154 Trans. Acad. Sci. of St. Louifi. 



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 i?, 



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



spherical surfaces in a contracting gaskugel. 

 That value is 



\dT/~ 



By (21) 



2 — ?i Mk 



By differentiating (16) with R constant, 



(dv\ _ 27^^'(2•— n)2^ 

 \dT)p^~n{4. — 3?i) Cr2* 



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

 give (reversing the sign of dQ) 



{§1-0.-^ (33). 



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 w is found to be 



2(7^ + 4^ 

 n= ^ (33a). 



2(7p+3 y- 



