﻿Theory 
  of 
  Gravity. 
  643 
  

  

  Thus 
  the 
  energy 
  increases 
  by 
  the 
  amount 
  o£ 
  work 
  done 
  by 
  

   the 
  pressure 
  on 
  the 
  element 
  of 
  volume 
  dv. 
  

  

  I 
  am 
  not 
  aware 
  that 
  these 
  results 
  of 
  the 
  principle 
  of 
  

   relativity 
  are 
  generally 
  recognized. 
  Most 
  writers 
  seem 
  to 
  

   begin 
  with 
  a 
  material 
  particle 
  whose 
  mass 
  varies 
  as 
  

  

  ' 
  (l-uVc 
  2 
  )-*, 
  

  

  and 
  out 
  of 
  such 
  particles 
  construct 
  a 
  continuous 
  fluid. 
  

  

  According 
  to 
  the 
  relativist 
  it 
  appears 
  that 
  the 
  momentum 
  

   of 
  a 
  continuous 
  fluid 
  varies 
  as 
  the 
  square 
  of 
  its 
  density. 
  It 
  

   cannot 
  be 
  claimed 
  that 
  the 
  results 
  of 
  experience 
  contradict 
  

   this 
  view. 
  It 
  is 
  true 
  that 
  in 
  ordinary 
  mechanical 
  media 
  the 
  

   momentum 
  is 
  ordinarily 
  assumed 
  to 
  vary 
  as 
  the 
  density 
  

   merely. 
  But 
  such 
  media 
  are 
  not, 
  if 
  the 
  atomic 
  hypothesis 
  

   is 
  sound, 
  continuous. 
  The 
  present 
  theory 
  would 
  apply 
  

   not 
  to 
  them 
  but 
  only 
  within 
  the 
  atoms 
  of 
  which 
  they 
  are 
  com- 
  

   posed, 
  provided 
  we 
  can 
  imagine 
  these 
  to 
  be 
  formed 
  by 
  sub- 
  

   stance 
  continuously 
  distributed. 
  And 
  then 
  it 
  becomes 
  

   in 
  general 
  impossible 
  to 
  decide 
  on 
  experimental 
  grounds 
  

   between 
  the 
  two 
  rival 
  expressions 
  for 
  the 
  momentum 
  

  

  pu 
  and 
  p 
  2 
  u 
  

  

  since 
  p 
  the 
  density 
  within 
  an 
  atom 
  is 
  practically 
  invariable. 
  

   There 
  is 
  one 
  exception. 
  Kaufmann's 
  experiments 
  on 
  the 
  

   mass 
  of 
  the 
  electron 
  have 
  been 
  taken 
  to 
  indicate 
  that 
  there 
  is 
  

   a 
  change 
  of 
  volume 
  with 
  very 
  great 
  velocities. 
  And 
  taken 
  

   in 
  this 
  sense, 
  Kaufmann's 
  results 
  are 
  decisive 
  in 
  favour 
  of 
  

   the 
  relativist's 
  formula 
  for 
  the 
  momentum. 
  

  

  For 
  according 
  to 
  Kaufmann 
  the 
  mass 
  of 
  the 
  electron 
  

   varies 
  as 
  

  

  (l-tf/c 
  2 
  )-*- 
  

   Its 
  volume 
  varies 
  on 
  Lorentz's 
  theory 
  as 
  

  

  (l_u 
  2 
  /c 
  2 
  )t. 
  

   Thus 
  the 
  mass 
  per 
  unit 
  volume 
  is 
  proportional 
  to 
  

   (l-u 
  2 
  /c 
  2 
  )-\ 
  

  

  or 
  to 
  the 
  square 
  of 
  the 
  density, 
  taking 
  the 
  electron 
  to 
  be 
  a 
  

   continuous 
  distribution 
  of 
  electric 
  charge. 
  

  

  From 
  (7) 
  a 
  vortex 
  theory 
  analogous 
  to 
  that 
  of 
  ordinary 
  

   mechanics 
  can 
  easily 
  be 
  deduced. 
  (7) 
  may 
  be 
  written 
  

  

  --,(pu) 
  + 
  c 
  2 
  Vp-v 
  v 
  pu 
  = 
  0, 
  .... 
  (8) 
  

  

  { 
  

  

  dt 
  

  

  A 
  V 
  B 
  is 
  the 
  vector 
  whose 
  a; 
  component 
  is 
  

  

  cW, 
  dB, 
  dB 
  3 
  \ 
  

  

  Al 
  l^ 
  +A 
  >llx+ 
  A 
  ^J- 
  

  

  