274 MEASUREMENT OF CURRENTS. 







If /! is the mean time / + - of the impulse, we have 



+ e . 7<9 



2 sin 



2W , yO 2 



w cos yt dt = cos y/ x sin = v cos y/ x , 



o 7 



Q * 



w sin y/ <// = sin y/ x sin = v sin y^. 



. <.-j . 2 T 



If we replace these values in equation (47), and compare the 

 expressions thus obtained with the second members of the equations 

 (45), we see that a uniform impulse during the time O l produces the 

 same effect as if at the time t l the instantaneous velocity 



y e 



sin 



a T i^l 



v 7r**v 1-7- 

 yO 64 



had been given to the system 



Replacing v^ by this value in equation (46), we get to the same 

 degree of approximation 



(48) __ =I __ , , 



l 



r 



\^ 



If the middle of the impulse corresponds to the position of 

 equilibrium, we must make /=0 in this expression. 



If, finally, the needle was at rest at the moment of the impulse, 

 we have u = 0, and therefore 



V I 2 2 7T 2 # 2 6* 



892. Another particularly interesting case is that of an impulse 

 which has a sinusoidal character, like that which would result from 



