of a horse he would -ride, or the character of a nation he would govern; and the moment he -presumes either to thwart her fundamental rules, or ventures to measure -his strength with hers, he is at once rendered severely sensible of -his imbecility, and meets the deserved punishment of his rashness and -folly. But if, on the other hand, he will consent to use, without -abusing, the resources thus abundantly placed at his disposal, and obey -that he may command, there seems scarcely any conceivable limit to the -degree in which the _average_ physical condition of great masses of -mankind may be improved, their wants supplied, and their conveniences -and comforts increased. Without adopting such an exaggerated view, -as to assert that the meanest inhabitant of a civilized society is -superior in physical condition to the lordly savage, whose energy and -uncultivated ability gives him a natural predominance over his fellow -denizens of the forest,--at least, if we compare like with like, and -consider the multitude of human beings who are enabled, in an advanced -state of society, to subsist in a degree of comfort and abundance, -which at best only a few of the most fortunate in a less civilized -state could command, we shall not be at a loss to perceive the -principle on which we ought to rest our estimate of the advantages of -civilization; and which applies with hardly less force to every degree -of it, when contrasted with that next inferior, than to the broad -distinction between civilized and barbarous life in general. - -(61.) The difference of the degrees in which the individuals of a great -community enjoy the good things of life has been a theme of declamation -and discontent in all ages; and it is doubtless our paramount duty, in -every state of society, to alleviate the pressure of the purely evil -part of this distribution as much as possible, and, by all the means -we can devise, secure the lower links in the chain of society from -dragging in dishonour and wretchedness: but there is a point of view -in which the picture is at least materially altered in its expression. -In comparing society on its present immense scale, with its infant -or less developed state, we must at least take care to enlarge every -feature in the same proportion. If, on comparing the _very_ lowest -states in civilized and savage life, we admit a difficulty in deciding -to which the preference is due, at least in every superior grade we -cannot hesitate a moment; and if we institute a similar comparison in -every different stage of its progress, we cannot fail to be struck with -the rapid _rate of dilatation_ which every degree upward of the scale, -so to speak, exhibits, and which, in an estimate of averages, gives -an immense preponderance to the present over every former condition -of mankind, and, for aught we can see to the contrary, will place -succeeding generations in the same degree of superior relation to the -present that this holds to those passed away. Or we may put the same -proposition in other words, and, admitting the existence of every -inferior grade of advantage in a higher state of civilization which -subsisted in the preceding, we shall find, first, that, taking state -for state, the proportional numbers of those who enjoy the higher -degrees of advantage increases with a constantly accelerated rapidity -as society advances; and, secondly, that the superior extremity of -the scale is constantly enlarging by the addition of new degrees. The -condition of a European prince is now as far superior, in the command -of real comforts and conveniences, to that of one in the middle ages, -as that to the condition of one of his own dependants. - -(62.) The advantages conferred by the augmentation of our physical -resources through the medium of increased knowledge and improved art -have this peculiar and remarkable property,--that they are in their -nature diffusive, and cannot be enjoyed in any exclusive manner by a -few. An eastern despot may extort the riches and monopolize the art -of his subjects for his own personal use; he may spread around him an -unnatural splendour and luxury, and stand in strange and preposterous -contrast with the general penury and discomfort of his people; he may -glitter in jewels of gold and raiment of needlework; but the wonders -of well contrived and executed manufacture which we use daily, and -the comforts which have been invented, tried, and improved upon by -thousands, in every form of domestic convenience, and for every -ordinary purpose of life, can never be enjoyed by him. To produce a -state of things in which the physical advantages of civilized life -can exist in a high degree, the stimulus of increasing comforts and -constantly elevated desires, must have been felt by millions; since it -is not in the power of a few individuals to create that wide demand -for useful and ingenious applications, which alone can lead to great -and rapid improvements, unless backed by that arising from the speedy -diffusion of the same advantages among the mass of mankind. - -(63.) If this be true of physical advantages, it applies with still -greater force to intellectual. Knowledge can neither be adequately -cultivated nor adequately enjoyed by a few; and although the conditions -of our existence on earth may be such as to preclude an abundant -supply of the physical necessities of all who may be born, there -is no such law of nature in force against that of our intellectual -and moral wants. Knowledge is not, like food, destroyed by use, but -rather augmented and perfected. It acquires not, perhaps, a greater -certainty, but at least a confirmed authority and a probable duration, -by universal assent; and there is no body of knowledge so complete, -but that it may acquire accession, or so free from error but that it -may receive correction in passing through the minds of millions. Those -who admire and love knowledge for its own sake ought to wish to see -its elements made accessible to all, were it only that they may be -the more thoroughly examined into, and more effectually developed in -their consequences, and receive that ductility and plastic quality -which the pressure of minds of all descriptions, constantly moulding -them to their purposes, can alone bestow. But to this end it is -necessary that it should be divested, as far as possible, of artificial -difficulties, and stripped of all such technicalities as tend to place -it in the light of a craft and a mystery, inaccessible without a kind -of apprenticeship. Science, of course, like every thing else, has its -own peculiar terms, and, so to speak, its idioms of language; and these -it would be unwise, were it even possible, to relinquish: but every -thing that tends to clothe it in a strange and repulsive garb, and -especially every thing that, to keep up an appearance of superiority -in its professors over the rest of mankind, assumes an unnecessary -guise of profundity and obscurity, should be sacrificed without mercy. -Not to do this, is to deliberately reject the light which the natural -unencumbered good sense of mankind is capable of throwing on every -subject, even in the elucidation of principles: but where principles -are to be applied to practical uses it becomes absolutely necessary; -as all mankind have then an interest in their being so familiarly -understood, that no mistakes shall arise in their application. - -(64.) The same remark applies to arts. They cannot be perfected till -their whole processes are laid open, and their language simplified and -rendered universally intelligible. Art is the application of knowledge -to a practical end. If the knowledge be merely accumulated experience, -the art is _empirical_; but if it be experience reasoned upon and -brought under general principles, it assumes a higher character, and -becomes a _scientific art_. In the progress of mankind from barbarism -to civilised life, the arts necessarily precede science. The wants and -cravings of our animal constitution must be satisfied; the comforts, -and some of the luxuries, of life must exist. Something must be given -to the vanity of show, and more to the pride of power: the round of -baser pleasures must have been tried and found insufficient, before -intellectual ones can gain a footing; and when they have obtained it, -the delights of poetry and its sister arts still take precedence of -contemplative enjoyments, and the severer pursuits of thought; and -when these in time begin to charm from their novelty, and sciences -begin to arise, they will at first be those of pure speculation. The -mind delights to escape from the trammels which had bound it to earth, -and luxuriates in its newly found powers. Hence, the abstractions of -geometry--the properties of numbers--the movements of the celestial -spheres--whatever is abstruse, remote, and extramundane--become the -first objects of infant science. Applications come late: the arts -continue slowly progressive, but their realm remains separated from -that of science by a wide gulf which can only be passed by a powerful -spring. They form their own language and their own conventions, which -none but artists can understand. The whole tendency of empirical -art, is to bury itself in technicalities, and to place its pride in -particular short cuts and mysteries known only to adepts; to surprise -and astonish by results, but conceal processes. The character of -science is the direct contrary. It delights to lay itself open to -enquiry, and is not satisfied with its conclusions, till it can make -the road to them broad and beaten: and in its applications it preserves -the same character; its whole aim being to strip away all technical -mystery, to illuminate every dark recess, and to gain free access to -all processes, with a view to improve them on rational principles. -It would seem that a union of two qualities almost opposite to each -other--a going forth of the thoughts in two directions, and a sudden -transfer of ideas from a remote station in one to an equally distant -one in the other--is required to start the first idea of _applying -science_. Among the Greeks, this point was attained by Archimedes, but -attained too late, on the eve of that great eclipse of science which -was destined to continue for nearly eighteen centuries, till Galileo in -Italy, and Bacon in England, at once dispelled the darkness: the one, -by his inventions and discoveries; the other, by the irresistible force -of his arguments and eloquence. - -(65.) Finally, the improvement effected in the condition of mankind -by advances in physical science as applied to the useful purposes of -life, is very far from being limited to their direct consequences in -the more abundant supply of our physical wants, and the increase of our -comforts. Great as these benefits are, they are yet but steps to others -of a still higher kind. The successful results of our experiments and -reasonings in natural philosophy, and the incalculable advantages which -experience, systematically consulted and dispassionately reasoned on, -has conferred in matters purely physical, tend of necessity to impress -something of the well weighed and progressive character of science on -the more complicated conduct of our social and moral relations. It -is thus that legislation and politics become gradually regarded as -experimental sciences; and history, not, as formerly, the mere record -of tyrannies and slaughters, which, by immortalizing the execrable -actions of one age, perpetuates the ambition of committing them in -every succeeding one, but as the archive of experiments, successful -and unsuccessful, gradually accumulating towards the solution of the -grand problem--how the advantages of government are to be secured -with the least possible inconvenience to the governed. The celebrated -apophthegm, that nations never profit by experience, becomes yearly -more and more untrue. Political economy, at least, is found to have -sound principles, founded in the moral and physical nature of man, -which, however lost sight of in particular measures--however even -temporarily controverted and borne down by clamour--have yet a stronger -and stronger testimony borne to them in each succeeding generation, by -which they must, sooner or later, prevail. The idea once conceived and -verified, that great and noble ends are to be achieved, by which the -condition of the whole human species shall be permanently bettered, -by bringing into exercise a sufficient quantity of sober thought, and -by a proper adaptation of means, is of itself sufficient to set us -earnestly on reflecting what ends _are_ truly great and noble, either -in themselves, or as conducive to others of a still loftier character; -because we are not now, as heretofore, hopeless of attaining them. It -is not now equally harmless and insignificant, whether we are right -or wrong; since we are no longer supinely and helplessly carried down -the stream of events, but feel ourselves capable of buffetting at -least with its waves, and perhaps of riding triumphantly over them: -for why should we despair that the reason which has enabled us to -subdue all nature to our purposes, should (if permitted and assisted -by the providence of God) achieve a far more difficult conquest; and -ultimately find some means of enabling the collective wisdom of mankind -to bear down those obstacles which individual short-sightedness, -selfishness, and passion, oppose to all improvements, and by which -the highest hopes are continually blighted, and the fairest prospects -marred. - - - - - PART II. - - OF THE PRINCIPLES ON WHICH PHYSICAL SCIENCE RELIES FOR ITS - SUCCESSFUL PROSECUTION, AND THE RULES BY WHICH A SYSTEMATIC - EXAMINATION OF NATURE SHOULD BE CONDUCTED, WITH ILLUSTRATIONS OF - THEIR INFLUENCE AS EXEMPLIFIED IN THE HISTORY OF ITS PROGRESS. - - - - -CHAPTER I. - - OF EXPERIENCE AS THE SOURCE OF OUR KNOWLEDGE.--OF THE DISMISSAL OF - PREJUDICES.--OF THE EVIDENCE OF OUR SENSES. - - -(66.) Into abstract science, as we have before observed, the notion of -cause does not enter. The truths it is conversant with are _necessary_ -ones, and exist independent of cause. There may be no such real _thing_ -as a right-lined triangle marked out in space; but the moment we -conceive one in our minds, we cannot refuse to admit the sum of its -three angles to be equal to two right angles; and if in addition we -conceive one of its angles to be a right angle, we cannot thenceforth -refuse to admit that the sum of the squares on the two sides, including -the right angle, is equal to the square on the side subtending it. To -maintain the contrary, would be, in effect, to deny its being right -angled. No one _causes_ or _makes_ all the diameters of an ellipse -to be bisected in its centre. To assert the contrary, would not be -to rebel against a power, but to deny our own words. But in natural -science _cause_ and _effect_ are the ultimate relations we contemplate; -and _laws_, whether imposed or maintained, which, for aught we can -perceive, might have been other than they are. This distinction is -very important. A clever man, shut up alone and allowed unlimited -time, might reason out for himself all the truths of mathematics, by -proceeding from those simple notions of space and number of which he -cannot divest himself without ceasing to think. But he could never -tell, by any effort of reasoning, what would become of a lump of sugar -if immersed in water, or what impression would be produced on his eye -by mixing the colours yellow and blue. - -(67.) We have thus pointed out to us, as the great, and indeed only -ultimate source of our knowledge of nature and its laws, EXPERIENCE; -by which we mean, not the experience of one man only, or of one -generation, but the accumulated experience of all mankind in all ages, -registered in books or recorded by tradition. But experience may be -acquired in two ways: either, first, by noticing facts as they occur, -without any attempt to influence the frequency of their occurrence, or -to vary the circumstances under which they occur; this is OBSERVATION: -or, secondly, by putting in action causes and agents over which we -have control, and purposely varying their combinations, and noticing -what effects take place; this is EXPERIMENT. To these two sources we -must look as the fountains of all natural science. It is not intended, -however, by thus distinguishing observation from experiment, to -place them in any kind of contrast. Essentially they are much alike, -and differ rather in degree than in kind; so that, perhaps, the -terms _passive_ and _active observation_ might better express their -distinction; but it is, nevertheless, highly important to mark the -different states of mind in inquiries carried on by their respective -aids, as well as their different effects in promoting the progress of -science. In the former, we sit still and listen to a tale, told us, -perhaps obscurely, piecemeal, and at long intervals of time, with our -attention more or less awake. It is only by after-rumination that we -gather its full import; and often, when the opportunity is gone by, we -have to regret that our attention was not more particularly directed to -some point which, at the time, appeared of little moment, but of which -we at length appretiate the importance. In the latter, on the other -hand, we cross-examine our witness, and by comparing one part of his -evidence with the other, while he is yet before us, and reasoning upon -it in his presence, are enabled to put pointed and searching questions, -the answer to which may at once enable us to make up our minds. -Accordingly it has been found invariably, that in those departments -of physics where the phenomena are beyond our control, or into which -experimental enquiry, from other causes, has not been carried, the -progress of knowledge has been slow, uncertain, and irregular; while in -such as admit of experiment, and in which mankind have agreed to its -adoption, it has been rapid, sure, and steady. For example, in our -knowledge of the nature and causes of volcanoes, earthquakes, the fall -of stones from the sky, the appearance of new stars and disappearance -of old ones, and other of those great phenomena of nature which are -altogether beyond our command, and at the same time are of too rare -occurrence to permit any one to repeat and rectify his impressions -respecting them, we know little more now than in the earliest times. -Here our tale is told us slowly, and in broken sentences. In astronomy, -again, we have at least an uninterrupted narrative; the opportunity -of observation is constantly present, and makes up in some measure -for the impossibility of varying our point of view, and calling for -information at the precise moment it is wanted. Accordingly, astronomy, -regarded as a science of mere observation, arrived, though by very -slow degrees, to a state of considerable maturity. But the moment that -it became a branch of mechanics, a science essentially experimental, -(that is to say, one in which any principle laid down can be subjected -to immediate and decisive _trial_, and where experience does not -require to be waited for,) its progress suddenly acquired a tenfold -acceleration; nay, to such a degree, that it has been asserted, and -we believe with truth, that were the records of all observations from -the earliest ages annihilated, leaving only those made in a single -observatory[27], during a single lifetime[28], the whole of this most -perfect of sciences might, from those data, and as to the objects -included in them, be at once reconstructed, and appear precisely as -it stood at their conclusion. To take another instance: mineralogy, -till modern times, could hardly be said to exist. The description -of even the precious stones in Theophrastus and Pliny are, in most -cases, hardly sufficient to identify them, and in many fall short -even of that humble object; more recent observers, by attending more -carefully to the obvious characters of minerals, had formed a pretty -extensive catalogue of them, and made various attempts to arrange and -methodize the knowledge thus acquired, and even to deduce some general -conclusions respecting the forms they habitually assume: but from the -moment that chemical analysis was applied to resolve them into their -constituent elements, and that, led by a happy accident, the genius -of Bergmann discovered the general fact, that they could be _cloven_ -or split in such directions as to lay bare their peculiar primitive -or fundamental forms, (which lay concealed within them, as the statue -might be conceived encrusted in its marble envelope,)--from that -moment, mineralogy ceased to be an unmeaning list of names, a mere -laborious cataloguing of stones and rubbish, and became, what it now -is, a regular, methodical, and most important science, in which every -year is bringing to light new relations, new laws, and new practical -applications. - -(68.) Experience once recognized as the fountain of all our knowledge -of nature, it follows that, in the study of nature and its laws, we -ought at once to make up our minds to dismiss as idle prejudices, or -at least suspend as premature, any preconceived notion of what might -or what ought to be the order of nature in any proposed case, and -content ourselves with observing, as a plain matter of fact, what _is_. -To experience we refer, as the only ground of all physical enquiry. -But before experience itself can be used with advantage, there is one -preliminary step to make, which depends wholly on ourselves: it is -the absolute dismissal and clearing the mind of all prejudice, from -whatever source arising, and the determination to stand and fall by -the result of a direct appeal to facts in the first instance, and of -strict logical deduction from them afterwards. Now, it is necessary -to distinguish between two kinds of prejudices, which exercise very -different dominion over the mind, and, moreover, differ extremely -in the difficulty of dispossessing them, and the process to be gone -through for that purpose. These are,-- - - 1. Prejudices of opinion. - 2. Prejudices of sense. - -(69.) By prejudices of opinion, we mean opinions hastily taken up, -either from the assertion of others, from our own superficial views, -or from vulgar observation, and which, from being constantly admitted -without dispute, have obtained the strong hold of habit on our minds. -Such were the opinions once maintained that the earth is the greatest -body in the universe, and placed immovable in its centre, and all the -rest of the universe created for its sole use; that it is the nature -of fire and of sounds to ascend; that the moonlight is cold; that dews -_fall_ from the air, &c. - -(70.) To combat and destroy such prejudices we may proceed in two ways, -either by demonstrating the falsehood of the facts alleged in their -support, or by showing how the appearances, which seem to countenance -them, are more satisfactorily accounted for without their admission. -But it is unfortunately the nature of prejudices of opinion to adhere, -in a certain degree, to every mind, and to some with pertinacious -obstinacy, _pigris radicibus_, after all ground for their reasonable -entertainment is destroyed. Against such a disposition the student of -natural science must contend with all his power. Not that we are so -unreasonable as to demand of him an instant and peremptory dismission -of all his former opinions and judgments; all we require is, that -he will hold them without bigotry, retain till he shall see reason -to question them, and be ready to resign them when fairly proved -untenable, and to doubt them when the weight of probability is shown to -lie against them. If he refuse this, he is incapable of science. - -(71.) Our resistance against the destruction of the other class of -prejudices, those of sense, is commonly more violent at first, but less -persistent, than in the case of those of opinion. Not to trust the -evidence of our senses, seems, indeed, a hard condition, and one which, -if proposed, none would comply with. But it is not the direct evidence -of our senses that we are in any case called upon to reject, but only -the erroneous judgments we unconsciously form from them, and this only -when they can be shown to be so _by counter evidence of the same sort_; -when one sense is brought to testify against another, for instance; or -the same sense against itself, and the obvious conclusions in the two -cases disagree, so as to compel us to acknowledge that one or other -must be wrong. For example, nothing at first can seem a more rational, -obvious, and incontrovertible conclusion, than that the _colour_ of -an object is an inherent quality, like its weight, hardness, &c. and -that to _see_ the object, and see it _of its own colour_, when nothing -intervenes between our eyes and it, are one and the same thing. Yet -this is only a prejudice; and that it is so, is shown by bringing -forward the same sense of vision which led to its adoption, as evidence -on the other side; for, when the differently coloured prismatic rays -are thrown, in a dark room, in succession upon any object, whatever be -the colour we are in the habit of calling its own, it will appear of -the particular hue of the light which falls upon it: a yellow paper, -for instance, will appear scarlet when illuminated by red rays, yellow -when by yellow, green by green, and blue by blue rays; its own (so -called) proper colour _not in the least degree mixing with that it so -exhibits_. - -(72.) To give one or two more examples of the kind of illusion which -the senses practise on us, or rather which we practise on ourselves, -by a misinterpretation of their evidence: the moon at its rising -and setting appears much larger than when high up in the sky. This -is, however, a mere erroneous judgment; for when we come to measure -its diameter, so far from finding our conclusion borne out by fact, -we actually find it to measure materially less. Here is eyesight -opposed to eyesight, with the advantage of deliberate measurement. -In ventriloquism we have the hearing at variance with all the other -senses, and especially with the sight, which is sometimes contradicted -by it in a very extraordinary and surprising manner, as when the voice -is made to seem to issue from an inanimate and motionless object. If -we plunge our hands, one into ice-cold water, and the other into water -as hot as can be borne, and, after letting them stay awhile, suddenly -transfer them both to a vessel full of water at a blood heat, the one -will feel a sensation of heat, the other of cold. And if we cross the -two first fingers of one hand, and place a pea in the fork between -them, moving and rolling it about on a table, we shall (especially if -we close our eyes) be fully persuaded we have two peas. If the nose -be held while we are eating cinnamon, we shall perceive no difference -between its flavour and that of a deal shaving. - -(73.) These, and innumerable instances we might cite, will convince -us, that though we are never deceived in the _sensible impression_ -made by external objects on us, yet in forming our judgments of them -we are greatly at the mercy of circumstances, which either modify the -impressions actually received, or combine them with adjuncts which have -become habitually associated with different judgments; and, therefore, -that, in estimating the degree of confidence we are to place in our -conclusions, we must, of necessity, take into account these modifying -or accompanying circumstances, whatever they may be. We do not, of -course, here speak of deranged organization; such as, for instance, -a distortion of the eye, producing double vision, and still less of -mental delusion, which absolutely perverts the meaning of sensible -impressions. - -(74.) As the mind exists not in the place of sensible objects, and -is not brought into immediate relation with them, we can only regard -sensible impressions as signals conveyed from them by a wonderful, and, -to us, inexplicable mechanism, to our minds, which receives and reviews -them, and, by habit and association, connects them with corresponding -qualities or affections in the objects; just as a person writing down -and comparing the signals of a telegraph might interpret their meaning. -As, for instance, if he had constantly observed that the exhibition of -a certain signal was sure to be followed next day by the announcement -of the arrival of a ship at Portsmouth, he would connect the two facts -by a link of the very same nature with that which connects the notion -of a large wooden building, filled with sailors, with the impression of -her outline on the retina of a spectator on the beach. - -(75.) In captain Head’s amusing and vivid description of his journey -across the Pampas of South America occurs an anecdote quite in point. -His guide one day suddenly stopped him, and, pointing high into the -air, cried out, “A lion!” Surprised at such an exclamation, accompanied -with such an act, he turned up his eyes, and with difficulty perceived, -at an immeasurable height, a flight of condors soaring in circles in -a particular spot. Beneath that spot, far out of sight of himself or -guide, lay the carcass of a horse, and over that carcass stood (as the -guide well knew) the lion, whom the condors were eyeing with envy from -their airy height. The signal of the birds was to him what the sight of -the lion alone could have been to the traveller, a full assurance of -its existence. - - - - -CHAP. II. - -OF THE ANALYSIS OF PHENOMENA - - -(76.) _Phenomena_, then, or appearances, as the word is literally -rendered, are the sensible results of processes and operations carried -on among external objects, or their constituent principles, of which -they are only signals, conveyed to our minds as aforesaid. Now, these -processes themselves may be in many instances rendered _sensible_; -that is to say, analysed, and shown to consist in the motions or other -affections of sensible objects themselves. For instance, the phenomenon -of the sound produced by a musical string, or a bell, when struck, -may be shown to be the result of a process consisting in the rapid -vibratory motion of its parts communicated to the air, and thence to -our ears; though the immediate effect on our organs of hearing does -not excite the least idea of such a motion. On the other hand, there -are innumerable instances of sensible impressions which (at least -at present) we are incapable of tracing beyond the mere sensation; -for example, in the sensations of bitterness, sweetness, &c. These, -accordingly, if we were inclined to form hasty decisions, might be -regarded as ultimate qualities; but the instance of sounds, just -adduced, alone would teach us caution in such decisions, and incline -us to believe them mere results of some secret process going on in -our organs of taste, which is too subtle for us to trace. A simple -experiment will serve to set this in a clearer light. A solution of -the salt called by chemists _nitrate of silver_, and another of the -_hyposulphite of soda_, have each of them separately, when taken into -the mouth, a disgustingly bitter taste; but if they be mixed, or if -one be tasted before the mouth is thoroughly cleared of the other, -the sensible impression is that of intense sweetness. Again, the salt -called _tungstate of soda_ when first tasted is sweet, but speedily -changes to an intense and pure bitter, like quassia.[29] - -(77.) How far we may ever be enabled to attain a knowledge of the -ultimate and inward processes of nature in the production of phenomena, -we have no means of knowing; but, to judge from the degree of obscurity -which hangs about the only case in which we feel within ourselves -a _direct_ power to produce any one, there seems no great hope of -penetrating so far. The case alluded to is the production of motion by -the exertion of force. We are conscious of a power to move our limbs, -and by their intervention other bodies; and that this effect is the -result of a certain inexplicable process which we are aware of, but -can no way describe in words, by which we exert _force_. And even when -such exertion produces no visible effect, (as when we press our two -hands violently together, so as just to oppose each other’s effort,) we -still perceive, by the fatigue and exhaustion, and by the impossibility -of maintaining the effort long, that something is going on within us, -of which the mind is the agent, and the will the determining cause. -This impression which we receive of the nature of force, from our own -effort and our sense of fatigue, is quite different from that which -we obtain of it from seeing the effect of force exerted by others in -producing _motion_. Were there no such thing as motion, had we been -from infancy shut up in a dark dungeon, and every limb encrusted with -plaster, this internal consciousness would give us a complete idea -of _force_; but when set at liberty, habit alone would enable us to -recognize its exertion by its _signal_, motion, and _that_ only by -finding that the same action of the mind which in our confined state -enables us to fatigue and exhaust ourselves by the tension of our -muscles, puts it in our power, when at liberty, to move ourselves and -other bodies. But how obscure is our knowledge of the process going on -within us in the exercise of this important privilege, in virtue of -which alone we act as direct _causes_, we may judge from this, that -when we put any limb in motion, the seat of the exertion seems to us to -be _in_ the limb, whereas it is demonstrably no such thing, but either -in the brain or in the spinal marrow; the proof of which is, that if a -little fibre, called a nerve, which forms a communication between the -limb and the brain, or spine, be divided in any part of its course, -however we may make the effort, the limb will not move. - -(78.) This one instance of the obscurity which hangs about the only act -of direct _causation_ of which we have an immediate consciousness, will -suffice to show how little prospect there is that, in our investigation -of nature, we shall ever be able to arrive at a knowledge of ultimate -causes, and will teach us to limit our views to that of _laws_, and -to the analysis of complex phenomena by which they are resolved into -simpler ones, which, appearing to us incapable of further analysis, we -must consent to regard as causes. Nor let any one complain of this as a -limitation of his faculties. We have here “ample room and verge enough” -for the full exercise of all the powers we possess; and, besides, it -does so happen, that we are actually able to trace up a very large -portion of the phenomena of the universe to this one _cause_, viz. the -exertion of mechanical _force_; indeed, so large a portion, that it has -been made a matter of speculation whether this is not the only one that -is capable of acting on material beings. - -(79.) What we mean by the analysis of complex phenomena into simpler -ones, will best be understood by an instance. Let us, therefore, -take the phenomenon of sound, and, by considering the various cases -in which sounds of all kinds are produced, we shall find that they -all agree in these points:--1st, The excitement of a motion in the -sounding body. 2dly, The communication of this motion to the air or -other intermedium which is interposed between the sounding body and our -ears. 3dly, The propagation of such motion from particle to particle -of such intermedium in due succession. 4thly, Its communication, from -the particles of the intermedium adjacent to the ear, to the ear -itself. 5thly, Its conveyance in the ear, by a certain mechanism, to -the auditory nerves. 6thly, The excitement of sensation. Now, in this -analysis, we perceive that two principal matters must be understood, -before we can have a true and complete knowledge of sound:--1st, -The excitement and propagation of motion. 2dly, The production of -sensation. These, then, are two other phenomena, of a simpler, or, it -would be more correct to say, of a more general or elementary order, -into which the complex phenomenon of sound resolves itself. But again, -if we consider the communication of motion from body to body, or from -one part to another of the same, we shall perceive that it is again -resolvable into several other phenomena. 1st, The original setting in -motion of a material body, or any part of one. 2dly, The behaviour of -a particle set in motion, when it meets another lying in its way, or -is otherwise impeded or influenced by its connection with surrounding -particles. 3dly, The behaviour of the particles so impeding or -influencing it under such circumstances; besides which, the last two -point out another phenomenon, which it is necessary also to consider, -viz. the phenomenon of the connection of the parts of material bodies -in masses, by which they form aggregates, and are enabled to influence -each other’s motions. - -(80.) Thus, then, we see that an analysis of the phenomenon of sound -leads to the enquiry, 1st, of two _causes_, viz. the cause of motion, -and the cause of sensation, these being phenomena which (at least as -human knowledge stands at present) we are unable to analyse further; -and, therefore, we set them down as simple, elementary, and referable, -for any thing we can see to the contrary, to the immediate action of -their causes. 2dly, Of several questions relating to the connection -between the motion of material bodies and its cause, such as, _What -will happen_ when a moving body is surrounded on all sides by others -not in motion? _What will happen_ when a body not in motion is advanced -upon by a moving one? It is evident that the answers to such questions -as these can be no other than _laws of motion_, in the sense we have -above attributed to laws of nature, viz. a statement in words of what -will happen in such and such proposed general contingencies. Lastly, -we are led, by pursuing the analysis, and considering the phenomenon -of the aggregation of the parts of material bodies, and the way in -which they influence each other, to two other general phenomena, viz., -the cohesion and elasticity of matter; and these we have no means -of analysing further, and must, therefore, regard them (till we see -reasons to the contrary) as _ultimate phenomena_, and referable to the -direct action of causes, viz. an attractive and a repulsive _force_. - -(81.) Of force, as counterbalanced by opposing force, we have, as -already said, an internal consciousness; and though it may seem strange -to us that matter should be capable of exerting on matter the same kind -of effort, which, judging alone from this consciousness, we might be -led to regard as a mental one; yet we cannot refuse the direct evidence -of our senses, which shows us that when we keep a spring stretched with -one hand, we feel our effort opposed exactly in the same way as if we -had ourselves opposed it with the other hand, or as it would be by -that of another person. The enquiry, therefore, into the aggregation -of matter resolves itself into the general question, What will be the -behaviour of material particles under the mutual action of opposing -forces capable of counterbalancing each other? and the answer to -this question can be no other than the announcement of the _law_ of -equilibrium, whatever law that may be. - -(82.) With regard to the cause of sensation, it must be regarded as -much more obscure than that of motion, inasmuch as we have no conscious -knowledge of it, _i. e._ we have no power, by any act of our minds -and will, to call up a sensation. It is true, we are not destitute -of an approach to it, since, by an effort of memory and imagination, -we can produce in our minds an impression, or idea, of a sensation -which, in peculiar cases, may even approach in vividness to actual -reality. In dreams, too, and, in some cases of disordered nerves, we -have sensations without objects. But if force, as a cause of motion, -is obscure to us, even while we are in the act of exercising it, how -much more so is this other cause, whose exercise we can only imitate -imperfectly by any voluntary act, and of whose purely internal action -we are only fully conscious when in a state that incapacitates us from -reasoning, and almost from observation! - -(83.) Dismissing, then, as beyond our reach, the enquiry into causes, -we must be content at present to concentrate our attention on the laws -which prevail among phenomena, and which seem to be their immediate -results. From the instance we have just given, we may perceive that -every enquiry into the intimate nature of a complex phenomenon -branches out into as many different and distinct enquiries as there -are simple or elementary phenomena into which it may be analysed; and -that, therefore, it would greatly assist us in our study of nature, if -we could, by any means, ascertain what _are_ the ultimate phenomena -into which all the composite ones presented by it may be resolved. -There is, however, clearly no way by which this can be ascertained _à -priori_. We must go to nature itself, and be guided by the same kind -of rule as the chemist in his analysis, who accounts every ingredient -an _element_ till it can be decompounded and resolved into others. So, -in natural philosophy, we must account every phenomenon an elementary -or simple one till we can analyse it, and show that it is the result -of others, which in their turn become elementary. Thus, in a modified -and relative sense, we may still continue to speak of causes, not -intending thereby those ultimate principles of action on whose exertion -the whole frame of nature depends, but of those proximate links which -connect phenomena with others of a simpler, higher, and more general or -elementary kind. For example: we may regard the vibration of a musical -string as the proximate cause of the sound it yields, receiving it, -so far, as an ultimate fact, and waving or deferring enquiry into the -cause of vibrations, which is of a higher and more general nature. - -(84.) Moreover, as in chemistry we are sometimes compelled to -acknowledge the existence of elements different from those already -identified and known, though we cannot insulate them, and to perceive -that substances have the characters of compounds, and must therefore -be susceptible of analysis, though we do not see how it is to be set -about; so, in physics, we may perceive the complexity of a phenomenon, -without being able to perform its analysis. For example: in magnetism, -the agency of electricity is clearly made out, and they are shown to -stand to one another in the relation of effect and cause. But the -analysis of magnetism, in its relation to particular metals, is not -yet quite satisfactorily performed; and we are compelled to admit -the existence of some cause, whether proximate or ultimate, whose -presence in different metals, or in different states of the same metal, -determines that peculiar electric condition which constitutes permanent -magnetism. Cases like these, of all which science presents, offer the -highest interest. They excite enquiry, like the near approach to the -solution of an enigma; they show us that there is light, could only a -certain veil be drawn aside. - -(85.) In pursuing the analysis of any phenomenon, the moment we find -ourselves stopped by one of which we perceive no analysis, and which, -therefore, we are forced to refer (at least provisionally) to the -class of ultimate facts, and to regard as elementary, the study of -that phenomenon and of its laws becomes a separate branch of science. -If we encounter the same elementary phenomenon in the analysis of -several composite ones, it becomes still more interesting, and assumes -additional importance; while at the same time we acquire information -respecting the phenomenon itself, by observing those with which it -is habitually associated, that may help us at length to its analysis. -It is thus that sciences increase, and acquire a mutual relation and -dependency. It is thus, too, that we are at length enabled to trace -parallels and analogies between great branches of science themselves, -which at length terminate in a perception of their dependence on some -common phenomenon of a more general and elementary nature than that -which form the subject of either separately. It was thus, for example, -that, previous to Oërsted’s great discovery of electro-magnetism, -a general resemblance between the two sciences of electricity and -magnetism was recognised, and many of the chief phenomena in each were -ascertained to have their parallels, _mutatis mutandis_, in the other. -It was thus, too, that an analogy subsisting between sound and light -has been gradually traced into a closeness of agreement, which can -hardly leave any reasonable doubt of their ultimate coincidence in one -common phenomenon, the vibratory motion of an elastic medium. If it be -allowed to pursue our illustration from chemistry, and to ground its -application not on what has been, but on what may one day be, done, -it is thus that the general family resemblance between certain groups -of bodies, now regarded as elementary, (as nickel and cobalt, for -instance, chlorine, iode, and brome,) will, perhaps, lead us hereafter -to perceive relations between them of a more intimate kind than we can -at present trace. - -(86.) On those phenomena which are most frequently encountered in -an analysis of nature and which most decidedly resist further -decomposition, it is evident that the greatest pains and attention -ought to be bestowed, not only because they furnish a key to the -greatest number of enquiries, and serve to group and classify together -the greatest range of phenomena, but by reason of their higher nature, -and because it is in these that we must look for the direct action of -causes, and the most extensive and general enunciation of the laws of -nature. These, once discovered, place in our power the explanation of -all particular facts, and become grounds of reasoning, independent of -particular trial: thus playing the same part in natural philosophy -that axioms do in geometry; containing, in a refined and condensed -state, and as it were in a quintessence, all that our reason has -occasion to draw from experience to enable it to follow out the truths -of physics by the mere application of logical argument. Indeed, the -axioms of geometry themselves may be regarded as in some sort an appeal -to experience, not corporeal, but mental. When we say, the whole is -greater than its part, we announce a general fact, which rests, it -is true, on our ideas of whole and part; but, in abstracting these -notions, we begin by considering them as subsisting in space, and time, -and body, and again, in linear, and superficial, and solid space. -Again, when we say, the equals of equals are equal, we mentally make -comparisons, in equal spaces, equal times, &c.; so that these axioms, -however self-evident, are still general propositions so far of the -inductive kind, that, independently of experience, they would not -present themselves to the mind. - -The only difference between these and axioms obtained from extensive -induction is this, that, in raising the axioms of geometry, the -instances offer themselves spontaneously, and without the trouble of -search, and are few and simple; in raising those of nature, they are -infinitely numerous, complicated, and remote; so that the most diligent -research and the utmost acuteness are required to unravel their web, -and place their meaning in evidence. - -(87.) By far the most general phenomenon with which we are acquainted, -and that which occurs most constantly, in every enquiry into which we -enter, is motion, and its communication. Dynamics, then, or the science -of force and motion, is thus placed at the head of all the sciences; -and, happily for human knowledge, it is one in which the highest -certainty is attainable, a certainty no way inferior to mathematical -demonstration. As its axioms are few, simple, and in the highest degree -distinct and definite, so they have at the same time an immediate -relation to geometrical quantity, space, time, and direction, and -thus accommodate themselves with remarkable facility to geometrical -reasoning. Accordingly, their consequences may be pursued, by arguments -purely mathematical, to any extent, insomuch that the limit of our -knowledge of dynamics is determined only by that of pure mathematics, -which is the case in no other branch of physical science. - -(88.) But, it will now be asked, how we are to proceed to analyse a -composite phenomenon into simpler ones, and whether any general rules -can be given for this important process? We answer, None; any more -than (to pursue the illustration we have already had recourse to) -general rules can be laid down by the chemist for the analysis of -substances of which all the ingredients are unknown. Such rules, could -they be discovered, would include the whole of natural science; but -we are very far, indeed, from being able to propound them. However, -we are to recollect that the analysis of phenomena, philosophically -speaking, is principally useful, as it enables us to recognize, and -mark for special investigation, those which appear to us simple; to -set methodically about determining their laws, and thus to facilitate -the work of raising up general axioms, or forms of words, which shall -include the whole of them; which shall, as it were, transplant them -out of the external into the intellectual world, render them creatures -of pure thought, and enable us to reason them out _à priori_. And what -renders the power of doing this so eminently desirable is, that, in -thus reasoning back from generals to particulars, the propositions -at which we arrive apply to an immense multitude of combinations and -cases, which were never individually contemplated in the mental process -by which our axioms were first discovered; and that, consequently, when -our reasonings are pushed to the utmost limit of particularity, their -results appear in the form of _individual facts_, of which we might -have had no knowledge from immediate experience; and thus we are not -only furnished with the explanation of all known facts, but with the -actual discovery of such as were before unknown. A remarkable example -of this has already been mentioned in Fresnel’s _à priori_ discovery -of the extraordinary refraction of both rays in a doubly refracting -medium. To give another example:--The law of gravitation is a physical -axiom of a very high and universal kind, and has been raised by a -succession of inductions and abstractions drawn from the observation -of numerous facts and subordinate laws in the planetary system. When -this law is taken for granted, and laid down as a basis of reasoning, -and applied to the actual condition of our own planet, one of the -consequences to which it leads is, that the earth, instead of being an -exact sphere, must be compressed or flattened in the direction of its -polar diameter, the one diameter being about thirty miles shorter than -the other; and this conclusion, deduced at first by mere reasoning, has -been since found to be true in fact. All astronomical predictions are -examples of the same thing. - -(89.) In the important business of raising these axioms of nature, we -are not, as in the analysis of phenomena, left wholly without a guide. -The nature of abstract or general reasoning points out in a great -measure the course we must pursue. A law of nature, being the statement -of what will happen in certain general contingencies, may be regarded -as the announcement, in the same words, of a whole group or class of -phenomena. Whenever, therefore, we perceive that two or more phenomena -agree in so many or so remarkable points, as to lead us to regard -them as forming a class or group, if we lay out of consideration, or -_abstract_, all the circumstances in which they disagree, and retain in -our minds those only in which they agree, and then, under this kind of -mental convention, frame a definition or statement of one of them, in -such words that it shall apply equally to them all, such statement will -appear in the form of a general proposition, having so far at least the -character of a law of nature. - -(90.) For example: a great number of transparent substances, when -exposed, in a certain particular manner, to a beam of light which has -been prepared by undergoing certain reflexions or refractions, (and has -thereby acquired peculiar properties, and is said to be “_polarized_,”) -exhibit very vivid and beautiful colours, disposed in streaks, bands, -&c. of great regularity, which seem to arise within the substance, and -which, from a certain regular succession observed in their appearance, -are called “periodical colours.” Among the substances which exhibit -these periodical colours occur a great variety of transparent solids, -but no fluids and no opake solids. Here, then, there seems to be -sufficient community of nature to enable us to use a general term, and -to state the proposition as a law, viz. _transparent solids_ exhibit -periodical colours by exposure to polarized light. However, this, -though true of many, does not apply to _all_ transparent solids, and -therefore we cannot state it as a general truth or law of nature in -this form; although the reverse proposition, that all solids which -exhibit such colours in such circumstances are _transparent_, would -be correct and general. It becomes necessary, then, to make a list of -those to which it does apply; and thus a great number of substances of -all kinds become grouped together, in a class linked by this common -property. If we examine the individuals of this group, we find among -them the utmost variety of colour, texture, weight, hardness, form and -composition; so that, in these respects, we seem to have fallen upon -an assemblage of contraries. But when we come to examine them closely, -in all their properties, we find they have all one point of agreement, -in the property of double refraction, (see page 30.) and therefore we -may describe them all truly as _doubly refracting substances_. We may, -therefore, state the fact in the form, “Doubly refracting substances -exhibit periodical colours by exposure to polarized light;” and in -this form it is found, on further examination, to be true, not only -for those particular instances which we had in view when we first -propounded it, but in all cases which have since occurred on further -enquiry, without a single exception; so that the proposition is -general, and entitled to be regarded as a law of nature. - -(91.) We may therefore regard a law of nature either, 1st, as a general -proposition, announcing, in abstract terms, a whole group of particular -facts relating to the behaviour of natural agents in proposed -circumstances; or, 2dly, as a proposition announcing that a whole -class of individuals agreeing in one character agree also in another. -For example: in the case before us, the law arrived at includes, in -its general announcement, among others, the particular facts, that -rock crystal and saltpetre exhibit periodical colours; for these are -both of them doubly refracting substances. Or, it may be regarded as -announcing a relation between the two phenomena of double refraction, -and the exhibition of periodical colours; which in the actual case is -one of the most important, viz. the relation of _constant association_, -inasmuch as it asserts that in whatever individual the one character is -found, the other will invariably be found also. - -(92.) These two lights, in which the announcement of a general law may -be regarded, though at bottom they come to the same thing, yet differ -widely in their influence on our minds. The former exhibits a law as -little more than a kind of artificial memory; but in the latter it -becomes a step in philosophical investigation, leading directly to -the consideration of a proximate, if not an ultimate, cause; inasmuch -as, whenever two phenomena are observed to be invariably connected -together, we conclude them to be related to each other, either as cause -and effect, or as common effects of a single cause. - -(93.) There is still another light in which we may regard a law of -the kind in question, viz. as a proposition asserting the mutual -connection, or in some cases the entire identity, of two classes of -individuals (whether individual objects or individual facts); and this -is, perhaps, the simplest and most instructive way in which it can be -conceived, and that which furnishes the readiest handle to further -generalization in the raising of yet higher axioms. For example: in -the case above mentioned, if observation had enabled us to establish -the existence of a class of bodies possessing the property of double -refraction, and observations of another kind had, independently of the -former, led as to recognize a class possessing that of the exhibition -of periodical colours in polarized light, a mere comparison of lists -would at once demonstrate the identity of the two classes, or enable us -to ascertain whether one was or was not included in the other. - -(94.) It is thus we perceive the high importance in physical science of -just and accurate classifications of particular facts, or individual -objects, under general well considered heads or points of agreement -(for which there are none better adapted than the simple phenomena -themselves into which they can be analysed in the first instance); for -by so doing each of such phenomena, or heads of classification, becomes -not a particular but a general fact; and when we have amassed a great -store of such _general facts_, they become the objects of another and -higher species of classification, and are themselves included in laws -which, as they dispose of groups, not individuals, have a far superior -degree of generality, till at length, by continuing the process, we -arrive at _axioms_ of the highest degree of generality of which science -is capable. - -(95.) This process is what we mean by induction; and, from what -has been said, it appears that induction may be carried on in two -different ways,--either by the simple juxta-position and comparison of -ascertained classes, and marking their agreements and disagreements; -or by considering the individuals of a class, and casting about, as -it were to find in what particular they all agree, besides that which -serves as their principle of classification. Either of these methods -may be put in practice as one or the other may afford facilities in -any case; but it will naturally happen that, where facts are numerous, -well observed, and methodically arranged, the former will be more -applicable than in the contrary case: the one is better adapted to the -maturity, the other to the infancy, of science: the one employs, as an -engine, the division of labour; the other mainly relies on individual -penetration, and requires a union of many branches of knowledge in one -person. - - - - -CHAP. III. - -OF THE STATE OF PHYSICAL SCIENCE IN GENERAL, PREVIOUS TO THE AGE OF -GALILEO AND BACON. - - -(96.) It is to our immortal countryman Bacon that we owe the broad -announcement of this grand and fertile principle; and the developement -of the idea, that the whole of natural philosophy consists entirely -of a series of inductive generalizations, commencing with the most -circumstantially stated particulars, and carried up to universal laws, -or axioms, which comprehend in their statements every subordinate -degree of generality, and of a corresponding series of inverted -reasoning from generals to particulars, by which these axioms are -traced back into their remotest consequences, and all particular -propositions deduced from them; as well those by whose immediate -consideration we rose to their discovery, as those of which we had -no previous knowledge. In the course of this descent to particulars, -we must of necessity encounter all those facts on which the arts and -works that tend to the accommodation of human life depend, and acquire -thereby the command of an unlimited practice, and a disposal of the -powers of nature co-extensive with those powers themselves. A noble -promise, indeed, and one which ought, surely, to animate us to the -highest exertion of our faculties; especially since we have already -such convincing proof that it is neither vain nor rash, but, on the -contrary, has been, and continues to be, fulfilled, with a promptness -and liberality which even its illustrious author in his most sanguine -mood would have hardly ventured to anticipate. - -(97.) Previous to the publication of the Novum Organum of Bacon, -natural philosophy, in any legitimate and extensive sense of the word, -could hardly be said to exist. Among the Greek philosophers, of whose -attainments in science alone, in the earlier ages of the world, we -have any positive knowledge, and that but a very limited one, we are -struck with the remarkable contrast between their powers of acute and -subtle disputation, their extraordinary success in abstract reasoning, -and their intimate familiarity with subjects purely intellectual, -on the one hand; and, on the other, with their loose and careless -consideration of external nature, their grossly illogical deductions of -principles of sweeping generality from few and ill-observed facts, in -some cases; and their reckless assumption of abstract principles having -no foundation but in their own imaginations, in others; mere forms of -words, with nothing corresponding to them in nature, from which, as -from mathematical definitions, postulates, and axioms, they imagined -that all phenomena could be derived, all the laws of nature deduced. -Thus, for instance, having settled it in their own minds, that a -circle is the most perfect of figures, they concluded, of course, that -the movements of the heavenly bodies must all be performed in exact -circles, and with uniform motions; and when the plainest observation -demonstrated the contrary, instead of doubting the principle, they saw -no better way of getting out of the difficulty than by having recourse -to endless combinations of circular motions to preserve their ideal -perfection. - -(98.) Undoubtedly among the Greek philosophers were many men of -transcendent talents and virtues, the ornaments of their species, -and justly entitled to the veneration of all posterity; but regarded -as a body they can hardly be considered otherwise than as a knot of -disputatious candidates for popular favour, too busy in maintaining -their ascendency over their followers and admirers, by an ostentatious -display of superior knowledge, to have the leisure (had they always the -inclination) to base their pretensions on a deep and sure foundation, -and yet too sensible of the disgrace and inconvenience of failure, -not to defend their dogmas, however shallow, when once promulgated, -against their keen and sagacious opponents, by every art of sophism -or appeal to passion. Hence the crudities and chimerical views with -which their systems of philosophy, both natural and moral, were -overloaded; their endless disputes about verbal subtleties, and, last -and worst, the proud assumption with which they sheltered ignorance -and indolence under the screen of unintelligible jargon or dogmatical -assertion. Perhaps, however, this character applies rather to the -later than to the earlier of the Greek philosophers. The spirit of -rational enquiry into nature seems, if we can judge from the uncertain -and often contradictory notices handed down to us of their tenets, to -have been far more alive, and less warped by this vain and arrogant -turn, then than at a later period. We know not now what was the -precise meaning attached by Thales to his opinion, that water was -the origin of all things; but modern geologists will not be at a loss -to conceive how an observant traveller might become impressed with -this notion, without having recourse to the mystic records of Egypt -or Chaldea. His ideas of eclipses and of the nature of the moon were -sound; and his prediction of an eclipse of the sun, in particular, -was attended with circumstances so remarkable as to have made it a -matter of important investigation to modern astronomers. Anaxagoras, -among a number of crude and imperfectly explained notions, speculated -rationally enough on the cause of the winds and of the rainbow, and -less absurdly on earthquakes than many modern geologists have done, and -appears generally to have had his attention alive to nature, and his -mind open to just reasoning on its phenomena; while Pythagoras, whether -he reasoned it out for himself, or borrowed the notion from Egypt or -India, had attained a just conception of the general disposition of -the parts of the solar system, and the place held by the earth in it; -nay, according to some accounts, had even raised his views so far as to -speculate on the attraction of the sun as the bond of its union. - -(99.) But the successors of these _bonâ fide_ enquirers into nature -debased the standard of truth; and, taking advantage of the credit -justly attached to their discoveries, renounced the modest character -of learners, and erected themselves into teachers, and, to maintain -their pretensions to this character, adopted the tone of men who had -nothing further to learn. Unfortunately for true science, the national -character gave every encouragement to pretensions of this kind. That -restless craving after novelty, which distinguished the Greeks in their -civil and political relations, pursued them into their philosophy. -Whatever speculations were only ingenious and new had irresistible -charms; and the teacher who could embody a clever thought in elegant -language, or at once save his followers and himself the trouble of -thinking or reasoning, by bold assertion, was too often induced to -acquire cheaply the reputation of superior knowledge, snatch a few -superficial notions from the most ordinary and obvious facts, envelope -them in a parade of abstruse words, declare them the primary and -ultimate principles of all things, and denounce as absurd and impious -all opinions opposed to his own. - -(100.) In this war of words the study of nature was neglected, and -an humble and patient enquiry after facts altogether despised, as -unworthy of the high _priori_ ground a true philosopher ought to take. -It was the radical error of the Greek philosophy to imagine that the -same method which proved so eminently successful in mathematical, -would be equally so in physical, enquiries, and that, by setting out -from a few simple and almost self-evident notions, or _axioms_, every -thing could be reasoned out. Accordingly, we find them constantly -straining their invention to discover these principles, which were to -prove so pregnant. One makes _fire_ the essential matter and origin -of the universe; another, _air_; a third, discovers the key to every -difficulty, and the explanation of all phenomena, in the “το απειρον” -or infinitude of things; a fourth, in the το ὁν and the το μη ὁν, that -is to say, in entity and nonentity;--till at length an authority, -which was destined to command opinions for nearly two thousand years, -settled this important point, by deciding, that _matter_, _form_, and -_privation_, were to be considered the principles of all things. - -(101.) It were to do injustice to Aristotle, however, to judge of him -by _such_ a sample of his philosophy. He, at least, saw the necessity -of having recourse to nature for something like principles of physical -science; and, as an observer, a collector and recorder of facts and -phenomena, stood without an equal in his age. It was the fault of that -age, and of the perverse and flimsy style of verbal disputation which -had infected all learning, rather than his own, that he allowed himself -to be contented with vague and loose notions drawn from general and -vulgar observation, in place of seeking carefully, in well arranged -and thoroughly considered instances, for the true laws of nature. His -voluminous works, on every department of human knowledge existing in -his time, have nearly all perished. From his work on animals, which -has descended to us, we are, however, enabled to appreciate his powers -of observation; and a parallel drawn by an eminent Oxford professor -between his classifications and those of the most illustrious of -living naturalists, shows him to have attained a view of animated -nature in a remarkable degree comprehensive, and which contrasts -strikingly with the confusion, vagueness, and assumption of his -physical opinions and dogmas. In these it is easy to recognize a mind -not at home, and an impression of the necessity of saying something -learned and systematic, without knowing what to say. Thus he divides -motions into natural and unnatural; the natural motion of fire and -light bodies being upwards, those of heavy downwards, each seeking its -kindred nature in the heavens and the earth. Thus, too, the immediate -impressions made on us by external objects, such as hardness, colour, -heat, &c. are referred at once, in the Aristotelian philosophy, to -occult qualities, in virtue of which they are as they are, and beyond -which it is useless to enquire.