﻿Theory 
  of 
  Gravity. 
  653 
  

  

  Where 
  m 
  is 
  not 
  zero 
  (36) 
  gives 
  

  

  -y- 
  -f 
  Divou= 
  — 
  iirm 
  (41) 
  

  

  or 
  

  

  *(£) 
  +D 
  K1&)=-^ 
  ^ 
  

  

  (41) 
  shows 
  that 
  the 
  quantity 
  kirm 
  o£ 
  aether 
  disappears 
  per 
  

   second 
  and 
  per 
  unit 
  volume, 
  and 
  (42) 
  written 
  in 
  the 
  form 
  

  

  •j-i(dv 
  a 
  ds 
  a 
  ) 
  = 
  — 
  (Air)%mdv 
  a 
  ds 
  a 
  

  

  CUT 
  

  

  shows 
  that 
  the 
  quantity 
  

  

  dvjs 
  a 
  xe^ 
  imr 
  ' 
  (43) 
  

  

  is 
  a 
  constant. 
  The 
  volume 
  of 
  any 
  given 
  element 
  of 
  aether 
  

   decays 
  where 
  matter 
  is 
  present. 
  

  

  When, 
  as 
  in 
  this 
  section, 
  matter 
  is 
  treated 
  as 
  a 
  substance 
  

   distinct 
  from 
  aether, 
  the 
  momentum 
  of 
  the 
  aether 
  destroyed 
  

   is 
  handed 
  over 
  to 
  matter, 
  and 
  this 
  is 
  the 
  origin 
  of 
  gravita- 
  

   tional 
  force. 
  We 
  have 
  to 
  consider 
  how 
  that 
  can 
  be 
  done 
  

   without 
  interference 
  with 
  the 
  irrotational 
  aether-flow. 
  We 
  

   may 
  imagine 
  that 
  each 
  element 
  of 
  aether 
  removed 
  drops 
  out 
  

   without 
  interfering 
  with 
  the 
  rest. 
  The 
  principle 
  of 
  minimum 
  

   action 
  may 
  then 
  be 
  modified 
  in 
  the 
  manner 
  expressed 
  bv 
  the 
  

   formulae 
  (44) 
  to 
  (46), 
  

  

  8NN\L 
  a 
  dv 
  a 
  ds 
  a 
  dT 
  + 
  M!\\Ldv 
  m 
  ds 
  m 
  dT 
  

  

  4 
  m(47r)*(| 
  , 
  |T(Y^Sr 
  a 
  - 
  d 
  ~^hs^dv 
  a 
  ds 
  a 
  dT 
  

  

  + 
  m(47r)*f|^ff 
  . 
  . 
  (44) 
  

  

  ^=-K&) 
  2+ 
  K&) 
  2+ 
  ^ 
  (E2 
  ~ 
  H2) 
  -: 
  * 
  * 
  ' 
  * 
  (45) 
  

  

  L 
  ^ 
  ma 
  -^ 
  F 
  - 
  *£♦) 
  + 
  PW{ 
  (i) 
  2 
  -(tJ} 
  m 
  

  

  The 
  function 
  L 
  a 
  exists 
  wherever 
  there 
  is 
  aether, 
  L 
  m 
  only 
  

   where 
  there 
  is 
  matter. 
  In 
  applying 
  (44) 
  we 
  must 
  remember 
  

   that 
  the 
  variations 
  are 
  subject 
  not 
  only 
  to 
  

  

  &(dv 
  m 
  ds 
  m 
  ) 
  = 
  0, 
  

  

  but 
  also 
  by 
  (43) 
  as 
  long 
  as 
  the 
  time 
  t 
  is 
  not 
  varied 
  to 
  

  

  8{dv 
  a 
  ds 
  a 
  )=0. 
  

  

  