INFLUENCE OF THE DURATION AND TIME OF THE IMPULSE. 275 



the current produced by induction when the coil is turned, with a 

 constant velocity, through an angle of 180, in the terrestrial field. 

 If we neglect the extra current, we may write 



w = w l sin TT - , 



and the value of the total impulse which the charge would impart 

 to a free system is 



^J^^^-Sg. 



If, then, /j is the mean time of the impulse, 



A sinusoidal impulse produces thus the same effect as if we 



imparted to the needle at the period / x the velocity 



yO 

 cos - - 



7T 2 



and equation (46) gives 



T2 



