154 Trans. Acad. Sci. of St. Louis. 



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

 determined by n is 



(§)=o,-mMi <-) . 



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 i?, 



the value of ( -pjyj may be found at any of the concentric 



spherical surfaces in a contracting gaskugel. 

 That value is 



\dT/„^ 7rkHP{2—ny 

 By (21) 



2 — n Mh 



By differentiating (16) with R constant, 



(dv\ _ 2'7rk(2 — nyE^ 

 [JT/p n(4— 3n)(7T2* 



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

 give (reversing the sign of dQ) 



(!§.=- -.-f <'"■ 



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

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

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



2(7p + 4^ 



n= — — ^ (33a). 



2(7p+3y 



