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?^ at whose sur- 

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

 (15) become, 



P = (I — n^-) Q . (16) 



d = n— 7/2X ^^0 (17) 



M = 2(l + n)^^ (18) 



k 

 7 



g^=2il^n)^- (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 



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 v^^ times thedensity 



at its surface. 



Hence by the law of gases 



^ P V — vR^ (I ?l2\ ^0 



l_n ^0 ^0 - 1— n ^0 ^ ^ 27^^^i^,2 