[30] Of course there will occur a limit -beyond which it _is_ useless for merely human faculties to enquire; but -where that limit is placed, experience alone can teach us; and at least -to assert that we _have_ attained it, is now universally recognized as -the sure criterion of dogmatism. - -(102.) In the early ages of the church the writings of Aristotle were -condemned, as allowing too much to reason and sense; and even so late -as the twelfth century they were sought out and burned, and their -readers excommunicated. By degrees, however, the extreme injustice -of this impeachment of their character was acknowledged: they became -the favourite study of the schoolmen, and furnished the keenest -weapons of their controversy, being appealed to in all disputes as of -sovereign authority; so that the slightest dissent from any opinion -of the “great master,” however absurd or unintelligible, was at once -drowned by clamour, or silenced by the still more effectual argument of -bitter persecution. If the logic of that gloomy period could be justly -described as “the art of talking unintelligibly on matters of which we -are ignorant,” its physics might, with equal truth, be summed up in a -deliberate preference of ignorance to knowledge, in matters of every -day’s experience and use. - -(103.) In “this opake of nature and of soul,” the perverse activity of -the alchemists from time to time struck out a doubtful spark[31]; and -our illustrious countryman, Roger Bacon, shone out at the obscurest -moment, like an early star predicting dawn. It was not, however, till -the sixteenth century that the light of nature began to break forth -with a regular and progressive increase. The vaunts of Paracelsus -of the power of his chemical remedies and elixirs, and his open -condemnation of the ancient pharmacy, backed as they were by many -surprising cures, convinced all rational physicians that chemistry -could furnish many excellent remedies, unknown till that time[32], and -a number of valuable experiments began to be made by physicians and -chemists, desirous of discovering and describing new chemical remedies. -The chemical and metallurgic arts, exercised by persons empirically -acquainted with their secrets, began to be seriously studied with a -view to the acquisition of rational and useful knowledge, and regular -treatises on branches of natural science at length to appear. George -Agricola, in particular, devoted himself with ardour to the study -of mineralogy and metallurgy in the mining districts of Bohemia and -Schemnitz, and published copious and methodical accounts of all -the facts within his knowledge: and our countryman, Dr. Gilbert of -Colchester, in 1590, published a treatise on magnetism, full of -valuable facts and experiments, ingeniously reasoned on; and he -likewise extended his enquiries to a variety of other subjects, in -particular to electricity. - -(104.) But, as the decisive mark of a great commencing change in the -direction of the human faculties, astronomy, the only science in which -the ancients had made any real progress, and ascended to any thing like -large and general conceptions, began once more to be studied in the -best spirit of a candid philosophy; and the Copernican or Pythagorean -system arose or revived, and rapidly gained advocates. Galileo at -length appeared, and openly attacked and refuted the Aristotelian -dogmas respecting motion, by direct appeal to the evidence of sense, -and by experiments of the most convincing kind. The persecutions -which such a step drew upon him, the record of his perseverance and -sufferings, and the ultimate triumph of his opinions and reasonings, -have been too lately and too well related[33] to require repetition -here. - -(105.) By the discoveries of Copernicus, Kepler, and Galileo, the -errors of the Aristotelian philosophy were effectually overturned on a -plain appeal to the facts of nature; but it remained to show on broad -and general principles, how and why Aristotle was in the wrong; to set -in evidence the peculiar weakness of his method of philosophizing, -and to substitute in its place a stronger and better. This important -task was executed by Francis Bacon, Lord Verulam, who will, therefore, -justly be looked upon in all future ages as the great reformer of -philosophy, though his own actual contributions to the stock of -physical truths were small, and his ideas of particular points strongly -tinctured with mistakes and errors, which were the fault rather of the -general want of physical information of the age than of any narrowness -of view on his own part; and of this he was fully aware. It has been -attempted by some to lessen the merit of this great achievement, by -showing that the inductive method had been practised in many instances, -both ancient and modern, by the mere instinct of mankind; but it is not -the introduction of inductive reasoning, as a new and hitherto untried -process, which characterizes the Baconian philosophy, but his keen -perception, and his broad and spirit-stirring, almost enthusiastic, -announcement of its paramount importance, as the alpha and omega of -science, as the grand and only chain for the linking together of -physical truths, and the eventual key to every discovery and every -application. Those who would deny him his just glory on such grounds -would refuse to Jenner or to Howard their civic crowns, because a few -farmers in a remote province had, time out of mind, been acquainted -with vaccination, or philanthropists, in all ages, had occasionally -visited the prisoner in his dungeon. - -(106.) An immense impulse was now given to science, and it seemed as -if the genius of mankind, long pent up, had at length rushed eagerly -upon Nature, and commenced, with one accord, the great work of -turning up her hitherto unbroken soil, and exposing the treasures -so long concealed. A general sense now prevailed of the poverty and -insufficiency of existing knowledge in _matters of fact_; and, as -information flowed fast in, an era of excitement and wonder commenced, -to which the annals of mankind had furnished nothing similar. It -seemed, too, as if Nature herself seconded the impulse; and, while -she supplied new and extraordinary aids to those senses which were -henceforth to be exercised in her investigation,--while the telescope -and the microscope laid open _the infinite_ in both directions,--as -if to call attention to her wonders, and signalize the epoch, she -displayed the rarest, the most splendid and mysterious, of all -astronomical phenomena, the appearance and subsequent total extinction -of a new and brilliant fixed star twice within the lifetime of Galileo -himself.[34] - -(107.) The immediate followers of Bacon and Galileo ransacked all -nature for new and surprising facts, with something of that craving -for the marvellous, which might be regarded as a remnant of the age of -alchemy and natural magic, but which, under proper regulation, is a -most powerful and useful stimulus to experimental enquiry. Boyle, in -particular, seemed animated by an enthusiasm of ardour, which hurried -him from subject to subject, and from experiment to experiment, -without a moment’s intermission, and with a sort of undistinguishing -appetite; while Hooke (the great contemporary, and almost the worthy -rival, of Newton) carried a keener eye of scrutinizing reason into a -range of research even yet more extensive. As facts multiplied, leading -phenomena became prominent, laws began to emerge, and generalizations -to commence; and so rapid was the career of discovery, so signal the -triumph of the inductive philosophy, that a single generation and the -efforts of a single mind sufficed for the establishment of the system -of the universe, on a basis never after to be shaken. - -(108.) We shall now endeavour to enumerate and explain in detail the -principal steps by which legitimate and extensive inductions are -arrived at, and the processes by which the mind, in the investigation -of natural laws, purges itself by successive degrees of the -superfluities and incumbrances which hang about particulars, and -obscure the perception of their points of resemblance and connection. -We shall state the helps which may be afforded us, in a work of so -much thought and labour, by a methodical course of proceeding, and -by a careful notice of those means which have at any time been found -successful, with a view to their better understanding and adaptation -to other cases: a species of mental induction of no mean utility and -extent in itself; inasmuch as by pursuing it alone we can attain a more -intimate knowledge than we actually possess of the laws which regulate -our discovery of truth, and of the rules, so far as they extend, to -which invention is reducible. In doing this, we shall commence at the -beginning, with experience itself, considered as the accumulation of -the knowledge of individual objects and facts. - - - - -CHAP. IV. - -OF THE OBSERVATION OF FACTS AND THE COLLECTION OF INSTANCES. - - -(109.) Nature offers us two sorts of subjects of contemplation in the -external world,--objects, and their mutual actions. But, after what -has been said on the subject of sensation, the reader will be at no -loss to perceive that we know nothing of the objects themselves which -compose the universe, except through the medium of the impressions they -excite in us, which impressions are the results of certain actions and -processes in which sensible objects and the material parts of ourselves -are directly concerned. Thus, our observation of external nature is -limited to the mutual action of material objects on one another; and -to facts, that is, the associations of phenomena or appearances. We -gain no information by perceiving merely that an object is black; but -if we also perceive it to be fluid, we at least acquire the knowledge -that blackness is not incompatible with fluidity, and have thus made -a step, however trifling, to a knowledge of the more intimate nature -of these two qualities. Whenever, therefore, we would either analyse -a phenomenon into simpler ones, or ascertain what is the course or -law of nature under any proposed general contingency, the first step -is to accumulate a sufficient quantity of well ascertained facts or -recorded instances, bearing on the point in question. Common sense -dictates this, as affording us the means of examining the same subject -in several points of view; and it would also dictate, that the more -different these collected facts are in all other circumstances but that -which forms the subject of enquiry, the better; because they are then -in some sort brought into contrast with one another in their points of -disagreement, and thus tend to render those in which they agree more -prominent and striking. - -(110.) The only facts which can ever become useful as grounds of -physical enquiry are those which happen uniformly and invariably -under the same circumstances. This is evident: for if they have -not this character they cannot be included in laws; they want that -universality which fits them to enter as elementary particles into the -constitution of those universal axioms which we aim at discovering. -If one and the same result does not constantly happen under a given -combination of circumstances, apparently the same, one of two things -must be supposed,--caprice (_i. e._ the arbitrary intervention of -mental agency), or differences in the circumstances themselves, -really existing, but unobserved by us. In either case, though we may -record such facts as curiosities, or as awaiting explanation when -the difference of circumstances shall be understood, we can make -no use of them in scientific enquiry. Hence, whenever we notice a -remarkable effect of any kind, our first question ought to be, Can it -be reproduced? What are the circumstances under which it has happened? -And will it _always_ happen again if those circumstances, so far as we -have been able to collect them, co-exist? - -(111.) The circumstances, then, which accompany any observed fact, are -main features in its observation, at least until it is ascertained -by sufficient experience what circumstances have nothing to do with -it, and might therefore have been left unobserved without sacrificing -_the fact_. In observing and recording a fact, therefore, altogether -new, we ought not to omit any circumstance capable of being noted, -lest some one of the omitted circumstances should be essentially -connected with the fact, and its omission should, therefore, reduce -the implied statement of a _law of nature_ to the mere record of an -_historical event_. For instance, in the fall of meteoric stones, -flashes of fire are seen proceeding from a cloud, and a loud rattling -noise like thunder is heard. These circumstances, and the sudden stroke -and destruction ensuing, long caused them to be confounded with an -effect of lightning, and called thunderbolts. But one circumstance is -enough to mark the difference: the flash and sound have been perceived -occasionally to emanate from a _very small cloud_ insulated in _a clear -sky_; a combination of circumstances which never happens in a thunder -storm, but which is undoubtedly intimately connected with their real -origin. - -(112.) Recorded observation consists of two distinct parts: 1st, an -exact notice of the thing observed, and of all the particulars which -may be supposed to have any natural connection with it; and, 2dly, a -true and faithful record of them. As our senses are the only inlets -by which we receive impressions of facts, we must take care, in -observing, to have them all in activity, and to let nothing escape -notice which affects any one of them. Thus, if lightning were to -strike the house we inhabit, we ought to notice what kind of light we -saw--whether a sheet of flame, a darting spark, or a broken zig-zag; -in what direction moving, to what objects adhering, its colour, its -duration, &c.; what sounds were heard--explosive, crashing, rattling, -momentary, or gradually increasing and fading, &c.; whether any smell -of fire was perceptible, and if sulphureous, metallic, or such as -would arise merely from substances scorched by the flash, &c.; whether -we felt any shock, stroke, or peculiar sensation, or experienced any -strange taste in our mouths. Then, besides detailing the effects of the -stroke, all the circumstances which might in any degree seem likely to -attract, produce, or modify it, such as the presence of conductors, -neighbouring objects, the state of the atmosphere, the barometer, -thermometer, &c., and the disposition of the clouds, should be noted; -and after all this particularity, the question _how_ the house _came -to be struck?_ might ultimately depend on the fact that a flash of -lightning twenty miles off passed at that particular moment _from -the ground to the clouds_, by an effect of what has been termed the -returning stroke. - -(113.) A writer in the Edinburgh Philosophical Journal[35] states -himself to have been led into a series of investigations on the -chemical nature of a peculiar acid, by noticing, accidentally, a bitter -taste in a liquid about to be thrown away. Chemistry is full of such -incidents. - -(114.) In transient phenomena, if the number of particulars be -great, and the time to observe them short, we must consult our -memory before they have had time to fade, or refresh it by placing -ourselves as nearly as possible in the same circumstances again; go -back to the spot, for instance, and try the words of our statement -by appeal to all remaining indications, &c. This is most especially -necessary where we have not observed ourselves, but only collect and -record the observations of others, particularly of illiterate or -prejudiced persons, on any rare phenomenon, such as the passing of -a great meteor,--the fall of a stone from the sky,--the shock of an -earthquake,--an extraordinary hailstorm, &c. - -(115.) In all cases which admit of numeration or measurement, it is of -the utmost consequence to obtain precise numerical statements, whether -in the measure of time, space, or quantity of any kind. To omit this, -is, in the first place, to expose ourselves to illusions of sense which -may lead to the grossest errors. Thus, in alpine countries, we are -constantly deceived in heights and distances; and when we have overcome -the first impression which leads us to under-estimate them, we are then -hardly less apt to run into the opposite extreme. But it is not merely -in preserving us from exaggerated impressions that numerical precision -is desirable. It is the very soul of science; and its attainment -affords the only criterion, or at least the best, of the truth of -theories, and the correctness of experiments. Thus, it was entirely -to the omission of exact numerical determinations of quantity that the -mistakes and confusion of the Stahlian chemistry were attributable,--a -confusion which dissipated like a morning mist as soon as precision, -in this respect, came to be regarded as essential. Chemistry is in the -most pre-eminent degree a science of quantity; and to enumerate the -discoveries which have arisen in it, from the mere determination of -weights and measures, would be nearly to give a synopsis of this branch -of knowledge. We need only mention the law of definite proportions, -which fixes the composition of every body in nature in determinate -proportional weights of its ingredients. - -(116.) Indeed, it is a character of all the higher laws of nature to -assume the form of precise _quantitative_ statement. Thus, the law of -gravitation, the most universal truth at which human reason has yet -arrived, expresses not merely the general fact of the mutual attraction -of all matter; not merely the vague statement that its influence -decreases as the distance increases, but the exact numerical rate at -which that decrease takes place; so that when its amount is known at -any one distance it may be calculated exactly for any other. Thus, too, -the laws of crystallography, which limit the forms assumed by natural -substances, when left to their own inherent powers of aggregation, to -precise geometrical figures, with fixed angles and proportions, have -the same essential character of strict mathematical expression, without -which no exact particular conclusions could ever be drawn from them. - -(117.) But, to arrive at laws of this description, it is evident that -every step of our enquiry must be perfectly free from the slightest -degree of looseness and indecision, and carry with it the full force of -strict numerical announcement; and that, therefore, the observations -themselves on which all laws ultimately rest ought to have the same -property. None of our senses, however, gives us direct information -for the exact comparison of quantity. Number, indeed, that is to -say, integer number, is an object of sense, because we can count; -but we can neither weigh, measure, nor form any precise estimate of -fractional parts by the unassisted senses. Scarcely any man could tell -the difference between twenty pounds and the same weight increased or -diminished by a few ounces; still less could he judge of the proportion -between an ounce of gold and a hundred grains of cotton by balancing -them in his hands. To take another instance: the eye is no judge of the -proportion of different degrees of illumination, even when seen side -by side; and if an interval elapses, and circumstances change, nothing -can be more vague than its judgments. When we gaze with admiration -at the gorgeous spectacle of the golden clouds at sunset, which seem -drenched in light and glowing like flames of real fire, it is hardly -by any effort we can persuade ourselves to regard them as the very -same objects which at noonday pass unnoticed as mere white clouds -basking in the sun, only participating, from their great horizontal -distance, in the ruddy tint which luminaries acquire by shining through -a great extent of the vapours of the atmosphere, and thereby even -losing something of their light. So it is with our estimates of time, -velocity, and all other matters of quantity; they are absolutely vague, -and inadequate to form a foundation for any exact conclusion. - -(118.) In this emergency we are obliged to have recourse to -instrumental aids, that is, to contrivances which shall substitute for -the vague impressions of sense the precise one of number, and reduce -all measurement to counting. As a first preliminary towards effecting -this, we fix on convenient _standards_ of weight, dimension, time, -&c., and invent contrivances for readily and correctly repeating them -as often as we please, and counting how often such a standard unit is -contained in the thing, be it weight, space, time, or angle, we wish to -measure; and if there be a fractional part over, we measure this as a -new quantity by aliquot parts of the former standard. - -(119.) If every scientific enquirer observed only for his own -satisfaction, and reasoned only on his own observations, it would be -of little importance what standards he used, or what contrivances (if -only just ones) he employed for this purpose; but if it be intended -(as it is most important they should) that observations once made -should remain as records to all mankind, and to all posterity, it is -evidently of the highest consequence that all enquirers should agree on -the use of a common standard, and that this should be one not liable -to change by lapse of time. The selection and verification of such -standards, however, will easily be understood to be a matter of extreme -difficulty, if only from the mere circumstance that, to verify the -permanence of one standard, we must compare it with others, which it -is possible may be themselves inaccurate, or, at least, stand in need -of verification. - -(120.) Here we can only call to our assistance the presumed permanence -of the great laws of Nature, with all experience in its favour, and the -strong impression we have of the general composure and steadiness of -every thing relating to the gigantic mass we inhabit--“the great globe -itself.” In its uniform rotation on its axis, accordingly, we find a -standard of time, which nothing has ever given us reason to regard -as subject to change, and which, compared with other periods which -the revolutions of the planets about the sun afford, has demonstrably -undergone none since the earliest history. In the dimensions of the -earth we find a natural unit of the measure of space, which possesses -in perfection every quality that can be desired; and in its attraction -combined with its rotation the researches of dynamical science have -enabled us, through the medium of the pendulum, to obtain another -invariable standard, more refined and less obvious, it is true, in -its origin, but possessing a great advantage in its capability of -ready verification, and therefore easily made to serve as a check on -the other. The former, viz. direct measurement of the dimensions of -the earth, is the origin of the _mètre_, the French unit of linear -measure; the latter, of the British yard. Theoretically speaking, -they are equally eligible; but when we consider that the _quantity -directly measured_, in the case of the mètre, is a length a great many -thousand times the final unit, and in the pendulum or yard very nearly -the unit itself, there can be no hesitation in giving the preference -as an original measure to the former, because any error committed in -the process by which that is determined becomes subdivided in the -final result; while, on the other hand, any minute error committed -in determining the length of the pendulum becomes multiplied by the -repetition of the unit in all measurements of considerable lengths -performed in yards. - -(121.) The same admirable invention of the pendulum affords a means of -subdividing time to an almost unlimited nicety. A clock is nothing more -than a piece of mechanism for counting the oscillations of a pendulum; -and by that peculiar property of the pendulum, that one vibration -commences exactly where the last terminates, no part of time is lost -or gained in the juxta-position of the units so counted, so that the -precise fractional part of a day can be ascertained which each such -unit measures. - -(122.) It is owing to this peculiar property by which the -_juxta-position_ of units of time and weight can be performed _without -error_, that the whole of the accuracy with which time and weight can -be multiplied and subdivided is owing.[36] The same thing cannot be -accomplished in _space_, by any method we are yet acquainted with, so -that our means of subdividing space are much inferior in precision. -The beautiful principle of repetition, invented by Borda, offers the -nearest approach to it, but cannot be said to be absolutely free from -the source of error in question. The method of “double weighing,” which -we owe to the same distinguished observer, affords an instance of the -direct comparison of two equal weights independent of almost every -source of error which can affect the comparison of one object with -another. It has been remarked by Biot, that previous to the invention -of this elegant method, instruments afforded no perfect means of -ascertaining the weight of a body. - -(123.) But it is not enough to possess a standard of this abstract -kind: a real material measure must be constructed, and exact copies of -it taken. This, however, is not very difficult; the great difficulty -is to preserve it unaltered from age to age; for unless we transmit to -posterity the units of our measurements, _such as we have ourselves -used them_, we, in fact, only half bequeath to them our observations. -This is a point too much lost sight of, and it were much to be wished -that some direct provision for so important an object were made.[37] - -(124.) But, it may be asked, if our measurement of quantity is thus -unavoidably liable to error, how is it possible that our observations -can possess that quality of numerical veracity which is requisite to -render them the foundation of laws, whose distinguishing perfection -consists in their strict mathematical expression? To this the reply is -twofold. 1st, that though we admit the necessary existence of numerical -error in every observation, we can always assign a limit which such -error cannot possibly exceed; and the extent of this _latitude of -error of observation_ is less in proportion to the perfection of -the instrumental means we possess, and the care bestowed on their -employment. In the greater part of modern measurements it is, in point -of fact, extremely minute, and may be still further diminished, almost -to any required extent, by repeating the measurements a great number of -times, and under a great variety of circumstances, and taking a mean of -the results, when errors of opposite kinds will, at length, compensate -each other. But, 2dly, there exists a much more fundamental reply to -this objection. In reasoning upon our observations, the existence and -possible amount of quantitative error is always to be allowed for; and -the extent to which theories may be affected by it is never to be lost -sight of. In reasoning upwards, from observations confessedly imperfect -to general laws, we must take care always to regard our conclusions -as conditional, so far as they may be affected by such unavoidable -imperfections; and when at length we shall have arrived at our highest -point, and attained to axioms which admit of general and deductive -reasoning, the question, whether they _are_ vitiated by the errors of -observation or not, will still remain to be decided, and must become -the object of subsequent verification. This point will be made the -subject of more distinct consideration hereafter, when we come to speak -of the verification of theories and the laws of probability. - -(125.) With respect to our record of observations, it should be not -only circumstantial but _faithful_; by which we mean, that it should -contain all we did _observe_, and nothing else. Without any intention -of falsifying our record, we may do so unperceived by ourselves, owing -to a mixture of the views and language of an erroneous theory with -that of simple fact. Thus, for example, if, in describing the effect -of lightning, we should say, “The thunderbolt struck with violence -against the side of the house, and beat in the wall,” a fact would be -stated which we did not see, and would lead our hearers to believe that -a solid or ponderable projectile was concerned. The “strong smell of -sulphur,” which is sometimes said to accompany lightning, is a remnant -of the theory which made thunder and lightning the explosion of a kind -of aërial gunpowder, composed of sulphureous and nitrous exhalations. -There are some subjects particularly infested with this mixture of -theory in the statement of observed fact. The older chemistry was -so overborne by this mischief, as quite to confound and nullify the -descriptions of innumerable curious and laborious experiments. And in -geology, till a very recent period, it was often extremely difficult, -from this circumstance, to know what _were_ the facts observed. Thus, -Faujas de St. Fond, in his work on the volcanoes of central France, -describes with every appearance of minute precision craters existing -no where but in his own imagination. There is no greater fault (direct -falsification of fact excepted) which can be committed by an observer. - -(126.) When particular branches of science have acquired that degree -of consistency and generality, which admits of an abstract statement -of laws, and legitimate deductive reasoning, the principle of the -division of labour tends to separate the province of the observer from -that of the theorist. There is no accounting for the difference of -minds or inclinations, which leads one man to observe with interest -the developements of phenomena, another to speculate on their causes; -but were it not for this happy disagreement, it may be doubted whether -the higher sciences could ever have attained even their present degree -of perfection. As laws acquire generality, the influence of individual -observations becomes less, and a higher and higher degree of -refinement in their performance, as well as a great multiplication in -their number, becomes necessary to give them importance. In astronomy, -for instance, the superior departments of theory are completely -disjoined from the routine of practical observation. - -(127.) To make a perfect observer, however, either in astronomy -or in any other department of science, an extensive acquaintance -is requisite, not only with the particular science to which his -observations relate, but with every branch of knowledge which may -enable him to appretiate and neutralize the effect of extraneous -disturbing causes. Thus furnished, he will be prepared to seize on any -of those minute indications, which (such is the subtlety of nature) -often connect phenomena which seem quite remote from each other. He -will have his eyes as it were opened, that they may be struck at once -with any occurrence which, according to received theories, ought -not to happen; for these are the facts which serve as clews to new -discoveries. The deviation of the magnetic needle, by the influence -of an electrified wire, must have happened a thousand times to a -perceptible amount, under the eyes of persons engaged in galvanic -experiments, with philosophical apparatus of all kinds standing around -them; but it required the eye of a philosopher such as Oërsted to -seize the indication, refer it to its origin, and thereby connect -two great branches of science. The grand discovery of Malus of the -polarization of light by reflection originated in his casual remark of -the disappearance of one of the images of a window in the Luxembourg -palace, one evening, when strongly illuminated by the setting sun, -viewed through a doubly refracting prism. - -(128.) To avail ourselves as far as possible of the advantages which -a division of labour may afford for the collection of facts, by the -industry and activity which the general diffusion of information, -in the present age, brings into exercise, is an object of great -importance. There is scarcely any well-informed person, who, if he -has but the will, has not also the power to add something essential -to the general stock of knowledge, if he will only observe regularly -and methodically some particular class of facts which may most excite -his attention, or which his situation may best enable him to study -with effect. To instance one or two subjects, which can only be -effectually improved by the united observations of great numbers widely -dispersed:--Meteorology, one of the most complicated but important -branches of science, is at the same time one in which any person -who will attend to plain rules, and bestow the necessary degree of -attention, may do effectual service. What benefits has not Geology -reaped from the activity of industrious individuals, who, setting -aside all theoretical views, have been content to exercise the useful -and highly entertaining occupation of collecting specimens from the -countries which they visit? In short, there is no branch of science -whatever in which, at least, if useful and sensible queries were -distinctly proposed, an immense mass of valuable information might not -be collected from those who, in their various lines of life, at home -or abroad, stationary or in travel, would gladly avail themselves of -opportunities of being useful. Nothing would tend better to attain -this end than the circulation of printed skeleton forms, on various -subjects, which should be so formed as, 1st, to ask distinct and -pertinent questions, admitting of short and definite answers; 2dly, To -call for exact numerical statement on all principal points; 3dly, To -point out the attendant circumstances most likely to prove influential, -and which ought to be observed; 4thly, To call for their transmission -to a common centre. - - - - -CHAP. V. - -OF THE CLASSIFICATION OF NATURAL OBJECTS AND PHENOMENA, AND OF -NOMENCLATURE. - - -(129.) The number and variety of objects and relations which the -observation of nature brings before us are so great as to distract -the attention, unless assisted and methodized by such judicious -distribution of them in classes as shall limit our view to a few at -a time, or to groups so bound together by general resemblances that, -for the immediate purpose for which we consider them, they may be -regarded as individuals. Before we can enter into any thing which -deserves to be called a general and systematic view of nature, it is -necessary that we should possess an enumeration, if not complete, at -least of considerable extent, of her materials and combinations; and -that those which appear in any degree important should be distinguished -by names which may not only tend to fix them in our recollection, -but may constitute, as it were, nuclei or centres, about which -information may collect into masses. The imposition of a name on any -subject of contemplation, be it a material object, a phenomenon of -nature, or a group of facts and relations, looked upon in a peculiar -point of view, is an epoch in its history of great importance. It not -only enables us readily to refer to it in conversation or writing, -without circumlocution, but, what is of more consequence, it gives -it a recognized existence in our own minds, as a matter for separate -and peculiar consideration; places it on a list for examination; -and renders it a head or title, under which information of various -descriptions may be arranged; and, in consequence, fits it to perform -the office of a connecting link between all the subjects to which such -information may refer. - -(130.) For these purposes, however, a temporary or provisional name, -or one adapted for common parlance, may suffice. But when a very great -multitude of objects come to be referred to one class, especially of -such as do not offer very obvious and remarkable distinctions, a more -systematic and regular nomenclature becomes necessary, in which the -names shall recall the differences as well as the resemblances between -the individuals of a class, and in which the direct relation between -the name and the object shall materially assist the solution of the -problem, “_given the one, to determine the other_.” How necessary -this may become, will be at once seen, when we consider the immense -number of individual objects, or rather species, presented by almost -every branch of science of any extent; which absolutely require to be -distinguished by names. Thus, the botanist is conversant with from -80,000 to 100,000 species of plants; the entomologist with, perhaps, -as many, of insects: the chemist has to register the properties of -combinations, by twos, threes, fours, and upwards, in various doses -of upwards of fifty different elements, all distinguished from each -other by essential differences; and of which though a great many -thousands are known, by far the greater part have never yet been -formed, although hundreds of new ones are coming to light, in perpetual -succession, as the science advances; all of which are to be named as -they arise. The objects of astronomy are, literally, as numerous as the -stars of heaven; and although not more than one or two thousand require -to be expressed by distinct names, yet the number, respecting which -particular information is required, is not less than a hundred times -that amount; and all these must be registered in lists, (so as to be -at once referred to, and so that none shall escape,) if not by actual -names, at least by some equivalent means. - -(131.) Nomenclature, then, is, in itself, undoubtedly an important -part of science, as it prevents our being lost in a wilderness of -particulars, and involved in inextricable confusion. Happily, in those -great branches of science where the objects of classification are most -numerous, and the necessity for a clear and convenient nomenclature -most pressing, no very great difficulty in its establishment is felt. -The very multitude of the objects themselves affords the power of -grouping them in subordinate classes, sufficiently well defined to -admit of names, and these again into others, whose names may become -attached to, or compounded with, the former, till at length the -particular species is identified. The facility with which the botanist, -the entomologist, or the chemist, refers by name to any individual -object in his science shows what may be accomplished in this way -when characters are themselves distinct. In other branches, however, -considerable difficulty is experienced. This arises mostly where the -species to be distinguished are separated from each other chiefly by -difference in degree, of certain qualities common to all, and where the -degrees shade into each other insensibly. Perhaps such subjects can -hardly be considered ripe for systematic nomenclature; and that the -attempt to apply it ought only to be partial, embracing such groups -and parcels of individuals as agree in characters evidently natural -and generic, and leaving the remainder under trivial or provisional -denominations, till they shall be better known, and capable of being -scientifically grouped. - -(132.) Indeed, nomenclature, in a systematic point of view, is as -much, perhaps more, a consequence than a cause of extended knowledge. -Any one may give an arbitrary name to a thing, merely to be able to -talk of it; but, to give a name which shall at once refer it to a -place in a system, we must know its properties; and we must _have_ a -system, large enough, and regular enough, to receive it in a place -which belongs to it, and to no other. It appears, therefore, doubtful -whether it is desirable, for the essential purposes of science, that -extreme refinement in systematic nomenclature should be insisted on. -Were science perfect, indeed, systems of classification might be -agreed on, which should assign to every object in nature a place in -some class, to which it more remarkably and pre-eminently belonged -than to any other, and under which it might acquire a name, never -afterwards subject to change. But, so long as this is not the case, -and new relations are daily discovered, we must be very cautious how -we insist strongly on the establishment and extension of classes -which have in them any thing artificial, as a basis of a rigid -nomenclature; and especially how we mistake the means for the end, and -sacrifice convenience and distinctness to a rage for arrangement. Every -nomenclature dependent on artificial classifications is necessarily -subject to fluctuations; and hardly any thing can counterbalance the -evil of disturbing well-established names, which have once acquired a -general circulation. In nature, one and the same object makes a part of -an infinite number of different systems,--an individual in an infinite -number of groups, some of greater, some of less importance, according -to the different points of view in which they may be considered. Hence, -as many different systems of nomenclature may be imagined as there can -be discovered different heads of classification, while yet it is highly -desirable that each object should be universally spoken of under one -name, _if possible_. Consequently, in all subjects where comprehensive -heads of classification do not prominently offer themselves, all -nomenclature must be a balance of difficulties, and a good, short, -_unmeaning_ name, which has once obtained a footing in usage, is -preferable to almost any other. - -(133.) There is no science in which the evils resulting from a rage for -nomenclature have been felt to such an extent as in mineralogy. The -number of simple minerals actually recognised by mineralogists does not -exceed a few hundreds, yet there is scarcely one which has not four or -five names in different books. The consequence is most unhappy. No name -is suffered to endure long enough to take root; and every new writer -on this interesting science begins, as a matter of course, by making a -_tabula rasa_ of all former nomenclature, and proposing a new one in -its place. The climax has at length been put to this most inconvenient -and bewildering state of things by the appearance of a system supported -by extraordinary merit in other respects, and therefore carrying -the highest authority, in which names which had acquired universal -circulation, and had hitherto maintained their ground in the midst of -the general confusion, and even worked their way into common language, -as denotive of _species_ too definite to admit of mistake, are actually -rendered _generic_, and extended to whole groups, comprising objects -agreeing in nothing but the arbitrary heads of a classification -from which the most important natural relations are professedly and -purposely rejected.[38] - -(134.) The classifications by which science is advanced, however, are -widely different from those which serve as bases for artificial systems -of nomenclature. They cross and intersect one another, as it were, in -every possible way, and have for their very aim to interweave all the -objects of nature in a close and compact web of mutual relations and -dependence. As soon, then, as any resemblance or analogy, any point of -agreement whatever, is perceived between any two or more things,--be -they what they will, whether objects, or phenomena, or laws,--they -immediately and _ipso facto_ constitute themselves into a group or -class, which may become enlarged to any extent by the accession of -such new objects, phenomena, or laws, agreeing in the same point, as -may come to be subsequently ascertained. It is thus that the materials -of the world become grouped in natural families, such as chemistry -furnishes examples of, in its various groups of acids, alkalies, -sulphurets, &c.; or botany, in its euphorbiaceæ, umbelliferæ, &c. It is -thus, too, that phenomena assume their places under general points of -resemblance; as, in optics, those which refer themselves to the class -of periodic colours, double refraction, &c.; and that resemblances -themselves become traced, which it is the business of induction to -generalize and include in abstract propositions. - -(135.) But every class formed on a positive resemblance of characters, -or on a distinct analogy, draws with it the consideration of a negative -class, in which that resemblance either does not subsist at all, or the -contrary takes place; and again, there are classes in which a given -quality is possessed by the different individuals in a descending scale -of intensity. Now, it is of consequence to distinguish between cases -in which there is a real opposition of quality, or a mere diminution -of intensity, in some quality susceptible of degrees, till it becomes -imperceptible. For example, between transparency and opacity there -would at first sight appear a direct opposition; but, on nearer -consideration, when we consider the gradations by which transparency -diminishes in natural substances, we shall see reason to admit that -the latter quality, instead of being the _opposite_ of the former, -is only its _extreme lowest degree_. Again, in the arrangement of -natural objects under the head of weight or specific gravity, the scale -extends through all nature, and we know of no natural body in which the -opposite of gravity, or positive _levity_, subsists. On the other hand, -the opposite electricities; the north and south magnetic polarities; -the alkaline and acid qualities of chemical agents; the positive and -negative rotations impressed by plates of rock crystal on the planes -of polarization of the rays of light, and many other cases, exemplify -not merely a negation, but an active opposition of quality. Both these -modes of classification have their peculiar importance in the inductive -process: the one, as affording an opportunity of tracing a relation -between phenomena by the observation of a correspondence in their -scales of intensity; the other, by that of contrast, as we shall show -more at large in the next section. - -(136.) There is a very wide distinction, too, to be taken between such -classes as turn upon a single head of resemblance among individuals -otherwise very different, and such as bind together in natural groups, -by a great variety of analogies, objects which yet differ in many -remarkable particulars. For example: if we make colourless transparency -a head of classification, the list of the class will comprise objects -differing most widely in their nature, such as water, air, diamond, -spirit of wine, glass, &c. On the other hand, the chemical families of -alkalies, metals, &c. are instances of groups of the other kind; which, -with properties in many respects different, still agree in a general -resemblance of several others, which at once decides us in considering -them as having a natural relation. In the former cases, our ingenuity -is exercised to determine what can be the cause of their resemblance, -in the latter, of their difference; the former belong to the province -of inductive generalization, and afford the most instructive cases for -the investigation of causes; the latter appertain to the more secret -recesses of nature; the very existence of such families being in itself -one of the great and complicated phenomena of the universe, which we -cannot hope to unriddle without an intimate and extensive acquaintance -with the highest laws.[39] - - - - -CHAP. VI. - - OF THE FIRST STAGE OF INDUCTION.--THE DISCOVERY OF PROXIMATE - CAUSES, AND LAWS OF THE LOWEST DEGREE OF GENERALITY, AND THEIR - VERIFICATION. - - -(137.) The first thing that a philosophic mind considers, when any -new phenomenon presents itself, is its _explanation_, or reference -to an immediate producing cause. If that cannot be ascertained, the -next is to _generalize_ the phenomenon, and include it, with others -analogous to it, in the expression of some law, in the hope that its -consideration, in a more advanced state of knowledge, may lead to the -discovery of an adequate proximate cause. - -(138.) Experience having shown us the manner in which one phenomenon -depends on another in a great variety of cases, we find ourselves -provided, as science extends, with a continually increasing stock -of such antecedent phenomena, or causes (meaning at present merely -proximate causes), competent, under different modifications, to the -production of a great multitude of effects, besides those which -originally led to a knowledge of them. To such causes Newton has -applied the term _veræ causæ_; that is, causes recognized as having a -real existence in nature, and not being mere hypotheses or figments -of the mind. To exemplify the distinction:--The phenomenon of shells -found in rocks, at a great height above the sea, has been attributed -to several causes. By some it has been ascribed to a plastic virtue in -the soil; by some, to fermentation; by some, to the influence of the -celestial bodies; by some, to the casual passage of pilgrims with their -scallops; by some, to birds feeding on shell-fish; and by all modern -geologists, with one consent, to the life and death of real mollusca -at the bottom of the sea, and a subsequent alteration of the relative -level of the land and sea. Of these, the plastic virtue and celestial -influence belong to the class of figments of fancy. Casual transport -by pilgrims is a real cause, and might account for a few shells here -and there dropped on frequented passes, but is not extensive enough for -the purpose of explanation. Fermentation, generally, is a real cause, -so far as that there _is such a thing_; but it is not a real cause -of the production of a shell in a rock, since no such thing was ever -witnessed as one of its effects, and rocks and stones do not ferment. -On the other hand, for a shell-fish dying at the bottom of the sea to -leave his shell in the mud, where it becomes silted over and imbedded, -happens daily; and the elevation of the bottom of the sea to become dry -land has really been witnessed so often, and on such a scale, as to -qualify it for a _vera causa_ available in sound philosophy. - -(139.) To take another instance, likewise drawn from the same -deservedly popular science:--The fact of a great change in the general -climate of large tracts of the globe, if not of the whole earth, -and of a diminution of general temperature, having been recognised -by geologists, from their examination of the remains of animals and -vegetables of former ages enclosed in the strata, various causes for -such diminution of temperature have been assigned. Some consider -the whole globe as having gradually cooled from absolute fusion; -some regard the immensely superior activity of former volcanoes, and -consequent more copious communication of internal heat to the surface, -in former ages, as the cause. Neither of these can be regarded as -real causes in the sense here intended; for we do not _know_ that the -globe has so cooled from fusion, nor are we sure that such supposed -greater activity of former than of present volcanoes really did exist. -A cause, possessing the essential requisites of a _vera causa_, has, -however, been brought forward[40] in the varying influence of the -distribution of land and sea over the surface of the globe: a change -of such distribution, in the lapse of ages, by the degradation of the -old continents, and the elevation of new, being a demonstrated fact; -and the influence of such a change on the climates of particular -regions, if not of the whole globe, being a perfectly fair conclusion, -from what we know of continental, insular, and oceanic climates by -actual observation. Here, then, we have, at least, a cause on which a -philosopher may consent to reason; though, whether the changes actually -going on are such as to warrant the whole extent of the conclusion, -or are even taking place in the right direction, may be considered as -undecided till the matter has been more thoroughly examined. - -(140.) To this we may add another, which has likewise the essential -characters of a _vera causa_, in the astronomical _fact_ of the actual -slow diminution of the eccentricity of the earth’s orbit round the -sun; and which, as a general one, affecting the _mean temperature of -the whole globe_, and as one of which the effect is both inevitable, -and susceptible, to a certain degree, of exact estimation, deserves -consideration. It is evident that the _mean_ temperature of the -whole surface of the globe, in so far as it is maintained by the -action of the sun at a higher degree than it would have were the sun -extinguished, must depend on the mean quantity of the sun’s rays which -it receives, or, which comes to the same thing, on the _total_ quantity -received in a given invariable time: and the length of the year -being unchangeable in all the fluctuations of the planetary system, -it follows, that the total _annual_ amount of solar radiation will -determine, _cæteris paribus_, the general climate of the earth. Now, -it is not difficult to show that this amount is inversely proportional -to the minor axis of the ellipse described by the earth about the -sun, regarded as slowly variable; and that, therefore, the major axis -remaining, as we know it to be, constant, and the orbit being actually -in a state of approach to a circle, and, consequently, the minor axis -being on the _increase_, the mean annual amount of solar radiation -received by the whole earth must be actually on the _decrease_. We have -here, therefore, an evident real cause, of sufficient universality, and -acting _in the right direction_, to account for the phenomenon. Its -adequacy is another consideration.[41] - -(141.) Whenever, therefore, any phenomenon presents itself for -explanation, we naturally seek, in the first instance, to refer it to -some one or other of those real causes which experience has shown to -exist, and to be efficacious in producing similar phenomena. In this -attempt our probability of success will, of course, mainly depend, -1st, On the number and variety of causes experience has placed at our -disposal; 2dly, On our habit of applying them to the explanation of -natural phenomena; and, 3dly, On the number of analogous phenomena -we can collect, which have either been explained, or which admit of -explanation by some one or other of those causes, and the closeness of -their analogy with that in question. - -(142.) Here, then, we see the great importance of possessing a stock -of analogous instances or phenomena which class themselves with that -under consideration, the explanation of one among which may naturally -be expected to lead to that of all the rest. If the analogy of two -phenomena be very close and striking, while, at the same time, the -cause of one is very obvious, it becomes scarcely possible to refuse -to admit the action of an analogous cause in the other, though not so -obvious in itself. For instance, when we see a stone whirled round in a -sling, describing a circular orbit round the hand, keeping the string -stretched, and flying away the moment it breaks, we never hesitate -to regard it as retained in its orbit by the tension of the string, -that is, by _a force_ directed to the centre; for we feel that we do -really exert such a force. We have here _the direct perception_ of the -cause. When, therefore, we see a great body like the moon circulating -round the earth and not flying off, we cannot help believing it to -be prevented from so doing, not indeed by a material tie, but by -that which operates in the other case through the intermedium of the -string,--a _force_ directed constantly to the centre. It is thus that -we are continually acquiring a knowledge of the existence of causes -acting under circumstances of such concealment as effectually to -prevent their direct discovery. - -(143.) In general we must observe that motion, wherever produced or -changed, invariably points out the existence of _force_ as its cause; -and thus the forces of nature become known and measured by the -motions they produce. Thus, the _force_ of magnetism becomes known by -the deviation produced by iron in a compass needle, or by a needle -leaping up to a magnet held over it, as certainly as by that adhesion -to it, when in contact and at rest, which requires force to break the -connection; and thus the currents produced in the surface of a quantity -of quicksilver, electrified under a conducting fluid, have pointed out -the existence and direction of forces of enormous intensity developed -by the electric circuit, of which we should not otherwise have had the -least suspicion.