﻿300 
  PRACTICAL 
  RULE 
  FOR 
  CALCULATING 
  

  

  during 
  the 
  continuance 
  of 
  the 
  eclipse. 
  But 
  the 
  value 
  p 
  == 
  0, 
  and 
  the 
  

   values 
  of 
  q 
  and 
  H, 
  found 
  as 
  above, 
  appertain 
  only 
  to 
  the 
  time 
  T. 
  To 
  

   find 
  them 
  for 
  another 
  time 
  T', 
  proceed 
  thus. 
  As 
  60 
  minutes 
  : 
  diff. 
  

   of 
  T 
  and 
  T 
  : 
  : 
  p' 
  : 
  p. 
  If 
  T' 
  is 
  later 
  than 
  T, 
  the 
  value 
  of 
  p 
  is 
  -f-, 
  but 
  

   if 
  earlier, 
  it 
  is 
  — 
  . 
  Again, 
  as 
  60 
  minutes 
  : 
  diff. 
  of 
  T 
  and 
  T::q:a. 
  

   quantity 
  with 
  the 
  same 
  sign 
  as 
  q', 
  which, 
  added 
  to 
  the 
  value 
  of 
  </, 
  at 
  

   the 
  time 
  T, 
  when 
  T' 
  is 
  later 
  than 
  T, 
  but 
  subtracted 
  from 
  it 
  when 
  

   T' 
  is 
  earlier, 
  will 
  give 
  the 
  required 
  value 
  of 
  q. 
  Also, 
  as 
  60 
  minutes 
  : 
  

   diff. 
  of 
  T 
  and 
  T' 
  : 
  : 
  15° 
  : 
  a 
  quantity, 
  which 
  added 
  to 
  the 
  value 
  of 
  H, 
  

   at 
  the 
  time 
  T, 
  when 
  T' 
  is 
  later 
  than 
  T, 
  but 
  subtracted 
  when 
  it 
  is 
  

   earlier, 
  will 
  give 
  the 
  required 
  value 
  of 
  H. 
  

  

  5. 
  With 
  the 
  value 
  of 
  H, 
  at 
  the 
  time 
  T, 
  as 
  a 
  course, 
  and 
  the 
  value 
  

   of 
  X, 
  for 
  the 
  given 
  place, 
  as 
  a 
  distance, 
  enter 
  the 
  traverse 
  table, 
  and 
  

   take 
  the 
  corresponding 
  departure, 
  marking 
  it 
  with 
  the 
  same 
  sign 
  as 
  H, 
  

   and 
  denoting 
  it 
  by 
  u. 
  Take 
  also 
  the 
  difference 
  of 
  latitude, 
  marking 
  

   it 
  -j-, 
  when 
  H 
  is 
  less 
  than 
  90°, 
  but 
  — 
  , 
  when 
  H 
  exceeds 
  90°, 
  and 
  de- 
  

   note 
  it 
  by 
  C. 
  With 
  the 
  sun's 
  declination 
  as 
  a 
  course, 
  and 
  C 
  as 
  a 
  dis- 
  

   tance, 
  find 
  the 
  departure, 
  marking 
  with 
  the 
  same 
  sign 
  as 
  C 
  when 
  the 
  

   declination 
  is 
  -|-, 
  but 
  with 
  a 
  contrary 
  sign 
  when 
  it 
  is 
  — 
  , 
  and 
  denote 
  

   it 
  by 
  c. 
  Subtract 
  c 
  from 
  b, 
  and 
  denote 
  the 
  result 
  by 
  v. 
  Then 
  will 
  

   u 
  and 
  v 
  be 
  the 
  parallaxes 
  in 
  right 
  ascension 
  and 
  declination, 
  at 
  the 
  

   time 
  T. 
  

  

  Using 
  Table 
  IV., 
  add 
  together 
  the 
  squares 
  of 
  (p 
  — 
  u) 
  and 
  (q 
  — 
  «), 
  

   denoting 
  the 
  root 
  of 
  the 
  sum, 
  which 
  need 
  not 
  however 
  be 
  taken 
  out, 
  

   by 
  M. 
  Then 
  will 
  M 
  denote 
  the 
  apparent 
  distance 
  of 
  the 
  centres 
  of 
  

   the 
  sun 
  and 
  moon, 
  at 
  the 
  time 
  T. 
  

  

  6. 
  Take 
  a 
  time 
  T', 
  an 
  hour 
  earlier 
  or 
  later 
  lhan 
  T, 
  according 
  as 
  

   the 
  value 
  of 
  (p 
  — 
  u) 
  at 
  the 
  time 
  T, 
  is 
  -J- 
  or 
  — 
  , 
  and 
  find 
  for 
  this 
  time, 
  

   by 
  the 
  preceding 
  articles, 
  the 
  values 
  of 
  p, 
  q, 
  H, 
  u, 
  C, 
  c, 
  and 
  v 
  : 
  and 
  

   thence 
  the 
  square 
  of 
  the 
  apparent 
  distance 
  of 
  the 
  centres, 
  denoting 
  the 
  

   root 
  by 
  M'. 
  

  

  Subtract, 
  respectively, 
  the 
  values 
  of 
  (p 
  — 
  u) 
  and 
  (q 
  — 
  v) 
  at 
  the 
  earlier 
  

   of 
  the 
  times 
  T 
  and 
  T', 
  from 
  their 
  values 
  at 
  the 
  later 
  time, 
  and 
  denote 
  

   the 
  results 
  by 
  (p 
  — 
  w') 
  and 
  {q 
  — 
  v'). 
  Add 
  together 
  the 
  squares 
  of 
  

   (p 
  — 
  u) 
  and 
  (q 
  — 
  «'), 
  and 
  taking 
  from 
  the 
  table 
  the 
  corresponding 
  

   root, 
  denote 
  it 
  by 
  n. 
  Then 
  will 
  n 
  express 
  the 
  horary 
  motion 
  of 
  the 
  

  

  