﻿344 
  ON 
  THE 
  DIFFERENCE 
  OF 
  LONGITUDE 
  

  

  under 
  favourable 
  circumstances, 
  may 
  always 
  be 
  considered 
  as 
  near 
  

   approximations 
  to 
  the 
  truth, 
  and 
  are 
  particularly 
  valuable 
  in 
  a 
  country 
  

   like 
  our 
  own, 
  whose 
  geography 
  must 
  yet 
  be 
  regarded 
  as 
  very 
  imper- 
  

   fect. 
  

  

  The 
  difference 
  in 
  the 
  results 
  obtained 
  by 
  the 
  several 
  observers 
  in 
  

   Philadelphia, 
  confirms 
  the 
  opinion, 
  now 
  generally 
  entertained, 
  that 
  the 
  

   times 
  of 
  commencement 
  and 
  termination 
  of 
  a 
  solar 
  eclipse 
  cannot 
  be 
  

   observed 
  with 
  a 
  very 
  high 
  degree 
  of 
  precision 
  ; 
  and 
  the 
  same 
  inference 
  

   is 
  deducible 
  from 
  a 
  comparison 
  of 
  the 
  durations 
  of 
  the 
  eclipse 
  at 
  the 
  

   several 
  places 
  of 
  observation. 
  In 
  every 
  case 
  where 
  the 
  commencement 
  

   and 
  end 
  have 
  both 
  been 
  observed, 
  the 
  duration 
  indicated 
  the 
  necessity 
  

   of 
  a 
  reduction 
  in 
  the 
  sum 
  of 
  the 
  semi-diameters 
  of 
  the 
  sun 
  and 
  moon, 
  

   similar 
  to 
  that 
  usually 
  made 
  for 
  irradiation 
  and 
  inflexion, 
  but 
  the 
  amount 
  

   of 
  this 
  correction, 
  as 
  determined 
  by 
  the 
  observations 
  at 
  different 
  places, 
  

   varies 
  from 
  1".5 
  to 
  4". 
  5. 
  These 
  discrepances 
  are 
  undoubtedly 
  attri- 
  

   butable, 
  in 
  a 
  great 
  measure, 
  to 
  the 
  extreme 
  difficulty 
  of 
  fixing 
  with 
  

   precision 
  the 
  instants 
  at 
  which 
  the 
  eclipse 
  begins 
  and 
  terminates. 
  

  

  In 
  determining 
  the 
  times 
  of 
  conjunction 
  of 
  the 
  sun 
  and 
  moon, 
  the 
  

   correction 
  for 
  irradiation 
  and 
  inflexion 
  has 
  been 
  assumed 
  at 
  3". 
  3, 
  that 
  

   being 
  the 
  mean 
  result 
  furnished 
  by 
  all 
  the 
  observations 
  which 
  have 
  

   been 
  calculated. 
  To 
  ascertain 
  the 
  amount 
  of 
  this 
  correction 
  from 
  

   the 
  observations 
  at 
  each 
  place, 
  the 
  observed 
  duration 
  was 
  compared 
  

   with 
  that 
  which 
  would 
  have 
  occurred 
  had 
  such 
  correction 
  been 
  unne- 
  

   cessary 
  ; 
  likewise 
  with 
  the 
  duration 
  due 
  to 
  an 
  irradiation 
  and 
  inflexion 
  

   of 
  5". 
  Then, 
  by 
  a 
  simple 
  proportion, 
  the 
  value 
  of 
  the 
  correction 
  was 
  

   estimated. 
  

  

  The 
  parallaxes 
  in 
  latitude 
  and 
  longitude 
  were 
  calculated 
  by 
  the 
  

   method 
  of 
  the 
  nonagesimal, 
  and 
  the 
  deduced 
  terrestrial 
  longitude 
  was 
  

   found 
  in 
  every 
  case 
  to 
  agree 
  so 
  nearly 
  with 
  that 
  assumed, 
  as 
  to 
  render 
  

   a 
  repetition 
  of 
  the 
  calculation 
  unnecessary. 
  The 
  errors 
  in 
  the 
  Lunar 
  

   Tables, 
  being 
  very 
  nearly 
  eliminated 
  by 
  the 
  comparison 
  of 
  observations 
  

   at 
  different 
  places, 
  have 
  been 
  neglected. 
  

  

  Having 
  adopted 
  a 
  mean 
  value 
  for 
  the 
  correction 
  for 
  irradiation 
  and 
  

   inflexion, 
  the 
  times 
  of 
  conjunction 
  of 
  the 
  sun 
  and 
  moon, 
  as 
  deduced 
  

   from 
  the 
  commencement 
  and 
  termination 
  at 
  each 
  place, 
  are 
  found 
  to 
  

   differ 
  slightly 
  from 
  each 
  other. 
  Both 
  these 
  times 
  are 
  inserted 
  in 
  the 
  

  

  