﻿662 
  Prof. 
  S. 
  B. 
  McLaren 
  

  

  on 
  a 
  

  

  The 
  quantities 
  on 
  the 
  right 
  of 
  (75) 
  are 
  the 
  fictitious 
  

   stresses. 
  

  

  It 
  will 
  be 
  sufficient 
  to 
  consider 
  here 
  that 
  form 
  of 
  our 
  

   theory 
  in 
  which 
  there 
  is 
  no 
  true 
  material 
  substance 
  but 
  only 
  

   rather. 
  Then 
  we 
  have 
  to 
  do 
  with 
  gravitational 
  and 
  electro- 
  

   magnetic 
  energy. 
  Let 
  

  

  P 
  — 
  P 
  -4-P 
  

  

  ■*- 
  x 
  — 
  x 
  ex 
  i 
  x 
  nx 
  

  

  P 
  -= 
  W- 
  ^ 
  2 
  + 
  m, 
  - 
  ±(E 
  x 
  E 
  y+ 
  HH^ 
  - 
  A 
  (E 
  x 
  E 
  z 
  + 
  H 
  x 
  Il 
  z 
  y 
  

  

  h 
  w(s«) 
  + 
  4^W, 
  4tt< 
  

  

  UdJ 
  JL^dJdJ 
  

   4-7T 
  \cdt 
  J 
  ' 
  4:77 
  \dxj, 
  4tt 
  dx 
  dy 
  » 
  47r 
  rf« 
  <i? 
  ' 
  

  

  It 
  is 
  sometimes 
  necessary 
  to 
  deal 
  with 
  the 
  flux 
  of 
  energy 
  

   and 
  momentum 
  from 
  a 
  moving 
  element 
  of 
  volume 
  or 
  across 
  

   a 
  moving 
  surface. 
  Let 
  u 
  denote 
  the 
  velocity 
  of 
  dv. 
  

  

  Then 
  instead 
  of 
  (71) 
  and 
  (73) 
  

  

  -~(Wdv) 
  + 
  B\Y(c 
  2 
  M-vi.W)dv. 
  . 
  . 
  . 
  (78) 
  

   And 
  instead 
  of 
  (74) 
  equations 
  such 
  as 
  

  

  ■^(Al 
  x 
  dv) 
  + 
  I)iv{F 
  x 
  -iiM 
  x 
  )dv 
  = 
  0. 
  . 
  . 
  (79) 
  

  

  From 
  (78) 
  and 
  (79) 
  it 
  follows 
  that 
  the 
  flux 
  of 
  energy 
  

   ross 
  unit 
  ; 
  

   velocity 
  u 
  n 
  is 
  

  

  across 
  unit 
  area 
  of 
  a 
  surface 
  moving 
  with 
  the 
  normal 
  

  

  c 
  2 
  M 
  n 
  -u 
  n 
  W, 
  (80) 
  

  

  where 
  Mn 
  denotes 
  the 
  normal 
  component 
  of 
  M. 
  

   The 
  flux 
  of 
  momentum 
  has 
  the 
  components 
  

  

  P»-n„M 
  (81) 
  

  

  Pn 
  is 
  the 
  vector 
  whose 
  components 
  are 
  the 
  stresses 
  across 
  

   the 
  surface. 
  

  

  If 
  the 
  surface 
  is 
  a 
  perfect 
  reflector 
  as 
  before, 
  I 
  shall 
  

   now 
  show 
  that 
  conservation 
  of 
  energy 
  and 
  of 
  momentum 
  are 
  

   secured 
  by 
  the 
  condition 
  (69) 
  of 
  last 
  section, 
  a 
  condition 
  

   which 
  as 
  we 
  have 
  seen 
  is 
  equivalent 
  to 
  supposing 
  that 
  there 
  is 
  

   no 
  change 
  of 
  pressure 
  in 
  passing 
  from 
  " 
  matter 
  " 
  to 
  " 
  aether/'' 
  

  

  Take 
  the 
  x 
  axis 
  normal 
  to 
  the 
  surface 
  of 
  separation. 
  

  

  Referring 
  to 
  (81) 
  and 
  (76) 
  it 
  seems 
  that 
  the 
  flux 
  of 
  

   electromagnetic 
  momentum 
  into 
  the 
  rather 
  has 
  the 
  three 
  

  

  