540 BELL SYSTEM TECHNICAL JOURNAL 



On dividing (134) by (138) the ratio of j(0) to 7(0) is found to have 

 the simple value 



i(o) s 



/(O) K{y + 7')/2 



(139) 



In particular, when the two circuits have equal propagation constants 



(t' = 7), 



i(0) z 



J{0) z ' 



(140) 



where Z = yK is the mode-a 'complete series impedance''* of the 

 primary, per unit length; it will be recalled that z is the 'internal im- 

 pedance' of each primary wire, per unit length. The ratio z/Z is 

 ordinarily a very small fraction. 



At .T = 5 the formulas for the four current-ratios are 



/i(0) 'k'K {y-y')s/2 ' ^'^'^ 



/i(0) ^ K'' ' ^ ^ 



/i(0) ^ K'' ' ^^^^^ 



^^= 2r^.-(-+V)s/2. (144) 



The sum of the last three is 



-^ = - T^, [1 - e-^y-y'-i'Je-y\ (145) 



On dividing (141) by (145) the ratio of j(-^) to J(s) is found to have 

 the simple value 



j(s) _ z 



J{S) K{y - 7')/2 



(146) 



When the absolute value of (7 — y')sl2 is small compared to unity, 

 equations (141) and (145) become approximately 



J{s)_ ^ Ksz jy - y')s ,, .7. 



ii(0) K'K 2 ' ^ ^ 



Jjs) 



'f'^-^^^p-'"- ^'''^ 



