Equation of Electrical Flow, 425 



As in the case of the sustained discharge, I shall first take 

 the usual .formula, obtain the geometrical illustration of it, 

 and, observing where the defect shows itself, pass by an easy 

 transition to the truer state of things. 



In the case of the discharge of a condenser through a simple 

 circuit removed from proximity with any other, we have the 

 following equations to deal with : — 



The general equation V + F = E, (i.) 



E =RC, (ii.) 



F ="L^,. . . • • (m.) 



dV 



C ="K^, (iv.) 



where 



C is the current discharging the condenser ; 

 K is the capacity of the condenser ; 

 L is the coefficient of self-induction ; 

 R is the resistance ; 

 F is the induced electromotive force ; 

 E is the effective electromotive force ; 

 V is the potential difference of the plates of the con- 

 denser. 



Eliminating E and F from (i.) by means of (ii.) and (iii.)> 

 Differentiating, 



V-L^-RC = 0. ..... (v.) 



dt v y 



dV T d 2 G ^dG A 



and substituting for -— from (iv.), 

 a. t 



C T d 2 G „rfO . 



or 



C + KRf +LK gU, 



the differential equation of C. 

 F 

 Since C = tt , it follows that the equation 



dt dt 2 



is also true, and therefore is the differential equation of E. 



