﻿J; 
  

  

  1012 
  Prof. 
  A. 
  W. 
  Conway 
  on 
  an 
  .Electromagnetic 
  

   sphere 
  they 
  are 
  continuous. 
  If 
  we 
  write 
  P 
  for 
  the 
  integral 
  

  

  I 
  ^ 
  7rp'flr' 
  4 
  dr' 
  

   and 
  Q 
  for 
  the 
  integral 
  

  

  \ 
  ~ 
  Trp'flr'dr', 
  

  

  *y 
  r 
  

  

  where 
  a 
  is 
  the 
  radius 
  of 
  the 
  sphere, 
  we 
  can 
  easily 
  obtain 
  

  

  for 
  points 
  inside 
  the 
  sphere, 
  and 
  thus 
  we 
  get 
  

   Zxz 
  

  

  «=i* 
  p. 
  

  

  /3 
  = 
  ^P. 
  

  

  7 
  = 
  

  

  gP 
  +2Q 
  _ 
  3(^+/) 
  R 
  

  

  If 
  an 
  electron 
  of 
  charge 
  — 
  e 
  can 
  move 
  about 
  in 
  this 
  sphere 
  

   subjected 
  only 
  to 
  the 
  electromagnetic 
  forces, 
  and 
  if 
  it 
  

   describes 
  a 
  circular 
  orbit 
  with 
  angular 
  velocity 
  co 
  so 
  that 
  its 
  

   components 
  of 
  velocity 
  are 
  ( 
  — 
  yco, 
  xco, 
  0) 
  it 
  experiences 
  a 
  

   mechanical 
  force 
  which 
  is 
  equal 
  to 
  the 
  vector 
  product 
  of 
  

   (eym, 
  — 
  exec, 
  0) 
  and 
  (a, 
  ft, 
  7), 
  and 
  thus 
  we 
  get 
  the 
  com- 
  

   ponents 
  

  

  (1) 
  -e<ox(2Y/r 
  z 
  + 
  2Q)+3eG>lr 
  b 
  (x*+y 
  2 
  )Fx 
  

  

  (2) 
  -^^(2P/r 
  3 
  + 
  2Q) 
  +3^/r 
  5 
  (^ 
  2 
  + 
  ?/ 
  2 
  )Py 
  

  

  (3) 
  3ecolr 
  b 
  (z 
  2 
  +f)Pz. 
  

  

  It 
  will 
  be 
  noticed 
  that 
  this 
  force 
  can 
  be 
  made 
  up 
  of 
  (a) 
  an 
  

   attractive 
  force 
  intersecting 
  the 
  ^-axis 
  and 
  at 
  right 
  angles 
  to 
  

   it, 
  and 
  (b) 
  a 
  repulsive 
  radial 
  force. 
  

  

  In 
  addition 
  to 
  these 
  forces 
  of 
  magnetic 
  origin 
  we 
  have 
  the 
  

   electrostatic 
  force. 
  This 
  is 
  simply 
  an 
  attractive 
  radial 
  force 
  

   the 
  components 
  of 
  which 
  are 
  

  

  -c 
  2 
  exRlr\ 
  - 
  c%R/r 
  3 
  , 
  -c 
  2 
  ezR/r*, 
  

  

  where 
  c 
  is 
  the 
  velocity 
  of 
  lioht 
  and 
  R 
  is 
  the 
  integral 
  

  

  j 
  

  

  

  

  