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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..d7b82bc --- /dev/null +++ b/.gitattributes @@ -0,0 +1,4 @@ +*.txt text eol=lf +*.htm text eol=lf +*.html text eol=lf +*.md text eol=lf diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..645058f --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #54897 (https://www.gutenberg.org/ebooks/54897) 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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display: block; text-align: center;} - .narrow_container {width: 90%; margin-left: 5%;} -} - </style> - </head> - -<body> - - -<pre> - -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) - - - - - - -</pre> - - -<div class="transnote covernote"> -<p class="center">Transcriber’s Note: Cover created by Transcriber and placed in the Public Domain.</p> -</div> - -<h1 class="wspace"> -<i><span class="smcap">Preliminary discourse</span></i><br /> -<span class="smaller">on the Study of</span><br /> -<span class="larger">NATURAL PHILOSOPHY</span></h1> - -<p class="center large"><span class="small">BY</span><br /> -<span class="bold">SIR JOHN F. W. HERSCHEL, BART. K.H.</span><br /> -<span class="larger"><i>M.A.—D.C.L.—F.R.S.L&E.—M.R.I.A.—F.R.A.S.<br /> -F.G.S.—M.C.U.P.S.—&c. &c.</i></span></p> - -<p class="p1 center wspace">NEW EDITION.<br /> -1851. -</p> - -<div class="figcenter" style="max-width: 23em;"> -<img src="images/title.jpg" width="364" height="404" alt="Bacon" /> -<div class="caption floatl"><i>H. Corbould del.</i></div> -<div class="caption floatr"><i>E. Finden. sculp.</i></div> -</div> - -<p class="p2 center large"><span class="xxsmall">NATURÆ MINISTER ET INTERPRES.</span></p> - -<p class="p2 center vspace"> -<span class="bold">NEW EDITION.</span><br /> -London:<br /> -<span class="small">PRINTED FOR LONGMAN, BROWN, GREEN & LONGMANS, PATERNOSTER ROW</span> -</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_v">v</a></span></p> - -<div class="chapter"> -<h2><a id="CONTENTS"></a>CONTENTS.</h2> -</div> - -<table summary="Contents"> - <tr class="smaller"> - <td> </td> - <td class="tdr">Page</td></tr> - <tr> - <td class="tdc part nopad" colspan="2"><a href="#hdr_1">PART I.</a></td></tr> - <tr> - <td class="tdc" colspan="2">OF THE GENERAL NATURE AND ADVANTAGES OF THE STUDY OF THE PHYSICAL SCIENCES.</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_2">CHAP. I.</a></td></tr> - <tr> - <td class="tdl">Of Man regarded as a Creature of Instinct, of Reason, and Speculation.—General Influence of Scientific Pursuits on the Mind.</td> - <td class="tdr">1</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_3">CHAP. II.</a></td></tr> - <tr> - <td class="tdl">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.</td> - <td class="tdr">18</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_4">CHAP. III.</a></td></tr> - <tr> - <td class="tdl">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.</td> - <td class="tdr">35</td></tr> - <tr> - <td class="tdc part" colspan="2"><a href="#hdr_5">PART II.</a><span class="pagenum"><a id="Page_vi">vi</a></span></td></tr> - <tr> - <td class="tdl justify" colspan="2">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.</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_6">CHAP. I.</a></td></tr> - <tr> - <td class="tdl">Of Experience as the Source of our Knowledge.—Of the Dismissal of Prejudices.—Of the Evidence of our Senses.</td> - <td class="tdr">75</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_7">CHAP. II.</a></td></tr> - <tr> - <td class="tdl">Of the Analysis of Phenomena.</td> - <td class="tdr">85</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_8">CHAP. III.</a></td></tr> - <tr> - <td class="tdl">Of the State of Physical Science in General, previous to the Age of Galileo and Bacon.</td> - <td class="tdr">104</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_9">CHAP. IV.</a></td></tr> - <tr> - <td class="tdl">Of the Observation of Facts and the Collection of Instances.</td> - <td class="tdr">118</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_10">CHAP. V.</a></td></tr> - <tr> - <td class="tdl">Of the Classification of Natural Objects and Phenomena, and of Nomenclature.</td> - <td class="tdr">135</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_11">CHAP. VI.</a></td></tr> - <tr> - <td class="tdl">Of the First Stage of Induction.—The Discovery of Proximate Causes, and Laws of the lowest Degree of Generality, and their Verification.</td> - <td class="tdr">144</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_12">CHAP. VII.</a></td></tr> - <tr> - <td class="tdl">Of the higher Degrees of Inductive Generalization, and of the Formation and Verification of Theories.</td> - <td class="tdr">190</td></tr> - <tr> - <td class="tdc part" colspan="2"><a href="#hdr_13">PART III.</a><span class="pagenum"><a id="Page_vii">vii</a></span></td></tr> - <tr> - <td class="tdc" colspan="2">OF THE SUBDIVISION OF PHYSICS INTO DISTINCT BRANCHES, AND THEIR MUTUAL RELATIONS.</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_14">CHAP. I.</a></td></tr> - <tr> - <td class="tdl">Of the Phenomena of Force, and of the Constitution of Natural Bodies.</td> - <td class="tdr">221</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_15">CHAP. II.</a></td></tr> - <tr> - <td class="tdl">Of the Communication of Motion through Bodies.—Of Sound and Light.</td> - <td class="tdr">246</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_16">CHAP. III.</a></td></tr> - <tr> - <td class="tdl">Of Cosmical Phenomena.</td> - <td class="tdr">265</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_17">CHAP. IV.</a></td></tr> - <tr> - <td class="tdl">Of the Examination of the material Constituents of the World.</td> - <td class="tdr">290</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_18">CHAP. V.</a></td></tr> - <tr> - <td class="tdl">Of the Imponderable Forms of Matter.</td> - <td class="tdr">310</td></tr> - <tr> - <td class="tdc chap" colspan="2"><a href="#hdr_19">CHAP. VI.</a></td></tr> - <tr> - <td class="tdl">Of the Causes of the actual rapid Advance of the Physical Sciences compared with their Progress at an earlier Period.</td> - <td class="tdr">347</td></tr> -</table> - -<hr /> - -<p><span class="pagenum"><a id="Page_viii">viii</a></span></p> - -<div class="narrow_container"> -<p>“In primis, hominis est propria <span class="smcap smaller">VERI</span> 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 <span class="smcap smaller">VERUM</span>, 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.”</p> - -<p class="sigright"> -<span class="smcap">Cicero, de Officiis</span>, Lib. 1. § 13. -</p> - -<p>Before all other things, man is distinguished by his pursuit and investigation -of <span class="smcap smaller">TRUTH</span>. 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 <span class="smcap smaller">TRUE</span>, 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.</p> -</div> - -<hr /> - -<p><span class="pagenum"><a id="Page_1">1</a></span></p> - -<div class="chapter"> -<h2><span class="large wspace">PRELIMINARY DISCOURSE<br /> -ON<br /> -THE STUDY<br /> -OF<br /> -NATURAL PHILOSOPHY.</span></h2> -</div> - -<hr class="narrow" /> -<h2 id="hdr_1"><span class="larger">PART I.</span></h2> - -<p class="center">OF THE GENERAL NATURE AND ADVANTAGES OF -THE STUDY OF THE PHYSICAL SCIENCES</p> - -<hr class="narrow"/> -<h2 id="hdr_2">CHAPTER I.</h2> - -<blockquote class="hang"> - -<p>OF MAN REGARDED AS A CREATURE OF INSTINCT, OF -REASON, AND SPECULATION.—GENERAL INFLUENCE OF -SCIENTIFIC PURSUITS ON THE MIND.</p></blockquote> - -<p class="in0">(1.) <span class="smcap"><span class="flet">T</span>he</span> 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<span class="pagenum"><a id="Page_2">2</a></span> -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<span class="pagenum"><a id="Page_3">3</a></span> -regions, where the warmth of the climate, the paucity -of enemies, and the abundance of vegetable food, -might permit it to linger.</p> - -<p>(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<span class="pagenum"><a id="Page_4">4</a></span> -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<span class="pagenum"><a id="Page_5">5</a></span> -falls back on itself in utter hopelessness of arriving -at an end.</p> - -<p>(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 <em>how</em> 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 <em>himself</em>, 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.</p> - -<p>(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<span class="pagenum"><a id="Page_6">6</a></span> -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 <em>cause</em>, 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, “<em>a being -darkly wise</em>;” 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<span class="pagenum"><a id="Page_7">7</a></span> -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?</p> - -<p>(5.) Nothing, then, can be more unfounded than -the objection which has been taken, <i xml:lang="la" lang="la">in limine</i>, -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<span class="pagenum"><a id="Page_8">8</a></span> -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.</p> - -<p>(6.) But while we thus vindicate the study of natural -philosophy from a charge at one time formidable,<span class="pagenum"><a id="Page_9">9</a></span> -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<span class="pagenum"><a id="Page_10">10</a></span> -of <em>any</em> evidence may be destroyed by -tampering with its <em>honesty</em>; 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 <em>fair</em> discussion.</p> - -<p>(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 “<i xml:lang="la" lang="la">cui bono</i>” 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 <em>this</em> 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<span class="pagenum"><a id="Page_11">11</a></span> -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 “<em>Swing-swangs</em>” in -Hooke’s time<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">1</a> did not prevent him from reviving -the proposal of the <em>pendulum</em> 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<span class="pagenum"><a id="Page_12">12</a></span> -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.</p> - -<p>(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<a id="FNanchor_2" href="#Footnote_2" class="fnanchor">2</a>, 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 <em>prove</em> his sums, or a cautious -geometer to try his general theorems by particular -cases.<a id="FNanchor_3" href="#Footnote_3" class="fnanchor">3</a></p> - -<p><span class="pagenum"><a id="Page_13">13</a></span> -(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.</p> - -<p>(10.) We must never forget that it is principles, -not phenomena,—the interpretation, not the mere<span class="pagenum"><a id="Page_14">14</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_15">15</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_16">16</a></span> -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<span class="pagenum"><a id="Page_17">17</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_18">18</a></span></p> - -<div class="chapter"> -<h2 id="hdr_3">CHAP. II.</h2> -</div> - -<blockquote class="hang"> - -<p class="b2">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.</p></blockquote> - -<p class="in0">(13.) <span class="smcap"><span class="flet">S</span>cience</span> 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 <em>abstract</em>, that of -causes and their effects, and of the laws of nature, -<em>natural science</em>.</p> - -<p>(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 <em>be</em>, 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, <em>language</em>, -oral or written; its conventional forms, which constitute -grammar, and the rules for its use in argument,<span class="pagenum"><a id="Page_19">19</a></span> -in which consists the logic of the schools; secondly, -<em>notation</em>, which, applied to <em>number</em>, is <em>arithmetic</em>,—and, -to the more general relations of abstract quantity -or order, is <em>algebra</em>; 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 <em>rational</em><a id="FNanchor_4" href="#Footnote_4" class="fnanchor">4</a>; while, -to that inferior department which is conversant with -words alone, the epithet <em>verbal</em><a id="FNanchor_5" href="#Footnote_5" class="fnanchor">5</a> may, for distinction, -be applied.</p> - -<p>(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,<span class="pagenum"><a id="Page_20">20</a></span> -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 <em>iron</em> 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<span class="pagenum"><a id="Page_21">21</a></span> -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 <em>think</em> 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.<a id="FNanchor_6" href="#Footnote_6" class="fnanchor">6</a></p> - -<p>(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;<span class="pagenum"><a id="Page_22">22</a></span> -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.</p> - -<p id="p17">(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 -<em>is</em>, 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,<span class="pagenum"><a id="Page_23">23</a></span> -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<span class="pagenum"><a id="Page_24">24</a></span> -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 <em>how</em> such things were ever made out.</p> - -<p>(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 <em>difference</em> 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.<a id="FNanchor_7" href="#Footnote_7" class="fnanchor">7</a> Do not such things sound more like<span class="pagenum"><a id="Page_25">25</a></span> -the ravings of madmen, than the sober conclusions of -people in their waking senses?</p> - -<p>(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 <em>have</em> 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 <em>this</em>, not vaguely and generally, -but with all possible precision in time, place, -weight, and measure.</p> - -<p>(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<span class="pagenum"><a id="Page_26">26</a></span> -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 -<em>some</em> acquaintance with geometry, the principal -<em>results</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_27">27</a></span> -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<span class="pagenum"><a id="Page_28">28</a></span> -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<a id="FNanchor_8" href="#Footnote_8" class="fnanchor">8</a>, 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<span class="pagenum"><a id="Page_29">29</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_30">30</a></span> -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 <em>refraction</em> of light; and a simple rule discovered -by Willebrod Snell enables any one to say -exactly <em>how much</em> the stick will be bent, and <em>how -far</em>, and in what <em>direction</em>, 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 <em>aside</em> to the <em>right</em> or <em>left</em> of its true place, -however the eye be situated. The <em>plane</em>, 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 <em>vertical</em> plane; and this is one of the -principal characters in the <em>ordinary refraction</em> 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 <em>quit a plane -perpendicular to the refracting surface</em>. But there -are again other substances, such as rock-crystal, and -especially Iceland spar, which possess the singular -property of <em>doubling</em> 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<span class="pagenum"><a id="Page_31">31</a></span> -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 <em>double refraction</em>. 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 <em>extraordinary refraction</em>) <em>does</em> -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 <em>grain</em> which -glass has not. When other substances having this -peculiarity (and which are called <em>crystallized</em> substances) -were examined, they were all, or by far the -greater part, found to possess this singular property -of <em>double refraction</em>; 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, <em>one</em> only was turned aside out of its<span class="pagenum"><a id="Page_32">32</a></span> -<em>plane</em> and <em>extraordinarily</em> refracted, while the other -followed the <em>ordinary</em> 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.</p> - -<p>(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 -<em>principles</em> 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 <em>that</em>, when applied to the cases first mentioned, -these principles give a satisfactory account -of the <em>want</em> of the extraordinary image; <em>that</em> 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 <em>fact</em> -which had never been observed, viz. that in by far -the greater number of crystallized substances which -possess the property of double refraction, <em>neither</em> 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<span class="pagenum"><a id="Page_33">33</a></span> -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 <em>mere</em> 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.</p> - -<p>(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 <em>centre of the shadow</em> of a small circular -plate of metal, exposed in a dark room to a beam of -light emanating from a <em>very small brilliant point</em>,<span class="pagenum"><a id="Page_34">34</a></span> -there ought to be no darkness,—in fact, <em>no shadow</em> -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.<a id="FNanchor_9" href="#Footnote_9" class="fnanchor">9</a></p> - -<p>(25.) We shall now proceed to consider more -particularly, and in <span class="locked">detail,—</span></p> - -<blockquote class="hang2"> - -<p> <span class="ii">I.</span> 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.</p> - -<p> <span class="iii">II.</span> 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.</p> - -<p>III. The subdivision of physical science into distinct -branches, and their mutual relations.</p></blockquote> - -<hr /> - -<p><span class="pagenum"><a id="Page_35">35</a></span></p> - -<div class="chapter"> -<h2 id="hdr_4">CHAP. III.</h2> -</div> - -<blockquote class="hang"> - -<p>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.</p></blockquote> - -<p class="in0">(26.) <span class="smcap"><span class="flet">T</span>he</span> 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 -<em>has</em> 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 <em>order of nature</em> 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<span class="pagenum"><a id="Page_36">36</a></span> -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. “<i xml:lang="la" lang="la">Si -quis mala carmina condidisset, fuste ferito</i>;” 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 <em>may</em> occur, -and has relation to an infinite number of cases that -never have occurred, and never will. Now, it is -this provision, <i xml:lang="la" lang="la">à priori</i>, for contingencies, this contemplation -of possible occurrences, and predisposal -of what shall happen, that impresses us with -the notion of a <em>law</em> and a <em>cause</em>. 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 <em>some</em> 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 <em>already fixed</em> what they will do -when the case does occur. They will obey certain -laws, of which we know nothing at present, but -which must <em>be</em> 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<span class="pagenum"><a id="Page_37">37</a></span> -implicit obedience,—and of this kind are the laws -of nature.</p> - -<p>(27.) This use of the word <em>law</em>, 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 <em>compliance</em> 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 <em>spirit</em>, not the <em>letter</em>, 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.</p> - -<p>(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 <em>atoms</em>, 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<span class="pagenum"><a id="Page_38">38</a></span> -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, <em>exactly alike</em> 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<a id="FNanchor_10" href="#Footnote_10" class="fnanchor">10</a>, -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 -<em>all</em> respects and <em>for ever</em>, 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 <em>eternal self-existent matter</em>, by giving to -each of its atoms the essential characters, at once, -of a <em>manufactured article</em>, and a <em>subordinate agent</em>.</p> - -<p>(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<span class="pagenum"><a id="Page_39">39</a></span> -for him in the endeavour to discover, as far as our -faculties will permit, what <em>are</em> these primary qualities -originally and unalterably impressed on matter, and -to discover the <em>spirit</em> of the laws of nature, which -includes groups and classes of relations and facts -from the <em>letter</em> 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 <em>occult</em>, 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 -<em>represent</em> the greatest possible multitude and variety -of phenomena.</p> - -<p>(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 <em>have</em> 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<span class="pagenum"><a id="Page_40">40</a></span> -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.</p> - -<p>(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 <em>appearances</em> -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<span class="pagenum"><a id="Page_41">41</a></span> -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 <em>seems</em> 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 <em>whole</em> 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.</p> - -<p><span class="pagenum"><a id="Page_42">42</a></span> -(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, <i xml:lang="la" lang="la">à priori</i>, that the laws -of nature are <em>immutable</em>; but we can ascertain, by -enquiry, <em>whether they change or not</em>; 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.</p> - -<p>(33.) But the laws of nature are not only permanent, -but consistent, intelligible, and discoverable<span class="pagenum"><a id="Page_43">43</a></span> -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.</p> - -<p>(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.<span class="pagenum"><a id="Page_44">44</a></span> -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!