﻿ACADEMY 
  OF 
  SCIENCES. 
  309 
  

  

  By 
  the 
  ordinary 
  method 
  of 
  observing 
  successive 
  contacts 
  of 
  the 
  opposing 
  

   limbs 
  of 
  the 
  sun 
  with 
  the 
  horizon, 
  even 
  if 
  the 
  mind 
  from 
  one 
  observation 
  to 
  

   the 
  other 
  retains 
  fresh 
  and 
  full 
  the 
  vision 
  of 
  the 
  contact, 
  still 
  the 
  observer 
  will 
  

   fail 
  to 
  make 
  the 
  contact 
  of 
  the 
  horizon 
  with 
  the 
  perimeter 
  of 
  the 
  sun 
  at 
  equal 
  

   distances 
  from 
  its 
  center, 
  because 
  he 
  makes 
  these 
  contacts 
  at 
  different 
  instants 
  

   of 
  time, 
  when 
  the 
  eye 
  is 
  differently 
  affected 
  by 
  irradiation 
  and 
  fatigue. 
  And 
  

   hence, 
  what 
  would 
  appear 
  one 
  moment 
  a 
  delicate 
  contact, 
  would 
  one 
  minute 
  

   afterward 
  be 
  wide 
  of 
  the 
  mark. 
  And 
  thus 
  it 
  is, 
  in 
  the 
  observations 
  thus 
  made 
  

   with 
  an 
  instrument 
  that 
  is 
  varying, 
  with 
  a 
  vision 
  that 
  is 
  varying, 
  and 
  through 
  

   an 
  atmosphere 
  that 
  is 
  varying, 
  we 
  can 
  clearly 
  see 
  the 
  source 
  of 
  the 
  errors 
  which 
  

   have 
  lured 
  many 
  an 
  unsuspecting 
  ship 
  fatally 
  onward 
  against 
  rocks 
  and 
  reefs. 
  

  

  By 
  the 
  method 
  which 
  I 
  now 
  propose, 
  and 
  with 
  the 
  form 
  of 
  instrument 
  herein 
  

   designated, 
  we 
  avoid 
  in 
  part, 
  and 
  in 
  the 
  remainder 
  essentially 
  annihilate, 
  these 
  most 
  

   fruitful 
  sources 
  of 
  errors. 
  By 
  placing 
  within 
  the 
  instrument 
  itself 
  the 
  means 
  of 
  

   self-correction, 
  we 
  have 
  the 
  most 
  effectual 
  checks 
  upon 
  its 
  errors 
  of 
  construction 
  

   and 
  the 
  changes 
  of 
  its 
  adjustments. 
  Thus, 
  from 
  very 
  simple 
  geometrical 
  con- 
  

   siderations, 
  it 
  may 
  be 
  easily 
  shown 
  that 
  the 
  errors 
  of 
  eccentricity 
  and 
  of 
  gradu- 
  

   ation 
  are 
  totally 
  eliminated 
  by 
  the 
  mean 
  of 
  the 
  readings 
  of 
  two 
  verniers 
  180 
  

   deg. 
  apart, 
  and 
  by 
  measuring 
  the 
  angles 
  on 
  different 
  parts 
  of 
  the 
  arc 
  ; 
  and 
  by 
  

   using 
  an 
  index-glass 
  susceptible 
  of 
  reversal 
  between 
  the 
  parts 
  of 
  a 
  set 
  of 
  obser- 
  

   vations, 
  we 
  banish 
  every 
  trace 
  of 
  error 
  from 
  parallax 
  of 
  index-glass 
  from 
  our 
  

   results. 
  And 
  every 
  error 
  of 
  observation 
  — 
  such 
  as 
  arise, 
  for 
  example, 
  from 
  in- 
  

   expertness, 
  defective 
  vision, 
  slowness 
  in 
  seizing 
  the 
  exact 
  instant 
  of 
  occurrence 
  

   of 
  a 
  phenomenon, 
  and 
  from 
  atmospheric 
  indistinctness, 
  and 
  insufficient 
  optical 
  

   power 
  in 
  the 
  instrument 
  — 
  are 
  all 
  alike 
  essentially 
  checked 
  by 
  observing 
  the 
  con- 
  

   tacts 
  of 
  the 
  two 
  opposing 
  limbs 
  of 
  the 
  sun 
  with 
  the 
  horizon 
  at 
  the 
  same 
  instant. 
  

  

  Now, 
  since 
  we 
  have 
  the 
  contacts 
  of 
  the 
  upper 
  and 
  lower 
  limbs 
  of 
  the 
  sun 
  in 
  

   the 
  field 
  of 
  view 
  at 
  the 
  same 
  moment, 
  we 
  have 
  before 
  our 
  eyes 
  a 
  most 
  thorough 
  

   check 
  on 
  the 
  character 
  of 
  the 
  contacts, 
  since 
  by 
  direct 
  and 
  instantaneous 
  opti- 
  

   cal 
  comparison 
  we 
  make 
  each 
  of 
  them 
  equally 
  well. 
  And, 
  moreover, 
  since 
  we 
  

   make 
  the 
  contacts 
  of 
  both 
  limbs 
  of 
  the 
  sun 
  with 
  the 
  horizon 
  at 
  the 
  same 
  in- 
  

   stant, 
  we 
  have 
  in 
  " 
  each 
  sight" 
  an 
  altitude, 
  complete 
  in 
  itself, 
  without 
  the 
  aid 
  of 
  

   a 
  supposition 
  of 
  the 
  constancy 
  of 
  atmospheric 
  refraction, 
  or 
  the 
  stability 
  of 
  in- 
  

   strumental 
  adjustments, 
  or 
  the 
  constancy 
  of 
  the 
  impressibility 
  of 
  the 
  optic 
  

   nerve, 
  or 
  the 
  aid 
  of 
  memory. 
  

  

  But, 
  as 
  we 
  cannot 
  measure 
  what 
  we 
  cannot 
  see, 
  it 
  is 
  obvious 
  that 
  by 
  the 
  or- 
  

   dinary 
  method 
  of 
  successive 
  single 
  contacts, 
  those 
  errors, 
  too 
  minute 
  for 
  low 
  

   optical 
  powers, 
  enter 
  and 
  vitiate 
  the 
  results 
  to 
  their 
  full 
  extent. 
  But 
  by 
  

   this 
  method 
  of 
  double 
  contacts 
  at 
  the 
  same 
  instant, 
  we 
  detect 
  and 
  avoid 
  these 
  

   errors, 
  which 
  would 
  otherwise 
  elude 
  our 
  vision. 
  As 
  for 
  example, 
  suppose 
  we 
  

   make 
  what 
  appears 
  to 
  be 
  a 
  contact 
  of 
  the 
  upper 
  limb 
  of 
  the 
  sun 
  with 
  the 
  hor- 
  

   izon, 
  and 
  then 
  by 
  glancing 
  at 
  the 
  other 
  contact, 
  of 
  the 
  lower 
  limb 
  and 
  the 
  hori- 
  

   zon, 
  in 
  the 
  same 
  field 
  of 
  view, 
  it 
  will 
  appear 
  a 
  contact 
  equally 
  nice 
  as 
  the 
  other, 
  

   if 
  the 
  first 
  contact 
  was 
  exact, 
  but 
  if 
  it 
  was 
  at 
  all 
  in 
  error, 
  then 
  the 
  second 
  will 
  

   be 
  in 
  error 
  twice 
  as 
  much 
  as 
  the 
  first 
  : 
  and 
  thus 
  it 
  is 
  bi/ 
  doubling 
  t/iese 
  errors, 
  

  

  