[42] - -(144.) But when the cause of a phenomenon neither presents itself -obviously on the consideration of the phenomenon itself, nor is as it -were forced on our attention by a case of strong analogy, such as above -described, we have then no resource but in a deliberate assemblage of -all the parallel instances we can muster; that is, to the formation -of a class of facts, having the phenomenon in question for a head of -classification; and to a search among the individuals of this class -for some other common points of agreement, among which the cause will -of necessity be found. But if more than one cause should appear, we -must then endeavour to find, or, if we cannot find, to _produce, new -facts_, in which each of these in succession shall be wanting, while -yet they agree in the general point in question. Here we find the use -of what Bacon terms “_crucial instances_,” which are phenomena brought -forward to decide between two causes, each having the same analogies in -its favour. And here, too, we perceive the utility of _experiment_ as -distinguished from mere passive observation. We make an experiment of -the crucial kind when we form combinations, and put in action causes -from which some particular one shall be deliberately excluded, and -some other purposely admitted; and by the agreement or disagreement of -the resulting phenomena with those of the class under examination, we -decide our judgment. - -(145.) When we would lay down general rules for guiding and -facilitating our search, among a great mass of assembled facts, for -their common cause, we must have regard to the characters of that -relation which we intend by cause and effect. Now, these are,-- - - 1st, Invariable connection, and, in particular, invariable - antecedence of the cause and consequence of the effect, unless - prevented by some counteracting cause. But it must be observed, - that, in a great number of natural phenomena, the effect is - produced gradually, while the cause often goes on increasing in - intensity; so that the antecedence of the one and consequence - of the other becomes difficult to trace, though it really - exists. On the other hand, the effect often follows the cause - so instantaneously, that the interval cannot be perceived. In - consequence of this, it is sometimes difficult to decide, of two - phenomena constantly accompanying one another, which is cause or - which effect. - - 2d, Invariable negation of the effect with absence of the cause, - unless some other cause be capable of producing the same effect. - - 3d, Increase or diminution of the effect, with the increased - or diminished intensity of the cause, in cases which admit of - increase and diminution. - - 4th, Proportionality of the effect to its cause in all cases of - _direct unimpeded_ action. - - 5th, Reversal of the effect with that of the cause. - -(146.) From these characters we are led to the following observations, -which may be considered as so many propositions readily applicable to -particular cases, or rules of philosophizing: we conclude, 1st, That if -in our group of facts there be one in which any assigned peculiarity, -or attendant circumstance, is wanting or opposite, such peculiarity -cannot be the cause we seek. - -(147.) 2d, That any circumstance in which all the facts without -exception agree, _may_ be the cause in question, or, if not, at least -a collateral effect of the same cause: if there be but one such point -of agreement, this possibility becomes a certainty; and, on the other -hand, if there be more than one, they may be concurrent causes. - -(148.) 3d, That we are not to deny the existence of a cause in favour -of which we have a unanimous agreement of strong analogies, though -it may not be apparent how such a cause can produce the effect, or -even though it may be difficult to conceive its existence under the -circumstances of the case; in such cases we should rather appeal to -experience when possible, than decide _à priori_ against the cause, and -try whether it cannot be made apparent. - -(149.) For instance: seeing the sun vividly luminous, every analogy -leads us to conclude it intensely hot. How heat can produce light, -we know not; and how such a heat can be maintained, we can form no -conception. Yet we are not, therefore, entitled to deny the inference. - -(150.) 4th, That contrary or opposing facts are equally instructive for -the discovery of causes with favourable ones. - -(151.) For instance: when air is confined with moistened iron filings -in a close vessel over water, its bulk is diminished, by a certain -portion of it being abstracted and combining with the iron, producing -_rust_. And, if the remainder be examined, it is found that it will -_not_ support flame or animal life. This contrary fact shows that the -cause of the support of flame and animal life is to be looked for in -that part of the air which the iron abstracts, and which rusts it. - -(152.) 5th, That causes will very frequently become obvious, by a -mere arrangement of our facts in the order of intensity in which -some peculiar quality subsists; though not of necessity, because -counteracting or modifying causes may be at the same time in action. - -(153.) For example: sound consists in impulses communicated to our ears -by the air. If a series of impulses of equal force be communicated -to it at equal intervals of time, at first in slow succession, and -by degrees more and more rapidly, we hear at first a rattling noise, -then a low murmur, and then a hum, which by degrees acquires the -character of a musical note, rising higher and higher in acuteness, -till its pitch becomes too high for the ear to follow. And from -this correspondence between the pitch of the note and the rapidity -of succession of the impulse, we conclude that our sensation of -the different pitches of musical notes originates in the different -rapidities with which their impulses are communicated to our ears. - -(154.) 6th, That such counteracting or modifying causes may subsist -unperceived, and annul the effects of the cause we seek, in instances -which, but for their action, would have come into our class of -favourable facts; and that, therefore, exceptions may often be made -to disappear by removing or allowing for such counteracting causes. -This remark becomes of the greatest importance, when (as is often the -case) a single striking exception stands out, as it were, against an -otherwise unanimous array of facts in favour of a certain cause. - -(155.) Thus, in chemistry, the _alkaline_ quality of the alkaline -and earthy bases is found to be due to the presence of oxygen -combined with one or other of a peculiar set of metals. Ammonia is, -however, a violent outstanding exception, such as here alluded to, -being a compound of azote and hydrogen: but there are almost certain -indications that this exception is not a real one, but assumes that -appearance in consequence of some modifying cause not understood. - -(156.) 7th, If we can either find produced by nature, or produce -designedly for ourselves, two instances which agree _exactly_ in all -but one particular, and differ in that one, its influence in producing -the phenomenon, if it have any, _must_ thereby be rendered sensible. -If that particular be present in one instance and wanting altogether -in the other, the production or non-production of the phenomenon will -decide whether it be or be not the only cause: still more evidently, -if it be present _contrariwise_ in the two cases, and the effect be -thereby reversed. But if its total presence or absence only produces -a change in the _degree_ or intensity of the phenomenon, we can then -only conclude that it acts as a concurrent cause or condition with -some other to be sought elsewhere. In nature, it is comparatively -rare to find instances pointedly differing in one circumstance and -agreeing in every other; but when we call experiment to our aid, it -is easy to produce them; and this is, in fact, the grand application -of _experiments of enquiry_ in physical researches. They become more -valuable, and their results clearer, in proportion as they possess this -quality (of agreeing exactly in all their circumstances but one), since -the question put to nature becomes thereby more pointed, and its answer -more decisive. - -(157.) 8th, If we cannot obtain a complete negative or opposition of -the circumstance whose influence we would ascertain, we must endeavour -to find cases where it varies considerably in degree. If _this_ cannot -be done, we may perhaps be able to weaken or exalt its influence by -the introduction of some fresh circumstance, which, abstractedly -considered, seems _likely_ to produce this effect, and thus obtain -indirect evidence of its influence. But then we are always to remember, -that the evidence so obtained _is_ indirect, and that the new -circumstance introduced _may_ have a direct influence of its own, or -may exercise a modifying one on some _other_ circumstance. - -(158.) 9th, Complicated phenomena, in which several causes concurring, -opposing, or quite independent of each other, operate at once, so as to -produce a compound effect, may be simplified by subducting the effect -of all the known causes, as well as the nature of the case permits, -either by deductive reasoning or by appeal to experience, and thus -leaving, as it were, a _residual phenomenon_ to be explained. It is by -this process, in fact, that science, in its present advanced state, is -chiefly promoted. Most of the phenomena which nature presents are very -complicated; and when the effects of all known causes are estimated -with exactness, and subducted, the residual facts are constantly -appearing in the form of phenomena altogether new, and leading to the -most important conclusions. - -(159.) For example: the return of the comet predicted by professor -Encke, a great many times in succession, and the general good agreement -of its calculated with its observed place during any one of its periods -of visibility, would lead us to say that its gravitation towards the -sun and planets is the sole and sufficient cause of all the phenomena -of its orbitual motion; but when the effect of this cause is strictly -calculated and subducted from the observed motion, there is found to -remain behind a _residual phenomenon_, which would never have been -otherwise ascertained to exist, which is a small anticipation of the -time of its reappearances or a diminution of its periodic time, which -cannot be accounted for by gravity, and whose cause is therefore to be -enquired into. Such an anticipation would be caused by the resistance -of a medium disseminated through the celestial regions; and as there -are other good reasons for believing this to be a _vera causa_, it has -therefore been ascribed to such a resistance. - -(160.) This 9th observation is of such importance in science, that -we shall exemplify it by another instance or two. M. Arago, having -suspended a magnetic needle by a silk thread, and set it in vibration, -observed, that it came much sooner to a state of rest when suspended -over a plate of copper, than when no such plate was beneath it. Now, in -both cases there were two _veræ causæ_ why it _should_ come at length -to rest, viz. the resistance of the air, which opposes, and at length -destroys, all motions performed in it; and the want of perfect mobility -in the silk thread. But the effect of these causes being exactly known -by the observation made in the absence of the copper, and being thus -allowed for and subducted, a _residual_ phenomenon appeared, in the -fact that a retarding influence was exerted by the copper itself; -and this fact, once ascertained, speedily led to the knowledge of -an entirely new and unexpected class of relations. To add one more -instance. If it be true (as M. Fourrier considers it demonstrated to -be) that the celestial regions have a temperature independent of the -sun, not greatly inferior to that at which quicksilver congeals, and -much superior to some degrees of cold which have been artificially -produced, two causes suggest themselves: one is that assigned by the -author above mentioned; the radiation of the stars; another may be -proposed in the ether or elastic medium mentioned in the last section, -which the phenomena of light and the resistance of comets give us -reason to believe fills all space, and which, in analogy to all the -elastic media known, may be supposed to possess a temperature and a -specific heat of its own, which it is capable of communicating to -bodies surrounded by it. Now, if we consider that the heat radiated -by the sun follows the same proportion as its light, and regard it as -reasonable to admit with respect to stellar heat what holds good of -solar; the effect of stellar radiation in maintaining a temperature in -space should be as much inferior to that of the radiation of the sun -as the light of a moonless midnight is to that of an equatorial noon; -that is to say, almost inconceivably smaller. Allowing, then, the full -effect for this cause, there would still remain a great residuum due to -the presence of the ether. - -(161.) Many of the new elements of chemistry have been detected in -the investigation of _residual phenomena_. Thus, Arfwedson discovered -lithia by perceiving an _excess of weight_ in the sulphate produced -from a small portion of what he considered as magnesia present in a -mineral he had analysed. It is on this principle, too, that the _small -concentrated residues of great operations_ in the arts are almost -sure to be the lurking places of new chemical ingredients: witness -iodine, brome, selenium, and the new metals accompanying platina in the -experiments of Wollaston and Tennant. It was a happy thought of Glauber -to examine what every body else threw away. - -(162.) Finally, we have to observe, that the detection of a _possible_ -cause, by the comparison of assembled cases, _must_ lead to one of -two things: either, 1st, The detection of a real cause, and of its -manner of acting, so as to furnish a complete explanation of the facts; -or, 2dly, The establishment of an abstract law of nature, pointing -out two phenomena of a general kind as invariably connected; and -asserting, that where one is, there the other will always be found. -Such invariable connection is itself a phenomenon of a higher order -than any particular fact; and when many such are discovered, we may -again proceed to classify, combine, and examine them, with a view to -the detection of _their_ causes, or the discovery of still more general -laws, and so on without end. - -(163.) Let us now exemplify this inductive search for a cause by one -general example: suppose _dew_ were the phenomenon proposed, whose -cause we would know. In the first place, we must separate dew from rain -and the moisture of fogs, and limit the application of the term to -what is really meant, which is, the spontaneous appearance of moisture -on substances exposed in the open air when no rain or _visible_ wet -is falling. Now, here we have analogous phenomena in the moisture -which bedews a cold metal or stone when we breathe upon it; that which -appears on a glass of water fresh from the well in hot weather; that -which appears on the _inside_ of windows when sudden rain or hail -chills the external air; that which runs down our walls when, after -a long frost, a warm moist thaw comes on: all these instances agree -in one point (Rule 2. § 147.), the coldness of the object dewed, in -comparison with the air in contact with it. - -(164.) But, in the case of the night dew, is this a _real cause_--is it -a fact that the object dewed _is_ colder than the air? Certainly not, -one would at first be inclined to say; for what is to _make_ it so? But -the analogies are cogent and unanimous; and, therefore, (pursuant to -Rule 3. § 148.) we are not to discard their indications; and, besides, -the experiment is easy: we have only to lay a thermometer in contact -with the dewed substance, and hang one at a little distance above it -out of reach of its influence. The experiment has been therefore made; -the question has been asked, and the answer has been invariably in the -_affirmative_. Whenever an object contracts dew, _it is_ colder than -the air. Here, then, we have _an invariable concomitant_ circumstance: -but is this chill an effect of dew, or its cause? That dews are -accompanied with a chill is a common remark; but vulgar prejudice would -make the cold the _effect_ rather than the cause. We must, therefore, -collect more facts, or, which comes to the same thing, vary the -circumstances; since every instance in which the circumstances differ -is a fresh fact; and, especially, we must note the contrary or negative -cases (Rule 4. § 150.), _i. e._ where no dew is produced. - -(165.) Now, 1st, no dew is produced on the surface of _polished -metals_, but it is very copiously on glass, both exposed with their -faces upwards, and in some cases the under side of a horizontal plate -of glass is also dewed; which last circumstance (by Rule 1. § 146.) -excludes the _fall_ of moisture from the sky in an invisible form, -which would naturally suggest itself as a cause. In the cases of -polished metal and polished glass, the contrast shows evidently that -the _substance_ has much to do with the phenomenon; therefore, let -the substance _alone_ be diversified as much as possible, by exposing -polished surfaces of various kinds. This done, _a scale of intensity_ -becomes obvious (Rule 5. § 152.). Those polished substances are found -to be most strongly dewed which conduct heat worst; while those which -conduct well resist dew most effectually. Here we encounter a _law_ -of the first degree of generality. But, if we expose rough surfaces, -instead of polished, we sometimes find this law interfered with -(Rule 5. § 152.). Thus, roughened iron, especially if painted over -or blackened, becomes dewed sooner than varnished paper: the kind of -_surface_ therefore has a great influence. Expose, then, the _same_ -material in very diversified states as to surface (Rule 7. § 156.), and -another scale of intensity becomes at once apparent; those _surfaces_ -which _part with their heat_ most readily by radiation are found to -contract dew most copiously: and thus we have detected another law of -the same generality with the former, by a comparison of two classes of -facts, one relating to dew, the other to the radiation of heat from -surfaces. Again, the influence ascertained to exist of _substance_ and -_surface_ leads us to consider that of _texture_: and here, again, we -are presented on trial with remarkable differences, and with a third -_scale of intensity_, pointing out substances of a close firm texture, -such as stones, metals, &c. as unfavourable, but those of a loose one, -as cloth, wool, velvet, eiderdown, cotton, &c. as eminently favourable, -to the contraction of dew: and these are precisely those which are best -adapted for clothing, or for impeding the free passage of heat from -the skin into the air, so as to allow their outer surfaces to be very -cold while they remain warm within. - -(166.) Lastly, among the negative instances, (§ 150.) it is observed, -that dew is never copiously deposited in situations much screened -from the open sky, and not at all in _a cloudy night_; but if the -clouds withdraw, even for a few minutes, and leave a clear opening, -a deposition of dew presently begins, and goes on increasing. Here, -then, a cause is distinctly pointed out by its antecedence to the -effect in question (§ 145.). A clear view of the cloudless sky, then, -is an essential condition, or, which comes to the same thing, clouds or -surrounding objects act as _opposing causes_. This is so much the case, -that dew formed in clear intervals will often even evaporate again when -the sky becomes thickly overcast (Rule 4. § 150.). - -(167.) When we now come to assemble these partial inductions so as to -raise from them a general conclusion, we consider, 1st, That all the -conclusions we have come to have a reference to that first general -fact--the cooling of the exposed surface of the body dewed below -the temperature of the air. Those surfaces which part with their -heat outwards most readily, and have it supplied from within most -slowly, will, of course, become coldest if there be an opportunity -for their heat to escape, and not be restored to them from without. -Now, a clear sky affords such an opportunity. It is a law well known -to those who are conversant with the nature of heat, that heat is -constantly escaping from _all bodies_ in rays, or by _radiation_, but -is as constantly restored to them by the similar radiation of others -surrounding them. Clouds and surrounding objects therefore act as -opposing causes by replacing the whole or a great part of the heat so -radiated away, which can escape effectually, without being replaced, -only through openings into infinite space. Thus, at length, we arrive -at the general proximate cause of dew, in the cooling of the dewed -surface by radiation faster than its heat can be restored to it, by -communication with the ground, or by counter-radiation; so as to -become colder than the air, and thereby to cause a condensation of its -moisture. - -(168.) We have purposely selected this theory of dew, first developed -by the late Dr. Wells, as one of the most beautiful specimens we can -call to mind of inductive experimental enquiry lying within a moderate -compass. It is not possible in so brief a space to do it justice; but -we earnestly recommend his work[43] (a short and very entertaining one) -for perusal to the student of natural philosophy, as a model with which -he will do well to become familiar. - -(169.) In the analysis above given, the formation of dew is referred to -two more general phenomena; the radiation of heat, and the condensation -of invisible vapour by cold. The cause of the former is a much higher -enquiry, and may be said, indeed, to be totally unknown; that of the -latter actually forms a most important branch of physical enquiry. In -such a case, when we reason upwards till we reach an ultimate fact, we -regard a phenomenon as fully explained; as we consider the branch of -a tree to terminate when traced to its insertion in the trunk, or a -twig to its junction with the branch; or rather, as a rivulet retains -its importance and its name till lost in some larger tributary, or in -the main river which delivers it into the ocean. This, however, always -supposes that, on a reconsideration of the case, we see clearly how the -admission of such a fact, with all its attendant laws, will perfectly -account for _every particular_--as well those which, in the different -stages of the induction, have led us to a knowledge of it, as those -which we had neglected, or considered less minutely than the rest. -But, had we no previous knowledge of the radiation of heat, this same -induction would have made it known to us, and, duly considered, might -have led to the knowledge of many of its laws. - -(170.) In the study of nature, we must not, therefore, be scrupulous -as to _how_ we reach to a knowledge of such general facts: provided -only we verify them carefully when once detected, we must be content -to seize them wherever they are to be found. And this brings us to -consider the _verification_ of inductions. - -(171.) If, in our induction, every individual case has actually been -present to our minds, we are sure that it will find itself duly -_represented_ in our final conclusion: but this is impossible for -such cases as were _unknown_ to us, and hardly ever happens even -with all the known cases; for such is the tendency of the human mind -to speculation, that on the least idea of an analogy between a few -phenomena, it leaps forward, as it were, to a cause or law, to the -temporary neglect of all the rest; so that, in fact, almost all our -principal inductions must be regarded as a series of ascents and -descents, and of conclusions from a few cases, verified by trial on -many. - -(172.) Whenever, therefore, we think we have been led by induction to -the knowledge of the proximate cause of a phenomenon or of a law of -nature, our next business is to examine deliberately and _seriatim_ -all the cases we have collected of its occurrence, in order to satisfy -ourselves that they are explicable by our cause, or fairly included in -the expression of our law: and in case any exception occurs, it must -be carefully noted and set aside for re-examination at a more advanced -period, when, possibly, the cause of exception may appear, and the -exception itself, by allowing for the effect of that cause, be brought -over to the side of our induction; but should exceptions prove numerous -and various in their features, our faith in the conclusion will be -proportionally shaken, and at all events its importance lessened by the -destruction of its universality. - -(173.) In the conduct of this verification, we are to consider whether -the cause or law to which we are conducted be one already known and -recognised as a more general one, whose nature is well understood, and -of which the phenomenon in question is but one more case in addition -to those already known, or whether it be one less general, less known, -or altogether new. In the latter case, our verification will suffice, -if it merely shows that all the cases considered are plainly cases in -point. But in the former, the process of verification is of a much -more severe and definite kind. We must trace the action of our cause -with distinctness and precision, as modified by all the circumstances -of each case; we must estimate its effects, and show that nothing -unexplained remains behind; at least, in so far as the presence of -unknown modifying causes is not concerned. - -(174.) Now, this is precisely the sort of process in which _residual -phenomena_ (such as spoken of in art. 158.) may be expected to occur. -If our induction be really a valid and a comprehensive one, _whatever_ -remains unexplained in the comparison of its conclusion with particular -cases, under all their circumstances, _is_ such a phenomenon, and comes -in its turn to be a subject of inductive reasoning to discover its -cause or laws. It is thus that we may be said to witness facts with -the eyes of reason; and it is thus that we are continually attaining a -knowledge of new phenomena and new laws which lie beneath the surface -of things, and give rise to the creation of fresh branches of science -more and more remote from common observation. - -(175.) Physical astronomy affords numerous and splendid instances of -this. The law, for example, which asserts that the planets are retained -in their orbits about the sun, and satellites about their primaries, -by an attractive force, decreasing as the square of the distances -increases, comes to be verified in each particular case by deducing -from it the exact motions which, under the circumstances, ought to take -place, and comparing them with fact. This comparison, while it verifies -in general the existence of the law of gravitation as supposed, and -its adequacy to explain all the principal motions of every body in the -system, yet leaves some small deviations in those of the planets, and -some very considerable ones in that of the moon and other satellites, -still unaccounted for; residual phenomena, which still remain to be -traced up to causes. By further examining these, their causes have at -length been ascertained, and found to consist in the mutual actions of -the planets on each other, and the disturbing influence of the sun on -the motions of the satellites. - -(176.) But a law of nature has not that degree of generality which -fits it for a stepping-stone to greater inductions, unless it be -_universal_ in its application. We cannot rely on its enabling us to -extend our views beyond the circle of instances from which it was -obtained, unless we have already had experience of its power to do so; -unless it actually _has_ enabled us before trial to say what will take -place in cases analogous to those originally contemplated; unless, in -short, we have studiously placed ourselves in the situation of its -antagonists, and even perversely endeavoured to find exceptions to -it without success. It is in the precise proportion that a law once -obtained endures this extreme severity of trial, that its value and -importance are to be estimated; and our next step in the verification -of an induction must therefore consist in _extending_ its application -to cases not originally contemplated; in studiously varying the -circumstances under which our causes act, with a view to ascertain -whether their effect is general; and in pushing the application of our -laws to extreme cases. - -(177.) For example, a fair induction from a great number of facts led -Galileo to conclude that the accelerating power of gravity is the same -on all sorts of bodies, and on great and small masses indifferently; -and this he exemplified by letting bodies of very different natures -and weights fall at the same instant from a high tower, when it was -observed that they struck the ground at the same moment, abating a -certain trifling difference, due, as he justly believed it to be, to -the greater proportional resistance of the air to light than to heavy -bodies. The experiment could not, at that time, be fairly tried with -extremely light substances, such as cork, feathers, cotton, &c. because -of the great resistance experienced by these in their fall; no means -being then known of removing this cause of disturbance. It was not, -therefore, till after the invention of the air-pump that this law could -be put to the severe test of an extreme case. A guinea and a downy -feather were let drop at once from the upper part of a tall exhausted -glass, and struck the bottom at the same moment. Let any one make the -trial _in the air_, and he will perceive the force of an _extreme case_. - -(178.) In the verification of a law whose expression is _quantitative_, -not only must its generality be established by the trial of it in as -various circumstances as possible, but every such trial must be one of -precise measurement. And in such cases the means taken for subjecting -it to trial ought to be so devised as to repeat and multiply a great -number of times any deviation (if any exist); so that, let it be ever -so small, it shall at last become sensible. - -(179.) For instance, let the law to be verified be, that _the gravity -of every material body is in the direct proportion of its mass_, which -is only another mode of expressing Galileo’s law above mentioned. -The time of falling from any moderate height cannot be measured with -precision enough for our purpose: but if it can be repeated a very -great multitude of times _without any loss or gain_ in the intervals, -and the whole amount of the times of fall so repeated measured by -a clock; and if at the same time the resistance of the air can be -rendered _exactly alike_ for all the bodies tried, we have here -Galileo’s trial in a much more refined state; and it is evident that -almost unlimited exactness may be obtained. Now, all this Newton -accomplished by the simple and elegant contrivance of enclosing in a -hollow pendulum the same weights of a great number of substances the -most different that could be found in all respects, as gold, glass, -wood, water, wheat, &c.[44], and ascertaining the time required for -the pendulum so charged to make a great number of oscillations; in -each of which it is clear the weights had to fall, and be raised again -successively, without loss of time, through the same _identical_ -spaces. Thus any difference, however inconsiderable, that might -exist in the time of one such fall and rise would be multiplied and -accumulated till they became sensible. And none having been discovered -by so delicate a process in any case, the law was considered verified -both in respect of generality and exactness. This, however, is nothing -to the verifications afforded by astronomical phenomena, where the -deviations, if any, accumulate for thousands of years instead of a few -hours. - -(180.) The surest and best characteristic of a well-founded and -extensive induction, however, is when verifications of it spring up, -as it were, spontaneously, into notice, from quarters where they might -be least expected, or even among instances of that very kind which -were at first considered hostile to them. Evidence of this kind is -irresistible, and compels assent with a weight which scarcely any other -possesses. To give an example: M. Mitscherlich had announced a law to -this effect--_that_ the chemical elements of which all bodies consist -are susceptible of being classified in distinct groups, which he termed -_isomorphous_ groups; and _that_ these groups are so related, that -when similar combinations are formed of individuals belonging to two, -three, or more of them, such combinations will crystallize in the same -geometrical forms. To this curious and important law there appeared -a remarkable exception. According to professor Mitscherlich, the -arsenic and phosphoric acids _are_ similar combinations coming under -the meaning of his law, and their combinations with soda and water, -forming the salts known to chemists under the names of arseniate and -phosphate of soda, ought, if the law were general, to crystallize in -identical shapes. The fact, however, was understood to be otherwise. -But lately, Mr. Clarke, a British chemist, having examined the two -salts attentively, ascertained the fact that their compositions -deviate essentially from that similarity which M. Mitscherlich’s law -requires; and that, therefore, the exception in question disappears. -This was something: but, pursuing the subject further, the same -ingenious enquirer happily succeeded in producing a _new_ phosphate of -soda, differing from that generally known in containing a different -proportion of water, and agreeing in composition exactly with the -arseniate. The crystals of this new salt, when examined, were found by -him to be precisely identical in form with those of the arseniate: thus -verifying, in a most striking and totally unexpected manner, the law in -question, or, as it is called, the law of isomorphism. - -(181.) Unexpected and peculiarly striking confirmations of inductive -laws frequently occur in the form of residual phenomena, in the course -of investigations of a widely different nature from those which gave -rise to the inductions themselves. A very elegant example may be cited -in the unexpected confirmation of the law of the developement of heat -in elastic fluids by compression, which is afforded by the phenomena -of sound. The enquiry into the cause of sound had led to conclusions -respecting its mode of propagation, from which its velocity in the air -could be precisely calculated. The calculations were performed; but, -when compared with fact, though the agreement was quite sufficient -to show the general correctness of the cause and mode of propagation -assigned, _yet_ the _whole_ velocity could not be shown to arise from -this theory. There was still a _residual_ velocity to be accounted -for, which placed dynamical philosophers for a long time in a great -dilemma. At length Laplace struck on the happy idea, that this might -arise from the _heat_ developed in the act of that condensation which -necessarily takes place at every vibration by which sound is conveyed. -The matter was subjected to exact calculation, and the result was -at once the complete explanation of the residual phenomenon, and a -striking confirmation of the general law of the developement of heat by -compression, under circumstances beyond artificial imitation. - -(182.) In extending our inductions to cases not originally -contemplated, there is one step which always strikes the mind with -peculiar force, and with such a sensation of novelty and surprise, -as often gives it a weight beyond its due philosophic value. It is -the transition from the little to the great, and _vice versâ_, but -especially the former. It is so beautiful to see, for instance, an -experiment performed in a watch-glass, or before a blowpipe, succeed, -in a great manufactory, on many tons of matter, or, in the bosom of -a volcano, upon millions of cubic fathoms of lava, that we almost -forget that these great masses are made up of watch-glassfuls, and -blowpipe-beads. We see the enormous intervals between the stars and -planets of the heavens, which afford room for innumerable processes -to be carried on, for light and heat to circulate, and for curious -and complicated motions to go forward among them: we look more -attentively, and we see sidereal systems, probably not less vast and -complicated than our own, crowded apparently into a small space (from -the effect of their distance from us), and forming groups resembling -bodies of a substantial appearance, having form and outline: yet we -recoil with incredulous surprise when we are asked _why_ we cannot -conceive the atoms of a grain of sand to be as remote from each other -(proportionally to their sizes) as the stars of the firmament; and -why there may not be going on, in that little microcosm, processes -as complicated and wonderful as those of the great world around us. -Yet the student who makes any progress in natural philosophy will -encounter numberless cases in which this transfer of ideas from the one -extreme of magnitude to the other will be called for: he will find, -for instance, the phenomena of the propagation of winds referred to -the same laws which regulate the propagation of motions through the -smallest masses of air; those of lightning assimilated to the mere -communication of an electric spark, and those of earthquakes to the -tremors of a stretched wire: in short, he must lay his account to -finding the distinction of great and little altogether annihilated in -nature: and it is well for man that such is the case, and that the same -laws, which he can discover and verify in his own circumscribed sphere -of power, should prove available to him when he comes to apply them on -the greatest scale; since it is thus only that he is enabled to become -an exciting cause in operations of any considerable magnitude, and to -vindicate his importance in creation. - -(183.) But the business of induction does not end here: its final -result must be followed out into all its consequences, and applied to -all those cases which seem even remotely to bear upon the subject of -enquiry. Every new addition to our stock of causes becomes a means -of fresh attack with new vantage ground upon all those unexplained -parts of former phenomena which have resisted previous efforts. It -can hardly be pressed forcibly enough on the attention of the student -of nature, that there is scarcely any natural phenomenon which can be -fully and completely explained in all its circumstances, without a -union of several, perhaps of all, the sciences. The great phenomena of -astronomy, indeed, may be considered exceptions; but this is merely -because their scale is so vast that one only of the most widely -extending forces of nature takes the lead, and all those agents whose -sphere of action is limited to narrower bounds, and which determine -the production of phenomena nearer at hand, are thrown into the back -ground, and become merged and lost in comparative insignificance. But -in the more intimate phenomena which surround us it is far otherwise. -Into what a complication of different branches of science are we not -led by the consideration of such a phenomenon as rain, for instance, -or flame, or a thousand others, which are constantly going on before -our eyes? Hence, it is hardly possible to arrive at the knowledge of -a law of any degree of generality in any branch of science, but it -immediately furnishes us with a means of extending our knowledge of -innumerable others, the most remote from the point we set out from; so -that, when once embarked in any physical research, it is impossible for -any one to predict where it may ultimately lead him. - -(184.) This remark rather belongs to the inverse or _deductive_ -process, by which we pursue laws into their remote consequences. -But it is very important to observe, that the successful process of -scientific enquiry demands continually the alternate use of both -the _inductive_ and _deductive_ method. The path by which we rise to -knowledge must be made smooth and beaten in its lower steps, and often -ascended and descended, before we can scale our way to any eminence, -much less climb to the summit. The achievement is too great for a -single effort; stations must be established, and communications kept -open with all below. To quit metaphor; there is nothing so instructive, -or so likely to lead to the acquisition of general views, as this -pursuit of the consequences of a law once arrived at into every subject -where it may seem likely to have an influence. The discovery of a -new law of nature, a new ultimate fact, or one that even temporarily -puts on that appearance, is like the discovery of a new element in -chemistry. Thus, selenium was hardly discovered by Berzelius in the -vitriol works of Fahlun, when it presently made its appearance in the -sublimates of Stromboli, and the rare and curious products of the -Hungarian mines. And thus it is with every new law, or general fact. It -is hardly announced before its traces are found every where, and every -one is astonished at its having so long remained concealed. And hence -it happens that unexpected lights are shed at length over parts of -science that had been abandoned in despair, and given over to hopeless -obscurity. - -(185.) The verification of _quantitative_ laws has been already spoken -of (178.); but their importance in physical science is so very great, -inasmuch as they alone afford a handle to strict mathematical deductive -application, that something ought to be said of the nature of the -inductions by which they are to be arrived at. In their simplest or -least general stages (of which alone we speak at present) they usually -express some numerical relation between two quantities dependent on -each other, either as collateral effects of a common cause, or as the -amount of its effect under given numerical circumstances or _data_. -For example, the law of refraction before noticed (§ 22.) expresses, -by a very simple relation, the amount of angular deviation of a ray -of light from its course, when the _angle_ at which it is inclined to -the refracting surface is known, viz. that the _sine_ of the angle -which the incident ray makes with a perpendicular to the surface is -always to that of the angle made by the refracted ray with the same -perpendicular, in a constant proportion, so long as the refracting -substance is the same. To arrive inductively at laws of this kind, -where one quantity _depends_ on or _varies with_ another, all that is -required is a series of careful and exact measures in every different -state of the _datum_ and _quæsitum_. Here, however, the mathematical -form of the law being of the highest importance, the greatest attention -must be given to the _extreme cases_ as well as to all those points -where the one quantity changes rapidly with a small change of the -other.[45] The results must be set down in a table in which the _datum_ -gradually increases in magnitude from the lowest to the highest limit -of which it is susceptible. It will depend then entirely on our -habit of treating mathematical subjects, how far we may be able to -include such a table in the distinct statement of a mathematical law. -The discovery of such laws is often remarkably facilitated by the -contemplation of a class of phenomena to be noticed further on, under -the head of Collective Instances, (see § 194.) in which the nature of -the mathematical expression in which the law sought is comprehended, is -pointed out by the figure of some curve brought under inspection by a -proper mode of experimenting. - -(186.) After all, unless our induction embraces a series of cases which -absolutely include the whole scale of variation of which the quantities -in question admit, the mathematical expression so obtained cannot be -depended upon as the true one, and if the scale actually embraced be -small, the extension of laws so derived to extreme cases will in all -probability be exceedingly fallacious. For example, air is an elastic -fluid, and as such, if enclosed in a confined space and squeezed, its -bulk diminishes: now, from a great number of trials made in cases where -the air has been compressed into a half, a third, &c. even as far -as a fiftieth of its bulk, or less, it has been concluded that “the -density of air is proportional to the compressing force,” or the bulk -it occupies _inversely_ as that force; and when the air is rarefied -by taking off part of its natural pressure, the same is found to be -the case, within very extensive limits. Yet it is impossible that this -should be, strictly or mathematically speaking, the true law; for, if -it were so, there could be no limit to the condensation of air, while -yet we have the strongest analogies to show that long before it had -reached any very enormous pitch the air would be reduced into a liquid, -and even, perhaps, if pressed yet more violently, into a solid form. - -(187.) Laws thus derived, by the direct process of including in -mathematical formulæ the results of a greater or less number of -measurements, are called “empirical laws.” A good example of such a -law is that given by Dr. Young (Phil. Trans. 1826,) for the decrement -of life, or the law of mortality. Empirical laws in this state are -evidently _unverified inductions_, and are to be received and reasoned -on with the utmost reserve. No confidence can ever be placed in them -beyond the limits of the data from which they are derived; and even -within those limits they require a special and severe scrutiny to -examine _how nearly_ they do represent the observed facts; that is to -say, whether, in the comparison of their results with the observed -quantities, the differences are such as may fairly be attributed to -error of observation. When so carefully examined, they become, however, -most valuable; and frequently, when afterwards verified theoretically -by a deductive process (as will be explained in our next chapter), -turn out to be rigorous laws of nature, and afford the noblest and -most convincing supports of which theories themselves are susceptible. -The finest instances of this kind are the great laws of the planetary -motions deduced by Kepler, entirely from a comparison of observations -with each other, with no assistance from theory. These laws, viz. that -the planets move in ellipses round the sun; that each describes about -the sun’s centre equal areas in equal times; and that in the orbits of -different planets the squares of the periodical times are proportional -to the cubes of the distances; were the results of inconceivable -labour of calculation and comparison: but they amply repaid the -labour bestowed on them, by affording afterwards the most conclusive -and unanswerable proofs of the Newtonian system. On the other hand, -when empirical laws are unduly relied on beyond the limits of the -observations from which they were deduced, there is no more fertile -source of fatal mistakes. The formulæ which have been empirically -deduced for the elasticity of steam (till very recently), and those -for the resistance of fluids, and other similar subjects, have almost -invariably failed to support the theoretical structures which have been -erected on them. - -(188.) It is a remarkable and happy fact, that the shortest and most -direct of all inductions should be that which has led at once, or by -very few steps, to the highest of all natural laws,--we mean those of -motion and force. Nothing can be more simple, precise, and general, -than the enunciation of these laws; and, as we have once before -observed, their application to particular facts in the descending or -deductive method is limited by nothing but the limited extent of our -mathematics. It would seem, then, that dynamical science were taken -thenceforward out of the pale of induction, and transformed into a -matter of absolute _à priori_ reasoning, as much as geometry; and so -it would be, were our mathematics perfect, and all the _data_ known. -Unhappily, the first is so far from being the case, that in many -of the most interesting branches of dynamical enquiry they leave -us completely at a loss. In what relates to the motions of fluids, -for instance, this is severely felt. We can include our problems, -it is true, in algebraical equations, and we can demonstrate that -they _contain_ the solutions; but the equations themselves are so -intractable, and present such insuperable difficulties, that they often -leave us quite as much in the dark as before. But even were these -difficulties overcome, recourse to experience must still be had, to -establish the _data_ on which particular applications are to depend; -and although mathematical analysis affords very powerful means of -_representing_ in general terms the data of any proposed case, and -_afterwards_, by comparison of its results with fact, determining -_what_ those data must be to explain the observed phenomena, still, -in any mode of considering the matter, an appeal to experience in -every particular instance of application is unavoidable, even when -the general principles are regarded as sufficiently established -without it. Now, in all such cases of difficulty we must recur to our -inductive processes, and regard the branches of dynamical science where -this takes place as purely experimental. By this we gain an immense -advantage, viz. that in all those points of them where the abstract -dynamical principles _do_ afford distinct conclusions, we obtain -verifications for our inductions of the highest and finest possible -kind. When we work our way up inductively to one of these results, we -cannot help feeling the strongest assurance of the validity of the -induction. - -(189.) The necessity of this appeal to experiment in every thing -relating to the motions of fluids on the large scale has long been -felt. Newton himself, who laid the first foundations of hydrodynamical -science (so this branch of dynamics is called), distinctly perceived -it, and set the example of laborious and exact experiments on their -resistance to motion, and other particulars. Venturi, Bernoulli, and -many others, have applied the method of experiment to the motions -of fluids in pipes and canals; and recently the brothers Weber have -published an elaborate and excellent experimental enquiry into the -phenomena of waves. One of the greatest and most successful attempts, -however, to bring an important, and till then very obscure, branch -of dynamical enquiry back to the dominion of experiment, has been -made by Chladni and Savart in the case of sound and vibratory motion -in general; and it is greatly to be wished that the example may be -followed in many others hardly less abstruse and impracticable when -theoretically treated. In such cases the inductive and deductive -methods of enquiry may be said to go hand in hand, the one verifying -the conclusions deduced by the other; and the combination of experiment -and theory, which may thus be brought to bear in such cases, forms -an engine of discovery infinitely more powerful than either taken -separately. This state of any department of science is perhaps of -all others the most interesting, and that which promises the most to -research. - -(190.) It can hardly be expected that we should terminate this division -of our subject without some mention of the “prerogatives of instances” -of Bacon, by which he understands characteristic phenomena, selected -from the great miscellaneous mass of facts which occur in nature, -and which, by their number, indistinctness, and complication, tend -rather to confuse than to direct the mind in its search for causes -and general heads of induction. Phenomena so selected on account of -some peculiarly forcible way in which they strike the reason, and -impress us with a kind of sense of causation, or a particular aptitude -for generalization, he considers, and justly, as holding a kind of -prerogative dignity, and claiming our first and especial attention in -physical enquiries. - -(191.) We have already observed that, in forming inductions, it will -most commonly happen that we are led to our conclusions by the especial -force of some two or three strongly impressive facts, rather than by -affording the whole mass of cases a regular consideration; and hence -the need of cautious verification. Indeed, so strong is this propensity -of the human mind, that there is hardly a more common thing than to -find persons ready to assign a cause for every thing they see, and, in -so doing, to join things the most incongruous, by analogies the most -fanciful. This being the case, it is evidently of great importance -that these first ready impulses of the mind should be made on the -contemplation of the cases most likely to lead to good inductions. -The misfortune, however, is, in natural philosophy, that the choice -does not rest with us. We must take the instances as nature presents -them. Even if we are furnished with a list of them in tabular order, -we must understand and compare them with each other, before we can -tell which _are_ the instances thus deservedly entitled to the highest -consideration. And, after all, after much labour in vain, and groping -in the dark, accident or casual observation will present a case which -strikes us at once with a full insight into a subject, before we can -even have time to determine to what class its _prerogative_ belongs. -For example, the laws of crystallography were obscure, and its causes -still more so, till Haüy fortunately dropped a beautiful crystal of -calcareous spar on a stone pavement, and broke it. In piecing together -the fragments, he observed their facets not to correspond with those of -the crystal in its entire state, but to belong to another form; and, -following out the hint offered by a “_glaring instance_” thus casually -obtruded on his notice, he discovered the beautiful laws of the -cleavage, and the primitive forms of minerals. - -(192.) It has always appeared to us, we must confess, that the help -which the classification of instances, under their different titles of -prerogative, affords to inductions, however just such classification -may be in itself, is yet more apparent than real. The force of the -instance must be felt in the mind, before it can be referred to -its place in the system; and, before it can be either referred or -appretiated, it must be known; and when it _is_ appretiated, we are -ready enough to interweave it in our web of induction, without greatly -troubling ourselves with enquiring whence it derives the weight we -acknowledge it to have in our decisions. However, since much importance -is usually attached to this part of Bacon’s work, we shall here give a -few examples to illustrate the nature of some of his principal cases. -One, of what he calls “glaring instances,” has just been mentioned. -In these, the _nature_ or cause enquired into, (which in this case -is the cause of the assumption of a peculiar external form, or the -internal _structure_ of a crystal,) “stands naked and alone, and this -in an eminent manner, or in the highest degree of its power.” No doubt, -such instances as these are highly instructive; but the difficulty in -physics is to find such, not to perceive their force when found. - -(193.) The contrary of glaring are “clandestine instances,” where -“the nature sought is exhibited in its weakest and most imperfect -state.” Of this, Bacon himself has given an admirable example in the -cohesion of fluids, as a _clandestine instance_ of the “_nature_ or -quality of consistence, or solidity.” Yet here, again, the same acute -discrimination which enabled Bacon to perceive the analogy which -connects fluids with solids, through the common property of cohesive -attraction, would, at the same time, have enabled him to draw from it, -if properly supported, every consequence necessary to forming just -notions of the cohesive force; nor does its reference to the class of -clandestine instances at all assist in bringing forward and maturing -the final results. When, however, the final result is obtained,--when -our induction is complete, and we would verify it,--this class of -instances is of great use, being, in fact, frequently no other than -that of _extreme cases_, such as we have already spoken of (in § -177.); which, by placing our conclusions, as it were, in violent -circumstances, try their temper, and bring their vigour to the test. - -(194.) Bacon’s “collective instances” (_instantiæ unionis_), are no -other than general facts, or laws of some degree of generality, and -are themselves the results of induction. But there is a species of -collective instance which Bacon does not seem to have contemplated, of -a peculiarly instructive character; and that is, where particular cases -are offered to our observation in such numbers at once as to make the -induction of their law a matter of ocular inspection. For example, the -parabolic form assumed by a jet of water spouted from a round hole, -is a _collective instance_ of the velocities and directions of the -motions of all the particles which compose it _seen at once_, and which -thus leads us, without trouble, to recognize the law of the motion of -a projectile. Again, the beautiful figures exhibited by sand strewed -on regular plates of glass or metal set in vibration, are _collective -instances_ of an infinite number of points which remain at rest while -the remainder of the plate vibrates; and in consequence afford us, -as it were, a sight of the law which regulates their arrangement -and sequence throughout the whole surface. The beautifully coloured -lemniscates seen around the optic axes of crystals exposed to polarized -light afford a superb example of the same kind, pointing at once to -the general mathematical expression of the law which regulates their -production.