190 
MR, J. H. JEANS ON THE CONFIGURATIONS 
37. We now return to equation (126). The solution has been assumed to be 
Qo — Q'o+ (y ~ 2 ) Q^oj 
in which (y — 2) Q" 0 is the contribution from the terms on the right 
0( y-2) i(y-3)(2^)-(y-2)P" 0 (2 
,2\3 
a 
C x 
a 
It follows that Q'o must satisfy the equation 
d\ 
IQ'-if DQ'+ -hf 2 D 2 Q'-Y3W/ 3 I> 3 Q' + • ■ ^ - OQ'o 
= -«(y-2)F,(j:h + lf[ D F4/D , P'+...] 
Cl / Jo 
dx 
A 
AE,- 
- +Sn ( x 2 -\- if ). 
Substituting the values which have been assumed for the various terms in this 
equation, it becomes 
h l (5w* — 90w 4 z 2 + I20w 2 z i — I6z 6 ) + h. 2 (3w 4 —24wV + 8 z 4 ) + /g (w 2 —2z 2 ) 
-0 
R' « . 3S' 
3T' 
ere 
U' 
r 4 2s' o o t' 4 2u' 2 2v' 
,4 + —, w 2 z 2 + -z 4 + — w 2 + — 
«° a c c 8 a 4 c 
12 w 6 + -JiwV + ts wV + — 2 ' ; + vf + — w ‘ z ‘ ti^t-r^+TT 2 ‘ 
a 2 c 2 / \ cr 
= -e(y-2) ffi *■+^«v+ ^ «*+ b * 
4 4 
a c 
c 8 a 4 
+■§■ [y, (5w 6 — 90?c 4 z 2 + 12OrcV — 16z 6 ) + j 2 (3w 4 — 24ieV + 8z 4 ) + y 3 (re 2 —2z 2 )] 
+ -y- [&ne 6 + Sk 2 v/z 2 + 3k 3 w 2 z i + & 4 z 6 + /oqe 4 + 2 k ti w 2 z 2 + /qz 4 + 2k s w 2 + 2& 9 z 2 ] 
+ Sn (x 2 + y 2 ) . 
Equating coefficients of vf, w i z 2 , iv 2 z i and z 6 , we find 
(140) 
5/q-ffi 
r q.< 
— 90/q — 0 
120k,-e 
- 16/q-0 
R'-(y-2)LV~ 
a 
12 
bS'—( y -2)(2mV + L'c 2 )~ 
a 8 c 4 
3T'-(y-2)(NV + 2m'c 2 )' 
cdc 8 
U'-(y-2)N'c 2 )' 
a 
12 
5 • 4/b 
= ° J ' + abc' ■ ■ ■ 
• (in) 
_ 9 0 J i 12^2 
8 '>‘ abc' • ' 
• (142) 
= 120+ • • 
abc 
■ (113) 
— 16./)’ . 4R 
8 '^ a&c' ‘ ' 
• (HI) 
