158 Trans. Acad. Sci. of St. Louis. 



M 



in ?i would also be unity. Since — -7= is the mass, in astro- 



Vk 



nomical units of 3928 grammes, the expression would then be 



precisely like the one for the compression of an electrified 



M 



spherical surface having a charge numerically equal to ^^. 



vk 



It may be of interest to point out that if V represents the 



resulting volume of the sphere 



3 3n 2i? 



This is ^ of the work represented in (34). 



Equation (20) enables us to determine the average density 

 Sg of the mass M at any time during compression. 

 We have 



M=\^R^K -^--^^rz^^B^ 



K-^ tln^ = 3-86S. (35) 



4 



If n were « the average density would be infinite. 



To find where in the sphere, the gas would have average 

 density, we have from eq. (11), 



B' 2 — nB 



2 =3 



^^2-„ 4 — 3w ^^ 



-n 



where B' is the constant coefiicient in (11). Hence 



7? _/ 4— 3n \^ B = 0.5A5 B. (36) 



^^«-\3(2 — n)/ ^ ^ 



