156 Dr. Marchant on the Oscillatory Discharge 



variable self-induction when an E.M.F. is suddenly applied 

 to it. The results obtained by him were of very great 

 interest, as he clearly demonstrated both by experiment and 

 calculation the fact that with an iron core coil, such as that of 

 a large electromagnet, the current first increases very slowly 

 until the knee of the magnetization curve is reached, and 

 that it then increases with much greater rapidity. It ap- 

 peared that this method might be applicable to the case of 

 the oscillatory discharge from a condenser. We have as the 

 fundamental equation 



dt (J 



with the condition that just before the discharge takes place 

 there is a P.D. = E volts between the plates of the condenser. 



hi denotes the number of lines of force linked by the coil 

 when a current i is flowing through it. (With iron in the 

 circuit L (of course) is a function of i. With an " air core" 

 self-induction L will represent the self-induction of the coil 

 as ordinarily understood.) 



R denotes the resistance of the circuit in ohms. 



C the capacity of the condenser in farads. 



Q denotes the quantity of electricity on the plates of the 

 condenser at any instant. 



i denotes the instantaneous value of the current. 



The first term may be written 



d(Li) _ T di .dL di dif T .dh\_ T ,di 



' L It + l WIt = 7t\ L +l Jl)- L It 



MS)} - 



dt 

 We have therefore 



Q 

 di_ - i x "-"vc/j " fie 



dt~ L' " L' 



R 



It now remains to show how the value of ~- may be obtained 

 from this equation. 



It will be well first to take the simplest case where L is a 

 constant quantity. The equation then reduces to 



dt = v rc; 



dt " L 



R 



