chanical process. For a mass of water | sions, is found, when stretched by a conretains the temperature of freezing unchang. stant weight, to contract on being heated, ed, until it is all converted into ice, and and to raise the weight. according to Carnot's and even to the dynam We have several times alluded to the ical theory, no work is required to make fact, that the amount of heat developed by heat pass from one body to another at the the compression of air is only approximatesame temperature. J. Thomson, seeing ly equal to the equivalent of the work exthat this result, if correct, involved the pos- pended in compressing it, although in sibility of producing work from nothing Joule's experiment of 1844 it appeared to (since water expands with great force in the be exactly equal to it. There is, as before obact of freezing), was led, by carefully scru- served, no à priori reason for the existence tinizing the assumptions on which it de- of any such proportionality, for it is quite pended, to find that all were correct with the conceivable that a gas might exist in which possible exception of the temperature at the whole work expended in compressing it, which water freezes; which he then showed is employed in overcoming repulsive forces must depend, as the boiling-point had long among its particles, and would therefore be been known to do, upon the pressure; and wholly stored up as mechanical power in the he showed that the freezing point of water compressed gas, without any change of must be lower by 0·0135° Fahr. for each temperature whatever. That heat, nearly additional atmosphere of pressure. This equivalent to the work expended in comvery curious theoretical deduction was veri- pression, is actually developed, shows us fied, to its numerical details, by means of that the mutual molecular forces among Erstedt's Piezometer, by W. Thomson.* particles of a gas are exceedingly small, and Hopkins and Bunsen have since verified, experimentally, that, in cases where bodies contract on solidifying, as is the case with sulphur, wax, etc., the melting point is raised by increase of pressure. that the pressure of a gas is due almost entirely to the "repulsive motion" of Davy. Clausius, Maxwell, and others, have lately made some very beautiful investigations into the laws of gaseous pressure, diffusion, etc., on the supposition that a gas consists of free elastic particles, exerting no molecular action on each other, but moving in straight lines with immense velocity, until they impinge on each other or on the sides of a containing vessel, when they rebound according to the known laws of impact of spheres. The time has hardly yet come, however, in which much is to be expected from such hypotheses; we are as yet almost completely ignorant of the ultimate structure of the molecules or particles of matter. The complete theory of all such cases was, however, previously given by W. Thomson in his (already cited) paper of 1851 on the Dynamical Theory of Heat. Without encumbering himself with, or limiting the generality of his results by, any hypothesis, he applies the fundamental propositions of the dynamical theory (already given) to all bodies, and deduces many very curious and important results regarding the specific heats of all substances; with special conclusions agreeing with those of Rankine and Clausius for "perfect" gases, and for mixtures of portions of a body in different A method of experimentally discovering, states but at the same temperature, as ice with very great accuracy, the relation beand water, or water and saturated steam. tween the heat produced and the work Among these we may mention the follow-spent in the compression of a gas, was suging: When a substance contracts as its gested by Thomson in 1851* and employed temperature rises (as is the case, for instance, with some modifications in a series of exwith water between its freezing-point and periments, which he has since carried on in its point of maximum density) its tempera- conjunction with Joule, and whose results ture will be lowered by a sudden compression. have been from time to time published in In two most valuable experimental papers the Philosophical Transactions during the by Joule, Thomson's formulæ are com- last ten years, with the title Thermal pletely verified (within the limits of experi- Effects of Fluids in Motion. The principle mental error) for substances of the most of this method is excessively simple; it dissimilar qualities. One very curious re- consists merely in forcing the gas to be exsult is afforded by india-rubber, which, perimented on through a porous plug, and when suddenly extended, becomes warm; observing its temperature on each side of and, in agreement with Thomson's conclu- the plug. These temperatures should (theoretically) be exactly equal if the heat developed by compression is equal to the *Proc. R.S. E. 1850. On some Thermo-dynamic Properties of Solids, and On the Thermal Effects of compressing Fluids. -Phil. Trans. 