CHAPTER IV

.

PHYSICAL THEORIES OF HEAT.

WHEN we look at the condition of that branch of knowledge which, according to the phraseology already employed, we must call _Physical Thermotics_, in opposition to Formal Thermotics, which gives us detached laws of phenomena, we find the prospect very different from that which was presented to us by physical astronomy, optics, and acoustics. In these sciences, the maintainers of a distinct and comprehensive theory have professed at least to show that it explains and includes the principal laws of phenomena of various kinds; in Thermotics, we have only attempts to explain a part of the facts. We have here no example of an hypothesis which, assumed in order to explain one class of phenomena, has been found also to account exactly for another; as when central forces led to the precession of the equinoxes, or when the explanation of polarization explained also double refraction; or when the pressure of the atmosphere, as measured by the barometer, gave the true velocity of sound. Such coincidences, or _consiliences_, as I have elsewhere called them, are the test of truth; and thermotical theories cannot yet exhibit credentials of this kind. {181}

On looking back at our view of this science, it will be seen that it may be distinguished into two parts; the Doctrines of Conduction and Radiation, which we call Thermotics proper; and the Doctrines respecting the relation of Heat, Airs, and Moisture, which we have termed Atmology. These two subjects differ in their bearing on our hypothetical views.

_Thermotical Theories._--The phenomena of radiant heat, like those of radiant light, obviously admit of general explanation in two different ways;--by the emission of material particles, or by the propagation of undulations. Both these opinions have found supporters. Probably most persons, in adopting Prevost's theory of exchanges, conceive the radiation of heat to be the radiation of matter. The undulation hypothesis, on the other hand, appears to be suggested by the production of heat by friction, and was accordingly maintained by Rumford and others. Leslie[68\10] appears, in a great part of his _Inquiry_, to be a supporter of some undulatory doctrine, but it is extremely difficult to make out what his undulating medium is; or rather, his opinions wavered during his progress. In page 31, he asks, "What is this calorific and frigorific fluid? and after keeping the reader in suspense for a moment, he replies, "Quod petis hic est. It is merely the ambient AIR." But at page 150, he again asks the question, and, at page 188, he answers, "It is the same subtile matter that, according to its different modes of existence, constitutes either heat or light." A person thus vacillating between two opinions, one of which is palpably false, and the other laden with exceeding difficulties which he does not even attempt to remove, had little right to protest against[69\10] "the sportive freaks of some intangible _aura_;" to rank all other hypotheses than his own with the "occult qualities of the schools;" and to class the "prejudices" of his opponents with the tenets of those who maintained the _fuga vacui_ in opposition to Torricelli. It is worth while noticing this kind of rhetoric, in order to observe, that it may be used just as easily on the wrong side as on the right.

[Note 68\10: _An Experimental Inquiry into the Nature and Propagation of Heat_, 1804.]

[Note 69\10: Ib. p. 47.]

Till recently, the theory of material heat, and of its propagation by emission, was probably the one most in favor with those who had studied mathematical thermotics. As we have said, the laws of {182} conduction, in their ultimate analytical form, were almost identical with the laws of motion of fluids. Fourier's principle also, that the radiation of heat takes place from points below the surface, and is intercepted by the superficial particles, appears to favor the notion of material emission.

Accordingly, some of the most eminent modern French mathematicians have accepted and extended the hypothesis of a material caloric. In addition to Fourier's doctrine of molecular extra-radiation, Laplace and Poisson have maintained the hypothesis of _molecular intra-radiation_, as the mode in which conduction takes place; that is, they say that the particles of bodies are to be considered as _discrete_, or as points separated from each other, and acting on each other at a distance; and the conduction of heat from one part to another, is performed by radiation between all neighboring

## particles. They hold that, without this hypothesis, the differential

equations expressing the conditions of conduction cannot be made homogeneous: but this assertion rests, I conceive, on an error, as Fourier has shown, by dispensing with the hypothesis. The necessity of the hypothesis of discrete molecular action in bodies, is maintained in all cases by M. Poisson; and he has asserted Laplace's theory of capillary attraction to be defective on this ground, as Laplace asserted Fourier's reasoning respecting heat to be so. In reality, however, this hypothesis of discrete molecules cannot be maintained as a physical truth; for the law of molecular action, which is assumed in the reasoning, after answering its purpose in the progress of calculation, vanishes in the result; the conclusion is the same, whatever law of the intervals of the molecules be assumed. The definite integral, which expresses the whole action, no more proves that this action is actually made of the differential parts by means of which it was found, than the processes of finding the weight of a body by integration, prove it to be made up of differential weights. And therefore, even if we were to adopt the emission theory of heat, we are by no means bound to take along with it the hypothesis of discrete molecules.

