﻿THE 
  CIRCUMSTANCES 
  OF 
  AN 
  ECLIPSE 
  OF 
  THE 
  SUN. 
  303 
  

  

  tables, 
  containing 
  the 
  values 
  of 
  u 
  and 
  C, 
  for 
  each 
  degree 
  of 
  the 
  

   hour 
  angle, 
  and 
  b 
  and/ 
  for 
  each 
  degree 
  of 
  declination, 
  calculated 
  for 
  

   the 
  place, 
  from 
  the 
  expressions 
  u 
  = 
  X 
  sin. 
  H, 
  C 
  = 
  X 
  cos. 
  H, 
  & 
  == 
  Y 
  

   cos. 
  Decl., 
  &ndf 
  = 
  Y 
  sin. 
  Decl. 
  These 
  tables 
  will 
  also 
  be 
  equally 
  

   convenient 
  in 
  the 
  calculation 
  of 
  occultations. 
  Tables 
  VI. 
  and 
  VII. 
  

   contain 
  those 
  values, 
  calculated 
  for 
  the 
  latitude 
  of 
  Philadelphia. 
  

  

  2. 
  If 
  only 
  a 
  near 
  approximation 
  to 
  the 
  circumstances 
  of 
  the 
  eclipse 
  

   is 
  required, 
  the 
  value 
  of 
  r 
  may 
  be 
  used 
  instead 
  of 
  r', 
  and 
  the 
  values 
  of 
  

   h 
  and 
  n 
  at 
  the 
  time 
  of 
  greatest 
  obscuration 
  may 
  be 
  taken, 
  in 
  finding 
  

   the 
  corrected 
  times 
  of 
  beginning 
  and 
  end. 
  Also 
  in 
  finding 
  the 
  point 
  

   of 
  the 
  sun's 
  disc 
  at 
  which 
  the 
  eclipse 
  commences, 
  the 
  values 
  of 
  (p 
  — 
  w), 
  

   (q 
  — 
  v), 
  u 
  and 
  v, 
  at 
  the 
  approximate 
  time 
  of 
  beginning, 
  may 
  be 
  used 
  

   without 
  correction; 
  consequently, 
  in 
  this 
  case/*, 
  g 
  and 
  E 
  need 
  not 
  be 
  

   found. 
  The 
  error 
  thus 
  produced 
  in 
  the 
  time 
  of 
  beginning 
  or 
  end 
  will 
  

   seldom 
  exceed 
  a 
  minute; 
  and 
  the 
  error 
  in 
  the 
  magnitude 
  of 
  the 
  eclipse 
  

   cannot 
  amount 
  to 
  a 
  tenth 
  of 
  a 
  digit. 
  

  

  As 
  an 
  example, 
  let 
  it 
  be 
  required 
  to 
  calculate 
  for 
  Philadelphia, 
  lat. 
  

   39° 
  57' 
  N. 
  long., 
  5 
  h. 
  m. 
  44 
  sec. 
  W., 
  the 
  circumstances 
  of 
  the 
  eclipse 
  

   of 
  November 
  30th, 
  1834. 
  

  

  For 
  Philadelphia 
  X 
  == 
  7-68 
  and 
  Y 
  = 
  6-39. 
  

  

  In 
  the 
  following 
  calculation, 
  the 
  values 
  of 
  b, 
  f, 
  u 
  and 
  C 
  are 
  taken 
  

   from 
  Tables 
  VI. 
  and 
  VII. 
  ; 
  the 
  same 
  values 
  will, 
  however, 
  be 
  easily 
  

   obtained 
  from 
  the 
  traverse 
  table, 
  with 
  perhaps 
  occasionally 
  a 
  difference 
  

   of 
  a 
  unit 
  in 
  the 
  last 
  decimal 
  figure. 
  

  

  From 
  the 
  elements 
  in 
  the 
  Nautical 
  Almanac 
  we 
  obtain 
  : 
  

  

  Greenwich 
  mean 
  time 
  of 
  conjunc. 
  in 
  R. 
  A., 
  Nov. 
  30d. 
  6h. 
  32'9m. 
  

   Moon's 
  declination, 
  . 
  . 
  . 
  . 
  — 
  20° 
  48' 
  13" 
  

  

  Sun's 
  declination, 
  . 
  . 
  . 
  . 
  . 
  — 
  21 
  41 
  05 
  

  

  Sun's 
  semidiameter, 
  . 
  . 
  . 
  . 
  . 
  16 
  15 
  

  

  Diff. 
  of 
  sun's 
  and 
  moon's 
  declinations, 
  = 
  -j- 
  52' 
  52" 
  = 
  -j- 
  3172" 
  

   Diff.of 
  their 
  hor. 
  motions 
  in 
  R. 
  A., 
  = 
  -\-35 
  40 
  = 
  -j- 
  2140 
  

   Difif. 
  of 
  their 
  hor. 
  motions 
  in 
  declin., 
  = 
  — 
  8 
  48 
  == 
  — 
  528 
  

   DifF. 
  of 
  their 
  eq. 
  horizontal 
  parallaxes, 
  = 
  60 
  14 
  = 
  3614 
  

  

  