﻿^76 
  Dr. 
  C. 
  V. 
  Burton 
  on 
  the 
  Apparent 
  

  

  will 
  also 
  be 
  dispersion 
  according 
  to 
  an 
  identical 
  law. 
  Thus 
  

   the 
  general 
  form 
  of 
  (15) 
  does 
  not 
  appear 
  to 
  be 
  due 
  to 
  the 
  

   details 
  o£ 
  structure 
  of 
  the 
  vibrating 
  system, 
  but 
  rather 
  to 
  

   the 
  circumstance 
  that 
  the 
  system 
  has 
  a 
  structure 
  on 
  a 
  scale 
  

   not 
  infinitely 
  minute 
  compared 
  with 
  the 
  wave-length 
  X. 
  

   This 
  conclusion, 
  I 
  think, 
  is 
  confirmed 
  when 
  we 
  review 
  the 
  

   steps 
  by 
  which 
  (15) 
  was 
  obtained. 
  

  

  14. 
  Though 
  we 
  may 
  conceive 
  the 
  electromagnetic 
  vibra- 
  

   tions 
  o£ 
  the 
  sether 
  to 
  be 
  executed 
  in 
  a 
  manner 
  widely 
  different 
  

   from 
  anything 
  occurring 
  in 
  these 
  simple 
  mechanical 
  models, 
  

   we 
  may 
  yet 
  attempt 
  to 
  form 
  some 
  idea 
  of 
  the 
  coarseness 
  of 
  

   structure 
  of 
  the 
  aether 
  which 
  could 
  suffice 
  to 
  account 
  for 
  such 
  

   dispersions 
  as 
  Nordmann 
  and 
  Tikhoff 
  have 
  thought 
  to 
  be 
  

   indicated 
  by 
  their 
  observations. 
  The 
  conclusions 
  reached 
  

   are 
  in 
  any 
  case 
  quite 
  tentative, 
  and 
  (as 
  mentioned 
  in 
  § 
  17 
  

   below) 
  they 
  cannot 
  be 
  put 
  forward 
  without 
  further 
  reser- 
  

   vations. 
  

  

  15. 
  The 
  first 
  thing 
  to 
  be 
  observed 
  is 
  that, 
  in 
  the 
  case 
  of 
  

   our 
  mechanical 
  analogy, 
  the 
  group- 
  velocity 
  given 
  by 
  (16) 
  is 
  

   a 
  direct 
  function 
  of 
  the 
  wave-length 
  : 
  the 
  shorter 
  the 
  wave- 
  

   length 
  the 
  less 
  is 
  the 
  group- 
  velocity. 
  To 
  this 
  extent 
  the 
  

   indications 
  afforded 
  are 
  in 
  agreement 
  with 
  the 
  observations 
  

   of 
  Nordmann 
  and 
  and 
  Tikhoff. 
  In 
  one 
  set 
  of 
  measurements 
  

   made 
  by 
  Nordmann 
  on 
  Algol, 
  it 
  appeared 
  that 
  the 
  red 
  rays 
  

   (about 
  wave-length 
  0*6 
  8 
  yit) 
  arrived 
  16 
  minutes 
  in 
  advance 
  

   of 
  the 
  blue 
  rays 
  (about 
  wave-length 
  O'43/i,). 
  Moreover, 
  the 
  

   parallax 
  of 
  Algol 
  as 
  given 
  by 
  Pritchard 
  is 
  0"*0556, 
  corre- 
  

   sponding 
  to 
  a 
  distance 
  of 
  about 
  61 
  light-years. 
  Thus 
  if 
  we 
  

   assume 
  provisionally 
  that 
  an 
  equation 
  not 
  very 
  different 
  from 
  

   (16) 
  gives 
  the 
  relation 
  between 
  wave-length 
  and 
  group- 
  

   velocity 
  in 
  vacuo^ 
  b 
  then 
  representing 
  a 
  linear 
  magnitude 
  

   which 
  expresses 
  the 
  coarseness 
  of 
  structure 
  of 
  the 
  aether, 
  we 
  

   find 
  

  

  6 
  = 
  1-7x10-8 
  cm.; 
  ..... 
  (17) 
  

   or, 
  say, 
  1/3000 
  of 
  a 
  mean 
  wave-length 
  of 
  viable 
  light. 
  

   From 
  Tikhoff 
  's 
  observations 
  we 
  should 
  obtain 
  a 
  smaller 
  value 
  

   for 
  b 
  — 
  roughly 
  

  

  6 
  = 
  3-1 
  X 
  10-9 
  cm., 
  ..... 
  (18) 
  

  

  cr 
  1/16,500 
  of 
  a 
  mean 
  wave-length 
  of 
  visible 
  light. 
  

  

  16. 
  The 
  disparity 
  between 
  these 
  numbers 
  is 
  very 
  great, 
  

   and 
  arises 
  from 
  a 
  still 
  greater 
  disparity 
  between 
  the 
  values 
  

   found 
  for 
  the 
  dispersion 
  of 
  light 
  in 
  space, 
  Nordmann's 
  

   estimate 
  exceeding 
  Tikhoff 
  's 
  in 
  the 
  proportion 
  of 
  about 
  30 
  

   to 
  1. 
  On 
  this 
  discrepancy 
  Lebedew 
  bases 
  one 
  of 
  his 
  arguments 
  

   against 
  the 
  reality 
  of 
  the 
  supposed 
  dispersion 
  ; 
  another 
  point 
  

   of 
  view 
  is 
  gained 
  by 
  attempting 
  to 
  examine 
  how 
  far 
  the 
  value 
  

  

  