278 MEASUREMENT OF CURRENTS. 



in which /> and p are the roots of the equation 



R i 



(5) /> 2 + -p + = 0. 



The coefficients A and A' are defined by the conditions relative 

 to the commencement of the discharge, at the moment / 



If there is a galvanometer in the circuit, the acceleration of 

 motion, being proportional to the intensity of the current, is of 

 the form 



with the condition 



AA' 



Replacing cosy/ by its value in imaginary exponentials, we 

 have 



-2W cos y/ 

 = ap [*(P W 3 !)' + e (p-yJ~V i ] + a'p' 



an expression which may be written in the form 



We shall find, in like manner, 



- 2W J - i sin y/ = ap (e at - e&) + a'p (e a>t - e^' 1 ) . 



As the discharge is in strictness null only after an infinite time, 

 in calculating u' and x' Q by equations (47) we ought to integrate 

 these expressions between / and the very long time 0. But we have 



re 



\e^dt 

 Jt 



