﻿762 
  Prof. 
  R. 
  W. 
  Wood 
  on 
  Talbot's 
  Fringes 
  

  

  to 
  tlie 
  increasing 
  deviation 
  produced 
  by 
  the 
  prism. 
  If 
  the 
  

   compensation 
  is 
  perfect 
  the 
  prismatic 
  dispersion 
  will 
  shut 
  up 
  

   the 
  picket-fence 
  arrangement 
  of 
  lineis 
  in 
  the 
  diagram 
  into 
  

   single 
  lines 
  ; 
  in 
  other 
  words, 
  if 
  we 
  illuminate 
  the 
  slit 
  simul- 
  

   taneously 
  with 
  all 
  of 
  the 
  wave-lengths 
  in 
  the 
  given 
  range 
  of 
  

   100 
  A.E. 
  we 
  shall 
  not 
  see 
  a 
  short 
  continuous 
  spectrum, 
  but 
  

   single 
  bright 
  lines, 
  to 
  the 
  intensity 
  of 
  which 
  all 
  the 
  waves 
  

   contribute. 
  These 
  lines 
  are 
  of 
  course 
  much 
  narrower 
  than 
  

   the 
  corresponding 
  range 
  of 
  the 
  continuous 
  spectrum 
  which 
  

   would 
  be 
  formed 
  in 
  the 
  absence 
  of 
  the 
  plate. 
  We 
  thus 
  see 
  

   that 
  the 
  retardation 
  has 
  the 
  effect 
  of 
  compressing 
  a 
  narrow 
  

   region 
  of 
  the 
  spectrum 
  into 
  a 
  much 
  narrower 
  one 
  which 
  con- 
  

   stitutes 
  one 
  of 
  the 
  bright 
  Talbot 
  bands. 
  If 
  we 
  consider 
  what 
  

   happens 
  to 
  the 
  entire 
  spectrum, 
  we 
  can 
  perhaps 
  obtain 
  a 
  still 
  

   clearer 
  idea 
  of 
  how 
  the 
  bands 
  are 
  formed. 
  

  

  Consider 
  a 
  large 
  number 
  of 
  equidistant 
  monochromatic 
  

   constituents 
  of 
  the 
  spectrum: 
  call 
  these 
  the 
  lines 
  A. 
  Mid- 
  

   way 
  between 
  them 
  is 
  another 
  set 
  of 
  lines 
  B. 
  The 
  distance 
  

   from 
  a 
  line 
  A 
  to 
  B 
  is 
  such 
  that 
  the 
  difference 
  in 
  the 
  retarda- 
  

   tion 
  for 
  the 
  two 
  lines 
  is 
  half 
  a 
  wave-length. 
  If 
  the 
  retar- 
  

   dation 
  for 
  the 
  A 
  lines 
  is 
  an 
  even 
  number 
  of 
  half 
  waves, 
  they 
  

   will 
  remain 
  single 
  and 
  fixed 
  in 
  position. 
  The 
  lines 
  B 
  will, 
  

   however, 
  double 
  and 
  fall 
  upon 
  the 
  neighbouring 
  lines 
  A. 
  

   The 
  regions 
  previously 
  occupied 
  by 
  the 
  lines 
  B 
  are 
  the 
  dark 
  

   Talbot 
  fringes. 
  It 
  may 
  at 
  first 
  sight 
  appear 
  as 
  if 
  the 
  same 
  

   result 
  would 
  be 
  obtained 
  regardless 
  of 
  the 
  side 
  on 
  which 
  the 
  

   retarding 
  plate 
  was 
  introduced. 
  It 
  obviously 
  would 
  for 
  the 
  

   wave-lengths 
  A 
  and 
  B; 
  but 
  if 
  we 
  consider 
  the 
  elements 
  of 
  

   the 
  spectrum 
  between 
  the 
  A 
  and 
  B 
  lines, 
  we 
  shall 
  see 
  that 
  in 
  

   one 
  case 
  they 
  are 
  shifted 
  so 
  as 
  to 
  fall 
  upon 
  the 
  stationary 
  

   lines 
  A, 
  while 
  in 
  the 
  other 
  they 
  are 
  moved 
  into 
  the 
  region 
  

   between. 
  In 
  the 
  latter 
  case 
  we 
  have 
  a 
  continuous 
  spectrum 
  

   if 
  we 
  consider 
  the 
  widths 
  of 
  the 
  regions 
  A 
  and 
  B 
  infinitely 
  

   narrow\ 
  In 
  the 
  foregoing 
  treatment 
  we 
  have 
  considered 
  the 
  

   condition 
  as 
  that 
  of 
  the 
  " 
  best 
  thickness 
  " 
  which 
  obtains 
  -when 
  

   shifts 
  due 
  to 
  retardation 
  and 
  prismatic 
  dispersion 
  exactly 
  

   compensate. 
  It 
  is 
  clear 
  also 
  that 
  to 
  obtain 
  the 
  ])ands 
  the 
  

   aperture 
  must 
  be 
  somewhat 
  restricted 
  so 
  as 
  to 
  obtain 
  an 
  

   appreciable 
  doubling 
  of 
  the 
  lines 
  for 
  which 
  the 
  retardation 
  

   is 
  an 
  odd 
  number 
  of 
  half 
  waves. 
  

  

  I 
  have 
  verified 
  all 
  of 
  these 
  points 
  experimentally 
  to 
  make 
  

   sure 
  that 
  no 
  slip 
  had 
  been 
  made. 
  To 
  show 
  that 
  the 
  different 
  

   monochromatic 
  constituents 
  were 
  differently 
  affected 
  by 
  the 
  

   retarding 
  plate, 
  three 
  spectra 
  were 
  photographed 
  in 
  coinci- 
  

   dence. 
  The 
  first 
  (No. 
  3) 
  shows 
  the 
  Talbot 
  bands 
  with 
  white 
  

   light 
  illuminating 
  the 
  slit, 
  the 
  second 
  (No. 
  2) 
  with 
  the 
  iron 
  

  

  