214 Mr M'Connel, On the effects of [Nov. 24, 



When L is increased still further till it exceeds a certain value 

 a 2 , the motion ceases to be oscillatory and assumes its former 

 character. 



Here ct t and a 2 are the roots of the equation 



. a?-2CRa(y+2R)+C*By=0 (4) 



and are always real. 



The practical question is usually to decide how soon the 

 transient currents will die away. Let us then consider how L 

 affects the magnitude of the time constants. 



When L is very small 



X + fi is very large and is equal to j approximately, 



X — /* is equal to y,„ approximately. 



The larger depends mainly on the self-induction, the smaller 

 mainly on the capacity. 



As L increases, X — fi increases till L = a v 



Thus a moderate amount of self-induction has the effect of 

 diminishing the duration of the transient currents. 



While the motion is oscillatory X diminishes as L increases. 



When L>a 2 , X — fi diminishes as L increases and continually 



approximates to the value ^—j — , \ + /* continually approximates 



to the value -^ . Thus the smaller time constant is governed by 

 the self-induction, the larger by the capacity. 



When L is very large the behaviour of the currents is suf- 

 ficiently curious to merit a fuller statement. The condenser first 

 almost entirely discharges itself through the arm R. Then the 

 current from the condenser becomes indefinitely small in compari- 

 son with the current through g, and the current in R changes 

 sign. The current through g reaches its maximum value, which 

 is small, before the condenser is nearly discharged, and when once 

 started takes a long time to die away. Thus the only appreciable 

 current, that survives after a short time, is the one flowing through 

 g and back through R. 



We may now pass to the more complicated arrangement which 

 is actually employed in determining the capacity of a condenser. 



The first figure is a sketch of the arrangement, of which 

 Mr Wilberforce has given a full description. 



