536 BELL SYSTEM TECHNICAL JOURNAL 



The primary is energized by an alternating electromotive force Eo 

 inserted at x = 0. Stated precisely, the problem here contemplated 

 is the derivation of formulas for the currents produced in the two ends, 

 X = and x = 5, of the secondary circuit by the primary circuit, when 

 all reactions of the secondary on the primary are neglected. 



(0 (0 



K < Eo K,T I Primary 



(2) (2) 



s. 



(3) 



K'l K',Y' Secondary |K' 



Fig. 13 



The wires of the secondary circuit are numbered 3 and 4. The 

 primary wires are numbered 1 and 2, in the sense that 1 and 2 designate 

 the positions the wires would occupy if non-transposed ; in this sense, 

 wires 1 and 2 are each discontinuous at x = sjl, the transposition cross 

 thus being regarded as extraneous to the wires. -"^ 



Each circuit is terminated at each end in its mode-a characteristic 

 impedance — K for the primary, K' for the secondary. The mode-a 

 propagation constants of the primary and secondary, per unit length, 

 are denoted by 7 and 7' respectively. 



The earth is assumed to be a perfect conductor. This assumption 

 is effectively a good approximation because the contemplated circuits 

 are such that the distance between the two wires of each circuit is 

 small compared with their height above ground; at the same time the 

 assumption greatly facilitates and simplifies the solution. 



Evidently the first step is to formulate the primary current and the 

 primary systemic potential at any point x. The second step is to 

 formulate the electric field impressed on the secondary by the primary. 

 The third and final step is to formulate the currents produced in the 

 secondary by the impressed field of the primary; this third step will 

 be carried through by means of the synthetic method, employing the 

 set of equivalent electromotive forces formulated in the early part of 

 Section III. 



2'^ The transposition cross may conveniently be regarded as merely a particular 

 kind of transducer (four-terminal network) inserted in the primary, namely a revers- 

 ing transducer. 



