﻿12 
  Prof. 
  H. 
  Nagaoka 
  on 
  the 
  Diffraction 
  Phenomena 
  in 
  the 
  

   In 
  the 
  second 
  integral 
  we 
  have 
  to 
  put 
  

  

  TO/N 
  2 
  /\ 
  cos 
  2?' 
  1 
  — 
  sin 
  2r\ 
  

  

  Thus 
  we 
  shall 
  have 
  to 
  calculate 
  the 
  following 
  integrals 
  : 
  — 
  

  

  i 
  

  

  2 
  

  

  I 
  

  

  2a 
  dr 
  7T 
  . 
  _j5 
  

  

  V^?=^ 
  ~ 
  2 
  S1U 
  2a 
  ; 
  

  

  / 
  , 
  o 
  ., 
  = 
  — 
  5- 
  log 
  tan 
  -r, 
  where 
  6^ 
  = 
  sin 
  *— 
  ; 
  

  

  r 
  \ 
  f 
  ka 
  2 
  — 
  r 
  l 
  2a 
  & 
  2 
  2a 
  

  

  X, 
  

  

  2q 
  jr 
  1 
  cot^ 
  1 
  , 
  ^ 
  

  

  r- 
  3 
  y/±a*-r* 
  = 
  8o"b 
  ■ 
  S 
  W 
  ~ 
  8a 
  3 
  l0 
  § 
  tan 
  2 
  ; 
  

  

  1 
  _ 
  

  

  f 
  2 
  " 
  cos2rdr 
  1 
  ^^ 
  cos 
  2a?, 
  f 
  A 
  /i 
  r2 
  , 
  /cos 
  2r\ 
  

  

  J 
  

  

  01367 
  3 
  cos 
  4a 
  , 
  

  

  = 
  oh 
  2~- 
  nearly 
  ; 
  

  

  a 
  oz 
  ar 
  

  

  2a 
  sinjyjy 
  0*00322 
  5 
  cos 
  4a 
  , 
  

  

  "1 
  — 
  / 
  , 
  o 
  . 
  > 
  = 
  — 
  tt^ 
  r~ 
  nearly. 
  

  

  r 
  3 
  \/4a 
  2 
  — 
  r 
  1 
  a 
  lb 
  a 
  2 
  J 
  

  

  Arranging 
  the 
  integrals 
  in 
  a 
  suitable 
  way 
  and 
  writing 
  

  

  . 
  .*! 
  0-60984 
  0-3731 
  , 
  

   sin- 
  1 
  ~ 
  = 
  5— 
  + 
  

  

  1 
  . 
  .*! 
  0-60984 
  0-3731 
  , 
  0*6162 
  

   sin 
  -1 
  ^- 
  = 
  3 
  — 
  H 
  -5 
  . 
  . 
  . 
  . 
  , 
  

  

  it 
  2a 
  a 
  a 
  6 
  a 
  

  

  x 
  2 
  3 
  a?i 
  4 
  

   log 
  tan 
  4^ 
  = 
  ^.^ 
  -log 
  4a 
  -^-y^B^. 
  - 
  ., 
  

  

  we 
  find 
  for 
  the 
  intensity 
  at 
  the 
  rim 
  of 
  a 
  circular 
  disk 
  whose 
  

   radius 
  is 
  large 
  compared 
  to 
  .% 
  

  

  t 
  _l_ 
  ] 
  ^^_^^ 
  + 
  0-016^%early.. 
  (III.) 
  

   ±R 
  "~2 
  7r 
  2 
  a 
  a 
  a 
  2 
  

  

  As 
  was 
  before 
  remarked, 
  the 
  intensity 
  at 
  the 
  rim 
  approaches 
  

   i 
  with 
  increasing 
  values 
  of 
  a 
  ; 
  it 
  is, 
  moreover, 
  seen 
  how 
  the 
  

  

  fluctuation 
  due 
  to 
  the 
  term 
  ^-^ 
  is 
  negligibly 
  small. 
  By 
  

  

  a 
  

  

  applying 
  the 
  above 
  formula, 
  the 
  following 
  table 
  was 
  calcu- 
  

   lated 
  for 
  a>20:— 
  

  

  