</p> - -<p>(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 <span class="locked">mankind,—</span></p> - -<blockquote class="hang2"> - -<p><span class="ii">I.</span> <i>In showing us how to avoid attempting impossibilities.</i></p> - -<p><span class="iii">II.</span> <i>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.</i></p> - -<p>III. <i>In enabling us to accomplish our ends in the -easiest, shortest, most economical, and most -effectual manner.</i></p> - -<p><span class="iiv">IV.</span> <i>In inducing us to attempt, and enabling us to -accomplish, objects which, but for such knowledge, -we should never have thought of undertaking.</i></p></blockquote> - -<p class="in0"><span class="pagenum"><a id="Page_45">45</a></span> -We shall therefore proceed to illustrate by examples -the effect of physical knowledge under each of these -<span class="locked">heads:—</span></p> - -<p>(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 <em>in</em> the -Hastings’ <em>sand</em>; while this, on which Bexhill is -situated, is separated from the <em>coal-strata</em> by a -series of interposed beds of such enormous thickness -as to render all idea of penetrating <em>through</em> -them absurd. The history of mining operations is -full of similar cases, where a very moderate acquaintance -with the <em>usual order of nature</em>, to say -nothing of theoretical views, would have saved -many a sanguine adventurer from utter ruin.</p> - -<p>(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 -<em>air</em> into the furnace through the intervention of<span class="pagenum"><a id="Page_46">46</a></span> -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 -<em>blew it out</em>; 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.</p> - -<p>(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<span class="pagenum"><a id="Page_47">47</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_48">48</a></span> -easily explained without entering into particulars of -mineralogical detail.<a id="FNanchor_11" href="#Footnote_11" class="fnanchor">11</a></p> - -<p>(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.</p> - -<p>(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>i. e.</i> to the ordinary operation of natural -causes, are done, and well done, but with extreme<span class="pagenum"><a id="Page_49">49</a></span> -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 <em>directness</em> of application of the principles on -which they depend, to the objects intended to be -attained.</p> - -<p>(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<span class="pagenum"><a id="Page_50">50</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_51">51</a></span> -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<a id="FNanchor_12" href="#Footnote_12" class="fnanchor">12</a> 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 <i xml:lang="la" lang="la">goître</i>—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 <i xml:lang="la" lang="la">goître</i>, -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<span class="pagenum"><a id="Page_52">52</a></span> -person infallibly repays itself with interest, though -often in a way that could never have been at first -contemplated.</p> - -<p>(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.<a id="FNanchor_13" href="#Footnote_13" class="fnanchor">13</a> At present the scurvy is almost<span class="pagenum"><a id="Page_53">53</a></span> -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<a id="FNanchor_14" href="#Footnote_14" class="fnanchor">14</a> whose skill and discrimination have thus<span class="pagenum"><a id="Page_54">54</a></span> -strengthened the sinews of our most powerful arm, -and obliterated one of the darkest features in the -most glorious of all professions.</p> - -<p>(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<span class="pagenum"><a id="Page_55">55</a></span> -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 <em>conductor</em>, -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<a id="FNanchor_15" href="#Footnote_15" class="fnanchor">15</a>:—the <em>safety-lamp</em>, -which enables us to walk with light and<span class="pagenum"><a id="Page_56">56</a></span> -security while surrounded with an atmosphere more -explosive than gunpowder:—the <em>life-boat</em>, 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 -<em>lighthouse</em>, 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 <em>quinine</em>, -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 <em>comparative</em> comfort -and health through regions almost desolated by -pestiferous exhalations<a id="FNanchor_16" href="#Footnote_16" class="fnanchor">16</a>;—and, if we desist, it is -not because the list is exhausted, but because a -sample, not a catalogue, is intended.</p> - -<p>(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<span class="pagenum"><a id="Page_57">57</a></span> -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.<a id="FNanchor_17" href="#Footnote_17" class="fnanchor">17</a> 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 <em>strained</em> but <em>searched</em> in its passage through -them, and each obnoxious atom arrested and removed.</p> - -<p>(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 <em>usual order -of nature</em>, without any attempt on our part to modify -it, and apart from all consideration of its causes,<span class="pagenum"><a id="Page_58">58</a></span> -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 -<em>laws of mortality</em>, 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 <em>does</em> 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.</p> - -<p><span class="pagenum"><a id="Page_59">59</a></span> -(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 <em>are</em>, 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.</p> - -<p>(49.) It is well known to modern engineers, that -<em>there is virtue</em> in a bushel of coals properly consumed, -to raise seventy millions of pounds weight a -foot high. This is actually the <em>average</em> effect of an -engine at this moment working in Cornwall.<a id="FNanchor_18" href="#Footnote_18" class="fnanchor">18</a> Let -us pause a moment, and consider what this is -equivalent to in matters of practice.</p> - -<p>(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.<a id="FNanchor_19" href="#Footnote_19" class="fnanchor">19</a></p> - -<p><span class="pagenum"><a id="Page_60">60</a></span> -(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.</p> - -<p>(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.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_61">61</a></span> -we to say 100 millions instead of 70, we should probably -be nearer the truth.</p> - -<p>(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 <em>do</em> 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<a id="FNanchor_20" href="#Footnote_20" class="fnanchor">20</a> would seem a hopeless -project to any speculators but those who had the -steam-engine at their command, or had learnt in<span class="pagenum"><a id="Page_62">62</a></span> -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.<a id="FNanchor_21" href="#Footnote_21" class="fnanchor">21</a></p> - -<p>(56.) To gunpowder, as a source of mechanical -power, it seems hardly necessary to call attention; -yet it is only when we endeavour to <em>confine</em> 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, <em>which it just filled</em>, tore asunder -a piece of iron which would have resisted a strain of -400,000 lbs.<a id="FNanchor_22" href="#Footnote_22" class="fnanchor">22</a>, applied at no greater mechanical disadvantage.</p> - -<p>(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<span class="pagenum"><a id="Page_63">63</a></span> -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.<a id="FNanchor_23" href="#Footnote_23" class="fnanchor">23</a></p> - -<p>(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 <em>scientific art</em>; 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<span class="pagenum"><a id="Page_64">64</a></span> -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.</p> - -<p>(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 <em>more than their own weight</em> of sugar, by -the simple agency of one of the cheapest and most<span class="pagenum"><a id="Page_65">65</a></span> -abundant acids?<a id="FNanchor_24" href="#Footnote_24" class="fnanchor">24</a>—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?<a id="FNanchor_25" href="#Footnote_25" class="fnanchor">25</a>—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?<a id="FNanchor_26" href="#Footnote_26" class="fnanchor">26</a> 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!</p> - -<p><span class="pagenum"><a id="Page_66">66</a></span> -(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 <em>average</em> 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<span class="pagenum"><a id="Page_67">67</a></span> -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.</p> - -<p>(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 <em>very</em> 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 <em>rate of dilatation</em> which -every degree upward of the scale, so to speak, exhibits,<span class="pagenum"><a id="Page_68">68</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_69">69</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_70">70</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_71">71</a></span> -accumulated experience, the art is <em>empirical</em>; but -if it be experience reasoned upon and brought under -general principles, it assumes a higher character, -and becomes a <em>scientific art</em>. 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<span class="pagenum"><a id="Page_72">72</a></span> -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 <em>applying science</em>. 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.</p> - -<p>(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<span class="pagenum"><a id="Page_73">73</a></span> -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 <em>are</em> truly great and noble, either -in themselves, or as conducive to others of a still -loftier character; because we are not now, as heretofore,<span class="pagenum"><a id="Page_74">74</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_75">75</a></span></p> - -<div class="chapter"> -<h2 id="hdr_5"><span class="larger">PART II.</span></h2> -</div> - -<blockquote class="hang"> - -<p>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.</p></blockquote> - -<h2 id="hdr_6">CHAPTER I.</h2> - -<blockquote> - -<p class="center b2">OF EXPERIENCE AS THE SOURCE OF OUR KNOWLEDGE.—OF -THE DISMISSAL OF PREJUDICES.—OF THE EVIDENCE -OF OUR SENSES.</p></blockquote> - -<p class="in0">(66.) <span class="smcap"><span class="flet">I</span>nto</span> abstract science, as we have before observed, -the notion of cause does not enter. The -truths it is conversant with are <em>necessary</em> ones, and -exist independent of cause. There may be -no such real <em>thing</em> 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 <em>causes</em> or <em>makes</em> all -the diameters of an ellipse to be bisected in its<span class="pagenum"><a id="Page_76">76</a></span> -centre. To assert the contrary, would not be to -rebel against a power, but to deny our own words. -But in natural science <em>cause</em> and <em>effect</em> are the ultimate -relations we contemplate; and <em>laws</em>, 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.</p> - -<p>(67.) We have thus pointed out to us, as the great, -and indeed only ultimate source of our knowledge of -nature and its laws, <span class="smcap smaller">EXPERIENCE</span>; 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 <span class="smcap smaller">OBSERVATION</span>: -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 <span class="smcap smaller">EXPERIMENT</span>. To -these two sources we must look as the fountains of -all natural science. It is not intended, however, by<span class="pagenum"><a id="Page_77">77</a></span> -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 <em>passive</em> -and <em>active observation</em> 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<span class="pagenum"><a id="Page_78">78</a></span> -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 <em>trial</em>, 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<a id="FNanchor_27" href="#Footnote_27" class="fnanchor">27</a>, during -a single lifetime<a id="FNanchor_28" href="#Footnote_28" class="fnanchor">28</a>, the whole of this most perfect -of sciences might, from those data, and as to -the objects included in them, be at once reconstructed,<span class="pagenum"><a id="Page_79">79</a></span> -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 <em>cloven</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_80">80</a></span> -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 -<em>is</em>. 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 <span class="locked">are,—</span></p> - -<p class="in0 in4"> -1. Prejudices of opinion.<br /> -2. Prejudices of sense. -</p> - -<p>(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 <em>fall</em> -from the air, &c.</p> - -<p>(70.) To combat and destroy such prejudices we -may proceed in two ways, either by demonstrating<span class="pagenum"><a id="Page_81">81</a></span> -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, <i xml:lang="la" lang="la">pigris radicibus</i>, 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.</p> - -<p>(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 <em>by counter evidence of the same sort</em>; -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<span class="pagenum"><a id="Page_82">82</a></span> -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 <em>colour</em> of an object is an -inherent quality, like its weight, hardness, &c. and -that to <em>see</em> the object, and see it <em>of its own colour</em>, -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 <em>not in the least -degree mixing with that it so exhibits</em>.</p> - -<p>(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<span class="pagenum"><a id="Page_83">83</a></span> -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.</p> - -<p>(73.) These, and innumerable instances we might -cite, will convince us, that though we are never deceived -in the <em>sensible impression</em> 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.</p> - -<p>(74.) As the mind exists not in the place of sensible<span class="pagenum"><a id="Page_84">84</a></span> -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.</p> - -<p>(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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_85">85</a></span></p> - -<div class="chapter"> -<h2 id="hdr_7">CHAP. II.</h2> -</div> - -<p class="center b2">OF THE ANALYSIS OF PHENOMENA</p> - -<p class="in0">(76.) <i><span class="smcap"><span class="flet">P</span>henomena</span></i>, 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 <em>sensible</em>; 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<span class="pagenum"><a id="Page_86">86</a></span> -trace. A simple experiment will serve to set this -in a clearer light. A solution of the salt called by -chemists <em>nitrate of silver</em>, and another of the <em>hyposulphite -of soda</em>, 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 <em>tungstate of soda</em> when first tasted is -sweet, but speedily changes to an intense and pure -bitter, like quassia.<a id="FNanchor_29" href="#Footnote_29" class="fnanchor">29</a></p> - -<p>(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 <em>direct</em> 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 <em>force</em>. 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<span class="pagenum"><a id="Page_87">87</a></span> -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 <em>motion</em>. -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 -<em>force</em>; but when set at liberty, habit alone would -enable us to recognize its exertion by its <em>signal</em>, -motion, and <em>that</em> 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 <em>causes</em>, -we may judge from this, that when we put any limb -in motion, the seat of the exertion seems to us to -be <em>in</em> 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.</p> - -<p>(78.) This one instance of the obscurity which -hangs about the only act of direct <em>causation</em> 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<span class="pagenum"><a id="Page_88">88</a></span> -teach us to limit our views to that of <em>laws</em>, 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 <em>cause</em>, viz. the exertion of mechanical -<em>force</em>; 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.</p> - -<p>(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,<span class="pagenum"><a id="Page_89">89</a></span> -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.</p> - -<p>(80.) Thus, then, we see that an analysis of the -phenomenon of sound leads to the enquiry, 1st, of -two <em>causes</em>, 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<span class="pagenum"><a id="Page_90">90</a></span> -motion of material bodies and its cause, such as, -<em>What will happen</em> when a moving body is surrounded -on all sides by others not in motion? <em>What -will happen</em> 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 <em>laws of motion</em>, 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 <em>ultimate phenomena</em>, -and referable to the direct action of causes, viz. -an attractive and a repulsive <em>force</em>.</p> - -<p>(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<span class="pagenum"><a id="Page_91">91</a></span> -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 <em>law</em> of equilibrium, -whatever law that may be.</p> - -<p>(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>i. e.</i> 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!</p> - -<p>(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<span class="pagenum"><a id="Page_92">92</a></span> -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 <em>are</em> 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 -<i xml:lang="la" lang="la">à priori</i>. 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 <em>element</em> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_93">93</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_94">94</a></span> -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, <i xml:lang="la" lang="la">mutatis mutandis</i>, 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.</p> - -<p>(86.) On those phenomena which are most frequently -encountered in an analysis of nature and<span class="pagenum"><a id="Page_95">95</a></span> -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.</p> - -<p><span class="pagenum"><a id="Page_96">96</a></span> -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.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_97">97</a></span> -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 <i xml:lang="la" lang="la">à priori</i>. 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 <em>individual facts</em>, 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<span class="pagenum"><a id="Page_98">98</a></span> -in Fresnel’s <i xml:lang="la" lang="la">à priori</i> 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.</p> - -<p>(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 <em>abstract</em>, all the circumstances -in which they disagree, and retain in -our minds those only in which they agree, and<span class="pagenum"><a id="Page_99">99</a></span> -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.</p> - -<p>(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 “<em>polarized</em>,”) 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. <em>transparent solids</em> exhibit periodical colours by -exposure to polarized light. However, this, though -true of many, does not apply to <em>all</em> 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 <em>transparent</em>, -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<span class="pagenum"><a id="Page_100">100</a></span> -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 <a href="#Page_30">30</a>.) and therefore we -may describe them all truly as <em>doubly refracting -substances</em>. 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.</p> - -<p>(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<span class="pagenum"><a id="Page_101">101</a></span> -of double refraction, and the exhibition of -periodical colours; which in the actual case is one -of the most important, viz. the relation of <em>constant -association</em>, inasmuch as it asserts that in whatever -individual the one character is found, the other will -invariably be found also.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_102">102</a></span> -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.</p> - -<p>(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 <em>general facts</em>, 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 <em>axioms</em> of the -highest degree of generality of which science is -capable.</p> - -<p>(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<span class="pagenum"><a id="Page_103">103</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_104">104</a></span></p> - -<div class="chapter"> -<h2 id="hdr_8">CHAP. III.</h2> -</div> - -<p class="center">OF THE STATE OF PHYSICAL SCIENCE IN GENERAL, PREVIOUS -TO THE AGE OF GALILEO AND BACON.</p> - -<p class="in0">(96.) <span class="smcap"><span class="flet">I</span>t</span> 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<span class="pagenum"><a id="Page_105">105</a></span> -to be, fulfilled, with a promptness and liberality -which even its illustrious author in his most sanguine -mood would have hardly ventured to anticipate.</p> - -<p>(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<span class="pagenum"><a id="Page_106">106</a></span> -getting out of the difficulty than by having recourse -to endless combinations of circular motions to preserve -their ideal perfection.</p> - -<p>(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<span class="pagenum"><a id="Page_107">107</a></span> -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.</p> - -<p>(99.) But the successors of these <i xml:lang="la" lang="la">bonâ fide</i> 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<span class="pagenum"><a id="Page_108">108</a></span> -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.