﻿and 
  the 
  Electromagnetic 
  Mass 
  of 
  the 
  Electron. 
  427 
  

  

  Now 
  the 
  ratio 
  of 
  the 
  areas 
  of 
  a 
  given 
  portion 
  of 
  the 
  plate 
  

   as 
  seen 
  by 
  an 
  observer 
  at 
  rest 
  relative 
  to 
  them 
  and 
  to 
  the 
  

   electron 
  respectively, 
  is 
  sec 
  a, 
  : 
  sec 
  a', 
  go 
  that 
  if 
  a 
  is 
  the 
  true 
  

   density 
  of 
  the 
  electricity 
  on 
  the 
  plate, 
  the 
  apparent 
  density 
  

   to 
  an 
  observer 
  moving 
  with 
  the 
  electron 
  is 
  

  

  \A-£ 
  

  

  COS 
  a 
  

  

  V 
  

  

  and 
  En 
  = 
  4:7rcrv 
  2 
  . 
  

  

  Hence 
  the 
  electric 
  intensity 
  obtained 
  above 
  is 
  made 
  irp 
  of 
  

   two 
  components 
  

  

  ±ttg 
  ] 
  v 
  2 
  ' 
  —COS 
  a! 
  

  

  , 
  \.ttg 
  1 
  v 
  2 
  

  

  and 
  

  

  ( 
  1— 
  ^cos 
  2 
  «') 
  (1 
  - 
  2 
  cos 
  2 
  a 
  f 
  ) 
  

  

  in 
  the 
  directions 
  of 
  u 
  and 
  the 
  normal 
  to 
  the 
  plate 
  respectively 
  

   to 
  an 
  observer 
  moving 
  with 
  the 
  electron 
  ; 
  and 
  this 
  agrees 
  

   exactly 
  with 
  expression 
  (8) 
  for 
  the 
  force 
  on 
  the 
  electron. 
  

  

  With 
  regard 
  to 
  the 
  eA'aluation 
  of 
  the 
  mass 
  of 
  the 
  electron, 
  

   I 
  must 
  admit 
  that 
  I 
  did 
  not 
  fully 
  understand 
  Dr. 
  Bucherer\s 
  

   process, 
  but 
  I 
  cannot 
  rid 
  myself 
  of 
  the 
  feeling 
  that 
  he 
  

   has 
  somehow 
  supposed 
  the 
  electron 
  to 
  be 
  moving 
  and 
  at 
  rest 
  

   simultaneously 
  in 
  its 
  different 
  aspects 
  as 
  active 
  and 
  passive 
  

   respectively. 
  

  

  In 
  this 
  connexion 
  there 
  is 
  another 
  difficulty 
  that 
  appears, 
  

   if 
  the 
  transformation 
  of 
  space 
  and 
  time 
  measures 
  between 
  

   the 
  two 
  observers 
  be 
  neglected, 
  which 
  may 
  most 
  simply 
  be 
  

   illustrated 
  by 
  considering 
  the 
  case 
  of 
  two 
  electrons 
  which 
  at 
  

   a 
  certain 
  instant 
  have 
  the 
  same 
  velocity 
  u 
  through 
  the 
  sether. 
  

   Then, 
  since 
  the 
  relative 
  velocity 
  is 
  zero, 
  the 
  force 
  acting 
  on 
  

   either 
  will 
  according 
  to 
  Dr. 
  Bucherer's 
  principle 
  be 
  the 
  

  

  q 
  2 
  

   electrostatic 
  force 
  — 
  2 
  in 
  the 
  direction 
  of 
  the 
  line 
  joining 
  the 
  

  

  electrons. 
  But 
  the 
  longitudinal 
  and 
  transverse 
  masses 
  being 
  

   different, 
  the 
  acceleration 
  of 
  the 
  electron 
  will 
  not 
  in 
  general 
  

   be 
  in 
  the 
  direction 
  of 
  the 
  force, 
  so 
  that 
  instead 
  of 
  the 
  relative 
  

   motion 
  of 
  the 
  electrons 
  due 
  to 
  their 
  mutual 
  action 
  being 
  in 
  

   the 
  line 
  joining 
  them, 
  this 
  line 
  will 
  begin 
  to 
  rotate 
  ; 
  in 
  fact, 
  

   it 
  will 
  tend 
  to 
  set 
  itself 
  at 
  right 
  angles 
  to 
  the 
  direction 
  ol 
  

  

  