﻿4:24 
  Mr. 
  E. 
  Cunningham 
  on 
  the 
  Principle 
  of 
  Relativity 
  

  

  me 
  to 
  carefully 
  compare 
  it 
  with 
  that 
  of 
  Lorentz. 
  May 
  I 
  say 
  

   that 
  I 
  should 
  scarcely 
  have 
  ventured 
  to 
  approach 
  the 
  subject 
  

   in 
  this 
  Magazine 
  if 
  I 
  had 
  not 
  already 
  done 
  so, 
  and 
  that 
  on 
  

   exactly 
  the 
  point 
  to 
  which 
  my 
  attention 
  is 
  again 
  called, 
  viz., 
  

   the 
  expression 
  given 
  for 
  the 
  forces 
  on 
  a 
  moving 
  electron. 
  

   An 
  inspection 
  of 
  these 
  instead 
  of 
  showing 
  the 
  impossibity 
  of 
  

   obtaining 
  them 
  by 
  the 
  Lorentz-Einstein 
  transformation, 
  

   shows 
  that 
  they 
  may 
  actually 
  be 
  derived 
  from 
  the 
  ordinary 
  

   Maxwellian 
  expressions 
  by 
  means 
  of 
  that 
  process. 
  It 
  may 
  

   perhaps 
  be 
  worth 
  while 
  carrying 
  out 
  the 
  calculation. 
  

  

  Consider 
  first 
  two 
  electrons, 
  A, 
  B 
  moving 
  relatively 
  to 
  

   each 
  other, 
  the 
  notation 
  being 
  that 
  of 
  Dr. 
  Bucherer's 
  paper. 
  

   Taking 
  the 
  axis 
  of 
  x 
  in 
  the 
  direction 
  of 
  the 
  velocity 
  of 
  B 
  

   relative 
  to 
  A, 
  let 
  the 
  coordinates 
  of 
  B 
  relative 
  to 
  A 
  at 
  a 
  

   certain 
  instant 
  be 
  x', 
  y', 
  z' 
  to 
  an 
  observer 
  moving 
  with 
  A. 
  

   Then 
  taking 
  A 
  to 
  be 
  at 
  rest 
  in 
  the 
  sether, 
  the 
  electric 
  intensity 
  

  

  2 
  

  

  at 
  B 
  due 
  to 
  it 
  has 
  components 
  "73- 
  (V, 
  y\ 
  z 
  1 
  ). 
  Now 
  apply 
  the 
  

  

  Lorentz-Einstein 
  transformation. 
  Then 
  at 
  the 
  same 
  instant 
  

   to 
  an 
  observer 
  moving 
  with 
  B 
  the 
  electric 
  intensity 
  is 
  

  

  ov 
  

  

  ~ 
  (a 
  j 
  , 
  j3y', 
  ftz'). 
  But 
  the 
  coordinates 
  of 
  B 
  relative 
  to 
  A 
  to 
  

  

  x 
  f 
  

   an 
  observer 
  moving 
  with 
  B 
  will 
  be 
  x 
  = 
  -~ 
  , 
  y, 
  z 
  ; 
  so 
  that 
  the 
  

  

  intensity 
  may 
  be 
  expressed 
  as 
  

  

  /3qv\ 
  , 
  , 
  Q 
  (. 
  iA~ 
  1/2 
  

  

  -fi- 
  O, 
  y, 
  z) 
  where 
  /3 
  = 
  I 
  1- 
  -^ 
  J 
  . 
  

  

  If 
  7 
  is 
  the 
  angle 
  between 
  the 
  line 
  AB 
  and 
  the 
  direction 
  of 
  

   u 
  as 
  seen 
  by 
  the 
  observer 
  moving 
  with 
  B, 
  sin 
  7 
  = 
  ^ 
  V 
  "+ 
  z 
  * 
  

   and 
  r*- 
  2 
  = 
  /3V 
  ( 
  1 
  - 
  ^ 
  sin 
  2 
  7 
  \ 
  

  

  Thus 
  finally 
  the 
  intensity 
  to 
  an 
  observer 
  moving 
  with 
  B 
  is 
  

   qv 
  2 
  (x, 
  y, 
  z) 
  

  

  

  /3V(l-| 
  2S 
  in' 
  7 
  ) 
  

  

  

  

  

  

  or 
  in 
  Dr. 
  

  

  Bucherer's 
  notation 
  

  

  Xiqv 
  2 
  s 
  

   / 
  u 
  2 
  \ 
  3/2 
  > 
  

  

  

  

  

  

  and 
  therefore 
  the 
  force 
  upon 
  the 
  electron 
  

  

  B 
  

  

  supposed 
  

  

  at 
  

  

  rest 
  

  

  