352 



BELL SYSTEM TECHNICAL JOURNAL 



where 0, V, fio, and fg are the components of the secondary field set 

 up by the currents and charges in the system and 4>", V'\fw", and/o" 

 represent the resultant field about the system. 



E' (x,ej 



POSITIVE 

 < < DIRECTIONS 



(K./) 



y/////////////////////////////}/////////// ////////////////////^^^ 



O X s ' 



/%^ 



7^ 



®y 





4- 



«; 



'^^ 

 ''^^^n 

 %t^ 





Fig. 17. 



As a result of the impressed field, a current / flows in the wire, and 

 a corresponding superposed current distribution is induced in the 

 ground. If the internal impedance of the wire be Zw and that of the 

 ground be s^, the resultant longitudinal electric force along the wire 

 may be written 



jj' = Iz^=fJ-{-U (102) 



and similarly the resultant longitudinal electric force along the ground 



//'= (-/s. +//)=//+/« 



(103) 



The second curl law applied to the periphery of the rectangle formed 

 by the vertical at x, the wire, the vertical at (x + Ax), and the ground 

 yields 



dV" ^ d4>" 

 dx dt ' 



2/-// + 



(104) 



where z is the total series impedance of the wire and the ground circuit 

 and is 



z = Zg -\- Zyo (105) 



