280 MEASUREMENT OF CURRENTS. 



If a and a' are replaced by their values in equations (51), and 

 p and t l are two constants, we may write 



cos 



PP'(p + P') 



' ' =/ " any/,; 



The discharge still produces the same effect as if we gave the 

 needle an instantaneous impulse pv at the time t r We have further, 

 by equations (52), 



/ ' 



tan y^ 



This result is independent of the nature of the discharge, whether 

 it be continuous or oscillatory. 



It may further be remarked that the factor b, by which we 

 must multiply the total impulse to obtain the instantaneous one, 

 is independent of the resistance of the conductor. This factor 

 should be very large. The time / 15 which represents a kind of 

 retardation, is proportional to the resistance, other things being 

 equal. 



895. MEASUREMENT OF A VERY SHORT TIME. If the dis- 

 charge m which traverses a galvanometer arises from a constant 

 current I , the circuit of which has been closed for a time $, very 

 short compared with the time of oscillation of the needle, the 

 angle of swing, corrected for the damping (882) and for the time 

 of the discharge (891), satisfies the equation 



HT 

 m = I Q V = a. 



Lr 7T 



If 8 is the deflection which the permanent current I would give , 

 we deduce 



(53) O- 



