DURATION OF A DISCHARGE. 283 



If T is the time of oscillations corrected for damping, and a 1 

 the angle of swing, we have by known relations (681), 



or, for a very feeble damping, 



If the two coils of the electrodynamometer are traversed by 

 different currents, the angular velocity imparted by 'two discharges 

 which correspond respectively to intensities I and I', is determined 

 by the equation 



Kco n = S'G 



'G IVdt, 



the integral being merely extended to the time in which the two 

 currents exist simultaneously. It is assumed further that the 

 deflections are very small in this interval. The value of the 

 integral depends on the law of the variation of the two currents. 

 This law is generally the same, not only for two distinct discharges, 

 but also for the same discharge which is shared by the shunt 

 between the two coils. The swing produced in these conditions 

 is a very complex phenomenon. 



898. DURATION OF A DISCHARGE. The observation of swings 

 produced by the same discharge in the galvanometer and in the 

 electrodynamometer may, as Weber* showed, give an approximate 

 value of its duration and of the quantity of electricity which cor- 

 responds to it. 



For if we suppose the intensity I of the current constant, we 

 have in the galvanometer 



HT 



m = lO = a. 



G TT 



* W. WEBER. Electrodyn. Maasbestimmungen, Vol. I., p. 80, 1846. 



