516 PARTICULAR CASES OF INDUCTION. 



Disregarding the sign, the total quantity of electricity put in 

 motion is 



_Rir 



/ __ R JL _2R!T \ !+<> sL7' 



(2 5 ) Q (l + 2* 2La' +2 , 3La' + \ = Q Q _ _. 



\ / -**. 



i-e 2La' 



RTT 



This total mass is the greater the nearer the quantity e zLa? is 

 to unity, that is, the greater the factor - , or the greater is 



R 



. L 



mtl 



539. We pass to the case of a continuous current by making 



Q 

 Q o = oo, C = oo, and = 1&. The roots of equation (21) are then 



real, and the discharge is continuous ; we arrive thus at the formula 

 already found (532) 



E 



i e 



If we suppose the coefficient L of self-induction to be very small, 

 we always fall into the case of real roots ; the coefficient a then 



R / 2 L\ R i 



becomes equal to ( i-^r^s ) or -z---^ t an d the equations 

 2Li \ CK. 4 / 2JL CR 



(22) become 



The current accordingly starts at once with its maximum value, 

 and then diminishes indefinitely. 



It must, however, be remarked that all the preceding discussion 

 rests on the implied hypothesis that electricity does not possess 

 inertia, and that the intensity is the same throughout the whole 

 extent of the wire. These hypotheses appear justified in all cases 

 of permanent currents, or of slow variations, but we can no longer 

 assume them in the case of sudden discharges ; the results at 

 which we have arrived can only then be considered as a first 

 approximation. 



