﻿Telescopic 
  Vision. 
  963 
  

  

  nomical 
  telescopes. 
  The 
  sizes 
  of 
  these 
  depends 
  upon 
  the 
  

   wave-length 
  of 
  the 
  light, 
  and 
  therefore 
  differs 
  for 
  the 
  different 
  

   colours 
  of 
  the 
  spectrum. 
  With 
  light 
  of 
  one 
  wave-length 
  

   everything 
  would 
  be 
  definite. 
  At 
  the 
  centre 
  the 
  intensity 
  

   is 
  a 
  maximum, 
  and 
  at 
  a 
  certain 
  distance 
  from 
  the 
  centre 
  it 
  

   falls 
  to 
  cipher. 
  This 
  distance 
  will 
  be 
  the 
  radius 
  of 
  a 
  circle 
  

   of 
  no 
  intensity, 
  which 
  will 
  separate 
  the 
  central 
  boss 
  from 
  the 
  

   first 
  ring 
  ; 
  and 
  similar 
  circles 
  of 
  no 
  intensity 
  separate 
  the 
  

   successive 
  luminous 
  rings 
  from 
  one 
  another. 
  By 
  slightly 
  

   simplifying 
  Airy's 
  formula 
  (see 
  Transactions, 
  Cambridge 
  

   Philosophical 
  Society, 
  vol. 
  v. 
  1835, 
  p. 
  287), 
  the 
  angular 
  

   radii 
  of 
  the 
  innermost 
  three 
  of 
  these, 
  as 
  seen 
  from 
  the 
  optical 
  

   centre 
  of 
  lens 
  I/, 
  are 
  found 
  to 
  be 
  

  

  *, 
  = 
  (1-22>|, 
  2 
  =(2-27)|, 
  3 
  = 
  (3-24)J, 
  . 
  (1) 
  

  

  where 
  1 
  2 
  and 
  6 
  Z 
  are 
  the 
  angular 
  radii 
  as 
  seen 
  from 
  the 
  

   optical 
  centre 
  of 
  the 
  objective, 
  X 
  is 
  the 
  wave-length 
  of 
  the 
  

   light 
  for 
  which 
  the 
  computation 
  is 
  made, 
  and 
  A 
  is 
  the 
  aper- 
  

   ture 
  of 
  the 
  telescope, 
  which 
  in 
  the 
  case 
  supposed 
  is 
  1 
  mm. 
  

   Hence, 
  on 
  plane 
  Y 
  ; 
  which 
  is 
  about 
  a 
  metre 
  from 
  the 
  objective, 
  

   the 
  radii 
  of 
  these 
  innermost 
  dark 
  circles 
  will 
  approxi- 
  

   mately 
  be 
  

  

  *!= 
  1000(1-22)^ 
  

  

  * 
  2 
  = 
  1000(2-27)\L 
  (2) 
  

  

  * 
  3 
  = 
  1000(3-24) 
  J 
  

   and 
  if 
  we 
  insert 
  0*7 
  of 
  a 
  micron 
  for 
  X, 
  which 
  is 
  about 
  the 
  

   longest 
  wave-length 
  of 
  the 
  conspicuous 
  parts 
  of 
  the 
  spectrum, 
  

   we 
  find 
  that 
  for 
  that 
  wave-length 
  the 
  radii 
  of 
  the 
  three 
  dark 
  

   circles 
  will 
  be 
  

  

  ^i 
  = 
  0-854 
  mm., 
  t 
  2 
  = 
  l'5Sd 
  mm., 
  t 
  3 
  = 
  2'26S 
  mm. 
  (3) 
  

   These 
  the 
  observer 
  sees 
  magnified 
  seven 
  times 
  by 
  his 
  Steinheil 
  

  

  Part 
  of 
  concentration 
  image. 
  

  

  lens. 
  Bat 
  in 
  the 
  annexed 
  figure 
  they 
  are 
  magnified 
  only 
  

   four 
  times, 
  as 
  this 
  magnification 
  will 
  make 
  the 
  diagrams 
  in 
  

  

  3R2 
  

  

  