1859. * Trans. R.S.E. work expended, and not unless. By this | known laws from any previous distribution. process it is found that no gas perfectly sat- When Carnot's method, as adapted to the isfies the criterion; and as we might expect, dynamical theory of heat by Clausius, was the liquefiable gases are those which most applied by Thomson to the transformations diverge from it. By means of a sufficient of heat into work, and work into heat, it series of such experiments, carried on at led him to the following amongst other different temperatures and pressures, com- propositions. plete theoretical data for a gas-engine have been obtained; and the extensive and valuable experiments of Regnault (with additions, as to the density of steam at high pressures, suppplied by Joule and Thomson) have furnished corresponding data for the steam-engine; so that the theoretical treatment of these important instruments is now at all events approximately complete. But it is no part of our plan to enter into details of application. When heat is created by a reversible process, there is also transference from a cold. body to a hot one, of a quantity of heat, bearing to that created a definite ratio de pending on the temperatures of the two bodies. When heat is created by an unreversible process (such as friction) there is a dissipa tion of energy, and a full restoration of it to its primitive condition is impossible. From these it follows that any restoration of mechanical effect, from the state of heat, requires the using of more heat than the equivalent of the work obtained, this surplus going into a colder body. We make no further comment on this at present, but in our complementary article it will form a most important feature. As already mentioned, we have tried to keep to the direct relation between heat and mechanical effect, leaving to another occasion the far more extensive results which have been arrived at with reference to indirect relations; and we have refrained from entering upon the consideration of the relations which have been proved to exist be- We have, as yet, said nothing of Radiant tween heat and all other forms of energy. heat, of which the Caloristic idea seems to What we have given is almost entirely con- have been exactly analogous to the Corpusfined to the subject of the thermo-elastic cular Theory of Light. Davy coolly specproperties of liquids and gases. W. Thom-ulates on the combinations of light and son* has published an extremely general in- oxygen, in the very paper in which he devestigation of the laws of this subject, including crystalline solids; but to give a satisfactory account of it would lead us into details and difficulties far too great for any but a very small class of readers. stroyed the notion of the materiality of heat! The first really extensive, and on the whole trustworthy, experiments on radiant heat are those of Leslie, but we need not trouble ourselves with his theoretical speculations. There remains, however, one interesting The experiments of Forbes and Melloni portion of our subject, which, though hav- showed so complete a resemblance between ing most important bearings upon the sub- the laws of reflection, refraction, polarizaject of energy and its distribution through tion, absorption, etc., of light and radiant the universe, is in part a branch of Thermo- heat, that no doubt could remain as to their dynamics. This is the consideration, al-identity. And as light had, chiefly by the ready alluded to, of the Dissipation of En- theoretical and experimental investigations ergy. But in accordance with our plan, of Young and Fresnel, been shown to conwe shall only consider it at present as re- sist in the undulations of some highly elastic gards heat and mechanical effect. In the medium pervading all space; it followed first place, heat in a conducting body tends that radiant heat also is motion and not matto a state of dissipation or diffusion, never ter. Radiant heat differs from light merely to a concentration at one or more places. as a grave note does from a shrill one, or This is a direct consequence of the laws as the Atlantic roll differs from the ripple discovered by Fourier for the motion of on a lake. Light was shown by Leslie to heat in a solid. Their mathematical expres- heat bodies which absorb it, and on this prinsions point also to the fact that a uniform ciple he constructed his photometer. distribution of heat, or a distribution tending to become uniform, must have arisen from some primitive distribution of heat of a kind not capable of being produced by Quarterly Math. Journal, 1857. The law of exchanges, as it was called by Prevost, who first, enunciated it, explained what was erroneously called the radiation of cold, i.e., that a piece of ice brought near the bulb of a thermometer cooled it, with other more complex but perfectly analHe considDis-ogous experimental results. On a Universal Tendency in Nature to the VOL. XL. ered that all bodies radiate heat, but the more the higher is their temperature, so that, in the simple case above mentioned, | chirp of the cricket, are inaudible to many the thermometer gave more heat to