276 Trans. Acad. Sci. of St. Louis. 



By difFerentiation of (4) 



dM _ CT,R,- 



dR 



R^-" dT ,,, , R'-^dP 



P dR^ 



P dR 



B^ idP^ 

 P^ [dR] 



(5) 



By geometry and after substitution from (3) and (1) 



dM . „2^ 4.7rR^+^P 

 dR OT^R,'' • 



(6) 



Equating these values of -— - in (5) and (6), and we have 



dR 



the differential equation for pressure as function of radius. 



d^P 2 — n dP 1 / dP y 47r, 



dR^ 



+ 



+ 



kP'R^'' 



R dR P\dRI ^ a^T^'R,' 



n=0. (7) 



The solution of this equation is 



C'TJR''^ 



P= (l_n2) - 



27rA;ie2(i+»> 



(8) 



By equations (3) and (1) the density of the gas is there- 

 fore 



d = 



JPR^ 



CT,R, 



-„ = (1-'^^) 



CT,R,- 

 1'KhR''^'^' 



(9) 



The mass of gas internal to the sphere of radius R is, 



.R 



)dR = ^ (1 + n)^ 



M = 



C CTR"" 



= 47r R^ddR = 2 a + n) ^— 5-i2i-'^ 



^0 



(10) 



The weight of a gramme at the surface of the sphere is, 



(H) 



9= ^7^2 = 2 (1 + n) " ' 



i?"+i 



