'222 MEASUREMENT OF CURRENTS. 



When the circuit is open we have 1 = 0, and the phenomenon 

 is defined by the equation 



dx 



If the damping is so weak that the motion is not aperiodic, 

 and if we take as origin of the time the moment at which the 

 needle passes through the position of equilibrium (681), the integral 

 is of the form 



o 



x = A Q e~ tot sin y Q f= A <?~^ ' sin TT , 



the coefficient A depending on the initial condition. We have 

 further the condition 



A 2 

 If we put (2= i -f !J , and if T is the time of oscillations without 



7T 



damping, we have also 



, HM . . 



: K ~T' T' 



When the circuit is closed, the general integral of the equation 

 is of the form 



the values of p lt p 2) and p 3 being roots of the equation 

 (17) 



As the ratio of L to R is very small, one of the roots p t is- 



o 



very large, and nearly - . The two other roots, p 2 and /a 3 , differ 

 i_j 



very little from the roots of the equation 



2 + 

 which are imaginary. 



