SCATTERING OF PLANE ELECTRIC WAVES BY SPHERES. 

 Thus we now write 

 2n+l 



197 



sin 



n(n + l) 



A n P' B (cos0) = - (e** + 1) cos iflj,{(2n + i) sin 



and, proceeding as before, we are led to the conclusion that a is near to \ir ; thus the 

 value of n/z 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 formulae 



a = Tr- 



(6'8) <| and 

 Thus 



Hence the approximation corresponding to (6 '4) is now 

 (6-81) M = - 



KT 



In like manner the value of N is found to differ from (6 '81) only in having + sin </> 

 as a factor instead of cos 0. 



In the series (6 '81) the value of n 'may be supposed to vary from to o ; and so 

 we obtain the principal part of the sum by using the integral 



(6'82) 



and when sin J0 is very small the value of (6 '82) is approximately equal to 



sn < 



Thus 



(6'83) 



and 



M = +iz sin 0cosd>e 2 '" > 



,^v 



N = \z sin sin 





Accordingly the components of force are now found -to be 



(6'9) 



8M ]_3N 



80 sin 9 3< 



sm 6 



= -%Z COS 



KT 



