﻿10 
  Prof. 
  H. 
  Nagaoka 
  on 
  the 
  Diffraction 
  Phenomena 
  in 
  the 
  

  

  value 
  of 
  r 
  will 
  be 
  a 
  large 
  quantity. 
  Thus, 
  if 
  the 
  boundary 
  

   does 
  not 
  show 
  great 
  irregularities, 
  we 
  can 
  approximately 
  

   assume 
  the 
  bounding 
  edge 
  to 
  be 
  straight 
  for 
  contiguous 
  

   zones. 
  If 
  the 
  mean 
  angle 
  a 
  n 
  subtended 
  by 
  the 
  zone 
  at 
  the 
  

   given 
  point 
  be 
  found, 
  the 
  intensity 
  

  

  I 
  = 
  h~ 
  2«„(I(?v)— 
  I(r„_i)) 
  approximately. 
  

  

  We 
  notice 
  that 
  for 
  the 
  first 
  zone, 
  I(?' 
  L 
  ) 
  — 
  I(r 
  ) 
  =0*8378, 
  

   while 
  for 
  all 
  the 
  rest 
  I(r 
  oo 
  )— 
  I 
  {r^) 
  =0*1622 
  ; 
  it 
  is 
  thus 
  neces- 
  

   sary 
  to 
  subdivide 
  the 
  first 
  zone 
  into 
  a 
  series 
  of 
  subsidiary 
  

   zones 
  and 
  sum 
  their 
  effect 
  as 
  for 
  the 
  other 
  zones, 
  for 
  which 
  

   the 
  second 
  table 
  will 
  be 
  of 
  use. 
  In 
  addition 
  to 
  this, 
  we 
  shall 
  

   have 
  to 
  add 
  a 
  small 
  correction 
  for 
  a 
  few 
  zones 
  near 
  the 
  given 
  

   point, 
  inasmuch 
  as 
  we 
  multiply 
  the 
  height 
  of 
  the 
  step 
  by 
  the 
  

   arithmetical 
  mean 
  of 
  the 
  bounding 
  angles 
  of 
  zones, 
  instead 
  of 
  

   taking 
  some 
  other 
  proper 
  value 
  of 
  a 
  n 
  , 
  which 
  will 
  leave 
  no 
  

   error 
  during 
  the 
  mechanical 
  integration. 
  The 
  calculation 
  of 
  

   the 
  correction 
  will 
  be 
  simplified 
  by 
  assuming 
  the 
  zones 
  in 
  

   the 
  manner 
  above 
  described. 
  

  

  5. 
  Intensity 
  at 
  the 
  Rim 
  of 
  a 
  circular 
  Disk. 
  

  

  We 
  have 
  already 
  seen 
  how 
  the 
  intensity 
  at 
  the 
  centre 
  of 
  a 
  

   circular 
  disk 
  can 
  be 
  calculated 
  ; 
  we 
  shall 
  now 
  proceed 
  to 
  the 
  

   discussion 
  of 
  the 
  intensity 
  at 
  the 
  rim 
  of 
  the 
  disk, 
  and 
  then 
  

   obtain 
  the 
  result 
  for 
  a 
  general 
  case, 
  when 
  the 
  point 
  lies 
  inside 
  

   or 
  outside 
  the 
  disk. 
  

  

  Let 
  the 
  radius 
  of 
  the 
  circular 
  source 
  be 
  a 
  ; 
  then 
  the 
  dis- 
  

   tance 
  of 
  a 
  point 
  on 
  the 
  periphery 
  of 
  the 
  circle 
  will 
  be 
  

  

  r 
  = 
  2a 
  cos 
  0. 
  

  

  The 
  intensity 
  at 
  the 
  rim 
  r 
  = 
  is 
  given 
  by 
  

  

  drdO. 
  

  

  7T 
  Jo 
  J 
  V 
  

  

  Integrating 
  it 
  at 
  first 
  with 
  respect 
  to 
  y 
  we 
  can 
  bring 
  the 
  

   integral 
  under 
  the 
  form 
  

  

  = 
  -f 
  f 
  

  

  7T 
  JO 
  Jo 
  

   7T 
  Jo 
  T 
  

  

  2a 
  

  

  Ji 
  2 
  W 
  

  

  Ir 
  dd< 
  

  

  2« 
  

  

  cos 
  1 
  tt- 
  dr. 
  

  

  za 
  

  

  