$52 M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 
tion in the same envelope,—but after having introduced the body B, which: 
is at the same temperature,—and carry on the operation until the 
body B has restored to the gas the heat which it had received in the. 
preceding operation. We next remove the body B, and condense the 
gas in an inclosure impermeable to heat until its temperature again be- 
comes equal to T. We then introduce the body A, which possesses the 
same temperature, and continue the reduction of volume until all the 
heat taken from the body B is transferred to the body A. The gas will 
then be found to have the same temperature and to contain the same ab- 
solute quantity of heat as at the beginning of the operation, whence we 
may conclude that it occupies the same volume and is subjected to the 
same pressure. 
Here the gas passes successively, but in an inverse order, through all 
the states of temperature and pressure through which it had passed in 
the first series of operations; consequently the dilatations become com- 
pressions, and reciprocally, but they follow the same law. Further, the 
quantities of action developed in the first case are absorbed in the se- 
cond, and reciprocally ; but they retain the same numerical values, for 
the elements of the integrals which compose them are the same. 
We thus see that by causing heat to pass, in the manner first indi- 
cated, from a body retained at a determinate temperature, into a body 
retained at an inferior temperature, we develop a certain quantity of 
mechanical action, which is equal to the quantity which must be con- 
sumed in order to cause the same quantity of heat to pass from a cold 
to a hot body, by the inverse process we have subsequently described. 
We may arrive at a similar result by converting any liquid into va- 
pour. We take the liquid and bring it into contact with the body A in 
an extensible envelope impermeable to heat, and suppose the tempera- 
ture of the liquid to be equal to the temperature T of the body A. 
Upon the axis of the abscisses A X (fig. 2.) we describe a quantity A B 
equal to the volume of the liquid, and upon a line parallel to the axis 
of the ordinates A Y, a quantity B C equal to the pressure of the vapour 
of the liquid, which corresponds to the temperature T. 
If we increase the volume of the liquid, a portion of it will pass into 
the state of vapour; and as the source of heat A furnishes the latent 
caloric necessary to its formation, the temperature will remain constant 
and equalto T. Then if quantities representing the successive volumes 
occupied by the mixture of liquid and vapour are described upon the 
axis of the abscisses, and the corresponding values of the pressures are 
taken for ordinates, as the pressure remains constant, the curve of the 
pressures will here be reduced to aright line C E parallel to the axis of 
the abscisses. 
When a certain quantity of vapour has been formed, and the mixture 
of liquid and vapour occupies a volume A D, the body A may be with- 