[46] Of such collective instances as these, it is easy to -see the importance, and its reason. They lead us to a general law by an -induction which offers itself spontaneously, and thus furnish advanced -points in our enquiries; and when we start from these, already “a -thousand steps are lost.” - -(195.) A fine example of a collective instance is that of the system -of Jupiter or Saturn with its satellites. We have here, in miniature, -and seen at one view, a system similar to that of the planets about -the sun; of which, from the circumstance of our being involved in it, -and unfavourably situated for seeing it otherwise than in detail, we -are incapacitated from forming a general idea but by slow progressive -efforts of reason. Accordingly, the contemplation of the _circumjovial -planets_ (as they were called) most materially assisted in securing the -admission of the Copernican system. - -(196.) Of “Crucial instances” we have also already spoken, as affording -the readiest and securest means of eliminating extraneous causes, and -deciding between rival hypotheses. Owing to the disposition of the -mind to form hypotheses, and to prejudge cases, it constantly happens -that, among all the possible suppositions which may occur, two or three -principal ones occupy us, to the exclusion of the rest; or it may -be that, if we have been less precipitate, out of a great multitude -rejected for obvious inapplicability to some one or other case, two or -three of better claims remain for decision; and this such instances -enable us to do. One of the instances cited by Bacon in illustration of -his crucial class is very remarkable, being neither more nor less than -the proposal of a direct experiment to determine whether the tendency -of heavy bodies downwards is a result of some peculiar mechanism in -themselves, or of the attraction of the earth “by the corporeal mass -thereof, as by a collection of bodies of the same nature.” If it be so, -he says, “it will follow that the nearer all bodies approach to the -earth, the stronger and with the greater force and velocity they will -tend to it; but the farther they are, the weaker and slower:” and his -experiment consists in comparing the effect of a spring and a weight -in keeping up the motions of two “clocks,” regulated together, and -removed alternately to the tops of high buildings and into the deepest -mines. By _clocks_ he could not have meant pendulum clocks, which were -not then known, (the first made in England was in 1662,) _fly_-clocks, -so that the comparison, though too coarse, was not contrary to sound -mechanical principles. In short, its principle was the comparison of -the effect of a spring with that of a weight, in producing certain -motions in certain times, on heights and in mines. Now, this is the -very same thing that has really been done in the recent experiments -of professors Airy and Whewell in Dolcoath mine: a pendulum (a weight -moved by gravity) has been compared with a chronometer balance, moved -and regulated by a spring. In his 37th aphorism, Bacon also speaks of -gravity as an incorporeal power, acting at a distance, and _requiring -time for its transmission_; a consideration which occurred at a later -period to Laplace, in one of his most delicate investigations. - -(197.) A well chosen and strongly marked crucial instance is, -sometimes, of the highest importance; when two theories, which run -parallel to each other (as is sometimes the case) in their explanation -of great classes of phenomena, at length come to be placed at issue -upon a single fact. A beautiful instance of this will be cited in the -next section. We may add to the examples above given of such instances, -that of the application of chemical tests, which are almost universally -crucial experiments. - -(198.) Bacon’s “travelling instances” are those in which the _nature_ -or quality under investigation “travels,” or varies in degree; and thus -(according to § 152.) afford an indication of a cause by a gradation -of intensity in the effect. One of his instances is very happy, being -that of “paper, which is white when dry, but proves less so when wet, -and comes nearer to the state of transparency upon the exclusion of the -air, and admission of water.” In reading this, and many other instances -in the Novum Organum, one would almost suppose (had it been written) -that its author had taken them from Newton’s Optics. - -(199.) The travelling instances, as well as what Bacon terms “frontier -instances,” are cases in which we are enabled to trace that general -law which seems to pervade all nature--the law, as it is termed, of -continuity, and which is expressed in the well known sentence, “Natura -non agit per saltum.” The pursuit of this law into cases where its -application is not at first sight obvious, has proved a fertile source -of physical discovery, and led us to the knowledge of an analogy and -intimate connection of phenomena between which at first we should never -have expected to find any. - -(200.) For example, the transparency of gold leaf, which permits a -bluish-green light to pass through it, is a frontier instance between -the transparency of pellucid bodies and the opacity of metals, and it -prevents a breach of the law of continuity between transparent and -opake bodies, by exhibiting a body of the class generally regarded -the most opake in nature, as still possessed of some slight degree -of transparency. It thus proves that the quality of opacity is not a -_contrary_ or _antagonist_ quality to that of transparency, but only -its extreme lowest degree. - - - - -CHAP. VII. - - OF THE HIGHER DEGREES OF INDUCTIVE GENERALIZATION, AND OF THE - FORMATION AND VERIFICATION OF THEORIES. - - -(201.) As particular inductions and laws of the first degree of -generality are obtained from the consideration of individual facts, -so Theories result from a consideration of these laws, and of the -proximate causes brought into view in the previous process, regarded -all together as constituting a new set of phenomena, the creatures -of reason rather than of sense, and each representing under general -language innumerable particular facts. In raising these higher -inductions, therefore, more scope is given to the exercise of pure -reason than in slowly groping out our first results. The mind is more -disencumbered of matter, and moves as it were in its own element. What -is now before it, it perceives more intimately, and less through the -medium of sense, or at least not in the same manner as when actually at -work on the immediate objects of sense. But it must not be therefore -supposed that, in the formation of theories, we are abandoned to -the unrestrained exercise of imagination, or at liberty to lay down -arbitrary principles, or assume the existence of mere fanciful causes. -The liberty of speculation which we possess in the domains of theory is -not like the wild licence of the slave broke loose from his fetters, -but rather like that of the freeman who has learned the lessons of -self-restraint in the school of just subordination. The ultimate -objects we pursue in the highest theories are the same as those of the -lowest inductions; and the means by which we can most securely attain -them bear a close analogy to those which we have found successful in -such inferior cases. - -(202.) The immediate object we propose to ourselves in physical -theories is the analysis of phenomena, and the knowledge of the hidden -processes of nature in their production, so far as they can be traced -by us. An important part of this knowledge consists in a discovery -of the actual structure or mechanism of the universe and its parts, -through which, and by which, those processes are executed; and of the -agents which are concerned in their performance. Now, the mechanism of -nature is for the most part either on too large or too small a scale -to be immediately cognizable by our senses; and her agents in like -manner elude direct observation, and become known to us only by their -effects. It is in vain therefore that we desire to become witnesses to -the processes carried on with such means, and to be admitted into the -secret recesses and laboratories where they are effected. Microscopes -have been constructed which magnify more than a thousand times in -_linear_ dimension, so that the smallest visible grain of sand may -be enlarged to the appearance of one a thousand million times more -bulky; yet the only impression we receive by viewing it through such -a magnifier is, that it reminds us of some vast fragment of a rock, -while the intimate structure on which depend its colour, its hardness, -and its chemical properties, remains still concealed: we do not seem -to have made even an approach to a closer analysis of it by any such -scrutiny. - -(203.) On the other hand, the mechanism of the great system of which -our planet forms a part escapes immediate observation by the immensity -of its scale, nay, even by the slowness of its evolutions. The motion -of the minute hand of a watch can hardly be perceived without the -closest attention, and that of the hour hand not at all. But what are -these, in respect of the impression of slowness they produce in our -minds, compared with a revolving movement which takes a whole year, or -twelve, thirty, or eighty years to complete, as is the case with the -planets in their revolutions round the sun. Yet no sooner do we come -to reflect on the linear dimensions of these orbs, (which however we -do not _see_, nor can we measure them but by a long, circuitous, and -difficult process,) than we are lost in astonishment at the swiftness -of the very motions which before seemed so slow.[47] The motion of the -sails of a windmill offers (on a small scale) an illustrative case. At -a distance the rotation seems slow and steady--but when we stand close -to one of the sails in its sweep, we are surprised at the swiftness -with which it rushes by us. - -(204.) Again, the agents employed by nature to act on material -structures are invisible, and only to be traced by the effects they -produce. Heat dilates matter with an irresistible force; but what heat -is, remains yet a problem. A current of electricity passing along a -wire moves a magnetized needle at a distance; but except from this -effect we perceive no difference between the condition of the wire -when it conveys and when it does not convey the stream: and we apply -the terms current, or stream, to the electricity only because in some -of its relations it reminds us of something we have observed in a -stream of air or water. In like manner we see that the moon circulates -about the earth; and because we believe it to be a solid mass, and -have never seen one solid substance revolve round another within our -reach to handle and examine unless retained by a force or united by a -tie, we conclude that there _is_ a force, and a mode of connection, -between the moon and the earth; though, what that mode can be, we have -no conception, nor can imagine _how_ such a force can be exerted at a -distance, and with empty space, or at most an invisible fluid, between. -(See § 148.) - -(205.) Yet are we not to despair, since we see regular and beautiful -results brought about in human works by means which nobody would, at -first sight, think could have any thing to do with them. A sheet of -blank paper is placed upon a frame, and shoved forwards, and after -winding its way successively over and under half a dozen rollers, and -performing many other strange evolutions, comes out printed on both -sides. And, after all, the acting cause in this process is nothing -more than a few gallons of water boiled in an iron vessel, at a -distance from the scene of operations. But _why_ the water so boiled -should be capable of producing the active energy which sets the whole -apparatus in motion is, and will probably long remain, a secret to us. - -(206.) This, however, does not at all prevent our having a very perfect -comprehension of the whole subsequent process. We might frequent -printing-houses, and form a theory of printing, and having worked our -way up to the point where the mechanical action commenced (the boiler -of the steam-engine), and verified it by taking to pieces, and putting -together again, the train of wheels and the presses, and by sound -theoretical examination of all the transfers of motion from one part to -another; we should, at length, pronounce our theory good, and declare -that we understood printing thoroughly. Nay, we might even go away and -apply the principles of mechanism we had learned in this enquiry to -other widely different purposes; construct other machines, and put them -in motion by the same moving power, and all without arriving at any -correct idea as to the ultimate source of the force employed. But, if -we were inclined to theorize farther, we might do so; and it is easy -to imagine how two theorists might form very different _hypotheses_ as -to the origin of the power which alternately raised and depressed the -piston-rod of the engine. One, for example, might maintain that the -boiler (whose contents we will suppose that neither theorist has been -permitted to examine) was the den of some powerful unknown animal, and -he would not be without plausible analogies in the warmth, the supply -of fuel and water, the breathing noises, the smoke, and above all, the -mechanical power exerted. He would say (not without a show of reason), -that where there is a positive and wonderful effect, and many strong -analogies, such as materials consumed, and all the usual signs of life -maintained, we are not to deny the existence of animal life because -we know no animal that consumes such food. Nay, he might observe with -truth, that the fuel actually consists of the chemical ingredients -which constitute the chief food of all animals, &c.; while, on the -other hand, his brother theorist, who caught a glimpse of the fire, -and detected the peculiar sounds of ebullition, might acquire a better -notion of the case, and form a theory more in consonance with fact. - -(207.) Now, nothing is more common in physics than to find two, or even -many, _theories_ maintained as to the origin of a natural phenomenon. -For instance, in the case of heat itself, one considers it as a really -existing material fluid, of such exceeding subtlety as to penetrate -all bodies, and even to be capable of combining with them chemically; -while another regards it as nothing but a rapid vibratory or rotatory -motion in the ultimate particles of the bodies heated; and produces -a singularly ingenious train of mechanical reasoning to show, that -there is nothing contradictory to sound dynamical principles in such -a doctrine. Thus, again, with light: one considers it as consisting -in actual particles darted forth from luminous bodies, and acted -upon in their progress by forces of extreme intensity residing in the -substances on which they strike; another, in the vibratory motion of -the particles of luminous bodies, communicated to a peculiar subtle and -highly elastic ethereal medium, filling all space, and conveyed through -it into our eyes, as sounds are to our ears, by the undulations of the -air. - -(208.) Now, are we to be deterred from framing hypotheses and -constructing theories, because we meet with such dilemmas, and -find ourselves frequently beyond our depth? Undoubtedly not. _Est -quodam prodire tenus si non datur ultra._ Hypotheses, with respect -to theories, are what presumed proximate causes are with respect to -particular inductions: they afford us motives for searching into -analogies; grounds of citation to bring before us all the cases which -seem to bear upon them, for examination. A well imagined hypothesis, -if it have been suggested by a fair inductive consideration of general -laws, can hardly fail at least of enabling us to generalize a step -farther, and group together several such laws under a more universal -expression. But this is taking a very limited view of the value and -importance of hypotheses: it may happen (and it has happened in the -case of the undulatory doctrine of light) that such a weight of analogy -and probability may become accumulated on the side of an hypothesis, -that we are compelled to admit one of two things; either that it is -an actual statement of what really passes in nature, or that the -reality, whatever it be, must run so close a parallel with it, as to -admit of some mode of expression common to both, at least in so far -as the phenomena actually known are concerned. Now, this is a very -great step, not only for its own sake, as leading us to a high point in -philosophical speculation, but for its applications; because whatever -conclusions we deduce from an hypothesis so supported must have at -least a strong presumption in their favour: and we may be thus led to -the trial of many curious experiments, and to the imagining of many -useful and important contrivances, which we should never otherwise have -thought of, and which, at all events, if verified in practice, are real -additions to our stock of knowledge and to the arts of life. - -(209.) In framing a theory which shall render a rational account of -any natural phenomenon, we have _first_ to consider the agents on -which it depends, or the causes to which we regard it as ultimately -referable. These agents are not to be arbitrarily assumed; they -must be such as we have good inductive grounds to believe do exist -in nature, and do perform a part in phenomena analogous to those we -would render an account of; or such, whose presence in the actual -case can be demonstrated by unequivocal signs. They must be _veræ -causæ_, in short, which we can not only show to exist and to act, -but the laws of whose action we can derive independently, by direct -induction, from experiments purposely instituted; or at least make -such suppositions respecting them as shall not be contrary to our -experience, and which will remain to be verified by the coincidence of -the conclusions we shall deduce from them, with facts. For example, -in the theory of gravitation we suppose an agent,--_viz._ force, or -mechanical power,--to act on _any_ material body which is placed in -the presence of _any_ other, and to urge the two mutually towards each -other. This is a _vera causa_; for heavy bodies (that is, all bodies, -but some more, some less,) tend to, or endeavour to reach, the earth, -and require the exertion of force to counteract this endeavour, or -to keep them up. Now, that which opposes and neutralizes force _is_ -force. And again, a plumb-line, which, when allowed to hang freely, -always hangs perpendicularly; is found to hang observably aside from -the perpendicular when in the neighbourhood of a considerable mountain; -thereby proving that a force is exerted upon it, which draws it towards -the mountain. Moreover, since it is a fact that the moon does circulate -about the earth, it must be drawn towards the earth by a force; for if -there were no force acting upon it, it would go on in a straight line -without turning aside to circulate in an orbit, and would, therefore, -soon go away and be lost in space. This force, then, which we call the -_force_ of gravity, is a real cause. - -(210.) We have next to consider the laws which regulate the action of -these our primary agents; and these we can only arrive at in three -ways: 1st, By inductive reasoning; that is, by examining all the -cases in which we know them to be exercised, inferring, as well as -circumstances will permit, its amount or intensity in each particular -case, and then piecing together, as it were, these _disjecta membra_, -generalizing from them, and so arriving at the laws desired; 2dly, -By forming at once a bold hypothesis, particularizing the law, -and trying the truth of it by following out its consequences and -comparing them with facts; or, 3dly, By a process partaking of both -these, and combining the advantages of both without their defects, -viz. by assuming indeed the laws we would discover, but so generally -expressed, that they shall include an unlimited variety of particular -laws;--following out the consequences of this assumption, by the -application of such general principles as the case admits;--comparing -them in succession with all the particular cases within our knowledge; -and, lastly, _on this comparison_, so modifying and restricting the -general enunciation of our laws as to _make the results agree_. - -(211.) All these three processes for the discovery of those general -elementary laws on which the higher theories are grounded are -applicable with different advantage in different circumstances. -We might exemplify their successive application to the case of -gravitation: but as this would rather lead into a disquisition too -particular for the objects of this discourse, and carry us too much -into the domain of technical mathematics, we shall content ourselves -with remarking, that the method last mentioned is that which -mathematicians (especially such as have a considerable command of -those general modes of representing and reasoning on quantity, which -constitute the higher analysis,) find the most universally applicable, -and the most efficacious; and that it is applicable with especial -advantage in cases where subordinate inductions of the kind described -in the last section have already led to laws of a certain generality -admitting of mathematical expression. Such a case, for instance, -is the elliptic motion of a planet, which is a general proposition -including the statement of an infinite number of particular _places_, -in which the laws of its motion allow it to be some time or other -found, and for which, of course, the law of force must be so assumed as -to account. - -(212.) With regard to the first process of the three above enumerated, -it is in fact an induction of the kind described in § 185.; and all -the remarks we there made on that kind of induction apply to it in -this stage. The direct assumption of a particular hypothesis has been -occasionally practised very successfully. As examples, we may mention -Coulomb’s and Poisson’s theories of electricity and magnetism, in -both which, phenomena of a very complicated and interesting nature -are referred to the actions of attractive and repulsive forces, -following a law similar in its expression to the law of gravitation. -But the difficulty and labour, which, in the greater theories, always -attends the pursuit of a fundamental law into its remote consequences, -effectually precludes this method from being commonly resorted to as -a means of discovery, unless we have some good reason, from analogy -or otherwise, for believing that the attempt will prove successful, -or have been first led by partial inductions to particular laws which -naturally point it out for trial. - -(213.) In this case the law assumes all the characters of a general -phenomenon resulting from an induction of particulars, but not yet -verified by comparison with _all_ the particulars, nor extended to all -that it is capable of including. (See § 171.) It is the verification -of such inductions which constitutes theory in its largest sense, and -which embraces an estimation of the influence of all such circumstances -as may modify the effect of the cause whose laws of action we have -arrived at and would verify. To return to our example: particular -inductions drawn from the motions of the several planets about the -sun, and of the satellites round their primaries, &c. having led us -to the general conception of an attractive force exerted by every -particle of matter in the universe on every other according to the law -to which we attach the name of gravitation; when we would verify this -induction, we must set out with assuming this law, considering the -whole system as subjected to its influence and implicitly obeying it, -and nothing interfering with its action; we then, for the first time, -perceive a train of modifying circumstances which had not occurred to -us when reasoning upwards from particulars to obtain the fundamental -law; we perceive that _all the planets_ must attract _each other_, -must therefore draw each other out of the orbits which they would -have if acted on only by the sun; and as this was never contemplated -in the inductive process, its validity becomes a question, which can -only be determined by ascertaining precisely how great a deviation -this new class of mutual actions will produce. To do this is no easy -task, or rather, it is the most difficult task which the genius of -man has ever yet accomplished: still, it _has_ been accomplished by -the mere application of the general laws of dynamics; and the result -(undoubtedly a most beautiful and satisfactory one) is, that all -those observed deviations in the motions of our system which stood -out as exceptions (§ 154.), or were noticed as residual phenomena and -reserved for further enquiry (§ 158.), in that imperfect view of the -subject which we got in the subordinate process by which we rose to -our general conclusion, prove to be the immediate consequences of the -above-mentioned mutual actions. As such, they are neither exceptions -nor residual facts, but fulfilments of general rules, and essential -features in the statement of the case, _without_ which our induction -would be invalid, and the law of gravitation positively untrue. - -(214.) In the theory of gravitation, the law is all in all, applying -itself at once to the materials, and directly producing the result. -But in many other cases we have to consider not merely the laws -which regulate the actions of our ultimate causes, but a system of -mechanism, or a structure of parts, through the intervention of which -their effects become sensible to us. Thus, in the delicate and curious -electro-dynamic theory of Ampere, the mutual attraction or repulsion -of two magnets is referred to a more universal phenomenon, the mutual -action of electric currents, according to a certain fundamental law. -But, in order to bring the case of a magnet within the range of this -law, he is obliged to make a supposition of a peculiar structure or -mechanism, which constitutes a body a magnet, viz. that around each -particle of the body there shall be constantly circulating, in a -certain stated direction, a small current of electric fluid. - -(215.) This, we may say, is too complex; it is artificial, and cannot -be granted: yet, if the admission of this or any other structure -tenfold more artificial and complicated will enable any one to present -in a general point of view a great number of particular facts,--to make -them a part of one system, and enable us to reason from the known to -the unknown, and actually to _predict facts before trial_,--we would -ask, why should it _not_ be granted? When we examine those instances -of nature’s workmanship which we can take to pieces and understand, -we find them in the highest degree artificial in our own sense of the -word. Take, for example, the structure of an eye, or of the skeleton of -an animal,--what complexity and what artifice! In the one, a _pellucid -muscle_; a lens formed with elliptical surfaces; a circular aperture -capable of enlargement or contraction without loss of form. In the -other, a framework of the most curious carpentry; in which occurs -not a single straight line, nor any known geometrical curve, yet all -evidently systematic, and constructed by rules which defy our research. -Or examine a crystallized mineral, which we can in some measure -dissect, and thus obtain direct evidence of an internal structure. -Neither artifice nor complication are here wanting; and though it -is easy to assert that these appearances are, after all, produced -by something which would be very simple, if we did but know it, it -is plain that the same might be _said_ of a steam-engine executing -the most complicated movements, previous to any investigation of its -nature, or any knowledge of the source of its power. - -(216.) In estimating, however, the value of a theory, we are not to -look, _in the first instance_, to the question, whether it establishes -satisfactorily, or not, a particular process or mechanism; for of -this, after all, we can never obtain more than that indirect evidence -which consists in its leading to the same results. What, in the actual -state of science, is far more important for us to know, is whether our -theory truly represent _all_ the facts, and include _all_ the laws, to -which observation and induction lead. A theory which did this would, -no doubt, go a great way to establish any hypothesis of mechanism or -structure, which might form an essential part of it: but this is very -far from being the case, except in a few limited instances; and, till -it is so, to lay any great stress on hypotheses of the kind, except in -as much as they serve as a scaffold for the erection of general laws, -is to “quite mistake the scaffold for the pile.” Regarded in this -light, hypotheses have often an eminent use: and a facility in framing -them, if attended with an equal facility in laying them aside when -they have served their turn, is one of the most valuable qualities a -philosopher can possess; while, on the other hand, a bigoted adherence -to them, or indeed to peculiar views of any kind, in opposition to the -tenor of facts as they arise, is the bane of all philosophy. - -(217.) There is no doubt, however, that the safest course, when it -can be followed, is to rise by inductions carried on among laws, as -among facts, from law to law, perceiving, as we go on, how laws which -we have looked upon as unconnected become particular cases, either -one of the other, or all of one still more general, and, at length, -blend altogether in the point of view from which we learn to regard -them. An example will illustrate what we mean. It is a general law, -that all hot bodies throw out or _radiate_ heat in all directions, (by -which we mean, not that heat is an actual substance darted out from hot -bodies, but only that the laws of the transmission of heat to distant -objects are similar to those which would regulate the distribution -of particles thrown forth in all directions,) and that other colder -bodies placed in their neighbourhood become hot, _as if_ they received -the heat so radiated. Again, all solid bodies which become heated in -one part _conduct_, or diffuse, the heat from that part through their -whole substance. Here we have two modes of communicating heat,--by -radiation, and by conduction; and both these have their peculiar, -and, to all appearance, very different laws. Now, let us bring a hot -and a cold body (of the same substance) gradually nearer and nearer -together,--as they approach, the heat will be communicated from the hot -to the cold one by the _laws of radiation_; and from the nearer to the -farther part of the colder one, as it gradually grows warm, by _those -of conduction_. Let their distance be diminished till they just lightly -touch. How does the heat _now_ pass from one to the other? Doubtless, -by radiation; for it may be proved, that in such a contact there is yet -an interval. Let them then be _forced_ together, and it will seem clear -that it must now be by _conduction_. Yet their _interval_ must diminish -gradually, as the force by which they are pressed together increases, -till they actually cohere, and form one. The law of continuity, then, -of which we have before spoken (§ 199.), forbids us to suppose that -the intimate nature of the process of communication is changed in this -transition from light to violent contact, and from that to actual -union. If so, we might ask, at what point does the change happen? -Especially since it is also demonstrable, that the particles of the -most solid body are not, really, in contact. _Therefore_, the laws of -conduction and radiation have a mutual dependence, and the former are -only extreme cases of the latter. If, then, we would rightly understand -what passes, or what is the process of nature in the slow communication -of heat through the substance of a solid, we must ground our enquiries -upon what takes place at a distance, and then urge the laws to which we -have arrived, up to their extreme case. - -(218.) When two theories run parallel to each other, and each explains -a great many facts in common with the other, any experiment which -affords a crucial instance to decide between them, or by which one or -other must fall, is of great importance. In thus verifying theories, -since they are grounded on general laws, we may appeal, not merely -to particular cases, but to whole classes of facts; and we therefore -have a great range among the individuals of these for the selection -of some particular effect which ought to take place oppositely in the -event of one of the two suppositions at issue being right and the other -wrong. A curious example is given by M. Fresnel, as decisive, in his -mind, of the question between the two great opinions on the nature -of light, which, since the time of Newton and Huyghens, have divided -philosophers. (See § 207.) When two very clean glasses are laid one -on the other, if they be not perfectly flat, but one or both in an -almost imperceptible degree convex or prominent, beautiful and vivid -colours will be seen between them; and if these be viewed through a -red glass, their appearance will be that of alternate dark and bright -stripes. These stripes are formed _between_ the two surfaces in -apparent contact, as any one may satisfy himself by using, instead of -a flat _plate_ of glass for the upper one, a triangular-shaped piece, -called a prism, like a three-cornered stick, and looking through the -inclined side of it next the eye, by which arrangement the reflection -of light from the upper surface is prevented from intermixing with that -from the surfaces in contact. Now, the coloured stripes thus produced -are explicable on both theories, and are appealed to by both as strong -confirmatory facts; but there is a difference in one circumstance -according as one or the other theory is employed to explain them. -In the case of the Huyghenian doctrine, the intervals between the -bright stripes ought to appear _absolutely black_; in the other, -_half bright_, when so viewed through a prism. This curious case of -difference was tried as soon as the opposing consequences of the two -theories were noted by M. Fresnel, and the result is stated by him to -be decisive in favour of that theory which makes light to consist in -the vibrations of an elastic medium. - -(219.) Theories are best arrived at by the consideration of general -laws; but most securely verified by comparing them with particular -facts, because this serves as a verification of the whole train -of induction, from the lowest term to the highest. But then, the -comparison must be made with facts purposely selected so as to include -every variety of case, not omitting extreme ones, and in sufficient -number to afford every reasonable probability of detecting error. A -single numerical coincidence in a final conclusion, however striking -the coincidence or important the subject, is not sufficient. Newton’s -theory of sound, for example, leads to a numerical expression for the -actual velocity of sound, differing but little from that afforded by -the correct theory afterwards explained by Lagrange, and (when certain -considerations not contemplated by him are allowed for) agreeing with -fact; yet this coincidence is no verification of Newton’s view of the -general subject of sound, which is defective in an essential point, -as the great geometer last named has very satisfactorily shown. This -example is sufficient to inspire caution in resting the verification of -theories upon any thing but a very extensive comparison with a great -mass of observed facts. - -(220.) But, on the other hand, when a theory will bear the test -of such extensive comparison, it matters little how it has been -originally framed. However strange and, at first sight, inadmissible -its postulates may appear, or however singular it may seem that -such postulates should have been fixed upon,--if they only lead -us, by legitimate reasonings, to conclusions in exact accordance -with numerous observations purposely made under such a variety of -circumstances as fairly to embrace the whole range of the phenomena -which the theory is intended to account for, we cannot refuse to admit -them; or if we still hesitate to regard them as demonstrated truths, we -cannot, at least, object to receive them as temporary substitutes for -such truths, until the latter shall become known. If they suffice to -explain all the phenomena known, it becomes highly improbable that they -will not explain more; and if all their conclusions we have tried have -proved correct, it is probable that others yet untried will be found so -too; so that _in rejecting them altogether, we should reject all the -discoveries to which they may lead_. - -(221.) In all theories which profess to give a true account of the -process of nature in the production of any class of phenomena, by -referring them to general laws, or to the action of general causes, -through a train of modifying circumstances; before we can apply those -laws, or trace the action of those causes in any assigned case, we -require to know the circumstances: we must have data whereon to ground -their application. Now, these can be learned only from observation; -and it may seem to be arguing in a vicious circle to have recourse -to observation for any part of those theoretical conclusions, by -whose comparison with fact the theory itself is to be tried. The -consideration of an example will enable us to remove this difficulty. -The most general law which has yet been discovered in chemistry is -this, that all the elementary substances in nature are susceptible of -entering into combination with each other only in fixed or _definite -proportions_ by weight, and not arbitrarily; so that when any two -substances are put together with a view to unite them, if their weights -are not in some certain determinate proportion, a complete combination -will not take place, but some part of one or the other ingredient will -remain over and above, and uncombined. Suppose, now, we have found a -substance having all the outward characters of a homogeneous or unmixed -body, but which, on analysis, we discover to consist of sulphur, and -lead in the proportion of 20 parts of the former to 130 of the latter -ingredient; and we would know whether this is to be regarded as a -verification of the law of definite proportions or an exception to -it. The question is reduced to this, whether the proportion 20 to 130 -be or be not _that_ fixed and definite proportion, (or one of them, -if there be more than one proportion possible,) in which, according -to the law in question, sulphur and lead can combine; now, this can -never be decided by merely looking at the law in all its generality. -It is clear, that when particularized by restricting its expression -to sulphur and lead, the law should state _what are_ those particular -fixed proportions in which these bodies can combine. That is to say, -there must be certain data or numbers, by which these are distinguished -from all other bodies in nature, and which require to be known before -we can apply the general law to the particular case. To determine such -data, observation must be consulted; and if we were to have recourse -to that of the combination of the two substances in question with each -other, no doubt there would be ground for the logical objection of -a vicious circle: but this is not done; the determination of these -numerical data is derived from experiments purposely made on a great -variety of different combinations, among which that under consideration -does not of necessity occur, and all these being found, independently -of each other, to agree in giving the same results, they are therefore -safely assumed as part of the system. Thus, the law of definite -proportions, when applied to the actual state of nature, requires two -separate statements, the one announcing the general law of combination, -the other particularizing the numbers appropriate to the several -elements of which natural bodies consist, or the data of nature. Among -these data, if arranged in a list, there will be found opposite to the -element sulphur the number 16, and opposite to lead, 104[48]; and since -20 is to 130 in the exact proportion of 16 to 104, it appears that the -combination in question affords a satisfactory verification of the law. - -(222.) The great importance of physical data of this description, -and the advantage of having them well determined, will be obvious, -if we consider, that a list of them, when taken in combination with -the general law, affords the means of determining at once the exact -proportion of the ingredients of all natural compounds, if we only know -the place they hold in the system. In chemistry, the number of admitted -elements is between fifty and sixty, and new ones are added continually -as the science advances. Now, the moment the number corresponding to -any new substance added to the list is determined, we have, in fact, -ascertained all the proportions in which it can enter into combination -with all the others, so that a careful experiment made with the object -of determining this number is, in fact, equivalent to as many different -experiments as there are binary, ternary, or yet more complicated -combinations capable of existing, into which the new substance may -enter, as an ingredient. - -(223.) The importance of obtaining exact physical data can scarcely -be too much insisted on, for without them the most elaborate theories -are little better than mere inapplicable forms of words. It would be -of little consequence to be informed, abstractedly, that the sun and -planets attract each other, with forces proportional to their masses, -and inversely as the squares of their distances: but, as soon as we -know the data of our system, as soon as we have an accurate statement -(no matter how obtained) of the distances, masses, and actual motions -of the several bodies which compose it, we need no more to enable us to -predict all the movements of its several parts, and the changes that -will happen in it for thousands of years to come; and even to extend -our views backwards into time, and recover from the past, phenomena, -which no observation has noted, and no history recorded, and which yet -(it is possible) may have left indelible traces of their existence in -their influence on the state of nature in our own globe, and those of -the other planets. - -(224.) The proof, too, that our data _are_ correctly assumed, is -involved in the general verification of the whole theory, of which, -when once assumed, they form a part; and the same comparison with -observation which enables us to decide on the truth of the abstract -principle, enables us, at the same time, to ascertain whether we -have fixed the values of our data in accordance with the actual -state of nature. If not, it becomes an important question, whether -the assumed values can be corrected, so as to bring the results of -theory to agree with facts? Thus it happens, that as theories approach -to their perfection, a more and more exact determination of data -becomes requisite. Deviations from observed fact, which, in a first -or approximative verification, may be disregarded as trifling, become -important when a high degree of precision is attained. A difference -between the calculated and observed places of a planet, which would -have been disregarded by Kepler in his verification of the law of -elliptic motion, would now be considered fatal to the theory of -gravity, unless it could be shown to arise from an erroneous assumption -of some of the numerical data of our system. - -(225.) The observations most appropriate for the ready and exact -determination of physical data are, therefore, those which it is most -necessary to have performed with exactness and perseverance. Hence -it is, that their performance, in many cases, becomes a national -concern, and observatories are erected and maintained, and expeditions -despatched to distant regions, at an expense which, to a superficial -view, would appear most disproportioned to their objects. But it -may very reasonably be asked why the direct assistance afforded by -governments to the execution of continued series of observations -adapted to this especial end should continue to be, as it has hitherto -almost exclusively been, confined to astronomy. - -(226.) Physical data intended to be employed as elements of calculation -in extensive theories, require to be known with a much greater degree -of exactness than any single observation possesses, not only on account -of their dignity and importance, as affording the means of representing -an indefinite multitude of facts; but because, in the variety of -combinations that may arise, or in the changes that circumstances may -undergo, cases will occur when any trifling error in one of the data -may become enormously magnified in the final result to be compared -with observation. Thus, in the case of an eclipse of the sun, when -the moon enters very obliquely upon the sun’s disc, a trifling error -in the diameter of either the sun or moon may make a great one in the -time when the eclipse shall be announced to commence. It ought to -be remarked, that these are, of all others, the conjunctures where -observations are most available for the determination of data; for, -by the same rule that a small change in the data will, in such cases, -produce a great one in the thing to be observed; so, _vice versâ_, any -moderate amount of error, committed in an observation undertaken for -ascertaining its value, can produce but a very trifling one in the -_reverse_ calculation from which the data come to be determined by -observation. This remark extends to every description of physical data -in every department of science, and is never to be overlooked when the -object in view is the determination of data with the last degree of -precision. - -(227.) But how, it may be asked, are we to ascertain _by_ observation, -data more precise than observation itself? How are we to conclude the -value of that which we do not see, with greater certainty than that -of quantities which we actually see and measure? It is the number of -observations which may be brought to bear on the determination of data -that enables us to do this. Whatever error we may commit in a single -determination, it is highly improbable that we should always err the -same way, so that, when we come to take an average of a great number of -determinations, (unless there be some constant cause which gives a bias -one way or the other,) we cannot fail, at length, to obtain a very near -approximation to the truth, and, even allowing a bias, to come much -nearer to it than can fairly be expected from any single observation, -liable to be influenced by the same bias. - -(228.) This useful and valuable property of the average of a great -many observations, that it brings us nearer to the truth than any -single observation can be relied on as doing, renders it the most -constant resource in all physical enquiries where accuracy is desired. -And it is surprising what a rapid effect, in equalizing fluctuations -and destroying deviations, a moderate multiplication of individual -observations has. A better example can hardly be taken than the average -height of the quicksilver in the common barometer, which measures -the pressure of the air, and whose fluctuations are proverbial. -Nevertheless, if we only observe it regularly every day, and, at the -end of each month, take an average of the observed heights, we shall -find the fluctuations surprisingly diminished in amount; and if we -go on for a whole year, or for many years in succession, the annual -averages will be found to agree with still greater exactness. This -equalizing power of averages, by destroying all such fluctuations as -are irregular or accidental, frequently enables us to obtain evidence -of fluctuations really regular, periodic in their recurrence, and -so much smaller in their amount than the accidental ones, that, but -for this mode of proceeding, they never would have become apparent. -Thus, if the height of the barometer be observed four times a day, -constantly, for a few months, and the averages taken, it will be seen -that a regular _daily_ fluctuation, of very small amount, takes place, -the quicksilver rising and falling twice in the four-and-twenty hours. -It is by such observations that we are enabled to ascertain--what no -single measure (unless by a fortunate coincidence), could give us any -idea, and never any certain knowledge of--the true _sea level_ at any -part of the coast, or the height at which the water of the ocean would -stand, if perfectly undisturbed by winds, waves, or tides: a subject of -very great importance, and upon which it would be highly desirable to -possess an extensive series of observations, at a great many points on -the coasts of the principal continents and islands over the whole globe. - -(229.) In all cases where there is a direct and simple relation between -the phenomenon observed and a single _datum_ on which it depends, -every single observation will give a value of this quantity, and the -average of all (under certain restrictions) will be its exact value. We -say, under certain restrictions; for, if the circumstances under which -the observations are made be not alike, they may not all be equally -favourable to exactness, and it would be doing injustice to those most -advantageous, to class them with the rest. In such cases as these, -as well as in cases where the _data_ are numerous and complicated -together, so as not to admit of single, separate determination (a -thing of continual occurrence), we have to enter into very nice, and -often not a little intricate, considerations respecting the _probable_ -accuracy of our results, or the limits of error within which it is -_probable_ they lie. In so doing we are obliged to have recourse to -a refined and curious branch of mathematical enquiry, called the -doctrine of probabilities, the object of which (as its name imports) -is to reduce our estimation of the probability of any conclusion to -calculation, so as to be able to give more than a mere guess at the -degree of reliance which ought to be placed in it. - -(230.) To give some general idea of the considerations which such -computations involve, let us imagine a person firing with a pistol -at a wafer on a wall ten yards distant: we might, in a general way, -take it for granted, that he would hit the wall, but not the wafer, -at the first shot; but if we would form any thing like a probable -conjecture of _how near_ he would come to it, we must first have an -idea of his skill. No better way of judging could be devised than -by letting him fire a hundred shots at it, and marking where they -all struck. Suppose this done,--suppose the wafer has been hit once -or twice, that a certain number of balls have hit the wall within an -inch of it, a certain number between one and two inches, and so on, -and that one or two have been some feet wide of the mark. Still the -question arises, what estimate are we thence to form of his skill? how -_near_ (or nearer) may we, after this experience, safely, or at least -not unfairly, bet that he will come to the mark the next subsequent -shot? This the laws of probability enable us on such data to say. -Again, suppose, _before_ we were allowed to measure the distances, -the wafer were to have been taken away, and we were called upon, on -the mere evidence of the marks on the wall, to say where it had been -placed; it is clear that no reasoning would enable any one to say with -certainty; yet there is assuredly one place which we may fix on with -greater probability of being right than any other. Now, this is a very -similar case to that of an observer--an astronomer for example--who -would determine the exact place of a heavenly body. He points to it -his telescope, and obtains a series of results disagreeing among -themselves, but yet all agreeing within certain limits, and only a -comparatively small number of them deviating considerably from the mean -of all; and from these he is called upon to say, definitively, what he -shall consider to have been the most probable place of his star at the -moment. Just so in the calculation of physical _data_; where no two -results agree exactly, and where all come within limits, some wide, -some close, what have we to guide us when we would make up our minds -what to conclude respecting them? It is evident that any system of -calculation that can be shown to lead of necessity to the most probable -conclusion where certainty is not to be had must be valuable. However, -as this doctrine is one of the most difficult and delicate among the -applications of mathematics to natural philosophy, this slight mention -of it must suffice at present. - -(231.) In the foregoing pages we have endeavoured to explain the spirit -of the methods to which, since the revival of philosophy, natural -science has been indebted for the great and splendid advances it has -made. What we have all along most earnestly desired to impress on the -student is, that natural philosophy is essentially united in all its -departments, through all which one spirit reigns and one method of -enquiry applies. It cannot, however, be studied as a whole, without -subdivision into parts; and, in the remainder of this discourse, we -shall therefore take a summary view of the progress which has been made -in the different branches into which it may be most advantageously -so subdivided, and endeavour to give a general idea of the nature of -each, and of its relations to the rest. In the course of this, we shall -have frequent opportunity to point out the influence of those general -principles we have above endeavoured to explain, on the progress of -discovery. But this we shall only do as cases arise, without entering -into any regular analysis of the history of each department with that -view. Such an analysis would, indeed, be a most useful and valuable -work, but would far exceed our present limits. We are not, however, -without a hope that this great desideratum in science will, ere long, -be supplied from a quarter every way calculated to do it justice. - - - - - PART III. - - OF THE SUBDIVISION OF PHYSICS INTO DISTINCT BRANCHES, - AND THEIR MUTUAL RELATIONS. - - - - -CHAPTER I. - -OF THE PHENOMENA OF FORCE, AND OF THE CONSTITUTION OF NATURAL BODIES. - - -(232.) Natural History may be considered in two very different lights: -either, 1st, as a collection of facts and objects presented by nature, -from the examination, analysis, and combination of which we acquire -whatever knowledge we are capable of attaining both of the order of -nature, and of the agents she employs for producing her ends, and from -which, therefore, all sciences arise; or, 2dly, as an assemblage of -phenomena to be explained; of effects to be deduced from causes; and of -materials prepared to our hands, for the application of our principles -to useful purposes. Natural history, therefore, considered in the -one or the other of these points of view, is either the beginning or -the end of physical science. As it offers to us, in a confused and -interwoven mass, the elements of all our knowledge, our business is to -disentangle, to arrange, and to present them in a separate and distinct -state: and to this end we are called upon to resolve the important but -complicated problem,--Given the effect, or assemblage of effects, to -find the causes. The principles on which this enquiry relies are those -which constitute the relation of cause and effect, as it exists with -reference to our minds; and their rules and mode of application have -been attempted to be sketched out, (though in far less detail than the -intrinsic interest of the subject, both in a logical and practical -point of view, would demand,) in the foregoing pages. It remains -now to bring together, in a summary statement, the results of the -general examination of nature, so far as it has been prosecuted to the -discovery of natural agents, and the mode in which they act. - -(233.) The first great agent which the analysis of natural phenomena -offers to our consideration, more frequently and prominently than -any other, is force. Its effects are either, 1st, to counteract the -exertion of opposing force, and thereby to maintain _equilibrium_; or, -2dly, to produce _motion_ in matter. - -(234.) Matter, or that, whatever it be, of which all the objects in -nature which manifest themselves directly to our senses consist, -presents us with two general qualities, which at first sight appear -to stand in contradiction to each other--activity and inertness. Its -activity is proved by its power of spontaneously setting other matter -in motion, and of itself obeying their mutual impulse, and moving -under the influence of its own and other force; inertness, in refusing -to move unless obliged to do so by a force impressed externally, or -mutually exerted between itself and other matter, and by persisting in -its state of motion or rest unless disturbed by some external cause. -Yet in reality this contradiction is only apparent. Force being the -cause, and motion the effect produced by it on matter, to say that -matter is inert, or has _inertia_, as it is termed, is only to say -that the cause is expended in producing its effect, and that the -same cause cannot (without renewal) produce double or triple its own -proper effect. In this point of view, equilibrium may be conceived as -a continual production of two opposite effects, each undoing at every -instant what the other has done. - -(235.) However, if this should appear too metaphysical, at all events -this difference of effects gives rise to two great divisions of the -science of force, which are commonly known by the names of STATICS and -DYNAMICS; the latter term, which is general, and has been used by us -before in its general sense, being usually confined to the doctrine -of motion, as produced and modified by force. Each of these great -divisions again branches out into distinct subdivisions, according as -we consider the equilibrium or motion of matter in the three distinct -states in which it is presented to us in nature, the solid, liquid, and -aëriform state, to which, perhaps, ought to be added the _viscous_, -as a state intermediate between that of solidity and fluidity, the -consideration of which, though very obscure and difficult, offers a -high degree of interest on a variety of accounts. - - -_Statics and Dynamics._ - -(236.) The principles have been definitively fixed by Galileo and his -successors, down to Newton, on a basis of sound induction; and as they -are perfectly general, and apply to every case, they are competent, -as we have already before observed, to the solution of every problem -that can occur in the deductive processes, by which phenomena are -to be explained, or effects calculated. Hence, they include every -question that can arise respecting the motions and rest of the smallest -particles of matter, as well as of the largest masses. But the mode of -reasoning from these general principles differs materially, whether -we consider them as applied to masses of matter of a sensible size, -or to those excessively minute, and perhaps indivisible, molecules of -which such masses are composed. The investigations which relate to the -latter subject are extremely intricate, as they necessarily involve the -consideration of the hypotheses we may form respecting the intimate -constitution of the several sorts of bodies above enumerated. - -(237.) On the other hand, those which respect the equilibrium and -motions of sensible masses of matter are happily capable of being -so managed as to render unnecessary the adoption of any particular -hypothesis of structure. Thus, in reasoning respecting the application -of forces to a solid mass, we suppose its parts indissolubly and -unalterably connected; it matters not by what tie, provided this -condition be satisfied, that one point of it cannot be moved without -setting all the rest in motion, so that the relative situation of the -parts one among another be not changed. This is the abstract notion -of a solid which the mechanician employs in his reasonings. And their -conclusions will apply to natural bodies, of course, only so far as -they conform to such a definition. In strictness of speaking, however, -there are no bodies which absolutely conform to it. No substance is -known whose parts are absolutely incapable of yielding one among -another; but the amount by which they do yield is so excessively -small as to be demonstrably incapable, in most cases, of having any -influence on the results: and in those where it has such influence, an -especial investigation of its amount can always be made. This gives -rise to two subdivisions of the application of mechanical reasonings -to solid masses. Those which refer to the action of forces on flexible -or elastic, and on inflexible or rigid, bodies, comprehending under -the latter all such whose resistance to flexure or fracture is so -very great as to permit our adoption of the language and ideas of the -extreme case without fear of material error. - -(238.) In like manner, when we reason respecting the action of forces -on a fluid mass, all we have occasion to assume is, that its parts -are freely moveable one among the other. If, besides this, we choose -to regard a fluid as incompressible, and deduce conclusions on this -supposition, they will hold good only so far as there may be found -such fluids in nature. Now, in strictness, there are none such; but, -practically speaking, in the greater number of cases their resistance -to compression is so very great that the result of the reasoning so -carried on is not sensibly vitiated; and, in the remaining cases, -the same general principles enable us to enter on a special enquiry -directed to this point: and hence the division of fluids, in mechanical -language, into compressible and incompressible, the latter being only -the extreme or limiting case of the former. - -(239.) As we propose here, however, only to consider what is the actual -constitution of nature, we shall regard all bodies, as they really -are, more or less flexible and yielding. We know for certain, that -the space which any material body appears to occupy is not entirely -filled by it; because there is none which by the application of a -sufficient force may not be _compressed_ or forced into a smaller -space, and which, either wholly, as in air or liquids, or in part, as -in the greater number of solids, will not recover its former dimensions -when the force is taken off. In the case of air, this condensation -may be urged to almost any extent; and not only does a mass of air -so condensed completely recover its original bulk, when the applied -pressure is removed, but if that ordinary pressure under which it -exists at the earth’s surface (and which arises from the weight of -the atmosphere) be also removed by an air-pump, it will still further -dilate itself without limit so far as we have yet been able to try -it. Hence we are led to the conclusion that the particles of air are -mutually elastic, and have a _tendency to recede from one another_, -which can only be counteracted by _force_, and therefore is itself a -force of the repulsive kind. Nevertheless, as air is heavy, and as -gravitation is a universal property of matter, there is no doubt that -this repulsive tendency must have a limit, and that there is a distance -to which, if the particles of the air could be removed from each other, -their mutual repulsion would cease, and an attraction take its place. -This limit is probably attained at some very great height above the -earth’s surface, beyond which, of course, its atmosphere cannot extend. - -(240.) What, however, we can only conclude by this or similar reasoning -respecting air, we see distinctly in liquids. They are all, though -in a small degree, compressible, and recover their former dimensions -completely when the pressure is removed; but they cannot be dilated (by -mechanical means), and have no tendency, while they remain liquids, to -enlarge themselves beyond a certain limit, and therefore they assume a -determinate _surface_ while at rest, and their parts actually resist -further separation with a considerable force, thus giving rise to the -phenomenon of the _cohesion of liquids_. - -(241.) Both in air and in liquids, however, the most perfect freedom -of motion of the parts among each other subsists, which could hardly -be the case if they were not separate and independent of each other. -And from this, combined with the foregoing considerations, it has been -concluded that they do not actually touch, but are kept asunder at -determinate distances from each other, by the constant action of the -two forces of attraction and repulsion, which are supposed to balance -and counteract each other at the ordinary distances of the particles, -but to prevail, the one, or the other, according as they are forcibly -urged together or pulled asunder. - -(242.) In solids, however, the case is very different. The mutual free -motion of their parts _inter se_ is powerfully impeded, and in some -almost destroyed. In some, a slow and gradual change of figure may be -produced to a great extent, by pressure or blows, as for instance in -the metals, clay, butter, &c.; in others, fracture is the consequence -of any attempt to change the figure by violence beyond a certain very -small limit. In solids, then, it is evident, that the consideration of -their intimate structure has a very great influence in modifying the -general results of the action of such attractive and repulsive forces -as may be assumed to account for the phenomena they present; yet the -general facts that their parts _cohere_ with a certain energy, and that -they resist displacement or intrusion on the part of other bodies, -are sufficient to demonstrate at least the existence of such forces, -whatever obscurity may subsist as to their mode of action. - -(243.) This division of bodies into airs, liquids, and solids, gives -rise, then, to three distinct branches of mechanical science, in each -of which the general principles of equilibrium and motion have their -peculiar mode of application; viz. pneumatics, hydrostatics, and what -might, without impropriety, be termed stereostatics. - - -_Pneumatics._ - -(244.) Pneumatics relates to the equilibrium or movements of aërial -fluids under all circumstances of pressure, density, and elasticity. -The weight of the air, and its pressure on all the bodies on the -earth’s surface, were quite unknown to the