﻿N 
  on-reversed 
  Spectrum 
  Interferometry. 
  149 
  

  

  fig. 
  18, 
  that 
  if 
  N 
  is 
  displaced 
  to 
  M\ 
  over 
  a 
  distance 
  e, 
  the 
  

   pencil 
  J 
  is 
  displaced 
  parallel 
  to 
  itself 
  over 
  

  

  s 
  = 
  2e 
  sin 
  8/2 
  

  

  where 
  S 
  = 
  90° 
  — 
  0. 
  The 
  pencil 
  c 
  is 
  then 
  displaced 
  parallel 
  to 
  

   itself 
  over 
  a 
  distance 
  

  

  t 
  = 
  s 
  tan 
  <p' 
  /2 
  = 
  s. 
  

  

  Since 
  = 
  49° 
  45', 
  8/2 
  = 
  20° 
  7' 
  and 
  therefore 
  * 
  = 
  2e 
  X 
  '344 
  = 
  

   •7 
  <?, 
  nearly. 
  If 
  the 
  rotation 
  of 
  fringes 
  is 
  but 
  90°, 
  either 
  s 
  (or 
  

   s/2) 
  is 
  also 
  the 
  breadth 
  of 
  the 
  strips, 
  or 
  patches 
  of 
  like 
  origin 
  

   which, 
  when 
  sliding 
  over 
  each 
  other 
  more 
  or 
  less, 
  produce 
  the 
  

   fringes. 
  This 
  may 
  be 
  treated 
  from 
  a 
  graphic 
  point 
  of 
  view 
  as 
  

   follows, 
  a 
  theory 
  not 
  being 
  aimed 
  at. 
  

  

  In 
  fig. 
  18a, 
  let 
  a 
  and 
  b 
  be 
  two 
  patches 
  of 
  light 
  of 
  like 
  

   color 
  and 
  origin 
  at 
  the 
  objective 
  pp, 
  fig. 
  18, 
  producing 
  inter- 
  

   ferences 
  at 
  the 
  focus 
  F, 
  fig. 
  18. 
  Hence 
  the 
  fringes 
  will 
  be 
  

   arranged 
  in 
  the 
  direction 
  f, 
  fig. 
  18a, 
  at 
  right 
  angles 
  to 
  the 
  line 
  

   joining 
  a 
  and 
  b. 
  Since 
  a 
  and 
  b 
  here 
  correspond 
  to 
  c 
  and 
  c' 
  in 
  

   i\g. 
  18, 
  let 
  a 
  be 
  continually 
  displaced 
  to 
  the 
  right, 
  as 
  indi- 
  

   cated 
  by 
  the 
  arrows. 
  In 
  proportion 
  as 
  the 
  positions 
  ab, 
  a'b' 
  , 
  

   a"b" 
  ', 
  are 
  taken, 
  the 
  fringes 
  must 
  pass 
  by 
  rotation 
  from/, 
  into 
  

   /', 
  intoy", 
  etc. 
  ; 
  i. 
  e., 
  over 
  abont 
  90°. 
  In 
  the 
  present 
  experi- 
  

   ment, 
  c, 
  fig. 
  18, 
  can 
  never 
  pass 
  across 
  c' 
  , 
  for 
  they 
  are 
  essen- 
  

   tially 
  separated 
  by 
  the 
  edge 
  of 
  the 
  right 
  angled 
  prism 
  P 
  r 
  . 
  

   Hence 
  the 
  rotation 
  can 
  not 
  exceed 
  90°, 
  for 
  the 
  vertical 
  through 
  

   a 
  cannot 
  cross 
  the 
  vertical 
  through 
  b. 
  This 
  is 
  not 
  the 
  case 
  

   when 
  a 
  grating 
  replaces 
  P\ 
  as 
  in 
  iig. 
  14 
  ; 
  nor 
  is 
  it 
  the 
  case 
  

   when, 
  as 
  in 
  an 
  earlier 
  paper, 
  inverted 
  spectra 
  are 
  treated, 
  and 
  

   the 
  patches 
  a 
  and 
  b 
  slide 
  along 
  the 
  edge 
  of 
  the 
  prism. 
  In 
  such 
  

   cases 
  fig. 
  18a 
  may 
  be 
  continued 
  symmetrically, 
  toward 
  the 
  

   right 
  (mirror 
  images) 
  and 
  the 
  limit 
  of 
  rotation 
  is 
  therefore 
  

   180°. 
  All 
  these 
  suggestions 
  are 
  borne 
  out 
  by 
  experiment. 
  

  

  Moreover 
  if 
  the 
  first 
  prism 
  P, 
  fig. 
  15, 
  is 
  tilted 
  slightly 
  

   on 
  an 
  axis 
  parallel 
  to 
  LT, 
  a 
  i^g. 
  18a) 
  will 
  be 
  lowered 
  and 
  

   b 
  raised. 
  If 
  a 
  and 
  b 
  are 
  on 
  the 
  same 
  level, 
  the 
  fringes 
  are 
  

   always 
  vertical 
  and 
  pass 
  through 
  a 
  vertical 
  maximum, 
  when 
  ab 
  

   is 
  a 
  minimum. 
  On 
  the 
  other 
  hand, 
  if 
  a 
  and 
  b 
  are 
  not 
  in 
  the 
  

   same 
  level, 
  as 
  in 
  the 
  figure, 
  fore 
  and 
  aft 
  motion 
  brings 
  the 
  

   rays 
  c 
  and 
  c' 
  (fig. 
  18) 
  to 
  or 
  from 
  the 
  edge 
  of 
  the 
  prism 
  P' 
  . 
  

   Hence 
  the 
  case 
  ab 
  passes 
  into 
  a"b" 
  , 
  or 
  the 
  reverse 
  ; 
  in 
  other 
  

   words 
  the 
  fringes 
  pass 
  through 
  a 
  horizontal 
  maximum 
  when 
  

   ab 
  is 
  a 
  minimum 
  ; 
  etc. 
  This 
  is 
  also 
  shown 
  by 
  experiment. 
  

  

  The 
  experiment 
  made 
  by 
  moving 
  screens 
  with 
  slits, 
  forward 
  

   or 
  rearward, 
  successively, 
  by 
  which 
  the 
  appearance 
  and 
  evanes- 
  

   cence 
  of 
  fringes 
  may 
  be 
  repeated 
  through 
  several 
  cycles, 
  is 
  next 
  

   to 
  be 
  explained. 
  Here 
  it 
  is 
  merely 
  necessary 
  to 
  remember 
  that 
  

  

  