618 Mr. J. R. Carson on 



surface of the wire gives by direct equation of corresponding 

 terms of (22) and (25) : 



211 a = -B./a, ) 



B, =-21, \ W 



and 



(2I/a)^ K = -B„ +1 /a»+ 1 + ( -=^ n 1 (a/c)"- 1 2 n - u (28) 

 J [n — i) ! 



72 = 1, 2, 3, ... . 



Similarly, the boundary condition of the continuity of the- 

 normal magnetic induction applied to (23) and (26) gives : 



(2I/a)^h n = B B+1 K+i+ ( f^| (a/0)- 1 S„-i, (29) 



» = 1, 2, 3 



From (28) and (29) : 



B n+1 =-a»IlJ Jn '~T J - .... (30) 

 £d 

 and 



(I/a) ^■ / + 7 J " /, i = i-grV/o)-^,,-!. . (31) 



It is now convenient to introduce the following notation t 



Pn = GJ n '-ntfd/(&J + npJn), I _ (32) 



Qn = *"A> 



a/c = &. J 



In terms of this notation it follows from (30) that 



B„ +1 = -«"?J (33) 



If the B coefficients in the 2 functions as defined by (24) 

 are replaced by their values as given by (27) and (33), it is 

 easy to show that equations (31) may be written as 



?n= -(-i)» 2 ^-^ ! ^ : (^ % _^^ 2+ ...), 



which may conveniently be written as 



q m =(-lY*pJf'--£=}£ ] p % *t.(q), ■ ■ (34) 



n = 1, 2, 3 . . . . 



