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  636 
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  LIU. 
  A 
  Theory 
  of 
  Gravity. 
  By 
  S. 
  B. 
  McLaren, 
  M.A., 
  

   Professor 
  of 
  Mathematics 
  in 
  University 
  College, 
  Reading 
  . 
  

  

  Page 
  

   Introduction— 
  The 
  Principle 
  of 
  Relativity 
  and 
  the 
  Theory 
  

  

  of 
  Riemann. 
  — 
  Summary 
  636 
  

  

  § 
  1. 
  Relativist 
  Hydrodynamics 
  641 
  

  

  § 
  2. 
  Least 
  Action 
  in 
  Electrodynamics 
  645 
  

  

  § 
  3. 
  Time 
  and 
  the 
  Fourth 
  Dimension 
  646 
  

  

  § 
  4. 
  Electrodynamics 
  in 
  Four 
  Dimensions 
  649 
  

  

  § 
  5. 
  The 
  Newtonian 
  Potential 
  a 
  Velocity 
  Potential 
  652 
  

  

  § 
  6. 
  Matter 
  and 
  JEther 
  655 
  

  

  § 
  7. 
  Energy, 
  Momentum, 
  and 
  Stress 
  660 
  

  

  § 
  8. 
  Positive 
  and 
  Negative 
  Charge, 
  Magneton 
  and 
  Electron. 
  667 
  

  

  §9. 
  The 
  Electromagnetic 
  Equations 
  in 
  Moving 
  yEther 
  .... 
  668 
  

  

  § 
  10. 
  The 
  Limits 
  of 
  Mechanical 
  Theory 
  672 
  

  

  I 
  DESIRE 
  to 
  call 
  attention 
  again 
  to 
  a 
  theory 
  of 
  gravita- 
  

   tion 
  which 
  goes 
  back 
  at 
  least 
  to 
  Bernhard 
  Riemann. 
  

   For 
  Riemann 
  ( 
  Ges. 
  Math. 
  Werke, 
  p. 
  529) 
  " 
  .Ether 
  " 
  is 
  a 
  fluid 
  

   and 
  "Matter" 
  a 
  region 
  where 
  " 
  iEther 
  " 
  is 
  continually 
  

   destroyed. 
  Let 
  us 
  bring 
  to 
  the 
  consideration 
  of 
  these 
  ideas 
  

   the 
  most 
  revolutionary 
  principle 
  Physicists 
  have 
  accepted 
  

   since 
  Riem 
  aim's 
  day, 
  Einstein's 
  principle 
  of 
  the 
  relativity 
  

   of 
  time. 
  

  

  With 
  the 
  starting 
  point 
  indicated 
  by 
  Riemann 
  it 
  is 
  easy 
  

   to 
  account 
  for 
  Newton's 
  law 
  of 
  gravitation. 
  Any 
  piece 
  of 
  

   matter 
  is 
  an 
  aether-sink 
  and 
  from 
  all 
  directions 
  aether 
  flows 
  

   in 
  to 
  replace 
  the 
  aether 
  destroyed. 
  Given 
  two 
  finite 
  portions 
  

   of 
  matter, 
  it 
  is 
  evident 
  that 
  each 
  disturbs 
  the 
  motion 
  of 
  aether 
  

   towards 
  the 
  other. 
  Thus 
  Riemann's 
  line 
  of 
  argument 
  is 
  the 
  

   same 
  as 
  that 
  used 
  in 
  Lesage's 
  celebrated 
  hypothesis, 
  gravity 
  

   is 
  an 
  effect 
  of 
  interference. 
  

  

  We 
  may 
  illustrate 
  Riemann's 
  theory 
  by 
  considering 
  the 
  

   motion 
  of 
  any 
  falling 
  body, 
  take 
  in 
  fact 
  Newton's 
  legendary 
  

   apple. 
  When 
  the 
  apple 
  begins 
  to 
  fall 
  it 
  is 
  situated 
  in 
  a 
  

   stream 
  of 
  aether 
  flowing 
  vertically 
  downward. 
  But 
  it 
  is 
  

   quite 
  misleading 
  to 
  suppose 
  that 
  the 
  apple 
  falls 
  merely 
  

   because 
  it 
  is 
  carried 
  down 
  this 
  stream, 
  or 
  that 
  it 
  is 
  set 
  in 
  

   motion 
  by 
  an 
  ordinary 
  fluid 
  pressure. 
  In 
  this 
  paper 
  at 
  all 
  

   events 
  it 
  is 
  assumed 
  that 
  matter 
  is 
  something 
  freely 
  transfer- 
  

   able 
  through 
  an 
  aether 
  which 
  is 
  present 
  everywhere 
  and 
  

   so 
  cannot 
  press 
  upon 
  matter 
  as 
  upon 
  a 
  foreign 
  substance. 
  

   The 
  downward 
  momentum 
  of 
  the 
  apple 
  is 
  appropriated 
  from 
  

   the 
  aether 
  destroyed, 
  it 
  is 
  not 
  transferred 
  to 
  the 
  apple 
  by 
  a 
  

   mechanical 
  aether 
  pressure. 
  Indeed, 
  if 
  we 
  regard 
  matter 
  as 
  

   an 
  aether-source 
  instead 
  of 
  an 
  aether-sink, 
  the 
  Newtonian 
  law 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  