﻿640 
  Prof. 
  S. 
  B. 
  McLaren 
  

  

  on 
  a 
  

  

  speak 
  of 
  the 
  motion 
  and 
  velocity 
  of 
  the 
  four- 
  dimensional 
  

   liquid. 
  

  

  Fin 
  (51) 
  is 
  the 
  potential 
  of 
  an 
  external 
  field 
  of 
  force 
  (§ 
  10). 
  

  

  The 
  electromagnetic 
  energy 
  in 
  (51) 
  is 
  purely 
  statical 
  and 
  

   produces 
  in 
  aether 
  a 
  force 
  of 
  amount 
  

  

  ^V(H 
  2 
  -E 
  2 
  ) 
  

  

  per 
  unit 
  volume. 
  This, 
  without 
  disturbing 
  the 
  irrotational 
  

   motion, 
  alters 
  the 
  distribution 
  of 
  pressure. 
  The 
  condition 
  

   (94) 
  is 
  now 
  shown 
  to 
  involve 
  merely 
  that 
  the 
  pressure 
  

   of 
  the 
  liquid 
  does 
  not 
  change 
  in 
  passing 
  from 
  aether 
  to 
  

   matter. 
  The 
  electromagnetic 
  equations 
  involve 
  no 
  trace 
  of 
  

   the 
  aether's 
  motion, 
  because, 
  since 
  the 
  energy 
  is 
  wholly 
  

   statical, 
  each 
  particle 
  of 
  aether 
  takes 
  up 
  without 
  " 
  lag 
  " 
  the 
  

   polarization 
  appropriate 
  to 
  the 
  statical 
  (four-dimensional) 
  

   field 
  of 
  charge. 
  The 
  electromagnetic 
  stresses 
  must 
  equili- 
  

   brate 
  with 
  the 
  reaction 
  from 
  each 
  particle 
  of 
  aether 
  against 
  

   the 
  polarizing 
  apparatus 
  attached 
  to 
  it. 
  I 
  show 
  that 
  these 
  

   stresses 
  give 
  zero 
  pressures 
  and 
  shears 
  across 
  the 
  surface 
  of 
  

   matter. 
  They 
  differ 
  from 
  Maxwell's 
  system 
  of 
  stresses 
  

   owing 
  to 
  the 
  action 
  of 
  the 
  force 
  

  

  ^V(E'-H'), 
  

  

  which«is 
  the 
  reaction 
  to 
  the 
  force 
  of 
  translation 
  on 
  the 
  fluid. 
  

   The 
  physicist 
  will 
  naturally 
  demand 
  that 
  this 
  four- 
  

   dimensional 
  system 
  should 
  condescend 
  to 
  explain 
  itself 
  in 
  

   the 
  ordinary 
  language 
  of 
  space 
  and 
  time. 
  But 
  if 
  we 
  are 
  to 
  

   have 
  a 
  moving 
  aether, 
  its 
  properties 
  are 
  only 
  capable 
  of 
  rational 
  

   expression 
  in 
  the 
  physicist's 
  sense, 
  if 
  a 
  system 
  of 
  time 
  mea- 
  

   surement 
  is 
  used 
  relative 
  to 
  each 
  of 
  its 
  particles. 
  I 
  show 
  

   ( 
  § 
  9) 
  that 
  the 
  local 
  aether 
  time 
  is 
  simply 
  proportional 
  to 
  the 
  

   velocity 
  potential 
  ,/. 
  In 
  fact 
  

  

  t 
  a 
  =-J/c 
  2 
  (85) 
  

  

  Further, 
  there 
  is 
  now 
  a 
  local 
  density 
  p 
  a 
  given 
  by 
  

  

  p 
  =p(l-u 
  2 
  /c 
  2 
  )i. 
  (86) 
  

  

  Any 
  given 
  value 
  of 
  t 
  a 
  defines 
  a 
  three-dimensional 
  space 
  

   which 
  is 
  Euclidean 
  only 
  in 
  infinitesimal 
  elements. 
  The 
  

   electromagnetic 
  equations 
  become 
  

  

  4frJS^a.) 
  = 
  flCnrlH.c/S 
  fl 
  

   ata 
  \. 
  . 
  . 
  (91) 
  

  

  d 
  

  

  ^(pJUS^-cCurlE^S, 
  

  

  