﻿434 
  Dr. 
  S. 
  R. 
  Milner 
  on 
  Interference-Fringes 
  

  

  width 
  of 
  the 
  fringes 
  is 
  now 
  a 
  minimum, 
  and 
  it 
  may 
  be 
  so 
  

   small 
  that 
  they 
  cannot 
  be 
  seen 
  except 
  with 
  a 
  microscope*. 
  

  

  4. 
  Effect 
  of 
  Displacement 
  of 
  one 
  Plate 
  on 
  the 
  other. 
  — 
  This 
  

   will 
  in 
  general 
  alter 
  the 
  length 
  of 
  the 
  optical 
  path 
  of 
  one 
  of 
  

   the 
  interfering 
  beams, 
  and 
  produce 
  a 
  rapid 
  motion 
  of 
  the 
  

   fringes 
  across 
  the 
  field. 
  There 
  are, 
  however, 
  two 
  special 
  

   directions 
  of 
  motion 
  in 
  which 
  this 
  will 
  not 
  be 
  the 
  case. 
  If 
  

   the 
  plate 
  i. 
  is 
  moved 
  along 
  a 
  contour-line 
  of 
  ii., 
  the 
  fringes 
  

   will 
  remain 
  apparently 
  fixed 
  to 
  plate 
  i. 
  ; 
  if 
  it 
  is 
  moved 
  along- 
  

   one 
  of 
  its 
  own 
  contour-lines, 
  the 
  fringes 
  will 
  remain 
  apparently 
  

   fixed 
  to 
  plate 
  ii. 
  

  

  5. 
  Examination 
  of 
  Plate-glass 
  Sheet. 
  — 
  By 
  making 
  use 
  of 
  

   the 
  properties 
  of 
  the 
  fringes 
  enumerated 
  in 
  the 
  above 
  

   paragraphs, 
  one 
  can 
  run 
  over 
  a 
  large 
  sheet 
  of 
  plate-glass, 
  

   and 
  either 
  determine 
  its 
  best 
  portion 
  as 
  regards 
  uniformity 
  

   in 
  thickness, 
  or 
  plot 
  out 
  its 
  contour-lines 
  and 
  measure 
  the 
  

   angle 
  of 
  its 
  wedge, 
  with 
  great 
  ease. 
  Having 
  chosen 
  a 
  small 
  

   square 
  of 
  glass 
  of 
  approximately 
  the 
  same 
  thickness 
  as 
  the 
  

   sheet 
  (this 
  is 
  most 
  simply 
  done 
  by 
  cutting 
  off 
  a 
  small 
  piece 
  

   from 
  the 
  plate 
  itself), 
  we 
  place 
  it 
  anywhere 
  on 
  the 
  sheet, 
  and 
  

   Jet 
  the 
  light 
  from 
  a 
  sodium 
  burner 
  fall 
  on 
  the 
  two 
  at 
  an 
  

   angle 
  of 
  about 
  45°. 
  On 
  holding 
  a 
  card 
  in 
  the 
  incident 
  light 
  

   and 
  examining 
  the 
  shadow 
  the 
  fringes 
  can 
  often 
  be 
  seen 
  at 
  

   once. 
  They 
  may, 
  however, 
  be 
  too 
  tine 
  to 
  see, 
  in 
  which 
  case 
  

   they 
  will 
  usually 
  come 
  prominently 
  into 
  view 
  if 
  we 
  slowly 
  

   rotate 
  the 
  small 
  piece 
  on 
  the 
  surface 
  of 
  the 
  other, 
  and 
  by 
  

   further 
  rotation 
  they 
  may 
  be 
  broadened 
  as 
  desired 
  (v. 
  § 
  3). 
  

   If 
  we 
  then 
  fix 
  the 
  attention 
  on 
  a 
  particular 
  fringe 
  and 
  move 
  

   the 
  small 
  piece 
  by 
  trial 
  always 
  in 
  such 
  a 
  direction 
  that 
  the 
  

   fringe 
  remains 
  apparently 
  fixed 
  to 
  it, 
  a 
  contour-line 
  of 
  the 
  

   large 
  sheet 
  will 
  be 
  traced 
  out. 
  

  

  When 
  a 
  contour-line 
  has 
  been 
  obtained 
  it 
  is 
  easy 
  to 
  

   measure 
  the 
  angle 
  of 
  the 
  wedge 
  formed 
  by 
  the 
  sheet 
  at 
  any 
  

   point. 
  Move 
  the 
  small 
  piece 
  at 
  right 
  angles 
  to 
  the 
  contour- 
  

   line 
  and 
  count 
  the 
  number 
  of 
  fringes 
  which 
  pass 
  by 
  a 
  fixed 
  

  

  * 
  While 
  the 
  fringes 
  in 
  their 
  positions 
  of 
  maximum 
  and 
  minimum 
  

   fringe 
  width 
  are 
  always 
  parallel 
  to 
  the 
  contour-lines, 
  their 
  intermediate 
  

   positions 
  as 
  one 
  wedge 
  is 
  rotated 
  vary 
  considerably 
  with 
  the 
  angles 
  of 
  

   the 
  wedges. 
  All 
  possible 
  cases 
  are 
  comprised 
  in 
  the 
  following 
  formula 
  

   which 
  follows 
  simply 
  from 
  the 
  geometry 
  of 
  the 
  two 
  wedges. 
  Let 
  a 
  } 
  a 
  2 
  

   be 
  the 
  angles 
  of 
  the 
  wedges 
  i. 
  and 
  ii., 
  the 
  angle 
  BAB' 
  between 
  their 
  

   contour-lines, 
  <£ 
  the 
  angle 
  BAC 
  which 
  the 
  fringes 
  make 
  with 
  a 
  contour- 
  

   line 
  of 
  wedge 
  i., 
  £ 
  the 
  fringe 
  width, 
  then 
  

  

  2cosr 
  „ 
  . 
  n 
  1 
  . 
  . 
  , 
  1 
  . 
  

   — 
  -T- 
  — 
  £ 
  sin 
  = 
  - 
  sin 
  ((p—Q) 
  = 
  - 
  sin 
  (p, 
  

  

  r 
  being 
  the 
  angle 
  of 
  refraction, 
  and 
  X 
  the 
  wave-length 
  of 
  the 
  light 
  in 
  the 
  

   glass. 
  

  

  