254] ELECTROMAGNETIC WAVES. 539 



The values of the current for different points are shown in 

 Fig. 97 for times , J, , 1, 4 times KR. When x we have 



IT i 



so that when t = the value of the current is infinite, instan- 

 taneously. 



The rise of the potential at any given point other than 

 x is shown by the outside curve in Fig. 98, taken from Lord 



Fm. 98. 



Kelvin's paper, the abscissas representing the time, the ordinates 

 the potential. 



The potential rises asymptotically to its value at the origin, but 

 the current rises to a maximum, which occurs at the time 

 t = KRx z j%, and then dies away to zero. The maximum values of 

 / are inversely proportional to the distance from the origin, and to 

 the resistance R. 



Since our differential equations are linear, disturbances due to 

 different initial states are merely added. If the battery is con- 

 nected, instead of permanently, for a definite time T, and the 

 cable then put to earth, the effect is the same as if, in the preced- 

 ing case, after a time r we permanently apply the potential F 

 at the origin. If the preceding solution be called V(t) the present 

 will be V(i) V(t r), consequently we may obtain the graphical 



