144 Mr. 0. Heaviside on the Extra Current. 



or 



dQ _ 2 V 



dt 



where *= ™ and /8=cR. In the first case, when 1 >4^, the 



potential and current are never reversed ; but in the second 



case, when 4 5 > 1, they are reversed an infinite number of 



times, the successive charges of the condenser decreasing in 

 geometrical proportion. The current changes sign when t is 



!a7T 



any multiple of — . , and has its maxima or minima 



values when 



2« V *£ 2 V a 



The quantity Q' of electricity conveyed in the first current 

 is 



Q' = Q (l + e V<;-.) : 



where Q is the initial charge of the condenser. As -~ is in- 

 creased Q' approaches 2Q as its limit ; i. e. when the resist- 

 ance of the coil is reduced, or its magnetic capacity increased, 

 the quantity of electricity conveyed by any current increases 

 till it is nearly double the charge of the condenser at the com- 

 mencement of that current, and the oscillations are more slowly 

 diminished. The amount of energy expended by the first cur- 

 rent is 



where -g- is the energy of the original charge Q , which be- 

 comes indefinitely small as -r increases. The integral current, 

 irrespective of sign, is 



Qo 



which increases indefinitely with ~. From the number of 



1-e vr r i 



