442 



BELL SYSTEM TECHNICAL JOURNAL 



In going across boundary, we integrate (4) over the infinitesimal radial 

 distance which the current is assumed to occupy 



rdll^ — rJdr 

 iTrrJdr = i 



rjdr = 



Thus 



(11) 



Iirr Zira-i 



hiyai) + ~ — ,- A'i(7ai) — /i(7ai) ( 1 



B = 



B 



Ko(ya) 

 J oil a) 



Io{ya)Ko{yai) 

 Ko(ya)I(,(yai)/_ 



i Koiya) 





A'o(t«) /o(7<Zi) 

 A'i(7ai) A'oCTai)"^"^ 



1-Kax I^{yd)Ix{yax) L/)(7<?i) -^o(7<?i) 



at r = (7i 



-Ezl = -Ej2 



Now 



Hence 



— /7\ / '" \ Koiya) h{yaCj 



(joe / \2irai/ Io{ya) Ii(yai) 



1 - 



loiya) Kniyai) 



Kiiyai) Koiyai) 



Ki)iya) h{yai)/ \_h{ya\) h{yai) _ 



1 



Vti/i 



377 



^0 



^^V = E, = j ^ ll{yax)G{ya, yax)i 



V 



^(^^ lliyadG 



(ya, yih)ij 



G(ya, yai) — 60 



Ao(7tf) 1 

 /o(Xa) J 



Ao(7ai) 

 _-^o(7<^i) 



In obtaining this form, use was made of the fact that 



1 



K,{z)h(z) + Koiz)hiz) = 



(12) 

 i 



(13) 



(14) 



(15) 



(16) 

 (17) 