But the recent discovery of the refraction, polarization, and depolarization of heat, has quite altered the theoretical aspect of the subject, and, almost at a single blow, ruined the emission theory. Since heat is reflected and refracted like light, analogy would lead us to conclude that the mechanism of the processes is the same in the two cases. And when we add to these properties the property of polarization, it is scarcely possible to believe otherwise than that heat consists in {183} transverse vibrations; for no wise philosopher would attempt an explanation by ascribing poles to the emitted particles, after the experience which Optics affords, of the utter failure of such machinery.

But here the question occurs, If heat consists in vibrations, whence arises the extraordinary identity of the laws of its propagation with the laws of the flow of matter? How is it that, in conducted heat, this vibration creeps slowly from one part of the body to another, the part first heated remaining hottest; instead of leaving its first place and travelling rapidly to another, as the vibrations of sound and light do? The answer to these questions has been put in a very distinct and plausible form by that distinguished philosopher, M. Ampère, who published a _Note on Heat and Light considered as the results of Vibratory Motion_,[70\10] in 1834 and 1835; and though this answer is an hypothesis, it at least shows that there is no fatal force in the difficulty.

[Note 70\10: _Bibliothèque Universelle de Genève_, vol. xlix. p. 225. _Ann. Chim._ tom. lvii. p. 434.]

M. Ampère's hypothesis is this; that bodies consist of solid molecules, which may be considered as arranged at intervals in a very rare ether; and that the vibrations of the molecules, causing vibrations of the ether and caused by them, constitute heat. On these suppositions, we should have the phenomena of conduction explained; for if the molecules at one end of a bar be hot, and therefore in a state of vibration, while the others are at rest, the vibrating molecules propagate vibrations in the ether, but these vibrations do not produce heat, except in proportion as they put the quiescent molecules of the bar in vibration; and the ether being very rare compared with the molecules, it is only by the repeated impulses of many successive vibrations that the nearest quiescent molecules are made to vibrate; after which they combine in communicating the vibration to the more remote molecules. "We then find necessarily," M. Ampère adds, "the same equations as those found by Fourier for the distribution of heat, setting out from the same hypothesis, that the temperature or heat transmitted is proportional to the difference of the temperatures."

Since the undulatory hypothesis of heat can thus answer all obvious objections, we may consider it as upon its trial, to be confirmed or modified by future discoveries; and especially by an enlarged knowledge of the laws of the polarization of heat.

[2nd Ed.] [Since the first edition was written, the analogies between light and heat have been further extended, as I have already stated. It {184} has been discovered by MM. Biot and Melloni that quartz impresses a circular polarization upon heat; and by Prof. Forbes that mica, of a certain thickness, produces phenomena such as would be produced by the impression of circular polarization of the supposed transversal vibrations of radiant heat; and further, a rhomb of rock-salt, of the shape of the glass rhomb which verified Fresnel's extraordinary anticipation of the circular polarization of light, verified the expectation, founded upon other analogies, of the polarization of heat. By passing polarized heat through various thicknesses of mica, Prof. Forbes has attempted to calculate the length of an undulation for heat.

These analogies cannot fail to produce a strong disposition to believe that light and heat, essences so closely connected that they can hardly be separated, and thus shown to have so many curious properties in common, are propagated by the same machinery; and thus we are led to an Undulatory Theory of Heat.

Yet such a Theory has not yet by any means received full confirmation. It depends upon the analogy and the connexion of the Theory of Light, and would have little weight if those were removed. For the separation of the rays in double refraction, and the phenomena of periodical intensity, the two classes of facts out of which the Undulatory Theory of Optics principally grew, have neither of them been detected in thermotical experiments. Prof. Forbes has assumed alternations of heat for increasing thicknesses of mica, but in his experiments we find only one _maximum_. The occurrence of alternate maxima and minima under the like circumstances would exhibit visible waves of heat, as the fringes of shadows do of light, and would thus add much to the evidence of the theory.

