﻿THE 
  CIRCUMSTANCES 
  OF 
  AN 
  ECLIPSE 
  OF 
  THE 
  SUN. 
  

  

  311 
  

  

  TABLE 
  I. 
  

  

  Logarithms 
  x 
  and 
  y. 
  

   Arg. 
  Latitude 
  of 
  Place. 
  

  

  Arg. 
  

  

  Log. 
  x. 
  

  

  Log. 
  y. 
  

  

  0° 
  

   2 
  

   4 
  

   6 
  

  

  8 
  

  

  1-00000 
  

   1-00000 
  

   1-00001 
  

   100002 
  

   1-00003 
  

  

  0-99718 
  

   0-99719 
  

   0-99719 
  

   0-99720 
  

   0-99721 
  

  

  10 
  

   12 
  

   14 
  

   16 
  

  

  18 
  

  

  1-00004 
  

   1-00006 
  

   1-00008 
  

   1-00011 
  

   100013 
  

  

  0-99723 
  

  

  0-99725 
  

   0-99727 
  

   99729 
  

   0-99732 
  

  

  20 
  

   22 
  

   24 
  

  

  26 
  

  

  28 
  

  

  100016 
  

   1-00020 
  

   1-00023 
  

   1-00027 
  

   100031 
  

  

  0-99735 
  

   0-99738 
  

   0-99742 
  

   0-99745 
  

   0-99749 
  

  

  30 
  

   32 
  

   34 
  

   36 
  

  

  38 
  

  

  1-00035 
  

   1-00039 
  

   1-00044 
  

   1-00048 
  

   1-00053 
  

  

  0-99754 
  

   0-99758 
  

   0-99762 
  

   0-99767 
  

   0-99772 
  

  

  40 
  

   42 
  

   44 
  

   46 
  

  

  48 
  

  

  1-00058 
  

   1-00063 
  

   1-00068 
  

   1-00073 
  

   1-00078 
  

  

  0-99777 
  

   0-99781 
  

   0-99786 
  

   0-99791 
  

   0-99796 
  

  

  50 
  

   52 
  

   54 
  

   56 
  

  

  58 
  

  

  1-00082 
  

   1-00087 
  

   1-00092 
  

   1-00097 
  

   1-00101 
  

  

  0-99801 
  

   0-99806 
  

   0-99810 
  

   0-99815 
  

   0-99820 
  

  

  60 
  

   62 
  

   64 
  

   66 
  

  

  68 
  

  

  1-00105 
  

   100110 
  

   100114 
  

   100117 
  

   100121 
  

  

  0-99824 
  

   0-99828 
  

   0-99832 
  

   0-99836 
  

   0-99839 
  

  

  70 
  

   72 
  

  

  74 
  

   76 
  

  

  78 
  

  

  100124 
  

   100127 
  

   100130 
  

   100133 
  

   100135 
  

  

  0-99843 
  

   0-99846 
  

   0-99848 
  

   0-99851 
  

   0-99853 
  

  

  80 
  

   82 
  

   84 
  

   86 
  

   88 
  

   90 
  

  

  ] 
  00137 
  

   100138 
  

   100139 
  

   1-00140 
  

   100141 
  

   1 
  00141 
  

  

  0-99855 
  

   0-99856 
  

   0-99858 
  

   0-99859 
  

   0-99859 
  

   0-99859 
  

  

  Note. 
  — 
  In 
  the 
  calcula- 
  

   tion 
  of 
  the 
  above 
  Table, 
  

   the 
  earth's 
  compression 
  

  

  was 
  assumed 
  to 
  be 
  - 
  — 
  

   309- 
  

  

  

  TABLE 
  II. 
  

  

  Values 
  of 
  X 
  and 
  Y 
  for 
  each 
  Degree 
  of 
  

  

  

  Latitude. 
  

  

  Lat. 
  

  

  X. 
  

  

  Y. 
  

  

  Lat. 
  

  

  X. 
  

  

  Y. 
  

