

264 MEASUREMENT OF CURRENTS. 



and the following 



The limiting deflection a for a permanent condition of rever- 

 sals is 



i+g i+e~ K 

 i - q i e~ K ' 

 whence 



The method of multiplication is not very well suited for accurate 

 measurements, but it is excellent for demonstrating a very weak 

 current. 



883. TRANSIENT CURRENTS. BALLISTIC GALVANOMETER. 

 The quantity of electricity which a transient current or a dis- 

 charge of any form expends, may be determined by the first 

 throw of the needle of a galvanometer. 



For this purpose the duration of the discharge must be very 

 small compared with that of the oscillation of the needle in other 

 words, the current must stop before the needle is appreciably 

 deflected from its position of equilibrium. This is a ballistic 

 method analogous to that used in measuring the velocity of pro- 

 jectiles. 



If K is the moment of inertia of the needle, M its magnetic 

 moment, T the time of oscillations without damping, o> the angular 

 throw imparted to the needle by the instantaneous discharge of a 

 quantity of electricity m is (506) 



MG G 7T 2 

 "o "-HI*" 1 - 



On the other hand, if the deflections are very small, the initial 

 velocity w is connected with the corresponding angle of throw by 

 the expression 



A. 7T 



7T - arc tan - 



