﻿of 
  Matter 
  and 
  tlieir 
  Astronomical 
  Consequences. 
  483 
  

  

  the 
  motion 
  of 
  the 
  planets 
  seems 
  to 
  afford 
  a 
  good 
  illustration 
  

   of 
  its 
  fallibility. 
  But 
  it 
  seems 
  rather 
  unfair 
  to 
  blame 
  

   relativists 
  for 
  a 
  method 
  which 
  was 
  introduced 
  by 
  Abraham 
  

   in 
  a 
  non-relativity 
  theory. 
  I 
  am 
  not 
  sufficient^ 
  versed 
  in 
  

   the 
  history 
  of 
  the 
  subject 
  to 
  know 
  how 
  extensively 
  relativists 
  

   have 
  followed 
  his 
  example 
  ; 
  but 
  I 
  should 
  have 
  regarded 
  it 
  as 
  

   one 
  of 
  the 
  sins 
  of 
  our 
  youth 
  — 
  due 
  to 
  the 
  influence 
  of 
  evil 
  

   associates 
  — 
  and 
  long 
  since 
  repented. 
  

  

  I 
  understand 
  that 
  the 
  true 
  relativity 
  theory 
  of 
  Kaufmann's 
  

   experiment 
  (which 
  seems 
  to 
  be 
  the 
  point 
  in 
  dispute) 
  runs 
  

   something 
  like 
  this: 
  — 
  Consider 
  an 
  electron 
  momentarily 
  at 
  

   rest, 
  but 
  continually 
  accelerated, 
  in 
  an 
  electric 
  field 
  of 
  force 
  

   E 
  and 
  a 
  magnetic 
  field 
  H 
  ; 
  then 
  the 
  acceleration 
  a 
  is 
  given 
  

   by 
  the 
  equation 
  

  

  E<? 
  = 
  ma, 
  

  

  where 
  e/m 
  is 
  a 
  certain 
  universal 
  constant 
  for 
  the 
  negative 
  

   electron 
  ; 
  we 
  need 
  not 
  inquire 
  into 
  its 
  nature. 
  This 
  equation 
  

   expresses 
  the 
  ordinary 
  definition 
  of 
  E. 
  Now 
  choose 
  new 
  

   axes 
  of 
  coordinates 
  with 
  respect 
  to 
  which 
  the 
  electron 
  has 
  

   an 
  instantaneous 
  velocity 
  w. 
  Referred 
  to 
  these 
  axes 
  the 
  

   electric 
  and 
  magnetic 
  forces 
  take 
  known 
  values 
  E', 
  H', 
  and 
  

   the 
  new 
  value 
  of 
  the 
  acceleration 
  «' 
  is 
  obtained 
  by 
  making 
  

   Lorentz's 
  transformation 
  of 
  the 
  coordinates 
  and. 
  the 
  time. 
  

   Accordingly 
  the 
  relativity-theory 
  predicts 
  that 
  an 
  electron 
  

   moving 
  with 
  velocity 
  w 
  in 
  an 
  electromagnetic 
  field 
  E', 
  H' 
  

   will 
  experience 
  this 
  acceleration 
  a! 
  . 
  Keeping 
  E' 
  and 
  H' 
  

   constant, 
  we 
  find 
  how 
  a 
  depends 
  on 
  w. 
  Kaufmann's 
  expe- 
  

   riment 
  — 
  or 
  rather 
  the 
  recent 
  repetitions 
  of 
  it 
  — 
  confirm 
  the 
  

   predicted 
  relation 
  with 
  considerable 
  accuracy. 
  Not 
  only 
  

   does 
  this 
  give 
  the 
  prestige 
  of 
  successful 
  prediction 
  to 
  the 
  

   relativity 
  theory, 
  but 
  it 
  confirms 
  that 
  part 
  of 
  the 
  hypothesis 
  

   most 
  in 
  doubt. 
  It 
  is 
  generally 
  admitted 
  that 
  the 
  Lorentz 
  

   transformation 
  holds 
  for 
  the 
  differential 
  equations 
  of 
  the 
  

   field; 
  the 
  question 
  is, 
  Does 
  it 
  hold 
  for 
  the 
  boundary 
  con- 
  

   ditions 
  (whatever 
  they 
  maybe) 
  at 
  the 
  surface 
  of 
  an 
  electron 
  ? 
  

   The 
  Kaufmnnn 
  experiment, 
  -dealing 
  with 
  a 
  single 
  isolated 
  

   electron, 
  answers 
  this 
  in 
  the 
  affirmative. 
  If 
  then 
  the 
  

   differential 
  equations 
  and 
  the 
  boundary 
  conditions 
  satisfy 
  

   the 
  transformation, 
  nothing 
  more 
  is 
  needed 
  to 
  establish 
  its 
  

   validity*. 
  It 
  should 
  be 
  noted 
  that 
  the 
  experiment 
  does 
  not 
  

  

  * 
  Experiments 
  are, 
  however, 
  still 
  needed 
  to 
  test 
  whether 
  the 
  Lorentz 
  

   transformation 
  covers 
  the 
  phenomena 
  of 
  quanta, 
  which 
  appear 
  to 
  involve 
  

   something 
  outside 
  the 
  ordinary 
  electromagnetic 
  theory. 
  The 
  exception 
  

   is 
  of 
  special 
  importance 
  because 
  it 
  includes 
  the 
  vibration 
  of 
  an 
  atom, 
  which 
  

   is 
  the 
  simplest 
  form 
  of 
  a 
  natural 
  clock 
  that 
  could 
  be 
  used 
  for 
  measuring 
  

   the 
  time 
  in 
  the 
  two 
  svstems. 
  

  

  