﻿308 
  PRACTICAL 
  RULE 
  FOR 
  CALCULATING 
  

  

  subtracting 
  if 
  it 
  is 
  west, 
  and 
  denote 
  the 
  result 
  by 
  Z. 
  Find 
  also, 
  for 
  

   the 
  time 
  T', 
  the 
  sun's 
  right 
  ascension 
  in 
  arc, 
  denoting 
  it 
  by 
  A 
  ; 
  the 
  

   sun's 
  declination, 
  denoting 
  it 
  by 
  D 
  ; 
  the 
  moon's 
  right 
  ascension, 
  in 
  arc, 
  

   denoting 
  it 
  by 
  a 
  ; 
  the 
  moon's 
  declination, 
  denoting 
  it 
  by 
  d 
  ; 
  and 
  the 
  

   moon's 
  equatorial 
  horizontal 
  parallax. 
  Take 
  the 
  difference 
  of 
  the 
  sun's 
  

   and 
  moon's 
  parallaxes, 
  and 
  denote 
  it 
  by 
  G. 
  Also 
  denote 
  the 
  sun's 
  

   semidiameter 
  by 
  R. 
  Then 
  find 
  the 
  values 
  of 
  p, 
  q, 
  r, 
  u, 
  and 
  0, 
  to 
  four 
  

   decimal 
  places, 
  by 
  the 
  following 
  formulas. 
  

  

  10 
  sin. 
  (a 
  — 
  A) 
  cos. 
  d 
  

   p 
  = 
  smTG 
  

  

  10 
  sin. 
  Id 
  — 
  D) 
  

   q 
  ~ 
  smTG 
  + 
  * 
  P 
  sin> 
  D 
  sin> 
  ( 
  a 
  ~~ 
  A 
  ) 
  

  

  10 
  tang. 
  R 
  cos. 
  (d 
  — 
  D) 
  cos. 
  (a 
  — 
  A) 
  

   sin. 
  G 
  

   u 
  = 
  X 
  sin 
  (Z 
  — 
  A) 
  

   v 
  = 
  Y 
  cos. 
  D 
  — 
  X 
  sin. 
  D 
  cos. 
  (Z 
  — 
  A) 
  

  

  Find 
  the 
  value 
  of 
  g, 
  for 
  the 
  time 
  T, 
  as 
  directed 
  in 
  the 
  preceding 
  

   rule, 
  and 
  with 
  the 
  argument 
  (f 
  -f- 
  g) 
  take 
  the 
  correction 
  of 
  r 
  from 
  

   Table 
  IX., 
  and 
  subtracting 
  it 
  from 
  r, 
  obtain 
  r'. 
  Take 
  the 
  moon's 
  semi- 
  

   diameter 
  from 
  Table 
  VIII., 
  with 
  the 
  equatorial 
  parallax 
  as 
  the 
  argu- 
  

   ment, 
  and 
  adding 
  it 
  to 
  r\ 
  the 
  sum 
  will 
  be 
  the 
  value 
  of 
  k. 
  The 
  square 
  

   of 
  m, 
  and 
  the 
  value 
  of 
  n, 
  at 
  the 
  approximate 
  time 
  of 
  beginning, 
  found 
  

   in 
  the 
  preceding 
  calculation, 
  although 
  extending 
  only 
  to 
  two 
  decimal 
  

   places, 
  will 
  be 
  sufficiently 
  accurate 
  for 
  the 
  present 
  calculation. 
  

  

  Using 
  a 
  common 
  table 
  of 
  squares, 
  and 
  proportioning 
  for 
  the 
  last 
  two 
  

   figures 
  of 
  the 
  roots, 
  find 
  the 
  values 
  of 
  h 
  and 
  h\ 
  as 
  directed 
  in 
  article 
  

   8 
  of 
  the 
  foregoing 
  rule, 
  and 
  thence 
  a 
  second 
  correction 
  ; 
  which 
  

   being 
  applied 
  to 
  T', 
  as 
  there 
  directed, 
  will 
  give 
  the 
  true 
  time 
  of 
  be- 
  

   ginning. 
  

  

  A 
  similar 
  calculation 
  for 
  the 
  corrected 
  time 
  of 
  end, 
  will 
  give 
  the 
  

   true 
  time 
  of 
  end. 
  

  

  The 
  corrected 
  time 
  of 
  beginning 
  of 
  the 
  eclipse 
  just 
  calculated, 
  has 
  

   been 
  found 
  to 
  be 
  6 
  h. 
  0-3 
  m. 
  Take 
  therefore 
  T'= 
  6 
  h. 
  m. 
  The 
  

   sidereal 
  time 
  corresponding 
  to 
  this 
  time 
  is 
  339° 
  7' 
  22". 
  2, 
  expressed 
  in 
  

   arc. 
  Hence 
  for 
  Philadelphia, 
  long. 
  75° 
  10' 
  59" 
  W., 
  we 
  have,Z 
  = 
  263° 
  

   56' 
  23".2, 
  at 
  the 
  time 
  T'. 
  We 
  also 
  find 
  A 
  = 
  246° 
  21' 
  7".8, 
  D 
  = 
  

  

  