﻿the 
  Echelon 
  Spectroscope. 
  381 
  

  

  are 
  poorly 
  defined 
  and 
  the 
  spreading 
  of 
  the 
  light 
  brings 
  into 
  

   greater 
  prominence 
  the 
  broad 
  diffraction-bands 
  corresponding 
  

   to 
  the 
  narrow 
  sources 
  represented 
  by 
  the 
  illuminated 
  end- 
  

   faces 
  of 
  the 
  plates. 
  When 
  the 
  echelon 
  and 
  prism 
  are 
  used 
  

   together, 
  as 
  in 
  fig. 
  1 
  , 
  the 
  reflected 
  spectrum 
  of 
  the 
  green 
  

   mercury-line 
  may 
  be 
  made 
  to 
  overlap 
  the 
  direct 
  spectrum 
  of 
  

   the 
  violet 
  line 
  by 
  giving 
  a 
  small 
  negative 
  value. 
  I 
  think 
  

   it 
  would 
  be 
  an 
  advantage 
  to 
  have 
  the 
  ends 
  of 
  the 
  plates 
  

   polished 
  or 
  blackened. 
  

  

  The 
  position 
  of 
  minimum 
  deviation. 
  — 
  As 
  the 
  echelon 
  is 
  ro- 
  

   tated 
  from 
  one 
  side 
  of 
  the 
  normal 
  position 
  to 
  the 
  other, 
  the 
  

   orders 
  first 
  move 
  across 
  the 
  field 
  of 
  view 
  in 
  the 
  direction 
  of 
  

   decreasing 
  deviation 
  (measured 
  by 
  ^/r) 
  and 
  then 
  turn 
  round 
  

   and 
  go 
  back 
  again. 
  If 
  the 
  value 
  of 
  R 
  happens 
  to 
  be 
  a 
  whole 
  

   number 
  of 
  wave-lengths 
  for 
  normal 
  incidence, 
  say 
  m\, 
  then 
  

   the 
  mih. 
  order 
  will 
  come 
  to 
  its 
  position 
  of 
  minimum 
  deviation 
  

   in 
  the 
  position 
  of 
  greatest 
  brightness 
  when 
  ^ 
  = 
  0, 
  but 
  higher 
  

   and 
  lower 
  orders 
  will 
  not 
  then 
  be 
  quite 
  in 
  their 
  positions 
  

   of 
  minimum 
  deviation. 
  Consider, 
  for 
  example, 
  a 
  lower 
  

   order 
  : 
  i/r 
  (or 
  in 
  the 
  reversed 
  case 
  i|r') 
  will 
  be 
  positive, 
  and 
  

   its 
  value 
  when 
  ^ 
  = 
  can 
  be 
  reduced 
  a 
  little 
  by 
  increasing 
  

   6 
  (in 
  the 
  positive 
  direction), 
  as 
  at 
  first 
  the 
  value 
  of 
  R 
  is 
  

   almost 
  stationary, 
  while 
  e 
  is 
  increasing, 
  and 
  therefore 
  the 
  

   dispersion 
  is 
  decreasing. 
  

  

  By 
  differentiating 
  the 
  general 
  equations 
  (1) 
  and 
  (1 
  A), 
  it 
  

   will 
  be 
  found 
  that 
  the 
  conditions 
  for 
  the 
  turning-points 
  in 
  the 
  

   direct 
  and 
  reversed 
  cases 
  are, 
  

  

  ^R 
  , 
  de 
  , 
  ^R 
  ,,df 
  

  

  d6=^dd 
  ""''^ 
  d6=^de' 
  

  

  Substituting 
  the 
  values 
  of 
  the 
  differential 
  coefficients 
  and 
  

   calling 
  the 
  minimum 
  values 
  of 
  the 
  deviation 
  in 
  the 
  two 
  cases 
  

   yjr^ 
  and 
  -yjr^^ 
  and 
  the 
  corresponding 
  angles 
  of 
  incidence 
  

   ^jj- 
  and 
  6^^, 
  

  

  Hence 
  as 
  the 
  echelon 
  is 
  rotated, 
  so 
  as 
  to 
  increase 
  6, 
  the 
  orders 
  

   higher 
  than 
  the 
  ??ith 
  come 
  to 
  their 
  minimum 
  deviation 
  

   positions 
  before 
  the 
  echelon 
  is 
  normal 
  to 
  the 
  light, 
  and 
  the 
  

   lower 
  orders 
  have 
  their 
  minimum 
  deviation 
  after 
  the 
  normal 
  

   position 
  is 
  passed. 
  The 
  central 
  orders 
  are 
  very 
  nearly 
  in 
  

   their 
  positions 
  of 
  minimum 
  deviation 
  when 
  6 
  = 
  0. 
  If 
  a/tq 
  

   and 
  -^0^ 
  are 
  written 
  for 
  the 
  values 
  of 
  -^ 
  and 
  yjr' 
  in 
  this 
  case. 
  

  

  