﻿428 
  Mr. 
  J. 
  Hollingworth 
  on 
  a 
  Physical 
  

  

  application 
  to 
  the 
  electrical 
  problem, 
  and 
  can 
  be 
  obtained 
  as 
  

   follows. 
  

  

  The 
  general 
  equations 
  for 
  the 
  propagation 
  of 
  an 
  electric 
  

   disturbance 
  in 
  an 
  isotropic 
  medium 
  can 
  (cf. 
  ' 
  Recent 
  Re- 
  

   searches 
  in 
  Elec. 
  and 
  Mag.,' 
  Sir 
  J. 
  J. 
  Thomson, 
  § 
  256) 
  be 
  

   reduced 
  to 
  the 
  form 
  

  

  V 
  r 
  " 
  cr 
  dt 
  ^ 
  V 
  2 
  dt' 
  2 
  ' 
  * 
  * 
  ' 
  * 
  1J 
  - 
  

  

  and 
  two 
  similar 
  equations 
  for 
  Q 
  and 
  R, 
  

  

  where 
  P, 
  Q, 
  and 
  R 
  are 
  the 
  components 
  of 
  electromotive 
  

   intensity 
  parallel 
  to 
  the 
  axes 
  and 
  V 
  the 
  velocity 
  of 
  propa- 
  

   gation 
  of 
  electric 
  effects 
  in 
  the 
  medium. 
  

  

  If 
  the 
  disturbance 
  is 
  propagated 
  along 
  the 
  axis 
  of 
  z, 
  R 
  wilL 
  

   be 
  of 
  the 
  form 
  

  

  Hence 
  the 
  corresponding 
  equation 
  reduces 
  to 
  

  

  converting 
  to 
  polar 
  coordinates 
  this 
  becomes 
  

  

  d 
  2 
  R 
  1 
  dR 
  1 
  d 
  2 
  R 
  _ 
  ^TTfiip 
  _ 
  f 
  

   dr 
  2 
  r 
  dr 
  r 
  2 
  dO 
  2 
  a 
  V" 
  

  

  If, 
  in 
  addition, 
  the 
  system 
  is 
  symmetrical 
  about 
  the 
  z 
  axis 
  

   jg 
  = 
  always. 
  

  

  .*. 
  equation 
  becomes 
  

  

  d 
  2 
  R 
  ldR_ 
  lirjiip 
  __ 
  f 
  m 
  

  

  dr 
  2 
  r 
  dr 
  cr 
  V 
  2 
  ' 
  

  

  Now 
  let 
  us 
  apply 
  this 
  to 
  the 
  case 
  of 
  two 
  circular 
  con- 
  

   ducting 
  plates 
  separated 
  by 
  a 
  slab 
  of 
  dielectric, 
  the 
  line 
  

   joining 
  the 
  centres 
  of 
  the 
  plates 
  being 
  perpendicular 
  to 
  their 
  

   plane, 
  and 
  the 
  oscillations 
  propagated 
  in 
  this 
  line. 
  Then 
  in 
  

   the 
  dielectric, 
  equation 
  III. 
  reduces 
  to] 
  

  

  ^R, 
  i^R 
  = 
  A^ 
  

  

  dr 
  2 
  r 
  dr 
  V 
  2 
  dt 
  2 
  ' 
  

  

  