﻿664- 
  Prof. 
  S. 
  B. 
  McLaren 
  on 
  a 
  

  

  It 
  follows 
  therefore 
  that 
  matter 
  behaves 
  as 
  if 
  the 
  external 
  

   tension 
  

  

  were 
  applied 
  to 
  its 
  surface. 
  This 
  represents 
  the 
  action 
  of 
  

   a 
  body 
  force 
  

  

  w 
  

  

  which 
  arises 
  from 
  the 
  external 
  potential 
  V. 
  

  

  When 
  this 
  potential 
  is 
  continuous 
  it 
  has 
  no 
  effect 
  what- 
  

   ever. 
  But 
  if 
  forces 
  are 
  applied 
  only 
  to 
  matter 
  or 
  only 
  to 
  

   aether, 
  or 
  if 
  the 
  forces 
  are 
  not 
  continuous 
  at 
  the 
  surface, 
  

   then 
  the 
  quantity 
  V 
  m 
  — 
  V 
  a 
  does 
  not 
  vanish. 
  I 
  return 
  in 
  the 
  

   last 
  section 
  to 
  discuss 
  the 
  application 
  of 
  sueh 
  a 
  potential 
  

   function. 
  

  

  I 
  have 
  spoken 
  of 
  the 
  quantities 
  which 
  appear 
  in 
  (75) 
  as 
  the 
  

   fictitious 
  stresses. 
  It 
  may 
  be 
  asked 
  what 
  are 
  the 
  real 
  stresses. 
  

   These 
  ought 
  to 
  account 
  for 
  the 
  transfer 
  of 
  energy 
  and 
  

   momentum 
  alike. 
  Cunningham 
  (Proc. 
  Roy. 
  Soc. 
  vol. 
  lxxxiii. 
  

   p. 
  109) 
  has 
  shown 
  how 
  such 
  stresses 
  are 
  to 
  be 
  determined. 
  

  

  Suppose 
  electromagnetic 
  momentum 
  to 
  be 
  due 
  to 
  the 
  

   motion 
  of 
  a 
  substance. 
  The 
  stresses 
  required 
  are 
  those 
  

   which 
  act 
  across 
  a 
  surface 
  moving 
  with 
  the 
  same 
  velocity 
  as 
  

   the 
  substance. 
  

  

  Let 
  u 
  be 
  this 
  velocity. 
  Then 
  Cunningham 
  shows 
  that 
  

  

  i?V(c 
  2 
  + 
  u 
  2 
  )=^(E 
  2 
  + 
  H 
  2 
  ). 
  

  

  Here 
  it 
  is 
  evident 
  that 
  m 
  in 
  the 
  expression 
  for 
  the 
  

   momentum 
  and 
  energy 
  plays 
  the 
  same 
  part 
  as 
  does 
  the 
  

   density 
  p 
  in 
  the 
  fluid 
  of 
  § 
  1. 
  The 
  stress 
  system 
  acting 
  in 
  

   this 
  fluid 
  is 
  a 
  tension 
  

  

  and 
  an 
  equal 
  pressure 
  in 
  directions 
  perpendicular 
  to 
  the 
  

   tension. 
  The 
  direction 
  of 
  the 
  tension 
  is 
  parallel 
  to 
  either 
  of 
  

   the 
  (parallel) 
  vectors 
  E 
  and 
  H 
  

  

  E 
  =E+-[u 
  H] 
  and 
  H 
  =H-- 
  [u 
  E]. 
  

   c 
  c 
  

  

  Notice, 
  however, 
  that 
  there 
  is 
  no 
  equation 
  of 
  continuity. 
  If 
  

   m 
  Q 
  be 
  regarded 
  as 
  the 
  density 
  then 
  matter 
  appears 
  or 
  dis- 
  

   appears 
  according 
  to 
  no 
  simply 
  determined 
  formula. 
  

  

  At 
  a 
  reflecting 
  surface 
  the 
  momentum 
  is 
  parallel 
  to 
  the 
  

   surface. 
  If 
  that 
  surface 
  moves 
  momentum 
  disappears 
  across 
  it. 
  

  

  