﻿176 
  Prof. 
  J. 
  J. 
  Thomson 
  on 
  a 
  Theory 
  of 
  the 
  Connexion 
  

  

  Hence 
  ©j, 
  the 
  mean 
  value 
  of 
  tvex/r 
  3 
  , 
  is 
  

  

  ew 
  £ 
  (OP 
  2 
  -a 
  2 
  ^V^ 
  2 
  ) 
  1 
  x 
  

   I 
  2Vt. 
  a 
  J 
  

  

  Thus 
  

  

  Hence 
  

  

  2 
  . 
  OPU 
  2Yt. 
  a 
  J 
  OP* 
  

  

  d 
  , 
  . 
  1 
  ew 
  ( 
  ^ 
  Vt 
  \ 
  x 
  

  

  ft 
  """2"0F\ 
  i+ 
  7 
  JOP' 
  

  

  1 
  ew 
  f 
  Vt\ 
  y 
  

   " 
  2 
  ~ 
  2"0FV 
  + 
  ^/OP' 
  

  

  from 
  t 
  = 
  (r—a)fV 
  to 
  t 
  = 
  (r 
  + 
  a)/Y. 
  If 
  the 
  sphere 
  is 
  small, 
  

   V^/a 
  is 
  large 
  compared 
  with 
  unity, 
  and 
  Yt 
  is 
  approximately 
  

   equal 
  to 
  OP 
  ; 
  hence 
  

  

  1 
  e 
  yw 
  

   " 
  2 
  ~ 
  2 
  a 
  UP 
  2 
  ' 
  

  

  ~ 
  1 
  e 
  xw 
  

  

  2 
  a 
  OP 
  2 
  ' 
  

  

  « 
  2 
  and 
  /3 
  2 
  are, 
  when 
  a 
  is 
  small, 
  very 
  large 
  compared 
  with 
  a 
  x 
  

   and 
  /?!. 
  

  

  We 
  have 
  now 
  the 
  complete 
  solution 
  of 
  the 
  problem, 
  and 
  

   we 
  see 
  that 
  after 
  the 
  sphere 
  is 
  stopped, 
  the 
  magnetic 
  force 
  at 
  

   a 
  point 
  P 
  remains 
  unaltered 
  until 
  t=(r 
  — 
  a)/V, 
  when 
  a 
  very 
  

   thin 
  pulse 
  of 
  intense 
  negative 
  magnetic 
  force 
  arrives, 
  the 
  

   intensity 
  of 
  the 
  field 
  being 
  ew 
  sin 
  6/2a 
  . 
  OP, 
  where 
  6 
  is 
  the 
  

   angle 
  between 
  OP 
  and 
  the 
  axis 
  of 
  z 
  ; 
  the 
  magnetic 
  force 
  pre- 
  

   viously 
  at 
  P 
  was 
  in 
  the 
  opposite 
  direction, 
  and 
  equal 
  to 
  

   ew 
  sin 
  6 
  '/OP 
  2 
  . 
  This 
  very 
  intense 
  pulse 
  only 
  lasts 
  for 
  a 
  very 
  

   short 
  time 
  ; 
  and 
  the 
  view 
  I 
  wish 
  to 
  put 
  forward 
  is 
  that 
  this 
  

   pulse 
  constitutes 
  one 
  kind 
  of 
  Rontgen 
  radiation. 
  The 
  reasons 
  

   for 
  this 
  view 
  will 
  be 
  given 
  after 
  we 
  have 
  considered 
  the 
  case 
  

   of 
  a 
  sphere 
  moving 
  with 
  the 
  velocity 
  of 
  light. 
  We 
  may, 
  

   however, 
  point 
  out 
  that 
  since 
  the 
  state 
  represented 
  by 
  a 
  1 
  ^ 
  1 
  

   lasts 
  for 
  the 
  time 
  r/V, 
  while 
  that 
  for 
  the 
  state 
  a 
  2j 
  /3 
  2 
  only 
  for 
  

   the 
  time 
  2a 
  j 
  V, 
  

  

  jjotdt 
  = 
  j/3dt=0. 
  

  

  This 
  must 
  evidently 
  be 
  the 
  case, 
  for 
  the 
  line 
  integral 
  of 
  the 
  

   magnetic 
  force 
  round 
  a 
  circuit 
  is 
  equal 
  to 
  irr 
  times 
  the 
  current 
  

   through 
  the 
  circuit 
  ; 
  in 
  this 
  case 
  the 
  currents 
  are 
  dielectric 
  

   currents, 
  and 
  equal 
  the 
  rate 
  of 
  increase 
  of 
  the 
  electric 
  dis- 
  

   placement 
  through 
  the 
  circuit, 
  so 
  that 
  the 
  time 
  integral 
  of 
  

  

  