﻿T. 
  C. 
  Chamberlin 
  — 
  Mathematics 
  of 
  Isostasy. 
  313 
  

  

  duced 
  the 
  accompanying 
  figure 
  in 
  which 
  a 
  generalized 
  

   curve 
  of 
  what 
  I 
  thought 
  might 
  be 
  a 
  natural 
  distribution 
  

   of 
  density 
  was 
  superposed 
  on 
  two 
  of 
  the 
  distributions 
  

   used 
  by 
  Hayford. 
  Later, 
  Hayford 
  was 
  good 
  enough 
  to 
  

   make 
  the 
  curve 
  I 
  had 
  suggested 
  the 
  basis 
  of 
  trial 
  and 
  

   published 
  his 
  results 
  under 
  the 
  name 
  ' 
  i 
  Chamberlin 
  com- 
  

   pensation." 
  5 
  The 
  residuals 
  in 
  this 
  case 
  seemed 
  quite 
  as 
  

   favorable 
  as 
  in 
  the 
  best 
  of 
  the 
  distributions 
  previously 
  

   tested, 
  but 
  there 
  was 
  this 
  notable 
  difference 
  : 
  the 
  latter, 
  

   uniform 
  distribution, 
  gave 
  a 
  compensation 
  depth 
  of 
  76 
  

   miles, 
  while 
  my 
  supposedly 
  naturalistic 
  curve 
  gave 
  a 
  

   depth 
  of 
  178 
  miles. 
  From 
  the 
  geological 
  point 
  of 
  view 
  

   this 
  much 
  greater 
  depth 
  seemed 
  a 
  vital 
  matter, 
  for 
  some 
  

   geologists, 
  who 
  had 
  previously 
  tried 
  to 
  form 
  the 
  best 
  

   concepts 
  they 
  could 
  of 
  the 
  thickness 
  of 
  the 
  crust 
  from 
  

   considerations 
  of 
  ' 
  t 
  the 
  level 
  of 
  no 
  strain 
  ' 
  ' 
  and 
  other 
  cri- 
  

   teria 
  then 
  thought 
  trustworthy, 
  felt 
  that 
  even 
  76 
  miles 
  

   was 
  surprisingly 
  deep. 
  Major 
  Dutton, 
  the 
  father 
  of 
  the 
  

   formal 
  doctrine 
  of 
  isostasy, 
  so 
  expressed 
  himself 
  to 
  me 
  

   personally. 
  

  

  But, 
  strangely 
  enough, 
  as 
  it 
  seemed 
  to 
  me, 
  notwith- 
  

   standing 
  the 
  fact 
  that 
  the 
  first 
  trial 
  of 
  a 
  supposedly 
  

   natural 
  distribution 
  of 
  densities 
  gave 
  quite 
  as 
  favorable 
  

   residuals 
  as 
  the 
  best 
  of 
  the 
  artificial 
  distributions 
  previ- 
  

   ously 
  tried 
  — 
  and 
  in 
  the 
  face 
  of 
  the 
  obvious 
  probability 
  

   that 
  more 
  carefully 
  studied 
  naturalistic 
  distributions 
  

   would 
  give 
  even 
  better 
  results 
  — 
  nearly 
  every 
  quotation 
  

   of 
  Hayford 
  's 
  results 
  cited 
  the 
  depth 
  of 
  76 
  miles 
  as 
  though 
  

   it 
  were 
  the 
  essential 
  outcome 
  of 
  his 
  laborious 
  studies, 
  

   and 
  usually 
  in 
  such 
  a 
  way 
  as 
  to 
  imply 
  that 
  it 
  was 
  a 
  

   demonstration 
  of 
  the 
  real 
  depth 
  of 
  compensation, 
  though 
  

   Hayford 
  had 
  made 
  no 
  such 
  claim. 
  This 
  was 
  so 
  general 
  

   that 
  it 
  led 
  me 
  to 
  suspect 
  that 
  there 
  must 
  be 
  something 
  

   in 
  the 
  technical 
  treatment 
  of 
  the 
  case, 
  whose 
  meaning 
  I 
  

   had 
  failed 
  to 
  detect, 
  that 
  distinctly 
  favored 
  the 
  outcome 
  

   76 
  miles, 
  though 
  based 
  on 
  a 
  uniform 
  distribution 
  that 
  

   seemed 
  geologically 
  improbable, 
  rather 
  than 
  the 
  outcome 
  

   178 
  miles, 
  based 
  on 
  a 
  graded 
  distribution 
  that 
  seemed 
  

   more 
  probable. 
  And 
  so, 
  after 
  having 
  myself 
  recurred 
  

   to 
  the 
  published 
  treatment 
  repeatedly 
  without 
  finding 
  

   any 
  clue 
  to 
  such 
  hidden 
  evidence, 
  I 
  raised 
  the 
  question, 
  

   as 
  opportunity 
  offered, 
  with 
  my 
  mathematical 
  colleagues. 
  

  

  6 
  J. 
  F. 
  Hayford: 
  The 
  Figure 
  of 
  the 
  Earth 
  and 
  Isostasy 
  from 
  Measure- 
  

   ments 
  in 
  the 
  United 
  States, 
  Publ. 
  of 
  the 
  XJ. 
  S. 
  Coast 
  and 
  Geodetic 
  Survey, 
  

   p. 
  159, 
  1909. 
  

  

  