﻿Interpretation 
  of 
  the 
  Bessel 
  Function 
  of 
  Zero 
  Order. 
  437 
  

  

  But 
  this 
  is 
  the 
  same 
  equation 
  as 
  VIII., 
  p. 
  430. 
  Hence 
  it 
  

   has 
  been 
  shown 
  that 
  the 
  wave 
  obtained 
  as 
  a 
  solution 
  o£ 
  the 
  

   equations 
  (14) 
  and 
  (15) 
  is 
  identical 
  in 
  form 
  with 
  the 
  wave 
  

   obtained 
  by 
  the 
  original 
  method. 
  Certain 
  assumptions 
  have, 
  

   in 
  the 
  course 
  of 
  the 
  work, 
  been 
  tacitly 
  made. 
  

  

  (1) 
  The 
  disk 
  does 
  not 
  extend 
  to 
  the 
  origin, 
  for 
  then 
  terms 
  

  

  f: 
  +2iax 
  

  

  of 
  the 
  form 
  ■ 
  would 
  become 
  infinite. 
  This 
  is 
  equivalent 
  

  

  x 
  

  

  to 
  the 
  fact 
  that 
  in 
  a 
  simple 
  circuit 
  radiation 
  can 
  only 
  take 
  

  

  place 
  from 
  an 
  open 
  end. 
  

  

  (2) 
  That 
  either 
  the 
  disks 
  are 
  infinite 
  in 
  size, 
  or 
  that 
  

   the 
  distance 
  between 
  them 
  is 
  small 
  compared 
  with 
  the 
  wave- 
  

   length, 
  i. 
  e. 
  that 
  the 
  entire 
  radiation 
  from 
  one 
  plate 
  reaches 
  

   the 
  other. 
  

  

  For, 
  in 
  the 
  case 
  where 
  R 
  and 
  G- 
  are 
  zero, 
  i. 
  e. 
  the 
  system 
  

   consists 
  of 
  perfect 
  conductors 
  immersed 
  in 
  a 
  perfect 
  dielectric, 
  

   equation 
  (24) 
  becomes 
  

  

  $+.l& 
  + 
  KLtfy=0, 
  

  

  dx 
  z 
  x 
  c/x 
  M 
  u 
  

  

  the 
  solution 
  of 
  which 
  is 
  

  

  y 
  = 
  AJ^KLTpx) 
  + 
  BYoCv/KLp*), 
  

   i. 
  e. 
  voltage 
  is 
  real 
  part 
  of 
  

  

  -{AJoCVlK^+BYoCn/KL^)^^. 
  . 
  . 
  (25) 
  

  

  Now 
  since 
  for 
  a 
  particular 
  case 
  voltage 
  must 
  be 
  

   given 
  both 
  in 
  amplitude 
  and 
  phase 
  at 
  one 
  particular 
  point, 
  

   and 
  also 
  current, 
  therefore 
  A 
  and 
  B 
  may 
  be 
  taken 
  as 
  real. 
  

   Therefore 
  from 
  equation 
  VI., 
  p. 
  429, 
  

  

  dt 
  

  

  = 
  { 
  -AJ 
  '( 
  VKLpaO-BY 
  '( 
  y/KLpx)} 
  VKL 
  

   = 
  { 
  A 
  J/ 
  s/ 
  KLpx) 
  + 
  BY 
  X 
  ( 
  s/TLpx) 
  } 
  s/ 
  KL 
  e^ 
  

  

  .-. 
  c 
  = 
  ix\J\ 
  { 
  A 
  Ji( 
  y/KLpx) 
  + 
  BY 
  1 
  (y/KLpa) 
  } 
  «**. 
  

  

  .... 
  (26) 
  

  

  (comparing 
  (25) 
  and 
  {26), 
  we 
  see 
  that 
  at 
  all 
  points 
  current 
  

   and 
  voltage 
  are 
  90° 
  out 
  of 
  phase, 
  and 
  hence 
  there 
  is 
  no 
  loss 
  

   of 
  power, 
  i. 
  e. 
  in 
  this 
  case 
  radiation 
  with 
  outside 
  space 
  is 
  

   zero. 
  

  

  