﻿T. 
  C. 
  Chamberlin 
  — 
  Mathematics 
  of 
  Isostasy. 
  315 
  

  

  open 
  for 
  discussion 
  in 
  which 
  Moulton 
  and 
  Woodward 
  

   were 
  the 
  chief 
  participants. 
  As 
  nearly 
  as 
  I 
  recall, 
  

   essentially 
  all 
  the 
  points 
  referred 
  to 
  by 
  Dr. 
  Barrell 
  in 
  

   his 
  criticism 
  were 
  included 
  in 
  the 
  discussion, 
  and 
  much 
  

   besides. 
  Hayford 
  made 
  no 
  attempt 
  to 
  overthrow 
  Mac- 
  

   Millan 
  's 
  statement 
  as 
  to 
  the 
  inadequacy 
  of 
  the 
  geodetic 
  

   data 
  to 
  demonstrate 
  the 
  depth 
  of 
  compensation; 
  he 
  did 
  

   not 
  go 
  beyond 
  the 
  claim 
  that 
  the 
  chief 
  compensation 
  took 
  

   place 
  in 
  the 
  upper 
  levels, 
  to 
  which 
  no 
  dissent 
  was 
  

   expressed. 
  

  

  The 
  most 
  far-reaching 
  feature 
  of 
  the 
  discussion, 
  so 
  far 
  

   as 
  mathematical 
  competency 
  is 
  concerned, 
  was 
  a 
  chal- 
  

   lenge 
  by 
  Moulton 
  of 
  a 
  concession 
  incidentally 
  made 
  by 
  

   MacMillan 
  to 
  the 
  effect 
  that 
  geodesists 
  could 
  prove 
  a 
  

   specified 
  thing 
  named. 
  Moulton 
  insisted 
  that 
  they 
  could 
  

   not 
  prove 
  this 
  mathematically 
  in 
  the 
  strict 
  sense 
  of 
  the 
  

   term. 
  He 
  asserted 
  that 
  he 
  could 
  specify 
  a 
  distribution 
  

   of 
  density 
  that 
  would 
  satisfy 
  the 
  geodetic 
  data 
  perfectly 
  

   and 
  yet 
  would 
  be 
  quite 
  different 
  from 
  the 
  distribution 
  

   thought 
  to. 
  be 
  demonstrated. 
  He 
  admitted 
  that 
  his 
  

   assigned 
  distribution 
  might 
  be 
  open 
  to 
  physical 
  or 
  natu- 
  

   ralistic 
  criticism 
  — 
  might 
  indeed 
  be 
  absurd 
  from 
  these 
  

   points 
  of 
  view 
  — 
  but 
  mathematically 
  it 
  would 
  perfectly 
  

   satisfy 
  the 
  data. 
  Woodward 
  supported 
  Moulton 
  on 
  this 
  

   point, 
  and 
  quoted 
  Poincare, 
  one 
  of 
  the 
  most 
  brilliant 
  and 
  

   penetrating 
  of 
  modern 
  mathematicians, 
  as 
  having 
  said 
  

   in 
  effect 
  that 
  for 
  every 
  set 
  of 
  physical 
  data 
  assembled 
  by 
  

   observation 
  or 
  otherwise, 
  an 
  indefinite 
  number 
  of 
  mathe- 
  

   matical 
  solutions 
  could 
  be 
  offered, 
  each 
  one 
  of 
  which 
  

   would 
  perfectly 
  satisfy 
  the 
  data. 
  

  

  I 
  was 
  so 
  much 
  impressed 
  by 
  the 
  far-reaching 
  import 
  of 
  

   these 
  statements, 
  coming 
  from 
  mathematicians 
  of 
  such 
  

   standing, 
  that 
  later, 
  as 
  occasion 
  offered, 
  I 
  followed 
  up 
  

   the 
  matter 
  with 
  concrete 
  tests, 
  framing 
  specific 
  cases 
  

   made 
  as 
  favorable 
  as 
  possible 
  for 
  demonstration, 
  made 
  

   indeed 
  more 
  favorable 
  than 
  any 
  actual 
  case 
  realized 
  in 
  

   geodetic 
  practice. 
  But 
  in 
  all 
  cases 
  where 
  these 
  were 
  

   submitted 
  to 
  Moulton 
  or 
  MacMillan, 
  they 
  affirmed 
  un- 
  

   hesitatingly 
  that 
  other 
  solutions 
  than 
  the 
  one 
  purposely 
  

   made 
  the 
  basis 
  of 
  the 
  case 
  could 
  be 
  offered 
  that 
  would 
  

   satisfy 
  the 
  data 
  of 
  the 
  case 
  equally 
  well 
  in 
  a 
  mathemat- 
  

   ical 
  sense. 
  MacMillan 
  added 
  that, 
  if, 
  in 
  my 
  constructive 
  

   cases, 
  I 
  were 
  to 
  make 
  further 
  observations 
  and 
  add 
  new 
  

   data, 
  these 
  new 
  data 
  would 
  probably 
  knock 
  out 
  some 
  or 
  

  

  