  

  0° 
  

  

  10-00 
  

  

  0-00 
  

  

  45° 
  

  

  7-08 
  

  

  704 
  

  

  1 
  

  

  1000 
  

  

  0-17 
  

  

  46 
  

  

  6-96 
  

  

  7-16 
  

  

  2 
  

  

  9-99 
  

  

  0-35 
  

  

  47 
  

  

  6-83 
  

  

  7-28 
  

  

  3 
  

  

  9-99 
  

  

  0-52 
  

  

  48 
  

  

  6-70 
  

  

  7-40 
  

  

  4 
  

  

  9-98 
  

  

  0-69 
  

  

  49 
  

  

  6-57 
  

  

  7-51 
  

  

  5 
  

  

  9-96 
  

  

  0-87 
  

  

  50 
  

  

  6-44 
  

  

  7-63 
  

  

  6 
  

  

  9-95 
  

  

  1-04 
  

  

  51 
  

  

  6-31 
  

  

  7-74 
  

  

  7 
  

  

  9-93 
  

  

  1-21 
  

  

  52 
  

  

  617 
  

  

  7-84 
  

  

  8 
  

  

  9-90 
  

  

  1-38 
  

  

  53 
  

  

  603 
  

  

  7-95 
  

  

  9 
  

  

  9-88 
  

  

  1-55 
  

  

  54 
  

  

  5-89 
  

  

  8-06 
  

  

  10 
  

  

  9-85 
  

  

  1-73 
  

  

  55 
  

  

  5-75 
  

  

  8-16 
  

  

  11 
  

  

  9-82 
  

  

  1-90 
  

  

  56 
  

  

  5-60 
  

  

  8-25 
  

  

  12 
  

  

  9-73 
  

  

  2-07 
  

  

  57 
  

  

  5-46 
  

  

  8-35 
  

  

  13 
  

  

  9-74 
  

  

  2-24 
  

  

  58 
  

  

  5-31 
  

  

  8-45 
  

  

  14 
  

  

  9-70 
  

  

  2-40 
  

  

  59 
  

  

  516 
  

  

  S-54 
  

  

  15 
  

  

  9-66 
  

  

  2-57 
  

  

  60 
  

  

  501 
  

  

  8-63 
  

  

  16 
  

  

  9-62 
  

  

  2-74 
  

  

  61 
  

  

  4-86 
  

  

  8-71 
  

  

  17 
  

  

  9-57 
  

  

  2-91 
  

  

  62 
  

  

  4-71 
  

  

  8-79 
  

  

  18 
  

  

  9-51 
  

  

  3-07 
  

  

  63 
  

  

  4.55 
  

  

  8-87 
  

  

  19 
  

  

  9-46 
  

  

  3-24 
  

  

  64 
  

  

  4-40 
  

  

  8-95 
  

  

  20 
  

  

  9-40 
  

  

  3-40 
  

  

  65 
  

  

  4-24 
  

  

  9-03 
  

  

  21 
  

  

  9-34 
  

  

  3-56 
  

  

  66 
  

  

  4-08 
  

  

  9-10 
  

  

  22 
  

  

  9 
  28 
  

  

  3-72 
  

  

  67 
  

  

  3-92 
  

  

  9-17 
  

  

  23 
  

  

  921 
  

  

  3-88 
  

  

  68 
  

  

  3-76 
  

  

  9-24 
  

  

  24 
  

  

  9-14 
  

  

  4-04 
  

  

  69 
  

  

  3-59 
  

  

  9-30 
  

  

  25 
  

  

  9-07 
  

  

  4-20 
  

  

  70 
  

  

  3-43 
  

  

  9-36 
  

  

  26 
  

  

  8 
  99 
  

  

  4-36 
  

  

  71 
  

  

  3-27 
  

  

  9-42 
  

  

  27 
  

  

  8-92 
  

  

  4-51 
  

  

  72 
  

  

  3-10 
  

  

  9-48 
  

  

