74 MOTIVE POWER OF HEAT. 



to be V, the compression of TTT reduces it to 

 V-j^V. 



Direct heating under constant pressure should, 

 according to the rule of M. Gay-Lussac, increase 

 the volume of air T above what it would be at : 

 so the air is, on the one hand, reduced to the vol- 

 ume V TT7 F; on the other, it is increased to 



_ 



The difference between the quantities of heat 

 which the air possesses in both cases is evidently 

 the quantity employed to raise it directly one de- 

 gree; so then the quantity of heat that the air 

 would absorb in passing from the volume V -- T } T V 

 to the volume F -\- ^V is equal to that which 

 is required to raise it one degree. 



Let us suppose now that, instead of heating one 

 degree the air subjected to a constant pressure and 

 able to dilate freely, we inclose it within an invari- 

 able space, and that in this condition we cause it 

 to rise one degree in temperature. The air thus 

 heated one degree will differ from the air com- 

 pressed TT ^- only by its 1T -g- greater volume. So 

 then the quantity of heat that the air would set 

 free by a reduction of volume of yir is equal to 

 that which would be required to raise it one degree 

 Centigrade under constant volume. As the differ- 

 ences between the volumes F T |-g F, F, and 



