﻿and 
  the 
  Electromagnetic 
  Mass 
  of 
  the 
  Electron. 
  425 
  

  

  in 
  the 
  aether 
  is 
  

  

  r 
  x 
  q 
  2 
  v 
  2 
  s 
  

  

  ''( 
  1 
  -?W 
  

  

  

  Similarly, 
  suppose 
  B 
  to 
  be 
  a 
  unit 
  magnetic 
  pole 
  instead 
  or! 
  

   an 
  electron 
  o£ 
  charge 
  q. 
  We 
  require 
  now 
  to 
  know 
  the 
  mag- 
  

   netic 
  intensity 
  at 
  B 
  to 
  an 
  observer 
  moving 
  with 
  it. 
  Starting 
  

   from 
  the 
  electrostatic 
  force 
  due 
  to 
  A 
  as 
  before, 
  the 
  Lorentz- 
  

   Einstein 
  expression 
  for 
  the 
  magnetic 
  intensity 
  referred 
  to 
  

   axes 
  mo 
  vino- 
  with 
  B 
  is 
  

  

  % 
  w 
  (o,,W) 
  

  

  /3V(l-^sin 
  2 
  yJ 
  

  

  or 
  in 
  Dr. 
  Bucherer's 
  notation 
  

  

  72 
  (°> 
  Z 
  > 
  ~y): 
  

  

  qs 
  

  

  (l-5 
  sin 
  2 
  yj 
  

  

  Vwr 
  1? 
  

  

  which 
  is 
  his 
  expression 
  (3). 
  Similarly 
  expressions 
  (2) 
  and 
  

   (4) 
  may 
  be 
  derived. 
  

  

  Having 
  shown 
  that 
  these 
  expressions 
  may 
  be 
  obtained 
  by 
  

   means 
  of 
  the 
  Lorentz 
  transformation, 
  there 
  is 
  hardly 
  need 
  

   to 
  go 
  further 
  and 
  obtain 
  the 
  expressions 
  for 
  the 
  force 
  acting 
  

   on 
  an 
  electron 
  moving 
  in 
  a 
  uniform 
  magnetic 
  or 
  electric 
  field, 
  

   since 
  these 
  are 
  obtained 
  by 
  Dr. 
  Bucherer 
  by 
  integration 
  of 
  

   the 
  simpler 
  expressions. 
  But 
  as 
  a 
  further 
  verification 
  of 
  the 
  

   equivalence 
  of 
  the 
  two 
  principles 
  the 
  work 
  will 
  be 
  carried 
  out 
  

   for 
  the 
  case 
  of 
  the 
  electric 
  field, 
  which 
  gives 
  the 
  more 
  

   complicated 
  result. 
  

  

  Let 
  the 
  field 
  be 
  of 
  intensity 
  E 
  , 
  and 
  let 
  an 
  electron 
  of 
  charge 
  

   q 
  move 
  with 
  velocity 
  u 
  at 
  an 
  angle 
  a. 
  with 
  the 
  direction 
  of 
  

   E 
  as 
  seen 
  by 
  an 
  observer 
  at 
  rest 
  with 
  the 
  field. 
  Then 
  to 
  an 
  

   observer 
  moving 
  with 
  the 
  electron, 
  the 
  direction 
  of 
  the 
  normal 
  

   to 
  the 
  condenser 
  plates 
  will 
  be 
  slewed 
  round 
  to 
  an 
  angle 
  a! 
  

  

  a 
  2 
  

   with 
  the 
  direction 
  of 
  u 
  where 
  tan 
  a! 
  = 
  tan 
  ol\ 
  / 
  1 
  2 
  s0 
  ^ 
  na 
  ^ 
  

  

  sin 
  

  

  COS 
  « 
  i 
  • 
  / 
  

  

  : 
  - 
  and 
  sm 
  a 
  = 
  — 
  -= 
  

  

  

  