PROPAGATION OF PERIODIC CURRENTS 537 



Let Ir{x) — Ir and F, (.r) = V,- denote the current and the potential, 

 respectively, at any point x of wire r, where r = 1, 2, 3, 4. Then, 

 evidently, for the primary currents and potentials we have: 



7i = - /,, Fi = - F2, (115) 



Fi - Fo = Kh. (116) 



For X > 5/2 : 



h=±^e~y\ . (117) 



Fi = ±^"e~^^ (118) 



Thus the primary currents, Ii{x) and I^ix), and the corresponding 

 primary potentials, Fi(x) and F2(.t), are each discontinuous at x — s/l 

 (by reason of the transposition there). 



The electric field impressed on the individual wires of the secondary 

 circuit by the primary circuit can be formulated by means of equations 

 (106) and (96). Thus 



£3 = {Tu - r32)s/i, (119) 



£4 = (Tn - T,.)zh, (120) 



F3 = (7^31 - 7^32) Fi, (121) 



F4 = (7^41 - 7^42) Fi, (122) 



where z = Zi = Zo is the internal impedance of each wire of the 

 primary, per unit length, and the 7"s are 'voltage transfer factors' 

 given by (98). 



Evidently the secondary circuit constitutes a balanced two-wire 

 line in an arbitrary impressed field (the field due to the primary), 

 and hence is amenable to the treatment already fully described and 

 formulated in the subsection following equation (54). Thus the 

 current at any point .r in the secondary consists of two modes, a and c. 

 However, as already indicated, we shall ultimately be concerned only 

 with the currents in the ends .r = and x = s oi the secondary; 

 evidently these are mode-a currents, for at each end the mode-c 

 currents must be zero, since the circuit is insulated from ground at 

 each end. 



As we shall be concerned only with the mode-a currents produced 

 in the secondary, the next step is to formulate the mode-a constituents 

 of the electric field impressed by the primary. If £' and V denote 

 the mode-a constituents of the axial electric force and of the potential 



