cult to see how two such opposite processes could each produce a diminution of the capacity. And although the difficulty is lessened by considering a change in both capacity and latent heat to be produced by attrition or condensation, it is by no means removed. The mischievous consequences of long persistence in a false theory were perhaps never better exemplified than in the case of this supposed materiality of heat; for so completely were the scientific men of last century imbued with it, that when Davy gave a conclusive proof of the actual creation of heat in a very simple experiment, his consequent argument against the materiality of heat (or the existence of caloric) attracted little attention, and was treated by many of those who condescended to notice it as a wild and extravagant speculation. It is certain that even Davy himself was led astray in his argument, by using the hypothesis of change of capacity as the basis of his reasoning, and that he might have been met successfully by any able Calorist who, though maintaining the materiality of heat, might have been willing to throw overboard one or two of the less essential tenets of his school of philosophers. But Davy's experiment, rightly viewed, is completely decisive of the question; and, in spite of the imperfection of his reasoning from it (due entirely to the prevailing sophisms of the Calorists), was perfectly satisfactory to himself. He developed, in a singularly brief and lucid form, the fundamental principles of the true theory, in a tract, forming part of the Contributions to Physical and Medical Knowledge, principally from the West of England, collected by Thomas Beddoes, M.D., published at Bristol in 1799. Davy commenced by causing two pieces of ice to rub against each other, until both were almost entirely melted by the friction. Here water considerably above the freezing point was produced, and as the capacity of ice for heat was known to be less than that of water, it followed at once from this experiment, that the ice contained more caloric after being melted than before, because--(1.) Its temperature was raised, and its capacity for heat increased; (2.) It had in addition the latent heat of fusion. Unless, then, it had drawn caloric from surrounding bodies there must have been creation of caloric, a result perfeetly inadmissible to supporters of the material theory. To show that no heat was abstracted from surrounding bodies, he proceeded to cause two pieces of metal to rub against each other by means of clockwork, the whole apparatus being placed on a block of ice, which had some unfrozen water in a canal on its surface, and enclosed in a very perfect vacuum, produced by the now well-known application of carbonic-acid gas and caustic potash. Here again heat was developed by the friction, but it did not come from the ice (for the water in contact with it was not frozen), nor from surrounding bodies (for in this case it must have passed through, and melted, the ice, but the ice remained. unaltered). From these perfectly conclusive experiments, Davy proceeds thus: Heat, then, or that power which prevents the actual contact of the corpuscles of bodies, and which is the cause of our peculiar sensations of heat and cold, may be defined a peculiar motion, probably a vibration, of the corpuscles of bodies, tending to separate them. It may with propriety be called the repulsive motion." "Bodies exist in different states, and these states depend on the differences of the action of attraction, and of the repulsive power, on their corpuscles, or in other words, on their different quantities of attraction and repulsion." Let us here remark, incidentally, what an immense simplification is at once introduced into our conception of the laws which regulate the intermolecular forces in bodies. Davy, by a single sentence or two, thus demolished for ever the ingeniously unnatural speculations of Boscovich and his school, who represented the law of the force exerted by one molecule or particle of a body on another, by a most complex alternation of attractions and repulsions, succeeding each other as the distance between the two was gradually diminished, a law so inconsistent with the simplicity of that of gravitation, as to lead us to wonder that it was ever seriously propounded. Davy, in fact, makes this very application, and illustrates the effect of the repulsive motion in balancing the attraction of cohesion in bodies by the very apt comparison of the orbital motion of a planet preventing its being drawn nearer to the sun. We shall not attempt to follow his further development of this discovery, where he falls into an ingenious mistake in consequence of his belief in the corpuscular theory of light. It has nothing to do with our subject; yet, though now known to be erroneous, it is worthy of its author. The rest of this short tract, so far as it relates to heat, is concerned with the laws of communication of heat, which he shows to be quite analogous to those of the communication of motion. It was not, however, so far as we know, till 1812 that Davy distinctly laid down, in a perfectly comprehensive form, the law of the phenomenon. In his Chemical Philosophy, published in that year, he enunciates the following perfectly definite and most important proposition :— "The immediate cause of the phenomenon of heat, then, is motion, and the laws of its communication are precisely the same as the laws of the communication of motion." The im mense consequences of this statement we shall presently consider, after we have briefly described the labours of a contemporary of Davy, who almost succeeded in 1798, in demonstrating the immateriality of heat; but whose work is especially valuable as containing the first recorded approximation to the measurement of heat in terms of ordinary mechanical units, which, singularly enough, does not appear to have been attempted by Davy. In the Philosophical Transactions for the last-named year, there is a most instructive paper by Count Rumford, entitled, An Inquiry concerning the Source of the Heat which is excited by Friction. The author's experiments were made at Munich while he superintended the boring of cannon in the Arsenal; indeed, he remarks, that "very interesting philosophical experiments may often be made, almost without trouble or expense, by means of machinery contrived for the mere mechanical purposes of the arts and manufactures." He was struck with the very great heat developed by the friction or attrition of the steel