178 
MR. J. H. JEANS ON THE CONFIGURATIONS 
Then on equating coefficients of a: 2 , y* and z 2 in equation (59) we obtain 
Ad x — 
a 
An, 
(86) 
4d,-^=A n, .(87) 
id.- ^ = 0.(88) 
C 
The value of 4c?! is readily found to be* 
where 
4 d x = 2pJ AA 
AA 
AB - ' 
r 
2 I AC + ^ e \ s 
(89) 
m T 
c 2 A2C 
(90) 
The values of 4d 2 and 4d 3 can of course be written down from symmetry. 
It is immaterial whether we insert the values of L, M, N, ..., or of L/, M 7 , N r , ..., 
in these equations in evaluating 4e l5 &c., since the contributions from L", M", N", ..., 
which are proportional to a 4 , b i , c 4 , ... , must vanish by § 14. 
23. If we are content to use Approximation B, the solution of our problem assumes 
a very simple form. For L/, M 7 , N 7 , ... are now proportional to a 4 , b i , c 4 , ..., and 
therefore 
e i = e 2 = e 3 = 0 (Approximation B).(91) 
Thus equations (86), &c., reduce to 
2pJ AA -4l 4A -il AE -^I AO - 52 7= An, .(92) 
a b c ar 
and two similar equations. 
The quantity An, which has been introduced for convenience only, is entirely at 
our disposal. Let us take An = 0, then the solution of the equations is 
p = q = r = 0 (Approximation B).(93) 
Thus, corresponding to Approximation B, the solution corresponding to rotation « 
given by &>*/27 T/o 0 = n has for density 
(pq— o') 2 /& ' /x ' 
2 p \6 
„,2 \ 2 
“ (y—2)) f-j + tt + w 
a 
(94) 
* 
Of. ‘Phil. Trans.,’ A, vol. 215, p. 60. 
