﻿Gravity 
  to 
  Continental 
  Elevation. 
  83 
  

  

  distributed, 
  except 
  that 
  there 
  remains 
  for 
  the 
  time 
  being 
  a 
  

   break 
  of 
  a 
  little 
  more 
  than 
  ten 
  degrees 
  between 
  Salt 
  Lake 
  and 
  

   San 
  Francisco. 
  It 
  is 
  to 
  be 
  hoped 
  that 
  the 
  Coast 
  Survey 
  will 
  

   in 
  the 
  near 
  future 
  be 
  able 
  to 
  fill 
  up 
  this 
  break. 
  The 
  elevations 
  

   above 
  sea 
  level 
  are 
  also 
  given, 
  together 
  with 
  the 
  force 
  of 
  grav- 
  

   ity 
  at 
  each 
  station. 
  These 
  values 
  of 
  the 
  force 
  of 
  gravity 
  must 
  

   be 
  accepted 
  only 
  tentatively, 
  as 
  it 
  will 
  appear 
  that 
  they 
  are 
  all 
  

   made 
  to 
  depend 
  upon 
  the 
  value 
  at 
  Washington. 
  This 
  value 
  

   was 
  adopted 
  after 
  an 
  examination 
  of 
  several 
  values 
  for 
  this 
  

   point, 
  some 
  of 
  which 
  were 
  not 
  very 
  satisfactory 
  absolute 
  meas- 
  

   urements, 
  and 
  others 
  the 
  result 
  of 
  relative 
  determinations 
  at 
  

   Washington 
  and 
  various 
  absolute 
  stations 
  in 
  Europe. 
  It 
  is 
  not 
  

   believed 
  tbat 
  the 
  error 
  of 
  the 
  assumed 
  value 
  is 
  very 
  great, 
  and 
  

   hence 
  the 
  table 
  of 
  values 
  given 
  may 
  be 
  considered 
  as 
  very 
  

   close 
  approximations 
  to 
  the 
  absolute 
  results. 
  .Relatively 
  the 
  

   degree 
  of 
  accuracy 
  is, 
  of 
  course, 
  very 
  much 
  higher. 
  

  

  Xow 
  the 
  question 
  of 
  the 
  existence 
  at 
  any 
  point 
  of 
  an 
  excess 
  

   or 
  deficiency 
  of 
  the 
  force 
  of 
  gravitation 
  is 
  one 
  which 
  depends, 
  

   of 
  course, 
  purely 
  upon 
  definition. 
  Strictly 
  speaking 
  there 
  can 
  

   be 
  no 
  excess 
  or 
  deficiency 
  of 
  gravity 
  at 
  any 
  point 
  on 
  the 
  sur- 
  

   face 
  of 
  the 
  earth, 
  for 
  it 
  must 
  be 
  whatever 
  it 
  is 
  ; 
  but 
  if 
  compari- 
  

   sons 
  be 
  made 
  of 
  actual 
  values 
  with 
  a 
  theoretical 
  distribution 
  

   of 
  the 
  force 
  of 
  gravity 
  some 
  interesting 
  conclusions 
  can 
  be 
  

   drawn 
  from 
  an 
  examination 
  of 
  the 
  excesses 
  and 
  deficiencies. 
  

   Accepting 
  any 
  spheroid, 
  as 
  Clark's 
  spheroid 
  of 
  1866, 
  and 
  assum- 
  

   ing 
  any 
  distribution 
  of 
  gravity 
  that 
  may 
  be 
  chosen, 
  the 
  theo- 
  

   retical 
  values 
  may 
  be 
  calculated 
  for 
  any 
  point 
  on 
  the 
  surface 
  

   of 
  the 
  earth, 
  and 
  the 
  difference 
  between 
  these 
  theoretical 
  

   values 
  and 
  those 
  actually 
  observed 
  would 
  naturally 
  lead 
  to 
  

   some 
  conclusion 
  as 
  to 
  the 
  correctness 
  of 
  the 
  theory 
  of 
  distribu- 
  

   tion 
  which 
  had 
  been 
  adopted. 
  However, 
  the 
  greater 
  part 
  of 
  

   the 
  deviation 
  of 
  the 
  observed 
  values 
  of 
  the 
  force 
  of 
  gravity 
  at 
  

   the 
  several 
  points 
  given 
  in 
  the 
  table 
  above, 
  from 
  the 
  values 
  as 
  

   distributed 
  over 
  Clark's 
  spheroid, 
  in 
  accordance 
  with 
  the 
  gene- 
  

   rally 
  accepted 
  formula, 
  is 
  due 
  to 
  the 
  elevation 
  of 
  these 
  points 
  

   above 
  the 
  sea 
  level. 
  Now 
  in 
  order 
  to 
  bring 
  such 
  observations 
  

   at 
  elevated 
  points 
  into 
  the 
  same 
  category 
  as 
  those 
  observed 
  at 
  

   or 
  near 
  the 
  surface 
  of 
  the 
  imaginary 
  spheroid, 
  it 
  is 
  necessary 
  

   to 
  reduce 
  them 
  to 
  the 
  sea 
  level, 
  and 
  in 
  doing 
  that 
  we 
  are 
  

   obliged 
  to 
  take 
  account 
  not 
  only 
  of 
  the 
  actual 
  diminution 
  of 
  

   the 
  force 
  of 
  gravity 
  due 
  to 
  the 
  greater 
  distance 
  of 
  the 
  point 
  

   from 
  the 
  center 
  of 
  the 
  earth, 
  but 
  also 
  the 
  attraction 
  of 
  the 
  

   continental 
  mass 
  which 
  lies 
  above 
  the 
  spheroidal 
  surface. 
  This 
  

   correction 
  is 
  usually 
  made 
  by 
  the 
  application 
  of 
  a 
  formula 
  due 
  

   to 
  Bouger 
  and 
  used 
  by 
  him 
  many 
  years 
  ago 
  for 
  making 
  reduc- 
  

   tions 
  of 
  observations 
  made 
  by 
  the 
  Peruvian 
  expedition 
  of 
  the 
  

   French 
  Academy. 
  This 
  formula 
  is 
  : 
  — 
  

  

  