PROPAGATION OF PERIODIC CURRENTS 515 



mentioned, by the simple device of resolving the impressed field at 

 each wire into two constituents one of which has equal values at the 

 two wires while the other has equal but opposite values at the two 

 wires. This resolution is always possible, for it is merely in accordance 

 with the following pair of algebraic identities : 



Vi = Uvi + V2) + K^i - V2), (55) 



V2 = K^i + V2) - hivi - V2). (56) 



Although rji and 772 may in general denote any two quantities what- 

 ever, in the present application they refer to the impressed electric 

 field at the two wires No. 1 and No. 2 of the contemplated two-wire 

 line. It is convenient to introduce the symbols r]c and rja defined by 

 the equations 



Vc = hill + V2), (57) 



Va = vi — V2, (58) 



so that the resolutions (55) and (56) of 771 and 772 can be written in 

 the more compact forms 



Vi = Vc + hva, (59) 



V2 = Vc — hVa- (60) 



7]c and r]a will be termed respectively the mode-c and mode-a con- 

 stituents of the impressed field, because they give rise to mode-c and 

 mode-a effects respectively; mode-c effects being defined as those 

 which are equal in the two wires, mode-a effects as those which are 

 equal but opposite in the two wires — as discussed in connection with 

 equations (28). From (57) and (58) respectively it will be noted that 

 the mode-c effects and the mode-a effects depend respectively on the 

 average and on the difference of the impressed fields at the two wires. 



As in treating the one-wire line (in the preceding subsection), so 

 also in treating the balanced two-wire line (in the present subsection) 

 it is usually advantageous to deal separately with the axial electric 

 force and the potential of the impressed field. Furthermore, in the 

 case of the two-wire line each of these constituents of the impressed 

 field is to be resolved into two modes, c and a, in the manner repre- 

 sented by equations (59) and (60) together with (57) and (58). 



Owing to the balance (bilateral symmetry) of the assumed two- 

 wire line, the mode-c constituent rjc of the impressed field will produce 

 only mode-c effects, and the mode-a constituent only mode-a effects. 

 Thus, r]c will produce equal currents Ic and Ic in the two wires, while 

 7]a will produce equal but opposite currents /„ and — la in the two 



