﻿420 
  Prof. 
  E. 
  B. 
  Wilson 
  on 
  the 
  

  

  This 
  principle 
  has 
  been 
  discussed 
  by 
  Lorentz 
  *, 
  by 
  

   Poincare 
  t 
  with 
  reference 
  to 
  the 
  theory 
  of 
  groups, 
  by 
  

   Einstein 
  J, 
  and 
  recently 
  in 
  this 
  Magazine 
  by 
  Cunningham 
  §, 
  

   and 
  by 
  Bucherer 
  ||, 
  who 
  lintroduces 
  a 
  new 
  principle 
  of 
  

   relativity. 
  It 
  is 
  not 
  my 
  desire 
  at 
  this 
  time 
  to 
  go 
  into 
  the 
  

   mathematics 
  of 
  a 
  question 
  which 
  has 
  been 
  discussed 
  at 
  such 
  

   length, 
  but 
  merely 
  to 
  point 
  out 
  a 
  few 
  general 
  observations 
  

   suggested, 
  especially 
  with 
  reference 
  to 
  Bucherer's 
  formula 
  (1), 
  

   and 
  then 
  to 
  show 
  the 
  application 
  of 
  those 
  remarks 
  to 
  any 
  such 
  

   theory 
  of 
  relativity. 
  

  

  With 
  a 
  slightly 
  modified 
  notation, 
  Bucherer's 
  formula 
  for 
  

   the 
  force 
  F 
  exerted 
  by 
  one 
  electron 
  upon 
  another 
  is 
  

  

  r 
  2 
  (l-£ 
  2 
  sin 
  2 
  #' 
  K 
  } 
  

  

  where 
  q 
  is 
  the 
  charge 
  of 
  the 
  electron, 
  v 
  is 
  the 
  velocity 
  of 
  

   light, 
  u 
  is 
  the 
  total 
  relative 
  velocity 
  of 
  the 
  two 
  electrons, 
  

   r 
  is 
  the 
  distance 
  between 
  them, 
  /3 
  is 
  the 
  ratio 
  u/v, 
  and 
  y 
  is 
  

   the 
  angle 
  between 
  the 
  direction 
  of 
  motion 
  and 
  the 
  line 
  

   joining 
  the 
  electrons. 
  In 
  the 
  figure 
  the 
  velocity 
  u 
  is 
  divided 
  

  

  into 
  two 
  equal 
  parts, 
  one-half 
  being 
  attributed 
  to 
  each 
  of 
  the 
  

   electrons 
  which 
  are 
  assumed 
  to 
  be 
  moving 
  (instantaneously) 
  

   in 
  parallel 
  lines 
  H. 
  The 
  electron 
  at 
  A 
  is 
  what 
  Bucherer 
  calls 
  

   the 
  active 
  electron 
  ; 
  that 
  at 
  P, 
  the 
  passive 
  one. 
  The 
  role 
  of 
  

   P 
  and 
  A 
  could 
  be 
  interchanged, 
  and 
  a 
  force 
  equal 
  and 
  

   opposite 
  to 
  F 
  would 
  then 
  act 
  on 
  A 
  from 
  P. 
  In 
  this 
  theory, 
  

   action 
  and 
  reaction 
  are 
  equal 
  and 
  opposite. 
  

  

  It 
  will 
  be 
  taken 
  for 
  granted 
  that 
  Kauf 
  mann 
  and, 
  for 
  that 
  

   matter, 
  innumerable 
  other 
  experimenters 
  have 
  observed 
  and 
  

  

  * 
  " 
  Electromagnetic 
  Phenomena 
  in 
  a 
  system 
  moving 
  with 
  any 
  velocity 
  

   smaller 
  than 
  that 
  of 
  Light, 
  " 
  Proceedings 
  of 
  the 
  Amsterdam 
  Academy, 
  

   1904. 
  

  

  t 
  " 
  Sur 
  la 
  dynamique 
  de 
  Telectron," 
  JRendiconti 
  del 
  Circolo 
  Matematico 
  

   di 
  Palermo, 
  vol. 
  xxi. 
  

  

  X 
  Annalen 
  der 
  Physik, 
  vol. 
  xvii. 
  

  

  § 
  October 
  1907. 
  " 
  j) 
  April 
  1907. 
  

  

  % 
  Of 
  course, 
  on 
  any 
  strict 
  conception 
  of 
  relativity 
  such 
  an 
  apportion- 
  

   ment 
  would 
  be 
  impossible 
  ; 
  but 
  relative 
  to 
  the 
  floor 
  and 
  walls 
  of 
  the 
  

   laboratory, 
  it 
  is 
  not 
  only 
  possible 
  but 
  highly 
  convenient. 
  

  

  