﻿54 
  H. 
  E. 
  Merwin 
  — 
  Interpolations 
  on 
  Spectrograms. 
  

  

  \ 
  123456789 
  Diff. 
  

  

  52 
  -03 
  570 
  553 
  537 
  521 
  505 
  489 
  473 
  457 
  442 
  426 
  16-15 
  

  

  53 
  410 
  394 
  379 
  364 
  349 
  334 
  319 
  304 
  289 
  274 
  15-14 
  

  

  54 
  259 
  244 
  230 
  21H 
  201 
  187 
  172 
  158 
  144 
  130 
  15-14 
  

  

  55 
  -03 
  116 
  102 
  088 
  075 
  061 
  047 
  033 
  020 
  007 
  993 
  14-13 
  

  

  56 
  -02 
  980 
  967 
  954 
  941 
  928 
  915 
  902 
  889 
  876 
  863 
  13 
  

  

  57 
  851 
  838 
  826 
  813 
  801 
  789 
  776 
  764 
  752 
  740 
  

  

  58 
  727 
  715 
  703 
  691 
  680 
  668 
  656 
  644 
  633 
  621 
  12 
  

  

  59 
  610 
  599 
  587 
  575 
  564 
  553 
  542 
  531 
  519 
  508 
  

  

  60 
  497 
  486 
  475 
  465 
  454 
  443 
  432 
  421 
  411 
  400 
  11 
  

  

  61 
  390 
  380 
  369 
  359 
  349 
  338 
  328 
  318 
  307 
  297 
  

  

  62 
  287 
  277 
  267 
  257 
  247 
  237 
  227 
  218 
  208 
  198 
  10 
  

  

  63 
  188 
  179 
  169 
  160 
  150 
  140 
  131 
  121 
  112 
  102 
  

  

  64 
  093 
  084 
  075 
  065 
  056 
  047 
  038 
  029 
  020 
  Oil 
  

  

  65 
  -02 
  002 
  993 
  984 
  976 
  967 
  958 
  949 
  941 
  932 
  923 
  9 
  

  

  66 
  -01 
  914 
  906 
  897 
  889 
  880 
  872 
  863 
  855 
  846 
  838 
  

  

  67 
  830 
  822 
  813 
  805 
  797 
  789 
  781 
  772 
  764 
  756 
  

  

  68 
  748 
  740 
  732 
  724 
  716 
  708 
  701 
  693 
  685 
  677 
  8 
  

  

  69 
  669 
  661 
  653 
  646 
  638 
  631 
  623 
  616 
  608 
  601 
  

  

  70 
  593 
  586 
  578 
  571 
  563 
  556 
  549 
  541 
  534 
  527 
  

  

  71 
  520 
  513 
  506 
  498 
  491 
  484 
  477 
  470 
  463 
  456 
  

  

  72 
  449 
  442 
  435 
  428 
  421 
  414 
  407 
  400 
  393 
  386 
  7 
  

  

  73 
  380 
  373 
  366 
  359 
  352 
  346 
  339 
  332 
  326 
  319 
  

  

  74 
  313 
  306 
  299 
  293 
  286 
  280 
  273 
  267 
  260 
  254 
  

  

  75 
  247 
  241 
  235 
  228 
  222 
  216 
  209 
  203 
  196 
  190 
  

  

  76 
  184 
  178 
  172 
  165 
  159 
  153 
  147 
  141 
  135 
  129 
  

  

  77 
  123 
  117 
  111 
  105 
  099 
  093 
  087 
  081 
  075 
  069 
  6 
  

  

  78 
  063 
  057 
  051 
  045 
  039 
  033 
  027 
  022 
  016 
  010 
  

  

  79 
  -01 
  004 
  998 
  992 
  987 
  981 
  976 
  970 
  964 
  959 
  953 
  

  

  80 
  -00 
  947 
  942 
  936 
  931 
  925 
  920 
  914 
  909 
  903 
  898 
  

  

  Development 
  of 
  the 
  Formula. 
  

  

  Consider 
  a 
  narrow 
  beam 
  of 
  light 
  bent 
  twice 
  in 
  the 
  same 
  

   direction 
  and 
  dispersed 
  by 
  a 
  very 
  small 
  prism 
  and 
  formed 
  into 
  

   a 
  spectrum 
  which 
  is 
  photographed 
  without 
  intervening 
  lenses 
  

   on 
  a 
  llat 
  plate. 
  Then 
  if 
  i 
  is 
  the 
  angle 
  of 
  incidence 
  upon 
  the 
  

   prism, 
  r 
  the 
  angle 
  of 
  refraction 
  from 
  the 
  prism, 
  A 
  the 
  angle 
  of 
  

   the 
  prism, 
  n 
  the 
  refractive 
  index 
  of 
  the 
  prism, 
  i' 
  and 
  r' 
  the 
  

   angles 
  of 
  incidence 
  and 
  refraction 
  within 
  the 
  prism, 
  j3 
  the 
  

   angle 
  the 
  emergent 
  ray 
  makes 
  with 
  the 
  photographic 
  plate, 
  d 
  

   the 
  distance 
  on 
  the 
  plate 
  from 
  the 
  normal 
  to 
  the 
  back 
  face 
  of 
  

   the 
  prism 
  to 
  the 
  image 
  of 
  the 
  emergent 
  ray, 
  A 
  etc., 
  constants, 
  

  

  Then 
  sin 
  r 
  = 
  n 
  sin 
  i 
  1 
  , 
  and 
  i' 
  •== 
  A 
  — 
  r' 
  

  

  Then 
  sin 
  r 
  = 
  n 
  sin 
  (A 
  — 
  r) 
  

  

  Or 
  sin 
  r 
  = 
  n($'m 
  A 
  cos 
  r' 
  — 
  cos 
  A 
  sin 
  r') 
  

  

  But 
  

  

  , 
  sin 
  i 
  , 
  , 
  . 
  / 
  sin^ 
  

   sin 
  r 
  = 
  , 
  and 
  cosr 
  = 
  1/1 
  t~ 
  

  

  n 
  T 
  n 
  

  

  Then 
  sin 
  r 
  = 
  sin 
  A(\/u 
  u 
  — 
  sinY 
  — 
  sin 
  i 
  cot 
  A) 
  (1) 
  

  

  Also 
  sin 
  r 
  = 
  — 
  t— 
  - 
  (2) 
  

  

  A 
  v 
  ' 
  

  

  