In 1842 Mayer published a short note, in which he enunciated the conservation of energy as a metaphysical deduction from the maxim, Causa xgrat effectum. He made no experiments to prove this general statement, but lie made a calculation of the mechani cal equivalent of heat from the specific heats of air—assuming that when heat is produced by compression, its amount is the equivalent of the work spent in compressing. His result was erroneous, because his data were imperfect. But it appears that his asssump don. quite unwarranted as it was, is really very nearly true for air.
In 1843 Colding, led also by some metaphysical speculations, propounded the doc trine, but endeavoured to base it upon actual experiments.
Finally Joule (q.v.), also in 1843, published an experimental determination of the mechanical equivalent of heat (770 foot pounds as the work required to heat a pound of water one degree Fehr.), which is within half per cent of the most trustworthy results since obtained. Joule had been, since 1840 at least, making quantitative determinations of equivalence between various forms of energy; and was led to propound the general law of conservation of energy by the only legitimate process—viz., experiment, as contrasted with metaphysical assertions of what ought to be. The complete foundation of the science on a proper basis is thus due to him; though, as we have seen, portions of it were established thoroughly by Newton and by Davy.
Before we consider what are the principal features of the theory as now developed, it is necessary to refer to the admirable investigations of Fourier and Carnot, which, though in some respects defective, must be considered as real advances. Fourier's great work, Thiorie de la Chaleur, is devoted to the laws of conduction and radiation, i.e., to the dissipation, of heat, and is one of the most remarkable mathematical works ever written. Carnot's work, Sur la Puissance Motrice du Feu, is the first in which any attempt is made to explain the production of work from heat. It is unfortunately marred by his assump tion that heat is a material substance, though it is only fair to say that he expresses grave doubts as to the truth of this hypothesis.
(We borrow our notice of Carnot from a paper by sir W. Thompson (q.v.) in the Transactions of the Royal Society of Edinburgh, 1849.) He begins his investigation by the following correct principle, sadly neglected by many subsequent writers: " If abody, after having experienced a certain . - — number of transformations, be brought identically to its primitive physical state as to density, temperature, and molecular constitution, it must contain the same quantity of heat as that which it initially possessed." Hence he concludes that when heat produces work, it is in consequence of its being let down from a hot body to a cold one, as from the boiler to the condenser, of a steam-engine. His investigation, though based on as
eroneous hypothesis, is extremely ingenious, and forms the foundation of the modern theory. We give a sketch of it, preparatory to our account of the present state of the theory, and for this purpose we choose a somewhat hypothetical case, as simpler than the most common practical one. This the case of a piston working air-tight in a cylin der closed at the bottom.
Suppose•we have two bodies, A and B, whose temperatures, S and T, are maintained uniform, A being the warmer body, and suppose we have a stand, C, which is a non conductor of heat. Let the sides of the cylinder and the piston be also non-conductors, but let the bottom of the cylinder be a perfect conductor; and let the cylinder contain a little water, nearly touching the piston when pushed down. Set the cylinder on A; then the water will at once acquire the temperature S, and steam at the same tempera ture will be formed, so that a certain pressure must be exerted to prevent the piston from rising. Let us take this condition as our starting-point for the cycle of operations. 1. Allow the piston to rise gradually; work is done by the pressure of the steam, which goes on increasing iu quantity as the piston rises, so as always to be at the same tempera ture and pressure. And heat is abstracted from A, namely, the latent heat of the steam formed during the operation. 2. Place the cylinder on 0, and allow the steam to raise the piston further. More work is done, more steam is formed, but the temperature sinks on account of the latent heat required for the formation of the new steam. Allow this process to go on till the temperature falls to T, the temperature of the body B. 3. Now, place the cylinder on B; there is of course no transfer of heat; because two bodies are said to have the same temperature when, if they be put in contact, neither parts with heat to the other. But if we now press down the piston, we do work upon the contents of the cylinder, steam is liquefied; and the latent heat developed is a = once absorbed by B. Carry on this process till the amount of heat given to B is exactly equal to that taken from A in the first operation, and place the cylinder on the non-conductor C. The temperature of the contents is now T, and the amount of caloric in them is precisely the same as before the first operation. 4. Press down the piston further, till it occupies the same position as before the first operation ; additional work is done on the contents of the cylinder, a further amount of steam is liquified, and the temperature rises.