12 BELL SYSTEM TECHNICAL JOURNAL 



As regards the first phase of this problem it is found that the complete 

 specification of the system in terms of its self and mutual impedances 

 and capacities is only rigorously valid for the ideal case of perfect 

 conductors embedded in a perfect dielectric, and that it becomes quite 

 invalid if either the conductors or the dielectric are too imperfect. 

 Fortunately, however, it is valid to a high degree of approximation 

 for all systems which could be employed for the efficient transmission 

 of electrical energy. 



Under the circumstances where the approximations discussed in the 

 preceding paragraph are valid it is shown that the electric and magnetic 

 field in both dielectric and conductors are derivable from two wave 

 functions. The first of these is determined as a linear function of the 

 conductor charges by the solution of a well-known two-dimensional 

 potential problem, while the second is determined as a linear function 

 of the conductor currents by the solution of a generalization of the 

 two-dimensional potential problem. The latter problem is believed 

 to be novel, in its general form, and to possess both practical and 

 mathematical interest. For detailed application of the theory to 

 specific problems, the following papers may be consulted. 



"Wave Propagation over Parallel Wires: The Proximity Efifect." 



Phil, il/ag., April 1921. 

 "Transmission Characteristics of the Submarine Cable." Jour. Frank. 



Inst., Dec. 1921. 

 "Wave Propagation in Overhead Wires with Ground Return." 



B. S. T. J., Oct. 1926. 



I 



Maxwell's equations are the set of partial differential equations 

 which formulate the relations between the electric intensity E and 

 the magnetic intensity // in terms of the frequency ^^i!2w and the 

 electrical constants of the medium. Let X, tx and k denote the con- 

 ductivity, permeability and dielectric constant of the medium; let 

 it be supposed that all quantities vary with the time / as e^\ and let 



V = 1/ V^, 



v^ = 4:Tr\fxioi — UI-JV", 



i = v^n^. 



Then if we introduce the vector 



M = jiiwll, 



