﻿the 
  Echelon 
  Spectroscope. 
  

  

  377 
  

  

  These 
  equations 
  only 
  differ 
  from 
  (8) 
  and 
  (8 
  A) 
  by 
  the 
  

   addition 
  of 
  small 
  terms 
  depending 
  on 
  y^° 
  and 
  ^/r'^, 
  whose 
  

   values 
  are 
  given 
  in 
  Table 
  I. 
  below. 
  

  

  Position 
  of 
  the 
  Orders 
  in 
  the 
  Field 
  of 
  View 
  

   and 
  Dispersion. 
  

  

  According 
  to 
  the 
  first 
  approximation 
  formulae 
  (l)and 
  (lA) 
  

  

  R 
  — 
  nk 
  , 
  ,, 
  R 
  — 
  n\ 
  

  

  and 
  Y 
  — 
  

  

  e 
  ■ 
  t 
  

  

  R, 
  e. 
  and/ 
  depend 
  on 
  ^ 
  but 
  not 
  on 
  i/r 
  ; 
  so 
  the 
  orders 
  are 
  

   equally 
  spaced 
  and 
  the 
  dispersions, 
  given 
  by 
  

  

  d^ 
  

  

  d±_ 
  "-^a 
  

  

  d\ 
  p 
  

  

  ""•^ 
  s= 
  

  

  dfi, 
  

  

  : 
  ? 
  

  

  / 
  

  

  do 
  not 
  vary 
  along 
  the 
  spectrum. 
  

   The 
  second 
  approximation 
  formulae 
  (10) 
  and 
  (10 
  A) 
  give 
  

  

  , 
  R 
  — 
  72\ 
  , 
  ,, 
  R— 
  nX 
  

  

  \ 
  s 
  2 
  s 
  ^ 
  J 
  V 
  s 
  fju 
  2 
  s 
  fju 
  J 
  

  

  If 
  the 
  echelon 
  is 
  rotated 
  a 
  little, 
  so 
  that 
  one 
  order, 
  say 
  

   the 
  mth, 
  is 
  in 
  the 
  position 
  of 
  maximum 
  brightness 
  where 
  

   -v^ 
  or 
  -^' 
  — 
  0, 
  

  

  s 
  z 
  s 
  ^ 
  s 
  fjb 
  2 
  s 
  fji 
  

  

  Table 
  I. 
  gives 
  the 
  values 
  of 
  the 
  small 
  terms 
  in 
  the 
  denomi- 
  

   nators 
  depending 
  on 
  -^jr 
  and 
  -yjr' 
  for 
  the 
  first 
  five 
  orders 
  on 
  

   either 
  side 
  of 
  the 
  central 
  order. 
  

  

  Table 
  I. 
  

  

  m'^^i. 
  

  

  1 
  t 
  , 
  

  

  1 
  t 
  r. 
  

  

  2 
  s 
  fx 
  

  

  1 
  

  

  •003 
  

   •005 
  

   •008 
  

   •010 
  

   •013 
  

  

  •002 
  

   •003 
  

   •005 
  

   •006 
  

   •008 
  

  

  2 
  

  

  3 
  

  

  4 
  

  

  5 
  

  

  

  