﻿Focal 
  Plane 
  of 
  a 
  Telescope 
  with 
  Circular 
  Aperture. 
  9 
  

  

  11. 
  

  

  V 
  

  

  *<%>■ 
  

  

  i(g-i,(vi)- 
  

  

  0. 
  

  

  1. 
  

  

  0-00000 
  

   3-83171 
  

  

  o-ooooo 
  

  

  0-83778 
  

  

  

  0-83778 
  

  

  2. 
  

  

  7-01559 
  

  

  090994 
  

  

  0-07216 
  

  

  3. 
  

  

  1017347 
  

  

  093765 
  

  

  0-02771 
  

  

  4. 
  

  

  1332369 
  

  

  0-95232 
  

  

  001467 
  

  

  5. 
  

  

  16 
  47063 
  

  

  096140 
  

  

  0-00908 
  

  

  6. 
  

  

  1961586 
  

  

  096758 
  

  

  000618 
  

  

  7. 
  

  

  2276008 
  

  

  0-97205 
  

  

  000417 
  

  

  8. 
  

  

  25 
  90367 
  

  

  0-97544 
  

  

  00339 
  

  

  9. 
  

  

  29 
  04683 
  

  

  097809 
  

  

  00265 
  

  

  10. 
  

  

  32-18968 
  

  

  0-98023 
  

  

  000214 
  

  

  20. 
  

  

  63-61136 
  

  

  098999 
  

  

  000052 
  

  

  30. 
  

  

  9502923 
  

  

  0-99330 
  

  

  00023 
  

  

  40. 
  

  

  126 
  44614 
  

  

  99497 
  

  

  000013 
  

  

  50. 
  

  

  15786266 
  

  

  0-99597 
  

  

  0-00008 
  

  

  It 
  will 
  be 
  seen 
  from 
  the 
  table 
  that 
  the 
  effect 
  of 
  the 
  first 
  

   zone 
  is 
  five 
  times 
  greater 
  than 
  all 
  the 
  rest 
  combined. 
  Thus 
  

   the 
  illumination 
  at 
  the 
  centre 
  of 
  a 
  disk 
  of 
  small 
  radius 
  will 
  

   not 
  sensibly 
  differ 
  from 
  that 
  of 
  infinite 
  extent. 
  For 
  values 
  

   of 
  r 
  less 
  than 
  i\ 
  we 
  have 
  the 
  following 
  table 
  : 
  — 
  

  

  r. 
  

  

  I(r). 
  

  

  Difference. 
  

  

  r. 
  

  

  20 
  

  

  2-2 
  

  

  2-4 
  

  

  2-6 
  

  

  2-8 
  

  

  30. 
  

  

  3-2 
  

  

  3-4 
  

  

  36 
  

  

  3-8 
  

  

  I(r). 
  

  

  Difference. 
  

  

  00 
  

   02 
  

   0-4 
  

   0-6 
  

   0-8 
  

   10 
  

   1-2 
  

   1-4 
  

   1-6 
  

   1-8 
  

  

  000000 
  

   00995 
  

   003921 
  

   0-08605 
  

   0-14775 
  

   0-22187 
  

   030129 
  

   038497 
  

   046783 
  

   054625 
  

  

  0-00995 
  

   002926 
  

   004684 
  

   006170 
  

   007412 
  

   0-07942 
  

   0-08368 
  

   0-08286 
  

   07842 
  

   007101 
  

  

  0-61726 
  

   0-67873 
  

   0-72950 
  

   76896 
  

   079790 
  

   0-81741 
  

   082918 
  

   083518 
  

   0-83738 
  

   83778 
  

  

  0-06147 
  

   05077 
  

   03946 
  

   002894 
  

   001951 
  

   01177 
  

   00600 
  

   000220 
  

   00040 
  

  

  These 
  two 
  tables 
  enable 
  us 
  to 
  integrate 
  mechanically 
  the 
  

   expression 
  (II.), 
  

  

  I 
  = 
  ^ 
  f 
  (Jo 
  2 
  ('-o) 
  + 
  J/W 
  -Jo 
  2 
  (»-i) 
  -3x\n))d6, 
  

  

  for 
  a 
  source 
  of 
  any 
  given 
  shape. 
  About 
  a 
  point 
  at 
  which 
  the 
  

   intensity 
  is 
  sought, 
  describe 
  a 
  number 
  of 
  concentric 
  circles 
  

   dividing 
  the 
  region 
  of 
  integration 
  into 
  a 
  series 
  of 
  zones 
  

   whose 
  breadths 
  are 
  equal 
  to 
  the 
  differences 
  between 
  the 
  

   successive 
  roots 
  of 
  Ji(?')=0. 
  If 
  the 
  angle 
  subtended 
  at 
  the 
  

   point 
  by 
  these 
  zones 
  be 
  known, 
  we 
  can, 
  by 
  summation 
  of 
  

   these 
  separate 
  effects, 
  find 
  the 
  intensity 
  at 
  the 
  required 
  point. 
  

   If 
  the 
  luminous 
  source 
  subtend 
  several 
  seconds 
  of 
  arc, 
  the 
  

  

  