﻿W. 
  D. 
  MacMillan 
  — 
  Mathematics 
  of 
  Isostasy. 
  319 
  

  

  After 
  some 
  details 
  I 
  say: 
  

  

  This 
  is 
  a 
  very 
  notable 
  reduction 
  and 
  it 
  places 
  the 
  hypothesis 
  

   of 
  isostasy 
  on 
  a 
  solid* 
  foundation 
  of 
  credibility 
  (p. 
  106). 
  

  

  And 
  a 
  little 
  farther 
  on 
  I 
  say 
  : 
  

  

  Hayford's 
  success, 
  which 
  must 
  be 
  considered 
  a 
  notable 
  one, 
  

   consists 
  in 
  showing, 
  by 
  very 
  complete 
  computations 
  which 
  extend 
  

   over 
  a 
  large 
  mass 
  of 
  data, 
  that 
  assumptions 
  of 
  very 
  moderate 
  

   differences 
  of 
  density 
  are 
  sufficient 
  to 
  bring 
  the 
  observations 
  and 
  

   theory 
  into 
  fairly 
  close 
  accord. 
  Whether 
  or 
  not 
  any 
  other 
  hypo- 
  

   thesis 
  will 
  or 
  can 
  be 
  equally 
  successful 
  must 
  of 
  course 
  be 
  left 
  

   for 
  the 
  future. 
  Until 
  some 
  such 
  hypothesis 
  makes 
  its 
  appear- 
  

   ance 
  we 
  are 
  fairly 
  entitled 
  to 
  put 
  our 
  faith 
  in 
  the 
  broader 
  out- 
  

   lines 
  of 
  isostasy 
  and 
  leave 
  it 
  to 
  further 
  observations 
  and 
  

   discussions 
  to 
  make 
  the 
  details 
  of 
  the 
  theory 
  more 
  precise 
  (p. 
  

   106). 
  

  

  It 
  is 
  certainly 
  hard 
  to 
  find 
  anything 
  offensively 
  skep- 
  

   tical 
  or 
  destructive 
  in 
  this. 
  The 
  key 
  to 
  the 
  trouble, 
  I 
  

   think, 
  lies 
  in 
  the 
  paragraphs 
  that 
  follow 
  : 
  

  

  To 
  be 
  sure, 
  they 
  have 
  not 
  proved 
  the 
  reality 
  of 
  isostasy, 
  for 
  

   in 
  the 
  mathematical 
  sense 
  no 
  physical 
  hypothesis 
  can 
  be 
  proven. 
  

   But 
  they 
  have 
  formulated 
  precise 
  hypotheses 
  of 
  isostasy 
  and 
  

   have 
  shown 
  that 
  a 
  vast 
  mass 
  of 
  observational 
  data 
  covering 
  the 
  

   United 
  States 
  is 
  very 
  much 
  better 
  satisfied 
  by 
  theories 
  which 
  

   include 
  their 
  hypotheses 
  than 
  by 
  the 
  usual 
  gravitational 
  theory 
  

   which 
  excludes 
  the 
  hypothesis 
  of 
  isostasy 
  (p. 
  105). 
  

  

  From 
  a 
  purely 
  mathematical 
  point 
  of 
  view, 
  any 
  set 
  of 
  a 
  finite 
  

   number 
  of 
  observations 
  of 
  the 
  intensity 
  and 
  direction 
  of 
  gravity 
  

   can 
  be 
  satisfied, 
  not 
  approximately, 
  but 
  exactly, 
  in 
  infinitely 
  

   many 
  ways 
  by 
  a 
  proper 
  distribution 
  of 
  density 
  in 
  the 
  earth. 
  

   The 
  virtue 
  of 
  the 
  theory 
  of 
  isostasy, 
  therefore, 
  lies, 
  not 
  in 
  the 
  

   mere 
  fact 
  that 
  the 
  observations 
  are 
  more 
  nearly 
  satisfied 
  by 
  the 
  

   theory 
  than 
  without 
  it, 
  but 
  in 
  the 
  fact 
  that 
  a 
  definite 
  principle 
  

   is 
  laid 
  down 
  for 
  the 
  variations 
  of 
  density, 
  and 
  that 
  this 
  princi- 
  

   ple 
  brings 
  theory 
  and 
  observations 
  into 
  a 
  satisfactory 
  accord. 
  

   As 
  Hayford's 
  four 
  distinct 
  hypotheses 
  show, 
  any 
  smoothly 
  uni- 
  

   form 
  hypothesis 
  of 
  isostasy 
  can 
  be 
  regarded 
  only 
  as 
  a 
  first 
  

   approximation 
  to 
  the 
  actual 
  situation, 
  and 
  Hayford 
  has 
  been 
  

   successful 
  in 
  showing 
  that 
  any 
  one 
  of 
  these 
  four 
  hypotheses 
  is 
  

   a 
  good 
  first 
  approximation 
  (p. 
  111). 
  

  

  And 
  in 
  my 
  final 
  paragraph 
  : 
  

  

  While 
  the 
  theory 
  of 
  isostasy 
  has 
  made 
  a 
  very 
  successful 
  

   approach 
  to 
  the 
  solution 
  of 
  the 
  problem 
  of 
  bringing 
  the 
  anoma- 
  

   lies 
  of 
  observation 
  into 
  accord 
  with 
  the 
  theory 
  of 
  gravity, 
  it 
  

   must 
  be 
  admitted 
  that 
  there 
  is 
  no 
  evidence 
  to 
  show 
  that 
  the 
  solu- 
  

   tion 
  of 
  the 
  problem 
  is 
  necessarily 
  isostatic 
  (p. 
  111). 
  

  

  