﻿Principle 
  of 
  Relativity. 
  421 
  

  

  measured 
  swiftly-moving 
  ft 
  rajs 
  — 
  that 
  is 
  to 
  say, 
  electrons 
  

   moving 
  with 
  velocities 
  well 
  up 
  to 
  within 
  a 
  few 
  per 
  cent, 
  of 
  

   the 
  velocity 
  of 
  light, 
  or 
  at 
  any 
  rate 
  much 
  in 
  excess 
  of 
  half 
  

   that 
  velocity. 
  Suppose, 
  now, 
  that 
  two 
  sources 
  of 
  ft 
  rays 
  

   were 
  set 
  functioning 
  in 
  such 
  a 
  manner 
  as 
  to 
  discharge 
  the 
  

   rays 
  directly 
  towards 
  each 
  other 
  along 
  a 
  right 
  line. 
  The 
  

   distance 
  between 
  the 
  sources 
  is 
  quite 
  immaterial 
  so 
  long 
  

   as 
  the 
  ft 
  particles 
  mav 
  be 
  considered 
  as 
  subject 
  solely 
  to 
  

   their 
  mutual 
  action 
  without 
  disturbance 
  from 
  other 
  in- 
  

   fluences. 
  With 
  this 
  arrangement, 
  7 
  = 
  0. 
  If, 
  for 
  simplicity, 
  

   it 
  be 
  imagined 
  that 
  only 
  one 
  ft 
  particle 
  leaves 
  each 
  source, 
  

   the 
  two 
  particles 
  will 
  move 
  toward 
  each 
  other 
  along 
  the 
  line 
  

   joining 
  them, 
  and 
  the 
  force 
  becomes 
  merely 
  

  

  r 
  2 
  ' 
  

  

  If 
  the 
  rays 
  are 
  not 
  too 
  swift, 
  that 
  is, 
  if 
  their 
  velocity 
  

   relative 
  to 
  the 
  experimenter 
  is 
  under 
  half 
  that 
  of 
  light, 
  

   the 
  total 
  relative 
  velocity 
  is 
  less 
  than 
  v 
  and 
  the 
  force 
  F 
  

   is 
  negative 
  — 
  a 
  repulsion, 
  as 
  is 
  usual 
  with 
  negative 
  charges. 
  

   If, 
  however, 
  each 
  particle 
  has 
  the 
  velocity 
  \v, 
  their 
  relative 
  

   velocity 
  is 
  equal 
  to 
  v 
  and 
  the 
  force 
  F 
  vanishes 
  at 
  all 
  distances. 
  

   Inasmuch 
  as 
  the 
  electron, 
  on 
  any 
  theory, 
  is 
  generally 
  supposed 
  

   to 
  travel 
  with 
  a 
  uniform 
  velocity 
  unless 
  interfered 
  with, 
  it 
  

   would 
  appear 
  that 
  in 
  this 
  case 
  a 
  collision 
  were 
  imminent. 
  

   If, 
  on 
  the 
  other 
  hand, 
  the 
  rays 
  were 
  distinctly 
  swift, 
  their 
  

   relative 
  velocity 
  would 
  considerably 
  exceed 
  that 
  of 
  light 
  

   and, 
  indeed, 
  might 
  approach 
  2v. 
  In 
  this 
  case 
  the 
  force 
  

   would 
  actually 
  be 
  attractive 
  and 
  an 
  impact 
  would 
  appear 
  

   even 
  more 
  sure. 
  

  

  If, 
  then, 
  the 
  formula 
  (1) 
  has 
  been 
  correctly 
  interpreted, 
  

   one 
  of 
  two 
  consequences 
  would 
  appear 
  to 
  follow 
  7 
  . 
  Either 
  

   two 
  ft 
  particles 
  cannot 
  be 
  discharged 
  directly 
  toward 
  each 
  other 
  

   with 
  an 
  arbitrary 
  initial 
  distance 
  between 
  them 
  and 
  each 
  icith 
  

   a 
  velocity 
  greater 
  than 
  half 
  that 
  of 
  light 
  ; 
  or 
  two 
  particles 
  so 
  

   discharged 
  icould 
  attract 
  instead 
  of 
  repel. 
  

  

  In 
  practice, 
  it 
  w 
  7 
  ould 
  be 
  impossible 
  to 
  discharge 
  merely 
  

   two 
  particles, 
  and 
  we 
  should 
  have 
  to 
  consider 
  the 
  action 
  

   of 
  pencils 
  of 
  ft 
  rays. 
  It 
  does 
  not 
  seem, 
  how 
  r 
  ever, 
  as 
  if 
  the 
  

   main 
  conclusions 
  could 
  be 
  qualitatively 
  upset, 
  especially 
  if 
  

   the 
  force 
  on 
  an 
  electron 
  is 
  to 
  be 
  evaluated 
  by 
  summation 
  

   over 
  the 
  individual 
  particles 
  acting. 
  In 
  this 
  case 
  of 
  pencils 
  of 
  

   rays, 
  there 
  would 
  be 
  another 
  interesting 
  inference 
  from 
  (1). 
  

   Consider, 
  for 
  example, 
  two 
  particles 
  moving 
  in 
  opposite 
  

   directions 
  along 
  parallel 
  lines. 
  Let 
  the 
  initial 
  velocity 
  of 
  

   each 
  particle 
  be 
  greater 
  than 
  \o 
  y 
  and 
  for 
  convenience 
  it 
  may 
  

   be 
  assumed 
  that 
  -^ 
  = 
  0*578 
  r. 
  Then 
  the 
  force 
  F 
  in 
  (1) 
  

  

  