</p> - -<p>(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 <i xml:lang="la" lang="la">priori</i> 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 -<em>axioms</em>, 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 <em>fire</em> the essential matter -and origin of the universe; another, <em>air</em>; a third, -discovers the key to every difficulty, and the explanation -of all phenomena, in the “<span xml:lang="grc" lang="grc">το απειρον</span>” or -infinitude of things; a fourth, in the <span xml:lang="grc" lang="grc">το ὁν</span> and -the <span xml:lang="grc" lang="grc">το μη ὁν</span>, that is to say, in entity and nonentity;—<span class="pagenum"><a id="Page_109">109</a></span>till -at length an authority, which was destined to -command opinions for nearly two thousand years, -settled this important point, by deciding, that <em>matter</em>, -<em>form</em>, and <em>privation</em>, were to be considered the principles -of all things.</p> - -<p>(101.) It were to do injustice to Aristotle, however, -to judge of him by <em>such</em> 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<span class="pagenum"><a id="Page_110">110</a></span> -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.<a id="FNanchor_30" href="#Footnote_30" class="fnanchor">30</a><span class="pagenum"><a id="Page_111">111</a></span> -Of course there will occur a limit beyond which -it <em>is</em> 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 <em>have</em> attained -it, is now universally recognized as the sure criterion -of dogmatism.</p> - -<p>(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.</p> - -<p>(103.) In “this opake of nature and of soul,” -the perverse activity of the alchemists from time -to time struck out a doubtful spark<a id="FNanchor_31" href="#Footnote_31" class="fnanchor">31</a>; and our<span class="pagenum"><a id="Page_112">112</a></span> -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<a id="FNanchor_32" href="#Footnote_32" class="fnanchor">32</a>, 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<span class="pagenum"><a id="Page_113">113</a></span> -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.</p> - -<p>(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<a id="FNanchor_33" href="#Footnote_33" class="fnanchor">33</a> to require repetition here.</p> - -<p>(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<span class="pagenum"><a id="Page_114">114</a></span> -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.</p> - -<p>(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,<span class="pagenum"><a id="Page_115">115</a></span> -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 <em>matters of fact</em>; 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 <em>the infinite</em> 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.<a id="FNanchor_34" href="#Footnote_34" class="fnanchor">34</a></p> - -<p>(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,<span class="pagenum"><a id="Page_116">116</a></span> -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.</p> - -<p>(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,<span class="pagenum"><a id="Page_117">117</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_118">118</a></span></p> - -<div class="chapter"> -<h2 id="hdr_9">CHAP. IV.</h2> -</div> - -<p class="center">OF THE OBSERVATION OF FACTS AND THE COLLECTION -OF INSTANCES.</p> - -<p class="in0">(109.) <span class="smcap"><span class="flet">N</span>ature</span> 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,<span class="pagenum"><a id="Page_119">119</a></span> -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.</p> - -<p>(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>i. e.</i> 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 <em>always</em> happen again if those<span class="pagenum"><a id="Page_120">120</a></span> -circumstances, so far as we have been able to collect -them, co-exist?</p> - -<p>(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 <em>the fact</em>. 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 <em>law of nature</em> to the mere record of an -<em>historical event</em>. 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 <em>very -small cloud</em> insulated in <em>a clear sky</em>; a combination -of circumstances which never happens in a thunder -storm, but which is undoubtedly intimately connected -with their real origin.</p> - -<p>(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<span class="pagenum"><a id="Page_121">121</a></span> -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 <em>how</em> the house <em>came to be struck?</em> might -ultimately depend on the fact that a flash of lightning -twenty miles off passed at that particular -moment <em>from the ground to the clouds</em>, by an effect of -what has been termed the returning stroke.</p> - -<p>(113.) A writer in the Edinburgh Philosophical -Journal<a id="FNanchor_35" href="#Footnote_35" class="fnanchor">35</a> 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<span class="pagenum"><a id="Page_122">122</a></span> -liquid about to be thrown away. Chemistry is full -of such incidents.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_123">123</a></span> -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.</p> - -<p>(116.) Indeed, it is a character of all the higher laws -of nature to assume the form of precise <em>quantitative</em> -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.</p> - -<p>(117.) But, to arrive at laws of this description, it is<span class="pagenum"><a id="Page_124">124</a></span> -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<span class="pagenum"><a id="Page_125">125</a></span> -of time, velocity, and all other matters of -quantity; they are absolutely vague, and inadequate -to form a foundation for any exact conclusion.</p> - -<p>(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 <em>standards</em> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_126">126</a></span> -is possible may be themselves inaccurate, or, at least, -stand in need of verification.</p> - -<p>(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 <i xml:lang="fr" lang="fr">mètre</i>, the French unit of linear measure; the -latter, of the British yard. Theoretically speaking, -they are equally eligible; but when we consider that -the <em>quantity directly measured</em>, 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<span class="pagenum"><a id="Page_127">127</a></span> -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.</p> - -<p>(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.</p> - -<p>(122.) It is owing to this peculiar property by -which the <em>juxta-position</em> of units of time and weight -can be performed <em>without error</em>, that the whole of -the accuracy with which time and weight can be -multiplied and subdivided is owing.<a id="FNanchor_36" href="#Footnote_36" class="fnanchor">36</a> The same -thing cannot be accomplished in <em>space</em>, by any method<span class="pagenum"><a id="Page_128">128</a></span> -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.</p> - -<p>(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, -<em>such as we have ourselves used them</em>, 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.<a id="FNanchor_37" href="#Footnote_37" class="fnanchor">37</a></p> - -<p><span class="pagenum"><a id="Page_129">129</a></span> -(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 <em>latitude of error -of observation</em> 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<span class="pagenum"><a id="Page_130">130</a></span> -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 <em>are</em> 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.</p> - -<p>(125.) With respect to our record of observations, -it should be not only circumstantial but <em>faithful</em>; by -which we mean, that it should contain all we did -<em>observe</em>, 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<span class="pagenum"><a id="Page_131">131</a></span> -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 <em>were</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_132">132</a></span> -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.</p> - -<p>(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,<span class="pagenum"><a id="Page_133">133</a></span> -when strongly illuminated by the setting sun, viewed -through a doubly refracting prism.</p> - -<p>(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<span class="pagenum"><a id="Page_134">134</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_135">135</a></span></p> - -<div class="chapter"> -<h2 id="hdr_10">CHAP. V.</h2> -</div> - -<p class="center b2">OF THE CLASSIFICATION OF NATURAL OBJECTS AND -PHENOMENA, AND OF NOMENCLATURE.</p> - -<p class="in0">(129.) <span class="smcap"><span class="flet">T</span>he</span> 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<span class="pagenum"><a id="Page_136">136</a></span> -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.</p> - -<p>(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, “<em>given the one, to determine -the other</em>.” 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<span class="pagenum"><a id="Page_137">137</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_138">138</a></span> -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.</p> - -<p>(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 <em>have</em> 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<span class="pagenum"><a id="Page_139">139</a></span> -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, <em>if possible</em>. 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, <em>unmeaning</em> -name, which has once obtained a footing in -usage, is preferable to almost any other.</p> - -<p>(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<span class="pagenum"><a id="Page_140">140</a></span> -to take root; and every new writer on this interesting -science begins, as a matter of course, by -making a <i xml:lang="la" lang="la">tabula rasa</i> 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 <em>species</em> too definite to admit of mistake, -are actually rendered <em>generic</em>, 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.<a id="FNanchor_38" href="#Footnote_38" class="fnanchor">38</a></p> - -<p>(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<span class="pagenum"><a id="Page_141">141</a></span> -and <i xml:lang="la" lang="la">ipso facto</i> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_142">142</a></span> -<em>opposite</em> of the former, is only its <em>extreme lowest -degree</em>. 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 <em>levity</em>, 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.</p> - -<p>(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<span class="pagenum"><a id="Page_143">143</a></span> -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.<a id="FNanchor_39" href="#Footnote_39" class="fnanchor">39</a></p> - -<hr /> - -<p><span class="pagenum"><a id="Page_144">144</a></span></p> - -<div class="chapter"> -<h2 id="hdr_11">CHAP. VI.</h2> -</div> - -<blockquote class="hang"> - -<p class="center b2">OF THE FIRST STAGE OF INDUCTION.—THE DISCOVERY -OF PROXIMATE CAUSES, AND LAWS OF THE LOWEST -DEGREE OF GENERALITY, AND THEIR VERIFICATION.</p></blockquote> - -<p class="in0">(137.) <span class="smcap"><span class="flet">T</span>he</span> first thing that a philosophic mind -considers, when any new phenomenon presents -itself, is its <em>explanation</em>, or reference to an immediate -producing cause. If that cannot be ascertained, -the next is to <em>generalize</em> 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.</p> - -<p>(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 <i xml:lang="la" lang="la">veræ -causæ</i>; 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<span class="pagenum"><a id="Page_145">145</a></span> -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 <em>is such a thing</em>; 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 <i xml:lang="la" lang="la">vera causa</i> available in -sound philosophy.</p> - -<p>(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<span class="pagenum"><a id="Page_146">146</a></span> -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 -<em>know</em> 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 -<i xml:lang="la" lang="la">vera causa</i>, has, however, been brought forward<a id="FNanchor_40" href="#Footnote_40" class="fnanchor">40</a> -in the varying influence of the distribution of land<span class="pagenum"><a id="Page_147">147</a></span> -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.</p> - -<p>(140.) To this we may add another, which -has likewise the essential characters of a <i xml:lang="la" lang="la">vera -causa</i>, in the astronomical <em>fact</em> of the actual slow -diminution of the eccentricity of the earth’s orbit -round the sun; and which, as a general one, affecting -the <em>mean temperature of the whole globe</em>, 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 -<em>mean</em> 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 <em>total</em> 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<span class="pagenum"><a id="Page_148">148</a></span> -total <em>annual</em> amount of solar radiation will determine, -<i xml:lang="la" lang="la">cæteris paribus</i>, 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 <em>increase</em>, the mean annual amount -of solar radiation received by the whole earth must -be actually on the <em>decrease</em>. We have here, therefore, -an evident real cause, of sufficient universality, -and acting <em>in the right direction</em>, to account -for the phenomenon. Its adequacy is another -consideration.<a id="FNanchor_41" href="#Footnote_41" class="fnanchor">41</a></p> - -<p>(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.</p> - -<p><span class="pagenum"><a id="Page_149">149</a></span> -(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 <em>a force</em> directed to the centre; for we -feel that we do really exert such a force. We have -here <em>the direct perception</em> 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 <em>force</em> 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.</p> - -<p>(143.) In general we must observe that motion, -wherever produced or changed, invariably points -out the existence of <em>force</em> as its cause; and thus -the forces of nature become known and measured<span class="pagenum"><a id="Page_150">150</a></span> -by the motions they produce. Thus, the <em>force</em> 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.<a id="FNanchor_42" href="#Footnote_42" class="fnanchor">42</a></p> - -<p>(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 <em>produce, new facts</em>, 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 “<em>crucial instances</em>,” -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<span class="pagenum"><a id="Page_151">151</a></span> -of <em>experiment</em> 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.</p> - -<p>(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 <span class="locked">are,—</span></p> - -<blockquote class="hang"> - -<p>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.</p> - -<p>2d, Invariable negation of the effect with absence -of the cause, unless some other cause be capable -of producing the same effect.</p> - -<p>3d, Increase or diminution of the effect, with<span class="pagenum"><a id="Page_152">152</a></span> -the increased or diminished intensity of the -cause, in cases which admit of increase and diminution.</p> - -<p>4th, Proportionality of the effect to its cause in -all cases of <em>direct unimpeded</em> action.</p> - -<p>5th, Reversal of the effect with that of the cause.</p></blockquote> - -<p>(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.</p> - -<p>(147.) 2d, That any circumstance in which all -the facts without exception agree, <em>may</em> 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.</p> - -<p id="p148">(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 <i xml:lang="la" lang="la">à priori</i> against the cause, -and try whether it cannot be made apparent.</p> - -<p>(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;<span class="pagenum"><a id="Page_153">153</a></span> -and how such a heat can be maintained, we can -form no conception. Yet we are not, therefore, -entitled to deny the inference.</p> - -<p>(150.) 4th, That contrary or opposing facts are -equally instructive for the discovery of causes with -favourable ones.</p> - -<p>(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 -<em>rust</em>. And, if the remainder be examined, -it is found that it will <em>not</em> 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.</p> - -<p>(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.</p> - -<p id="p153">(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<span class="pagenum"><a id="Page_154">154</a></span> -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.</p> - -<p>(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.</p> - -<p>(155.) Thus, in chemistry, the <em>alkaline</em> 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.</p> - -<p>(156.) 7th, If we can either find produced by -nature, or produce designedly for ourselves, two instances -which agree <em>exactly</em> in all but one particular, -and differ in that one, its influence in producing -the phenomenon, if it have any, <em>must</em> 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<span class="pagenum"><a id="Page_155">155</a></span> -will decide whether it be or be not the -only cause: still more evidently, if it be present -<em>contrariwise</em> in the two cases, and the effect be -thereby reversed. But if its total presence or -absence only produces a change in the <em>degree</em> 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 <em>experiments of enquiry</em> -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.</p> - -<p>(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 <em>this</em> 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 <em>likely</em> to produce this effect, and thus -obtain indirect evidence of its influence. But then -we are always to remember, that the evidence so -obtained <em>is</em> indirect, and that the new circumstance -introduced <em>may</em> have a direct influence of its own, -or may exercise a modifying one on some <em>other</em> -circumstance.</p> - -<p><span class="pagenum"><a id="Page_156">156</a></span> -(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 <em>residual phenomenon</em> 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.</p> - -<p>(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 -<em>residual phenomenon</em>, 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<span class="pagenum"><a id="Page_157">157</a></span> -through the celestial regions; and as -there are other good reasons for believing this to -be a <i xml:lang="la" lang="la">vera causa</i>, it has therefore been ascribed to -such a resistance.</p> - -<p>(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 <i xml:lang="la" lang="la">veræ -causæ</i> why it <em>should</em> 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 <em>residual</em> -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<span class="pagenum"><a id="Page_158">158</a></span> -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.</p> - -<p>(161.) Many of the new elements of chemistry -have been detected in the investigation of <em>residual -phenomena</em>. Thus, Arfwedson discovered lithia by -perceiving an <em>excess of weight</em> 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 <em>small concentrated -residues of great operations</em> 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.</p> - -<p>(162.) Finally, we have to observe, that the detection -of a <em>possible</em> cause, by the comparison of<span class="pagenum"><a id="Page_159">159</a></span> -assembled cases, <em>must</em> 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 <em>their</em> -causes, or the discovery of still more general laws, -and so on without end.</p> - -<p>(163.) Let us now exemplify this inductive search -for a cause by one general example: suppose <em>dew</em> -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 -<em>visible</em> 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 <em>inside</em> 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.</p> - -<p><span class="pagenum"><a id="Page_160">160</a></span> -(164.) But, in the case of the night dew, is this a -<em>real cause</em>—is it a fact that the object dewed <em>is</em> colder -than the air? Certainly not, one would at first be -inclined to say; for what is to <em>make</em> 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 -<em>affirmative</em>. Whenever an object contracts dew, <em>it is</em> -colder than the air. Here, then, we have <em>an invariable -concomitant</em> 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 <em>effect</em> 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 xml:lang="la" lang="la">i. e.</i> where no dew is produced.</p> - -<p>(165.) Now, 1st, no dew is produced on the surface -of <em>polished metals</em>, 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 <em>fall</em> 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<span class="pagenum"><a id="Page_161">161</a></span> -shows evidently that the <em>substance</em> has much to do -with the phenomenon; therefore, let the substance -<em>alone</em> be diversified as much as possible, by exposing -polished surfaces of various kinds. This done, <em>a -scale of intensity</em> 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 <em>law</em> 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 <em>surface</em> therefore -has a great influence. Expose, then, the <em>same</em> material -in very diversified states as to surface (Rule 7. -§ 156.), and another scale of intensity becomes at once -apparent; those <em>surfaces</em> which <em>part with their heat</em> -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 <em>substance</em> and <em>surface</em> leads us to consider that of -<em>texture</em>: and here, again, we are presented on trial -with remarkable differences, and with a third <em>scale -of intensity</em>, 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<span class="pagenum"><a id="Page_162">162</a></span> -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.</p> - -<p>(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 <em>a cloudy night</em>; 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 <em>opposing causes</em>. 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.).</p> - -<p id="p167">(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 <em>all bodies</em> in -rays, or by <em>radiation</em>, but is as constantly restored<span class="pagenum"><a id="Page_163">163</a></span> -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.</p> - -<p>(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<a id="FNanchor_43" href="#Footnote_43" class="fnanchor">43</a> (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.