ancients, and only first -perceived by Galileo, on the occasion of a sucking-pump refusing to -draw water above a certain height. Before his time it had always been -supposed that water rose by suction in a pipe, in consequence of a -certain natural _abhorrence of a vacuum_ or empty space, which obliged -the water to enter by way of supplying the place of the air sucked out. -But if any such abhorrence existed, and had the force of an _acting -cause_, which could urge water a single foot into a pipe, there is no -reason why the same principle should not carry it up two, three, or -any number of feet; none why it should suddenly stop short at a certain -height, and refuse to rise higher, however violent the suction might -be, nay, even fall back, if purposely forced up too high. - -(245.) Galileo, however, at first contented himself with the -conclusion, that the natural abhorrence of a vacuum was not strong -enough to sustain the water more than about thirty-two feet above -its level; and, although the true cause of the phenomenon at length -occurred to him, in the pressure of the air on the general surface, -it was not satisfactorily demonstrated till his pupil, Torricelli, -conceived the happy idea of instituting an experiment on a small -scale by the use of a much heavier liquid, mercury, instead of water, -and, in place of sucking out the air from above, employing the much -more effectual method of filling a long glass tube with mercury, and -inverting it into a basin of the same metal. It was then at once seen, -as by a _glaring instance_, that the maintenance of the mercury in the -tube (which is nothing else than the common barometer) was the effect -of a perfectly definite external cause, while its fluctuations from day -to day, with the varying state of the atmosphere, strongly corroborated -the notion of its being due to the pressure of the external air on the -surface of the mercury in the reservoir. - -(246.) The discovery of Torricelli was, however, at first much -misconceived, and even disputed, till the question was finally decided -by appeal to a _crucial instance_, one of the first, if not the very -first on record in physics, and for which we are indebted to the -celebrated Pascal. His acuteness perceived that if the weight of the -incumbent air be the direct cause of the elevation of the mercury, -it must be measured by the amount of that elevation, and therefore -that, by carrying a barometer up a high mountain, and so ascending -into the atmosphere _above_ a large portion of the incumbent air, the -pressure, as well as the length of the column sustained by it, must -be diminished; while, on the other hand, if the phenomenon were due -to the cause originally assigned, no difference could be expected to -take place, whether the observation were made on a mountain or on the -plain. Perhaps the decisive effect of the experiment which he caused -to be instituted for the purpose, on the Puy de Dôme, a high mountain -in Auvergne, while it convinced every one of the truth of Torricelli’s -views, tended more powerfully than any thing which had previously been -done in science to confirm, in the minds of men, that disposition to -experimental verification which had scarcely yet taken full and secure -root. - -(247.) Immediately on this discovery followed that of the air-pump, -by Otto von Guericke of Magdeburgh, whose aim seems to have been to -decide the question, whether a vacuum could or could not exist, by -endeavouring to make one. The imperfection of his mechanism enabled -him only to diminish the aërial contents of his receivers, not -entirely to empty them; but the curious effects produced by even a -partial exhaustion of air speedily excited attention, and induced our -illustrious countryman, Robert Boyle, to the prosecution of those -experiments which terminated in his hands, and in those of Hauksbee, -Hooke, Mariotte, and others, in a satisfactory knowledge of the -general law of the equilibrium of the air under the influence of -greater or less pressures. These discoveries have since been extended -to all the various descriptions of aërial fluids which chemistry has -shown to exist, and to maintain their aëriform state under artificial -pressure, and even to those which may be produced from liquids reduced -to a state of vapour by heat, so long as they retain that state. - -(248.) The manner in which the observed law of equilibrium of an -elastic fluid, like air, may be considered to originate in the mutual -repulsion of its particles, has been investigated by Newton, and -the actual statement of the law itself, as announced by Mariotte, -“that the density of the air, or the quantity of it contained in the -same space, is, _cæteris paribus_, proportional to the pressure it -supports,” has recently been verified within very extensive limits by -direct experiment, by a committee of the Royal Academy of Paris. This -law contains the principle of solution of every dynamical question -that can occur relative to the equilibrium of elastic fluids, and is -therefore to be regarded as one of the highest _axioms_ in the science -of pneumatics. - - -_Hydrostatics._ - -(249.) The principles of the equilibrium of liquids, understanding -by this word such fluids as do not, though quite at liberty, attempt -to dilate themselves beyond a certain point, are at once few and -simple. The first steps towards a knowledge of them were made by -Archimedes, who established the general fact, that a solid immersed in -a liquid loses a portion of its weight equal to that of the liquid it -displaces. It seems very astonishing, after this, that it should not -have been at once concluded that the weight thus said to be _lost_ is -only _counteracted_ by the upward pressure of the liquid, and that, -therefore, a portion of any liquid, surrounded on all sides by a liquid -of the same kind, does really exert its weight in keeping its place. -Yet the prejudice that “liquids do not gravitate in their natural -place” kept its ground, and was only dispelled with the mass of error -and absurdity which the introduction of a rational and experimental -philosophy by Galileo swept away. - -(250.) The hydrostatical law of _the equal pressure of liquids in all -directions_, with its train of curious and important consequences, is -an immediate conclusion from the perfect mobility of their parts among -one another, in consequence of which each of them tends to recede from -an excess of pressure on one side, and thus bears upon the rest, and -distributes the pressure among its neighbours. In this form it was -laid down by Newton, and has proved one of the most useful and fertile -principles of physico-mathematical reasoning on the equilibrium of -fluid masses, as affording a means of tracing the action of a force -applied at any point of a liquid through its whole extent. It applies, -too, without any modification, to expansible fluids as well as to -liquids; and, in the applications of geometry to this subject, enables -us to dispense with any minute and intricate enquiries as to the mode -in which individual particles act on each other. - -(251.) In a practical point of view, this law is remarkable for the -directness of its application to useful purposes. The immediate and -perfect distribution of a pressure applied on any one part, however -small, of a fluid surface through the whole mass, enables us to -communicate _at one instant_ the same pressure to any number of such -parts by merely increasing the surface of the fluid, which may be done -by enlarging the containing vessel; and if the vessel be so constructed -that a large portion of its surface shall be moveable together, the -pressures on all the similar parts of this portion will be united into -one consentient force, which may thus be increased to any extent we -please. The hydraulic press, invented by Bramah, (or rather applied by -him after a much more ancient inventor, Stevin,) is constructed on this -principle. A small quantity of water is driven by sufficient pressure -into a vessel _already full_, and provided with a moveable surface or -piston of great size. Under such circumstances something must give way; -the great surface of the piston accumulates the pressure on it to such -an extent that nothing can resist its violence. Thus, trees are torn -up by the roots; piles extracted from the earth; woollen and cotton -goods compressed into the most portable dimensions; and even hay, for -military service, reduced to such a state of coercion as to be easily -packed on board transports. - -(252.) Liquids differ from aëriform fluids by their _cohesion_, which -may be regarded as a kind of approach to a solid state, and was so -regarded by Bacon (193.). Indeed, there can be little doubt that -the solid, liquid, and aëriform states of bodies are merely stages -in a progress of gradual transition from one extreme to the other; -and that, however strongly marked the distinctions between them may -appear, they will ultimately turn out to be separated by no sudden or -violent line of demarcation, but shade into each other by insensible -gradations. The late experiments of Baron Cagnard de la Tour may be -regarded as a first step towards the full demonstration of this (199.). -But the cohesion of liquids is not, like that of solids, so modified -by their structure in other respects as to destroy the mobility of -their parts one among another (unless in those cases of nearer approach -to the solid state which obtain in viscid or gummy liquids). On the -contrary, the two qualities co-exist, and give rise to a number of -curious and intricate phenomena. - -(253.) One of the most remarkable of these is capillary attraction, -or capillarity as it is sometimes called. Every body has remarked the -adhesion of water to glass. The elevation of the general surface of -the liquid where it is in contact with the containing vessel; the form -of a drop suspended at the under side of a solid: these are instances -of capillary attraction. If a small glass tube with a bore as fine as -a hair be immersed in water, the water will be observed to rise in -it to a certain height, and to assume a concave surface at its upper -extremity. The attraction of the glass on the water, and the cohesion -of the parts of the water to each other, are no doubt the joint causes -of this curious effect; but the mode of action is at once obscure and -complex; and although the researches of Laplace and Young have thrown -great light on it, further investigation seems necessary before we can -be said distinctly to understand it. - -(254.) As the capillarity and cohesion of the parts of liquids shows -them to possess the power of mutual attraction, so their elasticity -demonstrates that they also possess that of repulsion when forcibly -brought nearer than their natural state. From the extremely small -extent to which the compression of liquids can be carried by any force -we can employ, compared with that of air, we must conclude that this -repulsion is much more violent in the former than in the latter, but -counteracted also by a more powerful force of attraction. So much more -powerful, indeed, is the resistance of liquids to compression, that -they were usually regarded as incompressible; an opinion corroborated -by a celebrated experiment made at Florence, in which water was forced -through the pores (as it was said) of a golden ball. More recent -experiments by Canton, and since by Perkins, Oërsted, and others, -have demonstrated however the contrary, and assigned the amount of -compression. - -(255.) The consideration of the motions of fluids, whether liquid -or expansible, is infinitely more complicated than that of their -equilibrium. When their motions are slow, it is reasonable to suppose -that the law of the equable distribution of pressure obtains; but in -very rapid displacements of their parts one among the other, it is not -easy to see how such an equable distribution can be accomplished, and -some phenomena exist which seem to indicate a contrary conclusion. - -(256.) Independent of this, there are difficulties of an almost -insuperable nature to the regular deductive application of the general -principles of mechanics to this subject, which arise from the excessive -intricacy of the pure mathematical enquiries to which its investigation -leads. It was Newton who set the example of a first attempt to draw -any conclusions respecting the motion of fluid masses by direct -reasoning from dynamical principles, and thus laid the foundation of -HYDRODYNAMICS; but it was not till the time of D’Alembert that the -method of reducing any question respecting the motions of fluids under -the action of forces to strict mathematical investigation could be said -to be completely understood. But the cases even now in which this mode -of treating such questions can be applied with full satisfaction are -few in comparison of those in which the experimental method of enquiry -as already observed (189.) is preferable. Such, for example, is that -of the resistance of fluids to bodies moving through them; a knowledge -of which is of great importance in naval architecture and in gunnery, -where the resistance of the air acts to an enormous extent. Such, -too, among the practical subjects which depend mainly on this branch -of science, are the use of sails in navigation; the construction of -windmills, and water-wheels; the transmission of water through pipes -and channels; the construction of docks and harbours, &c. - - -_Nature of Solids in general._ - -(257.) The intimate constitution of solids is, in all probability, very -complicated, and we cannot be said to know much of it. By some recent -delicate experiments on the dimensions of wires violently strained, it -has been shown that they are to a certain small extent capable of being -dilated by tension, as they are also of being compressed by pressure, -but within limits even narrower than those of liquids. Usually, when -strained too far, they break, and refuse to re-unite; or, if compressed -too forcibly, take a permanent contraction of dimension. Thus, wood -may be indented by a blow, and metals rendered denser and heavier by -hammering or rolling. There is a certain degree of confusion prevalent -in ordinary language about the hardness, elasticity, and other similar -qualities, of solids, which it may be well to remove. Hardness is that -disposition of a solid which renders it difficult to displace its -parts among themselves. Thus, steel is harder than iron; and diamond -almost infinitely harder than any other substance in nature: but the -compressibility of steel, or the extent to which it will yield to a -given pressure and recover itself, is not much less than that of soft -iron, and that of ice is very nearly the same with that of water. - -(258.) Again, we call Indian rubber a very elastic body, and so it is; -but in a different sense from steel. Its parts admit of great mutual -displacement without permanent dislocation; however distorted, it -recovers its figure readily, but with a small force. Yet, if Indian -rubber were to be enclosed in a space that it just filled, so as not to -permit its parts to yield laterally, doubtless it would resist actual -compression with great violence. Here, then, we have an instance -of two kinds of elasticity in one substance; a feebler effort of -recovery from distorted figure, and a more violent one from a state -of altered dimension. Both, however, originate in the same causes, -and are referable to the same principles; the former being in fact -only a modified case of the latter, as the effort of a steel spring, -when bent, to recover its former shape, is referable to the same -forces which give to steel its hardness and strength to resist actual -compression and fracture. - -(259.) The toughness of a solid, or that quality by which it will -endure heavy blows without breaking, is again distinct from hardness -though often confounded with it. It consists in a certain yielding of -parts with a powerful general cohesion, and is compatible with various -degrees of elasticity. Malleability is again another quality of solids, -especially metals, quite distinct from toughness, and depends on their -capability of being deprived of their figure without an effort to -recover it and without fracture. - -(260.) Tenacity, again, is a property of solids more directly depending -on the cohesion of their parts than toughness. It consists in their -power of resisting separation by a strain steadily applied, while the -quality of toughness is materially influenced by their disposition -to communicate through their substance the jarring effect of a -blow. Accordingly, the tenacity of a solid is a direct measure of -the cohesive attraction of its parts, and is the best proof of the -existence of such a power. - - -_Crystallography._ - -(261.) It cannot be supposed that these and many other tangible -qualities, as they may be called, should subsist in solids without -a corresponding mechanism in their internal structure. That they -have such a mechanism, and that a very curious and intricate one, -the phenomena of crystallography sufficiently show. This interesting -and beautiful department of natural science is of comparatively very -modern date. That many natural substances affected certain forms must -have been known from the earliest times. Pliny appears to have been -acquainted with this fact, at least in some instances, as he describes -the forms of quartz and diamond. But till the time of Linnæus no -material attention seems to have been bestowed on the subject. He, -however, observed, and described with care, the crystalline forms -of a variety of substances, and even regarded them as so definite a -character of the solids which assumed them, that he supposed every -particular form to be generated by a particular salt. Romé de l’Isle -pursued the study of the crystalline forms of bodies yet farther. He -first ascertained the important fact of the constancy of the angles -at which their faces meet; and observing further that many of them -appear in several different shapes, first conceived the idea that these -shapes might be reducible to one, appropriated in a peculiar manner to -each _substance_, and modified by strict geometrical laws. Bergmann, -reasoning on a fact imparted to him by his pupil Gahn, made a yet -greater step, and showed how at least one species of crystal might -be built up of thin laminæ ranged in a certain order, and following -certain rules of superposition. He failed, however, in deducing just -and general conclusions from this remark, which, correctly viewed, is -the foundation of the most important law of crystallography, that which -connects the primitive form with other forms capable of being exhibited -by the same substance, by a certain fixed relation. An idea may be -formed of what is meant by this sort of connection of one form with -another, by considering a pointed pyramid built up of cubic stones, -disposed in layers, each of which separately is a square plate of the -thickness of a single stone. These layers, laid horizontally one on the -other, and decreasing regularly in size from the bottom to the top, -produce a pyramidal form with a rough or channeled surface; and if the -layers are so extremely thin that the channels cease to be visible to -the eye, the pyramid will seem smooth and perfect. - -(262.) Very shortly after this, and without knowledge of what had been -done by Gahn and Bergmann, the Abbé Haüy, instructed by the accidental -fracture of a fine group of crystals, made the remark noticed already -(in 67.), and reasoning on it with more caution and success, and -pursuing it into all its detail, developed the general laws which -regulate the superposition of the layers of particles of which he -supposes all crystals to be built up, and which enable us, from knowing -their primitive forms, to discover, previous to trial, what other -forms they are capable of assuming; and which, according to this idea, -are called derivative or secondary forms. Mohs and others have since -imagined processes and systems by which the derivation of forms from -each other is facilitated, and have corrected some errors of over-hasty -generalization into which their predecessors had fallen, as well as -advanced, by an extraordinary diligence of research, our knowledge of -the forms which the various substances which occur in nature and art -actually do assume. - -(263.) In what manner a variety in point of external form may originate -in a variety of figures in the ultimate particles of which a solid -is composed, may very readily be imagined by considering what would -happen if the bricks of which an edifice is constructed had all a -certain _leaning_ or bias in one direction out of the perpendicular. -Suppose every brick, for instance, when laid flat on its face, with -its longer edges north and south, had its eastern and western faces -upright, but its northern and southern ones leaning southwards at a -certain inclination the same for each brick; a house built of such -bricks would lean the same way, if the bricks fitted well together. -If, _besides this_, the eastern and western faces of the bricks, -instead of being truly upright, had an inclination eastward, the house -would have a similar one, and all its four corners, instead of being -upright, would lean to the south-east. Suppose, instead of a house, a -pyramid were built of such oblique bricks, with the sides of its base -directed to the four points of the compass; then its point, instead -of being situated vertically over the centre of its base, would stand -perpendicularly over some point to the south-east of that centre, and -the pyramid itself would have its sides facing the south and the east, -more highly inclined to the horizon than those towards the north and -west. - -(264.) Whatever conception we may form of the manner in which the -particles of a crystal cohere and form masses, it is next to impossible -to divest ourselves of the idea of a determinate figure common to them -all. Any other supposition, indeed, would be incompatible with that -exact similarity in all other respects which the phenomena of chemistry -may be considered as having demonstrated. However, it must be borne in -mind that this idea, plausible as it may appear, is yet in some degree -hypothetical, and that the laws of crystallography, as determined from -inductive observation, are quite independent of any supposition of the -kind, or even of the existence of such things as ultimate particles or -atoms at all. - -(265.) Still, that peculiar internal constitution of solid bodies, -whatever it be, which is indicated by the assumption of determinate -figures, by their splitting easier in some directions than in others, -and by their presenting glittering plane surfaces when broken into -fragments, cannot but have an important influence on all their -relations to external agents, as well as to their internal movements -and the mutual actions of their parts on one another. Accordingly, the -division of bodies into crystallized and uncrystallized, or imperfectly -crystallized, is one of the most universal importance; and almost all -the phenomena produced by those more intimate natural causes which -act within small limits, and as it were on the immediate mechanism -of solid substances, are remarkably modified by their crystalline -structure. Thus, in transparent solids, the course taken by the rays -of light, in traversing them, as well as the properties impressed upon -them in so doing, are intimately connected with this structure. The -recent experiments of M. Savart, too, have proved that this is also the -case with their power of resistance to external force, on which depends -their elasticity. Crystallized substances, according to the results of -these experiments, resist compression with different degrees of elastic -force, according to the direction in which it is attempted to compress -them; and all the phenomena dependent on their elasticity are affected -by this cause, especially those which relate to their vibratory -movements and their conveyance of sound. - -(266.) There can be little doubt that modifications, similarly -depending on the internal structure of crystals, will be traced through -every department of physics. In that interesting one which relates -to the action of heat in expanding the dimensions of substances, a -beginning has already been made by Professor Mitscherlich. It had long -been known that all substances are dilated by heat, and no exception -to this law has been found, so long as we regard the _bulk_ of the -heated body. Thus, an iron rod when hot is both longer and thicker than -when cold; and the difference of dimension, though but trifling in -itself, is yet capable of being made sensible, and is of considerable -consequence in engineering. Thus, too, the quicksilver in a common -thermometer occupies a larger space when hot than when cold; and being -confined by the glass ball, (which also expands, but _not so much in -proportion_,) it is forced to rise in the tube. These and similar facts -had long been known; and accurate measures of the total amount of -dilatation of a variety of different bodies, under similar accessions -of heat, had been obtained and registered in tables. But no one had -suspected the important fact, that this expansion in crystallized -bodies takes place under totally different circumstances from what -obtains in uncrystallized ones. M. Mitscherlich has lately shown that -such substances expand differently in different directions, and has -even produced a case in which expansion in one direction is actually -accompanied with contraction in another. This step, the most important -beyond a doubt which has yet been made in pyrometry, can however only -be regarded as the first in a series of researches which will occupy -the next generation, and which promises to afford an abundant harvest -of new facts, as well as the elucidation of some of the most obscure -and interesting points in the doctrine of heat. - -(267.) From what has been said, it is clear that if we look upon solid -bodies as collections of particles or atoms, held together and kept -in their places by the perpetual action of attractive and repulsive -forces, we cannot suppose these forces, at least in crystallized -substances, to act alike in all directions. Hence arises the conception -of _polarity_, of which we see an instance, on a great scale, in the -magnetic needle, but which, under modified forms, there is nothing to -prevent us from conceiving to act among the ultimate atoms of solid -or even fluid bodies, and to produce all the phenomena which they -exhibit in their crystallized state, either when acting on each other, -or on light, heat, &c. It is not difficult, if we give the reins to -imagination, to conceive how attractive and repulsive atoms, bound -together by some unknown tie, may form little machines or compound -particles, which shall have many of the properties which we refer to -polarity; and accordingly many ingenious suppositions have been made to -that effect: but in the actual state of science it is certainly safest -to wave these hypotheses, without however absolutely rejecting them, -and regard the _polarity of matter_ as one of the ultimate phenomena to -which the analysis of nature leads us, and of which it is our business -fully to investigate the laws, before we endeavour to ascertain its -causes, or trace the mechanism by which it is produced. - -(268.) The mutual attractions and repulsions of the particles of -matter, then, and their polarity, whether regarded as an original or a -derivative property, are the forces which, acting with great energy, -and within very confined limits, we must look to as the principles on -which the intimate constitution of all bodies and many of their mutual -actions depend. These are what are understood by the general term of -_molecular forces_. Molecular attraction has been attempted to be -confounded by some with the general attraction of gravity, which all -matter exerts on all other matter; but this idea is refuted by the -plainest facts. - - - - -CHAP. II. - -OF THE COMMUNICATION OF MOTION THROUGH BODIES.--OF SOUND AND LIGHT. - - -(269.) The propagation of motion through all substances, whether of a -single impulse, as a blow or thrust, or of one frequently and regularly -repeated, such as a jarring or vibratory movement, depends wholly on -these molecular forces; and it is on such propagation that sound and -very probably light depend. To conceive the manner in which a motion -may be conveyed from one part of a substance to another, whether solid -or fluid, we may attend to what takes place when a wave is made to -run along a stretched string, or the surface of still water. Every -part of the string, or water, is in succession moved from its place, -and agitated with a motion similar to that of the original impulse, -leaving its place and returning to it, and when one part ceases to move -the next receives as it were the impression, and forwards it onward. -This may seem a slow and circuitous process in description; but when -sound, for example, is conveyed through the air, we are to consider, -1st, that the air, the substance actually in motion, is extremely light -and acted upon by a very powerful elasticity, so that the force which -propagates the motion, or by which the particles adjacent act on, and -urge forward, each other, is very great, compared with the quantity of -materials set in motion by it: and the same is true, even in a greater -degree, in liquids and solids; for in these the elastic forces are even -greater, in proportion to the weight, than in air. - -(270.) A general notion of the mode in which sounds are conveyed -through the air was not altogether deficient among the ancients; but -it is to Newton that we owe the first attempt to analyze the process, -and show correctly what takes place in the communication of motion -from particle to particle. Reasoning on the properties of the air as -an elastic body, he showed the effect of an impulse on any portion of -it to consist in a condensation of the air immediately adjacent in the -direction of the impulse, which then, re-acting by its spring, drives -back the portion which had advanced to its original place, and at the -same time urges forward the portion before it, in the direction of the -impulse, so that every particle alternately advances and retreats. -But, in pursuing this idea into its details, Newton fell into some -errors which were pointed out by Cramer, though their origin was not -traced, nor the reasoning corrected, till the subject was resumed by -Lagrange and Euler; nor is this any impeachment of the penetration of -our immortal countryman. The mathematical theory of the propagation -of sound, and of vibratory and undulatory motions in general, is -one of the utmost intricacy; and, in spite of every exertion on the -part of the most expert geometers, continues to this day to give -continual occasion for fresh researches; while phenomena are constantly -presenting themselves, which show how far we are from being able to -deduce all the particulars, even of cases comparatively simple, by any -direct reasoning from first principles. - -(271.) Whenever an impulse of any kind is conveyed by the air, to our -ears, it produces the impression of sound; but when such an impulse -is regularly and uniformly repeated in extremely rapid succession, it -gives us that of a musical note, the pitch of the note depending on -the rapidity of the succession (see art. 153.). The sense of harmony, -too, depends on the periodical recurrence of coincident impulses on the -ear, and affords, perhaps, the only instance of a sensation for whose -pleasing impression a distinct and intelligible reason can be assigned. - -(272.) Acoustics, then, or the science of sound, is a very considerable -branch of physics, and one which has been cultivated from the earliest -ages. Even Pythagoras and Aristotle were not ignorant of the general -mode of its transmission through the air, and of the nature of harmony; -but as a branch of science, independent of its delightful application -in the art of music, it could be hardly said to exist, till its nature -and laws became a matter of experimental enquiry to Bacon and Galileo, -Mersenne and Wallis; and of mathematical investigation to Newton, and -his illustrious successors, Lagrange and Euler. From that time its -progress, as a branch both of mathematical and experimental science, -has been constant and accelerated. A curious and beautiful method of -observation, due to Chladni, consists in the happy device of strewing -sand over the surfaces of bodies in a state of sonorous vibration, -and marking the figures it assumes. This has made their motions -susceptible of ocular examination, and has been lately much improved -on, and varied in its application, by M. Savart, to whom we also owe a -succession of instructive researches on every point connected with the -subject of sound, which may rank among the finest specimens of modern -experimental enquiry. But the subject is far from being exhausted; and, -indeed, there are few branches of physics which promise at once so much -amusing interest, and such important consequences, in its bearings on -other subjects, and especially, through the medium of strong analogies, -on that of light. - - -_Light and Vision._ - -(273.) The nature of light has always been involved in considerable -doubt and mystery. The ancients could scarcely be said to have any -opinion on the subject, unless, indeed, it could be considered such -to affirm that distant bodies could not be put into communication -without an intermedium; and that, therefore, there must be _something_ -between the eye and the thing seen. What that something is, however, -they could only form crude and vague conjectures. One supposed that -the eyes themselves emit rays or emanations of some unknown kind, by -which distant objects are as it were felt; a singularly unfortunate -idea, since it gives no reason why objects should not be equally -well seen in the dark--no account, in short, of the part performed -by _light_ in vision. Others imagined that all visible objects are -constantly throwing out from them, in all directions, some sort of -resemblances or spectral forms of themselves, which, when received by -the eyes, produce an impression of the objects. Vague and clumsy as -this hypothesis obviously is, it assigns to the object a power, and to -light a diffusive propagation in all directions, which are, the one and -the other, independent of our eyes, and therefore goes to separate the -phenomena of _light_ from those of _vision_. - -(274.) The hypothesis of Newton is a refinement and improvement on -this idea. Instead of spectra or resemblances, he supposes luminous -objects actually to dart out from them in all directions, particles, -of inconceivable minuteness (as indeed they must be, having such -an enormous velocity (see 17.), not to dash in pieces every thing -they strike upon). These particles he supposes to be acted upon by -attractive and repulsive forces, residing in all material bodies, the -latter extending to some very small distance beyond their surfaces; and -by the action of these forces to be turned aside from their natural -straight-lined course, without ever coming in actual contact with the -particles themselves of the bodies on which they fall, but either being -turned back and _reflected_ by the repulsive forces before they reach -them, or penetrating between their intervals, as a bird may be supposed -to fly through the branches of a forest, and undergoing all their -actions, to take at quitting them a direction finally determined by -the position of the surface at which they emerge with respect to their -course. - -(275.) This hypothesis, which was discussed and reasoned upon by Newton -in a manner worthy of himself, affords, by the application of the -same dynamical laws which he had applied with so much success to the -explanation of the planetary motions, not merely a plausible, but a -perfectly reasonable and fair explanation of all the _usual_ phenomena -of light known in his time. His own beautiful discoveries, too, of -the different refrangibilities of the differently coloured rays, -were perfectly well represented in this theory, by simply admitting -a difference of velocity in the particles, which produce in the eye -the sensations of different colours. And had the properties of light -remained confined to these, there would have been no occasion to have -resorted to any other mode of conceiving it. - -(276.) A very different hypothesis had, however, been suggested about -the same period by Huyghens, who supposed light to be produced in the -same manner with sound, by the communication of a vibratory motion -from the luminous body to a highly elastic fluid, which he imagined -as filling all space, and as being less condensed within the limits -of space occupied by matter, and that to a greater or less extent, -according to the nature of the occupying substance. Thus, in place of -any thing actually thrown off, he substituted waves, or vibrations, -propagated in all directions from luminous bodies, through this medium, -or ether, as he called it. Huyghens, being himself a consummate -mathematician, was enabled to trace many of the consequences of this -hypothesis, and to show that the ordinary laws of reflection and -refraction were represented or accounted for by it, as well as by -Newton’s. But the hypothesis of Huyghens has not been fully successful -in accounting for what may be considered the chief of all optical -facts, the production of colours in the ordinary refraction of -light by a prism, of which the theory of Newton gives a complete and -elegant explanation; and the discovery of which by him marks one of -the greatest epochs in the annals of experimental science. This, which -has been often urged in objection to it, remains still, if not quite -unanswered, at least only imperfectly removed. - -(277.) Other phenomena, however, were not wanting to afford a further -trial of the _explanatory powers_ of either hypothesis. The diffraction -or inflection of light, discovered by Grimaldi, a Jesuit of Bologna, -seemed to indicate that the rays of light were turned aside from their -straight course by merely passing near bodies of every description. -These phenomena, which are very curious and beautiful, were minutely -examined by Newton, and referred by him to the action of repulsive -forces extending to a sensible distance from the surfaces of bodies; -and his explanation, so far as the facts known to him are concerned, -appears as satisfactory as could reasonably be then expected; and much -more so than any thing which could at that time be produced on the side -of the hypothesis of Huyghens, which, in fact, seemed incapable of -giving any account whatever of them. - -(278.) Another class of delicate and splendid optical phenomena, which -had begun to attract attention somewhat previous to Newton’s time, -seemed to leave both hypotheses equally at a loss. These were the -colours exhibited by very thin films, either of a liquid (such as a -soap-bubble), or of air, as when two glasses are laid together with -only air between them. These colours were examined by Newton with a -minuteness and care altogether unexampled in experimental philosophy -at that time, and with which few researches undertaken since will bear -to stand in competition. Their result was a theory of a very singular -nature, which he grounded on an hypothesis of what he termed _fits of -easy transmission and reflection_; and which supposed each ray of light -to pass in its progress periodically through a succession of states -such as would alternately dispose it to penetrate or be reflected back -from the surface of a body on which it might fall. The simplest way -in which the reader may conceive this hypothesis, is to regard every -particle of light as a sort of little magnet revolving rapidly about -its own centre while it advances in its course, and thus alternately -presenting its attractive and repulsive pole, so that when it arrives -at the surface of a body with its repulsive pole foremost, it is -repelled and reflected; and when the contrary, attracted, so as to -enter the surface. Newton, however, very cautiously avoided announcing -his theory in this or any similar form, confining himself entirely to -general language. In consequence, it has been confidently asserted -by all his followers, that the doctrine of fits of easy reflection -and transmission, as laid down by him, is substantially nothing more -than a statement of facts. Were it so, it is clear that any other -theory which should offer a just account of the same phenomena must -ultimately involve and coincide with that of Newton. But this, as we -shall presently see, is not the case; and this instance ought to serve -to make us extremely cautious how we employ, in stating physical laws -derived from experiment, language which involves any thing in the -slightest degree theoretical, if we would present the laws themselves -in a form which no future research shall modify or subvert. - -(279.) A third class of optical phenomena, which were likewise -discovered while Newton was yet engaged in his optical researches, was -that exhibited by doubly refracting crystals. In what the phenomenon of -double refraction consists, we have already had occasion to explain. -The fact itself was first noticed by Erasmus Bartolin in the crystal -called Iceland spar; and was studied with attention by Huyghens, who -ascertained its laws, and referred it with remarkable ingenuity and -success to his theory of light, by the additional hypothesis of such -a constitution of his ethereal medium within the crystal as should -enable it to convey an impulse faster in one direction than another: -as if, for example’s sake, we should suppose a sound conveyed through -the air with different degrees of rapidity in a vertical and horizontal -direction. - -(280.) Some remarkable facts accompanying the double refraction -produced by Iceland spar, which Bartolin, Huyghens, and Newton, had -observed, led the latter to conceive the singular idea that a ray of -light after its emergence from such a crystal acquires _sides_, that -is to say, distinct relations to surrounding space, which it carries -with it through its whole subsequent course, and which give rise to all -those curious and complicated phenomena which are now known under the -name of the _polarization of light_. These results, however, appeared -so extraordinary, and offered so little handle for further enquiry, -that their examination dropped, as if by common consent; Newton himself -resting content with urging strongly the apparent incompatibility of -these properties with the Huyghenian doctrine, but without making any -attempt to explain them by his own. - -(281.) From the period of Newton’s optical discoveries to the -commencement of the present century, no great accession to our -knowledge of the nature of light was made, if we except one, which, -from its invaluable practical application, must ever hold a prominent -place in the annals both of art and science: we mean, the discovery -of the principle of the achromatic telescope, which originated in a -discussion between the celebrated geometer Euler, Klingenstierna, an -eminent Swedish philosopher, and our own countryman, the admirable -optician Dollond, on the occasion of certain abstract theoretical -investigations of the former, which led him to speculate on its -_possibility_, and which ultimately terminated in its complete and -happy _execution_ by the latter; a memorable case in science, though -not a singular one, where the speculative geometer in his chamber, -apart from the world, and existing among abstractions, has originated -views of the noblest practical application.[49] - -(282.) The explanation which our knowledge of optical laws affords of -the mechanism of the eye, and the process by which vision is performed, -is as complete and satisfactory as that of hearing by the propagation -of motion through the air. The camera obscura, invented by Baptista -Porta in 1560, gave the first idea how the actual images of external -objects might be conveyed into the eye, but it was not till after a -considerable interval that Kepler, the immortal discoverer of those -great laws which regulate the periods and motions of the planets, -pointed out distinctly the offices performed by the several parts -of the eye in the act of vision. From this to the invention of the -telescope and microscope there would seem but a small step, but it is -to accident rather than design that it is due; and its re-invention -by Galileo, on a mere description of its effects, may serve, among -a thousand similar instances, to show that inestimable practical -applications lie open to us, if we can only once bring ourselves -to conceive their possibility, a lesson which the invention of the -achromatic telescope itself, as we have above related it, not less -strongly exemplifies. - -(283.) The little instrument with which Galileo’s splendid discoveries -were made was hardly superior in power to an ordinary finder of the -present day; but it was rapidly improved on, and in the hands of -Huyghens attained to gigantic dimensions and very great power. It was -to obviate the necessity of the enormous length required for these -telescopes, and yet secure the same power, that Gregory and Newton -devised the reflecting telescope, which has since become a much -more powerful instrument than its original inventors probably ever -contemplated. - -(284.) The telescope, as it exists at present, with the improvements -in its structure and execution which modern artists have effected, must -assuredly be ranked among the highest and most refined productions of -human art; that in which man has been able to approximate most closely -to the workmanship of nature, and which has conferred upon him, if -not another sense, at least an exaltation of one already possessed -by him that merits almost to be regarded as a new one. Nor does it -appear yet to have reached its ultimate perfection, to which indeed -it is difficult to assign any bounds, when we take into consideration -the wonderful progress which workmanship of every kind is making, -and the delicacy, far superior to that of former times, with which -materials may now be wrought, as well as the ingenious inventions and -combinations which every year is bringing forth for accomplishing the -same ends by means hitherto unattempted.[50] - -(285.) After a long torpor, the knowledge of the properties of light -began to make fresh progress about the end of the last century, -advancing with an accelerated rapidity, which has continued unabated -to the present time. The example was set by our late admirable and -lamented countryman, Dr. Wollaston, who re-examined and verified -the laws of double refraction in Iceland spar announced by Huyghens. -Attention being thus drawn to the subject, the geometry of Laplace -soon found a means of explaining at least one portion of the mystery -of this singular phenomenon, by the Newtonian theory of light, applied -under certain supposed conditions; and the reasoning which led him to -the result (at that time quite unexpected), may justly be regarded as -one of his happiest efforts. The prosecution of the subject, which had -now acquired a high degree of interest, was encouraged by the offer -of a prize on the part of the French Academy of Sciences; and it was -in a memoir which received this honourable reward on that occasion, -in 1810, that Malus, a retired officer of engineers in the French -army, announced the great discovery of the _polarization of light_ by -ordinary reflection at the surface of a transparent body. - -(286.) Malus found that when a beam of light is reflected from the -surface of such a body at a certain angle, it acquires precisely the -same singular property which is impressed upon it in the act of double -refraction, and which Newton had before expressed by saying that it -possessed _sides_. This was the first circumstance which pointed out a -connection between that hitherto mysterious phenomenon and any of the -ordinary modifications of light; and it proved ultimately the means of -bringing the whole within the limits, if not of a complete explanation, -at least of a highly plausible theoretical representation. So true is, -in science, the remark of Bacon, that no natural phenomenon can be -adequately studied _in itself alone_, but, to be understood, must be -considered _as it stands connected with all nature_. - -(287.) The new class of phenomena thus disclosed were immediately -studied with diligence and success, both abroad by Malus and Arago, and -at home by our countryman Dr. Brewster, and their laws investigated -with a care proportioned to their importance; when another and -apparently still more extraordinary class of phenomena presented -itself in the production of the most vivid and beautiful colours -(every way resembling those observed by Newton in thin films of air -or liquids, only infinitely more developed and striking,) in certain -transparent crystallized substances, when divided into flat plates in -particular directions, and exposed in a beam of polarized light. The -attentive examination of these colours by Wollaston, Biot, and Arago, -but more especially by Brewster, speedily led to the disclosure of a -series of optical phenomena so various, so brilliant, and evidently -so closely connected with the most important points relating to the -intimate structure of crystallized bodies, as to excite the highest -interest,--that sort of interest which is raised when we feel we are -on the eve of some extraordinary discovery, and expect every moment -that some leading fact will turn up, which will throw light on all that -appears obscure, and reduce into order all that seems anomalous. - -(288.) This expectation was not disappointed. So long before the time -we are speaking of as the first year of the present century, our -illustrious countryman, the late Dr. Thomas Young, had established a -principle in optics, which, regarded as a physical law, has hardly its -equal for beauty, simplicity, and extent of application, in the whole -circle of science. Considering the manner in which the vibrations of -two musical sounds arriving at once at the ear affect the sense with -an impression of sound or silence according as they conspire or oppose -each other’s effects, he was led to the idea that the same ought to -hold good with light as with sound, if the theory which makes light -analogous to sound be the true one; and that, therefore, two rays of -light, setting off from the same origin, at the same instant, and -arriving at the same place by different routes, ought to strengthen -or wholly or partially destroy each other’s effects according to -the difference in length of the routes described by them. That two -lights should in any circumstances combine to produce darkness may -be considered strange, but is _literally true_; and it had even been -noticed long ago as a singular and unaccountable fact by Grimaldi, in -his experiments on the inflection of light. The experimental means by -which Dr. Young confirmed this principle, which is known in optics -by the name of the _interference_ of the rays of light, were as -simple and satisfactory as the principle itself is beautiful; but the -verifications of it, drawn from the explanation it affords of phenomena -apparently the most remote, are still more so. Newton’s colours of thin -films were the first phenomena to which its author applied it with full -success. Its next remarkable application was to those of diffraction, -of which, in the hands of M. Fresnel, a late eminent French geometer, -it also furnished a complete explanation, and that, too, in cases to -which Newton’s hypothesis could not apparently be made to apply, and -through a complication of circumstances which might afford a very -severe test of any hypothesis. - -(289.) A simple and beautiful experiment on the interferences of -polarized light due to Fresnel and Arago enabled them to bring Dr. -Young’s law to bear on the colours produced by crystallized plates in a -polarized beam, and by so doing afforded a key to all the intricacies -of these magnificent but complex phenomena. Nothing now was wanting to -a rational theory of double refraction but to frame an hypothesis of -some mode in which light might be conceived to be propagated through -the elastic medium supposed to convey it in such a way as not to be -contradictory to any of the facts, nor to the general laws of dynamics. -This essential idea, without which every thing that had been before -done would have been incomplete, was also furnished by Dr. Young, who, -with a sagacity which would have done honour to Newton himself, had -declared, that to accommodate the doctrine of Huyghens to the phenomena -of polarized light it is necessary to conceive the mode of propagation -of a luminous impulse through the ether, differently from that of a -sonorous one through the air. In the latter, the particles of the air -_advance_ and _recede_; in the former, those of the ether must be -supposed to _tremble laterally_. - -(290.) Taking this as the groundwork of his reasoning, Fresnel -succeeded in erecting on it a theory of polarization and double -refraction, so happy in its adaptation to facts, and in the coincidence -with experience of results deduced from it by the most intricate -analysis, that it is difficult to conceive it unfounded. If it be -so, it is at least the most curiously artificial system that science -has yet witnessed; and whether it be so or not, so long as it serves -to group together in one comprehensive point of view a mass of facts -almost infinite in number and variety, to reason from one to another, -and to establish analogies and relations between them; on whatever -hypothesis it may be founded, or whatever arbitrary assumptions it -may make respecting structures and modes of action, it can never be -regarded as other than a most real and important accession to our -knowledge. - -(291.) Still, it is by no means impossible that the Newtonian theory of -light, if cultivated with equal diligence with the Huyghenian, might -lead to an equally plausible explanation of phenomena now regarded -as beyond its reach. M. Biot is the author of the hypothesis we have -already mentioned of a rotatory motion of the particles of light about -their axes. He has employed it only for a very limited purpose; but -it might doubtless be carried much farther; and by admitting only the -regular emission of the luminous particles at equal intervals of time, -and in similar states of motion from the shining body, which does not -seem a very forced supposition, all the phenomena of interference at -least would be readily enough explained without the admission of an -ether. - -(292.) The optical examination of crystallized substances affords -one among many fine examples of the elucidation which every branch -of science is capable of affording to every other. The indefatigable -researches of Dr. Brewster and others have shown that the phenomena -exhibited by polarized light in its transmission through crystals -afford a certain indication of the most important points relating to -the structure of the crystals themselves, and thus become most valuable -characters by which to recognise their internal constitution. It was -Newton who first showed of what importance as a physical character,--as -the indication of other properties,--the action of a body on light -might become; but the characters afforded by the use of polarized light -as an instrument of experimental enquiry are so marked and intimate, -that they may almost be said to have furnished us with a kind of -intellectual sense, by which we are enabled to scrutinize the internal -arrangement of those wonderful structures which Nature builds up by -her refined and invisible architecture, with a delicacy eluding our -conception, yet with a symmetry and beauty which we are never weary -of admiring. In this point of view the science of optics has rendered -to mineralogy and crystallography services not less important than to -astronomy by the invention of the telescope, or to natural history by -that of the microscope; while the relations which have been discovered -to exist between the optical properties of bodies and their crystalline -forms, and even their chemical habitudes, have afforded numerous -and beautiful instances of general laws concluded from laborious and -painful induction, and curiously exemplifying the simplicity of nature -as it emerges slowly from an entangled mass of particulars in which, at -first, neither order nor connection can be traced. - - - - -CHAP. III. - -OF COSMICAL PHENOMENA. - - -_Astronomy and Celestial Mechanics._ - -(293.) Astronomy, as has been observed in the former part of this -discourse, as a science of observation, had made considerable progress -among the ancients: indeed, it was the only branch of physical science -which could be regarded as having been cultivated by them with any -degree of assiduity or real success. The Chaldean and Egyptian records -had furnished materials from which the motions of the sun and moon -could be calculated with sufficient exactness for the prediction of -eclipses; and some remarkable cycles, or periods of years in which -the lunar eclipses return in very nearly the same order, had been -ascertained by observation. Considering the extreme imperfection of -their means of measuring time and space, this was, perhaps, as much -as could have been expected at that early period, and it was followed -up for a while in a philosophical spirit of just speculation, which, -if continued, could hardly have failed to lead to sound and important -conclusions. - -(294.) Unfortunately, however, the philosophy of Aristotle laid it -down as a principle, that the celestial motions were regulated by laws -proper to themselves, and bearing no affinity to those which prevail -on earth. By thus drawing a broad and impassable line of separation -between celestial and terrestrial mechanics, it placed the former -altogether out of the pale of experimental research, while it at the -same time impeded the progress of the latter by the assumption of -principles respecting natural and unnatural motions, hastily adopted -from the most superficial and cursory remark, undeserving even the -name of observation. Astronomy, therefore, continued for ages a -science of mere record, in which theory had no part, except in so -far as it attempted to conciliate the inequalities of the celestial -motions with that assumed law of uniform circular revolution which -was alone considered consistent with the perfection of the heavenly -mechanism. Hence arose an unwieldy, if not self-contradictory, mass -of hypothetical motions of sun, moon, and planets, in circles, whose -centres were carried round in other circles, and these again in others -without end,--“cycle on epicycle, orb on orb,”--till at length, as -observation grew more exact, and fresh epicycles were continually -added, the absurdity of so cumbrous a mechanism became too palpable to -be borne. Doubts were expressed, to which the sarcasm of a monarch[51] -gave a currency they might not have obtained in a period when men -scarcely dared trust themselves to think; and at length Copernicus, -promulgating his own, or reviving the Pythagorean doctrine, which -places the sun in the centre of our system, gave to astronomy a -simplicity which, contrasted with the complication of the preceding -views, at once commanded assent. - -(295.) An elegant writer[52], whom we have before had occasion to -quote, has briefly and neatly accounted for the confused notions which -so long prevailed respecting the constitution of our system, and the -difficulty experienced in acquiring a true notion of the disposition -of its parts. “We see it,” he observes, “not in _plan_, but in -_section_.” The reason of this is, that our point of observation lies -in its general plane, but the notion we aim at forming of it is not -that of its section, but of its plan. This is as if we should attempt -to read a book, or make out the countries on a map, with the eye on a -level with the paper. We can only judge directly of the distances of -objects by their sizes, or rather of their change of distance by their -change of size; neither have we any means of ascertaining, otherwise -than indirectly, even their positions, one among the other, from their -apparent places as seen by us. Now, the variations in apparent size -of the sun and moon are too small to admit of exact measure without -the use of the telescope, and the bodies of the planets cannot even be -distinguished as having any distinct size with the naked eye. - -(296.) The Copernican system once admitted, however, this difficulty -of conception, at least, is effectually got over, and it becomes -a mere problem of geometry and calculation to determine, from the -observed places of a planet, its real orbit about the sun, and the -other circumstances of its motion. This Kepler accomplished for the -orbit of Mars, which he ascertained to be an ellipse having the sun -in one of its foci; and the same law, being extended by inductive -analogy to all the planets, was found to be verified in the case of -each. This with the other remarkable laws which are usually cited in -physical astronomy by the name of Kepler’s laws, constitute undoubtedly -the most important and beautiful system of geometrical relations which -have ever been discovered by a mere inductive process, independent of -any consideration of a theoretical kind. They comprise within them a -compendium of the motions of all the planets, and enable us to assign -their places in their orbits at any instant of time past or to come -(disregarding their mutual perturbations), provided certain purely -geometrical problems can be numerically resolved. - -(297.) It was not, however, till long after Kepler’s time that the -real importance of these laws could be felt. Regarded in themselves, -they offered, it is true, a fine example of regular and harmonious -disposition in the greatest of all the works of creation, and a -striking contrast to the cumbersome mechanism of the cycles and -epicycles which preceded them; but there their utility seemed to -terminate, and, indeed, Kepler was reproached, and not without a -semblance of reason, with having rendered the actual calculation of -the places of the planets more difficult than before, the resources of -geometry being then inadequate to resolve the problems to which the -strict application of his laws gave rise. - -(298.) The