﻿378 
  Dr. 
  H. 
  Stansfield 
  on 
  

  

  The 
  Wave-Length 
  Intervals 
  between 
  the 
  Orders. 
  

  

  The 
  repetition 
  o£ 
  a 
  line 
  in 
  a 
  number 
  o£ 
  orders 
  provides 
  an 
  

   echelon 
  spectrum 
  with 
  a 
  wave-length 
  scale 
  o£ 
  nearly 
  equal 
  

   divisions, 
  and 
  the 
  wave-length 
  value 
  of 
  these 
  divisions, 
  AX, 
  is 
  a 
  

   constant 
  o£ 
  the 
  echelon 
  which 
  can 
  be 
  calculated 
  for 
  any 
  

   wave-length 
  from 
  the 
  thickness 
  of 
  the 
  plates 
  and 
  the 
  re- 
  

   fractive 
  indices 
  given 
  for 
  the 
  glass. 
  The 
  expressions 
  for 
  A\ 
  

   for 
  the 
  direct 
  and 
  reversed 
  cases 
  may 
  be 
  obtained 
  from 
  the 
  

   general 
  equations. 
  Neglecting 
  the 
  terms 
  depending 
  on 
  6'^, 
  

   which 
  do 
  not 
  affect 
  the 
  values 
  by 
  more 
  than 
  one 
  part 
  in 
  

   ten 
  thousand^ 
  they 
  both 
  reduce 
  to 
  

  

  AX=- 
  

  

  . 
  da 
  

   n—t 
  ~ 
  

   d\ 
  

  

  The 
  changes 
  that 
  are 
  made 
  in 
  n 
  by 
  rotating 
  the 
  echelon 
  

   are 
  so 
  small 
  compared 
  with 
  its 
  whole 
  value 
  (10,070 
  for 
  this 
  

   echelon 
  and 
  the 
  green 
  mercury 
  light) 
  that 
  AX 
  is 
  sensibly 
  

   constant 
  for 
  all 
  positions. 
  On 
  the 
  other 
  hand, 
  A\ 
  may 
  be 
  

   increased 
  or 
  decreased 
  by 
  2 
  per 
  cent, 
  by 
  means 
  of 
  the 
  auxiliary 
  

   prism, 
  as 
  described 
  on 
  p. 
  373. 
  

  

  Notes 
  on 
  Changes 
  pkoduced 
  by 
  rotating 
  the 
  Echelon 
  

   ABOUT 
  A 
  Vertical 
  Axis. 
  

  

  Changes 
  in 
  brightness, 
  and 
  the 
  position 
  of 
  greatest 
  brightness. 
  — 
  

   As 
  an 
  order 
  is 
  moved 
  across 
  the 
  field 
  of 
  view 
  by 
  rotating 
  

   the 
  echelon, 
  it 
  crosses 
  the 
  lateral 
  maxima 
  of 
  the 
  distribution 
  

   of 
  light 
  due 
  to 
  the 
  individual 
  step 
  apertures, 
  disappearing 
  as 
  

   it 
  crosses 
  the 
  diffraction 
  minima, 
  and 
  having 
  its 
  greatest 
  

   brightness 
  as 
  it 
  crosses 
  the 
  central 
  diffraction 
  maximum. 
  

   This 
  position 
  of 
  greatest 
  brightness 
  corresponds 
  to 
  the 
  direc- 
  

   tion 
  of 
  the 
  regularly 
  refracted 
  rays, 
  and 
  is 
  the 
  origin 
  from 
  

   which 
  the 
  angle 
  i/r 
  is 
  measured. 
  It 
  does 
  not 
  quite 
  coincide 
  

   with 
  the 
  position 
  of 
  the 
  image 
  of 
  the 
  slit 
  when 
  the 
  echelon 
  is 
  

   removed, 
  the 
  position 
  of 
  greatest 
  brightness 
  being 
  displaced 
  

   towards 
  the 
  side 
  on 
  which 
  the 
  step-faces 
  of 
  the 
  echelon 
  lie. 
  

   This 
  displacement 
  indicates 
  that 
  the 
  echelon-plates 
  are 
  slightly 
  

   prismatic. 
  

  

  Changes 
  in 
  dispersion 
  and 
  retardation. 
  — 
  Some 
  of 
  the 
  

   effects 
  produced 
  by 
  rotating 
  the 
  echelon 
  about 
  a 
  vertical 
  

   axis 
  are 
  represented 
  in 
  fig. 
  3. 
  The 
  echelon 
  is 
  shown 
  at 
  A 
  

   rotated 
  so 
  as 
  to 
  make 
  negative 
  ; 
  in 
  this 
  case 
  e 
  is 
  smaller 
  

   and 
  therefore 
  (see 
  p. 
  377) 
  the 
  dispersion 
  is 
  larger 
  than 
  in 
  

  

  