pass to the body , by some other process, it was possible to realize a larger quantity of mechanical action ; we should employ one part of it , to restore to the body from the body the quantity of heat , by one of the two means that we have just described. The vis viva employed for this purpose would be equal, as we have seen, to that which would be developed in the passage of the same quantity of heat , from the body to the body ; it is therefore, according to the hypothesis, smaller than ; a quantity of action , would therefore be produced, which would be created absolutely and without consumption of heat; an absurd result, which would imply the possibility of creating either force or heat in a gratuitous and indefinite manner. It appears to me that the impossibility of such a result might be accepted as a fundamental axiom of mechanics: the demonstration by pulleys, that Lagrange has given, of the principle of virtual velocities, against which no one has attempted to raise an objection, rests upon an analogous principle. In the same manner it may be proved that no gas or vapour exists which, employed in the processes described to transmit the heat of a hot body to a cold one, is capable of developing a larger quantity of action than any other gas or vapour.
We shall therefore admit the following principles as the basis of our researches.
Caloric passing from one body to another maintained at a lower temperature may cause the production of a certain quantity of mechanical action; there is a loss of vis viva whenever bodies of different temperature come into contact. The maximum effect will be produced when the passage of the caloric from the hot to the cold body takes place by one of the methods which we have just described. We may add, that the effect will be found to be independent of the chemical nature, of the quantity, and of the pressure of the gas or liquid employed; so that the maximum quantity of action, which the passage of a determinate quantity of heat from a hot to a cold body can develop, is independent of the nature of the agents which serve to realize it.
§III.
We shall now translate analytically the various operations that have been described in the preceding paragraph; we shall deduce from them the expression of the maximum quantity of action produced by the passage of a given quantity of heat from a body maintained at a determinate temperature, to another body maintained at a lower temperature, and we shall arrive at new relations between the volume, the pressure, the temperature, and the absolute quantity of heat or latent caloric of solid, liquid, or gaseous bodies.
Let us return to the two bodies and , and suppose that the tem-