  28 
  

  

  8-84 
  

  

  4-67 
  

  

  73 
  

  

  2-93 
  

  

  9-53 
  

  

  29 
  

  

  8-75 
  

  

  4-82 
  

  

  74 
  

  

  2-76 
  

  

  9-58 
  

  

  30 
  

  

  8-67 
  

  

  4-97 
  

  

  75 
  

  

  2-60 
  

  

  9-63 
  

  

  31 
  

  

  8-58 
  

  

  5 
  12 
  

  

  76 
  

  

  2-43 
  

  

  9-67 
  

  

  32 
  

  

  8-49 
  

  

  5-27 
  

  

  77 
  

  

  2-26 
  

  

  9-71 
  

  

  33 
  

  

  8-39 
  

  

  5-42 
  

  

  78 
  

  

  2-09 
  

  

  9-75 
  

  

  34 
  

  

  8-30 
  

  

  5-56 
  

  

  79 
  

  

  1-91 
  

  

  9-78 
  

  

  35 
  

  

  8-20 
  

  

  5-70 
  

  

  80 
  

  

  1-74 
  

  

  9-81 
  

  

  36 
  

  

  8-10 
  

  

  5-85 
  

  

  81 
  

  

  1-57 
  

  

  9-84 
  

  

  37 
  

  

  8-00 
  

  

  5-99 
  

  

  82 
  

  

  1-40 
  

  

  9-87 
  

  

  38 
  

  

  7-89 
  

  

  612 
  

  

  83 
  

  

  1-22 
  

  

  9-89 
  

  

  39 
  

  

  7-78 
  

  

  6-26 
  

  

  84 
  

  

  105 
  

  

  9-91 
  

  

  40 
  

  

  7-67 
  

  

  6-39 
  

  

  85 
  

  

  0-87 
  

  

  9-93 
  

  

  41 
  

  

  7-56 
  

  

  6-53 
  

  

  86 
  

  

  0-70 
  

  

  9-94 
  

  

  42 
  

  

  7-44 
  

  

  6-66 
  

  

  87 
  

  

  0-53 
  

  

  9-95 
  

  

  43 
  

  

  7-32 
  

  

  6-79 
  

  

  88 
  

  

  0-35 
  

  

  9-96 
  

  

  44 
  

  

  7-20 
  

  

  6-91 
  

  

  89 
  

  

  0-18 
  

  

  9-97 
  

  

  45 
  

  

  7-08 
  

  

  704 
  

  

  90 
  

  

  0-00 
  

  

  9-97 
  

  

  TABLE 
  III. 
  

  

  Values 
  of 
  

  

  u' 
  and 
  V. 
  

  

  Arg. 
  C 
  

  

  for 
  u'. 
  

  

  Arg. 
  E/or 
  v'. 
  

  

  Arg. 
  

  

  u'orv' 
  

  

  Arg. 
  u'orv' 
  

  

  0-0 
  

  

  0-00 
  

  

  50 
  

  

  1-31 
  

  

  0-1 
  

  

  0-03 
  

  

  51 
  

  

  1-34 
  

  

  0-2 
  

  

  0-05 
  

  

  5-2 
  

  

  1-36 
  

  

  0-3 
  

  

  0-08 
  

  

  5-3 
  

  

  1-39 
  

  

  0-4 
  

  

  0-10 
  

  

  5-4 
  

  

  1-41 
  

  

  0-5 
  

  

  0-13 
  

  

  5-5 
  

  

  1-44 
  

  

  0-6 
  

  

  015 
  

  

  5-6 
  

  

  1-47 
  

  

  0-7 
  

  

  0-18 
  

  

  5-7 
  

  

  1-49 
  

  

  0-8 
  

  

  0-21 
  

  

  5-8 
  

  

  1-52 
  

  

  0-9 
  

  

  0-24 
  

  

  5-9 
  

  

  1-54 
  

  

  1-0 
  

  

  0-26 
  

  

  60 
  

  

