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



and the contributions to Pj, P 2 , P 3 , P 4 , are found to be (cf. equations (128) to (131)), 



T ' \ a /' \ 2 



T> J. / :< v ij A ' _i_ >' 



% - - \ '* * 7^ Ta^ 1?J ("! 



4 A : 

 '3I/X . m'X 



3M'X n'X 



1 a 



We find as the contribution to d } , (equation (140), p. 60) 

 d\/l\ PA ^^\J2P, 1/3L/XXX 



"~ ++ 



from which it is easily verified that d! + d 2 + d 3 0, as it ought to be. 



In virtue of this relation it is only necessary to evaluate two of the contributions 

 4cZ 1; 4c? 3 , 4t? 3 , but I have calculated all three directly from the table on p. 61, so as to 

 obtain a check on the amount of error involved from the causes mentioned in 28, as 

 well as a .check on the accuracy of my own computations. The values I find are 



4^ = 0'85375 ^r - 0'073783 ~ - 0'089893 ^r 

 a 4 // c 



- 0-054134 ?j- a + 0-072732 -~ + 0'059701 -m , 

 be car a b 



4d 2 = -0-041149 ^ + 0-244072^-' -0'194266^;' 

 a b* c* 



V m' ??' 



+ 0-051069 ~ 3 - 0-054134 ~- a - 0'005568 



4tZ 3 = -G'044227 ^r - 0'170277 ~ + 0'284157 ^J 

 a 4 b* c 4 



+ 0-003091 y ^ - 0-018600 ~- 0'054134 - 



c 



From these figures the value of d^ + d^ + d^ would be given by 



= -0-000001 + 0-000012 -'-0-000002' 



+ 0-000026 ~ - 0-000002 4^. - O'OOOOOl n/ 



j y 2 v vwwv** 22 WWVA 27 



This check gives an idea of the amount of error involved. It illustrates the tendency 

 of the errors to accumulate in terms where 6's and c's are plentiful, and to be absent 



