512 PARTICULAR CASES OF INDUCTION. 



During a semi-period, the quantity of electricity which passes 

 through the circuit is 



[~$ f AT 



(15) Q = A " sin27r-^= , 



Jo 7T 



and the corresponding calorific work 



(16) W = RA 2 f 2 sin 2 27r-<//=R . 



Jo T 4 



From this is deduced, for the mean intensity I' of the current, 

 disregarding the sign, 



(17) r-^, 



and for the mean strength I", which would give the same quantity 

 of heat 



^' 



536. CURRENT OF DISCHARGE OSCILLATING DISCHARGES. 

 Let us finally consider, with Sir W. Thomson, the phenomena which 

 accompany the discharge of a conductor. Let C be the capacity 

 of the electrified body in electromagnetic measure, Q its charge ; 

 it is connected with the ground by a wire of resistance R, and 

 the coefficient of self-induction of which is L. At a given moment 



t t the charge of the conductor is Q, and its potential , which 



\-> 



gives the equation 



C~ ~dt 



Observing that I = , this may be written in the form 

 dt 



(19) 



dt* -Ldt CL 



