Quantities occurring in the Mechanical Theory of Heat, 267 



mass, and 7 the specific heat at constant volume referred to 

 the unit of volume, we have 



- V 



and 



hence 



M.c=V.7 J 

 and 



T 



a + t==— 

 V . y 



Hydrogen, oxygen, nitrogen, atmospheric air, and carbonic 

 oxide are permanent gases ; and their molecules contain the 

 same number of atoms. Now, as it follows from Regnault's 

 experiments that in these 7, independent of the nature of the 

 gas, is very nearly equal, therefore for the gases mentioned 



a + t_T % 



Consequently, when it is said that the temperature of tivo 

 gases (whose molecules contain the same number of atoms) is 

 equal, this much is meant — that the mean value of the vis viva 

 for the unit of volume, in the course of a complete oscillation, is 

 equal in the tivo gases. 



Having thus fixed the dynamic signification of the quanti- 

 ties which occur in the Second Proposition, let us return to 

 the equation 



If we divide it by 2T, we get 



a v J 2T 



and since the left side is a differential, the right side must also 

 be a differential. If we designate it simply by d&, then S will 

 signify the half of the " Entropy:" 



d\og(iT) = dS. 



Integrating this equation, and designating the integration-con- 

 stant by log C 1; 



e s 



T 



