﻿Telescopic 
  Vision. 
  337 
  

  

  object 
  z\ 
  we 
  may 
  regard 
  P 
  x 
  as 
  suppressed 
  and 
  substitute 
  

   4 
  Qi 
  for 
  it, 
  without 
  sensibly 
  altering 
  the 
  optical 
  effect 
  upon 
  

   that 
  small 
  patch. 
  In 
  like 
  manner, 
  we 
  may 
  withdraw 
  the 
  

   other 
  undulations 
  P 
  2 
  P 
  3 
  &c. 
  which 
  reach 
  z' 
  from 
  the 
  other 
  

   points 
  o£ 
  disk 
  s', 
  and 
  substitute 
  undulations 
  similar 
  to 
  them, 
  

   + 
  Q2J 
  + 
  Q3? 
  & 
  c 
  -5 
  travelling 
  in 
  the 
  fixed 
  direction 
  qz 
  f 
  . 
  We 
  

   have 
  now 
  no 
  undulations 
  but 
  the 
  Q's 
  outstanding, 
  and 
  since 
  

   these 
  all 
  travel 
  in 
  the 
  same 
  direction 
  and 
  are 
  of 
  one 
  wave- 
  

   length, 
  they 
  may 
  be 
  combined 
  (by 
  a 
  known 
  theorem) 
  into 
  

   a 
  single 
  resultant 
  undulation 
  which 
  we 
  shall 
  call 
  Q 
  0j 
  travelling 
  

   in 
  that 
  direction. 
  Moreover 
  it 
  follows 
  from 
  the 
  theorem 
  

   referred 
  to, 
  that 
  the 
  undulations 
  Q 
  1 
  Q 
  2 
  &c, 
  which 
  yield 
  this 
  

   single 
  resultant, 
  may 
  differ 
  to 
  any 
  extent 
  from 
  one 
  another 
  

   as 
  regards 
  intensities, 
  phases, 
  and 
  states 
  of 
  polarization 
  ; 
  the 
  

   only 
  property 
  that 
  they 
  must 
  have 
  in 
  common 
  being 
  that 
  

   their 
  wave-lengths 
  must 
  be 
  the 
  same. 
  

  

  A 
  similar 
  treatment 
  is 
  to 
  be 
  applied 
  to 
  the 
  light 
  of 
  other 
  

   wave-lengths 
  admitted 
  through 
  the 
  minute 
  hole 
  s 
  ! 
  , 
  so 
  that 
  

   what 
  we 
  finally 
  learn 
  is 
  that 
  the 
  numberless 
  u 
  f 
  w's 
  which 
  

   reach 
  the 
  small 
  objects' 
  from 
  the 
  pro-star 
  s' 
  — 
  that 
  this 
  whole 
  

   sheaf 
  of 
  undulations, 
  travelling 
  in 
  slightly 
  differing 
  directions, 
  

   may 
  be 
  replaced 
  by 
  a 
  single 
  u 
  f 
  W 
  (undulation 
  of 
  flat 
  waves) 
  

   for 
  each 
  wave-length, 
  travelling 
  in 
  the 
  one 
  definite 
  direction 
  

   qz 
  ; 
  always 
  provided 
  that 
  we 
  have 
  no 
  concern 
  except 
  with 
  

   the 
  effect 
  that 
  will 
  be 
  produced 
  in 
  the 
  neighbourhood 
  of 
  

   the 
  point 
  z 
  . 
  Observe 
  that 
  the 
  word 
  ' 
  waves 
  ' 
  must 
  be 
  here 
  

   used 
  instead 
  of 
  wavelet, 
  since 
  the 
  intensity 
  of 
  the 
  resultant 
  

   undulation 
  Q 
  need 
  not 
  be 
  infinitesimal. 
  

  

  30. 
  By 
  far 
  the 
  most 
  remarkable 
  instance 
  of 
  such 
  light 
  

   is 
  the 
  light 
  reaching 
  the 
  solar 
  system 
  from 
  a 
  star, 
  which, 
  

   though 
  it 
  arrives 
  from 
  all 
  parts 
  of 
  half 
  the 
  surface 
  of 
  an 
  

   immense 
  body, 
  and 
  in 
  all 
  varieties 
  of 
  phase 
  intensity 
  polari- 
  

   zation, 
  &c.j 
  nevertheless 
  comes 
  to 
  any 
  point 
  z 
  r 
  upon 
  the 
  earth 
  

   in 
  directions 
  passing 
  through 
  that 
  point 
  which 
  form 
  such 
  an 
  

   excessively 
  acute 
  cone 
  that 
  the 
  size 
  of 
  the 
  patch 
  in 
  the 
  neigh- 
  

   bourhood 
  of 
  z' 
  throughout 
  which 
  it 
  is 
  legtimate 
  to 
  regard 
  

   the 
  whole 
  of 
  the 
  light 
  of 
  each 
  wave-length 
  as 
  a 
  single 
  

   undulation 
  of 
  flat 
  waves, 
  is 
  so 
  large 
  as 
  to 
  be 
  dozens 
  of 
  metres 
  

   in 
  diameter. 
  

  

  31. 
  Light 
  of 
  various 
  wave-lengths. 
  — 
  In 
  the 
  foregoing 
  pages 
  

   we 
  have 
  only 
  taken 
  into 
  consideration 
  light 
  of 
  one 
  wave- 
  

   length. 
  Now 
  in 
  nature 
  light 
  of 
  one 
  wave-length 
  never 
  

   visibly 
  presents 
  itself 
  unaccompanied 
  by 
  light 
  of 
  neighbouring 
  

   wave-lengths. 
  The 
  nearest 
  approach 
  to 
  light 
  of 
  one 
  wave- 
  

   length 
  that 
  we 
  know 
  of 
  is 
  the 
  light 
  which 
  furnishes 
  a 
  thin 
  

   line 
  in 
  the 
  spectrum 
  of 
  a 
  gas, 
  but, 
  however 
  narrow 
  the 
  line, 
  

  

  