168 Mr Mayall, On Current Sheets, especially [Feb. 26, 



dp 



but since F = (%i + 1) E,, [ ^^ , 



" ^ ^ ^1 "LE:Jip--h;' 



therefore 



and (23) becomes 



E'F -F'E = 



n n n n 



-K'){p'-k') EJ)c 

 2n + l 



when p = a 



bo 



ip¥c' (A,+ A,) e: 



by (22); 



•(24), 



(2n + 1) ^ {n (n +l)a'-q (h' + F)| 



and therefore 



^ iphVEM, 



(2n + 1) ;^ [n (n + l)a''-q {h' + F)} - ipbVEJF: 



which gives A^ and A^ completely. The expression for the current 

 function is 



^ = ^ {A,F,, - A A) E,, (/.) E,, {v) e'^* 



{In + 1) ip¥c^'E,:AoE,, (p,) E,, (v) e'>* 

 (2n + 1)k {n (n+l)a'-q (h" + k')\ - 4>7ripb'c'E,,'Fn ' 



and the effect inside the shell is given by 

 n + n, = {A, + A,) E^ (p) E^ (f,) E^ (v) e^pt 



(2n + 1)k {n (n + l)a'-q jK' + F)| A, 

 {2n+l)K{n{n+l)a'-q{K'+k')}-4^'7rip¥c'EJFJ ^^ ^^^ •'■ 



= A, cos xK (p) K (/*) E„ iv) e ^p'-^\ 



^nrpb%^E:F: 



where tan ^ = 



{2n +l)K{q {K' + F) - n {n + 1) a? 



again as in the previous cases of the sphere and cylinder shewing 

 a diminished intensity and change of phase. 



