﻿W. 
  D. 
  MacMillan 
  — 
  Mathematics 
  of 
  Isostasy. 
  321 
  

  

  of 
  the 
  earth 
  and 
  at 
  these 
  points 
  place 
  masses 
  of 
  the 
  

   proper 
  numerical 
  value. 
  The 
  equations 
  which 
  determine 
  

   these 
  numerical 
  values 
  are 
  linear, 
  and 
  the 
  only 
  condition 
  

   upon 
  them 
  is 
  that 
  the 
  determinant 
  be 
  not 
  zero, 
  which 
  is 
  

   a 
  very 
  mild 
  condition 
  since 
  its 
  value 
  depends 
  only 
  upon 
  

   the 
  three 
  n 
  points 
  which 
  were 
  chosen. 
  Negative 
  masses 
  

   will 
  mean 
  deficiency 
  of 
  density 
  and 
  positive 
  masses 
  will 
  

   mean 
  excess 
  of 
  density. 
  By 
  this 
  means 
  the 
  n 
  observa- 
  

   tions 
  can 
  be 
  satisfied 
  exactly. 
  The 
  solution 
  is 
  non-isos- 
  

   tatic. 
  "Without 
  doubt 
  it 
  may 
  also 
  be 
  non-geologic. 
  It 
  

   has 
  no 
  virtue 
  that 
  I 
  can 
  see 
  except 
  to 
  show 
  that 
  non-isos- 
  

   tatic 
  solutions 
  are 
  conceivable. 
  

  

  A 
  telling 
  illustration 
  of 
  the 
  capacity 
  of 
  mathematics 
  to 
  

   develop 
  or 
  to 
  deal 
  with 
  relations 
  of 
  almost 
  any 
  sort 
  is 
  

   to 
  be 
  found 
  in 
  the 
  reduction 
  of 
  geodetic 
  observations 
  to 
  

   a 
  datum 
  surface, 
  on 
  which 
  I 
  made 
  some 
  suggestions, 
  and 
  

   to 
  the 
  criticism 
  of 
  which 
  Dr. 
  Barrell 
  devotes 
  six 
  pages. 
  

   The 
  issues 
  he 
  discusses, 
  however, 
  are 
  not 
  just 
  those 
  that 
  

   I 
  raised 
  or 
  at 
  least 
  supposed 
  I 
  had 
  raised. 
  The 
  matter 
  

   is 
  really 
  quite 
  simple. 
  There 
  is 
  an 
  ideal 
  geoid 
  that 
  was 
  

   often 
  pictured 
  by 
  teachers 
  of 
  the 
  old 
  geological 
  school, 
  

   and 
  easily 
  retained 
  by 
  those 
  of 
  us 
  who 
  forgot 
  most 
  of 
  

   what 
  little 
  else 
  we 
  learned 
  about 
  geology, 
  namely, 
  the 
  

   form 
  they 
  said 
  was 
  taken 
  by 
  the 
  earth 
  in 
  its 
  primitive 
  

   molten 
  state, 
  a 
  perfectly 
  symmetrical 
  spheroid, 
  each 
  

   layer 
  homogeneous, 
  the 
  whole 
  covered 
  by 
  an 
  ocean 
  of 
  

   uniform 
  depth. 
  This 
  was 
  really 
  an 
  ideal 
  picture 
  of 
  

   isostasy. 
  We 
  were 
  taught 
  that 
  all 
  later 
  deformations 
  

   took 
  their 
  departures 
  from 
  this. 
  Now 
  I 
  did 
  not 
  intrude 
  

   this 
  familiar 
  old 
  picture 
  on 
  the 
  readers 
  of 
  my 
  paper. 
  As 
  

   a 
  mathematician 
  I 
  had 
  no 
  right 
  to. 
  Besides, 
  it 
  might 
  be 
  

   out 
  of 
  date. 
  I 
  did, 
  however, 
  specify 
  the 
  mechanical 
  

   qualities 
  of 
  just 
  such 
  a 
  body 
  as 
  forming 
  the 
  true 
  base 
  of 
  

   reference 
  in 
  the 
  interpretation 
  of 
  isostatic 
  data. 
  I 
  did 
  

   not 
  mention 
  the 
  fact 
  that 
  Dr. 
  Barrell 
  had 
  used 
  the 
  same 
  

   base. 
  For 
  this 
  I 
  am 
  sorry, 
  not 
  because 
  it 
  was 
  obligatory 
  

   as 
  a 
  matter 
  of 
  priority, 
  but 
  because 
  he 
  seems 
  to 
  have 
  

   been 
  aggrieved 
  by 
  my 
  neglect 
  to 
  do 
  so. 
  I 
  do 
  not 
  think, 
  

   however, 
  that 
  there 
  was 
  anything 
  new 
  in 
  recognizing 
  this 
  

   as 
  the 
  ideal 
  base, 
  except 
  our 
  own 
  special 
  ways 
  of 
  dis- 
  

   cussing 
  it. 
  If 
  there 
  was 
  anything 
  in 
  common 
  between 
  

   us, 
  that 
  much 
  at 
  least 
  ought 
  to 
  be 
  right 
  and 
  I 
  don't 
  see 
  

   why 
  I 
  should 
  have 
  been 
  brought 
  to 
  bar 
  for 
  it. 
  At 
  any 
  

   rate 
  we 
  were 
  anticipated 
  in 
  the 
  basal 
  idea. 
  3 
  

  

  3 
  Jour. 
  GeoL, 
  vol. 
  21, 
  p. 
  528; 
  also 
  pp. 
  578-580, 
  1913. 
  

  

  