239] INDUCTION OF CURRENTS. 487 



This case is represented in Fig. 94. The charge is zero at times 

 such that 



FIG. 94. 



which is later than the time of the vanishing of the current by 

 the phase difference 0, which approaches Tr/2 the smaller /z. 



We may specify the damping, or decrease of the charge or 

 current, by the relaxation-time of the damping factor &*, namely 

 r = 2L/R, or by the logarithmic decrement, that is the logarithm 

 of the ratio of a maximum value to the absolute value of the 

 next following minimum. Since the maximum and minimum 

 values of the parenthesis in (17) are equal and opposite, and 

 separated by intervals of time T/2 = TT/V, the ratio of the absolute 



values of q is e " , and the logarithmic decrement X, 



nrrr nr 



(18) X = 



\/zs 



KR* 



If R = 0, there is no damping, X = and the period is 



Introducing these values of T Q and X we may write (15), 



(20) r=: 



so that if the damping is small it affects the period only by small 

 quantities of the second order. 