Even if I conceived the Undulatory Theory of Heat to be now established, I should not venture, as yet, to describe its establishment as an event in the history of the Inductive Sciences. It is only at an interval of time after such events have taken place that their history and character can be fully understood, so as to suggest lessons in the Philosophy of Science.]

_Atmological Theories._--Hypotheses of the relations of heat and air almost necessarily involve a reference to the forces by which the composition of bodies is produced, and thus cannot properly be treated of, till we have surveyed the condition of chemical knowledge. But we may say a few words on one such hypothesis; I mean the hypothesis on the subject of the atmological laws of heat, proposed by Laplace, in the twelfth Book of the _Mécanique Céléste_, and published in 1823. {185} It will be recollected that the main laws of phenomena for which we have to account, by means of such an hypothesis, are the following:--

(1.) The law of Boyle and Mariotte, that the elasticity of an air varies as its density. See Chap. iii., Sect. 1 of this Book.

(2.) The Law of Gay-Lussac and Dalton, that all airs expand equally by heat. See Chap. ii. Sect. 1.

(3.) The production of heat by sudden compression. See Chap. ii. Sect. 2.

(4.) Dalton's principle of the mechanical mixture of airs. See Chap. iii. Sect. 3.

(5.) The Law of expansion of solids and fluids by heat. See Chap. ii. Sect. 1.

(6.) Changes of consistence by heat, and the doctrine of latent heat. See Chap. ii. Sect. 3.

(7.) The Law of the expansive force of steam. See Chap. iii. Sect. 4.

Besides these, there are laws of which it is doubtful whether they are or are not included in the preceding, as the low temperature of the air in the higher parts of the atmosphere. (See Chap. iii. Sect. 5.)

Laplace's hypothesis[71\10] is this:--that bodies consist of

## particles, each of which gathers round it, by its attraction, a

quantity of caloric: that the particles of the bodies attract each other, besides attracting the caloric, and that the particles of the caloric repel each other.

[Note 71\10: _Méc. Cél._ t. v. p. 89.]

In gases, the particles of the bodies are so far removed, that their mutual attraction is insensible, and the matter tends to expand by the mutual repulsion of the caloric. He conceives this caloric to be constantly radiating among the particles; the density of this internal radiation is the _temperature_, and he proves that, on this supposition, the elasticity of the air will be as the density, and as this temperature. Hence follow the three first rules above stated. The same suppositions lead to Dalton's principle of mixtures (4), though without involving his mode of conception; for Laplace says that whatever the mutual action of two gases be, the whole pressure will be equal to the sum of the separate pressures.[72\10] Expansion (5), and the changes of consistence (6), are explained by supposing[73\10] that in solids, the mutual attraction of the

## particles of the body is the greatest force; in liquids, the

attraction of the particles for the caloric; in airs, the repulsion of {186} the caloric. But the doctrine of latent heat again modifies[74\10] the hypothesis, and makes it necessary to include latent heat in the calculation; yet there is not, as we might suppose there would be if the theory were the true one, any confirmation of the hypothesis resulting from the new class of laws thus referred to. Nor does it appear that the hypothesis accounts for the relation between the elasticity and the temperature of steam.

[Note 72\10: Ib. p. 110.]

[Note 73\10: Ib. p. 92.]

[Note 74\10: _Méc. Cél._ t. v. p. 93.]

It will be observed that Laplace's hypothesis goes entirely upon the materiality of heat, and is inconsistent with any vibratory theory; for, as Ampère remarks, "It is clear that if we admit heat to consist in vibrations, it is a contradiction to attribute to heat (or caloric) a repulsive force of the particles which would be a cause of vibration."

