﻿436 
  Mr. 
  J. 
  Hollingworth 
  on 
  a 
  Physical 
  

  

  Now 
  put 
  

  

  Ae~ 
  iax 
  = 
  t 
  

  

  Be 
  iax 
  =t\ 
  

   Then 
  the 
  complete 
  wave 
  is 
  of 
  form 
  : 
  — 
  

  

  real 
  part 
  of 
  (t 
  + 
  t')^. 
  

   Now 
  substitute 
  t 
  for 
  A 
  in 
  (20) 
  

  

  , 
  . 
  . 
  A 
  = 
  e 
  iax 
  t, 
  

  

  dA 
  . 
  {dt 
  . 
  \ 
  

  

  .-. 
  _ 
  =«" 
  w 
  ( 
  x 
  +iat) 
  

  

  dx 
  \dx 
  / 
  

  

  d 
  2 
  A 
  . 
  (dH 
  - 
  dt 
  9 
  \ 
  

  

  i. 
  <?. 
  (20) 
  becomes 
  (after 
  dividing 
  by 
  ^ 
  ar 
  ) 
  

   ^ 
  . 
  ... 
  rft 
  

  

  £+-i-5t-*«o 
  (22) 
  

  

  + 
  2i4-^-(2ia-3(| 
  + 
  ^)_5=0, 
  

  

  Again 
  substitute 
  B 
  = 
  e 
  - 
  iax 
  t' 
  in 
  (21), 
  

  

  2? 
  * 
  t^ 
  2 
  *"<** 
  fl 
  'j> 
  

  

  therefore 
  (21) 
  becomes 
  

  

  ^-^ 
  -2za-^ 
  a 
  2 
  £ 
  + 
  [2ia+- 
  )( 
  ^ 
  ia*'jH 
  =0, 
  

  

  dar 
  a# 
  \ 
  x)\dx 
  J 
  x 
  

  

  L 
  e. 
  d*t' 
  1 
  dt' 
  , 
  , 
  , 
  . 
  

  

  which 
  is 
  of 
  the 
  same 
  form 
  as 
  (22). 
  

  

  Therefore 
  t 
  + 
  t' 
  satisfies 
  an 
  equation 
  of 
  the 
  form 
  

  

  dx 
  2 
  + 
  x 
  dx+ 
  ay 
  - 
  V 
  ' 
  

   from 
  equation 
  (3), 
  p. 
  431. 
  

  

  