184 
MR. J. H. JEANS ON THE CONFIGURATIONS 
whence we readily obtain, writing A for a 2 + \ and so on, 
AE, - — 7 robe 
0 l 
A/\ A 
A 
+ 
j. ] 
x 
A 
yr* 
B 2 C 2 
+ 2 Up 1 
j 
. X 
(l2L v 
or'A 
V A 
192 l 
r 
B 2 
z 
C 2 
31. From § 8 , the value of Y { (l) is given by 
9Ay -LA’ , 1 (*y ^A 
" a 4 A 2 62 5VBC 
d\ 
A. (123) 
V l (l) + eAV J (l) + 6 2 3Y i (l) = -tt«6c [f+<p{ 1)]^-, • • • (124) 
Jo Za 
in which the value of <^(l) is now (cf equations (12) and (47)) 
0(l) = e[P-i/DP + ^/ 2 D 2 P] 
-h 2 [DP 2 -i/D 2 P 2 +Wtf/ 3 D 4 P 2 ] 
+ e 2 [Q - i/DQ+ ^f 2 B 2 Q -^W/ 3 D 3 Q +...] 
+ terms in e 3 , &c.(125) 
Thus the value of §V { (l), being the coefficient of e 2 on the right hand of equation 
(124), is given by 
■W(l) = -Trabc f [Q-i/DQ + A/ 2 D 2 Q-^/»D>Q+...] A 
Jo A 
+iwabe f"[DF-i/D a F+ x J 7 / 2 D»P- T J ri /«D‘P(] A. 
Jo A 
32. Collecting and rearranging terms equation (115) now becomes 
f[Q—i/DQ+*/ s D 2 Q—^ ¥ /»D s Q + ...] A — 6Q 0 
Jo A 
= e(v-2) 
i(y-3)(2 AY_[F,+( y -2)P" 0 ](2A 
' cr/ V a 
+ i[ pF-i/D > F+ T i,/*D , F 
Jo 
0216 
i_y 3 D 4 p-] — 
AE,- 0 /1) o\ 
^+Jn (*+?)• 
(126) 
This is an equation for the determination of Q, all the terms involving Q being on 
the left hand, and all the terms independent of Q on the right. The terms on the 
right are all of degrees 6 , 4, and 2 in x, y ; z, so that the value of Q will clearly 
consist of terms of degrees 6 , 4, and 2 in x, y , z. Further, from the linearity of the 
