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



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



cc 



P =r 1 gSdR 



Jr 



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



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

 the elimination of A, we have the equations, 



P — 7"o ^7\2 o^z. Z?2 (1^) 



(16) 

 M= ^-^ --^^' (17) 



^ 2 — n It 



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

 have 



Smi R' 



4 — 3w M 



47r(2— w) P' 



(20) 



2 — n Mk 



9 = -^ (^^)- 



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 P from the center. M is the 

 mass internal to the spherical surface of radius P. 



