﻿Telescopic 
  Vision, 
  

  

  32:; 
  

  

  long 
  focus 
  and 
  of: 
  vast 
  aperture 
  to 
  be 
  introduced 
  perpendi- 
  

   cularly 
  to 
  the 
  optic 
  axis 
  and 
  immediately 
  in 
  front 
  of 
  the 
  

   pro-Mars, 
  the 
  focal 
  length 
  of 
  this 
  lens 
  being 
  the 
  whole 
  

   distance 
  from 
  lens 
  L 
  to 
  disk 
  y, 
  which 
  latter 
  stands 
  im- 
  

   mediately 
  in 
  front 
  of 
  our 
  astronomical 
  telescope. 
  It 
  is 
  

   legitimate 
  to 
  introduce 
  this 
  lens, 
  inasmuch 
  as 
  such 
  a 
  lens 
  

   situated 
  close 
  to 
  the 
  planet, 
  or 
  to 
  the 
  pro-planet, 
  would 
  not 
  

   have 
  any 
  sensible 
  effect 
  upon 
  an 
  image 
  of 
  either 
  of 
  those 
  

   objects 
  formed 
  at 
  a 
  distance, 
  such 
  as 
  the 
  image 
  in 
  our 
  

   telescope. 
  Again, 
  if 
  both 
  Mars 
  and 
  the 
  pro-Mars 
  were 
  

   removed 
  from 
  behind 
  the 
  lens, 
  an 
  image 
  of 
  the 
  distant 
  star 
  

   would 
  be 
  formed 
  by 
  lens 
  L 
  upon 
  disk 
  y. 
  This 
  stellar 
  image, 
  

   which 
  we 
  may 
  call 
  the 
  star-burst 
  produced 
  by 
  the 
  light 
  that 
  

   has 
  come 
  from 
  the 
  star 
  through 
  a 
  lens, 
  would 
  present 
  that 
  

   appearance 
  of 
  a 
  spurious 
  disk 
  and 
  surrounding 
  rings 
  which 
  

   Airy 
  investigated, 
  and 
  the 
  size 
  of 
  which 
  for 
  light 
  of 
  each 
  

   wave-length 
  would 
  be, 
  as 
  appears 
  from 
  his 
  investigation, 
  

   directly 
  proportional 
  to 
  the 
  distance 
  from 
  lens 
  L 
  to 
  the 
  earth 
  

   and 
  inversely 
  proportional 
  to 
  the 
  diameter 
  of 
  lens 
  L. 
  Now 
  

   as 
  there 
  is 
  nothing 
  to 
  limit 
  our 
  conception 
  of 
  the 
  size 
  of 
  lens 
  L, 
  

   it 
  is 
  legitimate 
  for 
  us 
  to 
  imagine 
  it 
  of 
  such 
  immense 
  aperture 
  

   that 
  the 
  spurious 
  disk 
  and 
  rings, 
  which 
  are 
  the 
  image 
  of 
  the 
  

   star, 
  shall 
  shrink 
  into 
  being 
  a 
  mere 
  speck 
  upon, 
  disk 
  y. 
  Let 
  

   us 
  next 
  conceive 
  our 
  pro-Mars 
  to 
  be 
  restored 
  to 
  its 
  position 
  

   behind 
  lens 
  L. 
  Light 
  from 
  the 
  star 
  is 
  now 
  incident 
  upon 
  the 
  

   farther 
  side 
  of 
  the 
  pro-Mars, 
  and 
  this 
  single 
  undulation 
  of 
  flat 
  

   waves 
  in 
  passing 
  through 
  the 
  pro-Mars 
  changes 
  into 
  a 
  sheaf 
  

   of 
  u 
  f 
  w's 
  which 
  are 
  what 
  advance 
  towards 
  our 
  telescope. 
  

   Each 
  of 
  these 
  innumerable 
  undulations 
  will 
  by 
  lens 
  L 
  be 
  

   concentrated 
  into 
  a 
  speck 
  on 
  plane 
  Y 
  ; 
  and 
  those 
  of 
  them, 
  and 
  

   those 
  only, 
  which 
  produce 
  specks 
  that 
  fall 
  within 
  disk 
  y 
  will 
  be 
  

   the 
  undulations 
  emitted 
  by 
  the 
  pro-Mars 
  that 
  will 
  be 
  caught 
  

   by 
  our 
  telescope. 
  As 
  these 
  will 
  be 
  only 
  some 
  of 
  the 
  entire 
  

   sheaf 
  of 
  undulations 
  transmitted 
  forward 
  by 
  the 
  pro-Mars, 
  

   the 
  image 
  they 
  can 
  form 
  in 
  our 
  tel?scope 
  will 
  fall 
  short 
  of 
  

   being 
  the 
  best 
  which 
  the 
  light 
  emitted 
  by 
  the 
  pro-Mars 
  would 
  

   be 
  competent 
  to 
  form, 
  in 
  other 
  words, 
  it 
  will 
  fall 
  short 
  of 
  

   being 
  the 
  optimum 
  image. 
  

  

  11. 
  It 
  is 
  possible, 
  at 
  this 
  stage, 
  to 
  get 
  some 
  insight 
  into 
  

   the 
  true 
  character 
  of 
  the 
  image 
  presented 
  in 
  our 
  telescope. 
  

   Let 
  us 
  call 
  the 
  light 
  from 
  the 
  planet 
  which 
  is 
  admitted 
  into 
  

   the 
  telescope, 
  light* 
  A, 
  and 
  the 
  light 
  excluded 
  from 
  it, 
  light 
  E 
  ; 
  

   and 
  let 
  us 
  imagine 
  another 
  body 
  of 
  light 
  identical 
  with 
  E, 
  

   except 
  that 
  all 
  the 
  component 
  undulations 
  of 
  wavelets 
  of 
  

   which 
  it 
  consists 
  travel 
  half 
  a 
  wave-length 
  behind 
  those 
  of 
  E. 
  

   This 
  imagined 
  light 
  we 
  may 
  call 
  — 
  E. 
  Then 
  if 
  4-E 
  and 
  — 
  E 
  

  

  