516, 517] Discharge of a Condenser 



so that the solution (438) becomes 



449 



ixt 



ict 

 = e 2L D cos f TT-F e 



where D, e are new constants. In this case the discharge is oscillatory. The 



charge Q changes sign at intervals - , so that the charges surge backwards 



/c 



and forwards from one plate to the other. The presence of the exponential 



_m 



e 2L shews that each charge is less than the preceding one, so that the 

 charges ultimately die away. The graphs for Q and i in the two cases of 



4fL 



(i) R 2 > -~- (discharge continuous), 

 



(ii) _R 2 < -j^- (discharge oscillatory), 

 (j 



are given in figs. 132 and 133. 



FIG. 132. 

 (i) discharge continuous. 



Q 



FIG. 133. 

 (ii) discharge oscillatory. 



The existence of the oscillatory discharge is of interest, as the possibility 

 of a discharge of this type was predicted on purely theoretical grounds by 

 Lord Kelvin in 1853. Four years later the actual oscillations were observed 

 by Feddersen. 



517. It is of value to compare the physical processes in the two kinds of 

 discharge. 



j. 



29 



