188 
MR. J. H. JEANS ON THE CONFIGURATIONS 
35. The value of P is 
P = Lw 4 + 2m?*j 2 f 2 + N£ 4 + 2pw 2 + 2r£ 2 , 
whence we find 
DP 2 = + 3 SfaT + 3Ew 2 r + + m 4 + 2 0&T + tf 4 + 2tm 2 + 2bf, 
in which 
la = — x 64L 2 + x 8Lm 
a A. 
£ = 
48Lm 
4 (4m 2 + 2LN) 
® = 
Jj 6 - (4m 2 + 2LN) 
40mN 
m = 
16mN 
56N 2 
X = 
144pL 
2 (8_pm + 4?-L) 
s = 
5 
+ 
^8 
OO 
OO 
6 (4pN + 8 rm) 
t = 
4 (4pN + 8 rm) 
120Nr 
It = 
32 p 2 
8 pr 
b = 
I6pr 
24 r 2 
We may now assume (cf. equation (133)) 
£(DP-J/D ! P 2 + T -h/ 3 D s F- 5 *- 0 -/ 3 D<F)^ 
= j\ (5w 6 — 90wV+120wV — 16z 6 )+j’ 2 (3w 4 —24wV+82 4 )+y 3 (w 2 —2z 2 ), . (137) 
in which, on comparing coefficients, we obtain 
#i = 
F - IP & »«*^«S) + ^(^ ^6®+ ^ 1923 + ^72C 
9216 A 3 VA : 
X '-2304il+ , 3X3 90 384£+ _A^_ 2 88^- 
X 3 
«VA 2 C 
« 2 c 4 AC 2 
c 3 C 3 
20m 
d\ 
A ' 
(138) 
There are corresponding equations for Sj 2 and j 3 , but these are not written down 
as they can readily be obtained from equations (135) and (136). To change 3 k 2 into 
Sj 2 , change all accented coefficients into black letter type, and change X, X 2 , X 3 
wherever they occur explicitly, into ^-X, g-X 2 , ^X 3 respectively. The same procedure 
changes /+ into j 3 . 
The values of these coefficients at the ellipsoidal point of bifurcation can be 
calculated from the material already provided in § 18 and the values of p and r 
given in formulae (113). Using the exact solution throughout, I find 
5y\ = 001931 (y — 2) — 001473, 
3/ 2 = 0-01080 (y-2)+0-00576, 
*a = 0*5715 (y-2)+ 0-4094, 
all terms in (y- 2) 2 vanishing in accordance with the result of § 14. 
