86 MOTIVE POWER OF HEAT. 



The difference a a' should fulfil the same condi- 

 tions, and consequently also the difference V b, 

 which is equal to it. But b' is the caloric neces- 

 sary to raise the gas enclosed in abed (Fig. 2) one de- 

 gree ; b' is the caloric surrendered by the gas when, 

 enclosed in abcf, it is cooled one degree. These 

 quantities may serve as a measure for specific heats. 

 We are then led to the establishment of the follow- 

 ing proposition: 



The client ge in the specific heat of a gas caused 

 by change of volume depends entirely on the ratio 

 between the original volume and the altered volume. 

 That is, the difference of the specific heats does not 

 depend on the absolute magnitude of the volumes, 

 but only on their ratio. 



This proposition might also be differently ex- 

 pressed, thus: 



When a gas increases in volume in geometrical 

 progression, its specific heat increases in arith- 

 metical progression. 



Thus, a being the specific heat of air taken at a 

 given density, and a -\- h the specific heat for a 

 density one half less, it will be, for a density equal 

 to one quarter, a -f- 2h; for a density equal to one 

 eighth, a -f- 37^ ; and so on. 



The specific heats are here taken with reference 

 to weight. They are supposed to be taken at an 



