﻿484 
  Prof. 
  A. 
  S. 
  Eddington 
  on 
  Electrical 
  Theories 
  

  

  tell 
  us 
  what 
  are 
  the 
  boundary 
  conditions 
  at 
  the 
  electron, 
  but 
  

   only 
  how 
  they 
  are 
  transformed 
  by 
  uniform 
  motion. 
  

  

  There 
  is 
  no 
  reference 
  to 
  the 
  quasi-stationary 
  principle 
  in 
  

   this 
  theory. 
  It 
  is 
  true 
  also 
  that 
  there 
  is 
  no 
  reference 
  to 
  the 
  

   mass, 
  energy 
  or 
  momentum 
  of 
  the 
  electron 
  ; 
  the 
  motion 
  is 
  

   treated 
  geometrically. 
  It 
  is, 
  I 
  think, 
  inappropriate 
  to 
  speak 
  

   of 
  the 
  energy 
  or 
  momentum 
  of 
  an 
  electron 
  in 
  accelerated 
  

   motion 
  : 
  these 
  quantities 
  are 
  being 
  radiated, 
  and 
  it 
  is 
  im- 
  

   possible 
  to 
  define 
  the 
  precise 
  moment 
  at 
  which 
  an 
  element 
  

   of 
  energy 
  or 
  momentum 
  ceases 
  to 
  be 
  attached 
  to 
  the 
  electron 
  

   and 
  passes 
  into 
  the 
  general 
  field. 
  For 
  uniform 
  motion, 
  

   however, 
  the 
  valu«s 
  can 
  be 
  clearly 
  defined. 
  We 
  do 
  not 
  

   determine 
  them 
  directly 
  from 
  Kaufmann's 
  experiment 
  ; 
  but 
  

   we 
  arrive 
  at 
  them 
  indirectly 
  because 
  the 
  relativity 
  trans- 
  

   formation 
  is 
  verified. 
  These 
  expressions 
  for 
  the 
  momentum 
  

   and 
  energy 
  of 
  a 
  uniformly 
  moving 
  electron 
  are 
  of 
  limited 
  

   utility; 
  as 
  Walker 
  rightly 
  points 
  out, 
  it 
  is 
  not 
  permissible 
  to 
  

   differentiate 
  them. 
  

  

  I 
  gather 
  from 
  Walker's 
  remarks 
  on 
  p. 
  329 
  that 
  he 
  has 
  

   doubts 
  whether 
  the 
  Fitzgerald-Lorentz 
  contraction 
  should 
  

   theoretically 
  take 
  place 
  under 
  circumstances 
  such 
  as 
  those 
  of 
  

   the 
  Michelson-Morley 
  experiment 
  ; 
  that 
  is 
  to 
  say, 
  the 
  cor- 
  

   relation 
  found 
  by 
  Lorentz 
  and 
  Larmor 
  is 
  a 
  possible 
  one, 
  but 
  

   it 
  need 
  not 
  necessarily 
  be 
  the 
  correlation 
  occurring 
  in 
  Nature. 
  

   But 
  a 
  proof 
  based 
  on 
  statistical 
  mechanics 
  has 
  been 
  put 
  

   forward, 
  which 
  seems 
  to 
  be 
  sound 
  *. 
  The 
  arrangement 
  of 
  

   the 
  particles 
  constituting 
  a 
  solid 
  is 
  one 
  of 
  an 
  infinite 
  number 
  

   of 
  possible 
  states, 
  and 
  the 
  form 
  taken 
  up 
  by 
  the 
  solid 
  is 
  that 
  

   which 
  is 
  statistically 
  most 
  probable 
  ; 
  since 
  the 
  possible 
  states 
  

   of 
  the 
  stationary 
  and 
  moving 
  solid 
  are 
  correlated 
  one 
  to 
  one, 
  

   the 
  most 
  % 
  probable 
  states 
  (and 
  therefore 
  the 
  actual 
  states) 
  

   satisfy 
  the 
  same 
  correlation. 
  In 
  other 
  words 
  entropy 
  is 
  

   invariant 
  for 
  the 
  Lorentz 
  transformation. 
  

  

  The 
  relativity 
  principle 
  has 
  the 
  great 
  advantage 
  that 
  it 
  

   leads 
  directly 
  to 
  the 
  law 
  m 
  = 
  m 
  (l 
  — 
  w 
  2 
  /c 
  2 
  )~i 
  for 
  uniform 
  

   motion 
  of 
  matter 
  in 
  bulk, 
  and 
  it 
  is 
  unnecessary 
  to 
  consider 
  

   the 
  behaviour 
  of 
  an 
  electron, 
  or 
  indeed 
  to 
  adopt 
  an 
  electrical 
  

   theory 
  of 
  matter. 
  I 
  see 
  noway 
  of 
  deducing 
  from 
  the 
  various 
  

   electrons 
  treated 
  by 
  Walker 
  the 
  corresponding 
  laws 
  of 
  mass 
  

   for 
  matter 
  in 
  bulk, 
  so 
  that 
  the 
  discussion 
  of 
  these 
  does 
  not 
  

   seem 
  to 
  advance 
  the 
  astronomical 
  problem 
  except 
  by 
  sug- 
  

   gesting 
  possible 
  analogies. 
  

  

  * 
  E. 
  Cunningham, 
  ' 
  The 
  Principle 
  of 
  Relativity,' 
  p. 
  206. 
  Elsewhere 
  

   this 
  book 
  warns 
  the 
  reader 
  against 
  assuming 
  that 
  the 
  correlation 
  holds 
  

   for 
  a 
  non-uniform 
  translation 
  ; 
  and 
  indeed 
  those 
  who 
  accept 
  Einstein's 
  

   latest 
  theory 
  assert 
  definitely 
  that 
  it 
  does 
  not 
  hold. 
  

  

  