borer on the brass casting; and especially, in comparing it with the very small quantity of chips or powder removed from the metal, justly observing that it was inconceivable that a mere change of the capacity for heat in so small a relative quantity of brass, could develop heat sufficient in some cases to boil a large quantity of water. "In reasoning on this subject," he says, "we must not forget to consider that most remarkable circumstance, that the source of the heat generated by friction in these experiments, appeared evidently to be inexhaustible." "It is hardly necessary to add, that anything which any insulated body, or system of bodies, can continue to furnish without limitation, cannot possibly be a material substance, and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited, and communicated in the manner that heat was excited and communicated in these experiments, except it be MOTION." We shall have occasion again, more than once, to make valuable extracts from this extremely lucid and philosophical paper; meanwhile we may merely observe, that Rumford has pointed out other methods to be employed in determining the amount of heat produced by the expenditure of mechanical power, instancing particularly the agitation of water or other liquids, as in churning. It may be well to pause for a moment at this stage, and carefully consider to what extent the true theory of heat had really been advanced about the commencement of the present century. And it is easy to see from the preceding pages that the following important facts were then completely acquired to science: I. That Heat is Motion; or rather, in strict modern phraseo- II. That the laws of its communication are the same as brevity in the Scholium to his Third Law of Motion. IV. Hence, that Heat has a definite mechanical value, and may be converted into mechanical effect, and vice verså. V. That the determination of the accurate value of the mechanical equivalent of a given amount of heat, is a question to be resolved by experiment. VI. That Rumford had obtained an approximation (a pretty close one, as we now know) to the value of this equivalent. VII. That this equivalent may be determined by expending work in the boring or friction of solids, or in agitating liquids. For the benefit of such of our readers as may not have read the elements of mechanics, it will be useful to give a few explanations of some of the preceding statements, especially with the view of showing their logical sequence. I. and II. are simply Davy's own expression of his experimental conclusion. As to III., Newton shows, though not in precisely the same words, that when work is expended solely in setting a body in motion, the energy of the motion is the measure of the work expended. Work is here used in the ordinary engineering sense of so many "foot-pounds," i. e., so many pounds raised one foot. From this it follows that the sensible heat present in a body is really a certain definite amount of energy of motion, which is equivalent to a certain definite amount of mechanical effect or work. This is statement IV. With reference to VI., which is the only other requiring explanation, it is easily calculated from the data of one of Rumford's experiments (viz., that the work of one horse for 2h. 30m. raised, by 180° Fahr., the temperature of a mass equivalent in capacity for heat to 26:58 lbs. of water), that it requires about 940 foot-pounds of work to be expended to raise the temperature of a pound of water 1° Fahr. We have somewhat altered the result first deduced by Joule from this experiment; for we have used 30,000 instead of 33,000 foot-pounds per minute as the value of a horse-power-the latter, or Watt's estimate, being now allowed to be too great. Fourier. 47 No account was taken of the heat lost by radiation, which must have been considerable from the high temperature produced, and the duration of the experiment; so that, as Rumford himself noticed, this value must be too high. We now know that it is about 20 per cent. too great; still it is a most remarkable result. It does not follow that, if the chief fundamental laws and principles of a science are known, the development of them is an easy matter. Take, for instance, the law of gravitation. It is scarcely possible to conceive a simpler expression than this for the mutual action of two particles; yet, even for the simplest possible application, the motion of one particle about another, the numerical details are very troublesome; and when we have three mutually attracting particles, the problem (so far as exact solution is concerned) completely transcends the power of known mathematical processes. It is, of course, infinitely more formidable when we consider the mutual action of the particles of a body; and without the aid of hypotheses, suggested by experiment, such a case would be incapable of even approximate treatment. Thus we are prepared to find that for the practical application of the above facts regarding heat, hypotheses (of a kind suggested by experiment) will always be required until we know the nature of matter, and have immensely improved our mathematical methods. For a considerable portion of the present century, Davy's discoveries about heat were neglected, or only casually mentioned; but this was of comparatively little consequence, as their early reception might have kept back for a time the grand developments which we have next to mention-immense strides in the theoretical and mathematical treatment of the subject, and to a great extent independent of the nature of heat. These are due to Fourier and Carnot, and it may well be said that it is in great part attributable to their remarkable works that the true theory of heat, when revived some twenty years ago, received so rapidly its present enormous development. Fourier's Traité de la Chaleur, composed before 1812, is one of the most exquisite mathematical works ever written, abounding in novel processes of the highest originality as well as practical utility. It is devoted solely (so far as its physical applications are concerned) to the problems of the Conduction and Radiation of heat. Whatever may eventually be found to be the true laws of conduction and radiation, Fourier gives the means of completely solving any problem involving these processes only, and applies his methods to various cases of the highest interest. He works out in detail these important cases with the particular assumption that the flux of heat is proportional to the difference |