262 Dr. J. W. Nicholson on a General 



We have 



9 / • A\ ^' • ■ a 



~ - A (c sm 6) — _— — rx sin 6 

 _ ikrtz sin 6 



_ __ _ _ m m t C J-J-) 



and by the solenoid al relation, 



Thus (/>, c) each consist of two portions of different forms, 

 one derived from a, and the other from x. 



=r— , ^.sin#| on (11) 



d 2 



and (12), and subtracting, we obtain, since ^—5= — m 2 , 



To ■ sin e Ye (! ' sin 0) ~ m * b = -!^^ ( '"' 2 sin2 e) 



-^sine|2 . . . (13) 

 V (jo) 



Put 5 = ^ + ^2, where 6 X and 6 2 are the portions to which 

 a and x respectively give rise. 



The factors involving r in b x and b 2 are respectively 



1 d i T i -i t 



- — . r*J and r *J, 



where J is briefly written for J (kr). 

 Making' the substitutions 



61 = 7- . r«J . 6\ cos (??ia>4-e) 



r ar 



bo— > Tr B . — _ . S 2 sin (ma> + S) 

 V i/r 



(14) 



where (Sj &,) are fmietions o£ only, we obtain 

 J .sin^Minfl)-,™^:^. ^sin 2 0P,?(cos0) j- (15) 



~-. ? in^(8i8intf)-m 1 8, = sinffiT(oo8fl) . . . (16) 

 du d" 



and deduce at once, 



g = ■ 1 Pnfrosfl^ (1?) 



2 ?i . n + 1 sin 



