﻿Theory 
  of 
  Gravity. 
  665 
  

  

  But 
  the 
  stress 
  system 
  just 
  considered 
  involves 
  a 
  shear 
  at 
  the 
  

   surface 
  of 
  reflexion, 
  which 
  accounts 
  for 
  this 
  transfer 
  of 
  

   momentum. 
  

  

  We 
  saw 
  in 
  § 
  6 
  that 
  with 
  the 
  system 
  there 
  adopted 
  the 
  

   pressure 
  of 
  aether 
  can 
  be 
  continuous 
  at 
  the 
  boundary. 
  It 
  

   follows 
  therefore 
  that 
  the 
  electromagnetic 
  stresses 
  across 
  the 
  

   bounding 
  surface 
  vanish. 
  In. 
  fact 
  the 
  stress 
  system 
  to 
  which 
  

   our 
  methods 
  lead 
  differs 
  from 
  Cunningham's 
  owing 
  to 
  the 
  

   fact 
  that 
  part 
  of 
  the 
  electromagnetic 
  stress 
  is 
  transferred 
  to 
  

   the 
  fluid 
  pressure 
  of 
  the 
  aether. 
  It 
  is 
  also 
  to 
  be 
  remembered 
  

   that 
  in 
  four 
  dimensions 
  there 
  is 
  no 
  electromagnetic 
  momentum 
  

   but 
  only 
  stress, 
  ail 
  momentum 
  is 
  due 
  to 
  the 
  liquid 
  motion 
  of 
  

   the 
  aether. 
  

  

  We 
  have 
  by 
  combining 
  (71) 
  and 
  (74) 
  

  

  d 
  

  

  ds 
  

  

  dx 
  

  

  e 
  ih 
  

  

  + 
  4z(cK 
  z 
  )=o, 
  

  

  d 
  

  

  ds 
  y 
  dx 
  dy 
  dz 
  

  

  d 
  

  

  d 
  

  

  ^ 
  ) 
  + 
  tx 
  U 
  e 
  +~Q< 
  

  

  A 
  

  

  dz 
  

  

  d 
  

  

  s 
  e 
  =o, 
  

  

  K 
  (82) 
  

  

  (oM 
  e2 
  ) 
  + 
  ^T 
  e+ 
  ^S 
  e+ 
  ~I 
  

  

  These 
  equations 
  indicate 
  that 
  the 
  energy 
  and 
  the 
  momentum 
  

   multiplied 
  by 
  c 
  are 
  the 
  stresses 
  in 
  the 
  direction 
  of 
  the 
  s 
  axis 
  

   and 
  that 
  they 
  form 
  a 
  system 
  in 
  equilibrium. 
  But 
  the 
  

   equation 
  (61) 
  shows 
  that 
  the 
  electromagnetic 
  field 
  produces 
  

   a 
  force 
  on 
  unit 
  volume 
  of 
  aether 
  of 
  amount 
  

  

  8. 
  V 
  ^ 
  

  

  E 
  2 
  ). 
  

  

  Hence 
  there 
  must 
  be 
  a 
  reaction 
  equal 
  and 
  opposite 
  to 
  this 
  

   against 
  the 
  polarizing 
  apparatus. 
  The 
  results 
  (82) 
  do 
  not, 
  

   therefore, 
  indicate 
  the 
  true 
  electromagnetic 
  stresses. 
  These 
  

   are 
  not 
  in 
  equilibrium 
  with 
  each 
  other 
  but 
  with 
  the 
  applied 
  

  

  force 
  

  

  Thus 
  the 
  

   written 
  

  

  d_ 
  

  

  ds 
  

  

  second 
  

  

  1^ 
  

  

  87T 
  

  

  line 
  for 
  

  

  V 
  (E 
  2 
  -H 
  2 
  ). 
  

  

  example 
  of 
  (82) 
  ought 
  to 
  be 
  

  

  ( 
  - 
  cM 
  ^ 
  + 
  U 
  p 
  ^^-^) 
  

  

  d 
  

  

  d 
  

  

  + 
  dy^ 
  + 
  Tz^ 
  

  

  = 
  ~V(E 
  2 
  ~H 
  2 
  ). 
  

  

  