﻿Telescopic 
  Vision. 
  951 
  

  

  having 
  ascertained 
  this, 
  we 
  shall 
  inquire 
  what 
  the 
  final 
  

   outcome 
  will 
  be 
  when 
  these 
  causes, 
  or 
  any 
  selected 
  group 
  of 
  

   them, 
  are 
  allowed 
  to 
  come 
  simultaneously 
  into 
  operation. 
  

  

  55. 
  These 
  independent 
  causes 
  are 
  in 
  fact 
  the 
  several 
  

   uf 
  W's 
  (undulations 
  of 
  flat 
  waves) 
  into 
  which 
  the 
  diffused 
  

   light 
  incident 
  upon 
  z' 
  is 
  resolvable 
  and 
  which 
  we 
  may 
  call 
  

   Ui, 
  U 
  2 
  , 
  U 
  3 
  , 
  &c. 
  A 
  part 
  of 
  each 
  of 
  these 
  U's 
  passes 
  through 
  

   the 
  opening 
  at 
  z 
  ! 
  which 
  represents 
  in 
  our 
  experimental 
  

   apparatus 
  some 
  supposed 
  detail 
  upon 
  the 
  planet 
  which 
  is 
  

   being 
  examined 
  by 
  the 
  astronomer. 
  The 
  part 
  of 
  this 
  U 
  

   which 
  passes 
  through 
  z' 
  becomes 
  to 
  the 
  left 
  of 
  zf 
  what 
  is 
  

   called 
  a 
  ' 
  beam 
  ' 
  of 
  light. 
  This 
  beam 
  is 
  of 
  the 
  kind 
  which 
  

   light 
  from 
  a 
  star 
  produces 
  when 
  allowed 
  to 
  pass 
  through 
  an 
  

   opening 
  in 
  a 
  shutter. 
  We 
  shall 
  analyse 
  this 
  beam 
  and 
  find 
  

   it 
  to 
  be 
  a 
  definite 
  and 
  complex 
  optical 
  phenomenon. 
  We 
  

   learn 
  much 
  about 
  the 
  u 
  f 
  W's 
  (or 
  u 
  s 
  W's) 
  into 
  which 
  it 
  may 
  

   be 
  resolved 
  and 
  of 
  which 
  it 
  therefore 
  consists, 
  by 
  introducing 
  

   a 
  contrivance 
  (lens 
  I/) 
  by 
  which 
  the 
  light 
  of 
  each 
  ufW 
  

   (or 
  u 
  s 
  W, 
  as 
  the 
  case 
  may 
  be, 
  see 
  §68) 
  will 
  be 
  concentrated 
  

   into 
  a 
  speck 
  of 
  light 
  upon 
  plane 
  Y', 
  where 
  the 
  simultaneous 
  

   presence 
  of 
  the 
  specks 
  from 
  all 
  the 
  uf 
  W's 
  of 
  which 
  the 
  beam 
  

   consists 
  will 
  constitute 
  what 
  we 
  call 
  the 
  Concentration 
  Image 
  

   produced 
  by 
  that 
  beam. 
  

  

  56. 
  The 
  light 
  of 
  the 
  beam 
  after 
  becoming 
  this 
  concen- 
  

   tration 
  image 
  upon 
  plane 
  Y 
  7 
  , 
  continues 
  its 
  progress 
  towards 
  

   the 
  left, 
  and 
  if 
  it 
  or 
  a 
  part 
  of 
  it 
  is 
  admitted 
  into 
  the 
  pro- 
  

   telescope 
  T', 
  it 
  will 
  produce 
  at 
  x' 
  within 
  the 
  pro-telescope 
  

   that 
  image 
  of 
  object 
  z\ 
  which 
  the 
  light 
  admitted 
  to 
  the 
  

   pro-telescope 
  is 
  capable 
  of 
  forming. 
  This 
  is 
  the 
  image 
  

   which 
  the 
  pro-telescope 
  can 
  furnish, 
  when 
  the 
  incident 
  light 
  

   which 
  renders 
  object 
  z' 
  visible 
  has 
  been 
  the 
  light 
  of 
  the 
  

   particular 
  U 
  which 
  we 
  have 
  allowed 
  to 
  illuminate 
  that 
  object. 
  

   Let 
  us 
  suppose 
  that 
  it 
  is 
  Ui 
  which 
  we 
  have 
  so 
  employed, 
  

   and 
  let 
  us 
  call 
  the 
  image 
  of 
  z\ 
  which 
  is 
  then 
  formed 
  at 
  x' 
  \ 
  

   Pj. 
  Similarly 
  when 
  U 
  2 
  is 
  the 
  incident 
  light, 
  the 
  image 
  of 
  z 
  

   wall 
  be 
  P 
  2 
  , 
  and 
  so 
  on. 
  These 
  P's 
  we 
  may 
  call 
  the 
  partials, 
  

   or 
  partial 
  images 
  of 
  z, 
  which 
  the 
  U's 
  when 
  acting 
  separately 
  

   can 
  produce. 
  When 
  the 
  light 
  incident 
  upon 
  z 
  was 
  diffused 
  

   light, 
  all 
  the 
  U's 
  were 
  brought 
  into 
  operation, 
  and 
  the 
  image 
  

   then 
  formed 
  at 
  x', 
  which 
  we 
  may 
  call 
  the 
  complete 
  image, 
  

   was 
  due 
  to 
  the 
  simultaneous 
  presence 
  there 
  of 
  all 
  the 
  

   partials, 
  and 
  may 
  therefore 
  be 
  represented 
  by 
  the 
  expression 
  

   P 
  1 
  + 
  P 
  2 
  + 
  P 
  3 
  -|-&c. 
  The 
  complete 
  image 
  therefore 
  results 
  

   from 
  light 
  being 
  superposed 
  upon 
  light 
  at 
  x'. 
  Now 
  when 
  

   light 
  is 
  superposed 
  upon 
  light, 
  one 
  or 
  other 
  of 
  two 
  things 
  

   happens. 
  If 
  the 
  lights 
  that 
  are 
  superposed 
  can 
  permanently 
  

  

  