﻿Dispersion 
  of 
  Light 
  in 
  Space. 
  877 
  

  

  o£ 
  h 
  given 
  by 
  (17) 
  or 
  by 
  (18) 
  might 
  be 
  reconcileable 
  with 
  

   what 
  we 
  know 
  of 
  the 
  properties 
  o£ 
  the 
  aether. 
  

  

  17. 
  Sir 
  J. 
  J. 
  Thomson's 
  estimate 
  * 
  of 
  the 
  radius 
  o£ 
  a 
  cor- 
  

   puscle 
  (or 
  negatiA*e 
  electron) 
  is 
  10~'^ 
  cm., 
  and 
  if 
  we 
  adopt 
  

   this, 
  we 
  may 
  hold 
  it 
  probable 
  that 
  any 
  structure 
  possessed 
  

   by 
  the 
  free 
  sether 
  is 
  on 
  a 
  scale 
  considerably 
  more 
  minute 
  ; 
  

   that 
  is 
  to 
  say, 
  that 
  the 
  linear 
  magaitude 
  corresponding 
  to 
  6, 
  

   and 
  serving 
  to 
  define 
  the 
  coarseness 
  of 
  structure, 
  would 
  be 
  

   small 
  compared 
  with 
  10~^^ 
  cm. 
  From 
  such 
  a 
  standpoint, 
  

   even 
  the 
  lesser 
  value 
  (18) 
  deduced 
  from 
  Tikhoff's 
  observa- 
  

   tions 
  seems 
  altogether 
  excessive 
  ; 
  though 
  this 
  conclusion 
  is 
  

   necessarily 
  discounted 
  by 
  more 
  than 
  one 
  source 
  of 
  uncertainty. 
  

   In 
  the 
  first 
  place 
  the 
  applicability 
  of 
  (16) 
  depends 
  on 
  a 
  rather 
  

   elusive 
  analogy, 
  as 
  pointed 
  out 
  in 
  § 
  13 
  ; 
  and, 
  further, 
  the 
  

   value 
  10~^^cm. 
  for 
  the 
  radius 
  of 
  an 
  electron 
  is 
  unavoidably 
  

   based 
  on 
  the 
  assumption 
  that, 
  even 
  up 
  to 
  an 
  electromotive 
  

   intensity 
  of 
  5 
  x 
  10^^ 
  electrostatic 
  units 
  (1*5 
  x 
  10^^ 
  volts 
  per 
  cm.), 
  

   the 
  relation 
  of 
  electromotive 
  intensity 
  to 
  electric 
  polarization 
  

   remains 
  linear-. 
  

  

  18. 
  On 
  ths 
  whole, 
  in 
  any 
  medium 
  transmitting 
  disturbances 
  

   of 
  given 
  type, 
  it 
  does 
  not 
  seem 
  likely 
  that 
  the 
  effect 
  of 
  

   coarseness 
  of 
  structure 
  in 
  producing 
  dispersion 
  would 
  be 
  

   very 
  widely 
  different 
  from 
  that 
  expressed 
  by 
  (15) 
  and 
  (16) 
  ; 
  

   and 
  even 
  when 
  very 
  large 
  allowances 
  are 
  made 
  for 
  the 
  un- 
  

   certainty 
  regarding 
  the 
  actual 
  radius 
  of 
  an 
  electron, 
  it 
  appears 
  

   that 
  the 
  dispersion 
  announced 
  by 
  Tikhoff 
  (to 
  say 
  nothing 
  of 
  

   Kordmann's 
  much 
  larger 
  estimate) 
  is 
  of 
  an 
  altogether 
  greater 
  

   order 
  of 
  magnitude 
  than 
  could 
  be 
  accounted 
  for 
  by 
  coarse- 
  

   ness 
  of 
  structure 
  of 
  the 
  sether. 
  Lebedew 
  f 
  considers 
  that 
  any 
  

   dispersion 
  of 
  light 
  in 
  free 
  sether 
  would 
  be 
  contrary 
  to 
  estab- 
  

   lished 
  principles 
  of 
  electromagnetism 
  ; 
  it 
  is 
  not 
  necessary 
  to 
  

   take 
  so 
  uncompromising 
  a 
  view 
  in 
  order 
  to 
  realize 
  that 
  there 
  

   would 
  be 
  difficulty 
  in 
  explaining 
  setherial 
  dispersion 
  of 
  any- 
  

   thing 
  like 
  the 
  degree 
  which 
  has 
  been 
  suggested. 
  But 
  for 
  

   this 
  reason 
  all 
  the 
  more 
  it 
  is 
  to 
  be 
  hoped 
  that 
  the 
  observations 
  

   will 
  be 
  extended, 
  and 
  that 
  progress 
  will 
  be 
  made 
  in 
  the 
  delicate 
  

   task 
  of 
  disentangling 
  the 
  relative 
  retardations 
  due 
  to 
  disper- 
  

   sion 
  in 
  space 
  from 
  any 
  effects 
  arising 
  from 
  the 
  special 
  nature 
  

   of 
  the 
  star-systems 
  observed. 
  Apart 
  from 
  the 
  astronomical 
  

   importance 
  of 
  the 
  question, 
  any 
  addition 
  to 
  our 
  knowledge 
  

   of 
  the 
  properties 
  of 
  the 
  sether 
  must 
  be 
  of 
  the 
  highest 
  interest. 
  

  

  Kennington, 
  near 
  Oxford, 
  June 
  Sth, 
  1909. 
  

  

  * 
  Tlie 
  estimate 
  is 
  provisional 
  only, 
  and 
  is 
  conditional 
  on 
  the 
  whole 
  

   inertia 
  of 
  the 
  corpuscle 
  being 
  of 
  electromagnetic 
  origin. 
  Cf. 
  ' 
  Conduction 
  

   of 
  Electricity 
  through 
  Gases,' 
  2nd 
  ed. 
  p. 
  655. 
  

  

  t 
  Loc. 
  cit. 
  

  

  