﻿Fundamental 
  Laws 
  of 
  Matter 
  and 
  Energy, 
  713 
  

  

  m/m 
  found 
  for 
  the 
  different 
  observed 
  values 
  of 
  /3 
  in 
  the 
  

   second 
  column. 
  The 
  third 
  column 
  shows 
  those 
  values 
  of 
  /5 
  

   which 
  would 
  correspond 
  with 
  the 
  same 
  values 
  of 
  m/m 
  

   according 
  to 
  equation 
  (15). 
  

  

  It 
  will 
  be 
  seen 
  that 
  the 
  observed 
  values 
  of 
  ft 
  follow 
  to 
  a 
  

   remarkable 
  degree 
  the 
  same 
  trend 
  as 
  those 
  which 
  are 
  calculated 
  

   by 
  equation 
  (15), 
  but 
  are 
  in 
  every 
  case 
  six 
  to 
  eight 
  per 
  cent, 
  

   higher*. 
  I 
  believe 
  that 
  these 
  differences 
  lie 
  within 
  the 
  limits 
  

   of 
  experimental 
  error 
  of 
  Kaufmann's 
  measurements. 
  It 
  is 
  

   true 
  that 
  he 
  claims 
  a 
  higher 
  degree 
  of 
  accuracy, 
  but, 
  not- 
  

   withstanding 
  the 
  extreme 
  care 
  and 
  delicacy 
  with 
  which 
  the 
  

   observations 
  were 
  made, 
  it 
  seems 
  almost 
  incredible 
  that 
  

   measurements 
  of 
  this 
  character, 
  which 
  consisted 
  in 
  the 
  

   determination 
  of 
  the 
  minute 
  displacement 
  of 
  a 
  somewhat 
  

   hazy 
  spot 
  on 
  a 
  photographic 
  plate, 
  could 
  have 
  been 
  determined 
  

   with 
  the 
  precision 
  claimed. 
  Moreover, 
  Planck 
  f 
  and 
  Stark 
  J 
  

   have 
  pointed 
  out 
  certain 
  corrections 
  which 
  probably 
  should 
  

   have 
  been 
  made 
  by 
  Kaufmann 
  and 
  which 
  would 
  produce 
  a 
  

   material 
  change 
  in 
  his 
  results 
  §. 
  

  

  That 
  a 
  charged 
  particle 
  must 
  possess 
  mass 
  in 
  virtue 
  of 
  its 
  

   charge, 
  and 
  that 
  this 
  mass 
  must 
  vary 
  with 
  the 
  velocity 
  of 
  the 
  

   particle, 
  was 
  shown 
  to 
  be 
  a 
  consequence 
  of 
  the 
  electro- 
  

   magnetic 
  theory 
  by 
  J. 
  J. 
  Thomson 
  and 
  by 
  Heaviside, 
  and 
  

   numerous 
  attempts 
  have 
  been 
  made 
  to 
  find 
  the 
  exact 
  expression 
  

   for 
  the 
  change 
  of 
  mass 
  with 
  the 
  velocity. 
  But 
  before 
  this 
  

   can 
  be 
  done 
  some 
  assumption 
  is 
  necessary 
  as 
  to 
  the 
  shape 
  of 
  

   the 
  particle 
  and 
  the 
  distribution 
  of 
  its 
  charge. 
  The 
  three 
  

   theories 
  of 
  the 
  simple 
  negative 
  particle 
  or 
  electron 
  which 
  are 
  

   now 
  most 
  discussed 
  are 
  due 
  to 
  Abraham, 
  Bucherer, 
  and 
  

   Lorentz 
  ||. 
  The 
  first 
  assumes 
  that 
  the 
  electron 
  is 
  and 
  remains 
  

   a 
  rigid 
  sphere, 
  the 
  second 
  assumes 
  an 
  electron 
  which 
  is 
  

   spherical 
  when 
  at 
  rest 
  but 
  which 
  in 
  motion 
  contracts 
  in 
  the 
  

   direction 
  of 
  its 
  translation 
  and 
  expands 
  laterally 
  so 
  as 
  to 
  keep 
  

   a 
  constant 
  volume. 
  The 
  third 
  assumes 
  an 
  electron 
  similar 
  

   to 
  the 
  second, 
  w 
  T 
  hich 
  contracts 
  in 
  the 
  direction 
  of 
  translation 
  

   but 
  which 
  does 
  not 
  change 
  its 
  other 
  dimensions. 
  On 
  the 
  

   basis 
  of 
  these 
  theories 
  and 
  from 
  known 
  electromagnetic 
  

   principles, 
  three 
  equations 
  have 
  been 
  obtained 
  for 
  the 
  value 
  

  

  * 
  The 
  constancy 
  of 
  the 
  difference 
  between 
  the 
  observed 
  and 
  calculated 
  

   values 
  of 
  /3 
  is 
  striking, 
  and 
  would 
  alone 
  indicate 
  some 
  constant 
  error 
  in 
  

   Kaufmann's 
  results. 
  

  

  t 
  Verhandlung 
  Deutsch. 
  Phys. 
  Ges. 
  ix. 
  p. 
  301 
  (1907). 
  

  

  X 
  Ibid. 
  x. 
  p. 
  14 
  (1908). 
  

  

  § 
  In 
  reply 
  to 
  Planck 
  see 
  Kaufmann, 
  ibid. 
  ix. 
  p. 
  667 
  (1907). 
  

  

  1 
  1 
  For 
  a 
  discussion 
  of 
  these 
  theories 
  see 
  Abraham, 
  Theorie 
  der 
  Eiek- 
  

   tricitat, 
  vol. 
  ii. 
  Leipzig, 
  1905 
  ; 
  and 
  Bucherer, 
  Mathematische 
  Einfiihruny 
  

   in 
  die 
  Elektrontheorie, 
  Leipzig, 
  1904. 
  

  

  