SCATTEEING OF PLANE ELECTEIC WAVES BY SPHEEES. 
197 
Thus we now write 
2 n +1 
sin Q A„P'„ (cos 0 ) = —i + l) cos Jj {(27i+1) sin ^6}, 
and, proceeding as before, we are led to the conclusion that a is near to ^tt ; thus the 
value of njz is small, in the parts of the series which contribute the principal part of 
the sum. Then we can replace ( 6 ’l) by the approximate formulse 
(6‘8) ^ and 
Thus 
a = ^TT— {n + ^)fz 
i/r = z-\-\ir— {n + ^) {^tt) A-g- {n + ^Yfz. 
2i/^ + W7r = 2z+ [n + ^yiz. 
Hence the approximation corresponding to ( 6 ’4) is now 
(6-81) 
M = — i cos ^6 cos ch -2 {2n +1) sin ^6}. 
KV 
In like manner the value of N is found to differ from (6‘81) only in having + sin <f> 
as a factor instead of — cos 
In the series (6’81) the value of n may be supposed to vary from 0 to oo ; and so 
we obtain the principal part of the sum by using the integral 
(6-82) 
1 1 ( 2 ^ sin di 
Jo 
and when sin is very small the value of (6‘82) is approximately equal to 
{^iz sin ^6). 
p-lKV 
M = sin 0 cos - 
Thus 
(6-83) 
kv 
and 
N = — 5-2 sin d sin (pd 
kV 
Accordingly the components of force are now found to be 
Y: 
Zb 
+ Cy 
— C^ 
3M 1 BN 
00 sin 6 d(p 
1 0M 0N 
sin 6 d<p 00 
g2i^—IK?' 
|-z cos 0 - 
^ KV 
1 • ? ® 
sm (ji - 
2iz—iKr 
kV 
(6-9) 
