276 MEASUREMENT OF CURRENTS. 



Finally, if the needle was at first at rest in the position of 

 equilibrium, 



893. CORRECTION OF OBSERVATIONS. When a transient cur- 

 rent is measured by the swing of a needle originally at rest, the 

 effect of the duration of the discharge is to diminish the angular 

 deflection, which is proportional to the initial velocity, by the 



6 2 6 2 



fraction 0-4112 , or by 0-2337 , according as the current is 



uniform or sinusoidal. 



In the method of multiplication, for instance (886), the initial 

 swing for a single impulse is connected with the maximum de- 

 flection tf by the ratio 



In order to obtain the influence of the retardation and of the 

 duration of the impulse, substituting the swings for the initial 

 velocities, and supposing the impulse uniform, we must replace 

 T Q by a, ?/ by aq, and v by # in equation (48). Calling the second 

 member of the equation i - 8, we get 



or 



i-8 



Replacing # by its approximate value a (i-^), and 

 by a, we have for the term of correction 8 



and therefore 