An unfavorable judgment of Laplace's Theory of Gases is suggested by looking for that which, in speaking of Optics, was mentioned as the great characteristic of a true theory; namely, that the hypotheses, which were assumed in order to account for one class of facts, are found to explain another class of a different nature:--the consilience of inductions. Thus, in thermotics, the law of an intensity of radiation proportional to the sine of the angle of the ray with the surface, which is founded on direct experiments of radiation, is found to be necessary in order to explain the tendency of neighboring bodies to equality of temperature; and this leads to the higher generalization, that heat is radiant from points below the surface. But in the doctrine of the relation of heat to gases, as delivered by Laplace, there is none of this unexpected confirmation; and though he explains some of the leading laws, his assumptions bear a large proportion to the laws explained. Thus, from the assumption that the repulsion of gases arises from the mutual repulsion of the particles of caloric, he finds that the pressure in any gas is as the square of the density and of the quantity of caloric;[75\10] and from the assumption that the temperature is the internal radiation, he finds that this temperature is as the density and the square of the caloric.[76\10] Hence he obtains the law of Boyle and Mariotte, and that of Dalton and Gay-Lussac. But this view of the subject requires other assumptions when we come to latent heat; and accordingly, he introduces, to express the latent heat, a new quantity.[77\10] Yet this quantity produces no effect on his calculations, nor does he apply his reasoning to any problem in which latent heat is concerned. {187}

[Note 75\10: P = 2 π H K ρ^2_c_^2 (1) p. 107.]

[Note 76\10: _q_' Π (_a_) = ρ_c_^2 (2) p. 108.]

[Note 77\10: The quantity _i_, p. 113.]

Without, then, deciding upon this theory, we may venture to say that it is wanting in all the prominent and striking characteristics which we have found in those great theories which we look upon as clearly and indisputably established.

_Conclusion._--We may observe, moreover, that heat has other bearings and effects, which, as soon as they have been analysed into numerical laws of phenomena, must be attended to in the formation of thermotical theories. Chemistry will probably supply many such; those which occur to us, we must examine hereafter. But we may mention as examples of such, MM. De la Rive and Marcet's law, that the specific heat of all gases is the same;[78\10] and MM. Dulong and Petit's law, that single atoms of all simple bodies have the same capacity for heat.[79\10] Though we have not yet said anything of the relation of different gases, or explained the meaning of _atoms_ in the chemical sense, it will easily be conceived that these are very general and important propositions.

[Note 78\10: _Ann. Chim._ xxxv. (1827.)]

[Note 79\10: Ib. x. 397.]

Thus the science of Thermotics, imperfect as it is, forms a highly-instructive part of our survey; and is one of the cardinal points on which the doors of those chambers of physical knowledge must turn which hitherto have remained closed. For, on the one hand, this science is related by strong analogies and dependencies to the most complete portions of our knowledge, our mechanical doctrines and optical theories; and on the other, it is connected with properties and laws of a nature altogether different,--those of chemistry; properties and laws depending upon a new system of notions and relations, among which clear and substantial general principles are far more difficult to lay hold of and with which the future progress of human knowledge appears to be far more concerned. To these notions and relations we must now proceed; but we shall find an intermediate stage, in certain subjects which I shall call the _Mechanico-chemical_ Sciences; viz., those which have to do with Magnetism, Electricity, and Galvanism.

{{189}}

## BOOK XI.

_THE MECHANICO-CHEMICAL SCIENCES._

HISTORY OF ELECTRICITY.

PARVA metu primo: mox sese extollit in auras, Ingrediturque solo, et caput inter nubila condit. _Æn._ iv. 176.

A timid breath at first, a transient touch, How soon it swells from little into much! Runs o'er the ground, and springs into the air, And fills the tempest's gloom, the lightning's glare; While denser darkness than the central storm Conceals the secrets of its inward form.

{{191}} INTRODUCTION.

