356 M. CLAPEYRON ON THE MOTIVE POWER-OF HBAT.~ 
perature ¢ of the body B is lower by the infinitely small quantity d¢, 
than the temperature ¢ of the body A. We shall suppose in the first 
instance that a gas serves for the transmission to the body B, of the ca- 
loric of the body A. Let v, be the volume of the gas under the pres- 
sure py at a temperature of ¢,; let p and wv be the volume and the 
pressure of the same weight of gas at the temperature ¢ of the body A. 
The law enunciated by Mariotte, combined with that of Gay-Lussac, 
establishes between these different quantities the relation 
= reer (2 t 
Po ser qe eet ts 
or, for simplicity, Es = = =R 
pv=R (267 + 2). 
The body A is brought into contact with the gas. Let me = », 
ae = p (fig.3.). If the gas be allowed to expand by the infinitely 
small quantity dv = eg, the temperature will remain constant, in con- 
sequence of the presence of the source of heat A; the pressure will 
diminish, and become equal to the ordinate bg. We now remove the 
Fig. 3. 
body A, and allow the gas to expand, in an inclosure impermeable to 
heat, by the infinitely small quantity gh, until the heat becomes latent, 
reduces the temperature of the gas by the infinitely small quantity dé, 
and thus brings it to the temperature ¢ — dt of the body B. In eon- 
sequence of this reduction of temperature, the pressure will diminish 
more rapidly than in the first part of the operation, and will become 
ch. We now take the body B, and reduce the volume mh by the 
infinitely small quantity fh, calculated in such a manner that during 
this compression the gas may transmit to the body B all the heat 
it. has derived from the body A during the first part of the opera- 
tion. Let fd be the corresponding pressure; that done, we remove 
