﻿round 
  the 
  Focus 
  of 
  a 
  Lens, 
  at 
  Various 
  Apertures. 
  45 
  

  

  been 
  calculated. 
  These 
  values 
  of 
  A, 
  B, 
  as 
  denned 
  by 
  (24), 
  

   are 
  not 
  by 
  themselves 
  interesting, 
  and 
  will 
  not 
  be 
  given 
  

   here; 
  the 
  square 
  sums 
  A 
  2 
  + 
  B 
  2 
  , 
  however, 
  proportional 
  to 
  the 
  

   intensity, 
  (23 
  a) 
  , 
  may 
  be 
  useful. 
  They 
  are 
  collected, 
  together 
  

   with 
  those 
  for 
  «' 
  = 
  0, 
  in 
  the 
  following 
  Table, 
  which 
  may 
  be 
  a 
  

   good 
  supplement 
  to 
  the 
  P-curves 
  themselves 
  The 
  second 
  

   column 
  contains 
  the 
  sum 
  of 
  the 
  squares 
  of 
  the 
  Eresnelian 
  

   integrals, 
  the 
  third 
  etc. 
  the 
  values 
  of 
  A 
  2 
  + 
  B 
  2 
  , 
  for 
  v 
  = 
  0*l, 
  0*2 
  

   up 
  to 
  17 
  = 
  3*0, 
  corresponding 
  to 
  u 
  =2ir 
  ,10~ 
  32 
  etc., 
  that 
  is, 
  to 
  

   the 
  above 
  curves 
  [1], 
  and 
  so 
  on. 
  

  

  i 
  2 
  

   ; 
  dv 
  . 
  

  

  A 
  2 
  + 
  B 
  2 
  = 
  1 
  1 
  VTj 
  (av; 
  

  

  I 
  Jo 
  

  

  V. 
  

  

  a'=0. 
  a' 
  

  

  103/2 
  

  

  • 
  2tt 
  

  

  10. 
  

  

  20. 
  

  

  30. 
  

  

  00 
  

  

  o-oooo 
  

  

  00000 
  

  

  o-oooo 
  

  

  o-oooo 
  

  

  0-0000 
  

  

  0-1 
  

  

  •0099 
  8 
  

  

  •0099 
  5 
  

  

  •0096 
  

  

  •0068 
  

  

  •0042 
  

  

  02 
  

  

  •0399 
  

  

  •0399 
  

  

  •0327 
  

  

  •0174 
  

  

  •0050 
  

  

  03 
  

  

  •0898 
  

  

  •0895 
  

  

  •0663 
  

  

  •0243 
  

  

  0025 
  

  

  04 
  

  

  •1591 
  

  

  •1583 
  

  

  •1058 
  

  

  •0253 
  

  

  •0003 
  

  

  05 
  

  

  •2466 
  

  

  •2450 
  

  

  •1474 
  

  

  •0218 
  

  

  •0010 
  

  

  0-6 
  

  

  •3499 
  

  

  •3471 
  

  

  •1879 
  

  

  •0162 
  

  

  •0042 
  

  

  0-7 
  

  

  •4648 
  

  

  •4604 
  

  

  •2243 
  

  

  •0202 
  

  

  •0078 
  

  

  0-8 
  

  

  •5849 
  

  

  •5781 
  

  

  •2542 
  

  

  •0099 
  

  

  •0101 
  

  

  0-9 
  

  

  •7004 
  

  

  •6913 
  

  

  •2758 
  

  

  •0131 
  

  

  •0108 
  

  

  10 
  

  

  •8004 
  

  

  •7886 
  

  

  •2886 
  

  

  •0213 
  

  

  •0101 
  

  

  11 
  

  

  0-8728 
  

  

  0-8571 
  

  

  0-2932 
  

  

  0-0337 
  

  

  0-0103 
  

  

  1-2 
  

  

  •9004 
  

  

  •8847 
  

  

  •2918 
  

  

  •0481 
  

  

  •0117 
  

  

  1-3 
  

  

  •8788 
  

  

  •8668 
  

  

  •2875 
  

  

  •0618 
  

  

  •0183 
  

  

  1-4 
  

  

  •8040 
  

  

  •7952 
  

  

  •2838 
  

  

  •0722 
  

  

  •0318 
  

  

  1-5 
  

  

  •6848 
  

  

  •6792 
  

  

  •2833 
  

  

  •0774 
  

  

  •0494 
  

  

  1-6 
  

  

  •5410 
  

  

  •5408 
  

  

  •2868 
  

  

  •0777 
  

  

  •0643 
  

  

  1-7 
  

  

  •4065 
  

  

  •4106 
  

  

  •2923 
  

  

  •0747 
  

  

  •0715 
  

  

  1-8 
  

  

  •3164 
  

  

  •3228 
  

  

  •2957 
  

  

  •0711 
  

  

  0712 
  

  

  1-9 
  

  

  •3029 
  

  

  •3044 
  

  

  •2923 
  

  

  •0691 
  

  

  •0673 
  

  

  20 
  

  

  •3564 
  

  

  •3630 
  

  

  •2795 
  

  

  •0693 
  

  

  •0636 
  

  

  21 
  

  

  04781 
  

  

  0-4786 
  

  

  0-2599 
  

  

  00701 
  

  

  00611 
  

  

  22 
  

  

  •6123 
  

  

  •6049 
  

  

  •2411 
  

  

  •0687 
  

  

  •0614 
  

  

  23 
  

  

  •6981 
  

  

  •6852 
  

  

  •2332 
  

  

  0634 
  

  

  •0617 
  

  

  24 
  

  

  •6921 
  

  

  •6786 
  

  

  •2434 
  

  

  •0554 
  

  

  •0588 
  

  

  2-5 
  

  

  •5926 
  

  

  •5860 
  

  

  •2693 
  

  

  •0494 
  

  

  •0521 
  

  

  26 
  

  

  •4537 
  

  

  •4578 
  

  

  •2973 
  

  

  •0504 
  

  

  •0449 
  

  

  2-7 
  

  

  •3593 
  

  

  •3712 
  

  

  •3094 
  

  

  0595 
  

  

  •0430 
  

  

  2*8 
  

  

  •3718 
  

  

  •3820 
  

  

  •2957 
  

  

  0714 
  

  

  •0486 
  

  

  2-9 
  

  

  •4846 
  

  

  •4832 
  

  

  •2636 
  

  

  •0771 
  

  

  •0589 
  

  

  3-0 
  

  

  0-6132 
  

  

  0-5987 
  

  

  0-2368 
  

  

  00715 
  

  

  0-0659 
  

  

  