_Of the Mechanico-Chemical Sciences._

UNDER the title of Mechanico-Chemical Sciences, I include the laws of Magnetism, Electricity, Galvanism, and the other classes of phenomena closely related to these, as Thermo-electricity. This group of subjects forms a curious and interesting portion of our physical knowledge; and not the least of the circumstances which give them their interest, is that double bearing upon mechanical and chemical principles, which their name is intended to imply. Indeed, at first sight they appear to be purely Mechanical Sciences; the attractions and repulsions, the pressure and motion, which occur in these cases, are referrible to mechanical conceptions and laws, as completely as the weight or fall of terrestrial bodies, or the motion of the moon and planets. And if the phenomena of magnetism and electricity had directed us only to such laws, the corresponding sciences must have been arranged as branches of mechanics. But we find that, on the other side, these phenomena have laws and bearings of a kind altogether different. Magnetism is associated with Electricity by its mechanical analogies; and, more recently, has been discovered to be still more closely connected with it by physical influence; electric is identified with galvanic agency; but in galvanism, decomposition, or some action of that kind, universally appears; and these appearances lead to very general laws. Now composition and decomposition are the subjects of Chemistry; and thus we find that we are insensibly but irresistibly led into the domain of that science. The highest generalizations to which we can look, in advancing from the elementary facts of electricity and galvanism, must involve chemical notions; we must therefore, in laying out the platform of these sciences, make provision for that convergence of mechanical and chemical theory, which they are to exhibit as we ascend.

We must begin, however, with stating the mechanical phenomena of these sciences, and the reduction of such phenomena to laws. In this point of view, the phenomena of which we have to speak are those in which bodies exhibit attractions and repulsions, peculiarly determined by their nature and circumstances; as the magnet, and a {192} piece of amber when rubbed. Such results are altogether different from the universal attraction which, according to Newton's discovery, prevails among all particles of matter, and to which cosmical phenomena are owing. But yet the difference of these special attractions, and of cosmical attraction, was at first so far from being recognized, that the only way in which men could be led to conceive or assent to an action of one body upon another at a distance, in cosmical cases, was by likening it to magnetic attraction, as we have seen in the history of Physical Astronomy. And we shall, in the first part of our account, not dwell much upon the peculiar conditions under which bodies are magnetic or electric, since these conditions are not readily reducible to mechanical laws; but, taking the magnetic or electric character for granted, we shall trace its effects.

The habit of considering magnetic action as the type or general case of attractive and repulsive agency, explains the early writers having spoken of Electricity as a kind of Magnetism. Thus Gilbert, in his book _De Magnete_ (1600), has a chapter,[1\11] _De coitione Magniticâ, primumque de Succini attractione, sive verius corporum ad Succinum applicatione_. The manner in which he speaks, shows us how mysterious the fact of attraction then appeared; so that, as he says, "the magnet and amber were called in aid by philosophers as illustrations, when our sense is in the dark in abstruse inquiries, and when our reason can go no further. Gilbert speaks of these phenomena like a genuine inductive philosopher, reproving[2\11] those who before him had "stuffed the booksellers' shops by copying from one another extravagant stories concerning the attraction of magnets and amber, without giving any reason from experiment." He himself makes some important steps in the subject. He distinguishes magnetic from _electric_ forces,[3\11] and is the inventor of the latter name, derived from ἤλεκτρον, _electron_, amber. He observes rightly, that the electric force attracts all light bodies, while the magnetic force attracts iron only; and he devises a satisfactory apparatus by which this is shown. He gives[4\11] a considerable list of bodies which possess the electric property; "Not only amber and agate attract small bodies, as some think, but diamond, sapphire, carbuncle, opal, amethyst, Bristol gem, beryli, crystal, glass, glass of antimony, spar of various kinds, sulphur, mastic, sealing-wax," and other substances which he mentions. Even his speculations on the general laws of these phenomena, though vague and erroneous, as {193} at that period was unavoidable, do him no discredit when compared with the doctrines of his successors a century and a half afterwards. But such speculations belong to a succeeding part of this history.

[Note 1\11: Lib. ii. cap. 2.]

[Note 2\11: _De Magnete_, p. 48.]

[Note 3\11: Ib. p. 52.]

[Note 4\11: Ib. p. 48.]

In treating of these Sciences, I will speak of Electricity in the first place; although it is thus separated by the interposition of Magnetism from the succeeding subjects (Galvanism, &c.) with which its alliance seems, at first sight, the closest, and although some general notions of the laws of magnets were obtained at an earlier period than a knowledge of the corresponding relations of electric phenomena: for the theory of electric attraction and repulsion is somewhat more simple than of magnetic; was, in fact, the first obtained; and was of use in suggesting and confirming the generalization of magnetic laws.

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