the ice ears). The most important application of than it received from it a perfectly satis- this discovery has been to the rendering visfactory explanation. This theory has since ible these invisible rays, and thus studying been greatly extended by Stewart, Kirchhof, through a wider range of refrangibility the and De la Provostaye, who have independ- radiations from any source. Unfortunately, ently arrived at the conclusion that the ra- the principle of dissipation forbids us to andiating power of a body for any definite ray ticipate any similar method of studying raof heat is equal to its absorbing power for diant heat by changing it into light, so that the same. Light and radiant heat being here we are literally obliged to grope in the only different forms of the same phenome- dark for our results. The phenomena of non, we may (with Melloni) speak of the Phosphorescence, when not traceable to chemcolours of different kinds of radiant heat, ical combination, evidently belong to the and then the analogy with corresponding same class with those of fluorescence, and phenomena in the case of light becomes at have been recently studied with great care by once evident. A very curious example of Becquerel, who has obtained many remarkthe truth of this proposition, noticed by able results. Stewart, is furnished by heating to whiteness a willow-pattern plate, and looking at it in the dark, when we see instead of a dark pattern on a white ground, a white pattern on a dark ground; those parts which, when the plate is cold, appear dark, do so in consequence of their absorbing the incident light more freely than the white parts, and, when heated to whiteness, they appear bright because they radiate better. Kirchhof derived from his investigation, and verified by conclusive experiments, the explanation of the physical cause of the dark lines in the solar spectrum, which had, however, been previously suggested by Stokes. The very amazing results which Kirchhof and others have recently arrived at by the application of this principle, must be familiar to many of our readers, so that we have the less hesitation in passing over this beautiful part of our subject with so brief a notice. We shall now, taking for granted the dynamical theory of heat, consider very briefly the explanations which it furnishes of many important phenomena, not alluded to in the preceding semi historical sketch, because their explanation is very evident as soon as the true theory has been found. Thus, for instance, Heat of Combination, as it is called, is obviously now to be explained as arising from the mechanical effect of the force of chemical affinity-whatever may be the nature and origin of that force -just as a stone falling to the ground under the action of the earth's attraction generates heat by the impact. From this explanation also follow as obvious truths, the laws of this subject, experimentally arrived at by Andrews, Hess, and others; of which one,- viz., that the cold produced in the decomposition of a compound is exactly equal to the heat produced by the combination of Leslie's result, that a body, such as col- its elements,- may be taken as an instance. oured glass, is heated by absorbing light, When a salt is deposited in crystals from has recently received a most interesting ex- a supersaturated solution, we have, in gentension from the discovery by Stokes of eral, evolution of heat; formerly this was the physical cause of certain curious phe-attributed to the latent heat of solution, it nomena observed by Brewster and Herschel, is now easily seen to be, like ordinary latent in solutions of quinine and certain kinds of fluor-spar, from the latter of which the phenomena have been called by the general name Fluorescence. The physical fact is simply this, that these and other bodies, especially the green colouring matter of leaves and "canary" glass coloured with Oxide of Uranium, radiate as light instead of heat, part of the light which they absorb. This is, properly speaking, identical with Leslie's result, because the light radiated is lower in the scale than that absorbed, and is in gen. eral most freely produced from light so high in the scale as to be invisible to the eye (just as very shrill sounds, such as the heat, dependent on the change of relative position of the molecules involved. The contrary effect is of course produced when a salt is dissolved, and even when two crystalline solids, as ice and salt, liquefy in the act of combining. Hence the justice of the popular outcry against the common process of destroying ice on the pavements by sprinkling salt upon it; as, though the ice is melted, a great additional lowering of temperature is produced. Hence also the effect of the combinations called "freezing mixtures," which are of many kinds; from the simplest, such as the solution of nitrate of ammonia in water, to the most complex, such as the mixture of solid carbonic acid and ether in vacuo. As was cursorily noticed at the com mencement of this article, the so-called | vestigation, mainly due to Joule, has indislatent