276 BELL SYSTEM TECHNICAL JOURNAL 



As stated above, it is a reasonable inference from the general theory, 

 that the complementary waves modify the current and charge waves 

 appreciably only in the immediate neighborhood of the physical 

 terminals, at least in most actual transmission systems. The essence 

 of the method to be described consists of taking advantage of this 

 fact and directly calculating the fields of the principal current and 

 charge waves by means of their retarded potentials,^ instead of em- 

 ploying for calculations the principal wave fields as given by the 

 solution of the wave equation. This will now be explained in more 

 detail. 



In any transmission system energized by impressed forces introduced 

 through terminal networks, the electromagnetic field may be analyzed 

 as follows: (1) the impressed field, (2) the field of the terminal currents 

 and charges, and (3) the field of the line currents and charges proper. 

 The impressed field may be supposed to be concentrated in the 

 terminal network, and the field of the terminal currents and charges 

 may be supposed to be relatively unimportant except in the neigh- 

 borhood of the terminals; what we are essentially concerned with is 

 the field of the line currents and charges. Now let us suppose that 

 we have calculated the principal wave in the system in the usual 

 manner; corresponding to the resulting current and charge distribu- 

 tion, there will then be an unique corresponding field distribution 

 determined by the solution of the wave equation, and this field is 

 propagated in precisely the same way as the currents. But now 

 suppose that we calculate the field of this current and charge distribu- 

 tion directly by means of their retarded potentials. We will find 

 that the field so calculated is analyzable into two components: (1) 

 a field identical with that given by the solution of the wave equation, 

 and propagated in the same manner as the currents and charges, and 

 (2) an additional field propagated in an entirely difi^erent way and for 

 systems of small dissipation much more rapidly attenuated at least 

 in the neighborhood of the conductors. We find further that the field 

 of the principal current and charge wave does not correctly satisfy 

 the boundary conditions at the surfaces of the conductors, which 

 indicates that there must exist a compensating current and charge 

 distribution. However, it appears that this compensating distribution 

 will be relatively small and concentrated in the neighborhood of the 

 terminals, so that we infer that its field, as calculated from its retarded 

 potentials, can be ignored. Under such circumstances the inductive 

 field (and the radiation field) is calculable by means ot the retarded 

 potentials in terms of the principal wave of current and charge alone. 



•See reference (7). 