first result of the invention of the telescope and its -application to astronomical purposes, by Galileo, was the discovery -of Jupiter’s disc and satellites,--of a system offering a beautiful -miniature of that greater one of which it forms a portion, and -presenting to the eye of sense, at a single glance, that disposition of -parts which in the planetary system itself is discerned only by the eye -of reason and imagination (see 195.). Kepler had the satisfaction of -seeing it ascertained, that the law which he had discovered to connect -the times of revolution of the planets with their distances from the -sun, holds good also when applied to the periods of circulation of -these little attendants round the centre of their principal; thus -demonstrating it to be something more than a mere empirical rule, and -to depend on the intimate nature of planetary motion itself. - -(299.) It had been objected to the doctrine of Copernicus, that, were -it true, Venus should appear sometimes horned like the moon. To this -he answered by admitting the conclusion, and averring that, should we -ever be able to see its actual shape, it _would_ appear so. It is easy -to imagine with what force the application would strike every mind when -the telescope confirmed this prediction, and showed the planet just as -both the philosopher and his objectors had agreed it ought to appear. -The history of science affords perhaps only one instance analogous to -this. When Dr. Hutton expounded his theory of the consolidation of -rocks by the application of heat, at a great depth below the bed of -the ocean, and especially of that of marble by actual fusion; it was -objected that, whatever might be the case with others, with calcareous -or marble rocks, at least, it was impossible to grant such a cause -of consolidation, since heat decomposes their substance and converts -it into quicklime, by driving off the carbonic acid, and leaving a -substance perfectly infusible, and incapable even of agglutination -by heat. To this he replied, that the pressure under which the heat -was applied would prevent the escape of the carbonic acid; and that -being retained, it might be expected to give that fusibility to the -compound which the simple quicklime wanted. The next generation saw -this anticipation converted into an observed fact, and verified by the -direct experiments of Sir James Hall, who actually succeeded in melting -marble, by retaining its carbonic acid under violent pressure. - -(300.) Kepler, among a number of vague and even wild speculations on -the causes of the motions whose laws he had developed so beautifully -and with so much patient labour, had obtained a glimpse of the general -law of the inertia of matter, as applicable to the great masses of the -heavenly bodies as well as to those with which we are conversant on -the earth. After Kepler, Galileo, while he gave the finishing blow to -the Aristotelian dogmas which erected a barrier between the laws of -celestial and terrestrial motion, by his powerful argument and caustic -ridicule, contributed, by his investigations of the laws of falling -bodies and the motions of projectiles, to lay the foundation of a -true system of dynamics, by which motions could be determined from a -knowledge of the forces producing them, and forces from the motions -they produce. Hooke went yet farther, and obtained a view so distinct -of the mode in which the planets might be retained in their orbits -by the sun’s attraction, that, had his mathematical attainments been -equal to his philosophical acumen, and his scientific pursuits been -less various and desultory, it can hardly be doubted that he would have -arrived at a knowledge of the law of gravitation. - -(301.) But every thing which had been done towards this great end, -before Newton, could only be regarded as smoothing some first -obstacles, and preparing a state of knowledge, in which powers like his -could be effectually exerted. His wonderful combination of mathematical -skill with physical research enabled him to invent, at pleasure, new -and unheard-of methods of investigating the effects of those causes -which his clear and penetrating mind detected in operation. Whatever -department of science he touched, he may be said to have formed afresh. -Ascending by a series of close-compacted inductive arguments to the -highest axioms of dynamical science, he succeeded in applying them -to the complete explanation of all the great astronomical phenomena, -and many of the minuter and more enigmatical ones. In doing this, he -had every thing to create: the mathematics of his age proved totally -inadequate to grapple with the numerous difficulties which were to -be overcome; but this, so far from discouraging him, served only to -afford new opportunities for the exertion of his genius, which, in the -invention of the method of fluxions, or, as it is now more generally -called, the differential calculus, has supplied a means of discovery, -bearing the same proportion to the methods previously in use, that -the steam-engine does to the mechanical powers employed before its -invention. Of the optical discoveries of Newton we have already spoken; -and if the magnitude of the objects of his astronomical discoveries -excite our admiration of the mental powers which could so familiarly -grasp them, the minuteness of the researches into which he there set -the first example of entering, is no less calculated to produce a -corresponding impression. Whichever way we turn our view, we find -ourselves compelled to bow before his genius, and to assign to the -name of NEWTON a place in our veneration which belongs to no other in -the annals of science. His era marks the accomplished maturity of the -human reason as applied to such objects. Every thing which went before -might be more properly compared to the first imperfect attempts of -childhood, or the essays of inexpert, though promising, adolescence. -Whatever has been since performed, however great in itself, and worthy -of so splendid and auspicious a beginning, has never, in point of -intellectual effort, surpassed that astonishing one which produced the -Principia. - -(302.) In this great work, Newton shows all the celestial motions known -in his time to be consequences of the simple law, that every particle -of matter attracts every other particle in the universe with a force -proportional to the product of their masses directly, and the square -of their mutual distance inversely, and is itself attracted with an -equal force. Setting out from this, he explains how an attraction -arises between the great spherical masses of which our system consists, -regulated by a law precisely similar in its expression; how the -elliptic motions of planets about the sun, and of satellites about -their primaries, according to the exact rules inductively arrived at -by Kepler, result as necessary consequences from the same general law -of force; and how the orbits of comets themselves are only particular -cases of planetary movements. Thence proceeding to applications of -greater difficulty, he explains how the perplexing inequalities of -the moon’s motion result from the sun’s disturbing action; how tides -arise from the unequal attraction of the sun as well as of the moon -on the earth, and the ocean which surrounds it; and, lastly, how the -precession of the equinoxes is a necessary consequence of the very same -law. - -(303.) The immediate successors of Newton found full occupation -in verifying his discoveries, and in extending and improving the -mathematical methods which it had now become manifest were to prove -the keys to an inexhaustible treasure of knowledge. The simultaneous -but independent discovery of a method of mathematical investigation in -every respect similar to that of Newton, by Leibnitz, while it created -a degree of national jealousy which can now only be regretted, had the -effect of stimulating the continental geometers to its cultivation, and -impressing on it a character more entirely independent of the ancient -geometry, to which Newton was peculiarly attached. It was fortunate -for science that it did so; for it was speedily found that (with one -fine exception on the part of our countryman Maclaurin, followed up, -after a long interval, by the late Professor Robison of Edinburgh, with -equal elegance,) the geometry of Newton was like the bow of Ulysses, -which none but its master could bend; and that, to render his methods -available beyond the points to which he himself carried them, it was -necessary to strip them of every vestige of that antique dress in which -he had delighted to clothe them. This, however, the countrymen of -Newton were very unwilling to do; and they paid the penalty in finding -themselves condemned to the situation of lookers on, while their -continental neighbours both in Germany and France were pushing forward -in the career of mathematico-physical discovery with emulous rapidity. - -(304.) The legacy of research which Newton may be said to have left -to his successors was truly immense. To pursue, through all its -intricacies, the consequences of the law of gravitation; to account for -all the inequalities of the planetary movements, and the infinitely -more complicated, and to us more important ones, of the moon; and to -give, what Newton himself certainly never entertained a conception -of, a demonstration of the stability and permanence of the system, -under all the accumulating influence of its internal perturbations; -this labour, and this triumph, were reserved for the succeeding -age, and have been shared in succession by Clairaut, D’Alembert, -Euler, Lagrange and Laplace. Yet so extensive is the subject, and so -difficult and intricate the purely mathematical enquiries to which it -leads, that another century may yet be required to go through with -the task. The recent discoveries of astronomers have supplied matter -for investigation, to the geometers of this and the next generation, -of a difficulty far surpassing any thing that had before occurred. -Five primary planets have been added to our system; four of them -since the commencement of the present century, and these, singularly -deviating from the general analogy of the others, and offering _cases -of difficulty_ in theory, which no one had before contemplated. Yet -even the intricate questions to which these bodies have given rise -seem likely to be surpassed by those which have come into view, with -the discovery of several comets revolving in elliptic orbits, like the -planets, round the sun, in very moderate periods. But the resources of -modern geometry seem, so far from being exhausted, to increase with the -difficulties they have to encounter, and already, among the successors -of Lagrange and Laplace, the present generation has to enumerate a -powerful array of names, which promise to render it not less celebrated -in the annals of physico-mathematical research than that which has just -passed away. - -(305.) Meanwhile the positions, figures, and dimensions of all the -planetary orbits, are now well known, and their variations from century -to century in great measure determined; and it has been generally -demonstrated, that all the changes which the mutual actions of the -planets on each other can produce in the course of indefinite ages, -are _periodical_, that is to say, increasing to a certain extent (and -that never a very great one), and then again decreasing; so that the -system can never be destroyed or subverted by the mutual action of its -parts, but keeps constantly oscillating, as it were, round a certain -mean state, from which it can never deviate to any ruinous extent. In -particular the researches of Laplace, Lagrange, and Poisson, have shown -the ultimate invariability of the mean distance of each planet from the -sun, and consequently of its periodic time. Relying on these grand -discoveries, we are enabled to look forward, from the point of time -which we now occupy, many thousands of years into futurity, and predict -the state of our system without fear of material error, but such as -may arise from causes whose existence at present we have no reason to -suppose, or from interference which we have no right to anticipate. - -(306.) A correct enumeration and description of the fixed stars in -catalogues, and an exact knowledge of their position, supply the -only effectual means we can have of ascertaining what changes they -are liable to, and what motions, too slow to deprive them of their -usual epithet, _fixed_, yet sufficient to produce a sensible change -in the lapse of ages, may exist among them. Previous to the invention -of the compass, they served as guides to the navigator by night; but -for this purpose, a very moderate knowledge of a few of the principal -ones sufficed. Hipparchus was the first astronomer, who, excited -by the appearance of a new star, conceived the idea of forming a -catalogue of the stars, with a view to its use as an astronomical -record, “by which,” says Pliny, “posterity will be able to discover, -not only whether they are born and die, but also whether they change -their places, and whether they increase or decrease.” His catalogue, -containing more than 1000 stars, was constructed about 128 years before -Christ. It was in the course of the laborious discussion of his own and -former observations of them, undertaken with a view to the formation of -this catalogue, that he first recognised the fact of that slow, general -advance of all the stars eastward, when compared with the place of -the equinox, which is known under the name of the precession of the -equinoxes, and which Newton succeeded in referring to a motion in the -earth’s axis, produced by the attraction of the sun and moon. - -(307.) Since Hipparchus, at various periods in the history of -astronomy, catalogues of stars have been formed, among which that -of Ulugh Begh, comprising about 1000 stars, constructed in 1437, is -remarkable as the production of a sovereign prince, working personally -in conjunction with his astronomers; and that of Tycho Brahe, -containing 777 stars, constructed in 1600, as having originated in a -phenomenon similar to that which drew the attention of Hipparchus. In -more recent times, astronomers provided with the finest instruments -their respective eras could supply, and established in observatories, -munificently endowed by the sovereigns and governments of different -European nations, have vied and are still vying with each other, -in extending the number of registered stars, and giving the utmost -possible degree of accuracy to the determination of their places. -Among these, it would be ungrateful not to claim especial notice -for the superb series of observations which, under a succession of -indefatigable and meritorious astronomers, has, for a very long period, -continued to emanate from our own national observatory of Greenwich. - -(308.) The distance of the fixed stars is so immense, that every -attempt to assign a limit, _within which_ it _must_ fall, has hitherto -failed. The enquiries of astronomers of all ages have been directed -to ascertain this distance, by taking the dimensions of our own -particular system of sun and planets, or of the earth itself, as the -unit of a scale on which it might be measured. But although many have -imagined that their observations afforded grounds for the decision -of this interesting point, it has uniformly happened either that the -phenomena on which they relied have proved to be referable to other -causes not previously known, and which the superior accuracy of their -researches has for the first time brought to light; or to errors -arising from instrumental imperfections and unavoidable defects of the -observations themselves. - -(309.) The only indication we can expect to obtain of the actual -distance of a star, would consist in an annual change in its apparent -place corresponding to the motion of the earth round the sun, called -its _annual parallax_, and which is nothing more than the measure -of the apparent size of the earth’s orbit as seen from the star. -Many observers have thought they have detected a measurable amount -of this parallax; but as astronomical instruments have advanced in -perfection, the quantity which they have successively assigned to it -has been continually reduced within narrower and narrower limits, -and has invariably been commensurate with the errors to which the -instruments used might fairly be considered liable. The conclusion this -strongly presses on us is, that it is really a quantity too small to -admit of distinct measurement in the present state of our means for -that purpose; and that, therefore, the distance of the stars must be -a magnitude of such an order as the imagination almost shrinks from -contemplating. But this increase in our scale of dimension calls for -a corresponding enlargement of conception in all other respects. The -same reasoning which places the stars at such immeasurable remoteness, -exalts them at the same time into glorious bodies, similar to, and even -far surpassing, our own sun, the centres perhaps of other planetary -systems, or fulfilling purposes of which we can have no idea, from any -analogy in what passes immediately around us. - -(310.) The comparison of catalogues, published at different periods, -has given occasion to many curious remarks, respecting changes both -of place and brightness among the stars, to the discovery of variable -ones which lose and recover their lustre periodically, and to that of -the disappearance of several from the heavens so completely as to have -left no vestige discernible even by powerful telescopes. In proportion -as the construction of astronomical and optical instruments has gone on -improving, our knowledge of the contents of the heavens has undergone -a corresponding extension, and, at the same time, attained a degree of -precision which could not have been anticipated in former ages. The -places of all the principal stars in the northern hemisphere, and of a -great many in the southern, are now known to a degree of nicety which -must infallibly detect any real motions that may exist among them, -and has in fact done so, in a great many instances, some of them very -remarkable ones. - -(311.) It is only since a comparatively recent date, however, that -any great attention has been bestowed on the smaller stars, among -which there can be no doubt of the most interesting and instructive -phenomena being sooner or later brought to light. The minute -examination of them with powerful telescopes, and with delicate -instruments for the determination of their places, has, indeed, already -produced immense catalogues and masses of observations, in which -thousands of stars invisible to the naked eye are registered; and has -led to the discovery of innumerable important and curious facts, and -disclosed the existence of whole classes of celestial objects, of a -nature so wonderful as to give room for unbounded speculation on the -extent and construction of the universe. - -(312.) Among these, perhaps the most remarkable are the revolving -double stars, or stars which, to the naked eye or to inferior -telescopes, appear single; but, if examined with high magnifying -powers, are found to consist of two individuals placed almost close -together, and which, when carefully watched, are (many of them) found -to revolve in regular elliptic orbits about each other; and so far -as we have yet been able to ascertain, to obey the same laws which -regulate the planetary movements. There is nothing calculated to give a -grander idea of the scale on which the sidereal heavens are constructed -than these beautiful systems. When we see such magnificent bodies -united in pairs, undoubtedly by the same bond of mutual gravitation -which holds together our own system, and sweeping over their enormous -orbits, in periods comprehending many centuries, we admit at once that -they must be accomplishing ends in creation which will remain for ever -unknown to man; and that we have here attained a point in science -where the human intellect is compelled to acknowledge its weakness, and -to feel that no conception the wildest imagination can form will bear -the least comparison with the intrinsic greatness of the subject. - - -_Geology._ - -(313.) The researches of physical astronomy are confessedly incompetent -to carry us back to the origin of our system, or to a period when -its state was, in any great essential, different from what it is -at present. So far as the causes now in action go, and so far as -our calculations will enable us to estimate their effects, we are -equally unable to perceive in the general phenomena of the planetary -system either the evidence of a beginning, or the prospect of an end. -Geometers, as already stated, have demonstrated that, in the midst of -all the fluctuations which can possibly take place in the elements of -the orbits of the planets, by reason of their mutual attraction, the -general balance of the parts of the system will always be preserved, -and every departure from a mean state periodically compensated. But -neither the researches of the physical astronomer, nor those of -the geologist, give us any ground for regarding our system, or the -globe we inhabit, as of eternal duration. On the contrary, there are -circumstances in the physical constitution of our own planet which at -least obscurely point to an origin and a formation, however remote, -since it has been found that the figure of the earth is not globular -but elliptical, and that its attraction is such as requires us to admit -the interior to be more dense than the exterior, and the density to -increase with some degree of regularity from the surface towards the -centre, and _that_, in layers arranged elliptically round the centre, -circumstances which could scarcely happen without some such successive -deposition of materials as would enable pressure to be propagated with -a certain degree of freedom from one part of the mass to another, even -if we should hesitate to admit a state of primitive fluidity. - -(314.) But from such indications nothing distinct can be concluded; -and if we would speculate to any purpose on a former state of our -globe and on the succession of events which from time to time may have -changed the condition and form of its surface, we must confine our -views within limits far more restricted, and to subjects much more -within the reach of our capacity, than either the creation of the world -or its assumption of its present figure. These, indeed, were favourite -speculations with a race of geologists now extinct; but the science -itself has undergone a total change of character, even within the last -half century, and is brought, at length, effectually within the list -of the inductive sciences. Geologists now no longer bewilder their -imaginations with wild theories of the formation of the globe from -chaos, or its passage through a series of hypothetical transformations, -but rather aim at a careful and accurate examination of the records -of its former state, which they find indelibly impressed on the great -features of its actual surface, and to the evidences of former life -and habitation which organised remains imbedded and preserved in its -strata indisputably afford. - -(315.) Records of this kind are neither few nor vague; and though the -obsoleteness of their language when we endeavour to interpret it too -minutely, may, and no doubt often does, lead to misapprehension, still -its general meaning is, on the whole, unequivocal and satisfactory. -Such records teach us, in terms too plain to be misunderstood, that -the whole or nearly the whole of our present lands and continents -were formerly at the bottom of the sea, where they received deposits -of materials from the wearing and degradation of other lands not now -existing, and furnished receptacles for the remains of marine animals -and plants inhabiting the ocean above them, as well as for similar -spoils of the land washed down into its bosom. - -(316.) These remains are occasionally brought to light; and their -examination has afforded indubitable evidence of the former existence -of a state of animated nature widely different from what now obtains -on the globe, and of a period anterior to that in which it has been -the habitation of man, or rather, indeed, of a series of periods, of -unknown duration, in which both land and sea teemed with forms of -animal and vegetable life, which have successively disappeared and -given place to others, and these again to new races approximating -gradually more and more nearly to those which now inhabit them, and at -length comprehending species which have their counterparts existing. - -(317.) These wrecks of a former state of nature, thus wonderfully -preserved (like ancient medals and inscriptions in the ruins of an -empire), afford a sort of rude chronology, by whose aid the successive -depositions of the strata in which they are found may be marked out -in epochs more or less definitely terminated, and each characterized -by some peculiarity which enables us to recognise the deposits of any -period, in whatever part of the world they may be found. And, so far -as has been hitherto investigated, the _order_ of succession in which -these deposits have been formed appears to have been the same in every -part of the globe. - -(318.) Many of the strata which thus bear evident marks of having been -deposited at the bottom of the sea, and of course in a horizontal -state, are now found in a position highly inclined to the horizon, and -even occasionally vertical. And they often bear no less evident marks -of violence, in their bending and fracture, the dislocation of parts -which were once contiguous, and the existence of vast collections of -broken fragments which afford every proof of great violence having been -used in accomplishing some at least of the changes which have taken -place. - -(319.) Besides the rocks which carry this internal evidence of -submarine deposition, are many which exhibit no such proofs, but on the -contrary hold out every appearance of owing their origin to volcanoes -or to some other mode of igneous action; and in every part of the -world, and among strata of all ages, there occur evidences of such -action so abundant, and on such a scale, as to point out the volcano -and the earthquake as agents which may have been instrumental in the -production of those changes of level, and those violent dislocations -which we perceive to have taken place. - -(320.) At all events, in accounting for those changes, geologists -have no longer recourse, as formerly, to causes purely hypothetical, -such as a shifting of the earth’s axis of rotation, bringing the sea -to overflow the land, by a change in the place of the longer and -shorter diameters of the spheroidal figure, nor to tides produced by -the attraction of comets suddenly approaching very near the earth, -nor to any other fanciful and arbitrarily assumed hypotheses; but -rather endeavour to confine themselves to a careful consideration -of causes evidently in action at present, with a view to ascertain -how far they, in the first instance, are capable of accounting for -the facts observed, and thus legitimately bringing into view, as -residual phenomena, those effects which cannot be so accounted for. -When this shall have been in some measure accomplished, we shall be -able to pronounce with greater security than at present respecting the -necessity of admitting a long succession of tremendous and ravaging -catastrophes and cataclysms,--epochs of terrific confusion and violence -which many geologists (perhaps with justice) regard as indispensable to -the explanation of the existing features of the world. We shall learn -to distinguish between the effects which require for their production -the sudden application of convulsive and fracturing efforts, and those, -probably not less extensive, changes which may have been produced by -forces equally or more powerful, but acting with less irregularity, -and so distributed over time as to produce none of those _interregnums_ -of chaotic anarchy which we are apt to think (perhaps erroneously) -great disfigurements of an order so beautiful and harmonious as that of -nature. - -(321.) But to estimate justly the effects of causes now in action in -geology is no easy task. There is no _à priori_ or deductive process by -which we can estimate the amount of the annual erosion, for instance, -of a continent by the action of meteoric agents, rain, wind, frost, -&c., nor the quantity of destruction produced on its coasts by the -direct violence of the sea, nor the quantity of lava thrown up _per -annum_ by volcanoes over the whole surface of the earth, nor any -similar effect. And to consult experience on all such points is a -slow and painful process if rightly gone into, and a very fallible -one if only partially executed. Much, then, at present must be left -to opinion, and to that sort of clear-judging tact which sometimes -anticipates experience; but this ought not to stand in the way of our -making every possible effort to obtain accurate information on such -points, by which alone geology can be rendered, if not an experimental -science, at least a science of that kind of active observation which -forms the nearest approach to it, where actual experiment is impossible. - -(322.) Let us take, for example, the question, “What is the actual -direction in which changes of relative level are taking place between -the existing continents and seas?” If we consult partial experience, -that is, _all_ the information that we possess respecting ancient -sea-marks, soundings, &c., we shall only find ourselves bewildered in -a mass of conflicting, because imperfect, evidence. It is obvious that -the only way to decide the point is to ascertain, by very precise and -careful observations at proper stations on coasts, selected at points -where there exist natural marks not liable to change in the course of -at least a century, the true elevation of such marks above the _mean_ -level of the sea, and to multiply these stations sufficiently over the -whole globe to be capable of affording real available knowledge. Now, -this is not a very easy operation (considering the accuracy required); -for the _mean_ level of the sea can be determined by no single -observation, any more than the mean height of the barometer at a given -station, being affected both by periodical and accidental fluctuations -due to tides, winds, waves, and currents. Yet if an instrument adapted -for the purpose were constructed, and rendered easily attainable, and -rules for its use carefully drawn up, there is little doubt we should -soon (by the industry of observers scattered over the world) be in -possession of a most valuable mass of information, which could not fail -to afford a point of departure for the next generation, and furnish -ground for the only kind of argument which ever can be conclusive on -such subjects. - -(323.) Geology, in the magnitude and sublimity of the objects of -which it treats, undoubtedly ranks, in the scale of the sciences, -next to astronomy; like astronomy, too, its progress depends on the -continual accumulation of observations carried on for ages. But, unlike -astronomy, the observations on which it depends, when the whole extent -of the subject to be explored is taken into consideration, can hardly -yet be said to be more than commenced. Yet, to make up for this, there -is another important difference, that while in the latter science it is -impossible to recall the past or anticipate the future, and observation -is in consequence limited to a single fact in a single moment; in -the former, the records of the past are always present;--they may be -examined and re-examined as often as we please, and require nothing -but diligence and judgment to put us in possession of their whole -contents. Only a very small part of the surface of our globe has, -however, been accurately examined in detail, and of that small portion -we are only able to scratch the mere exterior, for so we must consider -those excavations which we are apt to regard as searching the bowels -of the earth; since the deepest mines which have been sunk penetrate -to a depth hardly surpassing the ten thousandth part of the distance -between its surface and its centre. Of course inductions founded on -such limited examination can only be regarded as provisional, except -in those remarkable cases where the same great formations in the same -order have been recognised in very distant quarters, and without -exception. This, however, cannot long be the case. The spirit with -which the subject has been prosecuted for many years in our own country -has been rewarded with so rich a harvest of surprising and unexpected -discoveries, and has carried the investigation of our island into such -detail, as to have excited a corresponding spirit among our continental -neighbours; while the same zeal which animates our countrymen on their -native shore accompanies them in their sojourns abroad, and has -already begun to supply a fund of information respecting the geology of -our Indian possessions, as well as of every other point where English -intellect and research can penetrate. - -(324.) Nothing can be more desirable than that every possible facility -and encouragement should be afforded for such researches, and indeed -to the pursuits of the enlightened resident or traveller in every -department of science, by the representatives of our national authority -wherever our power extends. By these only can our knowledge of the -actual state of the surface of the globe, and that of the animals -and vegetables of the ancient continents and seas, be extended and -perfected, while more complete information than we at present possess -of the habits of those actually existing, and the influence of changes -of climate, food, and circumstances, on them, may be expected to render -material assistance to our speculations respecting those which have -become extinct. - - - - -CHAP. IV. - -OF THE EXAMINATION OF THE MATERIAL CONSTITUENTS OF THE WORLD. - - -_Mineralogy._ - -(325.) The consideration of the history and structure of our globe, and -the examination of the fossil contents of its strata, lead us naturally -to consider the materials of which it consists. The history of these -materials, their properties as objects of philosophical enquiry, and -their application to the useful arts and the embellishments of life, -with the characters by which they can be certainly distinguished one -from another, form the object of mineralogy, taken in its most extended -sense. - -(326.) There is no branch of science which presents so many points -of contact with other departments of physical research, and serves -as a connecting link between so many distant points of philosophical -speculation, as this. To the geologist, the chemist, the optician, the -crystallographer, the physician, it offers especially the very elements -of their knowledge, and a field for many of their most curious and -important enquiries. Nor, with the exception of chemistry, is there any -which has undergone more revolutions, or been exhibited in a greater -variety of forms. To the ancients it could scarcely be said to be at -all known, and up to a comparatively recent period, nothing could -be more imperfect than its descriptions, or more inartificial and -unnatural than its classification. The more important minerals in the -arts, indeed, those used for economical purposes and those from which -metals were extracted, had a certain degree of attention paid to them, -for the sake of their utility and commercial value, and the precious -stones for that of ornament. But until their crystalline forms were -attentively observed and shown to be determinate characters on which -dependence could be placed, no mineralogist could give any correct -account of the real distinction between one mineral and another. - -(327.) It was only, however, when chemical analysis had acquired -a certain degree of precision and universal applicability that -the importance of mineralogy as a science began to be recognized, -and the connection between the external characters of a stone and -its ingredient constituents brought into distinct notice. Among -these characters, however, none were found to possess that eminent -distinctness which the crystalline form offers; a character, in the -highest degree geometrical, and affording, as might be naturally -supposed, the strongest evidence of its necessary connection with the -intimate constitution of the substance. The full importance of this -character was, however, not felt until its connection with the texture -or cleavage of a mineral was pointed out, and even then it required -numerous and striking instances of the critical discernment of Haüy -and other eminent mineralogists in predicting from the measurements -of the angles of crystals which had been confounded together that -differences would be found to exist in their chemical composition, all -which proved fully justified in their result before the essential value -of this character was acknowledged. This was no doubt in great measure -owing to the high importance set by the German mineralogists on those -external characters of touch, sight, weight, colour, and other sensible -qualities, which are little susceptible, with the exception of weight, -of exact determination, and which are subject to material variations -in different specimens of the same mineral. By degrees, however, the -necessity of ascribing great weight to a character so definite was -admitted, especially when it was considered that the same step which -pointed out the intimate connection of external form with internal -structure furnished the mineralogist with the means of reducing all -the forms of which a mineral is susceptible under one general type, or -primitive form, and afforded grounds for an elegant theoretical account -of the assumption of definite figures _ab initio_. - -(328.) A simple and elegant invention of Dr. Wollaston, the reflecting -goniometer, gave a fresh impulse to that view of mineralogy which makes -the crystalline form the essential or leading character, by putting -it in the power of every one, by the examination of even the smallest -portion of a broken crystal, to ascertain and verify that essential -character on which the identity of a mineral in the system of Haüy -was made to depend. The application of so ready and exact a method -speedily led to important results, and to a still nicer discrimination -of mineral species than could before be attained; and the confirmation -given to these results by chemical analysis stamped them with a -scientific and decided character which they have retained ever since. - -(329.) Meanwhile the progress made in chemical analysis had led to -the important conclusion that every chemical compound susceptible of -assuming the solid state assumed with it a determinate crystalline -form; and the progress of optical science had shown that the -fundamental crystalline form, in the case at least of transparent -bodies, drew with it a series of optical properties no less curious -than important in relation to the affections of light in its passage -through such substances. Thus, in every point of view, additional -importance became added to this character; and the study of the -crystalline forms of bodies in general assumed the form of a separate -and independent branch of science, of which the geometrical forms of -the mineral world constituted only a particular case. Mineralogy, -however, as a branch of natural history, remains still distinct either -from optics or crystallography. The mineralogist is content, and thinks -he has performed his task, if not as a natural historian at least as -a classifier and arranger, if he only gives such a characteristic -description of a mineral as shall effectually distinguish it from every -other, and shall enable any one who may encounter such a body in any -part of the world to impose on it its name, assign it a place in his -system, and turn to his books for a further description of all that -the chemist, the optician, the lapidary, or the artist, may require to -know. Still this is no easy matter: the laborious researches of the -most eminent mineralogists can hardly yet be said to have effectually -accomplished it; and its difficulty may be appreciated by the small -number of simple minerals, or minerals of perfectly definite and -well-marked characters, which have been hitherto made out. Nor can -this indeed be wondered at, when we consider that by far the greater -portion of the rocks and stones which compose the external crust of the -globe consists of nothing more than the accumulated _detritus_ of older -rocks, in which the fragments and powder of an infinite variety of -substances are mingled together, in all sorts of varying proportions, -and in such a way as to defy separation. Many of these rocks, however, -so compounded, occur with sufficient frequency and uniformity of -character to have acquired names and to have been usefully applied; -indeed, in the latter respect, minerals of this description far surpass -all the others. As objects of natural history, therefore, they are well -worthy of attention, however difficult it may be to assign them a place -in any artificial arrangement. - -(330.) This paucity of simple minerals, however, is probably rather -apparent than real, and in proportion as the researches of the chemist -and crystallographer shall be extended throughout nature, they will -no doubt become much more numerous. Indeed, in the great laboratories -of nature it can hardly be doubted that almost every kind of chemical -process is going forwards, by which compounds of every description are -continually forming. Accordingly, it is remarked, that the lavas and -ejected scoriæ of volcanoes are receptacles in which mineral products -previously unknown are constantly discovered, and that the primitive -formations, as they are called in geology, which bear no marks of -having been produced by the destruction of others, are also remarkable -for the beauty and distinctness of character of their minerals. - -(331.) The great difficulty which has been experienced in attempts to -classify mineral substances by their chemical constituents has arisen -from the observed presence, in some specimens of minerals bearing -that general resemblance in other respects as well as agreement in -form which would seem to entitle them to be considered as alike, of -ingredients foreign to the usual composition of the species, and that -occasionally in so large a proportion as to render it unjustifiable -to refer their occurrence to accidental impurities. These cases, as -well as some anomalies observed in the classification of minerals by -their crystalline forms, which seemed to show that the same substance -might occasionally appear under two distinct forms, as well as some -remarkable coincidences between the forms of substances quite distinct -from each other in a chemical point of view, have within a recent -period given rise to a branch of the science of crystallography of a -very curious and important nature. The _isomorphism_ of certain groups -of chemical elements has already afforded us an example illustrative -of the manner in which inductions sometimes receive unexpected -verifications (see 180.). The laws and relations thus brought to light -are among the most curious and interesting parts of modern science, -and seem likely in their further developement to afford ample scope -for the exercise of chemical and mineralogical research. They have -already afforded innumerable fine examples of that important step in -science by which anomalies disappear, and occasional incongruities -become reconciled under more general expressions of physical laws, -and thus unite in affording support to those very views which they -promised, when first observed, to overset. Nothing, indeed, can be -more striking than to see the very ingredient which every previous -chemist and mineralogist would agree to disregard and reject as a -mere casual impurity brought forward and appealed to in support of a -theory expressly directed to the object of rescuing science from the -imputation of disregarding, under any circumstances, the plain results -of direct experiment. - - -_Chemistry._ - -(332.) The laws which concern the intimate constitution of bodies, -not as respects their _structure_ or the manner in which their parts -are put together, but as regards their _materials_ or the ingredients -of which those parts are composed, form the objects of chemistry. A -solid body may be regarded as a fabric, more or less regularly and -artificially constructed, in which the materials and the workmanship -may be separately considered, and in which, though the latter be -ruined and confounded by violence, the former remain unchanged in -their nature, though differently arranged. In liquid or aërial bodies, -too, though there prevails a less degree of difference in point of -structure, and a greater facility of dispersion and dissipation, than -in solids, yet an equal diversity of _materials_ subsists, giving to -them properties differing extremely from each other. - -(333.) The inherent activity of matter is proved not only by the -production of motion by the mutual attractions and repulsions of -distant or contiguous masses, but by the changes and apparent -transformations which different substances undergo in their sensible -qualities by mere mixture. If water be added to water, or salt to salt, -the effect is an increase of quantity, but no change of quality. In -this case, the mutual action of the particles is entirely mechanical. -Again, if a blue powder and a yellow one, each perfectly dry, be mixed -and well shaken together, a green powder will be produced; but this -is a mere effect arising in the eye from the intimate mixture of the -yellow and blue light separately and independently reflected from -the minute particles of each; and the proof is had by examining the -mixture with a microscope, when the yellow and blue grains will be seen -separate and each quite unaltered. If the same experiment be tried with -coloured liquids, which are susceptible of mixing without chemical -action, a compound colour is likewise produced, but no examination -with magnifiers is in that case sufficient to detect the ingredients; -the reason obviously being, the excessive minuteness of the parts, and -their perfect intermixture, produced by agitating two liquids together. -From the mixture of two powders, extreme patience would enable any one, -by picking out with a magnifier grain after grain, to separate the -ingredients. But when liquids are mixed, no mechanical separation is -any longer practicable; the particles are so minute as to elude all -search. Yet this does not hinder us from regarding such a compound as -still a mere mixture, and its properties are accordingly intermediate -between those of the liquids mixed. But this is far from being the -case with all liquids. When a solution of potash, for example, and -another of tartaric acid, each perfectly liquid, are mixed together in -proper proportions, a great quantity of a solid saline substance falls -to the bottom of the containing vessel, which is quite different from -either potash or tartaric acid, and the liquid from which it subsided -offers no indications by its taste or other sensible qualities of the -ingredients mixed, but of something totally different from either. -It is evident that this is a phenomenon widely different from that -of mere mixture; there has taken place a great and radical change in -the intimate nature of the ingredients, by which a new substance is -produced which had no existence before. And it has been produced by the -_union_ of the ingredients presented to each other; for when examined -it is found that nothing has been _lost_, the weight of the whole -mixture being the sum of the weights mixed. Yet the potash and tartaric -acid have disappeared entirely, and the weight of the new product is -found to be exactly equal to that of the tartaric acid and potash -employed, taken together, abating a small portion held in solution in -the liquid, which may be obtained however by evaporation. They have -therefore combined, and adhere to one another with a cohesive force -sufficient to form a solid out of a liquid; a force which has thus been -called into action by merely presenting them to each other in a state -of solution. - -(334.) It is the business of chemistry to investigate these and similar -changes, or the reverse of such changes, where a single substance is -resolved into two or more others, having different properties from it, -and from each other, and to enquire into all the circumstances which -can influence them; and either determine, modify, or suspend their -accomplishment, whether such influence be exercised by heat or cold, by -time and rest, or by agitation or pressure, or by any of those agents -of which we have acquired a knowledge, such as electricity, light, -magnetism, &c. - -(335.) The wonderful and sudden transformations with which chemistry is -conversant, the violent activity often assumed by substances usually -considered the most inert and sluggish, and, above all, the insight -it gives into the nature of innumerable operations which we see daily -carried on around us, have contributed to render it the most popular, -as it is one of the most extensively useful, of the sciences; and -we shall, accordingly, find none which have sprung forward, during -the last century, with such extraordinary vigour, and have had such -extensive influence in promoting corresponding progress in others. One -of the chief causes of its popularity is, perhaps, to be sought for in -this, that it is, of all the sciences, perhaps, the most completely an -experimental one; and even its theories are, for the most part, of that -generally intelligible and readily applicable kind, which demand no -intense concentration of thought, and lead to no profound mathematical -researches. The simple process of inductive generalization, grounded on -the examination of numerous facts, all of them presenting considerable -intrinsic interest, has sufficed, in most instances, to lead, by a -clear and direct road, to its highest laws yet known. But, on the other -hand, these laws, when stated, are not yet fully sufficient to lead us, -except in very limited cases, to a deductive knowledge of particulars -never before examined, at least, not without great caution, and -constant appeal to experiment as a check on our reasoning; so that we -are justified in regarding the _axioms_ of chemistry, the true handles -of deductive reasoning, as still unknown, and, perhaps, likely long -to remain so. This is no fault of its cultivators, who have comprised -in their list the highest and most varied talents and industry, but -of the inherent complexity of the subject, and the infinite multitude -of causes which are concerned in the production of every, even the -simplest, chemical phenomenon. - -(336.) The history of chemistry (on which, however, we are not about -to enlarge,) is one of great interest to those who delight to trace -the steps by which mankind advance to the discovery of truth through -a series of mistakes and failures. It may be divided, 1st, into -the period of the alchemists, a lamentable epoch in the annals of -intellectual wandering; 2dly, that of the phlogistic doctrines of -Beccher and Stahl, in which, as if to prove the perversity of the human -mind, of two possible roads the wrong was chosen; and a theory obtained -universal credence on the strength of an induction, valid as such, but -wrongly interpreted, which is negatived, _in every instance_, by an -appeal to the balance. This, too, happened, not by reason of unlucky -coincidences, or individual oversights, but of necessity, and from an -inherent defect of the theory itself, which thus impeded the progress -of the science, as far as a science of experiment can be impeded by -a false theory, by perplexing its cultivators with the appearance of -contradictions in their experiments where none really subsisted, by -destroying all their confidence in the numerical exactness of their -own results, and by involving the subject in a mist of visionary and -hypothetical causes in place of the true acting principles. Thus, in -the combustion of any substance which is incapable of flying away in -fumes, an increase of weight takes place,--the ashes are heavier than -the fuel. Whenever this was observed, however, it was passed carelessly -over as arising from the escape of phlogiston, or the principle of -inflammability, which was considered as being either the element of -fire itself, or in some way combined with it, and thus essentially -_light_. It is now known that the increase of weight is owing to -the absorption of, and combination with, a quantity of a peculiar -ingredient called _oxygen_, from the air, a principle essentially -_heavy_. So far as weight is concerned, it makes no difference whether -a body having weight enters, or one having levity escapes; but there -is this plain difference in a philosophical point of view, that oxygen -is a real producible substance, and phlogiston is no such thing: the -former is a _vera causa_, the latter an hypothetical being, introduced -to account for what the other accounts for much better. - -(337.) The third age of chemistry--that which may be called -emphatically modern chemistry--commenced (in 1786) when Lavoisier, by -a series of memorable experiments, extinguished for ever this error, -and placed chemistry in the rank of one of the exact sciences,--a -science of number, weight, and measure. From that epoch to the -present day it has constantly advanced with an accelerated progress, -and at this moment may be regarded as more progressive than ever. -The principal features in this progress may be comprised under the -following general heads:-- - - 1. The discovery of the proximate, if not the ultimate, elements - of all bodies, and the enlargement of the list of known - elements to its present extent of between fifty and sixty - substances. - - 2. The developement of the doctrine of latent heat by Black, - with its train of important consequences, including the - scientific theory of the steam-engine. - - 3. The establishment of Wenzel’s law of definite proportions on - his own experiments, and those of Richter, a discovery - subsequently merged in the more general wording and better - development of Dalton’s atomic theory. - - 4. The precise determination of the atomic weights of the - different chemical elements, mainly due to the astonishing - industry of Berzelius, and his unrivalled command of chemical - resources, as well as to the researches of the other chemists - of the Swedish and German school. - - 5. The assimilation of gases and vapours, by which we are led - to regard the former, universally, as particular cases of - the latter, a generalization resulting chiefly from the - experiments of Faraday on the condensation of the gases, - and those of Gay-Lussac and Dalton, on the laws of their - expansion by heat compared with that of vapours. - - 6. The establishment of the laws of the combination of gases and - vapours by definite volumes, by Gay-Lussac. - - 7. The discovery of the chemical effects of electricity, and - the decomposing agency of the Voltaic pile, by Nicholson - and Carlisle; the investigation of the laws of such - decompositions, by Berzelius and Hisinger: the decomposition - of the alkalies by Davy, and the consequent introduction into - chemistry of new and powerful agents in their metallic bases. - - 8. The application of chemical analysis to all the objects of - organized and unorganized nature, and the discovery of - the ultimate constituents of all, and the proximate ones - of organic matter, and the recognisance of the important - distinctions which appear to divide these great classes of - bodies from each other. - - 9. The applications of chemistry to innumerable processes in the - arts, and among other useful purposes to the discovery of the - essential medical principles in vegetables, and to important - medicaments in the mineral kingdom. - - 10. The establishment of the intimate connection between - chemical composition and crystalline form, by Haüy - and Vauquelin, with the successive rectifications the - statement of that connection has undergone in the hands of - Mitscherlich, Rose, and others, with the progress of chemical - and crystallographical knowledge. - -(338.) To pursue these several heads into detail would lead us into -a treatise on chemistry; but a few remarks on one or two of them, as -they bear upon the general principles of all scientific enquiry, will -not be irrelevant. And first, then, with reference to the discovery -of new elements, it will be observed, that philosophical chemistry no -more aims at determining the one essential element out of which all -matter is framed--the one ultimate principle of the universe--than -astronomy at discovering the origin of the planetary movements in -the application of a determinate projectile force in a determinate -direction, or geology at ascending to the creation of the earth. There -may be such an element. Some singular relations which have been pointed -out in the atomic weights of bodies seem to suggest to minds fond of -speculation that there is; but philosophical chemistry is content to -wait for some striking fact, which may either occur unexpectedly or -be led to by the slow progress of enlarged views, to disclose to us -its existence. Still, the multiplication of so-considered elementary -bodies has been considered by some as an inconvenience. We confess -we do not coincide with this view. Whatever they be, the obstinacy -with which they resist decomposition shows that they are ingredients -of a very high and primary importance in the economy of nature; and -such as, in any state of science, it would be indispensably necessary -to be perfectly familiar with. Like particular theorems in geometry, -which, though not rising to the highest point of generality, have yet -their several scopes and ranges of extensive application, they must be -well and perfectly understood in all their bearings. Should we ever -arrive at an analysis of these bodies, the chemical properties of the -new elements which will then come into view will be known only by our -knowledge of these, or of other compounds of the same class, which they -may be capable of forming. Not but that such an analysis would be a -most important and indeed triumphant achievement, and change the face -of chemistry; but it would undo nothing that has been done, and render -useless no point of knowledge which we have yet arrived at. - -(339.) The atomic theory, or the law of definite proportions, which -is the same thing presented in a form divested of all hypothesis, -after the laws of mechanics, is, perhaps, the most important which -the study of nature has yet disclosed. The extreme simplicity which -characterizes it, and which is itself an indication, not unequivocal, -of its elevated rank in the scale of physical truths, had the effect -of causing it to be announced at once by Mr. Dalton, in its most -general terms, on the contemplation of a few instances[53], without -passing through subordinate stages of painful inductive ascent by the -intermedium of subordinate laws, such as, had the contrary course been -pursued by him, would have been naturally preparatory to it, and such -as would have led others to it by the prosecution of Wenzel’s and -Richter’s researches, had they been duly attended to. This is, in fact, -an example, and a most remarkable one, of the effect of that natural -propensity to generalize and simplify (noticed in 171.), which, if it -occasionally leads to over-hasty conclusions, limited or disproved by -further experience, is yet the legitimate parent of many of our most -valuable and soundest results. Instances like this, where great and, -indeed, immeasurable steps in our knowledge of nature are made at once, -and almost without intellectual effort, are well calculated to raise -our hopes of the future progress of science, and, by pointing out the -simplest and most obvious combinations as those which are actually -found to be agreeable to the harmony of creation, to hold out the -cheering prospect of difficulties diminishing as we advance, instead of -thickening around us in increasing complexity. - -(340.) A consequence of this immediate presentation of the law of -definite proportions in its most general form is, that its subordinate -laws--those which limit its generality in particular cases, which -diminish the number of combinations abstractly possible, and restrain -the indiscriminate mixture of elements,--remain to be discovered. Some -such limitations have, in fact, been traced to a certain extent, but by -no means so far as the importance of the subject requires; and we have -here abundant occupation for chemists for some time. - -(341.) The determination of the atomic weights of the chemical -elements, like that of other standard physical data, with the utmost -exactness, is in itself a branch of enquiry not only of the greatest -importance, but of extreme difficulty. Independent of the general -reasons for desiring accuracy in this respect, there is one peculiar -to the subject. It has been suggested (by Dr. Prout), and strongly -insisted on (by Dr. Thomson), that all the numbers representing these -weights, constituting a scale of great extent, in which the extremes -already known are in proportion to each other, as 1 to upwards of 200, -are simple even multiples of the least of them. If this be really the -case, it opens views of such importance as to justify any degree of -labour and pains in the verification of the law as a purely inductive -one. But in the actual state of chemical analysis, with all deference -to such high authority, we confess it appears to us to stand in great -need of further confirmation, since it seems doubtful whether such -accuracy has yet been attained as to enable us to answer positively -for a fraction not exceeding the three or four hundredth part of the -whole quantity to be determined: at least the results of the first -experimenters, obtained with the greatest care, differ often by a -greater amount; and this degree of exactness, at least, would be -required to verify the law satisfactorily in the higher parts of the -scale. - -(342.) The mere agitation of such a question, however, points out -a class of phenomena in physical science of a remote and singular -kind, and of a very high and refined order, which could never become -known but in an advanced state of science, not only practical, but -theoretical,--we mean, such as consist in observed relations among the -_data_ of physics, which show them to be quantities not _arbitrarily_ -assumed, but depending on laws and causes which they may be the means -of at length disclosing. A remarkable instance of such a relation is -the curious law which Bode observed to obtain in the progression of the -magnitudes of the several planetary orbits. This law was interrupted -between Mars and Jupiter, so as to induce him to consider a planet -as wanting in that interval;--a deficiency long afterwards strangely -supplied by the discovery of _four_ new planets in that very interval, -all of whose orbits conform in dimension to the law in question, within -such moderate limits of error as may be due to causes independent of -those on which the law itself ultimately rests.