70 ME. J. H. JEANS ON THE POTENTIAL OF ELLIPSOIDAL BODIES, AND 



Hence collecting all contributions to 4cZ 1( 4d 2 , 4d 3 , we obtain as their total values 



4d, = 0-303186 ^'-0141999 2^-0161187 - 2 -0'308839, 

 a 2 b* c' 



4(7 = _0141999 + 0'533622 f- 2 -0'391623 - 2 + 0156090, 

 a 6 <r 



4d, = -0161187 U-0'391623 ^ + 0'552810 -,+ 0152751. 



a* l> c' 



From the values already obtained for p, q, r, we can transform equations (112) to 

 (114) into the following : 



-in" = e(- + T-+^i} =0'1163013' + 0-6227300 f 2 + 0'9769708 ~0' 

 \ /v 4 7i 4 f>* / n. It r. 



_ , -I l_l J-J-U^^>J---' 



i 4 c 4 / a 



r 



.-3L\ =0-2326027^-1-2454600 ^-0' 

 a 4 6V a b 



r r' 



4cZ 3 ='20-t =1-9539416^+0'04462528. 



c c 



On substituting the values of 4(Z 1; 4cZ 2 , and 4tZ 3 , these reduce to 



' ' r' 



0-212582 ^ + 0'569839 f, + 0'230436 -. = 0'227126, 

 a o" c 



0'161187 ^ + 0'391623 ^+1-401132-.. = 0108126, 

 a 2 b 2 c 3 



0-116301 , + 0-622730 15 + 0-976971 - 2 = 0'0419475-4/j,". 

 a o c 



The solution of these equations is found to be 



= l-428257 + 32'04689w" ......... (157) 



a 



p = -0111620-11797935n" ........ (158) 



- 2 = -0-0559390-0-3891163/i" ....... (159) 



C 



and this solution has been verified by direct insertion into all the equations. 



34. This completes the solution of all the equations, and the determination of all 

 the coefficients except s'. 



