﻿308 
  PROCEEDINGS 
  OF 
  THE 
  CALIFORNIA 
  

  

  the 
  method 
  of 
  least 
  squares, 
  and 
  so 
  thoroughly 
  sift 
  them 
  by 
  Pierce's 
  criterion, 
  

   that 
  hardly 
  the 
  trace 
  of 
  a 
  large 
  error 
  remains 
  ; 
  and 
  the 
  more 
  minute 
  errors, 
  being 
  

   casual 
  and 
  accidental, 
  sometimes 
  lie 
  one 
  way, 
  sometimes 
  the 
  other 
  ; 
  sometimes 
  

   diminishing 
  and 
  sometimes 
  tending 
  to 
  increase 
  the 
  results. 
  And, 
  inasmuch 
  as 
  

   the 
  theory 
  of 
  probabilities 
  tells 
  us 
  that 
  these 
  accidental 
  errors 
  are 
  as 
  liable 
  to 
  

   lie 
  one 
  way 
  as 
  the 
  other, 
  we 
  hence 
  have 
  but 
  to 
  greatly 
  multiply 
  our 
  observations 
  

   under 
  varied 
  circumstances 
  and 
  take 
  the 
  mean 
  or 
  average 
  of 
  the 
  results 
  obtained, 
  

   and 
  we 
  have 
  this 
  class 
  of 
  errors 
  so 
  far 
  subdued, 
  by 
  thus 
  setting 
  them 
  to 
  destroy- 
  

   ing 
  one 
  another, 
  that 
  they 
  no 
  longer 
  sensibly 
  vitiate 
  our 
  practical 
  results. 
  

  

  This 
  principle 
  of 
  repetition, 
  though 
  so 
  simple 
  in 
  theory 
  and 
  so 
  beautiful 
  in 
  

   practice, 
  when 
  the 
  instrument 
  and 
  observer 
  are 
  upon 
  a 
  firm 
  basis, 
  utterly 
  fails 
  

   of 
  application 
  where 
  the 
  observer 
  and 
  his 
  instrument 
  are 
  tossed 
  alike 
  on 
  the 
  

   ocean's 
  wave, 
  and 
  the 
  object 
  observed 
  is 
  " 
  on 
  wing." 
  It 
  becomes 
  therefore 
  im- 
  

   perative 
  upon 
  the 
  navigator, 
  if 
  he 
  would 
  trace 
  accurately 
  his 
  ship's 
  path 
  over 
  the 
  

   trackless 
  ocean, 
  that 
  he 
  attain 
  rigorous 
  correctness 
  in 
  the 
  results 
  of 
  " 
  each 
  " 
  of 
  

   his 
  instrumental 
  measurements 
  ; 
  and 
  to 
  this 
  end, 
  his 
  constant 
  care 
  and 
  vigilance 
  

   must 
  be 
  directed 
  to 
  the 
  detection 
  and 
  compensation 
  of 
  errors, 
  either 
  by 
  annhil- 
  

   ating 
  or 
  taking 
  account 
  of 
  and 
  allowing 
  for 
  them. 
  This 
  latter 
  method 
  of 
  tak- 
  

   ing 
  account 
  of 
  and 
  allowing 
  for 
  errors, 
  is 
  that 
  ordinarily 
  pursued 
  by 
  the 
  navi" 
  

   gator 
  ; 
  but 
  it 
  has 
  navigated 
  so 
  many 
  noble 
  ships 
  to 
  the 
  bottom 
  of 
  the 
  sea, 
  that 
  

   the 
  voice 
  of 
  humanity 
  and 
  the 
  interests 
  of 
  commerce 
  alike 
  demand 
  such 
  a 
  mod- 
  

   ification 
  of 
  the 
  methods 
  of 
  observation, 
  and 
  the 
  forms 
  of 
  the 
  instruments, 
  as 
  to 
  

   annihilate 
  eSectually 
  and 
  alike 
  errors 
  inherent 
  in 
  the 
  observer, 
  in 
  the 
  instrument, 
  

   and 
  in 
  the 
  atmosphere. 
  

  

  In 
  the 
  method 
  of 
  taking 
  observations 
  now 
  generally 
  practiced 
  by 
  the 
  navi- 
  

   gator, 
  instrumental 
  adjustments, 
  atmospheric 
  refraction, 
  and 
  the 
  impressibility 
  of 
  

   the 
  optic 
  nerve, 
  are 
  all 
  depended 
  upon 
  as 
  constant 
  and 
  invariable 
  during 
  the 
  ob- 
  

   servations 
  ; 
  while, 
  in 
  fact, 
  they 
  all 
  are 
  ever 
  fluctuating. 
  The 
  ever-varying 
  fluc- 
  

   tuations 
  of 
  heat 
  and 
  cold 
  are 
  continually 
  changing 
  the 
  amount 
  of 
  atmospheric 
  

   refraction, 
  as 
  also 
  that, 
  of 
  every 
  instrumental 
  adjustment. 
  And 
  it 
  is 
  a 
  well 
  

   ■ 
  known 
  fact 
  in 
  optics 
  that 
  the 
  irradiation 
  (which 
  causes 
  bright 
  objects 
  to 
  appear 
  

   larger 
  than 
  they 
  really 
  are) 
  varies 
  with 
  the 
  length 
  of 
  time 
  during 
  which 
  we 
  

   look 
  upon 
  the 
  object, 
  during 
  the 
  first 
  few 
  moments 
  of 
  observation 
  gradually 
  de- 
  

   creasing 
  ; 
  and 
  then, 
  as 
  the 
  optic 
  nerve 
  becomes 
  fatigued, 
  the 
  optical 
  illusion 
  

   (irradiation) 
  reappears 
  magnified 
  ten-fold. 
  These 
  are 
  not 
  mere 
  speculative 
  

   sources 
  of 
  errors, 
  but 
  practical 
  annoyances, 
  which 
  every 
  observer 
  has 
  to 
  contend 
  

   with 
  — 
  the 
  incompetent 
  navigator, 
  of 
  course, 
  slurring 
  them 
  over 
  as 
  refinements 
  

   too 
  delicate 
  to 
  deal 
  with, 
  while 
  he 
  attributes 
  the 
  error 
  thus 
  introduced 
  into 
  his 
  

   position 
  to 
  the 
  action 
  of 
  imaginary 
  ocean 
  currents 
  ; 
  but 
  the 
  thorough 
  navigator 
  

   meets 
  these 
  errors 
  fairly, 
  and 
  sets 
  about 
  annihilating 
  them. 
  Yet 
  it 
  may 
  be 
  in- 
  

   teresting 
  to 
  those 
  navigators 
  who 
  insist 
  on 
  neglecting 
  these 
  finer 
  instrumental 
  

   errors, 
  to 
  know 
  that 
  very 
  many 
  of 
  the 
  sextants 
  used 
  in 
  navigating 
  vessels 
  have 
  

   an 
  eccentricity 
  ranging 
  from 
  one 
  to 
  four 
  minutes, 
  which 
  is 
  often 
  aggravated 
  by 
  

   parallax 
  of 
  index-glass 
  ; 
  and 
  his 
  positions 
  are 
  vitiated 
  to 
  the 
  full 
  extent 
  of 
  

   these 
  neglected 
  errors. 
  

  

  