﻿THE 
  CIRCUMSTANCES 
  OF 
  AN 
  ECLIPSE 
  OF 
  THE 
  SUN. 
  309 
  

  

  — 
  21° 
  40' 
  51".5, 
  a 
  = 
  246° 
  1' 
  33". 
  1, 
  d 
  = 
  — 
  20° 
  43' 
  8".l, 
  moon's 
  

   parallax 
  = 
  60' 
  23".3, 
  and 
  R 
  = 
  16 
  14".8. 
  

  

  Hence 
  Z 
  — 
  A 
  =: 
  17° 
  35' 
  15", 
  a 
  — 
  A 
  = 
  — 
  19' 
  34 
  ".7, 
  d 
  — 
  D 
  = 
  

   -f- 
  57' 
  43".4, 
  and 
  G 
  = 
  60' 
  14". 
  6. 
  

  

  With 
  these 
  values 
  we 
  obtain, 
  p 
  = 
  — 
  3-0398, 
  q 
  = 
  -f- 
  9-5787, 
  

   r 
  = 
  2-6965, 
  u 
  = 
  -f 
  2-3195, 
  and 
  v 
  = 
  -4- 
  8-6398. 
  

  

  The 
  value 
  of 
  g-, 
  for 
  the 
  time 
  T', 
  is 
  -f- 
  6-80, 
  and 
  consequently 
  (/-}- 
  

   g) 
  = 
  -f- 
  4-44. 
  This 
  gives 
  0-0210 
  for 
  the 
  correction 
  of 
  r. 
  Hence 
  

   r'= 
  2-6755. 
  The 
  moon's 
  semidiameter 
  taken 
  from 
  Table 
  VIII 
  is 
  

   2-7315; 
  consequently 
  k 
  = 
  5-4070. 
  Then, 
  

  

  k 
  = 
  5-4070 
  sq. 
  29-2357 
  p 
  — 
  u 
  = 
  — 
  5-3593 
  sq. 
  28-7221 
  

   m 
  sq. 
  0-3700 
  q 
  — 
  v 
  = 
  0-9389 
  sq. 
  0-8815 
  

  

  h 
  = 
  5-3727 
  sq. 
  28-8657 
  29-6036 
  

  

  h' 
  =5-4068 
  m 
  sq. 
  0-3700 
  

  

  Diff. 
  = 
  0-0341 
  h' 
  =5-4068 
  sq. 
  29-2336 
  

  

  m. 
  in. 
  sec. 
  

   3-83 
  : 
  0-0341 
  : 
  : 
  60 
  : 
  0-53 
  = 
  32 
  

  

  Hence 
  the 
  true 
  time 
  of 
  beginning 
  is 
  6 
  h. 
  m. 
  32 
  sec, 
  in 
  Greenwich 
  

   mean 
  time. 
  

  

  For 
  the 
  end 
  take 
  T'= 
  8 
  h. 
  38 
  m. 
  Then 
  we 
  shall 
  find 
  Z 
  = 
  303° 
  

   32' 
  52".6, 
  A 
  = 
  246° 
  28' 
  13".3, 
  D 
  = 
  — 
  21° 
  41' 
  55".3, 
  a 
  = 
  247° 
  

   42' 
  41".8, 
  d 
  = 
  — 
  21° 
  7' 
  4"-3, 
  moon's 
  parallax 
  == 
  60' 
  21 
  ".6, 
  and 
  as 
  be- 
  

   fore 
  R 
  = 
  16' 
  14".8. 
  We 
  also 
  find 
  g 
  = 
  3-88, 
  and 
  consequently 
  / 
  + 
  

   g=l-52. 
  

  

  Hence^ 
  = 
  -|- 
  11-5373, 
  # 
  = 
  -|- 
  5-7414, 
  r 
  = 
  2-6975,r' 
  = 
  2-6903, 
  

   k 
  = 
  5-4218, 
  u 
  = 
  -4- 
  6-4435 
  and 
  v 
  = 
  + 
  7-4782. 
  

  

  k 
  = 
  5-4218 
  sq. 
  29-3959 
  p 
  — 
  u 
  = 
  + 
  5-0938 
  sq. 
  25-9468 
  

   m 
  sq. 
  0-3700 
  q 
  — 
  v 
  = 
  — 
  • 
  1-7368 
  sq. 
  3-0165 
  

  

  h 
  = 
  5-3876 
  sq. 
  29-0259 
  

   h'= 
  5-3473 
  

  

  m 
  

  

  h'=z 
  5-3473 
  

   m. 
  sec. 
  

   : 
  0-53 
  =- 
  32 
  

  

  28-9633 
  

   sq. 
  0-3700 
  

  

  Diff. 
  = 
  0-0403 
  

  

  m. 
  

   4-57 
  : 
  0-0403 
  : 
  : 
  60 
  : 
  

  

  sq. 
  28-5933 
  

  

  Hence 
  the 
  true 
  time 
  of 
  end 
  is 
  8 
  h. 
  38 
  m. 
  32 
  sec. 
  in 
  Greenwich 
  

   vol. 
  v. 
  — 
  4 
  c 
  

  

  