ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 205 



where e is the voltage across the line at the place where the 

 current in the line is i. This equation may be established as 

 follows: The inductance of the element abed is L-Ax, and the 

 magnetic flux between the wires ab and cd is equal to the 

 inductance of the element multiplied by the current, everything 

 being expressed in c.g.s. units. Now, the current distribution 

 and the associated flux are assumed to travel to the right at 

 velocity V so that all of the flux between ab and cd will sweep 

 across the line be in Ax/V of a second. Therefore the voltage 

 e induced along be by the traveling flux is Li -Ax divided by 

 Ax/V which gives LiV ab volts. 



wire 



axis of reference 



wire 



wire 



\a. \b 



!d 



wire 



Fig. 140. 



Imagine electric charge to be distributed over the transmission 

 line in Fig. 140 (positive charge on one wire and an equal negative 

 charge on the other). This charge means a definite voltage 

 between wires at each point along the line, and we may imagine 

 the voltage e' at each point to be represented by the ordinate of 

 a curve CC. Imagine the electric charge and the associated 

 voltage distribution to travel along the line at velocity V '. 

 Such a traveling voltage distribution would produce a definite 

 current distribution over the line such that 



Ce'V 



(6) 



is the current in the line at the place where the voltage 

 across the line is e', and C is the capacity of the line per unit 



