84 MOTIVE POWER OF HEAT. 



that they be taken and maintained at a certain in- 

 variable temperature. But these theories furnish 

 no means of comparing the quantities of heat liber- 

 ated or absorbed by elastic fluids which change in 

 volume at different temperatures. Thus we are 

 ignorant what relation exists between the heat re- 

 linquished by a litre of air reduced one half, the 

 temperature being kept at zero, and the heat relin- 

 quished by the same litre of air reduced one half, 

 the temperature being kept at 100. The knowl- 

 edge of this relation is closely connected with that 

 of the specific heat of gases at various temperatures, 

 and to some other data that Physics as yet does not 

 supply. 



The second of our theorems offers us a means of 

 determining according to what law the specific 

 heat of gases varies with their density. 



Let us suppose that the operations described on 

 p. 70, instead of being performed with two bodies, 

 A, B, of temperatures differing indefinitely small, 

 were carried on with two bodies whose tempera- 

 tures differ by a finite quantity one degree, for 

 example. In a complete circle of operations the 

 body A furnishes to the elastic fluid a certain quan- 

 tity of heat, which may be divided into two por- 

 tions : (1) That which is necessary to maintain the 

 temperature of the fluid constant during dilata- 