</p> - -<p>(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<span class="pagenum"><a id="Page_164">164</a></span> -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 <em>every particular</em>—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.</p> - -<p>(170.) In the study of nature, we must not, -therefore, be scrupulous as to <em>how</em> 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 <em>verification</em> -of inductions.</p> - -<p id="p171">(171.) If, in our induction, every individual case -has actually been present to our minds, we are sure -that it will find itself duly <em>represented</em> in our final conclusion: -but this is impossible for such cases as -were <em>unknown</em> 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,<span class="pagenum"><a id="Page_165">165</a></span> -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.</p> - -<p>(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 <i xml:lang="la" lang="la">seriatim</i> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_166">166</a></span> -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.</p> - -<p>(174.) Now, this is precisely the sort of process in -which <em>residual phenomena</em> (such as spoken of in art. -158.) may be expected to occur. If our induction -be really a valid and a comprehensive one, <em>whatever</em> -remains unexplained in the comparison of its conclusion -with particular cases, under all their circumstances, -<em>is</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_167">167</a></span> -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.</p> - -<p>(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 <em>universal</em> 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 <em>has</em> 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 <em>extending</em> 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.</p> - -<p>(177.) For example, a fair induction from a<span class="pagenum"><a id="Page_168">168</a></span> -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 <em>in the air</em>, and he will perceive the force of an -<em>extreme case</em>.</p> - -<p>(178.) In the verification of a law whose expression -is <em>quantitative</em>, 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.</p> - -<p>(179.) For instance, let the law to be verified<span class="pagenum"><a id="Page_169">169</a></span> -be, that <em>the gravity of every material body is in the -direct proportion of its mass</em>, 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 <em>without any loss or gain</em> 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 <em>exactly alike</em> 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.<a id="FNanchor_44" href="#Footnote_44" class="fnanchor">44</a>, 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 <em>identical</em> 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.</p> - -<p><span class="pagenum"><a id="Page_170">170</a></span></p> - -<p id="p180">(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—<em>that</em> the chemical elements of which all -bodies consist are susceptible of being classified -in distinct groups, which he termed <i xml:lang="la" lang="la">isomorphous</i> -groups; and <em>that</em> 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 <em>are</em> 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,<span class="pagenum"><a id="Page_171">171</a></span> -pursuing the subject further, the same ingenious -enquirer happily succeeded in producing a <em>new</em> 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.</p> - -<p>(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, <em>yet</em> -the <em>whole</em> velocity could not be shown to arise -from this theory. There was still a <em>residual</em> 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 <em>heat</em> developed in the act<span class="pagenum"><a id="Page_172">172</a></span> -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.</p> - -<p>(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 -<i xml:lang="la" lang="la">vice versâ</i>, 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 <em>why</em> we<span class="pagenum"><a id="Page_173">173</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_174">174</a></span> -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.</p> - -<p>(184.) This remark rather belongs to the inverse -or <em>deductive</em> process, by which we pursue laws into -their remote consequences. But it is very important -to observe, that the successful process of scientific<span class="pagenum"><a id="Page_175">175</a></span> -enquiry demands continually the alternate use of -both the <em>inductive</em> and <em>deductive</em> 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.</p> - -<p>(185.) The verification of <em>quantitative</em> 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<span class="pagenum"><a id="Page_176">176</a></span> -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 <em>data</em>. 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 <em>angle</em> at which -it is inclined to the refracting surface is known, -viz. that the <em>sine</em> 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 <em>depends</em> on or <em>varies with</em> another, -all that is required is a series of careful and exact -measures in every different state of the <em>datum</em> and -<i xml:lang="la" lang="la">quæsitum</i>. Here, however, the mathematical form -of the law being of the highest importance, the -greatest attention must be given to the <em>extreme cases</em> -as well as to all those points where the one quantity -changes rapidly with a small change of the other.<a id="FNanchor_45" href="#Footnote_45" class="fnanchor">45</a> -The results must be set down in a table in which -the <em>datum</em> gradually increases in magnitude from -the lowest to the highest limit of which it is susceptible.<span class="pagenum"><a id="Page_177">177</a></span> -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 <a href="#p194">§ 194</a>.) 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.</p> - -<p>(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 <em>inversely</em> 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<span class="pagenum"><a id="Page_178">178</a></span> -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.</p> - -<p>(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 <em>unverified -inductions</em>, 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 <em>how nearly</em> 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<span class="pagenum"><a id="Page_179">179</a></span> -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.</p> - -<p>(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 -<i xml:lang="la" lang="la">à priori</i> reasoning, as much as geometry; and so it -would be, were our mathematics perfect, and all the -<em>data</em> known. Unhappily, the first is so far from being<span class="pagenum"><a id="Page_180">180</a></span> -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 <em>contain</em> -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 <em>data</em> on which particular applications -are to depend; and although mathematical analysis -affords very powerful means of <em>representing</em> in -general terms the data of any proposed case, and -<em>afterwards</em>, by comparison of its results with fact, -determining <em>what</em> 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 <em>do</em> 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.</p> - -<p><span class="pagenum"><a id="Page_181">181</a></span> -(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.</p> - -<p>(190.) It can hardly be expected that we -should terminate this division of our subject without -some mention of the “prerogatives of instances”<span class="pagenum"><a id="Page_182">182</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_183">183</a></span> -them with each other, before we can tell which <em>are</em> -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 -<em>prerogative</em> 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 -“<em>glaring instance</em>” thus casually obtruded on his -notice, he discovered the beautiful laws of the -cleavage, and the primitive forms of minerals.</p> - -<p>(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 <em>is</em> 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<span class="pagenum"><a id="Page_184">184</a></span> -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 <em>nature</em> or cause enquired -into, (which in this case is the cause of the -assumption of a peculiar external form, or the internal -<em>structure</em> 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.</p> - -<p>(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 <em>clandestine -instance</em> of the “<em>nature</em> 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 <em>extreme cases</em>, such as we have already spoken -of (in § 177.); which, by placing our conclusions, as<span class="pagenum"><a id="Page_185">185</a></span> -it were, in violent circumstances, try their temper, -and bring their vigour to the test.</p> - -<p id="p194">(194.) Bacon’s “collective instances” (<i xml:lang="la" lang="la">instantiæ -unionis</i>), 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 <em>collective instance</em> -of the velocities and directions of the motions -of all the particles which compose it <em>seen at once</em>, -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 <em>collective instances</em> 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.<a id="FNanchor_46" href="#Footnote_46" class="fnanchor">46</a> -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<span class="pagenum"><a id="Page_186">186</a></span> -offers itself spontaneously, and thus furnish advanced -points in our enquiries; and when we start -from these, already “a thousand steps are lost.”</p> - -<p id="p195">(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 <em>circumjovial planets</em> (as they -were called) most materially assisted in securing -the admission of the Copernican system.</p> - -<p>(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<span class="pagenum"><a id="Page_187">187</a></span> -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 <em>clocks</em> he could not have meant -pendulum clocks, which were not then known, (the -first made in England was in 1662,) <em>fly</em>-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 <em>requiring time for its transmission</em>; a consideration -which occurred at a later period to Laplace, -in one of his most delicate investigations.</p> - -<p>(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<span class="pagenum"><a id="Page_188">188</a></span> -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.</p> - -<p>(198.) Bacon’s “travelling instances” are those -in which the <em>nature</em> 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.</p> - -<p>(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.</p> - -<p>(200.) For example, the transparency of gold leaf,<span class="pagenum"><a id="Page_189">189</a></span> -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 <em>contrary</em> or <em>antagonist</em> quality to -that of transparency, but only its extreme lowest -degree.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_190">190</a></span></p> - -<div class="chapter"> -<h2 id="hdr_12">CHAP. VII.</h2> -</div> - -<blockquote class="hang"> - -<p class="center b2">OF THE HIGHER DEGREES OF INDUCTIVE GENERALIZATION, -AND OF THE FORMATION AND VERIFICATION -OF THEORIES.</p></blockquote> - -<p class="in0">(201.) <span class="smcap"><span class="flet">A</span>s</span> 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<span class="pagenum"><a id="Page_191">191</a></span> -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.</p> - -<p>(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 <em>linear</em> 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<span class="pagenum"><a id="Page_192">192</a></span> -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.</p> - -<p>(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 <em>see</em>, 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.<a id="FNanchor_47" href="#Footnote_47" class="fnanchor">47</a> 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.</p> - -<p><span class="pagenum"><a id="Page_193">193</a></span> -(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 <em>is</em> 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 <em>how</em> such a force can be exerted -at a distance, and with empty space, or at most an -invisible fluid, between. (See <a href="#p148">§ 148</a>.)</p> - -<p>(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,<span class="pagenum"><a id="Page_194">194</a></span> -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 <em>why</em> 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.</p> - -<p>(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 <em>hypotheses</em> 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<span class="pagenum"><a id="Page_195">195</a></span> -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.</p> - -<p id="p207">(207.) Now, nothing is more common in physics -than to find two, or even many, <em>theories</em> 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<span class="pagenum"><a id="Page_196">196</a></span> -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.</p> - -<p>(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. -<i xml:lang="la" lang="la">Est quodam prodire tenus si non datur ultra.</i> -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<span class="pagenum"><a id="Page_197">197</a></span> -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.</p> - -<p>(209.) In framing a theory which shall render -a rational account of any natural phenomenon, we -have <em>first</em> 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 <i xml:lang="la" lang="la">veræ -causæ</i>, 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<span class="pagenum"><a id="Page_198">198</a></span> -the theory of gravitation we suppose an agent,—<i>viz.</i> -force, or mechanical power,—to act on <em>any</em> material -body which is placed in the presence of <em>any</em> other, -and to urge the two mutually towards each other. -This is a <i xml:lang="la" lang="la">vera causa</i>; 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 <em>is</em> 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 <em>force</em> -of gravity, is a real cause.</p> - -<p>(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 <i xml:lang="la" lang="la">disjecta membra</i>, generalizing -from them, and so arriving at the laws desired; -2dly, By forming at once a bold hypothesis, particularizing<span class="pagenum"><a id="Page_199">199</a></span> -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, <em>on this comparison</em>, so modifying -and restricting the general enunciation of our -laws as to <em>make the results agree</em>.</p> - -<p>(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<span class="pagenum"><a id="Page_200">200</a></span> -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 <em>places</em>, 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.</p> - -<p>(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.</p> - -<p>(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 <em>all</em> the particulars, nor extended to all<span class="pagenum"><a id="Page_201">201</a></span> -that it is capable of including. (See <a href="#p171">§ 171</a>.) 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 <em>all the planets</em> must attract <em>each other</em>, -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 <em>has</em> been accomplished -by the mere application of the general laws -of dynamics; and the result (undoubtedly a most<span class="pagenum"><a id="Page_202">202</a></span> -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, <em>without</em> which our induction would -be invalid, and the law of gravitation positively untrue.</p> - -<p>(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.</p> - -<p><span class="pagenum"><a id="Page_203">203</a></span> -(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 <em>predict facts before -trial</em>,—we would ask, why should it <em>not</em> 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 <em>pellucid muscle</em>; 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 <em>said</em> 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.</p> - -<p><span class="pagenum"><a id="Page_204">204</a></span> -(216.) In estimating, however, the value of a -theory, we are not to look, <em>in the first instance</em>, -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 <em>all</em> the facts, and -include <em>all</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_205">205</a></span> -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 <em>radiate</em> 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, <em>as if</em> they received the heat -so radiated. Again, all solid bodies which become -heated in one part <em>conduct</em>, 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 <em>laws of radiation</em>; and from the nearer -to the farther part of the colder one, as it gradually -grows warm, by <em>those of conduction</em>. Let -their distance be diminished till they just lightly -touch. How does the heat <em>now</em> 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 <em>forced</em> together, -and it will seem clear that it must now be by -<em>conduction</em>. Yet their <em>interval</em> must diminish gradually,<span class="pagenum"><a id="Page_206">206</a></span> -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. <em>Therefore</em>, 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.</p> - -<p>(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<span class="pagenum"><a id="Page_207">207</a></span> -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 <a href="#p207">§ 207</a>.) -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 <em>between</em> the -two surfaces in apparent contact, as any one may -satisfy himself by using, instead of a flat <em>plate</em> 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 <em>absolutely -black</em>; in the other, <em>half bright</em>, 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.</p> - -<p><span class="pagenum"><a id="Page_208">208</a></span> -(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.</p> - -<p>(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<span class="pagenum"><a id="Page_209">209</a></span> -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 <em>in rejecting them altogether, -we should reject all the discoveries to which they may -lead</em>.</p> - -<p>(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<span class="pagenum"><a id="Page_210">210</a></span> -with each other only in fixed or <em>definite proportions</em> -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 <em>that</em> 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 <em>what are</em> 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<span class="pagenum"><a id="Page_211">211</a></span> -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<a id="FNanchor_48" href="#Footnote_48" class="fnanchor">48</a>; 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.</p> - -<p>(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<span class="pagenum"><a id="Page_212">212</a></span> -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.</p> - -<p>(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.</p> - -<p>(224.) The proof, too, that our data <em>are</em> correctly<span class="pagenum"><a id="Page_213">213</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_214">214</a></span> -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.</p> - -<p>(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, <i xml:lang="la" lang="la">vice versâ</i>, any moderate amount of error, committed -in an observation undertaken for ascertaining -its value, can produce but a very trifling one in the -<em>reverse</em> 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<span class="pagenum"><a id="Page_215">215</a></span> -when the object in view is the determination of -data with the last degree of precision.</p> - -<p>(227.) But how, it may be asked, are we to -ascertain <em>by</em> 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.</p> - -<p>(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.<span class="pagenum"><a id="Page_216">216</a></span> -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 <em>daily</em> -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 <em>sea level</em> 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.</p> - -<p>(229.) In all cases where there is a direct and -simple relation between the phenomenon observed<span class="pagenum"><a id="Page_217">217</a></span> -and a single <em>datum</em> 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 <em>data</em> -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 <em>probable</em> accuracy of our -results, or the limits of error within which it is -<em>probable</em> 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.</p> - -<p>(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 <em>how near</em> he -would come to it, we must first have an idea of his<span class="pagenum"><a id="Page_218">218</a></span> -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 -<em>near</em> (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, <em>before</em> 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 -<em>data</em>; where no two results agree exactly, and<span class="pagenum"><a id="Page_219">219</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_220">220</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_221">221</a></span></p> - -<div class="chapter"> -<h2 id="hdr_13"><span class="larger">PART III.</span></h2> -</div> - -<p class="center">OF THE SUBDIVISION OF PHYSICS INTO DISTINCT -BRANCHES, AND THEIR MUTUAL RELATIONS.</p> - -<h2 id="hdr_14">CHAPTER I.</h2> - -<p class="center b2">OF THE PHENOMENA OF FORCE, AND OF THE CONSTITUTION -OF NATURAL BODIES.</p> - -<p class="in0">(232.) <span class="smcap"><span class="flet">N</span>atural History</span> 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<span class="pagenum"><a id="Page_222">222</a></span> -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.</p> - -<p>(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 -<em>equilibrium</em>; or, 2dly, to produce <em>motion</em> in matter.</p> - -<p>(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<span class="pagenum"><a id="Page_223">223</a></span> -by it on matter, to say that matter is inert, -or has <em>inertia</em>, 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.</p> - -<p>(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 <span class="smcap">Statics</span> -and <span class="smcap">Dynamics</span>; 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 <em>viscous</em>, 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.