186 
MR. J. H. JEANS ON THE CONFIGURATIONS 
There remains the contribution from the term Sn (x 2 +y 2 ) on the right of equation 
(126). This contribution will consist of second degree terms in Q 0 , which represent 
merely a step along the fundamental series of ellipsoids to allow for the altered 
rotation, and the requisite terms can be easily calculated. 
Collecting all the approximate partial solutions which have been obtained, we find 
the complete approximate solution 
Q. = — (y-2) 
, AEj 
7 rated 
i(y-3)(s^) 8 -[F,+ (y- 2 )F'J 
+ terms in Sn . 
(130) 
Clearly this approximation is of a degree of accuracy comparable with that of our 
previous Approximation A for P 0 , with which it may be compared. This former 
approximation can be put in the form 
P 0 = !(y-2) (2 —}i + : + terms in An .(131) 
33. A less good approximation, comparable with the former Approximation B, can 
be obtained by further simplifying equation (130) by the help of approximate 
equations such as (69). The value of Q tf simplified in this way is found to reduce to 
a function of ('Ex 2 /a 2 ), so that the whole solution becomes ellipsoidal. 
34. The accurate solution for Q 0 may be supposed to be 
Qo = Q / o+Q"o(y-2), 
where Q" 0 (y — 2) is the part of Q 0 which is accurately given by formulae (127) and 
(128); thus 
Q ". = »( y - 2)+«(2 
I have calculated the value of Q'q accurately for one configuration only, namely, 
the ellipsoidal point of bifurcation. At this point a = b and x, y enter only through 
x 2 -\-y 2 . Let us write 
x 2 -\-y 2 — w 2 ; f 2 + r — to 2 . 
The general value of Q 0 will be of the form 
o B 6 , 3S 4 , , 3T 2 4 , U 
Qo = w + —; ^ z + — W + 
a 
a 8 c i 
a 4 c 8 
10 2 °+— w l + 
c 12 a s 
2 s 9 o t 4 
— w^z 2 +~z i 
arc c 
2u 
2v 
— W+ 4 
a c 
We may further put 
R = R / + R // (y — 2), &C., 
then the values of R /; , &c., are 
R" = [i (y-2) +i] a\ &c., 
