MOTIVE POWER OF HEAT. 91 



by means of the law demonstrated above. The 

 heat set free by compression, according to the 

 theorem of page 81, ought to be represented by an 

 expression of the form 



s = A + B log v, 



s being this heat, v the volume of the gas after 

 compression, A and B arbitrary constants depen- 

 dent on the primitive volume of the gas, on its 

 pressure, and on the units chosen. 



The specific heat varying with the volume ac- 

 cording to the law just demonstrated, should be 

 represented by an expression of the form 



z = A' + B' log v, 



A' and B' being the different arbitrary constants 

 of A and B. 



The increase of temperature acquired by the 

 gas, as the effect of compression, is proportional to 



the ratio - or to the relation .,,,, It 

 z A' + B' log v 



can be represented by this ratio itself; thus, calling 

 it t, we shall have 



A +B logv 

 ~ A' + H'Iogv 



If the original volume of the gas is 1, and the 

 original temperature zero, we shall have at the 



