278 Trans. Acad. Sci. of St. Louis. 



constancy. Since this is a measure of the mass within a 

 spherical volume, it follows that the condition approached is 

 one in which the mass within a sphere of radius R is the same 

 as that within a sphere of any other radius. The physical in- 

 terpretation of this is. that the mass within the smaller sphere 

 becomes infinite, and this mass is not increased by the addi- 

 tion of a finite quantity. 



At the surface of a sphere of larger radius i?Q at whose sur- 

 face the temperature is T^, the equations (12) (13) (14) aud 

 (15) become, 



P - (I _o,2>> ^ ^0 . (16) 



ili,= 2(l + n)-— , 



CT,R, 



CT, 



^o=2(14-n)-^°. 



(18) 

 (19) 



These are taken as initial values. Assume that the entire 

 mass contracts so as to preserve the same law of distribution 

 of density. Let r^ and r be any two radii, satisfying the con- 

 dition 



r R P' 



this ratio being the ratio of contraction. 



It is required to find the pressure necessary to compress the 



sphere of gas, whose initial volume is V^. 



3 

 The average density of the sphere is y—^ times the density 



at its surface. 



Hence by the law of gases 



^ P V — irE 3 / 1 n^\ 



= 2(l+n)^^^' = M,CT, 



