MOTIVE POWER OF HEAT. 85 



tion; (2) that which is necessary to restore the tem- 

 perature of the fluid from that of the body B to 

 that of the body A, when, after having brought 

 back this fluid to its primitive volume, we place it 

 again in contact with the body A. Let us call the 

 first of these quantities a and the second ~b. The 

 total caloric furnished by the body A will be ex- 

 pressed by a -\- b. 



The caloric transmitted by the fluid to the body 

 B may also be divided into two parts : one, Z>', due 

 to the cooling of the gas by the body B ; the other, 

 a', which the gas abandons as a result of its re- 

 duction of volume. The sum of these two quanti- 

 ties is a' -j- V ') it should be equal to a -j- #, for, 

 after a complete cycle of operations, the gas is 

 brought back exactly to its primitive state. It has 

 been obliged to give up all the caloric which has 

 first been furnished to it. We have then 



a+ b = a' + b'; 

 or rather, 



a - a' = V - I. 



Now, according to the theorem given on page 81, 

 the quantities a and a' are independent of the den- 

 sity of the gas, provided always that the ponderable 

 quantity remains the same and that the variations 

 of volume be proportional to the original volume. 