</p> - -<h3><i>Statics and Dynamics.</i></h3> - -<p>(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<span class="pagenum"><a id="Page_224">224</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_225">225</a></span> -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.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_226">226</a></span> -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 <em>compressed</em> 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 <em>tendency to recede -from one another</em>, which can only be counteracted by -<em>force</em>, 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.</p> - -<p>(240.) What, however, we can only conclude by -this or similar reasoning respecting air, we see distinctly<span class="pagenum"><a id="Page_227">227</a></span> -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 <em>surface</em> while at -rest, and their parts actually resist further separation -with a considerable force, thus giving rise to -the phenomenon of the <em>cohesion of liquids</em>.</p> - -<p>(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.</p> - -<p>(242.) In solids, however, the case is very different. -The mutual free motion of their parts <i xml:lang="la" lang="la">inter se</i> 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<span class="pagenum"><a id="Page_228">228</a></span> -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 -<em>cohere</em> 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.</p> - -<p>(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.</p> - -<h3><i>Pneumatics.</i></h3> - -<p>(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 <em>abhorrence of a -vacuum</em> 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 <em>acting cause</em>, which could urge water -a single foot into a pipe, there is no reason why the<span class="pagenum"><a id="Page_229">229</a></span> -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.</p> - -<p>(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 <em>glaring instance</em>, 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.</p> - -<p>(246.) The discovery of Torricelli was, however, -at first much misconceived, and even disputed, till -the question was finally decided by appeal to a <em>crucial -instance</em>, 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<span class="pagenum"><a id="Page_230">230</a></span> -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 <em>above</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_231">231</a></span> -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.</p> - -<p>(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, <i xml:lang="la" lang="la">cæteris -paribus</i>, 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 -<em>axioms</em> in the science of pneumatics.</p> - -<h3><i>Hydrostatics.</i></h3> - -<p>(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<span class="pagenum"><a id="Page_232">232</a></span> -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 <em>lost</em> is only <em>counteracted</em> 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.</p> - -<p>(250.) The hydrostatical law of <em>the equal pressure -of liquids in all directions</em>, 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.</p> - -<p>(251.) In a practical point of view, this law is<span class="pagenum"><a id="Page_233">233</a></span> -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 <em>at one instant</em> 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 -<em>already full</em>, 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.</p> - -<p>(252.) Liquids differ from aëriform fluids by -their <em>cohesion</em>, 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<span class="pagenum"><a id="Page_234">234</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_235">235</a></span> -investigation seems necessary before we can -be said distinctly to understand it.</p> - -<p>(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.</p> - -<p>(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.</p> - -<p>(256.) Independent of this, there are difficulties<span class="pagenum"><a id="Page_236">236</a></span> -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 <span class="smcap">Hydrodynamics</span>; -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.</p> - -<h3><i>Nature of Solids in general.</i></h3> - -<p>(257.) The intimate constitution of solids is, in all -probability, very complicated, and we cannot be said<span class="pagenum"><a id="Page_237">237</a></span> -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.</p> - -<p>(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,<span class="pagenum"><a id="Page_238">238</a></span> -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.</p> - -<p>(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.</p> - -<p>(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.</p> - -<p><span class="pagenum"><a id="Page_239">239</a></span></p> - -<h3><i>Crystallography.</i></h3> - -<p>(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 <em>substance</em>, 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<span class="pagenum"><a id="Page_240">240</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_241">241</a></span> -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.</p> - -<p>(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 <em>leaning</em> 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, <em>besides this</em>, 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<span class="pagenum"><a id="Page_242">242</a></span> -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.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_243">243</a></span> -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.</p> - -<p>(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 <em>bulk</em> 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<span class="pagenum"><a id="Page_244">244</a></span> -when hot than when cold; and being confined by -the glass ball, (which also expands, but <em>not so much -in proportion</em>,) 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.</p> - -<p>(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 <em>polarity</em>, 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<span class="pagenum"><a id="Page_245">245</a></span> -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 -<em>polarity of matter</em> 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.</p> - -<p>(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 <em>molecular forces</em>. 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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_246">246</a></span></p> - -<div class="chapter"> -<h2 id="hdr_15">CHAP. II.</h2> -</div> - -<p class="center b2">OF THE COMMUNICATION OF MOTION THROUGH -BODIES.—OF SOUND AND LIGHT.</p> - -<p class="in0">(269.) <span class="smcap"><span class="flet">T</span>he</span> 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:<span class="pagenum"><a id="Page_247">247</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_248">248</a></span> -of cases comparatively simple, by any direct reasoning -from first principles.</p> - -<p>(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 <a href="#p153">art. 153</a>.). 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.</p> - -<p>(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<span class="pagenum"><a id="Page_249">249</a></span> -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.</p> - -<h3><i>Light and Vision.</i></h3> - -<p>(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 <em>something</em> 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 <em>light</em> -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,<span class="pagenum"><a id="Page_250">250</a></span> -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 <em>light</em> from those of -<em>vision</em>.</p> - -<p>(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 <a href="#p17">17</a>.), 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 <em>reflected</em> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_251">251</a></span> -success to the explanation of the planetary motions, -not merely a plausible, but a perfectly reasonable -and fair explanation of all the <em>usual</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_252">252</a></span> -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.</p> - -<p>(277.) Other phenomena, however, were not -wanting to afford a further trial of the <em>explanatory -powers</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_253">253</a></span> -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 <em>fits -of easy transmission and reflection</em>; 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<span class="pagenum"><a id="Page_254">254</a></span> -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.</p> - -<p>(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.</p> - -<p>(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 -<em>sides</em>, 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 <em>polarization of light</em>. -These results, however, appeared so extraordinary,<span class="pagenum"><a id="Page_255">255</a></span> -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.</p> - -<p>(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 <em>possibility</em>, and which ultimately -terminated in its complete and happy <em>execution</em> -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.<a id="FNanchor_49" href="#Footnote_49" class="fnanchor">49</a></p> - -<p>(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<span class="pagenum"><a id="Page_256">256</a></span> -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.</p> - -<p>(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.</p> - -<p>(284.) The telescope, as it exists at present, with<span class="pagenum"><a id="Page_257">257</a></span> -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.<a id="FNanchor_50" href="#Footnote_50" class="fnanchor">50</a></p> - -<p>(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,<span class="pagenum"><a id="Page_258">258</a></span> -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 <em>polarization -of light</em> by ordinary reflection at the surface of -a transparent body.</p> - -<p>(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 <em>sides</em>. 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,<span class="pagenum"><a id="Page_259">259</a></span> -that no natural phenomenon can be adequately -studied <em>in itself alone</em>, but, to be understood, must -be considered <em>as it stands connected with all nature</em>.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_260">260</a></span> -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 <em>literally true</em>; 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 <em>interference</em> 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,<span class="pagenum"><a id="Page_261">261</a></span> -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.</p> - -<p>(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 <em>advance</em> and <em>recede</em>; -in the former, those of the ether must be supposed -to <em>tremble laterally</em>.</p> - -<p><span class="pagenum"><a id="Page_262">262</a></span> -(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.</p> - -<p>(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<span class="pagenum"><a id="Page_263">263</a></span> -would be readily enough explained without the admission -of an ether.</p> - -<p>(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,<span class="pagenum"><a id="Page_264">264</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_265">265</a></span></p> - -<div class="chapter"> -<h2 id="hdr_16">CHAP. III.</h2> -</div> - -<p class="center b2">OF COSMICAL PHENOMENA.</p> - -<h3><i>Astronomy and Celestial Mechanics.</i></h3> - -<p class="in0">(293.) <span class="smcap"><span class="flet">A</span>stronomy,</span> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_266">266</a></span> -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<a id="FNanchor_51" href="#Footnote_51" class="fnanchor">51</a> 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.</p> - -<p><span class="pagenum"><a id="Page_267">267</a></span> -(295.) An elegant writer<a id="FNanchor_52" href="#Footnote_52" class="fnanchor">52</a>, 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 <em>plan</em>, but in <em>section</em>.” 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.</p> - -<p>(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<span class="pagenum"><a id="Page_268">268</a></span> -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.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_269">269</a></span> -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 <a href="#p195">195</a>.). 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.</p> - -<p>(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 <em>would</em> 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,<span class="pagenum"><a id="Page_270">270</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_271">271</a></span> -less various and desultory, it can hardly be doubted -that he would have arrived at a knowledge of the -law of gravitation.</p> - -<p>(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<span class="pagenum"><a id="Page_272">272</a></span> -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 <span class="smcap">Newton</span> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_273">273</a></span> -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.</p> - -<p>(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,<span class="pagenum"><a id="Page_274">274</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_275">275</a></span> -deviating from the general analogy of the -others, and offering <em>cases of difficulty</em> 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.</p> - -<p>(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 <em>periodical</em>, -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<span class="pagenum"><a id="Page_276">276</a></span> -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.</p> - -<p>(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, <em>fixed</em>, 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<span class="pagenum"><a id="Page_277">277</a></span> -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.</p> - -<p>(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.</p> - -<p>(308.) The distance of the fixed stars is so immense, -that every attempt to assign a limit, <em>within -which</em> it <em>must</em> 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<span class="pagenum"><a id="Page_278">278</a></span> -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.</p> - -<p>(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 <em>annual parallax</em>, 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<span class="pagenum"><a id="Page_279">279</a></span> -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.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_280">280</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_281">281</a></span> -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.</p> - -<h3><i>Geology.</i></h3> - -<p>(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<span class="pagenum"><a id="Page_282">282</a></span> -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 <em>that</em>, 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.</p> - -<p>(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<span class="pagenum"><a id="Page_283">283</a></span> -evidences of former life and habitation which organised -remains imbedded and preserved in its -strata indisputably afford.</p> - -<p>(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.</p> - -<p>(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.</p> - -<p>(317.) These wrecks of a former state of nature,<span class="pagenum"><a id="Page_284">284</a></span> -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 <em>order</em> of succession in which these -deposits have been formed appears to have been -the same in every part of the globe.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_285">285</a></span> -have been instrumental in the production of those -changes of level, and those violent dislocations -which we perceive to have taken place.</p> - -<p>(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,<span class="pagenum"><a id="Page_286">286</a></span> -and so distributed over time as to produce -none of those <em>interregnums</em> of chaotic anarchy which -we are apt to think (perhaps erroneously) great disfigurements -of an order so beautiful and harmonious -as that of nature.</p> - -<p>(321.) But to estimate justly the effects of -causes now in action in geology is no easy task. -There is no <i xml:lang="la" lang="la">à priori</i> 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 <i xml:lang="la" lang="la">per annum</i> 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.</p> - -<p>(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, <em>all</em> the information that we possess -respecting ancient sea-marks, soundings, &c., we<span class="pagenum"><a id="Page_287">287</a></span> -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 <em>mean</em> 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 <em>mean</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_288">288</a></span> -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<span class="pagenum"><a id="Page_289">289</a></span> -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.</p> - -<p>(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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_290">290</a></span></p> - -<div class="chapter"> -<h2 id="hdr_17">CHAP. IV.</h2> -</div> - -<p class="center b2">OF THE EXAMINATION OF THE MATERIAL CONSTITUENTS -OF THE WORLD.</p> - -<h3><i>Mineralogy.</i></h3> - -<p class="in0">(325.) <span class="smcap"><span class="flet">T</span>he</span> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_291">291</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_292">292</a></span> -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 <i xml:lang="la" lang="la">ab initio</i>.</p> - -<p>(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<span class="pagenum"><a id="Page_293">293</a></span> -by chemical analysis stamped them with a scientific -and decided character which they have retained ever -since.</p> - -<p>(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<span class="pagenum"><a id="Page_294">294</a></span> -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 <em>detritus</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_295">295</a></span> -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.</p> - -<p>(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 <em>isomorphism</em> -of certain groups of chemical elements has already -afforded us an example illustrative of the manner in -which inductions sometimes receive unexpected -verifications (see <a href="#p180">180</a>.). 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<span class="pagenum"><a id="Page_296">296</a></span> -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.</p> - -<h3><i>Chemistry.</i></h3> - -<p>(332.) The laws which concern the intimate constitution -of bodies, not as respects their <em>structure</em> or -the manner in which their parts are put together, -but as regards their <em>materials</em> 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 <em>materials</em> subsists,<span class="pagenum"><a id="Page_297">297</a></span> -giving to them properties differing extremely from -each other.</p> - -<p>(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<span class="pagenum"><a id="Page_298">298</a></span> -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 -<em>union</em> of the ingredients presented to each other; for -when examined it is found that nothing has been -<em>lost</em>, 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.</p> - -<p><span class="pagenum"><a id="Page_299">299</a></span> -(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.</p> - -<p>(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<span class="pagenum"><a id="Page_300">300</a></span> -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 <em>axioms</em> 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.</p> - -<p>(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, <em>in every instance</em>, -by an appeal to the balance. This, too, happened, -not by reason of unlucky coincidences, or individual<span class="pagenum"><a id="Page_301">301</a></span> -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 <em>light</em>. 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 <em>oxygen</em>, from the air, a principle -essentially <em>heavy</em>. 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 <i xml:lang="la" lang="la">vera -causa</i>, the latter an hypothetical being, introduced -to account for what the other accounts for much -better.</p> - -<p>(337.) The third age of chemistry—that which -may be called emphatically modern chemistry—<span class="pagenum"><a id="Page_302">302</a></span>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 <span class="locked">heads:—</span></p> - -<blockquote class="hang2"> - -<p> 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.</p> - -<p> 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.</p> - -<p> 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.</p> - -<p> 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.</p> - -<p> 5. The assimilation of gases and vapours, by which<span class="pagenum"><a id="Page_303">303</a></span> -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.</p> - -<p> 6. The establishment of the laws of the combination -of gases and vapours by definite volumes, -by Gay-Lussac.</p> - -<p> 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.</p> - -<p> 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.</p> - -<p> 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.</p> - -<p>10. The establishment of the intimate connection<span class="pagenum"><a id="Page_304">304</a></span> -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.</p></blockquote> - -<p>(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<span class="pagenum"><a id="Page_305">305</a></span> -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.</p> - -<p>(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<a id="FNanchor_53" href="#Footnote_53" class="fnanchor">53</a>, 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<span class="pagenum"><a id="Page_306">306</a></span> -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.</p> - -<p>(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.