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  LXX7III. 
  Talbot's 
  Fringes 
  and 
  the 
  Echelon 
  Grating. 
  By 
  

   R. 
  W. 
  Wood, 
  Professor 
  of 
  Experimental 
  Physics, 
  Johns 
  

   Hopkins 
  University* 
  , 
  , 
  . 
  

  

  [Plate 
  XXIIL] 
  ^ 
  . 
  

  

  SO 
  much 
  has 
  been 
  written 
  in 
  explanation 
  o£ 
  Talbot's 
  

   fringes 
  and 
  the 
  curious 
  circumstance 
  that 
  they 
  appear 
  

   only 
  when 
  the 
  retarding 
  plate 
  is 
  introduced 
  from 
  the 
  side 
  

   upon 
  which 
  the 
  red 
  of 
  the 
  spectrum 
  appears 
  (in 
  the 
  case 
  

   where 
  the 
  plate 
  is 
  in 
  front 
  of 
  the 
  objective 
  of 
  the 
  spectroscope) 
  

   that 
  it 
  may 
  appear 
  at 
  first 
  sight 
  that 
  anything 
  further 
  must 
  

   be 
  superfluous. 
  Personally 
  I 
  never 
  felt 
  satisfied 
  that 
  I 
  fully 
  

   understood 
  the 
  physical 
  explanation 
  of 
  this 
  circumstance 
  

   until 
  Schuster's 
  explanation 
  appeared, 
  which 
  is 
  quite 
  satisfying 
  

   and 
  very 
  easily 
  grasped. 
  On 
  looking 
  into 
  the 
  matter 
  a 
  little 
  

   more 
  fully, 
  and 
  subjecting 
  some 
  of 
  the 
  conclusions 
  drawn 
  

   fr 
  m 
  theoretical 
  considerations 
  to 
  the 
  test 
  of 
  experiment, 
  

   it 
  has 
  seemed 
  to 
  me 
  that 
  this 
  explanation 
  does 
  not 
  account 
  

   for 
  the 
  failure 
  of 
  the 
  fringes 
  to 
  appear 
  when 
  the 
  plate 
  is 
  

   introduced 
  from 
  the 
  wrong 
  side. 
  I 
  have 
  accordingly 
  been 
  

   forced 
  to 
  work 
  out 
  another 
  explanation, 
  which 
  I 
  believe 
  to 
  

   be 
  more 
  complete 
  and 
  to 
  present 
  less 
  difficulty 
  than 
  the 
  

   previous 
  ones. 
  The 
  conclusions 
  arrived 
  at 
  are 
  doubtless 
  

   contained 
  in 
  the 
  elaborate 
  mathematical 
  treatments 
  which 
  

   have 
  been 
  given 
  by 
  Airy 
  and 
  Stokes, 
  but 
  there 
  seems 
  to 
  be 
  a 
  

   good 
  deal 
  of 
  difficulty 
  in 
  forming 
  a 
  deffiiite 
  idea 
  of 
  just 
  what 
  

   happens 
  in 
  each 
  case 
  from 
  an 
  inspection 
  of 
  these 
  equations. 
  

   Incidentally 
  we 
  shall 
  find 
  that 
  the 
  echelon 
  grating 
  is 
  a 
  

   special 
  case 
  of 
  Talbot's 
  plate, 
  the 
  aperture 
  with 
  its 
  retarding 
  

   plate 
  being 
  simply 
  an 
  echelon 
  grating 
  of 
  two 
  elements. 
  

  

  The 
  treatment 
  given 
  by 
  Walker 
  (Phil. 
  Mag. 
  April 
  1906), 
  

   while 
  correct 
  as 
  far 
  as 
  it 
  goes, 
  makes 
  no 
  mention 
  of 
  the 
  

   splitting 
  of 
  certain 
  monochromatic 
  elements 
  of 
  the 
  continuous 
  

   spectrum 
  into 
  double 
  lines, 
  which 
  I 
  pointed 
  out 
  in 
  my 
  

   ' 
  Physical 
  Optics,' 
  and 
  is 
  in 
  addition 
  a 
  little 
  difficult 
  to 
  follow. 
  

   An 
  explanation 
  to 
  be 
  perfectly 
  satisfactory 
  should 
  enable 
  us 
  

   to 
  form 
  a 
  clear 
  picture 
  of 
  exactly 
  what 
  happens 
  to 
  each 
  

   monochromatic 
  element 
  of 
  the 
  continuous 
  spectrum, 
  and 
  how 
  

   these 
  elements 
  are 
  re-arranged 
  so 
  as 
  to 
  give 
  us 
  a 
  spectrum 
  

   traversed 
  by 
  black 
  bands. 
  

  

  The 
  following 
  brief 
  treatment 
  enables 
  us 
  to 
  understand 
  

   the 
  action 
  of 
  the 
  echelon 
  grating 
  and 
  all 
  of 
  the 
  peculiarities 
  

   of 
  the 
  Talbot 
  fringes. 
  Assume 
  plane 
  waves 
  of 
  monochro- 
  

   matic 
  light 
  incident 
  upon 
  a 
  rectangular 
  aperture, 
  brought 
  to 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  