[54] - -(343.) Neither is it irrelevant to our subject to remark, that the -progress which has been made in this department of chemistry, and -the considerable exactness actually attainable in chemical analysis, -have been owing, in great measure, to a circumstance which might at -first have been hardly considered likely to exercise much influence -on the progress of a science,--the discovery of platina. Without the -resources placed at the ready disposal of chemists by this invaluable -metal, it is difficult to conceive that the multitude of delicate -analytical experiments which have been required to construct the fabric -of existing knowledge could have ever been performed. This, among many -such lessons, will teach us that the most important uses of natural -objects are not those which offer themselves to us most obviously. The -chief use of the moon for man’s immediate purposes remained unknown to -him for five thousand years from his creation. And, since it cannot but -be that innumerable and most important uses remain to be discovered -among the materials and objects already known to us, as well as among -those which the progress of science must hereafter disclose, we may -hence conceive a well-grounded expectation, not only of constant -increase in the physical resources of mankind, and the consequent -improvement of their condition, but of continual accessions to our -power of penetrating into the arcana of nature, and becoming acquainted -with her highest laws. - - - - -CHAP. V. - -OF THE IMPONDERABLE FORMS OF MATTER. - - -_Heat._ - -(344.) One of the chief agents in chemistry, on whose proper -application and management the success of a great number of its -enquiries depends, and many of whose most important laws are disclosed -to us by phenomena of a chemical nature, is HEAT. Although some of -its effects are continually before our eyes as matters of the most -common occurrence, insomuch that there is scarcely any process in the -useful arts and manufactures which does not call for its intervention, -and although, independent of this high utility, and the proportionate -importance of a knowledge of its nature and laws, it presents in itself -a subject of the most curious speculation; yet there is scarcely -any physical agent of which we have so imperfect a knowledge, whose -intimate nature is more hidden, or whose laws are of such delicate and -difficult investigation. - -(345.) The word heat generally implies the sensation which we -experience on approaching a fire; but, in the sense it carries in -physics, it denotes the cause, whatever it be, of that sensation, and -of all the other phenomena which arise on the application of fire, -or of any other heating cause. We should be greatly deceived if we -referred only to sensation as an indication of the presence of this -cause. Many of those things which excite in our organs, and especially -of those of taste, a sensation of heat, owe this property to chemical -stimulants, and not at all to their being actually _hot_. This error -of judgment has produced a corresponding confusion of language, and -hence had actually at one period[55] crept into physical philosophy -a great many illogical and absurd conclusions. Again, there are a -number of chemical agents, which, from their corroding, blackening, and -dissolving, or drying up the parts of some descriptions of bodies, and -producing on them effects not generally unlike (though intrinsically -very different from) those produced by heat, are said, in loose and -vulgar language, to burn them; and this error has even become rooted -into a prejudice, by the fact that some of these agents are capable -of becoming actually and truly _hot_ during their action on moist -substances, by reason of their combination with the water the latter -contain. Thus, quicklime and oil of vitriol both exercise a powerful -corrosive action on animal and vegetable substances, and both become -violently hot by their combination with water. They are, therefore, -set down in vulgar parlance as substances of a hot nature; whereas, -in their relations to the physical cause of heat, they agree with the -generality of bodies similarly constituted. - -(346.) The nature of heat has hitherto been chiefly studied under the -general heads of-- - - 1st, Its sources, or the phenomena which it usually accompanies. - - 2d, Its communication from its sources to substances capable of - receiving it, and from these to others, with a view to - discover the laws which regulate its distribution through - space or through the bodies which occupy it. - - 3d, Its effects, on our senses, and on the bodies to which it is - communicated in its various degrees of intensity, by which, - means are afforded us of measuring these degrees. - - 4th, Its intimate relations to the atoms of matter, as exhibited - in its capability of acquiring a latent state under certain - circumstances, and of entering into something like chemical - combinations. - -(347.) The most obvious sources of heat are, the sun, fire, animal -life, fermentations, violent chemical actions of all kinds, friction, -percussion, lightning, or the electric discharge, in whatever manner -produced, the sudden condensation of air, and others, so numerous, -and so varied, as to show the extensive and important part it has -to perform in the economy of nature. The discoveries of chemists, -however, have referred most of these to the general head of chemical -combination. Thus, fire, or the combustion of inflammable bodies, is -nothing more than a violent chemical action attending the combination -of their ingredients with the oxygen of the air. Animal heat is, in -like manner, referable to a process bearing no remote analogy to -a slow combustion, by which a portion of carbon, an inflammable -principle existing in the blood, is united with the oxygen of the air -in respiration; and thus carried off from the system: fermentation -is nothing more than a decomposition of chemical elements loosely -united, and their re-union in a more permanent state of combination. -The analogy between the sun and terrestrial fire is so natural as to -have been chosen by Newton to exemplify the irresistible force of an -inference derived from that principle. But the nature of the sun and -the mode in which its wonderful supply of light and heat is maintained -are involved in a mystery which every discovery that has been made -either in chemistry or optics, so far from elucidating, seems only to -render more profound. Friction as a source of heat is well known: we -rub our hands to warm them, and we grease the axles of carriage-wheels -to prevent their setting fire to the wood; an accident which, in -spite of this precaution, does sometimes happen. But the effect of -friction, as a means of producing heat with little or no consumption -of materials, was not fully understood till made the subject of direct -experiment by count Rumford, whose results appear to have established -the extraordinary fact, that an unlimited supply of heat may be derived -by friction from the same materials. Condensation, whether of air by -pressure, or of metals by percussion, is another powerful source of -heat. Thus, iron may be so dexterously hammered as to become red-hot, -and the rapid condensation of a confined portion of air will set tinder -on fire. - -(348.) The most violent heats known are produced by the concentration -of the solar rays by burning glasses,--by the combustion of oxygen and -hydrogen gases mixed in the exact proportion in which they combine to -produce water,--and by the discharge of a continued and copious current -of electricity through a small conductor. As these three sources of -heat are independent of each other, and each capable of being brought -into action in a very confined space, there seems no reason why they -might not all three be applied at once at the same point, by which -means, probably, effects would be produced infinitely surpassing any -hitherto witnessed. - -(349.) Heat is communicated either by _radiation_ between bodies at a -distance, or by _conduction_ between bodies in contact, or between the -contiguous parts of one and the same body. The laws of the radiation -of heat have been studied with great attention, and have been found -to present strong analogies with that of light in some points, and -singular differences in others. Thus, the heat which accompanies the -sun’s rays comports itself, in all respects, like light; being subject -to similar laws of reflection, refraction, and even of polarization, as -has been shown by Berard. Yet they are not identical with each other; -Sir William Herschel having shown, by decisive experiments, verified by -those of Sir H. Englefield, that there exist in a solar beam both rays -of heat which are not luminous, and rays of light which have no heating -power. - -(350.) The heat, radiated by terrestrial fires, and by bodies -_obscurely_ hot, by whatever means they have acquired their heat -(even by exposure to the sun’s rays), differs very materially from -solar heat in their power of penetrating transparent substances. This -singular and important difference was first noticed by Mariotte, and -afterwards made the subject of many curious and interesting experiments -by Scheele, who found that terrestrial heat, or that radiated from -fires or heated bodies, is intercepted and detained by glass or -other transparent bodies, while solar heat is not; and that, being -so detained, it heats them: which the latter, as it passes freely -through them, is incapable of doing. The more recent researches of -Delaroche, however, have shown that this detention is complete only -when the temperature of the source of heat is low; but that, as that -temperature is higher, a portion of the heat radiated acquires a -power of penetrating glass; and that the quantity which does so bears -continually a larger and larger proportion to the whole, as the heat -of the radiant body is more intense. This discovery is very important, -as it establishes a community of nature between solar and terrestrial -heat; while at the same time it leads us to regard the actual -temperature of the sun as far exceeding that of any earthly flame. - -(351.) A variety of theories have been framed to account for these -curious phenomena; but the subject stands rather in need of further -elucidation from experiment, and is one which merits, and will probably -amply repay, the labours of those who may hereafter devote their -attention to it. The theory of the radiation of heat, in general, which -seems to agree best with the known phenomena, is that of M. Prevost, -who considers all bodies as constantly radiating out heat in all -directions, and receiving it by a similar means of communication from -others, and thus tending, in any space filled, wholly or in part, with -bodies at various temperatures, to establish an equilibrium or equality -of heat in all parts. The application of this idea to the explanation -of the phenomenon of dew we have already seen (see 167.). The laws -of such radiation, under various circumstances, have been lately -investigated in a beautiful series of experiments on the cooling of -bodies by their own radiation in vacuo, by Messrs. Dulong and Petit, -which offer some of the best examples in science of the inductive -investigation of quantitative laws. - -(352.) The communication of heat between bodies in contact, or between -the different parts of the same body, is performed by a process called -conduction. It is, in fact, only a particular case of radiation, as -has been explained above (217.); but a case _so_ particular as to -require a separate and independent investigation of its laws. The most -important consideration introduced into the enquiry by this peculiarity -is that of time. The communication of heat by conduction is performed, -for the most part, with extreme slowness, while that performed by -direct radiation is probably not less rapid than the propagation -of light itself. The analysis of the delicate and difficult points -which arise in the investigation of this subject in its reduction -to direct geometrical treatment has been executed with admirable -success by the late Baron Fourrier, whose recent lamented death has -deprived science of an ornament it could ill spare, thinned as its -ranks have been within the last few years. This acute philosopher and -profound mathematician has developed, in a series of elaborate memoirs -presented to the French Institute, the laws of the communication of -heat through the interior of solid masses, placed under the influence -of any external heating and cooling causes, and has in particular -applied his results to the conditions on which the maintenance of the -actual observed temperature on the earth’s surface depends; to the -possible influence of a supposed central heat on our climates; and to -the determination of the actual amount of the heat, derived to us from -the sun, or at least that portion of it on which the difference of the -seasons depends. - -(353.) The principal effects of heat are the sensations of warmth or -cold consequent on its entry or egress into or out of our bodies; the -dilatation it causes in the dimensions of all substances in which it is -accumulated; the changes of state it produces in the melting of solids, -and the conversion of them and of liquids into vapour; and the chemical -changes it performs by actual decompositions effected in the intimate -molecules of various substances, especially those of which vegetables -and animals are composed; to which we may add, the production of -electric phenomena under certain circumstances in the contact of -metals, and the developement of electric polarity in crystallised -substances. - -(354.) Cold has been considered by some as a positive quality, the -effect of a cause antagonist to that of heat; but this idea seems -now (with perhaps a single exception) to be universally abandoned. -The sensation of cold is as easily explicable by the passage of heat -outwards through the surface of the body as that of heat by its ingress -from without; and the experiments cited in proof of a radiation of -cold are all perfectly explained by Prevost’s theory of reciprocal -interchange. It is remarkable, however, how very limited our means -of producing intense cold are, compared with those we possess of -effecting the accumulation of heat in bodies. This is one of the -strongest arguments adducible in favour of the doctrines of those who -maintain the possibility of exhausting the heat of a body altogether, -and leaving it in a state absolutely devoid of it. But we ought to -consider, that the known methods of generating heat chiefly turn on the -production of chemical combinations: we may easily conceive, therefore, -that, to obtain equally powerful corresponding frigorific effects, we -ought to possess the means of effecting a disunion equally extensive -and rapid between such elements, actually combined, as have already -produced heat by their union. This, however, we can only accomplish by -engaging them in combinations still more energetic, that is to say, -in which we may reasonably expect more heat to be produced by the new -combination than would be destroyed or abstracted by the proposed -decomposition. Chemistry, however, (unaided by electric agency,) -affords no means of suddenly breaking the union of two elements, and -presenting _both_ in an uncombined state. A certain analogy to such -disunion, however, and its consequences, may be traced in the sudden -expansion of condensed gases from a liquid state into vapour, which is -the most powerful source of cold known. - -(355.) The dilatation of bodies by heat forms the subject of that -branch of science called pyrometry. There is no body but is capable -of being penetrated by heat, though some with greater, others with -less rapidity; and being so penetrated, all bodies (with a very few -exceptions, and those depending on very peculiar circumstances,) are -dilated by it in bulk, though with a great diversity in the amount -of dilatation produced by the same degree of heat. Of the several -forms of natural bodies, gases and vapours are observed to be most -dilatable; liquids next, and solids least of all. The dilatation of -solids has been made a subject of repeated and careful measurement by -several experimenters; among whom, Smeaton, Lavoisier, and Laplace, are -the principal. The remarkable discovery of the unequal dilatation of -crystallised bodies by Mitscherlich has already been spoken of. (266.) -That of gases and vapours was examined about the same time by Dalton -and Gay-Lussac, who both arrived independently at the conclusion of an -equal dilatability subsisting in them all, which constitutes one of the -most remarkable points in their history. - -(356.) The dilatation of air by heat affords, perhaps, the most -unexceptionable means known of measuring degrees of heat. The -thermometer, as originally constructed by Cornelius Drebell, was an -air thermometer. Those now in common use measure accessions of heat -not by the degree of dilatation of air but of mercury. It has been -shown, by the researches of Dulong and Petit, that its indications -coincide exactly with that of the air-thermometer in moderate -temperatures; though at very elevated ones they exhibit a sensible, -and even considerable, deviation. By this instrument, which owes its -present convenience and utility to the happy idea of Newton, who first -thought of fixing determinate points on its scale, we are enabled -to estimate, or at least identify, the degrees of heat; and thereby -to investigate with accuracy the laws of its communication and its -other properties. Were we sure that equal additions of heat produced -equal increments of dimension in any substance, the indications of a -thermometer would afford a true and secure _measure_ of the quantity -present; but this is so far from being the case, that we are nearly in -total ignorance on this important point; a circumstance which throws -the greatest difficulty in the way of all theoretical reasoning, and -even of experimental enquiry. The laws of the dilatation of liquids, in -consequence of this deficiency of necessary preliminary knowledge, are -still involved in great obscurity, notwithstanding the pains which have -been bestowed on them by the elaborate experiments and calculations of -Gilpin, Blagden, Deluc, Dalton, Gay-Lussac, and Biot. - -(357.) The most striking and important of the effects of heat consist, -however, in the liquefaction of solid substances, and the conversion of -the liquids so produced into vapour. There is no solid substance known -which, by a sufficiently intense heat, may not be melted, and finally -dissipated in vapour; and this analogy is so extensive and cogent, -that we cannot but suppose that all those bodies which are liquid -under ordinary circumstances, owe their liquidity to heat, and would -freeze or become solid if their heat could be sufficiently reduced. -In many we see this to be the case in ordinary winters; for some, -severe frosts are requisite; others freeze only with the most intense -artificial colds; and some have hitherto resisted all our endeavours; -yet the number of these last is few, and they will probably cease to be -exceptions as our means of producing cold become enlarged. - -(358.) A similar analogy leads us to conclude that all aëriform -fluids are merely liquids kept in the state of vapour by heat. Many -of them have been actually condensed into the liquid state by cold -accompanied with violent pressure; and as our means of applying these -causes of condensation have improved, more and more refractory ones -have successively yielded. Hence we are fairly entitled to extend our -conclusion to those which we have not yet been able to succeed with; -and thus we are led to regard it as a general fact, that the liquid and -aëriform or vaporous states are entirely dependent on _heat_; that were -it not for this cause, there would be nothing but solids in nature; and -that, on the other hand, nothing but a sufficient intensity of heat is -requisite to destroy the cohesion of every substance, and reduce all -bodies, first to liquids, and then into vapour. - -(359.) But solids, themselves, by the abstraction of heat shrink in -dimension, and at the same time become harder, and more brittle; -yielding less to pressure, and permitting less separation between -their parts by tension. These facts, coupled with the greater -compressibility of liquids, and the still greater of gases, strongly -induce us to believe that it is heat, and heat alone, which holds -the particles of all bodies at that distance from each other which -is necessary to allow of compression; which in fact gives them -their elasticity, and acts as the antagonist force to their mutual -attraction, which would otherwise draw them into actual contact, and -retain them in a state of absolute immobility and impenetrability. -Thus we learn to regard heat as one of the great maintaining powers of -the universe, and to attach to all its laws and relations a degree of -importance which may justly entitle them to the most assiduous enquiry. - -(360.) It was first ascertained by Dr. Black that when heat produces -the liquefaction of a solid, or the conversion of a liquid into vapour, -the liquid or the vapour resulting is no _hotter_ than the solid or -liquid from which it was produced, though a great deal of heat has been -expended in producing this effect, and has actually entered into the -substance. - -(361.) Hence he drew the conclusion that it has become _latent_, and -continues to exist in the product, maintaining it in its new state, -without increasing its temperature. He further proved, that when the -vapour condenses, or the liquid freezes, this latent heat is again -given out from it. This great discovery, with its natural and hardly -less important concomitant, that of the difference of specific heats in -different bodies, or the different quantities of heat they require to -raise their temperature equally, are the chief reasons for regarding -heat as a material substance in a more decided manner than light, with -which in its radiant state it holds so close an analogy. - -(362.) The subject of latent heat has been far less attentively -studied than its great practical importance would appear to demand, -when we consider that it is to this part of physical science that the -theory of the steam-engine is mainly referable, and that material -improvements may not unreasonably be expected in that wonderful -instrument, from a more extended knowledge than we possess of the -latent heats of different vapours. This is not the case, however, -with the subject of specific heat, which was followed up immediately -after its first promulgation with diligence by Irvine; and, after a -brief interval, by Lavoisier and Laplace, as well as by our countryman -Crawfurd, who determined the specific heats of many substances, both -solid and liquid. After a considerable period of inactivity, the -subject was again resumed by Delaroche and Berard, and subsequently -by Dulong and Petit: the result of whose investigations has been the -inductive establishment of one of those simple and elegant physical -laws which carry with them, if not their own evidence, at least their -own recommendation to our belief, as being in unison with every thing -we know of the harmony of nature. The law to which we allude is -this:--that the atoms of all the simple chemical elements have exactly -the same capacity for heat, or are all equally heated or cooled by -equal accessions or abstractions of heat. It is only among laws like -this that we can expect to find a clew capable of guiding us to a -knowledge of the true nature of heat, and its relations to ponderable -matter. - - -_Magnetism and Electricity._ - -(363.) These two subjects, which had long maintained a distinct -existence, and been studied as separate branches of science, are at -length effectually blended. This is, perhaps, the most satisfactory -result which the experimental sciences have ever yet attained. All -the phenomena of magnetic polarity, attraction, and repulsion, have -at length been resolved into one general fact, that two currents of -electricity, moving in the same direction repel, and in contrary -directions attract, each other. The phenomena of the communication -of magnetism and what is called its induced state, alone remain -unaccounted for; but the interesting theory which has been developed -by M. Ampere, under the name of Electro-dynamics, holds out a hope -that this difficulty will also in its turn give way, and the whole -subject be at length completely merged, as far as the consideration of -the acting causes goes, in the more general one of electricity. This, -however, does not prevent magnetism from maintaining its separate -importance as a department of physical enquiry, having its own peculiar -laws and relations of the highest practical interest, which are capable -of being studied quite apart from all consideration of its electrical -origin. And not only so, but to study them with advantage, we must -proceed as if that origin were totally unknown, and, at least up to -a certain point, and that a considerably advanced one, conduct our -enquiries into the subject on the same inductive principles as if this -branch of physics were absolutely independent of all others. - -(364.) Iron, and its oxides and alloys, were for a long time the only -substances considered susceptible of magnetism. The loadstone was -even one of the examples produced by Bacon of that class of physical -instances to which he applies the term “Instantiæ monodicæ”--_singular -instances_. And the history of magnetism affords a beautiful comment -on his remark on instances of this sort. “Nor should our enquiries,” -he observes, “into their nature be broken off, till the properties and -qualities found in such things as may be esteemed wonders in nature -are reduced and comprehended under some certain law; so that all -irregularity or singularity may be found to depend upon some common -form, and the wonder only rest in the exact differences, degrees, -or extraordinary concurrence, and not in the species itself.” The -discovery of the magnetism of nickel, which though inferior to that -of iron, is still considerable; that of cobalt, yet feebler, and -that of titanium, which is only barely perceptible, have effectually -broken down the imaginary limit between iron and the other materials -of the world, and established the existence of that general law of -continuity which it is one chief business of philosophy to trace -throughout nature. The more recent discoveries of M. Arago (mentioned -in 160.) have completed this generalization, by showing that there -is no substance but which, under proper circumstances, is capable of -exhibiting unequivocal signs of the magnetic virtue. And to obliterate -all traces of that line of separation which was once so broad, we are -now enabled, by the great discovery of Oërsted, to communicate at and -during pleasure to a coiled wire of any metal indifferently all the -properties of a magnet;--its attraction, repulsion, and polarity; and -_that_ even in a more intense degree than was previously thought to -be possible in the best natural magnets. In short, in this case, and -in this case only, perhaps, in science, have we arrived at that point -which Bacon seems to have understood by the discovery of “forms.” “The -_form_ of any nature,” says he, “is such, that where it is, the given -nature must infallibly be. The form, therefore, is perpetually present -when that nature is present; ascertains it universally, and accompanies -it every where. Again, this form is such, that when removed, the given -nature infallibly vanishes. Lastly, a true form is such as can deduce -a given nature from some essential property, which resides in many -things.” - -(365.) Magnetism is remarkable in another important point of view. It -offers a prominent, or “_glaring instance_” of that quality in nature -which is termed _polarity_ (267.), and that under circumstances which -peculiarly adapt it for the study of this quality. It does not appear -that the ancients had any knowledge of this property of the magnet, -though its attraction of iron was well known to them. The first mention -of it in modern times cannot be traced earlier than 1180, though it -was probably known to the Chinese before that time. The polarity of -the magnet consists in this, that if suspended freely, one part of it -will invariably direct itself towards a certain point in the horizon, -the other towards the opposite point; and that, if two magnets, so -suspended, be brought near each other, there will take place a mutual -action, in consequence of which, the positions of both will be -disturbed, in the same manner as would happen if the corresponding -parts of each repelled, and those oppositely directed attracted, each -other; and by properly varying the experiment, it is found that they -really do so. If a small magnet, freely suspended, be brought into -the neighbourhood of a larger one, it will take a position depending -on the position of the _poles_ of the larger one, with respect to its -point of suspension. And it has been ascertained that these and all -other phenomena exhibited by magnets in their mutual attractions and -repulsions are explicable on the supposition of two forces or virtues -lodged in the particles of the magnets, the one predominating at one -end, the other at the other; and such that each particle shall attract -those in which the _opposite_ virtue to its own prevails, and repel -those in which a _similar_ one resides with a force proportional to the -inverse square of their mutual distance. - -(366.) The direction in which a magnetic bar, or needle of steel, -freely suspended, places itself, has been ascertained to be different -at different points of the earth’s surface. In some places it points -exactly north and south, in others it deviates from this direction -more or less, and at some actually stands at right angles to it. This -remarkable phenomenon, which is called the variation of the needle, -and which was discovered by Sebastian Cabot in the year 1500, is -accompanied with another called the dip, noticed by Robert Norman in -1576. It consists in a tendency of a needle, nicely balanced on its -centre, when unmagnetized, to _dip_ or point downwards when rendered -magnetic, towards a point below the horizon, and situated within the -earth. By tracing the variation and dip over the whole surface of the -globe, it has been found that these phenomena take place as they would -do if the earth itself were a great magnet, having its poles deeply -situated below the surface,--and, what is very remarkable, possessing -a slow motion within it, in consequence of which neither the variation -nor dip remain constantly the same at the same place. The laws of this -motion are at present unknown; but the discovery of electro-magnetism, -by rendering it almost certain that the earth’s magnetism is merely an -effect of the continual circulation of great quantities of electricity -round it, in a direction generally corresponding with that of its -rotation, have dissipated the greater part of the mystery which hung -over these phenomena; since a variety of causes, both geological and -others, may be imagined which may produce considerable deviations in -the intensity, and partial ones in the direction, of such electric -currents. The unequal distribution of land and sea in the two -hemispheres, by affecting the operation of the sun’s heat in producing -evaporation from the latter, which is probably one of the great sources -of terrestrial electricity, may easily be conceived to modify the -general tendency of such currents, and to produce irregularities in -them, which may render a satisfactory account of whatever still appears -anomalous in the phenomena of terrestrial magnetism. This branch -of science thus becomes connected, on a great scale, with that of -meteorology, one of the most complicated and difficult, but at the same -time interesting, subjects of physical research; one, however, which -has of late begun to be studied with a diligence which promises the -speedy disclosure of relations and laws of which at present we can form -but a very imperfect notion. - -(367.) The communication of magnetism from the earth to a magnetic -body, or from one magnetic body to another, is performed by a process -to which the name of induction has been given, and the laws and -properties of such induced magnetism have been studied with much -perseverance and success,--practically, by Gilbert, Boyle, Knight, -Whiston, Cavallo, Canton, Duhamel, Rittenhouse, Scoresby, and others; -and theoretically, by Æpinus, Coulomb, and Poisson, and in our own -country by Messrs. Barlow and Christie, who have investigated with -great care the curious phenomena which take place when masses of iron -are presented successively, in different positions, by rotation on -an axis, to the influence of the earth’s magnetism. The magnetism of -crystallized bodies (partly from the extreme rarity of such as are -susceptible of any considerable magnetic virtue) has not hitherto been -at all examined, but would probably afford very curious results. - -(368.) To electricity the views of the physical enquirer now turn -from almost every quarter, as to one of those universal powers which -Nature seems to employ in her most important and secret operations. -This wonderful agent, which we see in intense activity in lightning, -and in a feebler and more diffused form traversing the upper regions -of the atmosphere in the northern lights, is present, probably in -immense abundance, in every form of matter which surrounds us, but -becomes sensible only when disturbed by excitements of peculiar -kinds. The most effectual of these is friction, which we have already -observed to be a powerful source of heat. Everybody is familiar -with the crackling sparks which fly from a cat’s back when stroked. -These, by proper management, may be accumulated in bodies suitably -disposed to receive them, and, although then no longer visible, give -evidence of their existence by the exhibition of a vast variety of -extraordinary phenomena,--producing attractions and repulsions in -bodies at a distance,--admitting of being transferred by contact, or -by sudden and violent transilience of the interval of separation, from -one body to another, under the form of sparks and flashes;--traversing -with perfect facility the substance of the densest metals, and a -variety of other bodies called conductors, but being detained by -others, such as glass, and especially _air_, which are thence called -non-conductors,--producing painful shocks and convulsive motions, and -even death itself if in sufficient quantity, in animals through which -they pass, and finally imitating, on a small scale, all the effects of -lightning. - -(369.) The study of these phenomena and their laws until a -comparatively recent period occupied the entire attention of -electricians, and constituted the whole of the science of electricity. -It appears, as the result of their enquiries, that all the phenomena in -question are explicable on the supposition that electricity consists -in a rare, subtle, and highly elastic fluid, which in its tendency -to expand and diffuse itself pervades with more or less facility -the substance of conductors, but is obstructed and detained from -expansion more or less completely by non-conductors. It is supposed, -moreover, that this electric fluid possesses a power of attraction -for the particles of all ponderable matter, together with that of a -repulsion for particles of its own kind. Whether it has weight, or is -rather to be regarded as a species of matter distinct from that of -which ponderable bodies consist, is a question of such delicacy, that -no direct experiments have yet enabled us to decide it; but at all -events its _inertia_ compared with its elastic force must be conceived -excessively small, so that it is to be regarded as a fluid in the -highest degree _active_, obeying every impulse, internal or external, -with the greatest promptitude; in short, a fluid whose energies can -only be compared with those of the ethereal medium by which, in the -undulatory doctrine, light is supposed to be conveyed. The properties -of hydrogen gas compared with those of the denser aëriform fluids will, -in some slight degree, aid our conception of the excessive mobility and -penetrating activity of a fluid so constituted. Electricity, however, -must be regarded as differing in some remarkable points from all those -fluids to which we have hitherto been accustomed to apply the epithet -elastic, such as air, gases, and vapours. In these, the repulsive force -of the particles on which their elasticity depends is considered as -extending only to very small distances, so as to affect only those in -the immediate vicinity of each other, while their attractive power, by -which they obey the general gravitation of all matter, extends to any -distance. In electricity, on the other hand, the very reverse must be -admitted. The force by which its particles repel each other extends to -great distances, while its force of adhesion to ponderable matter must -be regarded as limited in its extent to such minute intervals as escape -observation. - -(370.) The conception of a single fluid of this kind, which when -accumulated in excess in bodies tends constantly to escape, and seek -a restoration of equilibrium by communicating itself to any others -where there may be a deficiency, is that which occurs most naturally -to the mind, and was accordingly maintained by Franklin, to whom the -science of electricity is under great obligations for those decisive -experiments which informed us respecting the true nature of lightning. -The same theory was afterwards advocated by Æpinus, who first showed -how the laws of equilibrium of such a fluid might be reduced to strict -mathematical investigation. But there are phenomena accompanying its -transfer from body to body and the state of equilibrium it affects -under various circumstances, which appear to require the admission of -_two distinct fluids_ antagonist to each other, each attracting the -other, and repelling itself; but each, alike, susceptible of adhesion -to material substances, and of transfer more or less rapid from -particle to particle of them. These fluids in the natural undisturbed -state are conceived to exist in a state of combination and mutual -saturation; but this combination may be broken, and either of them -separately accumulated in a body to any amount without the other, -provided its escape be properly obstructed by surrounding it with -non-conductors. When so accumulated, its repulsion for its own kind -and attraction of the opposite species in neighbouring bodies tends -to disturb the natural equilibrium of the two fluids present in them, -and to produce phenomena of a peculiar description, which are termed -_induced_ electricity. Curious and artificial as this theory may -appear, there has hitherto been produced no phenomenon of which it -will not afford at least a plausible, and in by far the majority of -cases a very satisfactory, explanation. It has one character which is -extremely valuable in any theory, that of admitting the application of -strict mathematical reasoning to the conclusions we would draw from -it. Without this, indeed, it is scarcely possible that any theory -should ever be fairly brought to the test by a comparison with facts. -Accordingly, the mathematical theory of electrical equilibrium, -and the laws of the distribution of the electric fluids over the -surfaces of bodies in which they are accumulated, have been made the -subject of elaborate geometrical investigation by the most expert -mathematicians, and have attained a degree of extent and elegance -which places this branch of science in a very high rank in the scale -of mathematico-physical enquiry. These researches are grounded on -the assumption of a law of attraction and repulsion similar to those -of gravity and magnetism, and which by the general accordance of the -results with facts, as well as by experiments instituted for the -express purpose of ascertaining the laws in question, are regarded as -sufficiently demonstrated. - -(371.) The most obscure part of the subject is no doubt the original -mode of disturbance of electrical equilibrium, by which electricity is -excited in the first instance, either by friction or by any other of -those causes which have been ascertained to produce such an effect: -analogies, it is true, are not wanting[56]; but it must be allowed that -hitherto nothing decisive has been offered on the subject; and that -conjectural modes of action have in this instance too often usurped the -place of those to which a careful examination of facts alone can lead -us. - -(372.) Philosophers had long been familiar with the effects of -electricity above referred to, and with those which it produces in -its sudden and violent transfer from one body to another, in rending -and shattering the parts of the substances through which it passes, -and where in great quantity, producing all the effect of intense -heat, igniting, fusing, and volatilizing metals, and setting fire to -inflammable bodies; even its occasional influence in destroying or -altering the polarity of the magnetic needle had been noticed: but as -heat was known to be produced by mechanical violence, and as magnetism -was also known to be greatly affected by the same cause, these effects -were referred rather to that cause than to any thing in the peculiar -nature of the electric matter, and regarded rather as an indirect -consequence of its mode of action than as connected with its intimate -nature. In short, electricity seemed destined to furnish another in -addition to many instances of subjects insulated from the rest of -philosophy, and capable of being studied only in its own internal -relations, when the great discoveries of Galvani and Volta placed a new -power at the command of the experimenter, by whose means those effects -which had before been crowded within an inappreciable instant could -be developed in detail and studied at leisure; and those forces which -had previously exhibited themselves only in a state of uncontrollable -intensity were tamed down, as it were, and made to distribute their -efficacy over an indefinite time, and to regulate their action at the -will of the operator. It was then soon ascertained that electricity -in the act of its passage along conductors, produces a variety of -wonderful effects, which had never been previously suspected; and these -of such a nature, as to afford points of contact with several other -branches of physical enquiry, and to throw new and unexpected lights on -some of the most obscure operations of nature. - -(373.) The history of this grand discovery affords a fine illustration -of the advantage to be derived in physical enquiry from a close and -careful attention to any phenomenon, however apparently trifling, -which may at the moment of observation appear inexplicable on received -principles. The convulsive motions of a dead frog in the neighbourhood -of an electric discharge, which originally drew Galvani’s attention to -the subject, had been noticed by others nearly a century before his -time, but attracted no further remark than as indicating a peculiar -sensibility to electrical excitement depending on that remnant of -vitality which is not extinguished in the organic frame of an animal -by the deprivation of actual life. Galvani was not so satisfied. He -analysed the phenomenon; and in investigating all the circumstances -connected with it was led to the observation of a peculiar electrical -excitement which took place when a circuit was formed of three distinct -parts, a muscle, a nerve, and a metallic conductor, each placed in -contact with the other two, and which was manifested by a convulsive -motion produced in the muscle. To this phenomenon he gave the name of -animal electricity, an unfortunate epithet, since it tended to restrict -enquiry into its nature to the class of phenomena in which it first -became apparent. But this circumstance, which in a less enquiring age -of science might have exercised a fatal influence on the progress of -knowledge, proved happily no obstacle to the further developement of -its principles, the subject being immediately taken up with a kind -of prophetic ardour by Volta, who at once generalized the phenomena, -rejecting the physiological considerations introduced by Galvani, as -foreign to the enquiry, and regarding the contraction of the muscles -as merely a delicate means of detecting the production of electrical -excitements too feeble to be rendered sensible by any other means. -It was thus that he arrived at the knowledge of a general fact, that -of the disturbance of electrical equilibrium by the mere contact of -different bodies, and the circulation of a current of electricity in -one constant direction, through a circuit composed of three different -conductors. To increase the intensity of the very minute and delicate -effect thus observed became his next aim, nor did his enquiry terminate -till it had placed him in possession of that most wonderful of all -human inventions, the pile which bears his name, through the medium of -a series of well conducted and logically combined experiments, which -has rarely, if ever, been surpassed in the annals of physical research. - -(374.) Though the original pile of Volta was feeble compared to those -gigantic combinations which were afterwards produced, it sufficed, -however, to exhibit electricity under a very different aspect from any -thing which had gone before, and to bring into view those peculiar -modifications in its action which Dr. Wollaston was the first to -render a satisfactory account of, by referring them to an increase -of _quantity_, accompanied with a diminution of _intensity_ in the -supply afforded. The discovery had not long been made public, and -the instrument in the hands of chemists and electricians, before it -was ascertained that the electric current, transmitted by it through -conducting liquids, produces in them chemical decompositions. This -capital discovery appears to have been made, in the first instance, by -Messrs. Nicholson and Carlisle, who observed the decomposition of water -so produced. It was speedily followed up by the still more important -one of Berzelius and Hisinger, who ascertained it as a general law, -that, in all the decompositions so effected, the acids and oxygen -become transferred to, and accumulated around, the positive,--and -hydrogen, metals, and alkalies round the negative, pole of a Voltaic -circuit; being transferred in an invisible, and, as it were, a latent -or torpid state, by the action of the electric current, through -considerable spaces, and even through large quantities of water or -other liquids, again to re-appear with all their properties at their -appropriate resting-places. - -(375.) It was in this state of things that the subject was taken up -by Davy, who, seeing that the strongest chemical affinities were thus -readily subverted by the decomposing action of the pile, conceived -the happy idea of bringing to bear the intense power of the enormous -batteries of the Royal Institution on those substances which, though -strongly suspected to be compounds, had resisted all attempts to -decompose them--the alkalies and earths. They yielded to the force -applied, and a total revolution was thus effected in chemistry; not so -much by the introduction of the new elements thus brought to light, as -by the mode of conceiving the nature of chemical affinity, which from -that time has been regarded (as Davy broadly laid it down, in a theory -which was readily adopted by the most eminent chemists, and by none -more readily than by Berzelius himself,) as entirely due to electric -attractions and repulsions, those bodies combining most intimately -whose particles are habitually in a state of the most powerful -electrical antagonism, and dispossessing each other, according to the -amount of their difference in this respect. - -(376.) The connection of magnetism and electricity had long been -suspected, and innumerable fruitless trials had been made to determine, -in the affirmative or negative, the question of such connection. The -phenomena of many crystallized minerals which become electric by heat, -and develope opposite electric poles at their two extremities, offered -an analogy so striking to the polarity of the magnet, that it seemed -hardly possible to doubt a closer connection of the two powers. The -developement of a similar polarity in the Voltaic pile pointed strongly -to the same conclusion; and experiments had even been made with a -view to ascertain whether a pile in a state of excitement might not -manifest a disposition to place itself in the magnetic meridian; but -the essential condition had been omitted, that of allowing the pile to -discharge itself freely, a condition which assuredly never would have -occurred of itself to any experimenter. Of all the philosophers who -had speculated on this subject, none had so pertinaciously adhered to -the idea of a necessary connection between the phenomena as Oërsted. -Baffled often, he returned to the attack; and his perseverance was at -length rewarded by the complete disclosure of the wonderful phenomena -of electro-magnetism. There is something in this which reminds us of -the obstinate adherence of Columbus to his notion of the necessary -existence of the New World; and the whole history of this beautiful -discovery may serve to teach us reliance on those general analogies -and parallels between great branches of science by which one strongly -reminds us of another, though no direct connection appears; as an -indication not to be neglected of a community of origin. - -(377.) It is highly probable that we are still ignorant of many -interesting features in electrical science, which the study of the -Voltaic circuit will one day disclose. The violent mechanical effects -produced by it on mercury, placed under conducting liquids which have -been referred by Professor Erman to a modified form of capillary -attraction, but which a careful and extended view of the phenomena -have led others[57] to regard in a very different light, as pointing -out a primary action of a dynamical rather than a statical character, -deserve, in this point of view, a further investigation; and the -curious relations of electricity to heat, as exhibited in the phenomena -of what has been called thermo-electricity, promise an ample supply of -new information. - -(378.) Among the remarkable effects of electricity disclosed by the -researches of Galvani and Volta, perhaps the most so consisted in its -influence on the nervous system of animals. The origin of muscular -motion is one of those profound mysteries of nature which we can -scarcely venture to hope will ever be fully explained. Physiologists, -however, had long entertained a general conception of the conveyance -of some subtle fluid or spirit from the brain to the muscles of -animals along the nerves; and the discovery of the rapid transmission -of electricity along conductors, with the violent effects produced by -shocks, transmitted through the body, on the nervous system, would -very naturally lead to the idea that this nervous fluid, if it had -any real existence, might be no other than the electrical. But until -the discoveries of Galvani and Volta, this could only be looked upon -as a vague conjecture. The character of a _vera causa_ was wanting to -give it any degree of rational plausibility, since no reason could -be imagined for the disturbance of the electrical equilibrium in the -animal frame, composed as it is entirely of conductors, or rather, it -seemed contrary to the then known laws of electrical communication -to suppose any such. Yet one strange and surprising phenomenon might -be adduced indicative of the possibility of such disturbance, viz. -the powerful shock given by the torpedo and other fishes of the same -kind, which presented so many analogies with those arising from -electricity, that they could hardly be referred to a different source, -though _besides_ the shock neither spark nor any other indication of -electrical tension could be detected in them. - -(379.) The benumbing effect of the torpedo had been ascertained to -depend on certain singularly constructed organs composed of membranous -columns, filled from end to end with laminæ, separated from each other -by a fluid: but of its mode of action no satisfactory account could be -given; nor was there any thing in its construction, and still less in -the nature of its materials, to give the least ground for supposing -it an electrical apparatus. But the pile of Volta supplied at once -the analogies both of structure and of effect, so as to leave little -doubt of the electrical nature of the apparatus, or of the power, a -most wonderful one certainly, of the animal, to determine, by an effort -of its will, that concurrence of conditions on which its activity -depends. This remained, as it probably ever will remain, mysterious -and inexplicable; but the principle once established, that there -exists in the animal economy a power of determining the developement -of electric excitement, capable of being transmitted along the nerves, -and it being ascertained, by numerous and decisive experiments, that -the transmission of Voltaic electricity along the nerves of even -a dead animal is sufficient to produce the most violent muscular -action, it became an easy step to refer the origin of muscular motion -in the living frame to a similar cause; and to look to the brain, a -wonderfully constituted organ, for which no mode of action possessing -the least plausibility had ever been devised, as the source of the -required electrical power.