154 Trans. Acad. Set. of St. Louis. 



By a well-known equation, the specific heat along any path 

 determined by n is 



This equation assumes expansion of the gas, with the 

 addition of heat. To correspond to eq. (5) the sign of dQ 

 must be reversed. 



If eqs. (19) and (21 ) be combined by the elimination of H, 



the value of ( -pj,) may be found at any of the concentric 



spherical surfaces in a contracting gaskugel. 

 That value is 



\dT)„^ Trk^3P(2—ny " 



By (21) 



2 — n Mk 

 ^ ~ 7iC 2E 



By differentiating (16) with 7? constant, 



(dv\ _ 2'7rk(2 — nyir- 

 \dTJF^~n(4.—3n)CT' 



2 



These values in (32), by further substitution from (17) 

 give (reversing the sign of dQ) 



{§l-0.-^ (33), 



This is the specific heat at any point in a gravitating gas- 

 kugel, in terms wholly independent of ?i. If this value be 

 equated with (5), the value of n is found to be 



2CV + 4^' 



n 



2Cp+3 -r 



C 

 J 



(33a). 



