﻿Theory 
  of 
  Gravity. 
  659 
  

  

  Consider 
  the 
  " 
  circulation. 
  " 
  It 
  is 
  easily 
  proved 
  that 
  

  

  d 
  fdr 
  

   ~dr 
  

  

  KS*-s*)-^MI*-£*)-*' 
  • 
  (63) 
  

  

  Thus 
  if 
  we 
  take 
  any 
  complete 
  circuit 
  in 
  matter 
  or 
  in 
  gether 
  

   the 
  circulation 
  satisfies 
  the 
  equation 
  

  

  and 
  i£ 
  the 
  circulation 
  vanishes 
  initially 
  round 
  any 
  circuit 
  it 
  

   remains 
  always 
  zero. 
  

  

  We 
  are 
  it 
  is 
  true 
  concerned 
  only 
  with 
  steady 
  motion. 
  This 
  

   result 
  suggests, 
  however, 
  that 
  we 
  should 
  investigate 
  the 
  

   conditions 
  under 
  which 
  an 
  irrotational 
  steady 
  motion 
  is 
  

   possible. 
  

  

  As 
  in 
  (40) 
  we 
  are 
  to 
  have 
  

  

  (*,)** 
  -VJ, 
  (4^=-^- 
  • 
  (40 
  tt) 
  

  

  It 
  is 
  easily 
  shown 
  that 
  the 
  equations 
  {62) 
  are 
  all 
  satisfied 
  

   if 
  both 
  in 
  matter 
  and 
  in 
  aether 
  the 
  quantity 
  

  

  l/ds\ 
  2 
  T 
  Jr 
  

   1 
  -7- 
  —mJ+ 
  V 
  

  

  >*k<»-™+ffi-\® 
  

  

  is 
  a 
  constant. 
  It 
  is 
  not 
  shown 
  that 
  this 
  constant 
  is 
  the 
  same 
  

   in 
  matter 
  and 
  aether. 
  

   Hence 
  I 
  write 
  

  

  ^• 
  + 
  i(?T 
  , 
  ) 
  2 
  ~Ki) 
  2 
  ~™ 
  ,/+F 
  "' 
  =c 
  - 
  • 
  • 
  (66) 
  

  

  The 
  last 
  type 
  of 
  variation 
  to 
  be 
  considered 
  is 
  that 
  in 
  which 
  

   the 
  boundaries 
  between 
  matter 
  and 
  aether 
  are 
  aLtered. 
  I 
  

   shall 
  confine 
  myself 
  to 
  variations 
  in 
  which 
  (40) 
  holds 
  and 
  

   the 
  state 
  is 
  steady. 
  The 
  variation 
  consists 
  in 
  the 
  fact 
  that 
  

   a 
  volume 
  element 
  

  

  8 
  (dv 
  ds) 
  

   is 
  transferred 
  from 
  aether 
  to 
  matter. 
  

  

  