﻿Telescopic 
  Vision. 
  979 
  

  

  concentration 
  image. 
  This 
  is 
  what 
  renders 
  it 
  necessary 
  to 
  

   retain 
  lens 
  L' 
  as 
  part 
  of 
  the 
  apparatus. 
  The 
  concentration 
  

   image 
  upon 
  plane 
  Y' 
  can 
  he 
  seen, 
  but 
  very 
  poorly 
  seen, 
  

   without 
  its 
  intervention. 
  

  

  Of 
  course, 
  the 
  experimental 
  apparatus 
  would 
  most 
  closely 
  

   represent 
  the 
  Cosmical 
  Apparatus 
  described 
  in 
  Chapter 
  1, 
  if 
  

   the 
  focal 
  length 
  of 
  lens 
  1/ 
  were 
  a 
  metre, 
  and 
  if 
  at 
  the 
  same 
  

   time 
  a 
  collimating 
  lens 
  were 
  introduced 
  between 
  z' 
  and 
  s', 
  to 
  

   parallelize 
  the 
  light 
  from 
  pro-star 
  s\ 
  

  

  Note 
  4. 
  On 
  the 
  analysis 
  of 
  light 
  into 
  u 
  f 
  w 
  's. 
  — 
  In 
  all 
  

   Mathematical 
  and 
  experimental 
  investigations 
  into 
  Nature, 
  

   what 
  in 
  each 
  case 
  w 
  T 
  e 
  deal 
  with 
  is 
  not 
  the 
  whole 
  of 
  th> 
  

   activities 
  that 
  are 
  going 
  on, 
  but 
  some 
  immense 
  simplification 
  

   of 
  them 
  effected 
  by 
  ignoring 
  the 
  bulk 
  of 
  what 
  is 
  really 
  taking 
  

   place, 
  and 
  considering 
  only 
  the 
  small 
  residues 
  which 
  are 
  

   what 
  can 
  be 
  perceived 
  by 
  man. 
  Thus 
  we 
  can 
  perceive 
  a 
  wind 
  

   in 
  air, 
  which 
  is 
  in 
  fact 
  only 
  a 
  residual 
  effect, 
  a 
  slight 
  pre- 
  

   ponderance 
  in 
  one 
  direction 
  of 
  all 
  the 
  momentums 
  which 
  are 
  

   consequent 
  upon 
  the 
  vastly 
  swifter 
  motions 
  of 
  the 
  molecules 
  

   between 
  their 
  encounters 
  ; 
  and 
  these 
  motions 
  are 
  themselves 
  

   only 
  the 
  residues 
  which 
  remain 
  over 
  as 
  a 
  preponderance 
  

   in 
  one 
  direction 
  of 
  the 
  enormously 
  more 
  subtile 
  momentums 
  

   that 
  are 
  going 
  on 
  within 
  those 
  travelling 
  missiles. 
  

  

  So 
  also, 
  in 
  his 
  investigations 
  of 
  wave 
  motion, 
  the 
  mathe- 
  

   matician 
  finds 
  it 
  necessary 
  to 
  substitute 
  untextured 
  mediums, 
  

   devoid 
  of 
  all 
  that 
  majority 
  of 
  events 
  which 
  he 
  ignores, 
  — 
  he 
  

   has 
  to 
  substitute 
  this 
  simplification 
  of 
  nature 
  for 
  the 
  real, 
  

   immeasurably 
  more 
  complicated 
  activities 
  that 
  are 
  really 
  in 
  

   operation. 
  The 
  untextured 
  medium 
  is 
  the 
  mathematician's 
  

   hypothesis 
  ; 
  and 
  is 
  legitimate 
  because, 
  under 
  his 
  handling 
  of 
  

   it, 
  it 
  furnishes 
  results 
  which 
  are 
  correct 
  under 
  certain 
  definable 
  

   circumstances, 
  though 
  incorrect 
  under 
  others. 
  They 
  are 
  

   correct 
  whenever 
  we 
  have 
  not 
  to 
  deal 
  with 
  distances 
  that 
  

   approach 
  to 
  being 
  molecular. 
  The 
  mathematician, 
  however, 
  

   in 
  order 
  to 
  carry 
  out 
  his 
  work, 
  has 
  to 
  explore 
  the 
  whole 
  

   field, 
  as 
  he 
  has 
  to 
  base 
  his 
  reasoning 
  upon 
  limiting 
  conditions 
  

   which 
  occur 
  within 
  the 
  part 
  of 
  the 
  field 
  that, 
  when 
  he 
  comes 
  

   to 
  interpret 
  his 
  results, 
  is 
  the 
  very 
  part 
  that 
  must 
  be 
  

   rejected. 
  Resolutions 
  into 
  ufw's, 
  — 
  undulations 
  of 
  wavelets 
  

   — 
  are 
  of 
  this 
  kind, 
  and 
  are 
  of 
  value 
  because 
  although 
  the 
  

   results 
  to 
  which 
  they 
  lead 
  at 
  close 
  quarters 
  are 
  incorrect, 
  all 
  

   the 
  results 
  to 
  which 
  they 
  lead 
  beyond 
  those 
  limits 
  are 
  true, 
  

   and 
  may 
  be 
  used 
  in 
  the 
  present 
  memoir 
  which 
  nowhere 
  has 
  

   occasion 
  to 
  explore 
  the 
  extremely 
  small 
  in 
  space, 
  or 
  the 
  

   extremely 
  brief 
  in 
  time. 
  

  

  