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



in n would also be unity. Since —-^ is the mass, in astro- 



nomical units of 3928 oframmes, 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=-. 



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

 resulting volume of the sphere 



3 3n 27? 



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

 o 



Equation (20) enables us to determine the average density 



h^ of the mass ilfat any time during compression. 



We have 



4 2 — n ^ 



3 " 4 — on 



S^=S 1 8 = 3.868. (35) 



"4 — 6n ^ ^ 



4 



If n were ^ the average density would be infinite. 

 o 



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



density, we have from eq. (11), 



B' 2 — n B' 



— 2=3 -j — -^- 2 



7-> 9-n 4 371 -rt 



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



_ ( ^~^'' ] ' R = 0.545 R. (36) 



