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XL.— ON A METHOD OF STUDYING TEANSIENT CUEEENTS 

 BY MEANS OF AN ELECTEODYNAMOMETEE. Bx 

 GEOEGE FEANCIS FITZGEEALD, A.M., F.T.C.D. 



[Eead June 7, 1884.] 



When a current of short duration, compared with the period of 

 free vibration of a galvanometer needle, is passed through the 

 galvanometer, the total quantity of the current is proportional to 

 the sine of half the angle of swing of the needle. The swing pro- 

 duced is independent of the distribution of intensity of the current 

 during its passage. 



Now, if a similar transient current be passed through an electro- 

 dynamometer, we have the following equation for the motion of the 

 suspended coil while a current C is passing : — 



where / is the moment of inertia of the coil and K a constant. 



K 



Hence ^ 



dt 



7- \0'dt 



gives the angular velocity with which the needle begins to swing. 

 If the suspension be bifilar during its free swing the motion is 

 given by the equation 



I -iw = - « . sm C/, 



dt~ 



where ^ is a 'constant depending on the method of suspension, &c. 

 Hence, for the maximum swing, 



sin I Q. 



-1 



Comparing this with the other value, we obtain 



djQ 



di 



K 



Now the value of J C^ dt depends upon how the current varies 

 during its period of transit, and if we can form any hypothesis as 



