﻿The 
  Apparent 
  Dispersion 
  of 
  Light 
  in 
  Space. 
  873 
  

  

  turbance 
  o£ 
  given 
  type 
  and 
  of 
  sufficiently 
  small 
  amplitude 
  

   ^vill 
  be 
  propagated 
  with 
  a 
  velocity 
  entirely 
  independent 
  o£ 
  

   the 
  wave-lengths 
  involved. 
  This 
  is 
  readily 
  proved 
  from 
  

   general 
  considerations, 
  and 
  familiar 
  examples 
  immediately 
  

   present 
  themselves. 
  There 
  is 
  no 
  better 
  instance 
  than 
  the 
  

   elementary 
  form 
  of 
  electromagnetic 
  theory, 
  according 
  to 
  

   which 
  an 
  isotropic 
  nonconducting 
  medium 
  is 
  characterized 
  

   simply 
  by 
  a 
  definite 
  dielectric 
  capacity 
  together 
  with 
  a 
  

   definite 
  magnetic 
  permeability 
  ; 
  and 
  the 
  failure 
  of 
  any 
  such 
  

   simple 
  theory 
  to 
  account 
  for 
  dispersion, 
  

  

  4. 
  But 
  although 
  the 
  dispersive 
  and 
  other 
  optical 
  properties 
  

   of 
  material 
  substances 
  compel 
  our 
  attention 
  to 
  their 
  structure, 
  

   there 
  are 
  as 
  yet 
  no 
  well-established 
  facts 
  of 
  observation 
  which 
  

   forbid 
  us 
  to 
  regard 
  the 
  free 
  aether 
  as 
  an 
  absolutely 
  homo- 
  

   geneous 
  medium, 
  ideally 
  divisible 
  to 
  any 
  extent 
  ; 
  in 
  a 
  word, 
  

   structureless. 
  It 
  is 
  interesting 
  to 
  attempt 
  to 
  form 
  some 
  idea 
  

   as 
  to 
  how 
  far 
  this 
  elementary 
  conception 
  would 
  have 
  to 
  be 
  

   modified 
  if 
  the 
  velocity 
  of 
  light 
  in 
  vacuo 
  were 
  actually 
  found 
  

   to 
  be 
  a 
  function 
  of 
  the 
  wave-length. 
  

  

  5. 
  Not 
  knowing 
  what 
  kind 
  of 
  structure 
  should 
  be 
  provi- 
  

   sionally 
  assumed 
  for 
  the 
  aether, 
  we 
  are 
  driven 
  back 
  on 
  the 
  

   consideration 
  of 
  mechanical 
  models 
  and 
  analogies 
  ; 
  these 
  

   may 
  perhaps 
  furnish 
  a 
  hint 
  as 
  to 
  the 
  order 
  of 
  magnitude 
  of 
  

   the 
  quantities 
  involved 
  ; 
  as 
  to 
  the 
  sort 
  of 
  relation 
  which 
  must 
  

   hold 
  between 
  wave-lengths 
  and 
  the 
  scale 
  of 
  structure 
  of 
  the 
  

   sether 
  if 
  certain 
  specified 
  dispersion 
  effects 
  are 
  to 
  be 
  accounted 
  

   for. 
  Essentially 
  we 
  must 
  aim 
  at 
  representing 
  a 
  structure 
  

   which 
  will 
  produce 
  dispersion 
  without 
  absorption; 
  or 
  at 
  least 
  

   in 
  which 
  the 
  absorption 
  is 
  far 
  less 
  than 
  in 
  any 
  material 
  

   medium 
  of 
  comparable 
  dispersive 
  power. 
  

  

  6. 
  In 
  the 
  first 
  place, 
  consider 
  waves 
  of 
  transverse 
  dis- 
  

   turbance 
  which 
  are 
  being 
  propagated 
  along 
  a 
  loaded 
  string 
  

   of 
  indefinite 
  length. 
  Suppose 
  the 
  string 
  itself 
  to 
  be 
  without 
  

   appreciable 
  inertia, 
  while 
  the 
  loads, 
  each 
  equal 
  to 
  ?7i, 
  are 
  

   concentrated 
  at 
  points 
  which 
  succeed 
  one 
  another 
  at 
  regular 
  

   intervals 
  (h) 
  along 
  the 
  string. 
  The 
  transverse 
  vibrations 
  of 
  

   a 
  limited 
  length 
  of 
  such 
  a 
  loaded 
  string 
  are 
  fully 
  investigated 
  

   in 
  Lord 
  Rayleigh's 
  'Theory 
  of 
  Sound 
  ^*, 
  and 
  the 
  results 
  

   there 
  obtained 
  could 
  be 
  adapted 
  to 
  the 
  problem 
  now 
  proposed. 
  

   But 
  the 
  required 
  relations 
  can 
  in 
  this 
  case 
  be 
  more 
  simply 
  

   deduced 
  from 
  first 
  principles. 
  We 
  may 
  confine 
  our 
  attention 
  

   to 
  vibrations 
  taking 
  place 
  in 
  a 
  single 
  plane 
  which 
  passes 
  

   through 
  the 
  string 
  in 
  its 
  undisturbed 
  state. 
  

  

  7. 
  Calling 
  S 
  the 
  tension 
  of 
  the 
  string, 
  let 
  ^^ 
  denote 
  the 
  

  

  * 
  Vol. 
  i. 
  § 
  120. 
  

  

  