﻿Theory 
  of 
  Gravity, 
  639 
  

  

  There 
  is 
  evidently 
  much 
  to 
  query 
  in 
  this 
  system. 
  First, 
  

   what 
  is 
  the 
  dynamical 
  nature 
  o£ 
  the 
  fluid 
  whose 
  motion 
  is 
  

   determined 
  by 
  (40) 
  ? 
  Relativist 
  hydrodynamics 
  suggest 
  (§1) 
  

   that 
  we 
  should 
  deduce 
  the 
  laws 
  of 
  fluid 
  motion 
  from 
  the 
  

   minimum 
  action 
  formula 
  

  

  Sjjjj 
  Ldvdt 
  = 
  0, 
  w 
  h 
  ere 
  L 
  = 
  \ 
  P 
  2 
  (u 
  2 
  - 
  c 
  2 
  ) 
  . 
  

  

  In 
  this 
  fluid 
  motion 
  without 
  circulation 
  is 
  represented 
  by 
  

   (40). 
  

  

  Granted 
  that 
  (40) 
  may 
  exist 
  in 
  an 
  ideal 
  fluid, 
  how 
  are 
  we 
  

   to 
  ensure 
  that 
  the 
  passage 
  of 
  a 
  wave 
  of 
  light 
  and 
  the 
  electro- 
  

   magnetic 
  stresses 
  do 
  not 
  disturb 
  this 
  type 
  of 
  motion, 
  and, 
  on 
  

   the 
  other 
  hand, 
  that 
  the 
  motion 
  itself 
  does 
  not 
  affect 
  the 
  form 
  

   of 
  Maxwell's 
  equations 
  ? 
  For 
  according 
  to 
  (40) 
  the 
  density 
  as 
  

   well 
  as 
  the 
  velocity 
  of 
  the 
  sether 
  vary 
  from 
  point 
  to 
  point. 
  

  

  I 
  approach 
  these 
  problems 
  in 
  the 
  first 
  instance 
  as 
  a 
  believer 
  

   in 
  the 
  physical 
  reality 
  of 
  a 
  fourth 
  dimension. 
  I 
  argue 
  (§ 
  3) 
  

   that 
  the 
  four-dimensional 
  geometry 
  of 
  Minkowski 
  is 
  not 
  a 
  

   mathematical 
  fiction, 
  but 
  a 
  necessary 
  inference 
  from 
  ordinary 
  

   experience. 
  Further, 
  though 
  as 
  with 
  Minkowski 
  the 
  four- 
  

   dimensional 
  universe 
  is 
  without 
  change, 
  it 
  is 
  not 
  without 
  

   time 
  or 
  motion. 
  Time 
  is 
  not, 
  however, 
  here 
  anything 
  but 
  a 
  

   purely 
  logical 
  succession, 
  the 
  symbol 
  of 
  an 
  order 
  in 
  which 
  

   the 
  elements 
  of 
  Minkowski's 
  space 
  are 
  thought. 
  The 
  symbol 
  

   t 
  which 
  I 
  use 
  is 
  the 
  symbol 
  of 
  an 
  infinitesimal 
  poin^ 
  trans- 
  

   formation 
  (§3). 
  

  

  All 
  the 
  formulae 
  of 
  our 
  universe 
  are 
  deduced 
  (§ 
  6) 
  from 
  

   the 
  formula 
  for 
  the 
  minimum 
  action. 
  

  

  B^LdvdsdT=0, 
  .... 
  (50) 
  

  

  Here 
  the 
  vector 
  r 
  and 
  scalar 
  s 
  furnish 
  four 
  coordinates. 
  

   The 
  liquid 
  substance 
  is 
  now 
  (in 
  four 
  dimensions) 
  incom- 
  

   pressible 
  ; 
  the 
  volume 
  element 
  in 
  (50) 
  

  

  dv 
  ds 
  

  

  is 
  not 
  to 
  vary 
  at 
  all 
  in 
  aether, 
  and 
  in 
  matter 
  it 
  varies 
  so 
  as 
  

   to 
  grow 
  or 
  decay 
  exponentially. 
  Hence 
  

  

  S{dvdse^ 
  7r)imr 
  )=0 
  (53) 
  

  

  I 
  use 
  the 
  ordinary 
  language 
  of 
  phenomenal 
  time, 
  and 
  

  

  