  1-57 
  

  

  11 
  

  

  0-29 
  

  

  61 
  

  

  1-60 
  

  

  1*2 
  

  

  0-31 
  

  

  6-2 
  

  

  1-62 
  

  

  1-3 
  

  

  0-34 
  

  

  6-3 
  

  

  1-65 
  

  

  1-4 
  

  

  0-37 
  

  

  6-4 
  

  

  1-68 
  

  

  1-5 
  

  

  0-39 
  

  

  6-5 
  

  

  1-70 
  

  

  1-6 
  

  

  0-42 
  

  

  6-6 
  

  

  1-73 
  

  

  1-7 
  

  

  0-45 
  

  

  6-7 
  

  

  1-75 
  

  

  1-8 
  

  

  0-47 
  

  

  6-8 
  

  

  1-78 
  

  

  1-9 
  

  

  0-50 
  

  

  6-9 
  

  

  1-81 
  

  

  20 
  

  

  0-52 
  

  

  7.0 
  

  

  1-83 
  

  

  21 
  

  

  0-55 
  

  

  71 
  

  

  1-86 
  

  

  2-2 
  

  

  0-58 
  

  

  7-2 
  

  

  1-88 
  

  

  2-3 
  

  

  0-60 
  

  

  7-3 
  

  

  1-91 
  

  

  2-4 
  

  

  0-63 
  

  

  7-4 
  

  

  1-94 
  

  

  2-5 
  

  

  0-65 
  

  

  7-5 
  

  

  1-96 
  

  

  2-6 
  

  

  0-68 
  

  

  7-6 
  

  

  1-99 
  

  

  2-7 
  

  

  0-71 
  

  

  7-7 
  

  

  2-02 
  

  

  2-8 
  

  

  0-73 
  

  

  7-8 
  

  

  204 
  

  

  2-9 
  

  

  0-76 
  

  

  7-9 
  

  

  207 
  

  

  30 
  

  

  0-79 
  

  

  8-0 
  

  

  209 
  

  

  31 
  

  

  0-81 
  

  

  8-1 
  

  

  212 
  

  

  3-2 
  

  

  0-84 
  

  

  8-2 
  

  

  215 
  

  

  3-3 
  

  

  0-86 
  

  

  8-3 
  

  

  2-17 
  

  

  3-4 
  

  

  0-89 
  

  

  8-4 
  

  

  2-20 
  

  

  3-5 
  

  

  0-92 
  

  

  8-5 
  

  

  2-23 
  

  

  3-6 
  

  

  0-94 
  

  

  8-6 
  

  

  2-25 
  

  

  3-7 
  

  

  0-97 
  

  

  8-7 
  

  

  2-28 
  

  

  3-8 
  

  

  0-99 
  

  

  8-8 
  

  

  2-30 
  

  

  3-9 
  

  

  102 
  

  

  8-9 
  

  

  2-33 
  

  

  4-0 
  

  

  1-05 
  

  

  9-0 
  

  

  2-36 
  

  

  4-1 
  

  

  1-07 
  

  

  91 
  

  

  2-38 
  

  

  4-2 
  

  

  1-10 
  

  

  9-2 
  

  

  2-41 
  

  

  4-3 
  

  

  113 
  

  

  9-3 
  

  

  2-43 
  

  

  4-4 
  

  

  115 
  

  

  9-4 
  

  

  2-46 
  

  

  4-5 
  

  

  118 
  

  

  9-5 
  

  

  2-49 
  

  

  4-6 
  

  

  1-20 
  

  

  9-6 
  

  

  2-51 
  

  

  4-7 
  

  

  1-23 
  

  

  9-7 
  

  

  2-54 
  

  

  4-8 
  

  

  1-26 
  

  

  9-8 
  

  

  2.57 
  

  

  4-9 
  

  

  1-28 
  

  

  9-9 
  

  

  2-59 
  

  

  50 
  

  

  1-31 
  

  

  100 
  

  

  2-62 
  

  

  