122 On the Relation between the Changes of 



which shews that the heat developed by compressing the air 



to 5^th of the bulk is so much as to raise the temperature of 



that compressed air (N^ — 1) x (480 + T) degrees above T, its 



previous temperature. And by derivation, 



^T /T + ^ + 480\3. ^_ t 



N= (— p .Q„ ) andT=-— 480 



\ T + 480 / N^-1 



The question of the specific heat of gases may be deter- 

 mined by the preceding data and the dynamic equivalent of 

 heat, which, after the researches of Joule and Rankine, may 

 be considered to be about 700 foot-pounds for one degree of 

 temperature in one pound of water. 



The above formula also indicates — 



1. That the specific heat of a gas is the same, for equal 



weights, under any pressure. 



2. That for different gases, at equal pressure and tem- 



perature, the specific heat for equal weights is in- 

 versely as their specific gravities; or, that it is 

 equal for equal volumes, in all gases. 



3. That the specific heat of equal volumes of a gas, at 



the same pressure, but at difi'erent temperatures, 

 varies inversely as the temperature, reckoning the 

 number of degrees from 480 below the freezing 

 point of water ; and, therefore, the specific heat for 

 equal weights of the same gas is the same at all 

 temperatures. 

 If the experimental determinations of the specific heat of 

 gases could, on the other hand, be sufiiciently relied on, the 

 dynamic equivalent of heat might be determined by calcula- 

 tion with these data, independently of direct experiments. 



In the preceding formula, it will be seen that such ele- 

 ments as the absolute amount of the initial unit of pressure, 

 the specific gravity, the specific heat, and the chemical nature 

 of the gas itself, do not aff^ect the mutual relations of the 

 elements which are there concerned, where the absolute 



