208 



ADVANCED ELECTRICITY AND MAGNETISM. 



from positively charged wire to negatively charged wire; and 

 the current in the positively charged wire may be thought of as 

 carrying the positive charge forwards from the back of the wave 

 and laying it down on the wire in front of the wave. 



axis of e 



> 



Fig. 142. 



Showing voltage e as a function 

 of the time. 



axis of x 



* x(=.vt) >i 



Fig. 143. 



Showing shape of wave which shoots out 

 from the end of a transmission line when 

 the voltage of Fig. 142 is connected across 

 the end of the line. 



The wave which is represented in Fig. 141 is called an isolated 

 wave or a wave pulse. . Such a wave is produced when an electro- 

 motive force is connected across the end of the transmission line 

 for a moment and then disconnected. The relation between 

 the voltage across the end of the line and the shape of the wave 

 produced thereby is shown in Figs. 142 and 143. The ordinates 

 of the curve in Fig. 142 represent the varying value of the voltage 

 e across the end of the line as a function of elapsed time t, time 

 being measured to the left along the axis of abscissas. The 

 ordinates of the exactly similar curve in Fig. 143 represent the 

 values of e and i in the wave which shoots out on the line. 

 The line is assumed to be very long so that no complications 

 arise from the reflection of the wave from the distant end of the 

 line. That Fig. 143 shows the actual wave produced when the 

 varying voltage of Fig. 142 is connected across the end of the 

 line is evident from the following considerations: A particular 

 solution of any differential equation must satisfy the equation 

 itself throughout the region to which the solution applies, and 

 it must satisfy the conditions which are impressed at the bound- 



