MEASUREMENT OF DISCHARGES. 537 



If I + / and I' + i' are the currents during the variable state, and 

 if account be taken of the preceding equation, and if L and L' are 

 the coefficients of self-induction of the two circuits, we have 



The quantities m and m' of electricity put in motion by induction, 

 throughout the entire duration of the variable state satisfy equations 



it follows that 



,_ M ^ 



r'-R 2 R R + 



If the resistance R of the bridge is very small in comparison with 

 the resistances r and r' of the two circuits, we may expand this 

 expression in a very converging series, which gives 



m' M f 2 R 2 "I 



_ = _ i+_ - + ... , 



I' R |_ rr' + R(r+r') J 



or sensibly 



m 1 M 



The current I' is given by the permanent deflection 8 of the 

 galvanometer, and the discharge m by the swing a. The resistance 

 R is then 



TT tan 3 f 2 R 



= M- i+- 



T a 



~| 



+ ... . 

 ') J 



If the deflection 8 is very feeble, we may assume that the arc 

 of the swing from the position of equilibrium is the same as starting 

 from zero. 



1119. M. Roi'ti, instead of a single swing, measures the de- 

 flection produced by a series of discharges corresponding to breaking 



