Mr. 0. Heaviside on the Extra Current. 143 



coils, and then, acquiring momentum, carries to earth a greater 

 quantity of electricity than the line or condenser originally 

 contained, thus reversing the potential of the line. Hence a 

 reverse current follows to restore the equilibrium, which in its 

 turn carries to the line more than enough electricity to supply 

 the deficiency ; hence another current from line to earth ; and 

 so on, till the currents are too weak to produce any observable 

 effect. 



By supposing that the current at any moment is of the same 

 strength in all parts of the coil, the theory of these alternating 

 currents when a charged condenser is discharged through the 

 coil is much simplified. Let Q be the initial charge and V 

 the initial potential of the condenser, whose capacity is c ; and 

 let R be the resistance and L the coefficient of self-induction 

 of the coil. Then, if Q is the charge and v the potential of the 

 condenser at the time t, the current in the coil is 



dQ __ dv 

 and 



dt ~ C dt' 



dQ^jd'Q 



B = R -^ +L * 



since v is the difference of potential between the ends of the 

 coil. Therefore 



cL— 4-CR-+0-O 



cL^ 2 +c±t^+t-U, 



the solution of which satisfying the conditions v = Y when 

 * = (and ^ = when * = 0) is 



Y6 2a _____ 



according as 1 — 4-~- is + or — . And the current in the coil is 



or 

 v = Ve~ 2^ 



dt R 



\A- 4 ! 



