OF ROTATING COMPRESSIBLE MASSES. 
185 
equation, it is clear that the value of Q will be the sum of a number of contributions 
arising from the separate terms on the right. 
Consider now what is the contribution from the first term on the right. Or, in 
other words, consider what would be the solution if the whole equation were 
reduced to 
f [Q-i/DQ + A/ 2 D S Q-„W 3 D 3 Q +...] A -0Q„ 
Jo A 
= i«(y-2)(y-3)(2 !J. 
The solution would be 
Q.= -i(y-2)(y-3)(s^J,.(127) 
for, in accordance with the principles arrived at in § 14, this value makes the integral 
on the left vanish, and the equation is then satisfied. 
Similarly the contribution from the term in P" 0 on the right is 
Qo = A-zmfbA*),.( 128 ) 
for P" 0 is equal to i (Xv 2 /a 2 ) 2 , and so the integral on the left again vanishes. 
The contribution from the term in P' 0 in equation (126) cannot be so simply 
evaluated. If, however, we are content to use Approximation B for P' 0 , then P' 0 
becomes proportional to P" 0 , and an approximate solution is 
Q, = (y-2)F„(2^).(129) 
On referring back to § 16, it becomes clear that the accuracy of the approximate 
solution is of the same order as that which we previously called Approximation A. 
Again, if we use Approximation B for P 0 , the contribution from the whole second 
line in equation (126) will be 
Q u = o, 
for the whole second line in question now represents merely the second order terms in 
the potential of a thick homeoiclal shell, and so vanishes. 
We proceed next to the contribution from the term in AE,-. From equation (123) 
it appears that if' we use Approximation B for the values of L, M, N, ..., and also use 
equations of the type of (69), the first line in AE ( , as given by equation (123), 
becomes a function of (H,x 2 /a 2 ), while the remaining lines vanish. 
It follows that an approximate solution is 
O =J^_. 
tt abed 
