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



Hence, by comparison, we obtain as the values of the coefficients 





Cn =; 4 Jo 'A I A^ r A 4 ! T A*C " A 4 ' AV 



. i f <**(__ + M.' iVj (135) 



4 Jo A \AB 4 B 4 BV 



1 d\ I y L 3 ) ^1S6^ 



= . ^IAC? + C I cv 



! f" rfX /12/9 6/9 2 2/9y 2n ; PI P 2 \ 

 r " " : t Jo "A U 8 B 3 A 2 B :i + A 2 B 2 C A 2 B 2 " A 2 B """ AB 2 / 



Cl3 = *. '~& ( A 1 ? + ife + A 8 BC a + A 2 !! 2 + A% + ICV ' ' 



-, ............... (143) 



Jo A \ A 



Evaluation of Certain Integrals. 



28. It is clear that before these coefficients can be evaluated, certain integrals 

 must be calculated of the types JBCA...> IABC... > where the notation is that of 21 

 (equation (67)). 



The values of J A , J B , J c have already been evaluated in 23, as also of I A A> IAB, 

 I AC and I AAB , I AAC , I ABC . We also have 



Z BC = J B - i J o = T = 0-3916228. 



These 10 integrals will form an adequate basis from which to calculate all the 



