M.CLAPEYRON ON THE MOTIVE POWER OF HEAT. 355 



pa«s to the body B, by some other process, it \v£is possible to realize a 

 larger quantity of mechanical action F'; we should employ one part of 

 it F, to restore to the body A from the body B the quantity of heat C, 

 by one of tiie two means that we have just described. The vis viva F 

 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 

 C, from the body A to the body B ; it is therefore, according to the 

 hypothesis, smaller than F' ; a quantity of action F' — F, would there- 

 fore be produced, which would be created absolutely and without con- 

 sumption 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 analo- 

 gous 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 tem- 

 perature may cause the production of a certain quantity of mechanical 

 action ; there is a loss of vis viva whenever bodies of different tem- 

 perature 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 em- 

 ployed; 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. 



§111. 



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 deter- 

 minate temperature, to another body maintained at a lower tempera- 

 ture, 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 A and B, and suppose that the tem- 



