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



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



00 



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 ^, we have the equations. 



(15) 

 (16) 

 (17) 

 (18) 



n R 



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

 have 



_ 4 — 3n M'^k 



(20) 

 (21) 

 (22). 



i?2 



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 R from the center. M is the 

 mass internal to the spherical surface of radius R. 



