﻿Theory 
  of 
  Gravity. 
  647 
  

  

  and 
  sees 
  it 
  as 
  a 
  whole. 
  Change 
  is 
  relative 
  to 
  us 
  ignorant 
  of 
  

   the 
  future, 
  the 
  distant, 
  and 
  almost 
  all 
  the 
  past. 
  

  

  If 
  a 
  liquid 
  moves 
  in 
  four 
  dimensions 
  the 
  equation 
  of 
  con- 
  

   tinuity 
  is 
  evidently 
  

  

  dm 
  d 
  f 
  ds 
  

  

  &t 
  ds 
  

  

  ( 
  m 
  g) 
  + 
  Div( 
  TO 
  J) 
  = 
  (22) 
  

  

  5 
  is 
  the 
  fourth 
  spatial 
  coordinate 
  and 
  r 
  the 
  absolute 
  time. 
  

   The 
  vector 
  notation 
  is 
  kept 
  for 
  three 
  axes 
  x, 
  y, 
  z. 
  Where 
  

   the 
  motion 
  is 
  steady 
  

  

  dr 
  

   Then 
  (22) 
  becomes 
  

  

  i(-*) 
  + 
  H»fc° 
  (23) 
  

  

  Along 
  any 
  steady 
  stream-line 
  r 
  is 
  a 
  function 
  of 
  s. 
  Thus 
  

   if 
  we 
  put 
  

  

  ds 
  

   m 
  J 
  T 
  =P 
  a 
  ^ 
  ( 
  24 
  ) 
  

  

  a 
  being 
  an 
  arbitrary 
  constant, 
  (22) 
  is 
  replaced 
  by 
  

  

  a«+w<4r)=o. 
  ...;,. 
  (25) 
  

  

  It 
  is 
  only 
  necessary 
  to 
  write 
  

  

  s 
  = 
  ct 
  (26) 
  

  

  and 
  (25) 
  becomes 
  the 
  equation 
  of 
  continuity 
  in 
  the 
  ordinary 
  

   form, 
  t 
  now 
  standing 
  for 
  the 
  time. 
  

  

  The 
  density 
  p 
  is 
  by 
  (24) 
  proportional 
  to 
  the 
  flux 
  across 
  a 
  

   plane 
  parallel 
  to 
  the 
  s 
  axis. 
  Along 
  any 
  tube 
  of 
  constant 
  

   flow 
  the 
  flux 
  is 
  the 
  same 
  whatever 
  section 
  of 
  the 
  tube 
  be 
  

   taken. 
  Thus 
  the 
  invariance 
  of: 
  electric 
  charge 
  in 
  Lorentz's 
  

   substitution 
  is 
  simply 
  explained. 
  

  

  It 
  may 
  be 
  objected 
  that 
  by 
  retaining 
  the 
  idea 
  of 
  an 
  absolute 
  

   time 
  I 
  have 
  sacrificed 
  the 
  essential 
  feature 
  of 
  Minkowski's 
  

   theory. 
  That 
  proposes 
  to 
  substitute 
  for 
  the 
  time 
  and 
  space 
  

   of 
  our 
  ordinary 
  experience 
  a 
  universe 
  of 
  space 
  alone. 
  I, 
  it 
  

   appears, 
  would 
  have 
  four 
  dimensions 
  in 
  space 
  and 
  retain 
  time 
  

   as 
  well. 
  But 
  if 
  I 
  assume 
  the 
  right 
  to 
  imagine 
  a 
  fourth 
  

   dimension, 
  why 
  not 
  a 
  fifth 
  and 
  a 
  sixth 
  ? 
  What 
  is 
  the 
  value 
  of 
  a 
  

   theory 
  which 
  supplements 
  the 
  real 
  world 
  by 
  such 
  figments 
  ? 
  

   These 
  objections 
  misrepresent 
  my 
  meaning. 
  I 
  deny 
  that 
  there 
  

   is 
  anything 
  in 
  my 
  universe 
  beyond 
  what 
  is 
  given 
  in 
  immediate 
  

  

  2X2 
  

  

  