M.CLAPEYRON ON THE MOTIVE POWER OF HEAT. 355 
pass to the body B, by some other process, it was 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 the 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 ina 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 wis 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. 
§ 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 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- 
