﻿570 
  Prof. 
  E. 
  H. 
  Barton 
  and 
  Mr. 
  W. 
  B. 
  Kilby 
  on 
  

   By 
  consideration 
  of 
  the 
  metallic 
  circuit 
  we 
  have 
  

  

  V= 
  Q 
  =RC+L 
  f 
  

  

  The 
  dielectric 
  current 
  is 
  given 
  by 
  

  

  (1) 
  

  

  But 
  the 
  rate 
  of 
  decrease 
  of 
  Q 
  is 
  the 
  sum 
  of 
  the 
  two 
  currents, 
  

   that 
  is 
  

  

  _dQ 
  

   dt 
  

  

  C 
  + 
  I, 
  

  

  or 
  

  

  

  c= 
  

  

  dt 
  ' 
  

  

  NQ 
  

  

  s 
  

  

  :liis 
  

  

  , 
  we 
  

  

  obtain 
  

  

  

  dC 
  

  

  dt 
  

  

  = 
  - 
  

  

  d 
  2 
  Q 
  

  

  ' 
  dt 
  2 
  

  

  N 
  dQ 
  

  

  S 
  * 
  dt 
  

  

  Thus, 
  substituting 
  from 
  (2) 
  and 
  (3) 
  in 
  (1), 
  we 
  find 
  

  

  The 
  solution 
  o£ 
  this 
  may 
  be 
  written 
  

  

  Q= 
  e~ 
  "'(A 
  sin 
  qt 
  + 
  B 
  cos 
  qt) 
  . 
  . 
  . 
  

  

  where 
  

  

  2k 
  - 
  L 
  + 
  S 
  ' 
  

  

  , 
  1 
  + 
  RN 
  

  

  1/R 
  N\« 
  [ 
  ; 
  ' 
  

   4\L 
  + 
  SJ', 
  

  

  (2) 
  

  

  (3) 
  

  

  (4) 
  

  

  (5) 
  

  

  (6) 
  

  

  and 
  A, 
  B 
  are 
  arbitrary 
  constants 
  depending 
  on 
  the 
  initial 
  

   conditions. 
  

  

  Let 
  us 
  denote 
  by 
  q 
  the 
  value 
  of 
  g 
  for 
  N 
  = 
  0. 
  Then 
  we 
  

   may 
  write 
  

  

  9 
  q 
  ° 
  -2SVL 
  2S> 
  

  

  (7) 
  

  

  