﻿430 
  Mr. 
  J. 
  Hollingworth 
  on 
  a 
  Physical 
  

  

  Eliminating 
  C 
  and 
  V 
  successively 
  from 
  these 
  equations, 
  we 
  

   obtain 
  the 
  two 
  equations 
  

  

  d 
  2 
  V 
  IdV 
  d 
  2 
  V 
  dV 
  1 
  

  

  k 
  VII. 
  

   d 
  2 
  C 
  ldG 
  T 
  „d 
  2 
  C 
  fT> 
  „ 
  Tn 
  ,dG 
  ^„ 
  r 
  , 
  \ 
  

  

  If, 
  as 
  before, 
  we 
  assume 
  the 
  oscillations 
  to 
  be 
  periodic 
  in 
  

   time 
  and 
  of 
  form 
  \e 
  ipt 
  , 
  the 
  equations 
  VII. 
  reduce 
  to 
  

  

  <PC_ldC 
  = 
  s 
  > 
  c 
  

  

  dx 
  2 
  x 
  dx 
  ' 
  

  

  }-,viir. 
  

  

  and 
  these 
  equations 
  give 
  rise 
  to 
  a 
  solution 
  similar 
  in 
  form 
  to 
  

   that 
  of 
  equation 
  IV. 
  

  

  This 
  is 
  the 
  solution 
  of 
  the 
  problem 
  according 
  to 
  the 
  first 
  

   method 
  mentioned 
  at 
  the 
  beginning 
  of 
  the 
  paper. 
  

  

  Now 
  to 
  consider 
  the 
  same 
  question 
  from 
  another 
  point 
  of 
  

   view. 
  

  

  It 
  is 
  a 
  well-recognized 
  fact 
  that 
  if 
  we 
  have 
  a 
  wave 
  travel- 
  

   ling 
  in 
  any 
  homogeneous 
  medium, 
  at 
  the 
  surface 
  of 
  separation 
  

   of 
  two 
  such 
  media 
  whose 
  physical 
  constants 
  differ 
  the 
  wave 
  

   is 
  partially 
  refracted 
  and 
  partially 
  reflected. 
  

  

  If 
  the 
  change 
  in 
  these 
  constants 
  is 
  only 
  of 
  the 
  first 
  order, 
  

   it 
  appears 
  probable 
  that 
  the 
  amplitude 
  of 
  the 
  reflected 
  wave 
  

   is 
  not 
  greater 
  than 
  a 
  first-order 
  quantity, 
  and 
  that 
  the 
  ampli- 
  

   tude 
  of 
  the 
  transmitted 
  wave 
  will 
  be 
  reduced 
  by 
  a 
  quantity 
  

   of 
  the 
  same 
  order. 
  

  

  Applying 
  this 
  idea 
  to 
  the 
  disk 
  it 
  suggests 
  that 
  at 
  every 
  

   point 
  there 
  is 
  such 
  refraction 
  and 
  reflexion 
  taking 
  place. 
  

   The 
  resultant 
  wave 
  will 
  therefore 
  consist 
  of 
  

  

  (i.) 
  the 
  original 
  impressed 
  wave 
  ; 
  

  

  (ii.) 
  the 
  sum 
  of 
  a 
  number 
  of 
  first-order 
  reflected 
  waves 
  

  

  due 
  to 
  the 
  changes 
  all 
  along 
  the 
  wire 
  ; 
  

   (iii.) 
  the 
  totally 
  reflected 
  wave 
  (if 
  the 
  length 
  of 
  wire 
  is 
  

  

  finite) 
  ; 
  

   (iv.) 
  a 
  forward 
  travelling 
  wave 
  consisting 
  of 
  first 
  order 
  

   reflexions 
  of 
  (iii.)« 
  

  

  No 
  further 
  first 
  order 
  reflexions 
  will 
  be 
  found 
  to 
  occur, 
  

   as 
  it 
  will 
  be 
  found 
  that 
  second 
  reflexions 
  give 
  a 
  wave 
  with 
  

   an 
  amplitude 
  of 
  the 
  second 
  order. 
  

  

  