﻿650 
  Prof. 
  S. 
  B. 
  McLaren 
  on 
  a 
  

  

  Euclidean. 
  ni 
  J 
  represents 
  the 
  density 
  of 
  a 
  fluid-substance 
  

   and 
  dm 
  1 
  / 
  dr{\ 
  d 
  ( 
  ds 
  x 
  \ 
  ~ 
  /9Q 
  n 
  

  

  Let 
  (27) 
  and 
  (28) 
  be 
  transformed 
  by 
  the 
  substitution 
  

  

  ar 
  = 
  ^ 
  1 
  (aT 
  1 
  -a 
  1 
  5 
  1 
  ), 
  ft 
  s 
  («i 
  8 
  — 
  1) 
  =1, 
  • 
  

   s 
  = 
  f! 
  1 
  {s 
  1 
  — 
  a 
  1 
  aT 
  1 
  ), 
  *i>l, 
  I 
  .-g, 
  

  

  r 
  = 
  r 
  1? 
  am 
  = 
  pi\ 
  am 
  l 
  — 
  a 
  l 
  m 
  1 
  - 
  T 
  - 
  1. 
  ] 
  

  

  This 
  substitution 
  corresponds 
  to 
  a 
  reference 
  to 
  axes 
  movino- 
  

   with 
  the 
  velocity 
  au 
  x 
  greater 
  than 
  a 
  the 
  quantity 
  which 
  in 
  

   (28) 
  plays 
  the 
  same 
  part 
  as 
  c, 
  the 
  velocity 
  of 
  light 
  in 
  three 
  

   dimensions. 
  It 
  is 
  referred 
  to 
  these 
  axes 
  that 
  I 
  suppose 
  the 
  

   state 
  steady. 
  Then 
  (29) 
  becomes 
  (23). 
  For 
  (27) 
  there 
  is 
  

   to 
  be 
  substituted 
  

  

  S$fi§LdvdsdT=0. 
  ...... 
  (30) 
  

  

  L 
  x 
  transforms 
  into 
  L 
  and 
  it 
  will 
  be 
  enough 
  to 
  retain 
  only 
  

   those 
  terms 
  found 
  in 
  a 
  steady 
  state. 
  

  

  Z=_(87r)- 
  1 
  (V^) 
  2 
  + 
  (87r)- 
  1 
  ^J 
  + 
  7^7 
  

   + 
  (^W^ 
  +V*) 
  -(8tt) 
  - 
  1 
  (Curl 
  F) 
  2 
  

  

  In 
  (31) 
  s 
  no 
  longer 
  enters 
  on 
  the 
  same 
  terms 
  as 
  the 
  other 
  

   coordinates, 
  s 
  is 
  in 
  fact 
  the 
  time 
  variable 
  of 
  ordinary 
  physics. 
  

   We 
  have 
  only 
  to 
  replace 
  t 
  by 
  using 
  [26). 
  In 
  (31) 
  all 
  terms 
  

   containing 
  F 
  and 
  cf) 
  become 
  identical 
  with 
  the 
  terms 
  of 
  (16). 
  

  

  We 
  have 
  merely 
  to 
  write 
  as 
  in 
  (21) 
  

  

  w-r 
  - 
  =ora 
  (32) 
  

  

  and 
  the 
  equation 
  of 
  continuity 
  (23) 
  into 
  which 
  (29) 
  transforms 
  

   finally 
  becomes 
  (17). 
  

  

  I 
  shall 
  suppose 
  that 
  m 
  is 
  an 
  absolute 
  constant, 
  so 
  that 
  the 
  

   electric 
  fluid 
  is 
  incompressible 
  in 
  four 
  dimensions. 
  Then 
  

   the 
  variations 
  in 
  (30) 
  are 
  restricted 
  by 
  

  

  8(dvds)=Q 
  (33) 
  

  

  (33) 
  introduces 
  therefore 
  a 
  liquid 
  pressure 
  p 
  m 
  into 
  the 
  

  

  