﻿312 
  T. 
  C. 
  Chamberlin 
  — 
  Mathematics 
  of 
  Isostasy. 
  

  

  paper 
  was 
  an 
  ill-considered 
  intrusion 
  into 
  the 
  discussion 
  

   of 
  * 
  a 
  complicated 
  subject 
  to 
  which 
  others 
  had 
  given 
  long 
  

   and 
  laborious 
  study. 
  It 
  is 
  obligatory 
  upon 
  me, 
  for 
  

   reasons 
  that 
  will 
  at 
  once 
  appear, 
  to 
  show 
  that, 
  quite 
  on 
  

   the 
  contrary, 
  Dr. 
  MacMillan's 
  paper 
  was 
  the 
  outcome 
  of 
  

   protracted 
  consideration 
  and 
  that 
  it 
  was 
  regardful 
  of 
  

   other 
  workers 
  in 
  quite 
  an 
  exceptional 
  way. 
  It 
  was 
  par- 
  

   ticularly 
  considerate 
  of 
  our 
  great 
  leader 
  in 
  modern 
  isos- 
  

   tatic 
  w^ork. 
  The 
  whole 
  story 
  is 
  worth 
  telling 
  merely 
  as 
  

   a 
  matter 
  of 
  method. 
  

  

  To 
  reach 
  the 
  real 
  origin 
  of 
  MacMillan's 
  paper, 
  it 
  is 
  

   necessary 
  to 
  go 
  back 
  almost 
  to 
  the 
  beginning 
  of 
  Dr. 
  

   Hayford's 
  monumental 
  work 
  on 
  isostasy. 
  It 
  sprang 
  

   remotely 
  from 
  my 
  review 
  of 
  one 
  of 
  Dr. 
  Hayford's 
  earli- 
  

   est 
  contributions 
  a 
  dozen 
  years 
  ago. 
  3 
  By 
  reference 
  to 
  

  

  this 
  review, 
  it 
  will 
  be 
  seen 
  that, 
  at 
  that 
  early 
  stage 
  of 
  the 
  

   inquiry, 
  Dr. 
  Hayford 
  was 
  feeling 
  about, 
  by 
  the 
  use 
  of 
  

   trial 
  hypotheses 
  tested 
  by 
  the 
  method 
  of 
  the 
  least 
  

   squares, 
  to 
  find 
  the 
  depth 
  of 
  compensation 
  that 
  would 
  

   best 
  satisfy 
  the 
  data 
  at 
  his 
  command. 
  In 
  these 
  trials 
  he 
  

   made 
  three 
  assumptions 
  as 
  to 
  the 
  distribution 
  of 
  density. 
  

   "While 
  he 
  did 
  not 
  hold 
  either 
  of 
  these 
  as 
  excluding 
  the 
  

   others, 
  he 
  regarded 
  a 
  uniform 
  distribution 
  to 
  a 
  depth 
  of 
  

   113-7 
  Inns. 
  4 
  below 
  the 
  surface 
  as 
  most 
  satisfactory, 
  be- 
  

   cause 
  it 
  gave 
  the 
  least 
  residuals. 
  

  

  My 
  review 
  urged 
  that 
  it 
  was 
  important 
  (1) 
  to 
  discrimi- 
  

   nate 
  between 
  what 
  was 
  really 
  determined 
  and 
  what 
  was 
  

   only 
  interpretation, 
  and 
  (2) 
  to 
  adhere 
  as 
  closely 
  as 
  prac- 
  

   ticable 
  to 
  the 
  natural 
  distribution 
  of 
  density. 
  I 
  recog- 
  

   nized, 
  of 
  course, 
  the 
  propriety 
  of 
  using 
  arbitrary 
  

   distributions 
  of 
  density 
  to 
  save 
  mathematical 
  labor, 
  es- 
  

   pecially 
  where 
  the 
  labor 
  was, 
  as 
  in 
  this 
  case, 
  scarcely 
  

   less 
  than 
  heroic. 
  To 
  make 
  my 
  point 
  tangible, 
  I 
  intro- 
  

  

  3 
  Jour, 
  of 
  GeoL, 
  vol. 
  15, 
  pp. 
  73-81, 
  1907. 
  

  

  * 
  Later 
  he 
  found 
  122 
  kms., 
  76 
  miles, 
  more 
  satisfactory 
  and 
  as 
  this 
  figure 
  

   appears 
  most 
  widely 
  in 
  the 
  literature 
  of 
  the 
  subject, 
  it 
  will 
  be 
  used 
  in 
  the 
  

   rest 
  of 
  this 
  article. 
  

  

  