﻿\ 
  

  

  Theory 
  of 
  Gravity. 
  

   and 
  the 
  equations 
  are 
  

  

  -J 
  (P»E^S„) 
  = 
  ejH^Jfe. 
  = 
  a 
  Curl 
  H 
  a 
  dS 
  n 
  , 
  

   A 
  Cp.H^SJ 
  = 
  - 
  c 
  J 
  E 
  a 
  d 
  Va 
  = 
  - 
  e 
  Curl 
  E.dS 
  t 
  

  

  671 
  

  

  (91) 
  

  

  It 
  must 
  be 
  remembered 
  that 
  the 
  space 
  is 
  not 
  Euclidean, 
  

   except 
  in 
  infinitesimal 
  portions. 
  

  

  Thus 
  (91) 
  shows 
  that 
  the 
  specific 
  inductive 
  capacity 
  and 
  

   magnetic 
  permeability 
  of 
  the 
  aether 
  are 
  equal 
  and 
  propor- 
  

   tional 
  to 
  its 
  density. 
  

  

  There 
  is 
  a 
  point 
  of 
  resemblance 
  to 
  Stokes's 
  theory 
  of 
  

   aberration. 
  Referred 
  to 
  the 
  local 
  time 
  t 
  x 
  kept 
  by 
  a 
  rigid 
  

   body 
  moving 
  with 
  the 
  aether 
  at 
  any 
  point 
  write 
  (40) 
  

  

  Pl 
  u 
  1 
  = 
  W, 
  P^ 
  = 
  ~ 
  cd 
  ^ 
  

   The 
  equation 
  

  

  Curl 
  piTL] 
  = 
  0, 
  

  

  becomes 
  in 
  the 
  neighbourhood 
  of 
  this 
  point 
  since 
  the 
  

   velocity 
  Ux 
  is 
  there 
  zero 
  

  

  Curl 
  Hi 
  = 
  0. 
  

  

  Hence 
  the 
  motion 
  viewed 
  from 
  any 
  moving 
  particle 
  of 
  sether 
  

   is 
  in 
  the 
  ordinary 
  sense 
  irrotational 
  for 
  points 
  in 
  the 
  imme- 
  

   diate 
  neighbourhood. 
  

  

  The 
  equations 
  (91) 
  seem 
  to 
  show 
  that 
  in 
  regions 
  where 
  

   p 
  a 
  has 
  different 
  values 
  the 
  velocity 
  of 
  light 
  varies 
  inversely 
  

   as 
  p 
  a 
  the 
  density 
  of 
  the 
  aether. 
  Could 
  such 
  a 
  result 
  be 
  

   observed 
  ? 
  Not 
  if 
  the 
  velocity 
  of 
  light 
  is 
  measured, 
  as 
  it 
  

   must 
  be, 
  by 
  the 
  passage 
  of 
  observable 
  events, 
  by 
  the 
  ticking 
  

   of 
  the 
  clock. 
  

  

  To 
  measure 
  velocities 
  at 
  all 
  a 
  constant 
  material 
  system 
  is 
  

   required, 
  moving 
  with 
  the 
  aether 
  at 
  the 
  point 
  and 
  keeping 
  

   the 
  local 
  time 
  t 
  x 
  . 
  The 
  motion 
  of 
  the 
  pendulum 
  will 
  in 
  this 
  

   system 
  be 
  defined 
  by 
  a 
  variable 
  6 
  such 
  that 
  

  

  d*6 
  . 
  « 
  a 
  ri 
  

  

  Making 
  the 
  substitution 
  (87) 
  

  

  If 
  the 
  velocity 
  of 
  light 
  is 
  decreased 
  inversely 
  as 
  p 
  a 
  the 
  

  

  