[58] - -(380.) It is not our intention, however, to enter into any further -consideration of physiological subjects. They form, it is true, a -most important and deeply interesting province of philosophical -enquiry; but the view that we have taken of physical science has -rather been directed to the study of inanimate nature, than to that of -the mysterious phenomena of organization and life, which constitute -the object of physiology. The history of the animal and vegetable -productions of the globe, as affording objects and materials for the -convenience and use of man, and as dependent on and indicative of the -general laws which determine the distribution of heat, moisture, and -other natural agents, over its surface, and the revolutions it has -undergone, are of course intimately connected with our subject, and -will, therefore, naturally afford room for some remarks, but not such -as will long detain the reader’s attention. - -(381.) In _zoology_, the connection of peculiar modes of life and -food, with peculiarities of structure, has given rise to systems of -classification at once obvious and natural; and the great progress -which has been made in comparative anatomy has enabled us to trace -a graduated scale of organization almost through the whole chain of -animal being; a scale not without its intervals, but which every -successive discovery of animals heretofore unknown has tended to fill -up. The wonders disclosed by microscopic observation have opened to -us a new world, in which we discover, with astonishment, the extremes -of minuteness and complexity of structure united; while, on the other -hand, the examination of the fossil remains of a former state of -creation has demonstrated the existence of animals far surpassing in -magnitude those now living, and brought to light many forms of being -which have nothing analogous to them at present, and many others -which afford important connecting links between existing genera. And, -on the other hand, the researches of the comparative anatomist and -conchologist have thrown the greatest light on the studies of the -geologist, and enabled him to discern, through the obscure medium of a -few relics, scattered here and there through a stratum, circumstances -connected with the formation of the stratum itself which he could have -recognised by no other indication. This is one among many striking -instances of the unexpected lights which sciences, however apparently -remote, may throw upon each other. - -(382.) To _botany_ many of the same remarks apply. Its artificial -systems of classification, however convenient, have not prevented -botanists from endeavouring to group together the objects of their -science in natural classes having a community of character more -intimate than those which determine their place in the Linnean or any -similar system; a community of character extending over the whole -habit and properties of the individuals compared. The important -chemical discoveries which have been lately made of peculiar proximate -principles which, in an especial manner, characterize certain -families of plants, hold out the prospect of a greatly increased -field of interesting knowledge in this direction, and not only -interesting, but in a high degree important, when it is considered -that the principles thus brought into view are, for the most part, -very powerful medicines, and are, in fact, the essential ingredients -on which the medical virtues of the plants depend. The law of the -distribution of the generic forms of plants over the globe, too, has, -within a comparatively recent period, become an object of study to the -naturalist; and its connection with the laws of climate constitutes one -of the most interesting and important branches of natural-historical -enquiry, and one on which great light remains to be thrown by future -researches. It is this which constitutes the chief connecting link -between botany and geology, and renders a knowledge of the vegetable -fossils, of any portion of the earth’s surface, indispensable to the -formation of a correct judgment of the circumstances under which it -existed in its ancient state. Fossil botany is accordingly cultivated -with great and increasing ardour; and the subterraneous “Flora” of a -geological formation is, in many instances, studied with a degree of -care and precision little inferior to that which its surface exhibits. - - - - -CHAP. VI. - - OF THE CAUSES OF THE ACTUAL RAPID ADVANCE OF THE PHYSICAL SCIENCES - COMPARED WITH THEIR PROGRESS AT AN EARLIER PERIOD. - - -(383.) There is no more extraordinary contrast than that presented by -the slow progress of the physical sciences, from the earliest ages -of the world to the close of the sixteenth century, and the rapid -developement they have since experienced. In the former period of -their history, we find only small additions to the stock of knowledge, -made at long intervals of time; during which a total indifference -on the part of the mass of mankind to the study of nature operated -to effect an almost complete oblivion of former discoveries, or, -at best, permitted them to linger on record, rather as literary -curiosities, than as possessing, in themselves, any intrinsic interest -and importance. A few enquiring individuals, from age to age, might -perceive their value, and might feel that irrepressible thirst after -knowledge which, in minds of the highest order, supplies the absence -both of external stimulus and opportunity. But the total want of a -right direction given to enquiry, and of a clear perception of the -objects to be aimed at, and the advantages to be gained by systematic -and connected research, together with the general apathy of society -to speculations remote from the ordinary affairs of life, and -studiously kept involved in learned mystery, effectually prevented -these occasional impulses from overcoming the inertia of ignorance, and -impressing any regular and steady progress on science. Its objects, -indeed, were confined in a region too sublime for vulgar comprehension. -An earthquake, a comet, or a fiery meteor, would now and then call the -attention of the whole world, and produce from all quarters a plentiful -supply of crude and fanciful conjectures on their causes; but it was -never supposed that sciences could exist among common objects, have a -place among mechanical arts, or find worthy matter of speculation in -the mine or the laboratory. Yet it cannot be supposed, that all the -indications of nature continually passed unremarked, or that much good -observation and shrewd reasoning on it failed to perish unrecorded, -before the invention of printing enabled every one to make his ideas -known to all the world. The moment this took place, however, the sparks -of information from time to time struck out, instead of glimmering -for a moment, and dying away in oblivion, began to accumulate into a -genial glow, and the flame was at length kindled which was speedily to -acquire the strength and rapid spread of a conflagration. The universal -excitement in the minds of men throughout Europe, which the first -out-break of modern science produced, has been already spoken of. But -even the most sanguine anticipators could scarcely have looked forward -to that steady, unintermitted progress which it has since maintained, -nor to that rapid succession of great discoveries which has kept up -the interest of the first impulse still vigorous and undiminished. It -may truly, indeed, be said, that there is scarcely a single branch of -physical enquiry which is either stationary, or which has not been, -for many years past, in a constant state of advance, and in which the -progress is not, at this moment, going on with accelerated rapidity. - -(384.) Among the causes of this happy and desirable state of things, -no doubt we are to look, in the first instance, to that great -increase in wealth and civilization which has at once afforded the -necessary leisure and diffused the taste for intellectual pursuits -among numbers of mankind, which have long been and still continue -steadily progressive in every principal European state, and which the -increase and fresh establishment of civilized communities in every -distant region are rapidly spreading over the whole globe. It is not, -however, merely the increased number of cultivators of science, but -their enlarged opportunities, that we have here to consider, which, in -all those numerous departments of natural research that require local -information, is in fact the most important consideration of all. To -this cause we must trace the great extension which has of late years -been conferred on every branch of natural history, and the immense -contributions which have been made, and are daily making, to the -departments of zoology and botany, in all their ramifications. It is -obvious, too, that all the information that can possibly be procured, -and reported, by the most enlightened and active travellers, must fall -infinitely short of what is to be obtained by individuals actually -resident upon the spot. Travellers, indeed, may make collections, -may snatch a few hasty observations, may note, for instance, the -distribution of geological formations in a few detached points, and now -and then witness remarkable local phenomena; but the resident alone can -make continued series of regular observations, such as the scientific -determination of climates, tides, magnetic variations, and innumerable -other objects of that kind, requires; can alone mark all the details -of geological structure, and refer each stratum, by a careful and long -continued observation of its fossil contents, to its true epoch; can -alone note the habits of the animals of his country, and the limits -of its vegetation, or obtain a satisfactory knowledge of its mineral -contents, with a thousand other particulars essential to that complete -acquaintance with our globe as a whole, which is beginning to be -understood by the extensive designation of physical geography. Besides -which, ought not to be omitted multiplied opportunities of observing -and recording those extraordinary phenomena of nature which offer an -intense interest, from the rarity of their occurrence as well as the -instruction they are calculated to afford. To what, then, may we not -look forward, when a spirit of scientific enquiry shall have spread -through those vast regions in which the process of civilization, its -sure precursor, is actually commenced and in active progress? And what -may we not expect from the exertions of powerful minds called into -action under circumstances totally different from any which have yet -existed in the world, and over an extent of territory far surpassing -that which has hitherto produced the whole harvest of human intellect? -In proportion as the number of those who are engaged on each department -of physical enquiry increases, and the geographical extent over which -they are spread is enlarged, a proportionately increased facility -of communication and interchange of knowledge becomes essential to -the prosecution of their researches with full advantage. Not only -is this desirable, to prevent a number of individuals from making -the same discoveries at the same moment, which (besides the waste of -valuable time) has always been a fertile source of jealousies and -misunderstandings, by which great evils have been entailed on science; -but because methods of observation are continually undergoing new -improvements, or acquiring new facilities, a knowledge of which, it is -for the general interest of science, should be diffused as widely and -as rapidly as possible. By this means, too, a sense of common interest, -of mutual assistance, and a feeling of sympathy in a common pursuit, -are generated, which proves a powerful stimulus to exertion; and, on -the other hand, means are thereby afforded of detecting and pointing -out mistakes before it is too late for their rectification. - -(385.) Perhaps it may be truly remarked, that, next to the -establishment of institutions having either the promotion of science -in general, or, what is still more practically efficacious in its -present advanced state, that of particular departments of physical -enquiry, for their express objects, nothing has exercised so powerful -an influence on the progress of modern science as the publication -of monthly and quarterly scientific journals, of which there is now -scarcely a nation in Europe which does not produce several. The quick -and universal circulation of these, places observers of all countries -on the same level of perfect intimacy with each other’s objects and -methods, while the abstracts they from time to time (if well conducted) -contain of the most important researches of the day consigned to the -more ponderous tomes of academical collections, serve to direct the -course of general observation, as well as to hold out, in the most -conspicuous manner, models for emulative imitation. In looking forward -to what may hereafter be expected from this cause of improvement, we -are not to forget the powerful effect which must in future be produced -by the spread of elementary works and digests of what is actually known -in each particular branch of science. Nothing can be more discouraging -to one engaged in active research, than the impression that all he -is doing may, very likely, be labour taken in vain; that it may, -perhaps, have been already done, and much better done, than, with his -opportunities, or his resources, he can hope to perform it; and, on the -other hand, nothing can be more exciting than the contrary impression. -Thus, by giving a connected view of what has been done, and what -remains to be accomplished in every branch, those digests and bodies -of science, which from time to time appear, have, in fact, a very -important weight in determining its future progress, quite independent -of the quantity of information they communicate. With respect to -elementary treatises, it is needless to point out their utility, or -to dwell on the influence which their actual abundance, contrasted -with their past remarkable deficiency, is likely to exercise over the -future. It is only by condensing, simplifying, and arranging, in the -most lucid possible manner, the acquired knowledge of past generations, -that those to come can be enabled to avail themselves to the full of -the advanced point from which they will start. - -(386.) One of the means by which an advanced state of physical science -contributes greatly to accelerate and secure its further progress, -is the exact knowledge acquired of physical data, or those normal -quantities which we have more than once spoken of in the preceding -pages (222.); a knowledge which enables us not only to appretiate -the accuracy of experiments, but even to correct their results. As -there is no surer criterion of the state of science in any age than -the degree of care bestowed, and discernment exhibited, in the choice -of such data, so as to afford the simplest possible grounds for the -application of theories, and the degree of accuracy attained in their -determination, so there is scarcely any thing by which science can be -more truly benefited than by researches directed expressly to this -object, and to the construction of tables exhibiting the true numerical -relations of the elements of theories, and the actual state of nature, -in all its different branches. It is only by such determinations that -we can ascertain what changes are slowly and imperceptibly taking place -in the existing order of things; and the more accurate they are, the -_sooner_ will this knowledge be acquired. What might we not now have -known of the motions of the (so-called) fixed stars, had the ancients -possessed the means of observation we now possess, and employed them -as we employ them now? - -(387.) In any enumeration of causes which have contributed to -the recent rapid advancement of science, we must not forget the -very important one of improved and constantly improving means of -observation, both in instruments adapted for the exact measurement of -quantity, and in the general convenience and well-judged adaptation -to its purposes, of every description of scientific apparatus. In -the actual state of science there are few observations which can -be productive of any great advantage but such as afford accurate -measurement; and an increased refinement in this respect is constantly -called for. The degree of delicacy actually attained, we will not say -in the most elaborate works of the highest art, but in such ordinary -apparatus as every observer may now command, is such as could not have -been arrived at unless in a state of the mechanical arts, which in -its turn (such is the mutual re-action of cause and effect) requires -for its existence a very advanced state of science. What an important -influence may be exercised over the progress of a single branch of -science by the invention of a ready and convenient mode of executing a -definite measurement, and the construction and common introduction of -an instrument adapted for it cannot be better exemplified than by the -instance of the reflecting goniometer. This simple, cheap, and portable -little instrument, has changed the face of mineralogy, and given it all -the characters of one of the exact sciences. - -(388.) Our means of perceiving and measuring minute quantities, in the -important relations of weight, space, and time, seem already to have -been carried to a point which it is hardly conceivable they should -surpass. Balances have been constructed which have rendered sensible -the millionth part of the whole quantity weighed; and to turn with the -thousandth part of a grain is the performance of balances pretending -to no very extraordinary degree of merit. The elegant invention of -the sphærometer, by substituting the sense of touch for that of sight -in the measurement of minute objects, permits the determination of -their dimensions with a degree of precision which is fully adequate -to the nicest purposes of scientific enquiry. By its aid an inch may -be readily subdivided into ten or even twenty thousand parts; and the -lever of contact, an instrument in use among the German opticians, -enables us to appretiate quantities of space even yet smaller. For -the subdivision of time, too, the perfection of modern mechanism has -furnished resources which leave very little to be desired. By the -aid of clocks and chronometers, as they are now constructed, a few -tenths of a second is all the error that need be apprehended in the -subdivision of a day; and for the further subdivision of smaller -portions of time, instruments have been imagined which admit of -almost unlimited precision, and permit us to appreciate intervals to -the nicety of the hundredth, or even the thousandth part of a single -second.[59] When the precision attainable by such means is contrasted -with what could be procured a few generations ago, by the rude and -clumsy workmanship of even the early part of the last century, it will -be no matter of astonishment that the sciences which depend on exact -measurements should have made a proportional progress. Nor will any -degree of nicety in physical determinations appear beyond our reach, if -we consider the inexhaustible resources which science itself furnishes, -in rendering the quantities actually to be determined by measure great -multiples of the elements required for the purposes of theory, so as to -diminish in the same proportion the influence of any errors which may -be committed on the final results. - -(389.) Great, indeed, as have been of late the improvements in the -construction of instruments, both as to what regards convenience and -accuracy, it is to the discovery of improved _methods_ of observation -that the chief progress of those parts of science which depend on -exact determinations is owing. The balance of torsion, the ingenious -invention of Cavendish and Coulomb, may be cited as an example of what -we mean. By its aid we are enabled not merely to render sensible, -but to subject to precise measurement and subdivision, degrees of -force infinitely too feeble to affect the nicest balance of the usual -construction, even were it possible to bring them to act on it. The -galvanometer, too, affords another example of the same kind, in an -instrument whose range of utility lies among electric forces which we -have no other means of rendering sensible, much less of estimating -with exactness. In determinations of quantities less minute in -themselves, the methods devised by Messrs. Arago and Fresnel, for the -measurement of the refractive powers of transparent media by means of -the phenomenon of diffraction, may be cited as affording a degree of -precision limited only by the wishes of the observer, and the time and -patience he is willing to devote to his observation. And in respect of -the direction of observations to points from which real information -is to be obtained, and positive conclusions drawn, the hygrometer of -Daniell may be cited as an elegant example of the introduction into -general use of an instrument substituting an indication founded on -strict principles for one perfectly arbitrary. - -(390.) In speculating on the future prospects of physical science, -we should not be justified in leaving out of consideration the -probability, or rather certainty, of the occasional occurrence of those -happy accidents which have had so powerful an influence on the past; -occasions, where a fortunate combination opportunely noticed may admit -us in an instant to the knowledge of principles of which no suspicion -might occur but for some such casual notice. Boyle has entitled one of -his essays thus remarkably,--“_Of Man’s great Ignorance of the Uses -of natural Things; or that there is no one Thing in Nature whereof -the Uses to human Life are yet thoroughly understood_.”[60] The whole -history of the arts since Boyle’s time has been one continued comment -on this text; and if we regard among the uses of the works of nature, -_that_, assuredly the noblest of all, which leads us to a knowledge -of the Author of nature through the contemplation of the wonderful -means by which he has wrought out his purposes in his works, the -sciences have not been behind hand in affording their testimony to its -truth. Nor are we to suppose that the field is in the slightest degree -narrowed, or the chances in favour of such fortunate discoveries at all -decreased, by those which have already taken place: on the contrary, -they have been incalculably extended. It is true that the ordinary -phenomena which pass before our eyes have been minutely examined, and -those more striking and obvious principles which occur to superficial -observation have been noticed and embodied in our systems of science; -but, not to mention that by far the greater part of natural phenomena -remain yet unexplained, every new discovery in science brings into -view whole classes of facts which would never otherwise have fallen -under our notice at all, and establishes relations which afford to -the philosophic mind a constantly extending field of speculation, -in ranging over which it is next to impossible that he should not -encounter new and unexpected principles. How infinitely greater, for -instance, are the mere chances of discovery in chemistry among the -innumerable combinations with which the modern chemist is familiar, -than at a period when two or three imaginary elements, and some ten -or twenty substances, whose properties were known with an approach to -distinctness, formed the narrow circle within which his ideas had to -revolve? How many are the instances where a new substance, or a new -property, introduced into familiar use, by being thus brought into -relation with all our actual elements of knowledge, has become the -means of developing properties and principles among the most common -objects, which could never have otherwise been discovered? Had not -platina (to take an instance) been an object of the most ordinary -occurrence in a laboratory, would a suspicion have ever occurred that -a lamp could be constructed to burn without flame; and should we have -ever arrived at a knowledge of those curious phenomena and products of -semi-combustion which this beautiful experiment discloses? - -(391.) Finally, when we look back on what has been accomplished in -science, and compare it with what remains to be done, it is hardly -possible to avoid being strongly impressed with the idea that we have -been and are still executing the labour by which succeeding generations -are to profit.[61] In a few instances only have we arrived at those -general axiomatic laws which admit of direct deductive inference, -and place the solutions of physical phenomena before us as so many -problems, whose principles of solution we fully possess, and which -require nothing but acuteness of reasoning to pursue even into their -farthest recesses. In fewer still have we reached that command of -abstract reasoning itself which is necessary for the accomplishment of -so arduous a task. Science, therefore, in relation to our faculties, -still remains boundless and unexplored, and, after the lapse of a -century and a half from the æra of Newton’s discoveries, during which -every department of it has been cultivated with a zeal and energy which -have assuredly met their full return, we remain in the situation in -which he figured himself,--standing on the shore of a wide ocean, from -whose beach we may have culled some of those innumerable beautiful -productions it casts up with lavish prodigality, but whose acquisition -can be regarded as no diminution of the treasures that remain. - -(392.) But this consideration, so far from repressing our efforts, or -rendering us hopeless of attaining any thing intrinsically great, ought -rather to excite us to fresh enterprise, by the prospect of assured -and ample recompense from that inexhaustible store which only awaits -our continued endeavours. “It is no detraction from human capacity to -suppose it incapable of infinite exertion, or of exhausting an infinite -subject.”[62] In whatever state of knowledge we may conceive man to -be placed, his progress towards a yet higher state need never fear a -check, but must continue till the last existence of society. - -(393.) It is in this respect an advantageous view of science, which -refers all its advances to the discovery of general laws, and to -the inclusion of what is already known in generalizations of still -higher orders; inasmuch as this view of the subject represents it, as -it really is, essentially incomplete, and incapable of being fully -embodied in any system, or embraced by any single mind. Yet it must be -recollected that, so far as our experience has hitherto gone, every -advance towards generality has at the same time been a step towards -simplification. It is only when we are wandering and lost in the mazes -of particulars, or entangled in fruitless attempts to work our way -downwards in the thorny paths of applications, to which our reasoning -powers are incompetent, that nature appears complicated:--the moment we -contemplate it as it is, and attain a position from which we can take a -commanding view, though but of a small part of its plan, we never fail -to recognise that sublime simplicity on which the mind rests satisfied -that it has attained the truth. - - - - -INDEX. - - - Acoustics cultivated by Pythagoras and Aristotle, page 248. - - Æpinus, his laws of equilibrium of electricity, 332. - - Aëriform fluids, liquids kept in a state of vapour, 321. - - Agricola, George, his knowledge of mineralogy and metallurgy, 112. - - Air, compressibility and elasticity of; limitation to the repulsive - tendency of, 226. - Weight of, unknown to the ancients, 228. - First perceived by Galileo, 228. - Proved by a crucial instance, 229. - Equilibrium of, established, 231. - Dilatation of, by heat, 319. - - Air-pump, discovery of, 230. - - Airy, his experiments in Dolcoath mine, 187. - - Alchemists, advantages derived from, 11. - - Algebra, 19. - - Ampere, his electro-dynamic theory, 202. - Utility of, 203, 324. - - Analysis of force, 86. - Of motion, 87. - Of complex phenomena, 88. - - Anaxagoras, philosophy of, 107. - - Animal electricity, 337. - - Arago, M., his experiment with a magnetic needle and a plate of - copper, 157. - - Archimedes, his practical application of science, 72. - His knowledge of hydrostatics, 231. - - Arfwedson, his discovery of lithia, 158. - - Aristotle, his knowledge of natural history, 109. - His works condemned, and subsequently studied with avidity, 111. - His philosophy overturned by the discoveries of Copernicus, Kepler, - and Galileo, 113. - - Arithmetic, 19. - - Art, empirical and scientific, differences between, 71. - Remarks on the language, terms, or signs, used in treating of - it, 70. - - Assurances, life, utility and abuses of, 58. - - Astronomy, cause of the slow progress of our knowledge of, 78. - Theory and practical observations distinct in, 132. - An extensive acquaintance with science and every branch of knowledge - necessary to make a perfect observer in, 132. - Five primary planets added to our system, 274. - Positions, figures, and dimensions of all the planetary orbits now - well known, 275. - - Atomic theory, 305. - Advantage of, 306. - - Atomic weights of chemical elements, 306. - - Attraction, capillary, or capillarity, investigated by Laplace and - Young, 234. - - - Bacon, celebrated in England for his knowledge of science, 72. - Benefits conferred on Natural Philosophy by him, 104. - His Novum Organum, 105. - His reform in philosophy proves the paramount importance of - induction, 114. - His prerogative of facts, 181. - Illustrated by the fracture of a crystallized substance, 183. - His collective instances, 184. - Importance of, 185. - His experiment on the weight of bodies, 186. - Travelling instances of, frontier instances of, 188. - His difference between liquids and aëriform fluids, 233. - - Bartolin, Erasmus, first discovers the phenomena exhibited by doubly - refracting crystals, 254. - - Beccher, phlogistic doctrines of, 300. - - Bergmann, his advancement in crystallography, 239. - - Bernoulli, experiments of, in hydrodynamical science, 181. - - Biot, his hypothesis of a rotatory motion of the particles of light - about their axes, 262. - - Black, Dr., his discovery of latent heat, 322. - - Bode, his curious law observed in the progression of the magnitudes of - the several planetary orbits, 308. - - Bodies, natural constitution of, 221. - Division of, into crystallized and uncrystallized, 242. - - Bones, dry, a magazine of nutriment, 65. - - Borda, his invention for subdivision, 128. - - Botany, general utility of, 345. - - Boyle, Robert, his enthusiasm in the pursuit of science, 115. - His improvement on the air-pump, 230. - - Brain, hypothesis of its being an electric pile, 343. - - Bramah’s press, principle and utility of, 233. - - Brewster, Dr., his improvement on lenses for lighthouses, 56. - His researches prove that the phenomena exhibited by polarized - light, in its transmission through crystals, afford a certain - indication of the most important points relating to the - structure of crystals themselves, 263. - - - Cabot, Sebastian, his discovery of the variation of the needle, 327. - - Cagnard, Baron de la Tour, utility of his experiments, 234. - - Causes and consequences directors of the will of man, 6. - - Causes, proximate, discovery of, called by Newton _veræ causæ_, 144. - - Celestial mechanics, 265. - - Chaldean records, 265. - - Chemistry furnishes causes of sudden action, also fulminating - compositions, 62. - Analogy of the complex phenomena of, with those of physics, 92. - Benefits arising from the analysis of, 94. - Axioms of, analogous to those of geometry, 95. - Many of the new elements of, detected in the investigation of - residual phenomena, 158. - The most general law of, 209. - Illustration of, 210. - Between fifty and sixty elements in, 211. - Objects of, 296. - General heads of the principal improvements in, 302. - Remarks on those general heads, 304. - - Chemistry, Stahlian, cause of the mistakes and confusions of, 123. - - Chladni, experiments of, in dynamical science, 181. - - Chlorine, disinfectant powers of, 56. - - Clarke, Dr., his experiments on the arseniate and phosphate - of soda, 170. - His success in producing a new phosphate of soda, 171. - - Climate, change of, in large tracts of the globe, alleged - cause of, 145. - - Coals, power of a bushel of, properly consumed, 59. - Quantity consumed in London, 60. - - Cohesion, an ultimate phenomenon, 90. - - Cold, qualities of, 318. - - Compass, mariner’s, 55. - - Condensation, a source of heat, 313. - - Conduction of heat, laws of, 205. - - Copernicus, effect of his discoveries on the Aristotelian - philosophy, 113. - Objections to his astronomical doctrines, 269. - - Crystallography, laws of, 123, 239. - A determinate figure supposed to be common to all the particles of a - crystal, 242. - - - D’Alembert, his improvements in hydrodynamics, 236. - - Dalton, his announcement of the atomic theory, 305. - His examination of gases and vapours, 319. - - Davy, Sir H., brings the voltaic pile to bear upon the earths and - alkalies, 339. - - Deduction, utility of, 174. - - De l’Isle, Romé, his study of crystalline bodies, 239. - - Dew, causes of, investigated, 159. - Effects of, on different substances, 160. - Objects capable of contracting it, 161. - A cloudless sky favourable to its production, 162. - General proximate cause of, 163. - - Drummond, lieutenant, his improvement on lenses for lamps of - lighthouses, 56. - - Dynamics, importance of, 96, 223. - - - Earth, the orbit of,--diminution of its eccentricity round - the sun, 147. - - Economy, political, 73. - - Egypt, great pyramid of, height, weight, and ground occupied by - it, 60. - Accuracy of the astronomical records of, 265. - - Elasticity, an ultimate phenomenon, 90. - - Electricity may be the cause of magnetism, 93. - Universality of, 329. - Effects of, 330. - Activity of, 331. - Equilibrium of, 332. - Productive of chemical decomposition, 338. - - Empirical laws, 178. - Evils resulting from, 179. - - Encke, professor, his prediction of the return of the comet so many - times in succession, 156. - - Englefield, sir H., his analysis of a solar beam, 314. - - Equilibrium maintained by force, 222. - - Erman, professor, his opinion of the effects of the voltaic - circuit, 340. - - Euler, his improvement on Newton’s theory of sound, 247. - - Experience, source of our knowledge of nature’s laws, 76. - - Experiment, a means of acquiring experience, 76. - Utility of, 151. - - - Facts, the observation of, 118. - - Faujas de St. Fond, imaginary craters of, 131. - - Fluids, laws of the motion of, 181. - Compressibility of, 225. - Consideration of the motions of, more complicated than that of - equilibrium, 235. - - Force, analysis of, 86. - The cause of motion, 149. - Phenomena of, 221. - Molecular forces, 245. - - Fourier, baron, his opinion that the celestial regions have a - temperature, independent of the sun, not greatly inferior - to that at which quicksilver congeals, 157. - His analysis of the laws of conduction and radiation of heat, 317. - - Franklin, Dr., his experiments on electricity, 332. - - Fresnel, M., his mathematical explanation of the phenomena of double - refraction, 32. - His improvement on lenses for lamps of lighthouses, 56. - His opinions on the nature of light, 207. - His experiments on the interference of polarized light, 261. - His theory of polarization, 262. - - Friction, a source of heat, 313. - - - Galileo, celebrity of, for his knowledge of science, 72. - His exposition of the Aristotelian philosophy, 110. - His refutation of Aristotle’s dogmas respecting motion, his - persecution in consequence of it, 113. - His knowledge of the accelerating power of gravity, 168. - His knowledge of the weight of the atmosphere, 228. - - Galvani, utility of his discoveries in electricity, 335. - His application of it to animals, 336. - - Gay-Lussac, his examination of gases and vapours, 319. - - Generalization, inductive, 1, 90. - - Geology, 281. - Its rank as a science, 287. - - Geometry, axioms of, an appeal to experience, not corporeal, but - mental, 95. - - Gilbert, Dr., of Colchester, his knowledge of magnetism and - electricity, 112. - - Gravitation, law of, a physical axiom of a very high and universal - kind, 98. - Influence of, decreases in the inverse ratio of the square of the - distance, 123. - - Greece, philosophers of, their extraordinary success in abstract - reasoning, and their careless consideration of external - nature, 105. - Their general character, 106. - Philosophy of, 108. - - Grimaldi, a jesuit of Bologna, his discovery of diffraction, or - inflection of light, 252. - - Guinea and feather experiment, 168. - - Gunpowder, invention of, 55. - A mechanical agent, 62. - - - Haarlem lake, draining of, 61. - - Harmony, sense of, 248. - - Head, captain, anecdote of, 84. - - Heat, 193. - Radiation and conduction of, 205. - One of the chief agents in chemistry, 310. - Our ignorance of the nature of, 310. - Abuse of the sense of the term, 311. - The general heads under which it is studied, 312. - Its most obvious sources, 312. - Animal heat, to what process referable, 313. - Radiation and conduction of, 314. - Solar heat differs from terrestrial fires, or hot bodies, 315. - Principal effects of, 317. - The antagonist to mutual attraction, 322. - Latent heat, 322. - Specific heat, 323. - - Herschel, sir William, his analysis of a solar beam, 314. - - Hipparchus, his catalogue of stars, 276. - - Holland drained of water by windmills, 61. - - Hooke almost the rival of Newton, 116. - - Huel Towan, steam-engine at, 59. - - Huyghens, his doctrine of light, 207. - Ascertains the laws of double refraction, 254. - - Hydrostatics, first step towards a knowledge of, made by - Archimedes, 231. - Law of the equal pressure of liquids, 232. - General applicability of, 232. - - Hypothesis, not to be deterred from framing them, 196. - Conditions on which they should be framed, 197. - Illustrated by the laws of gravitation, 198. - Use and abuse of, 204. - - - Induction, different ways of carrying it on, 102. - Steps by which it is arrived at on a legitimate and extensive - scale, 118. - First stage of, 144. - Verification of, 164. - Instanced in astronomy, 166. - Must be followed into all its consequences, and applied to all those - cases which seem even remotely to bear upon the subject of - enquiry, 173. - Nature of the inductions by which quantitative laws are arrived - at, 176. - Necessity of induction embracing a series of cases which absolutely - include the whole scale of variation of which the quantities - in question admit, 177. - - Induced electricity, 333. - - Inertia, 223. - - Iodine, discovery of, 50. - Efficacy of, in curing goître, 51. - - Isomorphism, law of, 170. - - - Kepler, effect of his discoveries on the Aristotelian philosophy, 113. - Nature of his laws of the planetary system, 178. - Proofs of the Newtonian system, 179. - - Knowledge, physical facts illustrative of the utility of, 45. - Diffusion of, how to take advantage of in the investigation of - nature, 138. - - - Lagrange, his improvements on Newton’s theory of sound, 247. - His astronomical researches, 275. - - Lamp, safety, 55. - - Laplace, his explanation of the residual velocity of sound and - confirmation of the general law of the developement of heat - by compression, 172. - His astronomical research, 275. - His experiments on the dilatation of bodies by heat, 319. - His study of specific heat, 323. - Latent heat, 323. - - Laws, inductive, 171. - General, 198. - How applicable, 199. - Illustrated by the planetary system, 201. - Empirical laws, 178. - - Lavoisier, his improvements in chemical science, 302. - Experiments on dilatation of bodies by heat, 319. - His investigation on specific heat, 323. - - Light, refraction of, 30. - Double refraction of, 31. - Polarization of, 254. - - Light and vision, ignorance of the ancients respecting, 249. - - Lighthouse, 56. - - Lightning, how to judge philosophically of it, 120. - Returning stroke of, 121. - - Liquids, cohesion, attraction and repulsion of the particles of, 227. - Differ from aëriform fluids by their cohesion, 233. - The Florentine experiment on; experiments by Canton, Perkins, - Oërsted, and others on, 235. - Obscurity of the laws of dilatation of, 320. - - Linnæus, his knowledge of crystalline substances, 239. - - Logic, 19. - - Lyell’s Principles of Geology, extract from, 146. - - - Magnetism may be caused by electricity, 93. - Offers a “glaring instance” of polarity, 326. - Experiments illustrative of, 327. - - Malus, a French officer of engineers, discovers the polarization of - light, 132, 258. - - Man, regarded as a creature of instinct, 1. - Of reason and speculation, 3. - His will determined by causes and consequences, 6. - Advantages to, from the study of science, 7. - His necessity to study the laws of nature illustrated, 66. - Happiness and the opposite state of man in the aggregate, 67. - Advantages conferred on, by the augmentation of physical - resources, 68. - Advantages from intellectual resources, 69. - - Mariotte, his law of equilibrium of an elastic fluid recently verified - by the Royal Academy of Paris, 231. - His difference between solar and other heat, 315. - - Matter, indestructibility of; Divided by grinding, 40. - By fire, 41. - Dilated by heat, 193. - Inertia of, 202. - Polarity of, one of the ultimate phenomena to which the analysis of - nature leads us, 245. - Inherent activity of, 297. - Causes of the polarity of, 299. - Imponderable forms of, 310. - - Measure, the standard, difficulty of preserving it unaltered, 128. - How to be assisted in measurement, 129. - Our conclusions from, should be conditional, 130. - - Menai Bridge, weight and height of, 60. - - Mechanics, practical, 63. - - Mètre, the French, 126. - - Microscopes, power of, 191. - - Millstones, method of making in France, 48. - - Mind, its transition from the little to the great, and _vice versâ_, - illustrated, 172. - - Mineralogy unknown to the ancients, 79. - Prejudiced by the rage for nomenclature, 139. - Benefited by the progress of chemical analysis, 293. - - Minerals, simple, apparent paucity of, 294. - Difficulty in classing them, 295. - - Mitscherlich, his law of isomorphism, 170. - His experiments on the expansion of substances by heat, 243. - - Motion, 87. - Simplicity and precision of the laws of, 179. - - - Nature, laws of, 37. - Immutability of, 42. - Harmony of, and advantage of studying them, 43. - Prove the impossibility of attaining the declared object of the - alchemist. How they serve mankind generally, 44. - Illustrated by mining, 45. - Economy derived from a knowledge of, 65. - How to be regarded, 100, 101. - - Nature, objects of, an enumeration and nomenclature of, useful in the - study of, 135. - Mechanism of, on too large or too small a scale to be immediately - cognisable by our senses, 191. - - Newton, his proof of Galileo’s laws of gravitation by an experiment - with a hollow glass pendulum, 160. - His foundation to hydrodynamical science, 181. - Fixes the division between statics and dynamics, 223. - His investigation of the law of equilibrium of elastic fluids, 231. - His law of hydrostatics, 232. - His foundation of hydrodynamics 236. - His analysis of sound, 247. - Hypothesis of light, 250. - Examination of a soap-bubble, 252. - His hypothesis of fits of easy transmission and reflection, 253. - His combination of mathematical skill with physical research, 271. - His Principia, 272. - His successors; his geometry, 273. - - Nomenclature, importance of, to science, 136. - More a consequence than a cause of extended knowledge, 138. - Prejudicial to mineralogy, 139. - - Norman, Robert, his discovery of the dip of the needle, 327. - - Numerical precision, necessity of, in science, 122. - - - Objects, and their mutual actions, subjects of contemplation, 118. - - Observation, a means of acquiring experience, 76. - Passive and active, 77. - Recorded observation, 120. - Necessity of, to acquire precise physical data, 215. - Illustrated by the barometer, 216. - - Oërsted, his discoveries in electricity and magnetism, 132. - Of electro-magnetism, 340. - - Opacity, 189. - - Otto von Guericke of Magdeburgh, his invention of the air-pump, 230. - - - Paracelsus, power of his chemical remedies; his use of mercury, - opium, and tartar, 112. - - Pascal, his crucial instances proving the weight of air, 229. - - Pendulum, 126. - - Phenomena, analysis of, illustrated by musical sounds, the sensation - of taste, 85. - The ultimate and inward process of nature in the production of, 86. - Analysis of complex phenomena, 88. - Ultimate phenomena, 90. - How the analysis of, is useful, 97. - A transient phenomenon, how to judge of, 122. - Method of explaining one when it presents itself, 148. - How to discover the cause of one, 150. - Two, or many, theories, maintained as the origin of, in - physics, 195. - Cosmical phenomena, 265. - - Philosophy, natural, unfounded objections to the study of, 7. - Advantages derivable from the study of, 10. - Pleasure and happiness, the consequences of the study of, 15. - - Phlogistic doctrines of Beccher and Stahl, 300. - - Physical data, necessity of, 209. - Great importance of, 211. - Illustrated by the erection of observatories, 213. - Necessity of an exact knowledge of, 214. - More precise than the observations by which we acquire them, 215. - - Physics, axioms of; analysis of, 102. - - Planets, circumjovial, 186. - - Platina, discovery of, 308. - - Pliny, his knowledge of quartz and diamond, 239. - - Pneumatics, 228. - - Political economy, 73. - - Prejudices of opinion and sense, 80. - Conditions on which such are injurious, 81. - Illustrated by the division of the rays of light, by the moon at the - horizon, and by ventriloquism, 82. - By the transition of the hand from heat to cold, 83. - - Prevost, M., his theory of heat, 316. - His theory of reciprocal interchanges, a proof of the radiation - of cold, 318. - - Printing, the art of, 193. - Performed by steam, 194. - - Probabilities, doctrine of, 217. - Illustrated by shooting at a wafer, 218. - - Prout, Dr., his opinion of the atomic weights, 307. - - Pyrometry, 319. - - Pythagoras, philosophy of, 107. - - - Quinine, sulphate of, comparative comfort and health resulting from - the use of, 56. - - - Radiation of heat, laws of, 205. - - Repulsion in fluids and solids, 227. - - Rules, general, for guiding and facilitating our search among a great - mass of assembled facts, 151. - - Rumford, count, experiments of, on gunpowder, 62. - - - Savart, M., his experiments on solids, 243. - His researches on sound, 249. - - Science, abstract, a preparation for the study of physics, 19. - Not indispensable to the study of physical laws, 25. - Instances illustrative of, 27. - - Science, physical, nature and objects, immediate and collateral, as - regarded in itself and in its application to the practical - purposes of life, and its influence on society, 35. - State of, previous to the age of Galileo and Bacon, 104. - Causes of the rapid advance of, compared with the progress at an - earlier period, 347. - - Science, natural, cause and effect, the ultimate relations of, 76. - - Sciences and Arts, remarks on the language, terms, or signs used in - treating of them, 70. - Receive an impulse by the Baconian philosophy, 114. - - Sensation, cause of, 91. - - Senses, inadequate to give us direct information for the exact - comparison of quantity, 124. - Substitutes for the inefficiency of, 125. - - Seringapatam, method of breaking blocks from the quarries of, 47. - - Shells found in rocks at a great height above the sea, supposed - cause of, 145. - - Smeaton, his experiments on bodies dilated by heat, 319. - - Solids, transparent, exhibit periodical colours when exposed to - polarized light, 99. - Influence of, on the Mind, 101. - - Solids in general, nature of, 236. - Constitution of, complicated, 237. - Toughness of, distinct from hardness; tenacity of, 238. - Become liquefied by the addition of heat, 321. - - Sounds, musical, illustrative of the analysis of phenomena, 85. - Means of having a knowledge of, 89. - Propagation of, through the air, 246. - Newton’s analysis of, 247. - - Standard measurement, necessity of, 125. - Laws of nature used as such, illustrated by the rotation of the - earth, 126. - - Substances all subject to dilatation by the addition of heat, 243. - - Sun, the character of the heat of, 315. - - - Thales, philosophy of, 107. - - Theories, how to estimate the value of, 204. - Best arrived at by the consideration of general laws, 208. - Explanatory of the phenomena of nature; on what their application - ought to be grounded, 209. - - Thomson, Dr., his opinion of the atomic weights, 307. - - Thermometer, air, 319. - - Thermo-electricity, 341. - - Time, division of, 126, 127. - - Torricelli, pupil of Galileo, his experiments proving the weight of - atmosphere, 229. - - Torpedo, shock of, 341, 342. - - - Ulugh Begh, his catalogue of stars, 277. - - - Vaccination, success of, as a preventive to small-pox, 52. - - Vision and light, ignorance of the ancients respecting, 249. - - Volta, his discoveries in electricity, 335. - Electric pile of, 337. - - Voltaic circuit, 338. - - - Water, effects of the power of, 61. - - Whewell, his experiments, 187. - - Wells, Dr., his theory of dew, 163. - - Wind, effects of the power of, 61. - - Wire steel, magnetized masks of, used by needle-makers, 57. - - Wollaston, Dr., his verification of the laws of double refraction in - Iceland spar, 258. - His invention of the goniometer, 292. - - World, the materials of the, 290. - - - Young, Dr., his experiments on the interference of the rays of - light, 260. - - - Zoology, fossil, 344. - - -THE END. - - - LONDON - PRINTED BY SPOTTISWOODE AND CO. - NEW-STREET SQUARE. - - - - -FOOTNOTES - - -[1] Hooke’s Posthumous Works. Lond. 1705.--p. 472 and p. 458. - -[2] Wealth of Nations, book i. chap. i. p. 15. - -[3] On this subject, we cannot forbear citing a passage from one of -the most profound but at the same time popular writers of our time, on -a subject unconnected it is true with our own, but bearing strongly -on the point before us. “But, if science be manifestly incomplete, -and yet of the highest importance, it would surely be most unwise -to restrain enquiry, conducted on just principles, even where the -immediate practical utility of it was not visible. In mathematics, -chemistry, and every branch of natural philosophy, how many are the -enquiries necessary for their improvement and completion, which, taken -separately, do not appear to lead to any specifically advantageous -purpose! how many useful inventions, and how much valuable and -improving knowledge, would have been lost, if a rational curiosity, -and a mere love of information, had not generally been allowed to be a -sufficient motive for the search after truth!”--Malthus’s Principles of -Political Economy, p. 16. - -[4] Λογος, _ratio_, reason. - -[5] Λογος, _verbum_, a word. - -[6] It were much to be wished that navigators would be more cautious in -laying themselves open to a similar censure. On looking hastily over -a map of the world we see three Melville Islands, two King George’s -Sounds, and Cape Blancos innumerable. - -[7] Young. Lectures on Nat. Phil. ii. 627. See also Phil. Trans. 1801-2. - -[8] Captain Basil Hall, R. N. - -[9] We must caution our readers who would assure themselves of it by -trial, that it is an experiment of some delicacy, and not to be made -without several precautions to ensure success. For these we must refer -to our original authority (Fresnel. Mémoire sur la Diffraction de la -Lumiere, p. 124.); and the principles on which they depend will of -course be detailed in that volume of the Cabinet Cyclopædia which is -devoted to the subject of LIGHT. - -[10] Little reels used in cotton mills to twist the thread. - -[11] Such a block would weigh between four and five hundred thousand -pounds. See Dr. Kennedy’s “Account of the Erection of a Granite Obelisk -of a Single Stone about Seventy Feet high, at Seringapatam.”--_Ed. -Phil. Trans._ vol. ix, p. 312. - -[12] Dr. Coindet of Geneva. - -[13] Journal of a Voyage to the South Seas, &c. &c. under the Command -of Commodore George Anson, in 1740-1744, by Pascoe Thomas, Lond. 1745, -So tremendous were the ravages of scurvy, that, in the year 1726, -admiral Hosier sailed with seven ships of the line to the West Indies, -and buried his ships’ companies twice, and died himself in consequence -of a broken heart. Dr. Johnson, in the year 1778, could describe a -sea-life in such terms as these:--“As to the sailor, when you look down -from the quarter deck to the space below, you see the utmost extremity -of human misery, such crowding, such filth, such stench!”--“A ship is -a prison with the chance of being drowned--it is worse--worse in every -respect--worse room, worse air, worse food--worse company!” Smollet, -who had personal experience of the horrors of a seafaring life in those -days, gives a lively picture of them in his Roderick Random. - -[14] Lemon juice was known to be a remedy for scurvy far superior -to all others 200 years ago, as appears by the writings of Woodall. -His work is entitled “The Surgeon’s Mate, or Military and Domestic -Medicine. By John Woodall, Master in Surgery London, 1636,” p. 165. In -1600, Commodore Lancaster sailed from England with three other ships -for the Cape of Good Hope, on the 2d of April, and arrived in Saldanha -Bay on the 1st of August, the commodore’s own ship being in perfect -health, from the administration of three table-spoonsfull of lemon -juice every morning to each of his men, whereas the other ships were so -sickly as to be unmanageable for want of hands, and the commander was -obliged to send men on board to take in their sails and hoist out their -boats. (Purchas’s Pilgrim, vol. i. p. 149.) A Fellow of the college, -and an eminent practitioner, in 1753 published a tract on sea scurvy, -in which he adverts to the superior virtue of this medicine; and Mr. A. -Baird, surgeon of the Hector sloop of war, states, that from what he -had seen of its effects on board of that ship, he “thinks he shall not -be accused of presumption in pronouncing it, if properly administered, -a _most infallible remedy_, both in the cure and prevention of -scurvy.” (Vide Trotter’s Medicina Nautica.) The precautions adopted -by captain Cook in his celebrated voyages, had fully demonstrated by -their complete success the practicability of keeping scurvy under in -the longest voyages, but a uniform system of prevention throughout the -service was still deficient. - -It is to the representations of Dr. Blair and sir Gilbert Blane, in -their capacity of commissioners of the board for sick and wounded -seamen, in 1795, we believe, that its _systematic introduction into -nautical diet_, by a general order of the admiralty, is owing. The -effect of this wise measure (taken, of course, in conjunction with the -general causes of improved health,) may be estimated from the following -facts:--In 1780, the number of cases of scurvy received into Haslar -hospital was 1457; in 1806 _one_ only, and in 1807 _one_. There are now -many surgeons in the navy who have never seen the disease. - -[15] Throughout France the conductor is recognised as a most -valuable and useful instrument; and in those parts of Germany where -thunder-storms are still more common and tremendous they are become -nearly universal. In Munich there is hardly a modern house unprovided -with them, and of a much better construction than ours--several copper -wires twisted into a rope. - -[16] We have been informed by an eminent physician in Rome, (Dr. -Morichini) that a vast quantity of the sulphate of quinine is -manufactured there and consumed in the Campagna, with an evident effect -in mitigating the severity of the malarious complaints which affect its -inhabitants. - -[17] Dr. Johnson, Memoirs of the Medical Society, vol. v. - -[18] The engine at Huel Towan. See Mr. Henwood’s Statement “of the -performance of steam-engines in Cornwall for April, May, and June, -1829.” Brewster’s Journal, Oct. 1829.--The _highest_ monthly average of -this engine extends to 79 millions of pounds. - -[19] However, this is not quite a fair statement; a man’s daily labour -is about 4 lbs. of coals. The extreme toil of this ascent arises from -other obvious causes than the mere height. - -[20] Its surface is about 40,000 acres, and medium depth about 20 feet. -It was proposed to drain it by running embankments across it, and thus -cutting it up into more manageable portions to be drained by windmills. - -[21] No one doubts the _practicability_ of the undertaking. Eight or -nine thousand chaldrons of coals duly burnt would evacuate the whole -contents. But many doubt whether it would be profitable, and some, -considering that a few hundreds of fishermen who gain their livelihood -on its waters would be dispossessed, deny that it would be _desirable_. - -[22] “Experiments to determine the Force of fired Gunpowder.” Phil. -Trans. vol. lxxxvii. p. 254. et seq. - -[23] See a very ingenious application of this kind in Mr. Babbage’s -article on Diving in the Encyc. Metrop.--Others will readily suggest -themselves. For instance, the ballast in reserve of a balloon might -consist of materials capable of evolving great quantities of hydrogen -gas in proportion to their weight, should such be found. - -[24] The sulphuric. Bracconot, Annales de Chimie, vol. xii. p. 184. - -[25] D’Arcet, Annales de l’Industrie, Fevrier, 1829. - -[26] See Dr. Prout’s account of the experiments of professor Autenrieth -of Tubingen. Phil. Trans. 1827, p. 381. This discovery, which renders -famine next to _impossible_, deserves a higher degree of celebrity than -it has obtained. - -[27] Greenwich. - -[28] Maskelyne’s. - -[29] Thomson’s First Principles of Chemistry, vol. ii. p. 68. - -[30] Galileo exposes unsparingly the Aristotelian style of reasoning. -The reader may take the following from him as a specimen of its -quality. The object is to prove the immutability and incorruptibility -of the heavens; and thus it is done:-- - - I. Mutation is either generation or corruption. - - II. Generation and corruption only happen between contraries. - - III. The motions of contraries are contrary. - - IV. The celestial motions are circular. - - V. Circular motions have no contraries. - - α. Because there can be but three simple motions. - 1. To a centre. - 2. Round a centre. - 3. From a centre. - - β. Of three things, one only can be contrary to one. - - γ. But a motion to a centre is manifestly the contrary to a - motion from a centre. - - δ. Therefore a motion _round_ a centre (_i. e._ a circular - motion) remains without a contrary. - - VI. _Therefore_ celestial motions have no contraries--_therefore_ - among celestial _things_ there are no contraries--_therefore_ - the heavens are eternal, immutable, incorruptible, and so forth. - -It is evident that all this string of nonsense depends on the excessive -vagueness of the notions of generation, corruption, contrariety, &c. on -which the changes are rung.--_See_ GALILEO, _Systema Cosmicum_, Dial. -i. p. 30. - -[31] Macquer justly observes, that the alchemists would have rendered -essential service to chemistry had they only related their unsuccessful -experiments as clearly as they have obscurely related those which they -pretend to have been successful.--_Macquer’s Dictionary of Chemistry_, -i. x. - -[32] Paracelsus performed most of these cures by mercury and opium, -the use of which latter drug he had learned in Turkey. Of mercurial -preparations the physicians of his time were ignorant, and of opium -they were afraid, as being “cold in the fourth degree.” Tartar was -likewise a great favourite of Paracelsus, who imposed on it that name, -“because it contains the water, the salt, the oil, and the acid, which -burn the patient as hell does:” in short, a kind of counterbalance to -his opium. - -[33] See the Life of Galileo Galilei, by Mr. Drinkwater, with -Illustrations of the Advancement of Experimental Philosophy. - -[34] The temporary star in Cassiopeia observed by Cornelius Gemma, in -1572, was so bright as to be seen at noon-day. That in Serpentarius, -first seen by Kepler in 1604, exceeded in brilliancy all the other -stars and planets. - -[35] Edinburgh Phil. Journ. 1819, vol. i. p. 8. - -[36] The abstract principle of repetition in matters of measurement -(viz. juxta-position of units without error) is applicable to a great -variety of cases in which quantities are required to be determined to -minute nicety. In chemistry, in determining the standard atomic weights -of bodies, it seems easily and completely applicable, by a process -which will suggest itself at once to every chemist, and seems the only -thing wanting to place the exactness of chemical determinations on a -par with astronomical measurements. - -[37] Accurate and _perfectly_ authentic copies of the yard and pound, -executed in platina, and hermetically sealed in glass, should be -deposited deep in the interior of the massive stone-work of some great -public building, whence they could only be rescued with a degree -of difficulty sufficient to preclude their being disturbed unless -on some very high and urgent occasion. The fact should be publicly -recorded, and its memory preserved by an inscription. Indeed, how much -valuable and useful information of the actual existing state of arts -and knowledge at any period might be transmitted to posterity in a -distinct, tangible, and imperishable form, if, instead of the absurd -and useless deposition of a few coins and medals under the foundations -of buildings, specimens of ingenious implements or condensed statements -of scientific truths, or processes in arts and manufactures, were -substituted. Will books infallibly preserve to a remote posterity all -that we may desire should be hereafter known of ourselves and our -discoveries, or all that posterity would wish to know? and may not a -useless ceremony be thus transformed into an act of enrolment in a -perpetual archive of what we most prize, and acknowledge to be most -valuable? - -[38] In the system alluded to, the name of quartz is assigned to -iolite and obsidian; that of mica to plumbago, chlorite, and uranite; -sulphur, to orpiment and realgar, &c. See Mohs’s System of Mineralogy, -translated by Haidinger. - -[39] The following passage, from Lindley’s Synopsis of the British -Flora, characterises justly the respective merits, in a philosophical -point of view, of natural and artificial systems of classification -in general, though limited in its expression to his own immediate -science:--“After all that has been effected, or is likely to be -accomplished hereafter, there will always be more difficulty in -acquiring a knowledge of the natural system of botany than of the -Linnæan. The latter skims only the surface of things, and leaves the -student in the fancied possession of a sort of information which it is -easy enough to obtain, but which is of little value when acquired: the -former requires a minute investigation of every part and every property -known to exist in plants; but when understood has conveyed to the mind -a store of real information, of the utmost use to man in every station -of life. Whatever the difficulties may be of becoming acquainted with -plants according to this method, they are inseparable from botany, -which cannot be usefully studied without encountering them.” Schiller -has some beautiful lines on this, entitled “Menschliches Wissen” (or -Human Knowledge); Gedichte, vol. i. p. 72. Leipzig, 1800. - -[40] Lyell’s Principles of Geology, vol. i. Fourrier, Mém. de l’Acad. -des Sciences, tom. vii. p. 592. “L’établissement et le progrès des -sociétés humaines, l’action des forces naturelles, peuvent changer -notablement, et dans de vastes contrées, l’état de la surface du sol, -la distribution des eaux, et les grands mouvemens de l’air. De tels -effets sont propres à faire varier, dans le cours de plusieurs siècles, -le dégré de la chaleur moyenne; car les expressions analytiques -comprennent des coefficiens qui se rapportent à l’état superficiel, -et qui influent beaucoup sur la valeur de la température.” In this -enumeration, by M. Fourrier, of causes which may vary the general -relation of the surface of extensive continents to heat, it is but -justice to Mr. Lyell to observe, that the gradual shifting of the -_places_ of the continents themselves on the surface of the globe, -by the abrading action of the sea on the one hand, and the elevating -agency of subterranean forces on the other, does not expressly occur -and cannot be fairly included in the general sense of the passage, -which confines itself to the consideration of such changes as may take -place on the existing surface of the land. - -[41] The reader will find this subject further developed in a paper -lately communicated to the Geological Society. - -[42] Phil. Trans. 1824. - -[43] Wells on Dew. - -[44] Principia, book iii. prop. 6. - -[45] A very curious instance of the pursuit of a law completely -empirical into an extreme case is to be found in Newton’s rule for -the dilatation of his coloured rings seen between glasses at great -obliquities. Optics, book ii. part i. obs. 7. - -[46] See Phil. Trans. 1819. - -[47] “When we are told that Saturn moves in his orbit more than 22,000 -miles an hour, we fancy the motion to be swift; but when we find that -he is more than three hours moving his own diameter, we must then think -it, as it really is, slow.” Thirty Letters on various Subjects, by -William Jackson, 1795. - -[48] Thomson’s First Principles of Chemistry. - -[49] There seems no doubt, however, that an achromatic telescope had -been constructed by a private amateur, a Mr. Hall, some time before -either Euler or Dollond ever thought of it. - -[50] We allude to the recently invented achromatic combinations of -Messrs. Barlow and Rogers, and the dense glasses of which Mr. Faraday -has recently explained the manufacture in a memoir full of the most -beautiful examples of delicate and successful chemical manipulation, -and which promise to give rise to a new era in optical practice, by -which the next generation at least may benefit. See Phil. Trans. 1830. - -[51] Alphonso of Castile, 1252. - -[52] Jackson, Letters on Various Subjects, &c. - -[53] Thomson’s First Principles of Chemistry, Introduction. - -[54] The progress of astronomical discovery has since shown that this -law cannot be relied on (1851). - -[55] Novum Organum, part ii. table 2. (24), (30), &c. on the form or -nature of heat. - -[56] We will mention one which we do not remember to have seen -noticed elsewhere in the case of a disturbance of the equilibrium of -heat produced by means purely mechanical, and by a process depending -entirely on a certain order and sequence of events, and the operation -of known causes. Suppose a quantity of air enclosed in a metallic -reservoir, of some good conductor of heat, and suddenly compressed by -a piston. After giving time for the heat developed by the condensation -to be communicated from the air to the metal which will be thereby -more or less raised in temperature _above_ the surrounding atmosphere, -let the piston be suddenly retracted and the air restored to its -original volume in an instant. The whole apparatus is now precisely in -its initial situation, as to the disposition of its material parts, -and the whole quantity of heat it contains remains unchanged. But it -is evident that the distribution of this heat within it is now very -different from what it was before; for the air in its sudden expansion -cannot re-absorb in an instant of time all the heat it had parted with -to the metal: it will, therefore, have a temperature _below_ that of -the general atmosphere, while the metal yet retains one above it. Thus, -a subversion of the equilibrium of temperature has been _bonâ fide_ -effected. Heat has been driven from the air into the metal, while every -thing else remains unchanged. - -We have here a means by which, it is evident, heat may be obtained, to -any extent, from the air, without fuel. For if, in place of withdrawing -the piston and letting the _same_ air expand, within the reservoir, it -be allowed to escape so suddenly as not to re-absorb the heat given -off, and fresh air be then admitted and the process repeated, any -quantity of air may thus be _drained_ of its heat. - -[57] See Phil. Trans. 1824. - -[58] If the brain be an electric pile, constantly in action, it may be -conceived to discharge itself at regular intervals, when the tension -of the electricity developed reaches a certain point, along the nerves -which communicate with the heart, and thus to excite the pulsations of -that organ. This idea is forcibly suggested by a view of that elegant -apparatus, the dry pile of Deluc; in which the successive accumulations -of electricity are carried off by a suspended ball, which is kept by -the discharges in a state of regular pulsation for any length of time. -We have witnessed the action of such a pile maintained in this way for -whole years in the study of the above-named eminent philosopher. The -same idea of the cause of the pulsation of the heart appears to have -occurred to Dr. Arnott; and is mentioned in his useful and excellent -work on physics, to which however, we are not indebted for the -suggestion, it having occurred to us independently many years ago. - -[59] See a description of a contrivance of this kind by Dr. Young, -Lectures, vol. i. p. 191. - -[60] Boyle’s Works, folio, vol. iii. Essay x. p. 185. - -[61] Jackson, The Four Ages, p. 52. London: Cadell and Davies, 1798. -8vo. - -[62] Jackson, The Four Ages, p. 90. - - - - -Transcriber’s Notes - - -Cover created by Transcriber and placed in the Public Domain. - -Punctuation, hyphenation, and spelling were made consistent when a -predominant preference was found in this book; otherwise they were not -changed. - -Simple typographical errors were corrected; occasional unbalanced -quotation marks retained. - -Ambiguous hyphens at the ends of lines were retained. - -Spelling of non-English words was not reviewed. - -Text uses both “appreciate” and “appretiate”; both retained. - -Index not checked for proper alphabetization or correct page references. - - - - - -End of the Project Gutenberg EBook of Preliminary Discourse on the Study of -Natural Philosophy, by John F. W. 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