</p> - -<p>(341.) The determination of the atomic weights -of the chemical elements, like that of other standard<span class="pagenum"><a id="Page_307">307</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_308">308</a></span> -in observed relations among the <em>data</em> of physics, -which show them to be quantities not <em>arbitrarily</em> -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 <em>four</em> 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.<a id="FNanchor_54" href="#Footnote_54" class="fnanchor">54</a></p> - -<p>(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,<span class="pagenum"><a id="Page_309">309</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_310">310</a></span></p> - -<div class="chapter"> -<h2 id="hdr_18">CHAP. V.</h2> -</div> - -<p class="center b2">OF THE IMPONDERABLE FORMS OF MATTER.</p> - -<h3><i>Heat.</i></h3> - -<p class="in0">(344.) <span class="smcap"><span class="flet">O</span>ne</span> 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 <span class="smcap smaller">HEAT</span>. 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.</p> - -<p>(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<span class="pagenum"><a id="Page_311">311</a></span> -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 <em>hot</em>. This error of -judgment has produced a corresponding confusion -of language, and hence had actually at one period<a id="FNanchor_55" href="#Footnote_55" class="fnanchor">55</a> -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 <em>hot</em> -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.</p> - -<p><span class="pagenum"><a id="Page_312">312</a></span> -(346.) The nature of heat has hitherto been -chiefly studied under the general heads <span class="locked">of—</span></p> - -<blockquote class="hang2"> - -<p>1st, Its sources, or the phenomena which it usually -accompanies.</p> - -<p>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.</p> - -<p>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.</p> - -<p>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.</p></blockquote> - -<p>(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,<span class="pagenum"><a id="Page_313">313</a></span> -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.</p> - -<p>(348.) The most violent heats known are produced<span class="pagenum"><a id="Page_314">314</a></span> -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.</p> - -<p>(349.) Heat is communicated either by <em>radiation</em> -between bodies at a distance, or by <em>conduction</em> -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.</p> - -<p>(350.) The heat, radiated by terrestrial fires, and -by bodies <em>obscurely</em> hot, by whatever means they -have acquired their heat (even by exposure to the<span class="pagenum"><a id="Page_315">315</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_316">316</a></span> -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 -<a href="#p167">167</a>.). 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.</p> - -<p>(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 <em>so</em> 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<span class="pagenum"><a id="Page_317">317</a></span> -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.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_318">318</a></span> -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 <em>both</em> 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<span class="pagenum"><a id="Page_319">319</a></span> -state into vapour, which is the most powerful source -of cold known.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_320">320</a></span> -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 <em>measure</em> 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.</p> - -<p>(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<span class="pagenum"><a id="Page_321">321</a></span> -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.</p> - -<p>(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 <em>heat</em>; 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.</p> - -<p>(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<span class="pagenum"><a id="Page_322">322</a></span> -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.</p> - -<p>(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 <em>hotter</em> 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.</p> - -<p>(361.) Hence he drew the conclusion that it has -become <em>latent</em>, 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,<span class="pagenum"><a id="Page_323">323</a></span> -with which in its radiant state it holds so close an -analogy.</p> - -<p>(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.</p> - -<p><span class="pagenum"><a id="Page_324">324</a></span></p> - -<h3><i>Magnetism and Electricity.</i></h3> - -<p>(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.</p> - -<p><span class="pagenum"><a id="Page_325">325</a></span> -(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”—<em>singular instances</em>. 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<span class="pagenum"><a id="Page_326">326</a></span> -wire of any metal indifferently all the properties of -a magnet;—its attraction, repulsion, and polarity; -and <em>that</em> 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 <em>form</em> 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.”</p> - -<p>(365.) Magnetism is remarkable in another important -point of view. It offers a prominent, or -“<em>glaring instance</em>” of that quality in nature which -is termed <em>polarity</em> (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<span class="pagenum"><a id="Page_327">327</a></span> -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 -<em>poles</em> 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 <em>opposite</em> virtue to its own prevails, and -repel those in which a <em>similar</em> one resides with a -force proportional to the inverse square of their -mutual distance.</p> - -<p>(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 <em>dip</em> or point downwards when rendered magnetic,<span class="pagenum"><a id="Page_328">328</a></span> -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<span class="pagenum"><a id="Page_329">329</a></span> -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.</p> - -<p>(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.</p> - -<p>(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<span class="pagenum"><a id="Page_330">330</a></span> -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 -<em>air</em>, 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.</p> - -<p>(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<span class="pagenum"><a id="Page_331">331</a></span> -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 <em>inertia</em> compared -with its elastic force must be conceived excessively -small, so that it is to be regarded as a fluid in the -highest degree <em>active</em>, 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.<span class="pagenum"><a id="Page_332">332</a></span> -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.</p> - -<p>(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 <em>two distinct fluids</em> -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,<span class="pagenum"><a id="Page_333">333</a></span> -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 <em>induced</em> 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.</p> - -<p>(371.) The most obscure part of the subject is no<span class="pagenum"><a id="Page_334">334</a></span> -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<a id="FNanchor_56" href="#Footnote_56" class="fnanchor">56</a>; but it must be allowed that hitherto<span class="pagenum"><a id="Page_335">335</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_336">336</a></span> -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.</p> - -<p>(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,<span class="pagenum"><a id="Page_337">337</a></span> -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.</p> - -<p>(374.) Though the original pile of Volta was feeble<span class="pagenum"><a id="Page_338">338</a></span> -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 -<em>quantity</em>, accompanied with a diminution of <em>intensity</em> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_339">339</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_340">340</a></span> -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.</p> - -<p>(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<a id="FNanchor_57" href="#Footnote_57" class="fnanchor">57</a> 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<span class="pagenum"><a id="Page_341">341</a></span> -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.</p> - -<p>(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 <i xml:lang="la" lang="la">vera causa</i> 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<span class="pagenum"><a id="Page_342">342</a></span> -those arising from electricity, that they could hardly -be referred to a different source, though <em>besides</em> the -shock neither spark nor any other indication of electrical -tension could be detected in them.</p> - -<p>(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<span class="pagenum"><a id="Page_343">343</a></span> -been devised, as the source of the required electrical -power.<a id="FNanchor_58" href="#Footnote_58" class="fnanchor">58</a></p> - -<p>(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,<span class="pagenum"><a id="Page_344">344</a></span> -but not such as will long detain the reader’s -attention.</p> - -<p>(381.) In <em>zoology</em>, 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.</p> - -<p><span class="pagenum"><a id="Page_345">345</a></span> -(382.) To <em>botany</em> 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<span class="pagenum"><a id="Page_346">346</a></span> -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.</p> - -<hr /> - -<p><span class="pagenum"><a id="Page_347">347</a></span></p> - -<div class="chapter"> -<h2 id="hdr_19">CHAP. VI.</h2> -</div> - -<blockquote class="hang"> - -<p class="center b2">OF THE CAUSES OF THE ACTUAL RAPID ADVANCE OF THE -PHYSICAL SCIENCES COMPARED WITH THEIR PROGRESS -AT AN EARLIER PERIOD.</p></blockquote> - -<p class="in0">(383.) <span class="smcap"><span class="flet">T</span>here</span> 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<span class="pagenum"><a id="Page_348">348</a></span> -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<span class="pagenum"><a id="Page_349">349</a></span> -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.</p> - -<p>(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,<span class="pagenum"><a id="Page_350">350</a></span> -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<span class="pagenum"><a id="Page_351">351</a></span> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_352">352</a></span> -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<span class="pagenum"><a id="Page_353">353</a></span> -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.</p> - -<p>(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 <em>sooner</em> -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<span class="pagenum"><a id="Page_354">354</a></span> -observation we now possess, and employed them as -we employ them now?</p> - -<p>(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.</p> - -<p><span class="pagenum"><a id="Page_355">355</a></span> -(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.<a id="FNanchor_59" href="#Footnote_59" class="fnanchor">59</a> -When the precision attainable by such means is<span class="pagenum"><a id="Page_356">356</a></span> -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.</p> - -<p>(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 <em>methods</em> 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<span class="pagenum"><a id="Page_357">357</a></span> -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.</p> - -<p>(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,—“<cite>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</cite>.”<a id="FNanchor_60" href="#Footnote_60" class="fnanchor">60</a> 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, <em>that</em>, assuredly the noblest of all, -which leads us to a knowledge of the Author of -nature through the contemplation of the wonderful<span class="pagenum"><a id="Page_358">358</a></span> -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,<span class="pagenum"><a id="Page_359">359</a></span> -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?</p> - -<p>(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.<a id="FNanchor_61" href="#Footnote_61" class="fnanchor">61</a> 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,<span class="pagenum"><a id="Page_360">360</a></span> -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.</p> - -<p>(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.”<a id="FNanchor_62" href="#Footnote_62" class="fnanchor">62</a> -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.</p> - -<p>(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<span class="pagenum"><a id="Page_361">361</a></span> -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.</p> - -<p><span class="pagenum"><a id="Page_363">363</a></span></p> - -<hr /> - -<div class="chapter"><div class="index"> -<h2 class="nobreak"><a id="INDEX">INDEX.</a></h2> - -<ul class="index"> -<li class="ifrst">Acoustics cultivated by Pythagoras and Aristotle, page <a href="#Page_248">248</a>.</li> - -<li class="indx">Æpinus, his laws of equilibrium of electricity, <a href="#Page_332">332</a>.</li> - -<li class="indx">Aëriform fluids, liquids kept in a state of vapour, <a href="#Page_321">321</a>.</li> - -<li class="indx">Agricola, George, his knowledge of mineralogy and metallurgy, <a href="#Page_112">112</a>.</li> - -<li class="indx">Air, compressibility and elasticity of; limitation to the repulsive tendency of, <a href="#Page_226">226</a>.</li> -<li class="isub1">Weight of, unknown to the ancients, <a href="#Page_228">228</a>.</li> -<li class="isub1">First perceived by Galileo, <a href="#Page_228">228</a>.</li> -<li class="isub1">Proved by a crucial instance, <a href="#Page_229">229</a>.</li> -<li class="isub1">Equilibrium of, established, <a href="#Page_231">231</a>.</li> -<li class="isub1">Dilatation of, by heat, <a href="#Page_319">319</a>.</li> - -<li class="indx">Air-pump, discovery of, <a href="#Page_230">230</a>.</li> - -<li class="indx">Airy, his experiments in Dolcoath mine, <a href="#Page_187">187</a>.</li> - -<li class="indx">Alchemists, advantages derived from, <a href="#Page_11">11</a>.</li> - -<li class="indx">Algebra, <a href="#Page_19">19</a>.</li> - -<li class="indx">Ampere, his electro-dynamic theory, <a href="#Page_202">202</a>.</li> -<li class="isub1">Utility of, <a href="#Page_203">203</a>, <a href="#Page_324">324</a>.</li> - -<li class="indx">Analysis of force, <a href="#Page_86">86</a>.</li> -<li class="isub1">Of motion, <a href="#Page_87">87</a>.</li> -<li class="isub1">Of complex phenomena, <a href="#Page_88">88</a>.</li> - -<li class="indx">Anaxagoras, philosophy of, <a href="#Page_107">107</a>.</li> - -<li class="indx">Animal electricity, <a href="#Page_337">337</a>.</li> - -<li class="indx">Arago, M., his experiment with a magnetic needle and a plate of copper, <a href="#Page_157">157</a>.</li> - -<li class="indx">Archimedes, his practical application of science, <a href="#Page_72">72</a>.</li> -<li class="isub1">His knowledge of hydrostatics, <a href="#Page_231">231</a>.</li> - -<li class="indx">Arfwedson, his discovery of lithia, <a href="#Page_158">158</a>.</li> - -<li class="indx">Aristotle, his knowledge of natural history, <a href="#Page_109">109</a>.</li> -<li class="isub1">His works condemned, and subsequently studied with avidity, <a href="#Page_111">111</a>.</li> -<li class="isub1">His philosophy overturned by the discoveries of Copernicus, Kepler, and Galileo, <a href="#Page_113">113</a>.</li> - -<li class="indx">Arithmetic, <a href="#Page_19">19</a>.</li> - -<li class="indx">Art, empirical and scientific, differences between, <a href="#Page_71">71</a>.</li> -<li class="isub1">Remarks on the language, terms, or signs, used in treating of it, <a href="#Page_70">70</a>.</li> - -<li class="indx">Assurances, life, utility and abuses of, <a href="#Page_58">58</a>.</li> - -<li class="indx">Astronomy, cause of the slow progress of our knowledge of, <a href="#Page_78">78</a>.</li> -<li class="isub1">Theory and practical observations distinct in, <a href="#Page_132">132</a>.</li> -<li class="isub1">An extensive acquaintance with science and every branch of knowledge necessary to make a perfect observer in, <a href="#Page_132">132</a>.</li> -<li class="isub1">Five primary planets added to our system, <a href="#Page_274">274</a>.</li> -<li class="isub1">Positions, figures, and dimensions of all the planetary orbits now well known, <a href="#Page_275">275</a>.</li> - -<li class="indx">Atomic theory, <a href="#Page_305">305</a>.</li> -<li class="isub1">Advantage of, <a href="#Page_306">306</a>.</li> - -<li class="indx">Atomic weights of chemical elements, <a href="#Page_306">306</a>.</li> - -<li class="indx">Attraction, capillary, or capillarity, investigated by Laplace and Young, <a href="#Page_234">234</a>.</li> - -<li class="ifrst">Bacon, celebrated in England for his knowledge of science, <a href="#Page_72">72</a>.<span class="pagenum"><a id="Page_364">364</a></span></li> -<li class="isub1">Benefits conferred on Natural Philosophy by him, <a href="#Page_104">104</a>.</li> -<li class="isub1">His Novum Organum, <a href="#Page_105">105</a>.</li> -<li class="isub1">His reform in philosophy proves the paramount importance of induction, <a href="#Page_114">114</a>.</li> -<li class="isub1">His prerogative of facts, <a href="#Page_181">181</a>.</li> -<li class="isub1">Illustrated by the fracture of a crystallized substance, <a href="#Page_183">183</a>.</li> -<li class="isub1">His collective instances, <a href="#Page_184">184</a>.</li> -<li class="isub1">Importance of, <a href="#Page_185">185</a>.</li> -<li class="isub1">His experiment on the weight of bodies, <a href="#Page_186">186</a>.</li> -<li class="isub1">Travelling instances of, frontier instances of, <a href="#Page_188">188</a>.</li> -<li class="isub1">His difference between liquids and aëriform fluids, <a href="#Page_233">233</a>.</li> - -<li class="indx">Bartolin, Erasmus, first discovers the phenomena exhibited by doubly refracting crystals, <a href="#Page_254">254</a>.</li> - -<li class="indx">Beccher, phlogistic doctrines of, <a href="#Page_300">300</a>.</li> - -<li class="indx">Bergmann, his advancement in crystallography, <a href="#Page_239">239</a>.</li> - -<li class="indx">Bernoulli, experiments of, in hydrodynamical science, <a href="#Page_181">181</a>.</li> - -<li class="indx">Biot, his hypothesis of a rotatory motion of the particles of light about their axes, <a href="#Page_262">262</a>.</li> - -<li class="indx">Black, Dr., his discovery of latent heat, <a href="#Page_322">322</a>.</li> - -<li class="indx">Bode, his curious law observed in the progression of the magnitudes of the several planetary orbits, <a href="#Page_308">308</a>.</li> - -<li class="indx">Bodies, natural constitution of, <a href="#Page_221">221</a>.</li> -<li class="isub1">Division of, into crystallized and uncrystallized, <a href="#Page_242">242</a>.</li> - -<li class="indx">Bones, dry, a magazine of nutriment, <a href="#Page_65">65</a>.</li> - -<li class="indx">Borda, his invention for subdivision, <a href="#Page_128">128</a>.</li> - -<li class="indx">Botany, general utility of, <a href="#Page_345">345</a>.</li> - -<li class="indx">Boyle, Robert, his enthusiasm in the pursuit of science, <a href="#Page_115">115</a>.</li> -<li class="isub1">His improvement on the air-pump, <a href="#Page_230">230</a>.</li> - -<li class="indx">Brain, hypothesis of its being an electric pile, <a href="#Page_343">343</a>.</li> - -<li class="indx">Bramah’s press, principle and utility of, <a href="#Page_233">233</a>.</li> - -<li class="indx">Brewster, Dr., his improvement on lenses for lighthouses, <a href="#Page_56">56</a>.</li> -<li class="isub1">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, <a href="#Page_263">263</a>.</li> - -<li class="ifrst">Cabot, Sebastian, his discovery of the variation of the needle, <a href="#Page_327">327</a>.</li> - -<li class="indx">Cagnard, Baron de la Tour, utility of his experiments, <a href="#Page_234">234</a>.</li> - -<li class="indx">Causes and consequences directors of the will of man, <a href="#Page_6">6</a>.</li> - -<li class="indx">Causes, proximate, discovery of, called by Newton <i xml:lang="la" lang="la">veræ causæ</i>, <a href="#Page_144">144</a>.</li> - -<li class="indx">Celestial mechanics, <a href="#Page_265">265</a>.</li> - -<li class="indx">Chaldean records, <a href="#Page_265">265</a>.</li> - -<li class="indx">Chemistry furnishes causes of sudden action, also fulminating compositions, <a href="#Page_62">62</a>.</li> -<li class="isub1">Analogy of the complex phenomena of, with those of physics, <a href="#Page_92">92</a>.</li> -<li class="isub1">Benefits arising from the analysis of, <a href="#Page_94">94</a>.<span class="pagenum"><a id="Page_365">365</a></span></li> -<li class="isub1">Axioms of, analogous to those of geometry, <a href="#Page_95">95</a>.</li> -<li class="isub1">Many of the new elements of, detected in the investigation of residual phenomena, <a href="#Page_158">158</a>.</li> -<li class="isub1">The most general law of, <a href="#Page_209">209</a>.</li> -<li class="isub1">Illustration of, <a href="#Page_210">210</a>.</li> -<li class="isub1">Between fifty and sixty elements in, <a href="#Page_211">211</a>.</li> -<li class="isub1">Objects of, <a href="#Page_296">296</a>.</li> -<li class="isub1">General heads of the principal improvements in, <a href="#Page_302">302</a>.</li> -<li class="isub1">Remarks on those general heads, <a href="#Page_304">304</a>.</li> - -<li class="indx">Chemistry, Stahlian, cause of the mistakes and confusions of, <a href="#Page_123">123</a>.</li> - -<li class="indx">Chladni, experiments of, in dynamical science, <a href="#Page_181">181</a>.</li> - -<li class="indx">Chlorine, disinfectant powers of, <a href="#Page_56">56</a>.</li> - -<li class="indx">Clarke, Dr., his experiments on the arseniate and phosphate of soda, <a href="#Page_170">170</a>.</li> -<li class="isub1">His success in producing a new phosphate of soda, <a href="#Page_171">171</a>.</li> - -<li class="indx">Climate, change of, in large tracts of the globe, alleged cause of, <a href="#Page_145">145</a>.</li> - -<li class="indx">Coals, power of a bushel of, properly consumed, <a href="#Page_59">59</a>.</li> -<li class="isub1">Quantity consumed in London, <a href="#Page_60">60</a>.