174 
MR. J. H. JEANS ON THE CONFIGURATIONS 
in which the quantities in square brackets are the most general zonal harmonics of 
appropriate type, and the coefficients c n , d u are chosen so as to be identical with 
those used in my previous paper. Either by direct calculation or by comparison with 
the results obtained in this previous paper, we find 
4c n = L (J A + — — 2 Ia 4 H—iH A * 
\ a a 
+m (— ^T A 3 c + H A 3 C j + ^NH A 2 C 2.(74) 
• • (75) 
in which the notation is that already defined in formula (37), supplemented by the 
further abbreviations : 
4dj — 2p (J AA — 2 I aa )— 2 I ac 
\. a J c 
6L 
2L 
-} -r I A 3-rUH-9 ( 2l A 2n — 
a 
2 X A 3 
4 X A 2 T ~2 
a c 
l A 2 C ' 
L AB.. 
= f 
XdX 
A (a 2 + X) (6 2 + X)... 
Hab... = 
X 2 dX 
A (a 2 + X) (6 2 + X)... ’ 
• (76) 
and the further abbreviations G AB , F AB , will be used when required, to denote 
similar integrals having terms X 3 , X 4 in the numerator. 
18. For computation, it is necessary to construct tables of these integrals. The 
table on the next page contains values which are required both here and later in the 
paper. The method of computation has been fully described elsewhere.* 
Using these values, I find in place of equation (74) 
4c n = 0'010947L —0‘064325m + 0'094707N.(77) 
On equating coefficients of x 2 z 2 and z i in equation (59) we obtain 
4Cn- 0 — |J aa 2 (y 2) . 
(Jj CO 
16c n — S—— IJac — 2 (y —2 )-j-j > 
(a/ O Cv 1/ 
6 
—0— — aJcc - 2 (y —2)-j 
(78) 
* ‘ Phil. Trans.,’ A, vol. 215, p. 60. 
