Discharges in Electrodeless Vacuum- Tubes. 515 



and if - = ^r or the time-constant of the coil equals the time- 

 r ±v x 



constant of the whole circuit, 



T R 



T = L=- 2a ' 



.*. tan?/= — r=tan?7, or r)' = 7}. 



That is x is in phase with v the P.D. at the inner coatings of 

 the jars. 



To find the maxima and minima of x we have 



dv V 



~= ^e at [{ar + l{a 2 -b 2 )} sin bt + b(r f 2Za)cos6<]=0. 



b{r + 2la) 



.'. tZLYlbt=- — 



ar + l(a?—b 2 ) 



_ (rL-Ul) VK(4L-KR 2 ) 

 L(KUr + 2L) 



= tan 8. 



Then x has its greatest positive or negative values when 



bt = b, 7T + 8, 2tt+8, &c. 8 is in general a small angle, and 



is positive if 



L / 



r > -' 

 R r 



and negative if 



L , I 



U < r 



If 



L I 



R ~r ; ' 



8=0. 

 r 



If ^ be not greater than - the first largest value of x will 



occur at t = Q, and as the rate of change of current is also 

 greatest at this instant the two will occur simultaneously. 

 The next greatest value of x occurs when 



**="■-« (4 < ?)• 



and the next greatest rate of change of current when 



bt = 7T — y. 



