﻿484 
  Mr. 
  L. 
  Wright 
  on 
  Microscopic 
  linages 
  and 
  Vision. 
  

  

  illuminate 
  the 
  object, 
  no 
  objection 
  need 
  be 
  made. 
  But 
  in 
  

   this 
  case 
  his 
  first 
  focus 
  of 
  the 
  beam 
  (described 
  as 
  " 
  parallel 
  " 
  

   rays) 
  at 
  x, 
  can 
  no 
  longer 
  be 
  regarded 
  as 
  a 
  focus 
  of 
  rays 
  

   emitted 
  from 
  the 
  object 
  C, 
  but 
  contrariwise, 
  of 
  rays 
  pro- 
  

   ceeding 
  from 
  the 
  much 
  more 
  distant 
  source 
  of 
  light. 
  And 
  

   accordingly, 
  as 
  a 
  simple 
  phenomenon, 
  or 
  fact 
  of 
  observation, 
  

   it 
  is 
  not 
  an 
  image 
  of 
  any 
  point 
  of 
  the 
  object, 
  but 
  of 
  the 
  whole 
  

   source 
  of 
  light, 
  which 
  is 
  focussed 
  at 
  #, 
  and 
  is 
  seen 
  there 
  on 
  

   removing 
  the 
  eyepiece 
  and 
  looking 
  down 
  the 
  tube. 
  

  

  6. 
  Consider 
  next 
  the 
  supposed 
  dynamical 
  system. 
  This 
  is 
  

   by 
  hypothesis 
  set 
  up, 
  not 
  by 
  the 
  object 
  alone, 
  or 
  in 
  ordinary 
  

   method: 
  " 
  We 
  begin 
  by 
  positing 
  repetitions 
  of 
  the 
  objective 
  

   field'''' 
  (Prop. 
  1, 
  § 
  6). 
  Then 
  it 
  is 
  assumed 
  that 
  all 
  these 
  

   replicas 
  emit 
  light 
  from 
  their 
  similar 
  points 
  u 
  the 
  same 
  in 
  

   direction, 
  intensity, 
  phase, 
  and 
  position 
  of 
  transversal." 
  This 
  

   postulate 
  seems 
  altogether 
  illegitimate 
  in 
  a 
  theory 
  purporting 
  

   to 
  represent 
  actual 
  phenomena 
  ; 
  we 
  know 
  that 
  it 
  is 
  not 
  true 
  

   in 
  physical 
  reality. 
  It, 
  too, 
  depends 
  for 
  the 
  qualified 
  truth 
  

   which 
  it 
  does 
  possess, 
  upon 
  plane-wave 
  illumination 
  ; 
  then 
  it 
  

   is 
  true, 
  so 
  far 
  as 
  that 
  when 
  approximately 
  plane 
  waves 
  fall 
  

   upon 
  a 
  grating, 
  the 
  width 
  or 
  number 
  of 
  lines 
  does 
  not 
  affect 
  

   the 
  image 
  of 
  the 
  ruling, 
  as 
  ruling. 
  But 
  it 
  seems 
  to 
  push 
  the 
  

   result 
  of 
  certain 
  mathematical 
  expressions 
  to 
  an 
  extent 
  which 
  

   can 
  hardly 
  be 
  justified. 
  That 
  opinion 
  must 
  be 
  expressed 
  

   with 
  diffidence, 
  since 
  my 
  very 
  small 
  amount 
  of 
  mathematical 
  

   knowledge 
  has 
  become 
  so 
  rusty, 
  that 
  it 
  is 
  only 
  with 
  difficulty 
  I 
  

   can 
  follow 
  (and 
  but 
  too 
  vaguely) 
  even 
  the 
  general 
  drift 
  of 
  the 
  

   analyses 
  in 
  the 
  discussion 
  which 
  so 
  interests 
  me. 
  I 
  did, 
  how- 
  

   ever, 
  gather 
  that 
  the 
  ground 
  of 
  the 
  immense 
  postulate 
  here 
  

   objected 
  to, 
  lay 
  in 
  the 
  fact 
  that 
  resolution 
  into 
  plane 
  waves 
  of 
  

   a3ther-disturbances 
  set 
  up 
  by 
  an 
  object, 
  is 
  represented 
  by 
  ex- 
  

   pressions 
  which 
  equally 
  represent 
  replicas 
  of 
  the 
  disturbances; 
  

   the 
  nature 
  of 
  circular 
  functions 
  involving 
  this 
  necessity. 
  From 
  

   a 
  private 
  reply 
  Dr. 
  Stoney 
  was 
  kind 
  enough 
  to 
  give 
  me, 
  it 
  

   appears 
  this 
  is 
  the 
  case. 
  But 
  mathematical 
  expressions 
  are 
  

   but 
  tools, 
  and 
  often 
  have 
  the 
  usual 
  defects 
  of 
  tools 
  ; 
  in 
  par- 
  

   ticular 
  that 
  of 
  not 
  being 
  sharp 
  enough. 
  Ask 
  these 
  functions 
  

   to 
  express 
  a 
  given 
  disturbance 
  and 
  many 
  surrounding 
  replicas, 
  

   and 
  they 
  will 
  do 
  it. 
  But 
  ask 
  them 
  next 
  to 
  express 
  an 
  actual 
  

   limited 
  disturbance 
  resolved 
  in 
  this 
  manner, 
  and 
  no 
  more, 
  

   and 
  they 
  fail 
  ; 
  their 
  edge 
  at 
  present 
  is 
  not 
  sharp 
  enough 
  to 
  do 
  

   that. 
  Such 
  failure, 
  however, 
  is 
  in 
  this 
  case 
  an 
  imperfection 
  ; 
  

   and 
  surely 
  to 
  ground 
  such 
  a 
  physical 
  postulate 
  upon 
  the 
  very 
  

   imperfection 
  of 
  an 
  imperfect 
  tool, 
  is 
  rather 
  arguing 
  in 
  a 
  

   circle. 
  It 
  seems 
  to 
  be 
  a 
  case 
  of 
  what 
  was 
  described 
  only 
  

   the 
  other 
  day 
  in 
  a 
  review 
  of 
  a 
  mathematical 
  work, 
  as 
  " 
  the 
  

  

  