108 ELECTRICAL MEASUREMENTS 



It is assumed that the time occupied by the passage of the 

 current is so short that the coil has not moved appreciably from 

 its zero position; in other words, during the discharge r0 is zero. 



Therefore, if Q is the total quantity in the discharge, 



0-0 



(-TT) is the angular velocity at the zero position of the 

 \dt/ 0=0 



movable system, that is, at the time when all the energy is 

 kinetic. The energy imparted to the system is then 



The coil deflects and this amount of energy is expended in twist- 

 ing the suspension through an angle 0/. The coil then swings 

 back through its zero position and continues to oscillate. 



The work done in twisting the suspension through the angle B\ 

 is 



W = r I0d9 = r (6,'y 

 Jo 2 



As by supposition there is no dissipation of energy during the 

 swing from 6 = to = 0/, 



0i is the first throw or elongation. The quantities P, T and C are 

 not easily determined and the formula may be put in a more 

 useful shape by introducing the time of vibration of the movable 

 system considered as a torsion pendulum. If T Q be the time of 

 vibration when there is no damping, 



To = 2 