heat probably depends upon molecu- solubly connected by laws of equivalence lar arrangement; the heat, which is lost to all forms of energy, including even such the thermometer, disappears in producing, mysterious forms as are observed in electroor is transformed into, the work of tearing chemistry and electro-magnetism; and that asunder the particles of a solid or liquid, a complete account of the dynamical theory and placing them in the positions of less of heat necessarily involves, what we prorelative constraint which they occupy in a pose to give on another occasion, an account liquid or a vapour respectively. It is con- of the one grand law of natural philosophyceivable, however, that it also may be mo- the CONSERVATION OF ENERGY. tion, but of a kind not tending to diffusion. But it is too early to speculate, with any prospect of useful results, on such a subject. The heat of the sun, and the internal heat of the earth-both of which, by the principle of dissipation, are now far less than they were ages ago-are to be traced almost entirely to their origin in the original distribution of matter through space, at creation, and the subsequent transformation into heat of the energy with which the various portions which compose the sun or a planet impinged on each other in meeting. But for the complete consideration of such immense and important transformations, we must refer to our second article, where they will be found to flow naturally from the known laws of transformation and transference of energy. Reviewing, for a moment, the path we have so far pursued, we may recapitulate briefly the details most important, in a historical point of view, of the development (not the applications) of the science. And we find them to be these: First, Newton's grand general statement of the laws of transference of mechanical energy from one body or system to another. Second, Davy's proof that heat is a form of energy subject to these laws. Third, Rumford's close approximation to a measure of the mechanical equivalent. Fourth, Fourier's great work on one form of dissipation of energy. In the brief sketch we have given, a vast amount of valuable matter has been of necessity omitted, but we are not conscious of having left unnoticed any direct step of real consequence to the development of the true theory of heat. Where the results of early experiments were sufficiently accurate, we have not alluded to subsequent more perfect ones; and many curious, but not very important, points have not been mentioned. The details of such a history as this would fill volumes. The work of M. Verdet consists of two lectures delivered in 1862 to the Chemical Society of Paris, and is evidently intended for an audience already well acquainted with the fundamental principles of natural philosophy. Like all the works of the most distinguished of French scientific men, it is clear and distinct almost to a fault; the author has evidently not only read deeply, but carefully arranged his ideas, before writing his lectures; and the consequence is the production of a little treatise, brief but comprehensive, in which every sentence has its meaning and its definite bearing on the development of the subject. We shall not consider the mathematical developments which are interspersed through the text, and which occur freely in the notes, further than to remark that they show how extensive is the author's acquaintance with all that has been done in the extension of the theory. Nor do we profess at present to review even the popular portion in all its details, because M. Verdet has considered in his lectures, not merely the direct relation between heat and mechanical effect, to which our article has been limited, but has included in his comprehensive sketch the indirect developments of heat from work by the intervention of electrical currents, etc., and has, in fact, treated of the whole theory of energy. To some of his remarks on this subject, we may take exception in our next article; but so Eighth, Thomson's theory of dissipation. far as our present subject is concerned, we As regards the true theory of the con- consider that M. Verdet has on the whole nexion of heat with mechanical effect, this fairly represented its history, and that he has list contains all the most important direct put it before his readers in an extremely steps, nearly in chronological order; but it clear and impressive form. More could is to be remembered that experimental in-hardly be said of an essay which does not in Fifth, Carnot's fundamental principle, and his cycles of operation. Sixth, Joule's exact determination of the mechanical equivalent of heat, and the general reception of the true theory in consequence of his experiments. Seventh, The adaptation, by Clausius and Rankine, and subsequently, with greater generality and freedom from hypothesis, by Thomson, of Carnot's methods to the true theory; with Joule's experimental verification of Thomson's general results. แ any way pretend to novelty. Since a critic the audience, medals "struck dead by the can hardly be