MEASUREMENT OF DISCHARGES. 489 



for instance, of the discharge of a condenser through a conducting 

 wire in which is a galvanometer; the total quantity of electricity 

 may be deduced from the angle of throw imparted to the needle. 



The strength of a permanent current in the galvanometer in 

 question* is given by an expression of the form 



in which f (B) reduces to the angle 8 when the deflections are very 

 small. If p, be the magnetic moment of the needle, the action 

 of the current on the needle produces a couple, the moment of 

 which is /xGI. 



We know, on the other hand, that when a body is movable 

 about an axis, the product of the moment of inertia K, by the 

 angular velocity is equal to the moment of the resultant couple 

 in reference to the axis of rotation. Hence, since the deflection 

 during the discharge is so small, that the action of the Earth can 

 be neglected, we have for the needle in question, 



v d{ * <-T 

 K =/xGI. 



dt 



If dm is the quantity of electricity which flows in unit time 

 dt, this equation becomes 



da) dm 



K = MG __ 



dt dt 



From which, if w o is the initial angular velocity, and m the total 

 discharge, we get 



Kw o = /xGw. 



The needle, once impelled with this velocity co o , has a vis 



K.CO*, 



viva equal to - L and it stops at an angle 0, when it has done 



work of the same value against the action of the terrestial field. 

 We have then 



TT- a f\ 



= H/x(i - cos 6) = 2H/x sin 2 - , 

 or 



n 2 -, 



i /HK 



m = L \ 2 sm - . 

 G \ /A 2 



