94 MOTIVE POWER OF HEAT. 



shown the relation between these temperatures and 

 the quantities of motive power produced. It would 

 at first seem natural enough to suppose that for 

 equal differences of temperature the quantities of 

 motive power produced are equal ; that is, for ex- 

 ample, the passage of a given quantity of caloric 

 from a body, A, maintained at 100, to a body, B, 

 maintained at 50, should give rise to a quantity of 

 motive power equal to that which would be devel- 

 oped by the transfer of the same caloric from a 

 body, B, at 50, to a body, C, at zero. Such a law 

 would doubtless be very remarkable, but we do not 

 see sufficient reason for admitting it a priori. We 

 will investigate its reality by exact reasoning. 



Let us imagine that the operations described on 

 p. 70 be conducted successively on two quantities 

 of atmospheric air equal in weight and volume, 

 but taken at different temperatures. Let us sup- 

 pose, further, the differences of temperature be- 

 tween the bodies A and B equal, so these bodies 

 would have for example, in one of these cases, the 

 temperatures 100 and 100 h (h being indefi- 

 nitely small), and in the other 1 and 1 h. The 

 quantity of motive power produced is, in each case, 

 the difference between that which the gas supplies 

 by its dilatation and that which must be expended 

 to restore its primitive volume. Now this differ- 



