﻿476 
  G. 
  C. 
  Comstock 
  — 
  The 
  Secular 
  Variation 
  of 
  Latitudes. 
  

  

  But 
  in 
  the 
  present 
  case 
  the 
  sine 
  flexure 
  is 
  eliminated 
  by 
  giving 
  

   equal 
  weight 
  to 
  the 
  observations 
  of 
  stars 
  on 
  opposite 
  sides 
  of 
  

   the 
  zenith 
  in 
  the 
  reduction 
  of 
  each 
  night's 
  work, 
  and 
  the 
  co- 
  

   sine 
  flexure 
  is 
  commonly 
  supposed 
  to 
  be 
  eliminated 
  from 
  the 
  

   mean 
  of 
  observations 
  made 
  Circle 
  W. 
  and 
  Circle 
  E. 
  

  

  I 
  know 
  of 
  no 
  other 
  reasonable 
  hypothesis 
  to 
  adopt 
  in 
  this 
  

   connection 
  except 
  that 
  of 
  an 
  actual 
  change 
  in 
  the 
  latitude, 
  but 
  

   before 
  coming 
  to 
  any 
  conclusion 
  it 
  will 
  be 
  well 
  to 
  consider 
  

   another 
  set 
  of 
  latitude 
  determinations 
  which 
  are 
  available. 
  

   The 
  latitude 
  of 
  Madison 
  was 
  first 
  determined 
  in 
  1873 
  by 
  offi- 
  

   cers 
  of 
  the 
  IT. 
  S. 
  Coast 
  Survey, 
  employing 
  the 
  Talcott 
  method, 
  

   and 
  since 
  that 
  date 
  five 
  other 
  determinations 
  have 
  been 
  made 
  

   by 
  the 
  same 
  method. 
  The 
  final 
  results 
  of 
  these 
  determinations 
  

   are 
  contained 
  in 
  the 
  following 
  table 
  : 
  

  

  No. 
  of 
  

  

  

  , 
  

  

  — 
  * 
  — 
  

  

  > 
  

  

  

  Periodic 
  

  

  Corrected 
  

  

  Date. 
  

  

  Obs'r. 
  

  

  Obs. 
  

  

  Pairs. 
  

  

  Seconds 
  of 
  Lat. 
  

  

  Term. 
  

  

  Latitude. 
  

  

  873-62 
  

  

  B. 
  

  

  60 
  

  

  12 
  

  

  36 
  /; 
  -24 
  ±0".05 
  

  

  + 
  // 
  .15 
  

  

  36"'39 
  

  

  81-64 
  

  

  C. 
  

  

  26 
  

  

  16 
  

  

  36-58 
  =fc 
  '13 
  

  

  4- 
  . 
  -17 
  

  

  36-75 
  

  

  84-50 
  

  

  C. 
  &H 
  

  

  72 
  

  

  11 
  

  

  3698 
  ± 
  -08 
  

  

  — 
  '03 
  

  

  36-95 
  

  

  89-33 
  

  

  T. 
  

  

  84 
  

  

  15 
  

  

  37-36 
  ± 
  '14 
  

  

  — 
  -23 
  

  

  37-13 
  

  

  90-50 
  

  

  T. 
  

  

  53 
  

  

  11 
  

  

  37-17 
  ± 
  '09 
  

  

  — 
  -03 
  

  

  37-14 
  

  

  91-50 
  

  

  C. 
  

  

  49 
  

  

  13 
  

  

  37-21 
  ± 
  *06 
  

  

  — 
  -02 
  

  

  37*19 
  

  

  The 
  latitudes 
  determined 
  in. 
  1884, 
  '90 
  and 
  '91 
  are 
  from 
  obser- 
  

   vation- 
  of 
  substantially 
  the 
  same 
  pairs 
  of 
  stars, 
  the 
  other 
  lati- 
  

   tudes 
  are 
  from 
  other 
  stars 
  but 
  all 
  of 
  the 
  declinations 
  employed 
  

   have 
  been 
  taken 
  either 
  directly 
  from 
  the 
  Berliner 
  Jahrbuch 
  or 
  

   from 
  a 
  discussion 
  of 
  the 
  data 
  contained 
  in 
  modern 
  catalogues 
  

   of 
  precision 
  reduced 
  by 
  the 
  application 
  of 
  systematic 
  correc- 
  

   tions 
  to 
  the 
  system 
  of 
  Pub. 
  XIV, 
  Astron. 
  Gesell. 
  While 
  the 
  

   star 
  places 
  thus 
  determined 
  doubtless 
  admit 
  of 
  further 
  improve- 
  

   ment, 
  it 
  seems 
  to 
  me 
  highly 
  improbable 
  that 
  any 
  one 
  of 
  the 
  

   above 
  latitudes 
  can 
  be 
  altered 
  in 
  this 
  way 
  by 
  so 
  much 
  as 
  //# 
  l 
  

   and 
  they 
  must 
  therefore 
  be 
  considered 
  as 
  representing 
  the 
  

   relation 
  of 
  the 
  latitude 
  at 
  the 
  epochs 
  of 
  observation 
  to 
  the 
  

   system 
  of 
  declinations 
  of 
  the 
  Berliner 
  Jahrbuch 
  within 
  the 
  

   limits 
  of 
  the 
  accidental 
  error 
  of 
  observation 
  and 
  such 
  sys- 
  

   tematic 
  error 
  as 
  may 
  affect 
  determinations 
  of 
  this 
  kind. 
  

  

  I 
  have 
  applied 
  to 
  the 
  observed 
  latitudes 
  the 
  correction 
  for 
  

   periodic 
  variation 
  

  

  — 
  0"-26sin 
  (0 
  + 
  73°) 
  

  

  and 
  have 
  obtained 
  by 
  a 
  graphical 
  treatment 
  of 
  the 
  corrected 
  

   results 
  the 
  

  

  Annual 
  variation 
  of 
  latitude 
  =-f-0"*043 
  

  

  