354 BELL SYSTEM TECHNICAL JOURNAL 



stant of the antenna circuit, equation (112) may be written 



When the boundaiy conditions are applied, equation (115) defines 

 the value of the current / in the wave-antenna in terms of the impressed 

 electromagnetic field specified by V and fw'- By equation (101) the 

 resultant voltages at the ends of the antenna are: 



V"(0) = V'(0) + no), (116) 



V"{s) = V'{s) + Vis). (117) 



To this point, the solution of the wave-antenna problem has been 

 in a rigidly analytic form. While it is possible to determine com- 

 pletely the received current by following through this method of 

 solution, the problem can be greatly simplified and a physical picture 

 of the problem gained by a synthetic process. 



The synthetic method of attack consists of replacing the impressed 

 field by a set of electromotive forces identically equivalent to the 

 impressed field in the sense that it produces the same currents and 

 charges. ^^ 



The proposed set of electromotive forces is as follows : 



A. A distributed longitudinal electromotive force /,i,' per unit length 



in the wire, i.e., an electromotive iorce fjdx in each element of 

 length dx; 



B. A distributed vertical electromotive force, V, in the superposed 



shunt admittance Y between the wire and ground, i.e., an electro- 

 motive force V in each elemental admittance path Ydx; 



C. In each end of the wire, x = and x = s, localized series electro- 



motive forces, equal respectively to minus and plus the impressed 

 voltages at those points; i.e., equal to — F'(0) and -f V'{s) 

 respectively. 



The electromotive force of A is suggested by (107), that of B by 

 (109) and (110), that of C by the terminal conditions expressed in 

 (116) and (117). In the case of a wave-antenna constructed to 

 maintain high insulation resistance, the conductance portion of the 

 superposed admittance Y can be made negligibly small. Under this 

 condition, the susceptance part of this admittance can be combined 

 with the linear capacitance of the wire to alter the propagation con- 

 stants (K and 7) of the antenna and the voltages induced in the super- 

 posed shunt admittances neglected. 



