The law by which bodies of different temperatures be come the one hotter and the other colder, or by which the equilibrium of heat is produced, was first laid down by Newton, and may be thus expressed in general terms ; that the heat lost by the one body, and gained by the other, is in proportion to the excess of the temperature of one above the other ; or, stating it in a more scientific manner, that the difference between the temperatures diminishes in a geometrical ratio, while the times increase in an arithme tical ratio. The external circumstances which influence the rapidity of the equalizing process, are the radiating power of the bodies themselves, their conducting power, and, provided they are not in contact, the nature of the me dium which is interposed between them, and the mechani cal changes which take place in the medium, relative to its position with respect to the heating and cooling bodies, constituting currents. These principally operate in what are styled the elastic fluids; but they have also considera ble effect in the action of liquids. The hypothesis which is commonly adopted, and which appears satisfactorily to account for this peculiar property of bodies, was proposed by M. Prevost. It is founded upon the following data. Heat is conceived to be a fluid, composed of distinct parti cles, which pass through space in right lines, and are pro jected in all directions, with very great velocity. The par ticles are so far removed from each other, that, analogous to what takes place with respect to light, a number of cur rents may flow in different directions, without interfering with each other. All bodies, except such as we suppose to be absolutely deprived of heat, send out rays to each other, although generally in very different degrees. Two bodies, exactly of the same temperature, will mutually give and receive heat, and even a cold body will radiate heat to a hot one ; but, in the former case, the quantities given and received by each will be exactly the same, so that the tem perature will not be changed ; and, in the latter case, the one will give much more than the other, until the tempe rature of the two is equalized. Phil. Trans. 1802, p. 443.
This hypothesis appears to have been originally formed, in order to account for the experiment of which we gave an account above, the radiation of cold. When a heated body parts with its caloric to the neighbouring bodies, and raises their temperature, the idea that presents itself, as the most natural explanation of the fact is, that the hotter body has merely given off its superabundant heat to the colder, in consequence of the tendency which heat has to distribute itself uniformly through all bodies subjected to its influence. It may be conceived in this case to pass off, in a greater or less degree, according to the excess of the temperature of the one body over the other, modified by the nature of the surface, and the other circumstances to which we have already alluded. But this simple view of the operation will not explain the rldiat ion of cold, or at least will not explain the appal cot reflection of it from a concave mirror. If the cold body acted only by attracting heat from the neighbouring bodies, it would take it from the thermo meter, the mirror, and all other contiguous substances ; and there seems to be no reason why the focus should be colder than any other part of the atmosphere, equally near the source whence the cold proceeds. According, however,
to Prevost's notion, when ice is placed in one of the foci, it sends out radiant heat, which strikes against the mirror, and is reflected into the opposite focus ; but these rays be ing comparatively colder than those which proceed from other bodies in the vicinity, have the effect of generating absolute cold in the second focus, and thus tend to depress the thermometer which is suspended there. A mutual ex change of heat thus takes place between the ice and the thermometer, and the equilibrium is established, by the ice acquiring, and the thermometer losing, each a portion of caloric. (Journ. Phys. t. xxxviii. p. 3.) The facility with which this hypothesis explains the radiation of cold, is it self an argument in favour of its validity ; and it must be admitted, that it applies equally well to all the other phe nomena in which caloric is concerned. An objection has indeed been urged against it, that it does not take into ac count the effect of the conducting power of bodies, which must have an important effect in the equalization of their temperature. This is not, however, properly an objection against the general doctrine of the reciprotal interchange of radiant heat, but an omission in Prevost's manner of ap plying it ; and it seems that the two operations are not in any degree incompatible with each other. Still, however, M. Prevost's opinion must be regarded rather as a plausi.4 ble conjecture, which has the merit of satisfactorily ex plaining the phenomena, than as a theory founded upon any direct experimental proofs. It has indeed been conceived, that Professor Leslie's researches afford considerable sup port to it, as they tend to establish the existence of a radiat ing energy in bodies, quite independent of their conducting power ; an energy, by which even the worst conductors of heat, under certain circumstances, become the most active radiators of it. Yet this radiation can never be proved to exist, except there be a previous difference of temperature between the bodies ; because the thermometer, which is our only measure of heat, and the only index which we pos sess of its presence, is never affected except by an unequal distribution of it.
Having now described the manner in which heat tends to pass from one body to another, we shall next proceed to the second of its specific properties, the power by which it moves among the particles of the same body ; or is conduct ed, as it is styled, through their substance. As bodies ap pear under the three states of solids, fluids, and gases, we should consider the power which heat exercises in its transmission through each of these different forms of mat ter. Our remarks will, however, be chiefly confined to the action of solids and liquids upon heat ; for in consequence of the tenuity of gases, or the distance at which their par ticles are situated from each other, it does not appear that any very notable effects can be attributed to them upon the passage of free caloric, at least in comparison with what we observe in the two other classes of bodies.