380 ELECTROSTATICS AND MAGNETISM. [PT. II. CH. IX. 



The condition (10) of the preceding section gives the corre- 

 sponding equations, 



(n) MiSi 



o 



00 



- fr 2 {B n na n -* -C n (n + 1) a~( n ^} Y n = (^ - ^ 







(12) -^ n (w + l) 



- ^ {5 n wa - O n (n + 1) -<+')} = (^ - ^) n, 



(13) -^SJW-'F, 

 o 



. <fr-*)2? F,, 







(14) - /^nfc* + ^ 2 {5 n n6 - C n (n + 1) 



Solving the equations (6), (7), (12), (14), we get, putting 



a 



271+1 



n + 1 MS -Mi 



The results are similar to those in the last section. Since 

 M n and M n ' have the same sign, and are greater in absolute value 

 than unity, N n is positive, and D n is negative. The field in the 

 cavity is given by 



06) P = FW = 1- - _ F, 



