148 Trans. Acad. Sci. of St. Louis. 



It will be observed that the value of P in (10), is 



00 



P = I gSdR 



I 



where 8 and g are given in (11) and (14j. 



If (12) be combined with (10), (11), (13), and (14), bj 

 the elimination of A, we have the equations, 



^— (2 — ?i)^ 2^rrkB' ^^^^ 



4?i— 3w2 CT 



n 2CTR 



n 2CT 



^ — 2 — 71 ^H 



(18) 



K (13) be similarly combined with the other equations we 

 have 



4_3n M'k 



P=-^ -»r (19) 



oirn H* ^ ^ 



4_3;i 3/ 

 ^ = 4,^2=^ ^' ^''^ 



2 — n Mk 

 ^=^Ur -2B (21) 



Equations (17) and (21) are of course identical. 



In equations (15) to (18), the values P, S, and g, are values 

 of these quantities at a distance i? from the center. M \^ the 

 mass internal to the spherical surface of radius R. 



