﻿422 
  On 
  the 
  Principle 
  of 
  Relativity. 
  

  

  will 
  again 
  be 
  attractive 
  when 
  the 
  particles 
  are 
  at 
  great 
  

   distances 
  relative 
  to 
  the 
  perpendicular 
  distance 
  between 
  

   their 
  paths. 
  But 
  here 
  the 
  denominator 
  of 
  F 
  has 
  the 
  

   form 
  a 
  

  

  r 
  2 
  [l 
  -(1-155 
  sin 
  7 
  ) 
  3 
  ] 
  2 
  ; 
  

  

  and 
  hence, 
  when 
  the 
  position 
  of 
  the 
  particles 
  is 
  such 
  that 
  

   7 
  is 
  nearly 
  60°, 
  the 
  attractive 
  force 
  becomes 
  enormous. 
  In 
  

   fact, 
  when 
  7 
  = 
  60° 
  and 
  sin 
  7 
  = 
  0*866, 
  the 
  force 
  is 
  infinite; 
  

   and 
  when 
  7 
  > 
  60°, 
  the 
  force 
  is 
  neither 
  attractive 
  nor 
  repulsive, 
  

   but 
  imaginary. 
  

  

  Without 
  going 
  into 
  the 
  question 
  of 
  the 
  inertia 
  of 
  the 
  

   particles, 
  it 
  would 
  be 
  impossible 
  to 
  state 
  what 
  would 
  be 
  their 
  

   final 
  configuration 
  if 
  they 
  were 
  started 
  in 
  such 
  a 
  position 
  

   that 
  7<60°; 
  however, 
  unless 
  the 
  inertia 
  became 
  infinite, 
  an 
  

   impact 
  at 
  an 
  angle 
  of 
  less 
  than 
  60° 
  appears 
  highly 
  probable. 
  

   It 
  is 
  conceivable 
  that 
  the 
  inertia 
  of 
  both 
  of 
  the 
  particles 
  

   would 
  be 
  infinite 
  when 
  their 
  relative 
  velocity 
  u 
  was 
  greater 
  

   than 
  v 
  • 
  in 
  which 
  case 
  the 
  impossibility 
  of 
  discharging 
  the 
  

   particles 
  in 
  the 
  manner 
  proposed 
  would 
  follow. 
  Bucherer, 
  

   however, 
  directly 
  asserts 
  (p. 
  419) 
  that 
  the 
  masses 
  are 
  the 
  

   same 
  as 
  those 
  derived 
  from 
  the 
  Maxwellian 
  theory. 
  What, 
  

   therefore, 
  the 
  result 
  of 
  an 
  attempt 
  to 
  start 
  the 
  particles 
  with 
  

   a 
  velocity 
  %u>0'57Sv 
  might 
  be 
  in 
  the 
  region 
  for 
  which 
  

   7 
  > 
  60° 
  and 
  the 
  force 
  is 
  imaginary, 
  is 
  difficult 
  to 
  conceive. 
  

  

  The 
  foregoing 
  observations 
  are 
  not 
  intended 
  specifically 
  as 
  

   an 
  objection 
  to 
  Bucherer's 
  theory. 
  It 
  is 
  quite 
  possible, 
  and 
  

   even 
  probable, 
  that 
  I 
  have 
  outraged 
  his 
  formula 
  and 
  mistaken 
  

   his 
  point 
  of 
  view, 
  as 
  he 
  asserts 
  in 
  the 
  current 
  (March) 
  number 
  

   of 
  this 
  Magazine 
  was 
  the 
  case 
  with 
  Cunningham. 
  I 
  should 
  

   not, 
  however, 
  merely 
  on 
  that 
  account 
  abandon 
  my 
  position; 
  

   for 
  it 
  seems 
  to 
  me 
  as 
  though, 
  now 
  that 
  very 
  swift 
  B 
  rays 
  are 
  

   a 
  common 
  subject 
  of 
  experiment, 
  the 
  question 
  of 
  relativity 
  

   has 
  an 
  aspect 
  somewhat 
  different 
  from 
  that 
  which 
  it 
  had 
  

   previously. 
  Either 
  we 
  can 
  or 
  we 
  cannot 
  obtain, 
  with 
  the 
  

   swift 
  /3 
  rays, 
  velocities 
  which, 
  measured 
  relatively, 
  are 
  

   greater 
  than 
  that 
  of 
  light. 
  If 
  we 
  cannot, 
  then 
  some 
  

   principle 
  of 
  relativity, 
  analogous 
  to 
  Bucherer's 
  new 
  prin- 
  

   ciple 
  by 
  which' 
  electrodynamics 
  is 
  based 
  wholly 
  on 
  the 
  

   relative 
  motion 
  of 
  the 
  electric 
  and 
  magnetic 
  masses 
  and 
  the 
  

   forces 
  between 
  systems 
  are 
  evaluated 
  by 
  summation 
  of 
  

   formulas 
  like 
  (1) 
  extended 
  over 
  the 
  masses 
  constituting 
  the 
  

   systems, 
  may 
  stand 
  ; 
  but 
  if 
  we 
  can, 
  then 
  it 
  appears 
  that, 
  

   unless 
  this 
  extreme 
  form 
  of 
  the 
  principle 
  of 
  relativity 
  is 
  

   abandoned, 
  at 
  any 
  rate 
  relative 
  to 
  swift 
  ft 
  rays, 
  there 
  must 
  

   ensue 
  a 
  veritable 
  tangle 
  of 
  results 
  fully 
  as 
  discordant 
  as 
  those 
  

   which 
  the 
  principle 
  hopes 
  to 
  avoid. 
  

  

  16 
  Lee 
  Street, 
  Cambridge 
  (Mass.). 
  

  

  