﻿Theory 
  of 
  Gravity. 
  641 
  

  

  dS 
  a 
  is 
  an 
  element 
  o£ 
  area 
  moving 
  with 
  the 
  aether. 
  Thus 
  (91) 
  

   expresses 
  that 
  the 
  specific 
  inductive 
  capacity 
  and 
  magnetic 
  

   permeability 
  of 
  the 
  aether 
  are 
  equal 
  to 
  each 
  other 
  and 
  

   proportional 
  to 
  the 
  density. 
  

  

  The 
  results 
  (36) 
  and 
  (40) 
  were 
  given 
  by 
  me 
  in 
  a 
  paper 
  

   read 
  at 
  the 
  Mathematical 
  Congress 
  of 
  1912. 
  The 
  expressions 
  

   for 
  the 
  energy 
  and 
  momentum 
  to 
  which 
  they 
  lead 
  are 
  the 
  

   same 
  as 
  those 
  given 
  by 
  Max 
  Abraham. 
  I 
  had 
  obtained 
  them 
  

   independently 
  at 
  the 
  time 
  when 
  his 
  work 
  was 
  published. 
  

   In 
  the 
  paper 
  referred 
  to 
  there 
  is 
  a 
  result 
  of 
  the 
  same 
  

   character 
  as 
  (94), 
  but 
  differing 
  from 
  it 
  because 
  I 
  there 
  

   assume 
  matter 
  as 
  a 
  substance 
  different 
  from 
  aether 
  and 
  

   having 
  momentum 
  of 
  its 
  own. 
  

  

  The 
  results 
  (91) 
  are 
  now 
  first 
  published. 
  Before 
  reading 
  

   my 
  former 
  paper 
  I 
  had 
  made 
  attempts 
  to 
  find 
  some 
  such 
  

   formula?, 
  but 
  had 
  failed 
  to 
  identify 
  the 
  local 
  time 
  at 
  any 
  

   point 
  of 
  the 
  aether 
  with 
  the 
  velocity 
  potential, 
  

  

  The 
  equations 
  (91) 
  may 
  be 
  interpreted 
  to 
  mean 
  that 
  

   in 
  regions 
  where 
  p 
  a 
  has 
  different 
  values 
  the 
  velocity 
  of 
  

   light 
  varies 
  inversely 
  as 
  p 
  a 
  the 
  density 
  of 
  the 
  aether. 
  The 
  

   suggestion 
  that 
  the 
  velocity 
  of 
  light 
  may 
  vary 
  has 
  already 
  

   been 
  made 
  by 
  Einstein 
  and 
  Abraham. 
  Their 
  ideas 
  have 
  not, 
  

   so 
  far 
  as 
  I 
  am 
  able 
  to 
  understand, 
  much 
  in 
  common 
  with 
  

   these 
  here 
  maintained. 
  The 
  change 
  of 
  velocity 
  is 
  not 
  an 
  

   observable 
  phenomenon, 
  for 
  all 
  physical 
  measure 
  of 
  time 
  is 
  

   a 
  measurement 
  by 
  events, 
  and 
  the 
  velocity 
  of 
  light 
  is 
  after 
  

   all 
  given 
  only 
  by 
  the 
  number 
  of 
  ticks 
  the 
  clock 
  has 
  made 
  

   ( 
  § 
  9). 
  Stokes's 
  theory 
  of 
  aberration 
  also 
  connects 
  itself 
  with 
  

   ours. 
  Taking 
  the 
  local 
  time 
  at 
  any 
  point 
  of 
  the 
  setter 
  the 
  

   motion 
  near 
  that 
  point 
  is 
  irrotational 
  (§ 
  9) 
  in 
  the 
  ordinary 
  

   sense. 
  In 
  § 
  8 
  I 
  suggest 
  a 
  physical 
  basis 
  for 
  the 
  distinction 
  

   between 
  negative 
  and 
  positive 
  charges. 
  If 
  the 
  electron 
  is 
  

   always 
  the 
  negative 
  the 
  magneton 
  may 
  always 
  be 
  the 
  positive 
  

   charge 
  (§8). 
  

  

  The 
  main 
  results 
  of 
  this 
  paper 
  are 
  in 
  §§ 
  1, 
  3, 
  6, 
  and 
  (9). 
  

  

  § 
  1. 
  Relativist 
  Hydrodynamics. 
  

  

  The 
  principle 
  of 
  relativity 
  assumed, 
  what 
  is 
  the 
  dynamical 
  

   behaviour 
  of 
  a 
  perfect 
  fluid 
  ? 
  As 
  fluid 
  its 
  physical 
  properties 
  

   can 
  depend 
  only 
  upon 
  its 
  density 
  p 
  and 
  its 
  velocity 
  u. 
  In 
  

   the 
  formula 
  of 
  least 
  action 
  

  

  8flfiLdvdt=0 
  (1) 
  

  

  L 
  is 
  a 
  function 
  only 
  of 
  the 
  values 
  of 
  p 
  and 
  u 
  at 
  the 
  volume 
  

   element 
  dv 
  and 
  at 
  the 
  time 
  t. 
  Also 
  the 
  principle 
  of 
  relativity 
  

  

  