WIRE TRANSMISSION THEORY 271 



axial electric force/ at the surface of the wire and an impressed poten- 

 tial F (line integral of electric force to ground). The differential 

 equations are then ^ 



^^=-£^+^' 



(Here g is a shunt admittance. See reference 10.) Writing 



7 = V(L«co + R){Cii^ + G), 





k '- + ^ 



this reduces to the differential equation 



^' -§?)'= If +4."- w 



The solution of this equation and its practical significance have been 

 discussed in a recent paper. The resulting analysis is of considerable 

 practical importance in connection with the theory and design of the 

 wave antenna and the problems of 'cross-talk' and induction. 



The elementary or classical theory sketched above is essentially 

 based on the simple concepts of electric circuit theory and its beautiful 

 simplicity is a consequence of the fact that it is approximate only. 

 For example the circuit parameters are only approximately calculable 

 from the geometry of the system and its electrical constants and then 

 only when the problem is treated as a two-dimensional one in which 

 the variation of current and charge along the system is ignored as well 

 as the finite velocity of propagation of their fields. Going further, 

 it is by no means evident that even the form of the equations is 

 rigorous. (We shall find that the form is rigorously valid only in an 

 ideal case.) In the extension of elementary transmission theory, then, 

 the first problem, as the writer sees it, is to examine the conditions 

 under which the specification of the system by series impedance and 

 shunt admittance parameters is justified; that is, to establish the 

 conditions under which the classical form of the differential equations 

 is valid. The second phase of this problem is to formulate a general 

 method for calculating these circuit parameters in terms of the geom- 

 etry and electrical constants of the system. The investigation of 

 these problems leads to still further problems, arising from the fact 



*See reference (10). 



