﻿A 
  Theory 
  of 
  Gravity. 
  637 
  

  

  of 
  attraction 
  is 
  not 
  changed 
  into 
  a 
  repulsion. 
  The 
  apple 
  is 
  

   now 
  in 
  an 
  ascending 
  stream 
  of 
  aether 
  created 
  by 
  the 
  earth. 
  

   Into 
  this 
  stream 
  it 
  throws 
  its 
  own 
  contributions. 
  If 
  there 
  is 
  

   still 
  to 
  be 
  conservation 
  of 
  momentum 
  the 
  body 
  falling 
  must 
  

   be 
  driven 
  downwards 
  in 
  the 
  reaction 
  against 
  its 
  own 
  upward 
  

   driven 
  jet 
  of 
  aether. 
  Repulsion 
  between 
  two 
  pieces 
  of 
  

   matter 
  could 
  only 
  arise 
  if 
  the 
  one 
  were 
  a 
  source 
  and 
  the 
  

   other 
  a 
  sink. 
  

  

  Riemann's 
  ideas 
  attract 
  by 
  their 
  simplicity 
  and 
  by 
  the 
  funda- 
  

   mental 
  explanation 
  of 
  Newtonian 
  attraction 
  they 
  offer. 
  But 
  

   they 
  raise 
  problems 
  insoluble, 
  it 
  seems 
  to 
  me, 
  by 
  any 
  methods 
  

   less 
  radical 
  than 
  those 
  of 
  the 
  relativists. 
  When 
  gravity 
  has 
  

   been 
  disposed 
  of 
  as 
  due 
  to 
  mass 
  motion 
  of 
  aether, 
  what 
  are 
  

   we 
  to 
  say 
  of 
  optics 
  ? 
  Perhaps 
  we 
  may 
  be 
  justified 
  in 
  

   treating 
  aether 
  as 
  polarizable 
  though 
  fluid. 
  Thus 
  it 
  may 
  

   possess 
  quasi-elastic 
  properties, 
  and 
  these 
  may 
  account 
  for 
  

   waves 
  of 
  light. 
  Then 
  the 
  problem 
  for 
  a 
  follower 
  of 
  

   Riemann 
  is 
  to 
  explain 
  how 
  the 
  path 
  of 
  a 
  ray 
  of 
  light 
  and 
  

   its 
  velocity 
  can 
  remain 
  unaltered 
  by 
  all 
  motions 
  of 
  the 
  medium 
  

   through 
  which 
  light 
  is 
  transmitted. 
  Even 
  this 
  incredible 
  

   feat 
  does 
  not 
  appear 
  to 
  be 
  beyond 
  the 
  relativist. 
  

  

  In 
  this 
  paper 
  I 
  suggest 
  the 
  following 
  conclusions. 
  Let 
  

   Jbea 
  function 
  finite 
  and 
  continuous 
  everywhere, 
  as 
  are 
  its 
  

   first 
  differential 
  coefficients. 
  J 
  satisfies 
  the 
  equation 
  

  

  ( 
  v2 
  -<?£) 
  j+w=o 
  ' 
  • 
  • 
  • 
  • 
  ( 
  36 
  > 
  

  

  m 
  is 
  the 
  absolute 
  weight 
  and 
  is 
  a 
  constant 
  the 
  same 
  for 
  all 
  

   matter, 
  The 
  force 
  on 
  an 
  element 
  of 
  volume 
  dv 
  of 
  matter 
  

   is 
  

  

  mdvS7J 
  or 
  mdvN, 
  .... 
  (39) 
  

  

  where 
  N 
  is 
  the 
  Newtonian 
  gravitational 
  force. 
  Let 
  p 
  be 
  

   the 
  density 
  of 
  the 
  aether 
  and 
  u 
  its 
  velocity. 
  The 
  motion 
  is 
  

   irrotational 
  in 
  a 
  sense 
  appropriate 
  to 
  the 
  theory 
  of 
  relativity 
  

   (§l),and 
  

  

  <™= 
  v 
  ^ 
  f»=--a- 
  '•" 
  • 
  • 
  ■ 
  (*>) 
  

  

  Thus 
  J 
  is 
  a 
  velocity 
  potential 
  (§ 
  5). 
  From 
  (36) 
  and 
  (40) 
  

   ~ 
  -f 
  Div 
  pu 
  = 
  — 
  4z7rm. 
  

  

  Hence 
  the 
  quantity 
  ±irm 
  of 
  aether 
  disappears 
  every 
  second 
  

   from 
  unit 
  volume 
  occupied 
  by 
  matter. 
  

  

  It 
  is 
  not 
  my 
  present 
  object 
  to 
  discuss 
  the 
  various 
  possible 
  

  

  