﻿646 
  

  

  Prof. 
  S. 
  B. 
  McLaren 
  

  

  on 
  a 
  

  

  If 
  the 
  distribution 
  of 
  electric 
  charge 
  is 
  varied 
  it 
  can 
  be 
  

   shown 
  that 
  

  

  ~(ea 
  2 
  udv) 
  + 
  V 
  {iea 
  2 
  c 
  2 
  -±ea 
  2 
  VL 
  2 
  )dv 
  = 
  ~E'<Tdv, 
  

  

  Instead 
  of 
  (9) 
  in 
  last 
  section 
  we 
  have 
  now 
  

  

  (20) 
  

   (21) 
  

  

  dt 
  

  

  ,{6o-u 
  + 
  c- 
  1 
  F)Jr}=^(eau 
  2 
  -eo-c 
  2 
  + 
  c- 
  1 
  uF-^)). 
  

  

  And 
  an 
  ir 
  rotational 
  motion 
  is 
  possible 
  such 
  that 
  

   ec7U 
  + 
  c- 
  1 
  F 
  = 
  V%, 
  e<ic 
  + 
  c- 
  1 
  <t>=— 
  -%. 
  

  

  (18) 
  now 
  gives 
  

  

  1 
  d 
  2 
  4tt\ 
  n 
  ^ 
  

  

  c 
  2 
  dt 
  2 
  

  

  

  J 
  

  

  The 
  formula 
  (16) 
  for 
  the 
  action 
  is 
  only 
  suitable 
  when 
  

   electricity 
  is 
  treated 
  as 
  a 
  continuous 
  fluid 
  substance. 
  An- 
  

   other 
  treatment 
  is 
  given 
  later 
  in 
  which 
  the 
  magnetic 
  energy 
  

   becomes 
  kinetic 
  energy 
  in 
  agreement 
  with 
  Larmor 
  ; 
  in 
  (16) 
  

   we 
  should 
  be 
  compelled 
  to 
  regard 
  it 
  as 
  potential 
  energy. 
  

  

  I 
  shall 
  show 
  in 
  §4 
  that 
  a 
  gravitational 
  potential 
  analogous 
  

   to 
  the 
  electrostatic 
  potential 
  <£ 
  of 
  (16) 
  is 
  reached 
  by 
  ex- 
  

   tending 
  that 
  formula 
  to 
  four 
  dimensions. 
  This 
  procedure 
  

   raises 
  questions 
  which 
  I 
  discuss 
  in 
  § 
  3. 
  

  

  § 
  3. 
  Time 
  and 
  the 
  Fourth 
  Dimension. 
  

  

  All 
  that 
  we 
  have 
  already 
  said 
  and 
  what 
  is 
  still 
  to 
  come 
  

   can 
  be 
  made 
  much 
  clearer 
  by 
  using 
  Minkowski's 
  idea 
  of 
  the 
  

   time 
  variable, 
  the 
  t 
  of 
  ordinary 
  physics, 
  as 
  the 
  fourth 
  co- 
  

   ordinate 
  of 
  a 
  four-dimensional 
  space. 
  It 
  is 
  far 
  easier 
  to 
  

   think 
  in 
  four 
  dimensions 
  than 
  in 
  three. 
  

  

  Minkowski, 
  it 
  is 
  well 
  known, 
  considered 
  a 
  timeless 
  

   universe. 
  What 
  he 
  speaks 
  of 
  as 
  time 
  is 
  in 
  reality 
  only 
  a 
  

   length. 
  I 
  propose 
  to 
  go 
  further. 
  The 
  universe 
  is 
  to 
  be 
  

   changeless 
  but 
  not 
  timeless. 
  All, 
  matter 
  and 
  aether 
  alike, 
  is 
  

   in 
  motion, 
  but 
  it 
  is 
  the 
  motion 
  of 
  the 
  sleeping 
  top 
  or, 
  rather, 
  

   the 
  waterfall. 
  iEther 
  and 
  matter 
  move 
  in 
  unvarying 
  streams 
  

   that 
  never 
  change 
  their 
  currents 
  or 
  their 
  banks. 
  Here 
  there 
  

   can 
  be 
  one 
  absolute 
  time 
  throughout 
  the 
  universe, 
  a 
  time 
  

   present 
  to 
  whatever 
  consciousness 
  sees 
  the 
  universe 
  steadily 
  

  

  