114 BELL SYSTEM TECHNICAL JOURNAL 



Note III — Determination of gi, q^, etc. 

 The equations (47), 



>-2n v-2n 

 g„ = ( - 1)"X„^ {A + Snn Bo) - {- iy\n ^-; l^n « = 1 « 



w nl 



are linear in the variables gi, 32 — , since 



n\ 



2„ = w! o„_i,„-f-i ?! — y: 0„_2,n+2 52 — — — • 



The values qi, 52 • • • may be determined by a method of approxi- 

 mations, g„ being the limit of the sequence 



y n t y n > y n > 



the successive terms of which are defined by the expressions 



>-2n 



g„(0) = {-ir\„^~{A +S„„Bo), 

 n 



5„(i + i) = (_i)« ^ (^ + 5„„5o) - (-1)" \- 2„ (5(^)), 

 where J„ ((^^■'') is the value of 7„ when gi, 92 — '-'i replaced by 



This method, however, while formally simple and direct is not 

 usually well adapted for numerical solution. For all sizes of armor 

 wire and for frequencies of practical importance the argument f in 

 the expression (48) is small compared with /i and the quantities, 



Xi, X2, 



are all nearly unity. This suggests the use of the following method 

 of solution of equations (47). 



The solution of the auxiliary set of equations 



p,= - iHA + SnBo) +^2i(^), 



>-2" >-2« 



Pn= {-\Y^—{A -V Sn Bo) - i- 1)" ^ 2„(^), 

 in the auxiliary variables pi, p2 — may be written. 



Pi = - ^' Cu (A + Sn Bo) + ^ Cu (^ + 522 Bo) + . . . + . 



Pn = - ^' Cnl {A + 5n Bo) + I' Cn2 (^1 + 522 Bp) + . . . + , 



