197] DIELECTRICS AND MAGNETIZABLE BODIES. 377 



which being multiplied by /* 2 and subtracted from (8) gives 



9F 



At the surface p = a this gives, differentiating (2), (3), (4), by p, 

 (ii) ^(-Ann 







- /, 2 (^a 71 " 1 - CUa-< n+1 >) T n = (/* 2 - /^) no,- 1 T n , 

 o o 



and consequently for every n 



(12) - frAnar* - ^ (B n a n - C n a~ n ) = (^ - ^), 

 and at p = b, 



(13) - 



_ T n , 

 and consequently 



(14) - ^ D n b n 



The four linear equations (6), (7), (12), and (14) determine the 

 four constants A n> B n , C n , D n . 



Solving, we obtain for their values, putting 

 If, 



f/7)\27l 



-^ - 



1 



(15) 



Since the absolute value of M is greater than 1, and since 

 b/a<l, N n is always positive, and accordingly D n is always 

 negative. Accordingly the effect of the induced polarization 