</li> - -<li class="indx">Cohesion, an ultimate phenomenon, <a href="#Page_90">90</a>.</li> - -<li class="indx">Cold, qualities of, <a href="#Page_318">318</a>.</li> - -<li class="indx">Compass, mariner’s, <a href="#Page_55">55</a>.</li> - -<li class="indx">Condensation, a source of heat, <a href="#Page_313">313</a>.</li> - -<li class="indx">Conduction of heat, laws of, <a href="#Page_205">205</a>.</li> - -<li class="indx">Copernicus, effect of his discoveries on the Aristotelian philosophy, <a href="#Page_113">113</a>.</li> -<li class="isub1">Objections to his astronomical doctrines, <a href="#Page_269">269</a>.</li> - -<li class="indx">Crystallography, laws of, <a href="#Page_123">123</a>, <a href="#Page_239">239</a>.</li> -<li class="isub1">A determinate figure supposed to be common to all the particles of a crystal, <a href="#Page_242">242</a>.</li> - -<li class="ifrst">D’Alembert, his improvements in hydrodynamics, <a href="#Page_236">236</a>.</li> - -<li class="indx">Dalton, his announcement of the atomic theory, <a href="#Page_305">305</a>.</li> -<li class="isub1">His examination of gases and vapours, <a href="#Page_319">319</a>.</li> - -<li class="indx">Davy, Sir H., brings the voltaic pile to bear upon the earths and alkalies, <a href="#Page_339">339</a>.</li> - -<li class="indx">Deduction, utility of, <a href="#Page_174">174</a>.</li> - -<li class="indx">De l’Isle, Romé, his study of crystalline bodies, <a href="#Page_239">239</a>.</li> - -<li class="indx">Dew, causes of, investigated, <a href="#Page_159">159</a>.</li> -<li class="isub1">Effects of, on different substances, <a href="#Page_160">160</a>.</li> -<li class="isub1">Objects capable of contracting it, <a href="#Page_161">161</a>.</li> -<li class="isub1">A cloudless sky favourable to its production, <a href="#Page_162">162</a>.</li> -<li class="isub1">General proximate cause of, <a href="#Page_163">163</a>.</li> - -<li class="indx">Drummond, lieutenant, his improvement on lenses for lamps of lighthouses, <a href="#Page_56">56</a>.</li> - -<li class="indx">Dynamics, importance of, <a href="#Page_96">96</a>, <a href="#Page_223">223</a>.</li> - -<li class="ifrst">Earth, the orbit of,—diminution of its eccentricity round the sun, <a href="#Page_147">147</a>.</li> - -<li class="indx">Economy, political, <a href="#Page_73">73</a>.</li> - -<li class="indx">Egypt, great pyramid of, height, weight, and ground occupied by it, <a href="#Page_60">60</a>.</li> -<li class="isub1">Accuracy of the astronomical records of, <a href="#Page_265">265</a>.</li> - -<li class="indx">Elasticity, an ultimate phenomenon, <a href="#Page_90">90</a>.</li> - -<li class="indx">Electricity may be the cause of magnetism, <a href="#Page_93">93</a>.</li> -<li class="isub1">Universality of, <a href="#Page_329">329</a>.<span class="pagenum"><a id="Page_366">366</a></span></li> -<li class="isub1">Effects of, <a href="#Page_330">330</a>.</li> -<li class="isub1">Activity of, <a href="#Page_331">331</a>.</li> -<li class="isub1">Equilibrium of, <a href="#Page_332">332</a>.</li> -<li class="isub1">Productive of chemical decomposition, <a href="#Page_338">338</a>.</li> - -<li class="indx">Empirical laws, <a href="#Page_178">178</a>.</li> -<li class="isub1">Evils resulting from, <a href="#Page_179">179</a>.</li> - -<li class="indx">Encke, professor, his prediction of the return of the comet so many times in succession, <a href="#Page_156">156</a>.</li> - -<li class="indx">Englefield, sir H., his analysis of a solar beam, <a href="#Page_314">314</a>.</li> - -<li class="indx">Equilibrium maintained by force, <a href="#Page_222">222</a>.</li> - -<li class="indx">Erman, professor, his opinion of the effects of the voltaic circuit, <a href="#Page_340">340</a>.</li> - -<li class="indx">Euler, his improvement on Newton’s theory of sound, <a href="#Page_247">247</a>.</li> - -<li class="indx">Experience, source of our knowledge of nature’s laws, <a href="#Page_76">76</a>.</li> - -<li class="indx">Experiment, a means of acquiring experience, <a href="#Page_76">76</a>.</li> -<li class="isub1">Utility of, <a href="#Page_151">151</a>.</li> - -<li class="ifrst">Facts, the observation of, <a href="#Page_118">118</a>.</li> - -<li class="indx">Faujas de St. Fond, imaginary craters of, <a href="#Page_131">131</a>.</li> - -<li class="indx">Fluids, laws of the motion of, <a href="#Page_181">181</a>.</li> -<li class="isub1">Compressibility of, <a href="#Page_225">225</a>.</li> -<li class="isub1">Consideration of the motions of, more complicated than that of equilibrium, <a href="#Page_235">235</a>.</li> - -<li class="indx">Force, analysis of, <a href="#Page_86">86</a>.</li> -<li class="isub1">The cause of motion, <a href="#Page_149">149</a>.</li> -<li class="isub1">Phenomena of, <a href="#Page_221">221</a>.</li> -<li class="isub1">Molecular forces, <a href="#Page_245">245</a>.</li> - -<li class="indx">Fourier, baron, his opinion that the celestial regions have a temperature, independent of the sun, not greatly inferior to that at which quicksilver congeals, <a href="#Page_157">157</a>.</li> -<li class="isub1">His analysis of the laws of conduction and radiation of heat, <a href="#Page_317">317</a>.</li> - -<li class="indx">Franklin, Dr., his experiments on electricity, <a href="#Page_332">332</a>.</li> - -<li class="indx">Fresnel, M., his mathematical explanation of the phenomena of double refraction, <a href="#Page_32">32</a>.</li> -<li class="isub1">His improvement on lenses for lamps of lighthouses, <a href="#Page_56">56</a>.</li> -<li class="isub1">His opinions on the nature of light, <a href="#Page_207">207</a>.</li> -<li class="isub1">His experiments on the interference of polarized light, <a href="#Page_261">261</a>.</li> -<li class="isub1">His theory of polarization, <a href="#Page_262">262</a>.</li> - -<li class="indx">Friction, a source of heat, <a href="#Page_313">313</a>.</li> - -<li class="ifrst">Galileo, celebrity of, for his knowledge of science, <a href="#Page_72">72</a>.</li> -<li class="isub1">His exposition of the Aristotelian philosophy, <a href="#Page_110">110</a>.</li> -<li class="isub1">His refutation of Aristotle’s dogmas respecting motion, his persecution in consequence of it, <a href="#Page_113">113</a>.</li> -<li class="isub1">His knowledge of the accelerating power of gravity, <a href="#Page_168">168</a>.</li> -<li class="isub1">His knowledge of the weight of the atmosphere, <a href="#Page_228">228</a>.</li> - -<li class="indx">Galvani, utility of his discoveries in electricity, <a href="#Page_335">335</a>.</li> -<li class="isub1">His application of it to animals, <a href="#Page_336">336</a>.</li> - -<li class="indx">Gay-Lussac, his examination of gases and vapours, <a href="#Page_319">319</a>.</li> - -<li class="indx">Generalization, inductive, <a href="#Page_1">1</a>, <a href="#Page_90">90</a>.</li> - -<li class="indx">Geology, <a href="#Page_281">281</a>.</li> -<li class="isub1">Its rank as a science, <a href="#Page_287">287</a>.</li> - -<li class="indx">Geometry, axioms of, an appeal to experience, not corporeal, but mental, <a href="#Page_95">95</a>.</li> - -<li class="indx">Gilbert, Dr., of Colchester, his knowledge of magnetism and electricity, <a href="#Page_112">112</a>.<span class="pagenum"><a id="Page_367">367</a></span></li> - -<li class="indx">Gravitation, law of, a physical axiom of a very high and universal kind, <a href="#Page_98">98</a>.</li> -<li class="isub1">Influence of, decreases in the inverse ratio of the square of the distance, <a href="#Page_123">123</a>.</li> - -<li class="indx">Greece, philosophers of, their extraordinary success in abstract reasoning, and their careless consideration of external nature, <a href="#Page_105">105</a>.</li> -<li class="isub1">Their general character, <a href="#Page_106">106</a>.</li> -<li class="isub1">Philosophy of, <a href="#Page_108">108</a>.</li> - -<li class="indx">Grimaldi, a jesuit of Bologna, his discovery of diffraction, or inflection of light, <a href="#Page_252">252</a>.</li> - -<li class="indx">Guinea and feather experiment, <a href="#Page_168">168</a>.</li> - -<li class="indx">Gunpowder, invention of, <a href="#Page_55">55</a>.</li> -<li class="isub1">A mechanical agent, <a href="#Page_62">62</a>.</li> - -<li class="ifrst">Haarlem lake, draining of, <a href="#Page_61">61</a>.</li> - -<li class="indx">Harmony, sense of, <a href="#Page_248">248</a>.</li> - -<li class="indx">Head, captain, anecdote of, <a href="#Page_84">84</a>.</li> - -<li class="indx">Heat, <a href="#Page_193">193</a>.</li> -<li class="isub1">Radiation and conduction of, <a href="#Page_205">205</a>.</li> -<li class="isub1">One of the chief agents in chemistry, <a href="#Page_310">310</a>.</li> -<li class="isub1">Our ignorance of the nature of, <a href="#Page_310">310</a>.</li> -<li class="isub1">Abuse of the sense of the term, <a href="#Page_311">311</a>.</li> -<li class="isub1">The general heads under which it is studied, <a href="#Page_312">312</a>.</li> -<li class="isub1">Its most obvious sources, <a href="#Page_312">312</a>.</li> -<li class="isub1">Animal heat, to what process referable, <a href="#Page_313">313</a>.</li> -<li class="isub1">Radiation and conduction of, <a href="#Page_314">314</a>.</li> -<li class="isub1">Solar heat differs from terrestrial fires, or hot bodies, <a href="#Page_315">315</a>.</li> -<li class="isub1">Principal effects of, <a href="#Page_317">317</a>.</li> -<li class="isub1">The antagonist to mutual attraction, <a href="#Page_322">322</a>.</li> -<li class="isub1">Latent heat, <a href="#Page_322">322</a>.</li> -<li class="isub1">Specific heat, <a href="#Page_323">323</a>.</li> - -<li class="indx">Herschel, sir William, his analysis of a solar beam, <a href="#Page_314">314</a>.</li> - -<li class="indx">Hipparchus, his catalogue of stars, <a href="#Page_276">276</a>.</li> - -<li class="indx">Holland drained of water by windmills, <a href="#Page_61">61</a>.</li> - -<li class="indx">Hooke almost the rival of Newton, <a href="#Page_116">116</a>.</li> - -<li class="indx">Huel Towan, steam-engine at, <a href="#Page_59">59</a>.</li> - -<li class="indx">Huyghens, his doctrine of light, <a href="#Page_207">207</a>.</li> -<li class="isub1">Ascertains the laws of double refraction, <a href="#Page_254">254</a>.</li> - -<li class="indx">Hydrostatics, first step towards a knowledge of, made by Archimedes, <a href="#Page_231">231</a>.</li> -<li class="isub1">Law of the equal pressure of liquids, <a href="#Page_232">232</a>.</li> -<li class="isub1">General applicability of, <a href="#Page_232">232</a>.</li> - -<li class="indx">Hypothesis, not to be deterred from framing them, <a href="#Page_196">196</a>.</li> -<li class="isub1">Conditions on which they should be framed, <a href="#Page_197">197</a>.</li> -<li class="isub1">Illustrated by the laws of gravitation, <a href="#Page_198">198</a>.</li> -<li class="isub1">Use and abuse of, <a href="#Page_204">204</a>.</li> - -<li class="ifrst">Induction, different ways of carrying it on, <a href="#Page_102">102</a>.</li> -<li class="isub1">Steps by which it is arrived at on a legitimate and extensive scale, <a href="#Page_118">118</a>.</li> -<li class="isub1">First stage of, <a href="#Page_144">144</a>.</li> -<li class="isub1">Verification of, <a href="#Page_164">164</a>.</li> -<li class="isub1">Instanced in astronomy, <a href="#Page_166">166</a>.</li> -<li class="isub1">Must be followed into all its consequences, and applied to all those cases which seem even remotely to bear upon the subject of enquiry, <a href="#Page_173">173</a>.</li> -<li class="isub1">Nature of the inductions by which quantitative laws are arrived at, <a href="#Page_176">176</a>.</li> -<li class="isub1">Necessity of induction embracing a series of cases which absolutely include the whole scale of variation of which the quantities in question admit, <a href="#Page_177">177</a>.</li> - -<li class="indx">Induced electricity, <a href="#Page_333">333</a>.<span class="pagenum"><a id="Page_368">368</a></span></li> - -<li class="indx">Inertia, <a href="#Page_223">223</a>.</li> - -<li class="indx">Iodine, discovery of, <a href="#Page_50">50</a>.</li> -<li class="isub1">Efficacy of, in curing goître, <a href="#Page_51">51</a>.</li> - -<li class="indx">Isomorphism, law of, <a href="#Page_170">170</a>.</li> - -<li class="ifrst">Kepler, effect of his discoveries on the Aristotelian philosophy, <a href="#Page_113">113</a>.</li> -<li class="isub1">Nature of his laws of the planetary system, <a href="#Page_178">178</a>.</li> -<li class="isub1">Proofs of the Newtonian system, <a href="#Page_179">179</a>.</li> - -<li class="indx">Knowledge, physical facts illustrative of the utility of, <a href="#Page_45">45</a>.</li> -<li class="isub1">Diffusion of, how to take advantage of in the investigation of nature, <a href="#Page_138">138</a>.</li> - -<li class="ifrst">Lagrange, his improvements on Newton’s theory of sound, <a href="#Page_247">247</a>.</li> -<li class="isub1">His astronomical researches, <a href="#Page_275">275</a>.</li> - -<li class="indx">Lamp, safety, <a href="#Page_55">55</a>.</li> - -<li class="indx">Laplace, his explanation of the residual velocity of sound and confirmation of the general law of the developement of heat by compression, <a href="#Page_172">172</a>.</li> -<li class="isub1">His astronomical research, <a href="#Page_275">275</a>.</li> -<li class="isub1">His experiments on the dilatation of bodies by heat, <a href="#Page_319">319</a>.</li> -<li class="isub1">His study of specific heat, <a href="#Page_323">323</a>.</li> -<li class="isub1">Latent heat, <a href="#Page_323">323</a>.</li> - -<li class="indx">Laws, inductive, <a href="#Page_171">171</a>.</li> -<li class="isub1">General, <a href="#Page_198">198</a>.</li> -<li class="isub1">How applicable, <a href="#Page_199">199</a>.</li> -<li class="isub1">Illustrated by the planetary system, <a href="#Page_201">201</a>.</li> -<li class="isub1">Empirical laws, <a href="#Page_178">178</a>.</li> - -<li class="indx">Lavoisier, his improvements in chemical science, <a href="#Page_302">302</a>.</li> -<li class="isub1">Experiments on dilatation of bodies by heat, <a href="#Page_319">319</a>.</li> -<li class="isub1">His investigation on specific heat, <a href="#Page_323">323</a>.</li> - -<li class="indx">Light, refraction of, <a href="#Page_30">30</a>.</li> -<li class="isub1">Double refraction of, <a href="#Page_31">31</a>.</li> -<li class="isub1">Polarization of, <a href="#Page_254">254</a>.</li> - -<li class="indx">Light and vision, ignorance of the ancients respecting, <a href="#Page_249">249</a>.</li> - -<li class="indx">Lighthouse, <a href="#Page_56">56</a>.</li> - -<li class="indx">Lightning, how to judge philosophically of it, <a href="#Page_120">120</a>.</li> -<li class="isub1">Returning stroke of, <a href="#Page_121">121</a>.</li> - -<li class="indx">Liquids, cohesion, attraction and repulsion of the particles of, <a href="#Page_227">227</a>.</li> -<li class="isub1">Differ from aëriform fluids by their cohesion, <a href="#Page_233">233</a>.</li> -<li class="isub1">The Florentine experiment on; experiments by Canton, Perkins, Oërsted, and others on, <a href="#Page_235">235</a>.</li> -<li class="isub1">Obscurity of the laws of dilatation of, <a href="#Page_320">320</a>.</li> - -<li class="indx">Linnæus, his knowledge of crystalline substances, <a href="#Page_239">239</a>.</li> - -<li class="indx">Logic, <a href="#Page_19">19</a>.</li> - -<li class="indx">Lyell’s Principles of Geology, extract from, <a href="#Page_146">146</a>.</li> - -<li class="ifrst">Magnetism may be caused by electricity, <a href="#Page_93">93</a>.</li> -<li class="isub1">Offers a “glaring instance” of polarity, <a href="#Page_326">326</a>.</li> -<li class="isub1">Experiments illustrative of, <a href="#Page_327">327</a>.</li> - -<li class="indx">Malus, a French officer of engineers, discovers the polarization of light, <a href="#Page_132">132</a>, <a href="#Page_258">258</a>.</li> - -<li class="indx">Man, regarded as a creature of instinct, <a href="#Page_1">1</a>.</li> -<li class="isub1">Of reason and speculation, <a href="#Page_3">3</a>.</li> -<li class="isub1">His will determined by causes and consequences, <a href="#Page_6">6</a>.</li> -<li class="isub1">Advantages to, from the study of science, <a href="#Page_7">7</a>.</li> -<li class="isub1">His necessity to study the laws of nature illustrated, <a href="#Page_66">66</a>.</li> -<li class="isub1">Happiness and the opposite state of man in the aggregate, <a href="#Page_67">67</a>.</li> -<li class="isub1">Advantages conferred on, by the augmentation of physical resources, <a href="#Page_68">68</a>.<span class="pagenum"><a id="Page_369">369</a></span></li> -<li class="isub1">Advantages from intellectual resources, <a href="#Page_69">69</a>.</li> - -<li class="indx">Mariotte, his law of equilibrium of an elastic fluid recently verified by the Royal Academy of Paris, <a href="#Page_231">231</a>.</li> -<li class="isub1">His difference between solar and other heat, <a href="#Page_315">315</a>.</li> - -<li class="indx">Matter, indestructibility of; Divided by grinding, <a href="#Page_40">40</a>.</li> -<li class="isub1">By fire, <a href="#Page_41">41</a>.</li> -<li class="isub1">Dilated by heat, <a href="#Page_193">193</a>.</li> -<li class="isub1">Inertia of, <a href="#Page_202">202</a>.</li> -<li class="isub1">Polarity of, one of the ultimate phenomena to which the analysis of nature leads us, <a href="#Page_245">245</a>.</li> -<li class="isub1">Inherent activity of, <a href="#Page_297">297</a>.</li> -<li class="isub1">Causes of the polarity of, <a href="#Page_299">299</a>.</li> -<li class="isub1">Imponderable forms of, <a href="#Page_310">310</a>.</li> - -<li class="indx">Measure, the standard, difficulty of preserving it unaltered, <a href="#Page_128">128</a>.</li> -<li class="isub1">How to be assisted in measurement, <a href="#Page_129">129</a>.</li> -<li class="isub1">Our conclusions from, should be conditional, <a href="#Page_130">130</a>.</li> - -<li class="indx">Menai Bridge, weight and height of, <a href="#Page_60">60</a>.</li> - -<li class="indx">Mechanics, practical, <a href="#Page_63">63</a>.</li> - -<li class="indx">Mètre, the French, <a href="#Page_126">126</a>.</li> - -<li class="indx">Microscopes, power of, <a href="#Page_191">191</a>.</li> - -<li class="indx">Millstones, method of making in France, <a href="#Page_48">48</a>.</li> - -<li class="indx">Mind, its transition from the little to the great, and <i xml:lang="la" lang="la">vice versâ</i>, illustrated, <a href="#Page_172">172</a>.</li> - -<li class="indx">Mineralogy unknown to the ancients, <a href="#Page_79">79</a>.</li> -<li class="isub1">Prejudiced by the rage for nomenclature, <a href="#Page_139">139</a>.</li> -<li class="isub1">Benefited by the progress of chemical analysis, <a href="#Page_293">293</a>.</li> - -<li class="indx">Minerals, simple, apparent paucity of, <a href="#Page_294">294</a>.</li> -<li class="isub1">Difficulty in classing them, <a href="#Page_295">295</a>.</li> - -<li class="indx">Mitscherlich, his law of isomorphism, <a href="#Page_170">170</a>.</li> -<li class="isub1">His experiments on the expansion of substances by heat, <a href="#Page_243">243</a>.</li> - -<li class="indx">Motion, <a href="#Page_87">87</a>.</li> -<li class="isub1">Simplicity and precision of the laws of, <a href="#Page_179">179</a>.</li> - -<li class="ifrst">Nature, laws of, <a href="#Page_37">37</a>.</li> -<li class="isub1">Immutability of, <a href="#Page_42">42</a>.</li> -<li class="isub1">Harmony of, and advantage of studying them, <a href="#Page_43">43</a>.</li> -<li class="isub1">Prove the impossibility of attaining the declared object of the alchemist. How they serve mankind generally, <a href="#Page_44">44</a>.</li> -<li class="isub1">Illustrated by mining, <a href="#Page_45">45</a>.</li> -<li class="isub1">Economy derived from a knowledge of, <a href="#Page_65">65</a>.</li> -<li class="isub1">How to be regarded, <a href="#Page_100">100</a>, <a href="#Page_101">101</a>.</li> - -<li class="indx">Nature, objects of, an enumeration and nomenclature of, useful in the study of, <a href="#Page_135">135</a>.</li> -<li class="isub1">Mechanism of, on too large or too small a scale to be immediately cognisable by our senses, <a href="#Page_191">191</a>.</li> - -<li class="indx">Newton, his proof of Galileo’s laws of gravitation by an experiment with a hollow glass pendulum, <a href="#Page_160">160</a>.</li> -<li class="isub1">His foundation to hydrodynamical science, <a href="#Page_181">181</a>.</li> -<li class="isub1">Fixes the division between statics and dynamics, <a href="#Page_223">223</a>.</li> -<li class="isub1">His investigation of the law of equilibrium of elastic fluids, <a href="#Page_231">231</a>.</li> -<li class="isub1">His law of hydrostatics, <a href="#Page_232">232</a>.</li> -<li class="isub1">His foundation of hydrodynamics <a href="#Page_236">236</a>.</li> -<li class="isub1">His analysis of sound, <a href="#Page_247">247</a>.<span class="pagenum"><a id="Page_370">370</a></span></li> -<li class="isub1">Hypothesis of light, <a href="#Page_250">250</a>.</li> -<li class="isub1">Examination of a soap-bubble, <a href="#Page_252">252</a>.</li> -<li class="isub1">His hypothesis of fits of easy transmission and reflection, <a href="#Page_253">253</a>.</li> -<li class="isub1">His combination of mathematical skill with physical research, <a href="#Page_271">271</a>.</li> -<li class="isub1">His Principia, <a href="#Page_272">272</a>.</li> -<li class="isub1">His successors; his geometry, <a href="#Page_273">273</a>.</li> - -<li class="indx">Nomenclature, importance of, to science, <a href="#Page_136">136</a>.</li> -<li class="isub1">More a consequence than a cause of extended knowledge, <a href="#Page_138">138</a>.</li> -<li class="isub1">Prejudicial to mineralogy, <a href="#Page_139">139</a>.</li> - -<li class="indx">Norman, Robert, his discovery of the dip of the needle, <a href="#Page_327">327</a>.</li> - -<li class="indx">Numerical precision, necessity of, in science, <a href="#Page_122">122</a>.</li> - -<li class="ifrst">Objects, and their mutual actions, subjects of contemplation, <a href="#Page_118">118</a>.</li> - -<li class="indx">Observation, a means of acquiring experience, <a href="#Page_76">76</a>.</li> -<li class="isub1">Passive and active, <a href="#Page_77">77</a>.</li> -<li class="isub1">Recorded observation, <a href="#Page_120">120</a>.</li> -<li class="isub1">Necessity of, to acquire precise physical data, <a href="#Page_215">215</a>.</li> -<li class="isub1">Illustrated by the barometer, <a href="#Page_216">216</a>.</li> - -<li class="indx">Oërsted, his discoveries in electricity and magnetism, <a href="#Page_132">132</a>.</li> -<li class="isub1">Of electro-magnetism, <a href="#Page_340">340</a>.</li> - -<li class="indx">Opacity, <a href="#Page_189">189</a>.