﻿16 
  Prof. 
  H. 
  Nagaoka 
  on 
  the 
  Diffraction 
  Phenomena 
  in 
  the 
  

  

  k. 
  

  

  *+*• 
  

  

  I 
  

   E 
  K 
  

  

  01 
  

  

  1-5748 
  

   1-5869 
  

   1-6084 
  

   1-6416 
  

   1-6901 
  

  

  1-7516 
  

   1-8727 
  

   20113 
  

  

  2-4848 
  

  

  ooooo 
  

   o-oooi 
  

  

  0-0009 
  

   00031 
  

   0-0088 
  

  

  00196 
  

   00511 
  

   0-1328 
  

  

  0-4080 
  

  

  02 
  

  

  0-3 
  

  

  04 
  

  

  05 
  

  

  0-6 
  

  

  0-7 
  

  

  0-8 
  

  

  0-9 
  

  

  

  The 
  formula 
  given 
  above 
  applies 
  only 
  to 
  points 
  far 
  from 
  

   the 
  rim 
  of 
  the 
  circular 
  image. 
  The 
  most 
  interesting 
  case 
  

   connected 
  with 
  the 
  present 
  problem 
  is 
  the 
  investigation 
  of 
  the 
  

   intensity 
  in 
  the 
  very 
  neighbourhood 
  of 
  the 
  rim, 
  where 
  the 
  

   well-known 
  phenomenon 
  of 
  drop-formation 
  makes 
  its 
  ap- 
  

   pearance. 
  As 
  the 
  semiconvergent 
  expansion 
  for 
  J 
  2 
  (/o) 
  

   + 
  JY 
  2 
  (/o) 
  is 
  no 
  longer 
  allowable 
  in 
  the 
  vicinity 
  of 
  the 
  rim, 
  we 
  

   must 
  have 
  recourse 
  to 
  another 
  method 
  of 
  integration 
  for 
  that 
  

   portion 
  of 
  the 
  region, 
  where 
  Jo 
  2 
  (p) 
  + 
  Ji 
  2 
  (/o) 
  must 
  be 
  expanded 
  

   according 
  to 
  ascending 
  powers 
  of 
  p. 
  

  

  We 
  shall 
  divide 
  the 
  region 
  of 
  integration 
  into 
  two 
  parts 
  by 
  

   describing 
  a 
  circle 
  with 
  radius 
  x 
  x 
  about 
  the 
  point 
  O 
  (figs. 
  5 
  

   and 
  6), 
  where 
  the 
  intensity 
  is 
  sought 
  ; 
  at 
  points 
  of 
  the 
  

  

  Fkr. 
  5. 
  

  

  Fig:. 
  6. 
  

  

  periphery 
  not 
  included 
  within 
  the 
  circle 
  thus 
  described, 
  we 
  

   can 
  use 
  the 
  semiconvergent 
  series 
  for 
  J 
  2 
  (/o) 
  + 
  Ji 
  2 
  (/o), 
  and 
  

   apply 
  the 
  method 
  of 
  integration 
  given 
  above, 
  while 
  in 
  the 
  

   interior 
  we 
  must 
  have 
  recourse 
  to 
  the 
  following 
  mode 
  of 
  

   procedure. 
  

  

  