150 THOMSON ON CARNOT'S 



the caturated steam and the water in the cylinder 

 have the same pressure p, and consequently the 

 same temperature, which we may denote by t. 

 Again, throughout the second operation the entire 

 contents of the cylinder possess a greater amount 

 of heat by H units than during the fourth ; and, 

 therefore, at any instant of the second operation 

 there is as much more steam as contains H units 

 of latent heat than at the corresponding instant 

 of the fourth operation. Hence if k denote the 

 latent heat in a unit of saturated steam at the 

 temperature t, the volume of the steam at the two 



TT 



corresponding instants must differ by -T-. Now, if 

 (T denote the ratio of the density of the steam to 



TT 



that of the water, the volume -j- of steam will be 



K 



TT 



formed from the volume a -y- of water ; and con- 



rC 



sequently we have, for the difference of volumes of 

 the entire contents at the corresponding instants, 



Hence the expression for the area of the quadri- 

 lateral figure becomes 