</li> - -<li class="indx">Otto von Guericke of Magdeburgh, his invention of the air-pump, <a href="#Page_230">230</a>.</li> - -<li class="ifrst">Paracelsus, power of his chemical remedies; his use of mercury, opium, and tartar, <a href="#Page_112">112</a>.</li> - -<li class="indx">Pascal, his crucial instances proving the weight of air, <a href="#Page_229">229</a>.</li> - -<li class="indx">Pendulum, <a href="#Page_126">126</a>.</li> - -<li class="indx">Phenomena, analysis of, illustrated by musical sounds, the sensation of taste, <a href="#Page_85">85</a>.</li> -<li class="isub1">The ultimate and inward process of nature in the production of, <a href="#Page_86">86</a>.</li> -<li class="isub1">Analysis of complex phenomena, <a href="#Page_88">88</a>.</li> -<li class="isub1">Ultimate phenomena, <a href="#Page_90">90</a>.</li> -<li class="isub1">How the analysis of, is useful, <a href="#Page_97">97</a>.</li> -<li class="isub1">A transient phenomenon, how to judge of, <a href="#Page_122">122</a>.</li> -<li class="isub1">Method of explaining one when it presents itself, <a href="#Page_148">148</a>.</li> -<li class="isub1">How to discover the cause of one, <a href="#Page_150">150</a>.</li> -<li class="isub1">Two, or many, theories, maintained as the origin of, in physics, <a href="#Page_195">195</a>.</li> -<li class="isub1">Cosmical phenomena, <a href="#Page_265">265</a>.</li> - -<li class="indx">Philosophy, natural, unfounded objections to the study of, <a href="#Page_7">7</a>.</li> -<li class="isub1">Advantages derivable from the study of, <a href="#Page_10">10</a>.</li> -<li class="isub1">Pleasure and happiness, the consequences of the study of, <a href="#Page_15">15</a>.</li> - -<li class="indx">Phlogistic doctrines of Beccher and Stahl, <a href="#Page_300">300</a>.</li> - -<li class="indx">Physical data, necessity of, <a href="#Page_209">209</a>.</li> -<li class="isub1">Great importance of, <a href="#Page_211">211</a>.</li> -<li class="isub1">Illustrated by the erection of observatories, <a href="#Page_213">213</a>.</li> -<li class="isub1">Necessity of an exact knowledge of, <a href="#Page_214">214</a>.</li> -<li class="isub1">More precise than the observations by which we acquire them, <a href="#Page_215">215</a>.</li> - -<li class="indx">Physics, axioms of; analysis of, <a href="#Page_102">102</a>.</li> - -<li class="indx">Planets, circumjovial, <a href="#Page_186">186</a>.</li> - -<li class="indx">Platina, discovery of, <a href="#Page_308">308</a>.</li> - -<li class="indx">Pliny, his knowledge of quartz and diamond, <a href="#Page_239">239</a>.<span class="pagenum"><a id="Page_371">371</a></span></li> - -<li class="indx">Pneumatics, <a href="#Page_228">228</a>.</li> - -<li class="indx">Political economy, <a href="#Page_73">73</a>.</li> - -<li class="indx">Prejudices of opinion and sense, <a href="#Page_80">80</a>.</li> -<li class="isub1">Conditions on which such are injurious, <a href="#Page_81">81</a>.</li> -<li class="isub1">Illustrated by the division of the rays of light, by the moon at the horizon, and by ventriloquism, <a href="#Page_82">82</a>.</li> -<li class="isub1">By the transition of the hand from heat to cold, <a href="#Page_83">83</a>.</li> - -<li class="indx">Prevost, M., his theory of heat, <a href="#Page_316">316</a>.</li> -<li class="isub1">His theory of reciprocal interchanges, a proof of the radiation of cold, <a href="#Page_318">318</a>.</li> - -<li class="indx">Printing, the art of, <a href="#Page_193">193</a>.</li> -<li class="isub1">Performed by steam, <a href="#Page_194">194</a>.</li> - -<li class="indx">Probabilities, doctrine of, <a href="#Page_217">217</a>.</li> -<li class="isub1">Illustrated by shooting at a wafer, <a href="#Page_218">218</a>.</li> - -<li class="indx">Prout, Dr., his opinion of the atomic weights, <a href="#Page_307">307</a>.</li> - -<li class="indx">Pyrometry, <a href="#Page_319">319</a>.</li> - -<li class="indx">Pythagoras, philosophy of, <a href="#Page_107">107</a>.</li> - -<li class="ifrst">Quinine, sulphate of, comparative comfort and health resulting from the use of, <a href="#Page_56">56</a>.</li> - -<li class="ifrst">Radiation of heat, laws of, <a href="#Page_205">205</a>.</li> - -<li class="indx">Repulsion in fluids and solids, <a href="#Page_227">227</a>.</li> - -<li class="indx">Rules, general, for guiding and facilitating our search among a great mass of assembled facts, <a href="#Page_151">151</a>.</li> - -<li class="indx">Rumford, count, experiments of, on gunpowder, <a href="#Page_62">62</a>.</li> - -<li class="ifrst">Savart, M., his experiments on solids, <a href="#Page_243">243</a>.</li> -<li class="isub1">His researches on sound, <a href="#Page_249">249</a>.</li> - -<li class="indx">Science, abstract, a preparation for the study of physics, <a href="#Page_19">19</a>.</li> -<li class="isub1">Not indispensable to the study of physical laws, <a href="#Page_25">25</a>.</li> -<li class="isub1">Instances illustrative of, <a href="#Page_27">27</a>.</li> - -<li class="indx">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, <a href="#Page_35">35</a>.</li> -<li class="isub1">State of, previous to the age of Galileo and Bacon, <a href="#Page_104">104</a>.</li> -<li class="isub1">Causes of the rapid advance of, compared with the progress at an earlier period, <a href="#Page_347">347</a>.</li> - -<li class="indx">Science, natural, cause and effect, the ultimate relations of, <a href="#Page_76">76</a>.</li> - -<li class="indx">Sciences and Arts, remarks on the language, terms, or signs used in treating of them, <a href="#Page_70">70</a>.</li> -<li class="isub1">Receive an impulse by the Baconian philosophy, <a href="#Page_114">114</a>.</li> - -<li class="indx">Sensation, cause of, <a href="#Page_91">91</a>.</li> - -<li class="indx">Senses, inadequate to give us direct information for the exact comparison of quantity, <a href="#Page_124">124</a>.</li> -<li class="isub1">Substitutes for the inefficiency of, <a href="#Page_125">125</a>.</li> - -<li class="indx">Seringapatam, method of breaking blocks from the quarries of, <a href="#Page_47">47</a>.</li> - -<li class="indx">Shells found in rocks at a great height above the sea, supposed cause of, <a href="#Page_145">145</a>.</li> - -<li class="indx">Smeaton, his experiments on bodies dilated by heat, <a href="#Page_319">319</a>.</li> - -<li class="indx">Solids, transparent, exhibit periodical colours when exposed to polarized light, <a href="#Page_99">99</a>.</li> -<li class="isub1">Influence of, on the Mind, <a href="#Page_101">101</a>.</li> - -<li class="indx">Solids in general, nature of, <a href="#Page_236">236</a>.</li> -<li class="isub1">Constitution of, complicated, <a href="#Page_237">237</a>.<span class="pagenum"><a id="Page_372">372</a></span></li> -<li class="isub1">Toughness of, distinct from hardness; tenacity of, <a href="#Page_238">238</a>.</li> -<li class="isub1">Become liquefied by the addition of heat, <a href="#Page_321">321</a>.</li> - -<li class="indx">Sounds, musical, illustrative of the analysis of phenomena, <a href="#Page_85">85</a>.</li> -<li class="isub1">Means of having a knowledge of, <a href="#Page_89">89</a>.</li> -<li class="isub1">Propagation of, through the air, <a href="#Page_246">246</a>.</li> -<li class="isub1">Newton’s analysis of, <a href="#Page_247">247</a>.</li> - -<li class="indx">Standard measurement, necessity of, <a href="#Page_125">125</a>.</li> -<li class="isub1">Laws of nature used as such, illustrated by the rotation of the earth, <a href="#Page_126">126</a>.</li> - -<li class="indx">Substances all subject to dilatation by the addition of heat, <a href="#Page_243">243</a>.</li> - -<li class="indx">Sun, the character of the heat of, <a href="#Page_315">315</a>.</li> - -<li class="ifrst">Thales, philosophy of, <a href="#Page_107">107</a>.</li> - -<li class="indx">Theories, how to estimate the value of, <a href="#Page_204">204</a>.</li> -<li class="isub1">Best arrived at by the consideration of general laws, <a href="#Page_208">208</a>.</li> -<li class="isub1">Explanatory of the phenomena of nature; on what their application ought to be grounded, <a href="#Page_209">209</a>.</li> - -<li class="indx">Thomson, Dr., his opinion of the atomic weights, <a href="#Page_307">307</a>.</li> - -<li class="indx">Thermometer, air, <a href="#Page_319">319</a>.</li> - -<li class="indx">Thermo-electricity, <a href="#Page_341">341</a>.</li> - -<li class="indx">Time, division of, <a href="#Page_126">126</a>, <a href="#Page_127">127</a>.</li> - -<li class="indx">Torricelli, pupil of Galileo, his experiments proving the weight of atmosphere, <a href="#Page_229">229</a>.</li> - -<li class="indx">Torpedo, shock of, <a href="#Page_341">341</a>, <a href="#Page_342">342</a>.</li> - -<li class="ifrst">Ulugh Begh, his catalogue of stars, <a href="#Page_277">277</a>.</li> - -<li class="ifrst">Vaccination, success of, as a preventive to small-pox, <a href="#Page_52">52</a>.</li> - -<li class="indx">Vision and light, ignorance of the ancients respecting, <a href="#Page_249">249</a>.</li> - -<li class="indx">Volta, his discoveries in electricity, <a href="#Page_335">335</a>.</li> -<li class="isub1">Electric pile of, <a href="#Page_337">337</a>.</li> - -<li class="indx">Voltaic circuit, <a href="#Page_338">338</a>.</li> - -<li class="ifrst">Water, effects of the power of, <a href="#Page_61">61</a>.</li> - -<li class="indx">Whewell, his experiments, <a href="#Page_187">187</a>.</li> - -<li class="indx">Wells, Dr., his theory of dew, <a href="#Page_163">163</a>.</li> - -<li class="indx">Wind, effects of the power of, <a href="#Page_61">61</a>.</li> - -<li class="indx">Wire steel, magnetized masks of, used by needle-makers, <a href="#Page_57">57</a>.</li> - -<li class="indx">Wollaston, Dr., his verification of the laws of double refraction in Iceland spar, <a href="#Page_258">258</a>.</li> -<li class="isub1">His invention of the goniometer, <a href="#Page_292">292</a>.</li> - -<li class="indx">World, the materials of the, <a href="#Page_290">290</a>.</li> - -<li class="ifrst">Young, Dr., his experiments on the interference of the rays of light, <a href="#Page_260">260</a>.</li> - -<li class="ifrst">Zoology, fossil, <a href="#Page_344">344</a>.</li> -</ul> -</div></div> - -<p class="p2 center smaller">THE END.</p> - -<p class="p2 center vspace"> -<span class="small">LONDON<br /> -PRINTED BY SPOTTISWOODE AND CO.<br /> -NEW-STREET SQUARE.</span> -</p> - -<div class="chapter"><div class="footnotes"> -<h2 class="nobreak p1"><a id="FOOTNOTES"></a>FOOTNOTES</h2> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_1" href="#FNanchor_1" class="fnanchor">1</a> Hooke’s Posthumous Works. Lond. 1705.—p. 472 -and p. 458.</p></div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_2" href="#FNanchor_2" class="fnanchor">2</a> Wealth of Nations, book i. chap. i. p. 15.</p></div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_3" href="#FNanchor_3" class="fnanchor">3</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_4" href="#FNanchor_4" class="fnanchor">4</a> <span xml:lang="grc" lang="grc">Λογος</span>, <em>ratio</em>, reason.</p></div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_5" href="#FNanchor_5" class="fnanchor">5</a> <span xml:lang="grc" lang="grc">Λογος</span>, <i xml:lang="la" lang="la">verbum</i>, a word.</p></div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_6" href="#FNanchor_6" class="fnanchor">6</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_7" href="#FNanchor_7" class="fnanchor">7</a> Young. Lectures on Nat. Phil. ii. 627. See also Phil. -Trans. 1801–2.</p></div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_8" href="#FNanchor_8" class="fnanchor">8</a> Captain Basil Hall, R. N.</p></div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_9" href="#FNanchor_9" class="fnanchor">9</a> 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 <span class="smcap">Light</span>.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_10" href="#FNanchor_10" class="fnanchor">10</a> Little reels used in cotton mills to twist the thread.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_11" href="#FNanchor_11" class="fnanchor">11</a> 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.”—<cite>Ed. Phil. Trans.</cite> vol. ix, -p. 312.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_12" href="#FNanchor_12" class="fnanchor">12</a> Dr. Coindet of Geneva.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_13" href="#FNanchor_13" class="fnanchor">13</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_14" href="#FNanchor_14" class="fnanchor">14</a> 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 -<em>most infallible remedy</em>, 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. -</p> -<p> -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 <em>systematic -introduction into nautical diet</em>, 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 <em>one</em> only, and in 1807 <em>one</em>. There -are now many surgeons in the navy who have never seen the -disease.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_15" href="#FNanchor_15" class="fnanchor">15</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_16" href="#FNanchor_16" class="fnanchor">16</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_17" href="#FNanchor_17" class="fnanchor">17</a> Dr. Johnson, Memoirs of the Medical Society, vol. v.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_18" href="#FNanchor_18" class="fnanchor">18</a> 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 -<em>highest</em> monthly average of this engine extends to 79 -millions of pounds.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_19" href="#FNanchor_19" class="fnanchor">19</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_20" href="#FNanchor_20" class="fnanchor">20</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_21" href="#FNanchor_21" class="fnanchor">21</a> No one doubts the <em>practicability</em> 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 <em>desirable</em>.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_22" href="#FNanchor_22" class="fnanchor">22</a> “Experiments to determine the Force of fired Gunpowder.” -Phil. Trans. vol. lxxxvii. p. 254. et seq.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_23" href="#FNanchor_23" class="fnanchor">23</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_24" href="#FNanchor_24" class="fnanchor">24</a> The sulphuric. Bracconot, Annales de Chimie, vol. xii. -p. 184.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_25" href="#FNanchor_25" class="fnanchor">25</a> D’Arcet, Annales de l’Industrie, Fevrier, 1829.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_26" href="#FNanchor_26" class="fnanchor">26</a> 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 <em>impossible</em>, deserves a -higher degree of celebrity than it has obtained.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_27" href="#FNanchor_27" class="fnanchor">27</a> Greenwich.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_28" href="#FNanchor_28" class="fnanchor">28</a> Maskelyne’s.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_29" href="#FNanchor_29" class="fnanchor">29</a> Thomson’s First Principles of Chemistry, vol. ii. p. 68.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_30" href="#FNanchor_30" class="fnanchor">30</a> 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:— -</p> - -<blockquote class="hang2"> - -<p class="ii">I. Mutation is either generation or corruption.</p> -<p class="iii">II. Generation and corruption only happen between contraries.</p> -<p class="iiii">III. The motions of contraries are contrary.</p> -<p class="iiv">IV. The celestial motions are circular.</p> -<p class="iv">V. Circular motions have no contraries.</p> -<div class="in2"> -<p class="in2"><span xml:lang="grc" lang="grc">α</span>. Because there can be but three simple motions.</p> -<p class="in0 in4">1. To a centre.<br /> -2. Round a centre.<br /> -3. From a centre.</p> -<p class="in2"><span xml:lang="grc" lang="grc">β</span>. Of three things, one only can be contrary to one.</p> -<p class="in2"><span xml:lang="grc" lang="grc">γ</span>. But a motion to a centre is manifestly the contrary to a motion from a centre.</p> -<p class="in2"><span xml:lang="grc" lang="grc">δ</span>. Therefore a motion <em>round</em> a centre (<i>i. e.</i> a circular motion) remains without a contrary.</p> -</div> -<p class="ivi"> -VI. <em>Therefore</em> celestial motions have no contraries—<em>therefore</em> -among celestial <em>things</em> there are no contraries—<em>therefore</em> -the heavens are eternal, immutable, incorruptible, and so forth.</p></blockquote> - -<p> -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.—<i>See</i> <span class="smcap">Galileo</span>, -<cite>Systema Cosmicum</cite>, Dial. i. p. 30.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_31" href="#FNanchor_31" class="fnanchor">31</a> 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.—<cite>Macquer’s -Dictionary of Chemistry</cite>, i. x.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_32" href="#FNanchor_32" class="fnanchor">32</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_33" href="#FNanchor_33" class="fnanchor">33</a> See the Life of Galileo Galilei, by Mr. Drinkwater, with -Illustrations of the Advancement of Experimental Philosophy.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_34" href="#FNanchor_34" class="fnanchor">34</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_35" href="#FNanchor_35" class="fnanchor">35</a> Edinburgh Phil. Journ. 1819, vol. i. p. 8.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_36" href="#FNanchor_36" class="fnanchor">36</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_37" href="#FNanchor_37" class="fnanchor">37</a> Accurate and <em>perfectly</em> 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?</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_38" href="#FNanchor_38" class="fnanchor">38</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_39" href="#FNanchor_39" class="fnanchor">39</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_40" href="#FNanchor_40" class="fnanchor">40</a> 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 <em>places</em> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_41" href="#FNanchor_41" class="fnanchor">41</a> The reader will find this subject further developed in a -paper lately communicated to the Geological Society.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_42" href="#FNanchor_42" class="fnanchor">42</a> Phil. Trans. 1824.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_43" href="#FNanchor_43" class="fnanchor">43</a> Wells on Dew.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_44" href="#FNanchor_44" class="fnanchor">44</a> Principia, book iii. prop. 6.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_45" href="#FNanchor_45" class="fnanchor">45</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_46" href="#FNanchor_46" class="fnanchor">46</a> See Phil. Trans. 1819.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_47" href="#FNanchor_47" class="fnanchor">47</a> “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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_48" href="#FNanchor_48" class="fnanchor">48</a> Thomson’s First Principles of Chemistry.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_49" href="#FNanchor_49" class="fnanchor">49</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_50" href="#FNanchor_50" class="fnanchor">50</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_51" href="#FNanchor_51" class="fnanchor">51</a> Alphonso of Castile, 1252.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_52" href="#FNanchor_52" class="fnanchor">52</a> Jackson, Letters on Various Subjects, &c.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_53" href="#FNanchor_53" class="fnanchor">53</a> Thomson’s First Principles of Chemistry, Introduction.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_54" href="#FNanchor_54" class="fnanchor">54</a> The progress of astronomical discovery has since shown -that this law cannot be relied on (1851).</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_55" href="#FNanchor_55" class="fnanchor">55</a> Novum Organum, part ii. table 2. (24), (30), &c. on the -form or nature of heat.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_56" href="#FNanchor_56" class="fnanchor">56</a> 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 <em>above</em> 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 <em>below</em> that of the general -atmosphere, while the metal yet retains one above it. Thus, -a subversion of the equilibrium of temperature has been <i xml:lang="la" lang="la">bonâ -fide</i> effected. Heat has been driven from the air into the -metal, while every thing else remains unchanged. -</p> -<p> -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 <em>same</em> 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 <em>drained</em> of its heat.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_57" href="#FNanchor_57" class="fnanchor">57</a> See Phil. Trans. 1824.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_58" href="#FNanchor_58" class="fnanchor">58</a> 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.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_59" href="#FNanchor_59" class="fnanchor">59</a> See a description of a contrivance of this kind by Dr. -Young, Lectures, vol. i. p. 191.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_60" href="#FNanchor_60" class="fnanchor">60</a> Boyle’s Works, folio, vol. iii. Essay x. p. 185.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_61" href="#FNanchor_61" class="fnanchor">61</a> Jackson, The Four Ages, p. 52. London: Cadell and -Davies, 1798. 8vo.</p></div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_62" href="#FNanchor_62" class="fnanchor">62</a> Jackson, The Four Ages, p. 90.</p></div> -</div></div> - -<div class="chapter"><div class="transnote"> -<h2 class="nobreak p1"><a id="Transcribers_Notes">Transcriber’s Notes</a></h2> - -<p>Cover created by Transcriber and placed in the Public Domain.</p> - -<p>Punctuation, hyphenation, and spelling were made consistent when a predominant -preference was found in this book; otherwise they were not changed.</p> - -<p>Simple typographical errors were corrected; occasional unbalanced -quotation marks retained.</p> - -<p>Ambiguous hyphens at the ends of lines were retained.</p> - -<p>Spelling of non-English words was not reviewed.</p> - -<p>Text uses both “appreciate” and “appretiate”; both retained.</p> - -<p>Index not checked for proper alphabetization or correct page references.</p> -</div></div> - - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of Preliminary Discourse on the Study of -Natural Philosophy, by John F. 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