﻿298 
  PRACTICAL. 
  RULE 
  FOR 
  CALCULATING 
  

  

  given 
  angle 
  exceeds 
  90°, 
  it 
  must 
  be 
  subtracted 
  from 
  180°, 
  and 
  the 
  

   remainder 
  taken 
  as 
  the 
  course. 
  

  

  In 
  calculating 
  the 
  parallaxes, 
  the 
  products 
  of 
  ten 
  times 
  the 
  distance 
  

   of 
  the 
  given 
  place 
  from 
  the 
  earth's 
  centre, 
  by 
  the 
  cosine 
  and 
  sine 
  of 
  

   its 
  reduced 
  latitude, 
  are 
  used. 
  These 
  products 
  being 
  constant 
  for 
  a 
  

   given 
  place, 
  serve, 
  when 
  once 
  obtained, 
  for 
  all 
  calculations 
  of 
  eclipses 
  

   of 
  the 
  sun, 
  or 
  of 
  occultations 
  for 
  that 
  place. 
  Let 
  them 
  be 
  denoted, 
  

   respectively, 
  by 
  X 
  and 
  Y. 
  Then, 
  to 
  obtain 
  them, 
  add 
  respectively, 
  to 
  

   the 
  logarithmic 
  cosine 
  and 
  sine 
  of 
  the 
  latitude 
  of 
  the 
  place, 
  the 
  loga- 
  

   rithms 
  x 
  and 
  y, 
  taken 
  from 
  Table 
  I. 
  of 
  the 
  annexed 
  tables, 
  with 
  the 
  

   latitude 
  of 
  the 
  place 
  as 
  the 
  argument, 
  and 
  reject 
  10 
  from 
  the 
  index 
  of 
  

   each 
  sum. 
  The 
  results 
  will 
  be 
  the 
  logarithms 
  of 
  X 
  and 
  Y. 
  These 
  

   logarithms 
  are 
  used 
  in 
  the 
  exact 
  calculation 
  of 
  the 
  parallaxes. 
  The 
  

   natural 
  numbers 
  corresponding 
  to 
  them, 
  taken 
  out 
  to 
  two 
  decimal 
  

   places, 
  are 
  the 
  values 
  of 
  X 
  and 
  Y,that 
  are 
  used 
  in 
  the 
  approximate 
  cal- 
  

   culation. 
  These 
  values 
  are 
  given 
  in 
  Table 
  II. 
  for 
  each 
  degree 
  of 
  lati- 
  

   tude. 
  

  

  In 
  the 
  addition 
  and 
  subtraction 
  of 
  quantities, 
  except 
  those 
  which 
  are 
  

   in 
  time, 
  the 
  algebraic 
  rules 
  for 
  performing 
  these 
  operations 
  are 
  to 
  be 
  

   observed. 
  Wherever 
  the 
  rule 
  directs 
  the 
  root 
  of 
  a 
  quantity 
  to 
  be 
  taken, 
  

   it 
  is 
  the 
  positive 
  square 
  root 
  that 
  is 
  implied. 
  

  

  The 
  quantities, 
  denominated 
  in 
  the 
  rule, 
  parallaxes 
  in 
  right 
  ascen- 
  

   sion 
  and 
  declination, 
  are 
  not 
  strictly 
  those 
  quantities 
  : 
  they, 
  however, 
  

   differ 
  but 
  little 
  from 
  them, 
  and 
  are 
  the 
  quantities 
  required 
  in 
  this 
  

   method 
  of 
  calculation. 
  

  

  RULE. 
  

  

  1. 
  Consider 
  north 
  declinations 
  and 
  north 
  horary 
  motions 
  as 
  -f-, 
  and 
  

   south 
  ones 
  as 
  — 
  . 
  Find 
  the 
  difference 
  of 
  the 
  sun's 
  and 
  moon's 
  decli- 
  

   nations, 
  by 
  subtracting 
  the 
  declination 
  of 
  the 
  sun, 
  as 
  given 
  in 
  the 
  ele- 
  

   ments, 
  from 
  that 
  of 
  the 
  moon. 
  In 
  like 
  manner 
  find 
  the 
  difference 
  of 
  

   the 
  horary 
  motions 
  of 
  the 
  sun 
  and 
  moon, 
  in 
  right 
  ascension, 
  the 
  differ- 
  

   ence 
  of 
  their 
  horary 
  motions 
  in 
  declination, 
  and 
  the 
  difference 
  of 
  their 
  

   equatorial 
  horizontal 
  parallaxes. 
  

  

  2. 
  Multiply 
  the 
  difference 
  of 
  the 
  sun's 
  and 
  moon's 
  declinations, 
  re- 
  

  

  