﻿336 
  

  

  Dr. 
  G. 
  Johnstone 
  Stoney 
  on 
  

  

  Let 
  5' 
  represent 
  diagrammatically 
  the 
  minute 
  hole 
  through 
  

   which 
  the 
  light 
  has 
  been 
  admitted 
  and 
  let 
  the 
  point 
  z' 
  be 
  

  

  N 
  

  

  Z'< 
  

  

  the 
  middle 
  point 
  o£ 
  the 
  small 
  object 
  z 
  f 
  upon 
  which 
  the 
  trans- 
  

   mitted 
  light 
  is 
  incident. 
  Then 
  the 
  light 
  of 
  any 
  one 
  wave- 
  

   length 
  \, 
  which 
  reaches 
  point 
  z' 
  through 
  the 
  hole 
  is 
  resolvable 
  

   into 
  innumerable 
  ufw's 
  (undulations 
  of 
  flat 
  wavelets) 
  to 
  

   which 
  the 
  lines 
  p\z 
  , 
  p 
  2 
  z', 
  p 
  3 
  z 
  f 
  , 
  &c. 
  will 
  be 
  normals 
  — 
  pi, 
  p 
  2 
  , 
  &c. 
  

   being 
  the 
  several 
  points 
  of 
  the 
  circular 
  disk 
  s'. 
  Consider 
  

   one 
  of 
  these 
  undulations, 
  suppose 
  that 
  which 
  has 
  p 
  x 
  z 
  } 
  for 
  its 
  

   normal, 
  and 
  which 
  we 
  shall 
  call 
  undulation 
  P 
  2 
  . 
  Next 
  

   imagine 
  two 
  other 
  u 
  f 
  w's, 
  + 
  Qi 
  and 
  — 
  Q 
  lf 
  to 
  be 
  transmitted 
  

   along 
  the 
  dotted 
  line 
  qz' 
  which 
  stands 
  for 
  the 
  axis 
  of 
  the 
  

   acute 
  cone 
  which 
  is 
  figured 
  in 
  the 
  diagram. 
  Of 
  these, 
  +Q 
  t 
  

   is 
  to 
  be 
  exactly 
  like 
  P 
  x 
  in 
  every 
  respect 
  except 
  that 
  it 
  is 
  to 
  

   advance 
  in 
  the 
  fixed 
  direction 
  qz' 
  instead 
  of 
  in 
  the 
  inclined 
  

   direction 
  p 
  x 
  z' 
  ; 
  and 
  let 
  — 
  Q 
  il 
  be 
  an 
  undulation 
  identical 
  

   with 
  + 
  Q 
  1 
  except 
  that 
  it 
  follows 
  it 
  half 
  a 
  wave-length 
  behind. 
  

   + 
  Qi 
  and 
  — 
  Q 
  x 
  will 
  then 
  be 
  everywhere 
  of 
  equal 
  intensity 
  

   but 
  in 
  opposite 
  phases, 
  and 
  will 
  simply 
  cancel 
  one 
  another. 
  

   Accordingly 
  their 
  introduction 
  has 
  been 
  legitimate, 
  since 
  it 
  

   has 
  made 
  no 
  optical 
  change. 
  We 
  may, 
  however, 
  take 
  

   another 
  view 
  of 
  what 
  has 
  been 
  done. 
  The 
  undulations 
  Pj 
  

   and 
  — 
  Qi 
  if 
  acting 
  alone 
  would 
  be 
  competent 
  to 
  produce 
  on 
  

   plane 
  Z' 
  a 
  ruling 
  of 
  alternate 
  bright 
  and 
  dark 
  bands, 
  the 
  

   point 
  z' 
  being 
  situated 
  in 
  the 
  middle 
  of 
  one 
  of 
  the 
  dark 
  bands 
  

   where 
  the 
  illumination 
  is 
  zero, 
  wdiile 
  at 
  situations 
  so 
  close 
  to 
  

   z' 
  that 
  they 
  are 
  within 
  the 
  darker 
  parts 
  of 
  the 
  dark 
  band, 
  

   the 
  illumination 
  due 
  to 
  the 
  presence 
  of 
  Pi 
  and 
  — 
  Qi 
  will 
  be 
  

   faint. 
  It 
  follows 
  from 
  this 
  that 
  the 
  resultant 
  effect 
  within 
  

   this 
  small 
  range 
  of 
  the 
  three 
  undulations 
  P 
  l5 
  — 
  Q 
  ± 
  and 
  + 
  Q 
  (1 
  

   will 
  be 
  practically 
  undistinguishable 
  from 
  the 
  effect 
  which 
  

   would 
  be 
  produced 
  by 
  + 
  Qj 
  acting 
  alone. 
  It 
  thus 
  appears 
  

   that 
  if 
  we 
  only 
  need 
  to 
  deal 
  with 
  what 
  happens 
  to 
  a 
  small 
  

  

  