﻿302 
  PRACTICAL 
  RULE 
  FOR 
  CALCULATING 
  

  

  From 
  the 
  square 
  of 
  k, 
  subtract 
  the 
  square 
  of 
  m, 
  and 
  taking 
  the 
  root, 
  

   denote 
  it 
  by 
  h. 
  Add 
  together 
  the 
  squares 
  of 
  (p 
  — 
  u) 
  and 
  (q 
  — 
  v), 
  

   and 
  from 
  the 
  sum 
  subtract 
  the 
  square 
  of 
  m. 
  Take 
  the 
  root 
  of 
  the 
  

   remainder, 
  and 
  denote 
  it 
  by 
  h 
  '. 
  Add 
  together 
  the 
  squares 
  of 
  (p' 
  ■ 
  — 
  u) 
  

   and 
  (q' 
  — 
  v'), 
  and 
  taking 
  the 
  root 
  of 
  the 
  sum, 
  it 
  will 
  be 
  the 
  value 
  of 
  

   n, 
  at 
  the 
  time 
  T'. 
  Then 
  as 
  n 
  : 
  diff. 
  of 
  h 
  and 
  li 
  : 
  : 
  60 
  minutes 
  : 
  a 
  cor- 
  

   rection, 
  in 
  minutes, 
  which 
  being 
  added 
  to 
  T', 
  or 
  subtracted 
  from 
  it, 
  ' 
  

   according 
  as 
  ti 
  is 
  greater 
  or 
  less 
  than 
  h, 
  will 
  give 
  the 
  corrected 
  time 
  

   of 
  beginning. 
  

  

  9. 
  The 
  corrected 
  time 
  of 
  end 
  is 
  found 
  in 
  exactly 
  the 
  same 
  manner, 
  

   except 
  that 
  the 
  correction 
  is 
  to 
  be 
  subtracted 
  from 
  T', 
  the 
  approximate 
  

   time 
  of 
  end, 
  when 
  h' 
  is 
  greater 
  than 
  /*, 
  but 
  added 
  to 
  it 
  when 
  h 
  is 
  less 
  

   than 
  h. 
  

  

  10. 
  From 
  the 
  values 
  of 
  (p 
  — 
  u), 
  (q 
  — 
  v), 
  u 
  and 
  v, 
  at 
  the 
  approxi- 
  

   mate 
  time 
  of 
  beginning, 
  find, 
  by 
  means 
  of 
  their 
  horary 
  changes 
  (j/ 
  — 
  w'), 
  

   (q' 
  — 
  v') 
  : 
  u 
  and 
  v', 
  their 
  values 
  at 
  the 
  corrected 
  time 
  of 
  beginning. 
  

   Then 
  taking 
  the 
  values 
  of 
  (p 
  — 
  u) 
  and 
  (q 
  — 
  v), 
  divide 
  the 
  less 
  by 
  the 
  

   greater, 
  extending 
  the 
  quotient 
  to 
  three 
  decimal 
  places, 
  and 
  marking 
  it 
  

   -(- 
  when 
  the 
  signs 
  of 
  (p 
  — 
  u) 
  and 
  (q 
  — 
  v) 
  are 
  alike, 
  but 
  — 
  when 
  

   the}' 
  are 
  different. 
  Then 
  with 
  the 
  quotient 
  as 
  the 
  argument, 
  take 
  the 
  

   corresponding 
  arc 
  from 
  the 
  proper 
  column 
  of 
  Table 
  V., 
  as 
  denoted 
  by 
  

   the 
  remarks 
  at 
  the 
  head 
  of 
  the 
  table. 
  If 
  (p 
  — 
  u) 
  is 
  -f-, 
  denote 
  this 
  

   arc 
  by 
  P, 
  but 
  if 
  it 
  is 
  — 
  , 
  add 
  180° 
  to 
  the 
  arc, 
  and 
  denote 
  the 
  sum 
  by 
  P. 
  

   With 
  the 
  values 
  of 
  u 
  and 
  v, 
  proceed 
  in 
  the 
  same 
  manner 
  to 
  find 
  another 
  

   arc, 
  denoting 
  it 
  by 
  Q, 
  if 
  u 
  is 
  -{-, 
  but 
  adding 
  180° 
  to 
  it 
  if 
  u 
  is 
  — 
  , 
  and 
  

   denoting 
  the 
  sum 
  by 
  Q. 
  Subtract 
  P 
  from 
  Q, 
  increasing 
  the 
  latter 
  by 
  

   360° 
  when 
  it 
  is 
  less 
  than 
  the 
  former, 
  and 
  denote 
  the 
  remainder 
  by 
  V. 
  

   Then 
  will 
  V 
  express 
  the 
  distance 
  from 
  the 
  sun's 
  vertex 
  to 
  the 
  point 
  of 
  

   the 
  disc 
  at 
  which 
  the 
  eclipse 
  commences, 
  measured 
  on 
  the 
  circumfe- 
  

   rence 
  of 
  the 
  disc, 
  from 
  the 
  vertex 
  to 
  the 
  right 
  hand. 
  

  

  11. 
  The 
  times 
  of 
  beginning, 
  greatest 
  obscuration, 
  and 
  end, 
  found 
  as 
  

   above, 
  are 
  expressed 
  in 
  Greenwich 
  mean 
  time, 
  and 
  may 
  be 
  changed 
  

   to 
  mean 
  time 
  of 
  the 
  given 
  place, 
  by 
  adding 
  or 
  subtracting 
  the 
  difference 
  

   of 
  meridians 
  in 
  time, 
  according 
  as 
  the 
  place 
  is 
  east 
  or 
  west 
  from 
  Green- 
  

   wich. 
  

  

  Note 
  1. 
  The 
  calculation 
  will 
  be 
  facilitated 
  by 
  having 
  two 
  small 
  

  

  