﻿50 
  E. 
  E. 
  Merwin— 
  Interpolations 
  on 
  Spectrograms. 
  

  

  gram, 
  we 
  read 
  n' 
  for 
  X 
  + 
  #, 
  where 
  k 
  is 
  small 
  compared 
  with 
  X. 
  

   Then 
  the 
  equation 
  is 
  written 
  d%= 
  E 
  ; 
  ?i\ 
  +k 
  — 
  R' 
  (see 
  equa- 
  

   tion 
  8b). 
  The 
  value 
  of 
  k 
  depends 
  upon 
  the 
  type 
  of 
  spectrograph, 
  

   and 
  in 
  some 
  cases 
  upon 
  the 
  part 
  of 
  the 
  spectrum 
  photo- 
  

   graphed. 
  The 
  relative 
  positions 
  of 
  the 
  lenses 
  and 
  the 
  photo- 
  

   graphic 
  plate 
  with 
  respect 
  to 
  the 
  prism 
  seldom 
  if 
  ever 
  affect 
  

   the 
  deviations 
  sufficiently 
  to 
  necessitate 
  a 
  change 
  in 
  the 
  value 
  

   of 
  k. 
  Therefore 
  k 
  can 
  be 
  found 
  once 
  for 
  all 
  for 
  a 
  given 
  

   spectrograph, 
  k 
  can 
  be 
  evaluated 
  in 
  a 
  few 
  minutes 
  by 
  trial 
  

   and 
  error, 
  by 
  selecting 
  such 
  values 
  of 
  X 
  + 
  k 
  as 
  will 
  make 
  the 
  

   deviation 
  for 
  some 
  central 
  line 
  nearly 
  zero. 
  (If 
  the 
  spectro- 
  

   gram 
  includes 
  wave-lengtbs 
  longer 
  than 
  *33 
  /-t, 
  then 
  k 
  need 
  not 
  

   be 
  determined 
  closer 
  than 
  *01 
  p.) 
  

  

  When 
  k 
  has 
  been 
  determined 
  it 
  may 
  be 
  added 
  to 
  the 
  values 
  

   of 
  X 
  at 
  the 
  margin 
  of 
  the 
  table, 
  and 
  X 
  + 
  k 
  written 
  in 
  place 
  of 
  

   X 
  in 
  the 
  table. 
  The 
  transformed 
  table 
  can 
  then 
  be 
  used 
  as 
  in 
  

   cases 
  I 
  and 
  II. 
  For 
  a 
  certain 
  flint 
  glass 
  spectrograph 
  k 
  = 
  '09 
  fi, 
  

   and 
  for 
  a 
  small 
  quartz 
  spectrograph 
  k 
  — 
  — 
  "02 
  /x. 
  

  

  If 
  great 
  dispersion 
  is 
  obtained 
  by 
  means 
  of 
  a 
  train 
  of 
  prisms 
  

   the 
  table 
  may 
  not 
  be 
  carried 
  to 
  a 
  sufficient 
  number 
  of 
  figures. 
  

   A 
  suitable 
  table 
  can, 
  however, 
  be 
  written 
  easily 
  in 
  the 
  same 
  

   way 
  this 
  table 
  was 
  written. 
  

  

  The 
  departures 
  of 
  the 
  true 
  values 
  of 
  X 
  from 
  those 
  obtained 
  

   by 
  means 
  of 
  the 
  linear 
  equation 
  and 
  the 
  table 
  are 
  less 
  than 
  the 
  

   departures 
  from 
  Cornu's 
  (or 
  Hartmann's) 
  formula. 
  

  

  Suppose 
  there 
  are 
  so 
  few 
  comparison 
  lines 
  (less 
  than 
  4 
  or 
  5) 
  

   on 
  a 
  spectrogram 
  that 
  a 
  sufficiently 
  accurate 
  departure 
  curve 
  

   cannot 
  be 
  made. 
  By 
  means 
  of 
  the 
  table 
  a 
  much 
  more 
  accurate 
  

   interpolation 
  can 
  be 
  made 
  by 
  using 
  the 
  table 
  and 
  the 
  following 
  

   formula* 
  than 
  can 
  be 
  made 
  by 
  means 
  of 
  Cornu's 
  formula. 
  

   Suppose 
  we 
  have 
  X,, 
  X 
  2 
  , 
  X 
  3 
  , 
  d^ 
  d„ 
  d 
  % 
  for 
  3 
  lines, 
  we 
  read 
  from 
  

   the 
  table 
  n\, 
  n\. 
  n\ 
  corresponding 
  to 
  X 
  x 
  etc., 
  and 
  write 
  

  

  % 
  = 
  n 
  = 
  A^ 
  + 
  ck 
  - 
  i) 
  

  

  and 
  solve 
  for 
  C. 
  

  

  Then 
  put 
  d 
  i 
  (known) 
  and 
  n\ 
  (unknown) 
  in 
  place 
  of 
  c/ 
  2 
  and 
  n 
  5 
  

   and 
  we 
  have 
  

  

  , 
  , 
  d, 
  — 
  d, 
  

  

  n\ 
  = 
  n\ 
  + 
  

  

  N-c(d 
  3 
  -dy 
  

  

  Finally 
  read 
  off 
  X 
  4 
  corresponding 
  to 
  n\. 
  

  

  *See 
  J. 
  Wash. 
  Acad. 
  Sci., 
  iv, 
  467, 
  1914. 
  

  

  