276 Trans. Acad. Set. of St. Louis. 



By differentiation of (4) 



dR ~ k 





P^ \dRI J 

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



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 /^y Mcm^_ 



(^i?2 + R dR 'PVdRJ "^ iJ-'Tm}^'^' ('^^ 



^'O 



The solution of this equation is 



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

 fore 



PR'^ = n —^2) -5^?o^. (9) 



CTJtl^ ^ ' 2iTkR^+^ 



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



C^ CTR'' 



ikf = 47r R^dR = 2 ( 1 + n) f^R^'^ ( 10) 



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



M CT R"" 



g=kf, = 2(l+n)^^j^. (11) 



