﻿Interpretation 
  of 
  the 
  Bessel 
  Function 
  of 
  Zero 
  Order. 
  429 
  - 
  

   Assume 
  the 
  imposed 
  oscillation 
  harmonic 
  in 
  time, 
  

   i.e. 
  write 
  ~Re 
  ipt 
  for 
  R, 
  

  

  then 
  this 
  becomes 
  

  

  ^ 
  + 
  i^ 
  +PR 
  = 
  IV. 
  

  

  dr' 
  r 
  dr 
  

  

  This 
  is 
  the 
  equation 
  which 
  will 
  be 
  considered. 
  

   Its 
  solution 
  is 
  of 
  course 
  

  

  AJ 
  (ikr) 
  4- 
  BY 
  (zIt), 
  V. 
  

  

  where 
  J 
  and 
  Y 
  have 
  their 
  usual 
  significance, 
  the 
  constants 
  

   A 
  and 
  B 
  being 
  determined 
  by 
  the 
  necessary 
  boundary 
  con- 
  

   ditions 
  between 
  the 
  dielectric 
  and 
  the 
  conducting 
  plates. 
  

  

  A 
  similar 
  expression 
  can 
  be 
  obtained 
  for 
  the 
  currents 
  in 
  

   the 
  dielectric 
  and 
  in 
  the 
  plates. 
  

  

  Now 
  consider 
  the 
  same 
  question 
  from 
  what 
  may 
  be 
  called 
  

   the 
  " 
  elementary 
  7> 
  point 
  of 
  view. 
  

  

  (Suppose 
  we 
  have 
  two 
  metal 
  disks, 
  situated 
  as 
  before, 
  and 
  

   between 
  the 
  middle 
  points 
  of 
  them 
  we 
  connect 
  a 
  source 
  of 
  

   harmonic 
  e.m.f. 
  

  

  Let 
  Y 
  be 
  the 
  voltage, 
  c 
  the 
  current 
  at 
  any 
  point 
  of 
  one 
  of 
  

   the 
  disks, 
  say 
  at 
  a 
  distance 
  x 
  from 
  the 
  centre. 
  We 
  now 
  

   have 
  an 
  electric 
  circuit 
  containing 
  resistance, 
  inductance, 
  

   leakage, 
  and 
  capacity, 
  but 
  these 
  quantities 
  are 
  not 
  constant 
  

   at 
  all 
  points 
  of 
  the 
  disk. 
  

  

  It 
  will 
  be 
  easily 
  seen 
  that 
  if 
  their 
  values 
  at 
  unit 
  distance 
  

   from 
  the 
  origin 
  are 
  represented 
  respectively 
  by 
  R, 
  L, 
  G, 
  K, 
  

   their 
  values 
  at 
  any 
  other 
  point 
  are 
  

  

  R'=-, 
  L' 
  = 
  -, 
  G' 
  = 
  GU, 
  K'^K*. 
  

  

  X 
  X 
  

  

  Considering 
  the 
  change 
  of 
  voltage 
  and 
  current 
  between 
  

   any 
  two 
  adjacent 
  points 
  on 
  a 
  radius 
  of 
  the 
  disk, 
  we 
  obtain 
  

   the 
  equations 
  

  

  dr 
  dV 
  

  

  d 
  x 
  dt 
  

  

  _^ 
  = 
  L'^+R'C. 
  

   dx 
  dt 
  

  

  Substituting 
  their 
  values 
  as 
  above 
  for 
  K' 
  G' 
  L' 
  R' 
  we 
  get 
  

  

  K 
  L 
  J 
  +R0 
  > 
  

  

  !. 
  . 
  . 
  . 
  .VI. 
  

  

  dx 
  x\ 
  dt 
  J 
  J 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  2G. 
  No. 
  153. 
  Sept. 
  1913. 
  2 
  G 
  

  

  