﻿W. 
  Bowie 
  — 
  Distribution 
  of 
  Isostatic 
  Compensation. 
  471 
  

  

  Art. 
  XLIV. 
  — 
  Local 
  Versus 
  Regional 
  Distribution 
  of 
  Isostatic 
  

   Compensation; 
  by 
  William 
  Bowie. 
  

  

  One 
  of 
  the 
  most 
  important 
  phases 
  of 
  the 
  subject 
  of 
  isostasy 
  

   is 
  that 
  of 
  the 
  distribution 
  of 
  the 
  compensation 
  of 
  the 
  topog- 
  

   raphy, 
  iu 
  a 
  horizontal 
  direction. 
  As 
  is 
  well 
  known, 
  the 
  com- 
  

   pensation 
  is 
  assumed, 
  in 
  the 
  computations 
  made 
  by 
  the 
  IT. 
  S. 
  

   Coast 
  and 
  Geodetic 
  Survey, 
  to 
  be 
  directly 
  under 
  the 
  topo- 
  

   graphic 
  features. 
  While 
  this 
  is 
  not 
  held 
  to 
  be 
  strictly 
  or 
  even 
  

   probably 
  true, 
  it 
  facilitates 
  the 
  reductions 
  which, 
  under 
  the 
  

   most 
  favorable 
  circumstances, 
  require 
  much 
  time 
  and 
  labor. 
  

  

  In 
  the 
  latest 
  investigation 
  by 
  the 
  Survey 
  on 
  the 
  subject 
  of 
  

   gravity 
  and 
  isostasy* 
  certain 
  tests 
  were 
  made 
  to 
  discover, 
  if 
  

   possible, 
  the 
  horizontal 
  distribution 
  of 
  the 
  compensation. 
  

  

  Three 
  tests 
  were 
  made, 
  with 
  the 
  data 
  from 
  124 
  stations 
  in 
  

   the 
  United 
  States. 
  First, 
  the 
  compensation 
  was 
  distributed 
  

   uniformly 
  from 
  the 
  station 
  out 
  to 
  the 
  limit 
  of 
  zone 
  K, 
  which 
  

   has 
  a 
  radius 
  of 
  18*8 
  kilometers 
  (11*7 
  miles). 
  At 
  each 
  station 
  

   the 
  average 
  elevation 
  of 
  the 
  topography 
  within 
  this 
  area 
  was 
  

   read 
  from 
  maps, 
  and 
  then 
  the 
  compensation 
  of 
  this 
  topography 
  

   was 
  distributed 
  uniformly 
  throughout 
  the 
  circle 
  with 
  the 
  given 
  

   radius. 
  It 
  was 
  assumed 
  to 
  extend 
  uniformly 
  to 
  a 
  depth 
  of 
  

   113'7 
  kilometers. 
  Second, 
  similar 
  computations 
  were 
  made 
  

   for 
  the 
  average 
  elevation 
  of 
  the 
  topography 
  from 
  the 
  station 
  

   to 
  the 
  outer 
  limit 
  of 
  zone 
  M, 
  58*8 
  kilometers 
  (36*5 
  miles). 
  

   Third, 
  this 
  was 
  done 
  for 
  the 
  average 
  elevation 
  of 
  the 
  topog- 
  

   raphy 
  to 
  the 
  outer 
  limit 
  of 
  zone 
  O, 
  166"7 
  kilometers 
  (103*6 
  

   miles) 
  from 
  the 
  station. 
  

  

  In 
  order 
  to 
  make 
  the 
  regional 
  method 
  of 
  reduction 
  logical, 
  

   the 
  compensation 
  of 
  each 
  topographic 
  feature 
  should 
  be 
  com- 
  

   puted 
  separately 
  to 
  the 
  limits 
  of 
  the 
  zone 
  having 
  the 
  topo- 
  

   graphic 
  feature 
  at 
  its 
  center. 
  The 
  method 
  of 
  computation 
  

   actually 
  adopted 
  may 
  give 
  erroneous 
  results. 
  For 
  instance, 
  let 
  

   us 
  assume 
  that 
  the 
  compensation 
  is 
  distributed 
  regionally 
  

   Avithin 
  zone 
  O, 
  with 
  the 
  station 
  at 
  its 
  center. 
  It 
  may 
  happen 
  

   that 
  the 
  station 
  is 
  in 
  a 
  broad 
  valley 
  or 
  on 
  a 
  plain 
  with 
  moun- 
  

   tains 
  surrounding 
  it 
  at 
  a 
  distance 
  of 
  about 
  167 
  kilometers. 
  

   None 
  of 
  the 
  compensation 
  under 
  the 
  mountains 
  would 
  be 
  taken 
  

   into 
  account 
  in 
  making 
  the 
  regional 
  reductions 
  and 
  the 
  com- 
  

   puted 
  value 
  of 
  gravity 
  would 
  be 
  too 
  great. 
  On 
  the 
  other 
  

   hand, 
  if 
  the 
  station 
  were 
  in 
  the 
  mountains 
  with 
  valleys 
  or 
  

   plains 
  just 
  beyond 
  the 
  limits 
  of 
  zone 
  O, 
  then 
  none 
  of 
  the 
  com- 
  

   pensation 
  of 
  the 
  mountains 
  would 
  be 
  distributed 
  to 
  the 
  valleys 
  

   or 
  plains, 
  and 
  the 
  computed 
  value 
  of 
  gravity 
  at 
  the 
  station 
  

   would 
  be 
  too 
  small. 
  Therefore, 
  in 
  making 
  the 
  reductions 
  by 
  

  

  * 
  Investigations 
  of 
  Gravity 
  and 
  Isostasy, 
  Special 
  Publication 
  No. 
  40 
  of 
  the 
  

   Coast 
  and 
  Geodetic 
  Survey. 
  

  

  Am. 
  Jour. 
  Sci.— 
  Fourth 
  Series, 
  Vol. 
  XLIII, 
  No. 
  258.— 
  June, 
  1917. 
  

   32 
  

  

  