supposed to have done his excitement of the magnet," and other cataswork properly unless he find some fault, we trophes too numerous to mention. In anare tempted to express our opinion that M. other sense, also, the language employed is Verdet would have done wisely in devoting bad; it is ambiguous, and this is utterly inmuch less space to the consideration of defensible in a scientific work. Examples Hirn's errors as to the actual amount of of such ambiguity can be quoted almost heat put out of existence in the working of a without number, but we shall confine oursteam-engine. Not that we object to the selves to one or two of the most important. introduction of the results, but there appears Thus, the words "force," strength," and to be no necessity for such an elaborate ref-" energy are sometimes used as antagonisutation of conclusions known to be wrong, tic, and anon as synonymous terms. Enespecially as M. Verdet tells us that Hirn ergy, again, is confounded with "moving has renounced his erroneous opinions. force," which has a perfectly definite meanAs to the history of the science, we are ing in no way related to energy. In colliastonished that M. Verdet should say of sions, we are told, "the heat generated inMayer's method of determining the equiva- creases as the square of the velocity." This lent of heat that it is "parfaitement exacte is a palpable mistake, evidently arising from quant au principe"! We have already the confusion in the author's mind of the shown that this idea is untenable. Besides, phrase A varies as B (or is proportional to we can hardly reconcile this statement of B) with the very different one, A increases M. Verdet's with the last clause of the fol- as B (i. e., the rate of change of A is proporlowing sentence, which occurs in the very tional to B). Again, what can be the next page of his work, with reference to meaning of such a sentence as this: "Let Joule: "C'est à ses expériences de 1845, sur les effets calorifiques de la dilatation et de la compression des gaz qu'il appartenait de donner droit de cité dans la science aux idées nouvelles; ce sont ses expériences sur le frottement qui ont donné de l'équivalent mécanique de la chaleur la première détermination digne de confiance; ce son ses vues sur la constitution des gaz qui ont With the exception of these blemishes, donné le premier, et jusqu'ici le seul ex- and of other more serious faults which we emple d'une explication complète d'un shall presently consider, the volume, so far phénomène dont la théorie fait prévoir les as it goes, is creditable enough. Many exlois sans en indiquer le mécanisme." No- perimental novelties, well suited to the thing could be more candid than this, nor lecture-room, are carefully described; and, could more have possibly been expected, as on the whole, the work is calculated to prove M. Verdet has evidently overlooked Joule's exceedingly interesting even to the scientific friction result of 1843, which was unfortu- reader. But we look in vain through its nately only mentioned, in few words and pages for so much as a mere mention of without any details, in an appendix to a Carnot; and, beyond a few casual remarks paper devoted to a totally different class of ex- about the disappearance of heat in the properiments. In our second article we shall reduction of mechanical effect, there is nothing cur to M. Verdet's very interesting lectures to give the reader even a hint, that the laws which regulate the production of work from me now pass from the sun to something less-in fact, to the opposite pole of nature?" Or this: " as we proceed light will gradually appear, and irradiate retrospectively our present gloom!" It is needless to collect further examples of this constant perversion of the common meanings not only of scientific, but even of popular, words. Dr. Tyndall's volume contains a series of heat are now as well known and as capable lectures delivered in the Royal Institution of being popularized, as anything in Natural in London, which of course are much more Philosophy. That radiant heat and light popular in form than those of M. Verdet. are identical, and that there are many peWe wish we could call them as clear and culiarities in their radiation and absorption definite. Unfortunately they are deficient by matter, which require only patient exin the precise qualities which the French periment for their discovery, was known philosopher possesses so completely. Gran- long ago; and though the new results ob diloquence, especially when rising almost to tained by the author are curious, and in the style of the modern sensational school of some cases even startling, they can scarcely, fiction-writers, is not adapted even to popu- even if completely verified by other experilar science; true scientific language is ever menters, claim anything like the comparacalm and dignified, and we fear the worst tive value which has been assigned them in when we hear of magnetic needles moving this work, to the exclusion of so much that as if "inspired by a sudden affection " for is of vital importance. |