158 Trans. Acad. Set. of St. Louis. 



in n would also be unity. Since ~—p=. is the mass, in astro- 



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 -7^. 



Vk 



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



resulting volume of the sphere 



3 3w 27? 



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



Equation (20) enables us to determine the average density 

 5„ of the mass M at any time during compression. 

 We have 



6 4 07l 



2 — n 



3 -. ^ S = 3.868. (35) 



4 — on ^ ^ 



4 



If n were o 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 — n B' 

 R2^ 4 — 3n ^ J- 



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



p _/4— 3n \ '2 ^^0 545 ^ /ggx 



^« ■-\3(2 — ri)/ ^ ^ 



