﻿II. 
  E. 
  Merwin 
  — 
  Interpolations 
  on 
  Spectrograms. 
  49 
  

  

  Art. 
  Y. 
  — 
  A 
  Table 
  for 
  Linear 
  and 
  Certain 
  Other 
  Interpo- 
  

   lations 
  on 
  Spectrograms 
  / 
  by 
  H. 
  E. 
  Merwin. 
  

  

  Method. 
  

  

  In 
  the 
  accompanying 
  table 
  each 
  wave-length, 
  X, 
  has 
  a 
  definite 
  

   value 
  for 
  each 
  value 
  of 
  a 
  quantity,* 
  n' 
  . 
  On 
  a 
  spectrogram 
  X 
  

   for 
  each 
  line 
  has 
  a 
  corresponding 
  value 
  of 
  d, 
  where 
  d 
  is 
  the 
  

   distance 
  of 
  the 
  line 
  from 
  some 
  chosen 
  line. 
  The 
  relation 
  of 
  

   the 
  values 
  of 
  n' 
  and 
  d 
  for 
  the 
  same 
  X 
  is 
  represented 
  more 
  or 
  

   less 
  approximately 
  by 
  the 
  linear 
  expression 
  d^= 
  Kn\ 
  — 
  7?, 
  

  

  where 
  H 
  and 
  K 
  are 
  constants 
  determined 
  for 
  each 
  spectro- 
  

   gram 
  (see 
  equation 
  So). 
  

  

  There 
  are 
  three 
  cases 
  to 
  consider 
  : 
  I. 
  Deviations 
  from 
  this 
  

   linear 
  equation 
  are 
  within 
  the 
  limits 
  of 
  observational 
  error 
  ; 
  

   II. 
  Deviations 
  are 
  small 
  but 
  not 
  negligible 
  ; 
  III. 
  Deviations 
  

   are 
  so 
  large 
  that 
  a 
  plotted 
  deviation 
  curve 
  does 
  not 
  give 
  

   accurately 
  the 
  required 
  corrections. 
  However, 
  case 
  III 
  can 
  be 
  

   modified 
  easily 
  so 
  as 
  to 
  come 
  under 
  case 
  I 
  or 
  II. 
  

  

  Case 
  I. 
  — 
  The 
  equation 
  is 
  solved 
  for 
  K 
  and 
  R 
  by 
  using 
  d 
  and 
  

   n' 
  for 
  the 
  wave-lengths 
  of 
  two 
  comparison 
  lines 
  near 
  the 
  ex- 
  

   tremities 
  of 
  that 
  portion 
  of 
  the 
  spectrogram 
  to 
  be 
  studied. 
  

   Then 
  for 
  other 
  values 
  of 
  d 
  values 
  of 
  n' 
  are 
  calculated, 
  and 
  the 
  

   corresponding 
  wave-lengths 
  read 
  from 
  the 
  table, 
  I.f 
  Values 
  of 
  

   X 
  thus 
  obtained 
  agree 
  with 
  values 
  known 
  from 
  other 
  com- 
  

   parison 
  lines 
  on 
  the 
  spectrogram.^: 
  

  

  Case 
  II 
  is 
  like 
  case 
  I 
  except 
  that 
  values 
  of 
  X 
  for 
  inter- 
  

   mediate 
  lines 
  deviate 
  slightly 
  from 
  true 
  values, 
  bat 
  the 
  devia- 
  

   tions 
  fall 
  on 
  a 
  smooth 
  curve 
  from 
  which 
  proper 
  corrections 
  can 
  

   be 
  read. 
  This 
  case 
  applies 
  to 
  most 
  work 
  with 
  quartz 
  spectro- 
  

   graphs. 
  The 
  deviations 
  are 
  at 
  most 
  a 
  small 
  fraction 
  of 
  the 
  

   length 
  of 
  the 
  spectrogram, 
  about 
  db 
  2 
  per 
  cent, 
  even 
  in 
  the 
  

   extreme 
  case 
  that 
  the 
  whole 
  spectrum 
  (*2 
  to 
  *8 
  fi) 
  is 
  taken 
  on 
  

   one 
  plate 
  and 
  lines 
  near 
  the 
  ends 
  are 
  used 
  as 
  standards. 
  

  

  Case 
  III 
  is 
  like 
  case 
  II, 
  but 
  the 
  deviations 
  are 
  too 
  large 
  to 
  

   handle 
  accurately 
  if 
  the 
  table 
  is 
  used 
  as 
  it 
  stands. 
  But, 
  instead 
  

   of 
  reading 
  from 
  the 
  table 
  n' 
  corresponding 
  to 
  X 
  of 
  the 
  spectro- 
  

  

  * 
  n' 
  = 
  — 
  — 
  - 
  — 
  '01 
  /I 
  2 
  , 
  where 
  a 
  is 
  expressed 
  in 
  ju, 
  

  

  A 
  1 
  — 
  •01 
  

  

  f 
  The 
  table 
  is 
  used 
  like 
  a 
  logarithm 
  table, 
  except 
  that 
  differences 
  are 
  sub- 
  

   tracted 
  instead 
  of 
  added, 
  a 
  corresponds 
  to 
  the 
  number 
  and 
  n' 
  to 
  the 
  log. 
  

   Thus 
  for 
  a 
  - 
  -18372//, 
  n' 
  = 
  '42066. 
  The 
  change 
  in 
  scale 
  at 
  a 
  = 
  -33 
  a 
  should 
  

   be 
  noted. 
  

  

  \ 
  A 
  plate 
  from 
  a 
  large 
  Hilgar 
  quartz 
  spectrograph 
  size 
  (d) 
  was 
  accurately- 
  

   represented 
  over 
  its 
  entire 
  range, 
  "4600 
  to 
  "30000 
  \i 
  of 
  the 
  table. 
  

  

  Am. 
  Jour. 
  Sci. 
  — 
  Fourth 
  Series, 
  Vol. 
  XLIII, 
  No. 
  253. 
  — 
  January, 
  1917. 
  

   4 
  

  

  