﻿760 
  Prof. 
  li. 
  W. 
  AVood 
  on 
  Talbot's 
  Fringes 
  

  

  oxist 
  simultaneously, 
  and 
  all 
  trace 
  of 
  the 
  maxima 
  and 
  minima 
  

   will 
  disappear 
  owing 
  to 
  the 
  form 
  of 
  the 
  intensity 
  curve 
  ; 
  in 
  

   other 
  words, 
  the 
  lines 
  are 
  not 
  resolved. 
  

  

  If, 
  however, 
  we 
  increase 
  the 
  number 
  of 
  retarding 
  plates, 
  

   placing 
  them 
  so 
  as 
  to 
  divide 
  the 
  aperture 
  into 
  a 
  number 
  of 
  

   vertical 
  strips 
  of 
  equal 
  width, 
  the 
  width 
  of 
  the 
  maxima 
  

   decreases 
  in 
  proportion 
  to 
  the 
  distance 
  between 
  them, 
  as 
  in 
  

   the 
  case 
  of 
  the 
  ordinary 
  diffraction-grating 
  when 
  we 
  increase 
  

   the 
  number 
  of 
  lines, 
  and 
  we 
  have 
  resolution 
  of 
  the 
  lines. 
  

   Our 
  aperture 
  is 
  now 
  acting 
  as 
  an 
  echelon 
  grating, 
  set 
  in 
  

   position 
  of 
  single 
  order 
  for 
  one 
  train 
  of 
  waves 
  and 
  double 
  

   order 
  for 
  the 
  other. 
  With 
  very 
  thick 
  plates, 
  as 
  in 
  the 
  case 
  

   of 
  echelons 
  such 
  as 
  are 
  actually 
  used, 
  it 
  is 
  evident 
  that 
  a 
  very 
  

   minute 
  change 
  in 
  wave-length 
  will 
  be 
  sufficient 
  to 
  change 
  

   the 
  retardation 
  by 
  the 
  amount 
  necessary 
  for 
  resolution. 
  We 
  

   are 
  now 
  in 
  a 
  position 
  to 
  discuss 
  the 
  effect 
  of 
  the 
  thickness 
  of 
  

   the 
  plates, 
  their 
  number, 
  and 
  the 
  width 
  of 
  the 
  steps. 
  De- 
  

   creasing 
  the 
  width 
  of 
  the 
  steps 
  increases 
  the 
  width 
  of 
  the 
  

   space 
  between 
  the 
  spectra, 
  in 
  other 
  words, 
  forms 
  the 
  system 
  

   of 
  maxima 
  and 
  minima 
  on 
  a 
  laro-er 
  scale. 
  Increasino- 
  the 
  

   thickness 
  decreases 
  the 
  change 
  in 
  wave-length 
  necessary 
  in 
  

   passing 
  from 
  the 
  condition 
  of 
  single 
  order 
  to 
  that 
  of 
  double 
  

   order, 
  in 
  other 
  words 
  the 
  greater 
  the 
  thickness 
  the 
  greater 
  

   will 
  be 
  the 
  shift 
  of 
  a 
  maximum 
  for 
  a 
  very 
  minute 
  change 
  in 
  

   X, 
  and 
  in 
  consequence 
  the 
  greater 
  the 
  resolving 
  power. 
  An 
  

   increase 
  in 
  the 
  number 
  of 
  plates 
  merely 
  reduces 
  the 
  width 
  

   of 
  the 
  maxima, 
  without 
  affecting 
  the 
  distance 
  between 
  them, 
  

   or 
  the 
  amount 
  of 
  shift 
  produced 
  by 
  a 
  given 
  change 
  of 
  X. 
  

   This 
  then 
  is 
  the 
  whole 
  theory 
  of 
  the 
  echelon 
  in 
  a 
  nutshell 
  

   (a 
  coco-nut 
  perhaps). 
  Personally 
  I 
  have 
  found 
  that 
  a 
  class 
  

   can 
  be 
  made 
  to 
  understand 
  the 
  echelon 
  much 
  more 
  clearly 
  

   by 
  this 
  method 
  than 
  by 
  prolonged 
  study 
  of 
  the 
  mathematical 
  

   treatment. 
  I 
  have 
  already 
  given 
  a 
  very 
  simple 
  treatment 
  of 
  

   the 
  decrease 
  in 
  the 
  width 
  of 
  the 
  principal 
  maxima, 
  and 
  the 
  

   increase 
  in 
  the 
  number 
  of 
  the 
  secondary 
  maxima 
  in 
  the 
  case 
  

   of 
  the 
  ordinary 
  diffraction-grating 
  as 
  the 
  number 
  of 
  lines 
  is 
  

   increased 
  (Phil. 
  Mag. 
  vol. 
  xiv. 
  p. 
  477 
  (1907)). 
  

  

  We 
  are 
  now 
  ready 
  for 
  the 
  Talbot 
  fringes. 
  

  

  Consider 
  the 
  slit 
  of 
  a 
  spectrometer 
  illuminated 
  with 
  mono- 
  

   chromatic 
  light, 
  the 
  prism, 
  aperture, 
  and 
  retarding 
  plate 
  

   arranged 
  as 
  shown 
  in 
  fig. 
  1. 
  If 
  the 
  plate 
  retards 
  the 
  stream 
  

   an 
  even 
  number 
  of 
  half 
  wave-lengths, 
  we 
  shall 
  see 
  in 
  the 
  

   instrument 
  a 
  single 
  bright 
  line 
  with 
  accompanying 
  faint 
  

   maxima 
  and 
  minima. 
  If 
  we 
  now 
  decrease 
  the 
  wave-length 
  

   a 
  trifle 
  the 
  line 
  will 
  move 
  a 
  little 
  to 
  the 
  right, 
  if 
  we 
  disregard 
  

   the 
  action 
  of 
  the 
  prism. 
  We 
  can 
  verify 
  this 
  experimentally 
  

  

  