﻿between 
  Cathode 
  and 
  Rontgen 
  Rays. 
  173 
  

  

  plane 
  through 
  the 
  centre 
  of 
  the 
  particle 
  at 
  right 
  angles 
  to 
  its 
  

   direction 
  of 
  motion 
  ; 
  this 
  tendency 
  increases 
  with 
  the 
  velocity 
  

   of 
  the 
  particle 
  until, 
  when 
  this 
  is 
  equal 
  to 
  the 
  velocity 
  of 
  light, 
  

   both 
  the 
  magnetic 
  force 
  and 
  the 
  electric 
  intensity 
  vanish 
  at 
  

   all 
  parts 
  of 
  the 
  field 
  except 
  the 
  equatorial 
  plane, 
  and 
  in 
  this 
  

   plane 
  they 
  are 
  infinite. 
  

  

  The 
  pulses 
  started 
  by 
  the 
  stopping 
  of 
  the 
  charged 
  particle 
  

   are, 
  as 
  might 
  be 
  expected, 
  different 
  when 
  the 
  ratio 
  of 
  the 
  

   velocity 
  of 
  the 
  particle 
  to 
  that 
  of 
  light 
  is 
  small, 
  and 
  when 
  it 
  

   is 
  nearly 
  unity. 
  But 
  even 
  when 
  the 
  velocity 
  is 
  small, 
  the 
  

   pulse 
  started 
  by 
  stopping 
  the 
  particle 
  carries 
  to 
  an 
  external 
  

   point 
  a 
  disturbance 
  in 
  which 
  the 
  magnetic 
  force 
  is 
  enormously 
  

   greater 
  than 
  it 
  was 
  at 
  the 
  same 
  point 
  before 
  the 
  particle 
  was 
  

   stopped. 
  The 
  time 
  the 
  pulse 
  takes 
  to 
  pass 
  over 
  a 
  point 
  P 
  is, 
  if 
  

   the 
  charged 
  particle 
  be 
  spherical, 
  equal 
  to 
  the 
  time 
  light 
  

   takes 
  to 
  pass 
  over 
  a 
  distance 
  equal 
  to 
  the 
  diameter 
  of 
  this 
  

   sphere 
  ; 
  the 
  thickness 
  of 
  this 
  pulse 
  is 
  excessively 
  small 
  com- 
  

   pared 
  with 
  the 
  wave-length 
  of 
  visible 
  light. 
  When 
  the 
  

   velocity 
  of 
  the 
  particle 
  approaches 
  that 
  of 
  fight 
  two 
  pulses 
  

   are 
  started 
  when 
  it 
  is 
  stopped. 
  One 
  of 
  these 
  is 
  a 
  thin 
  plane 
  

   sheet 
  whose 
  thickness 
  is 
  equal 
  to 
  the 
  diameter 
  of 
  the 
  charged 
  

   particle 
  ; 
  this 
  wave 
  is 
  propagated 
  in 
  the 
  direction 
  in 
  which 
  

   the 
  particle 
  was 
  moving 
  ; 
  there 
  is 
  no 
  corresponding 
  wave 
  

   propagated 
  backwards 
  : 
  the 
  other 
  is 
  a 
  spherical 
  pulse 
  spreading 
  

   outwards 
  in 
  all 
  directions, 
  whose 
  thickness 
  is 
  again 
  equal 
  to 
  

   the 
  diameter 
  of 
  the 
  charged 
  particle, 
  and 
  thus, 
  if 
  this 
  particle 
  

   is 
  of 
  molecular 
  dimensions, 
  or 
  perhaps 
  even 
  smaller, 
  very 
  

   small 
  compared 
  with 
  the 
  wave-length 
  of 
  ordinary 
  light. 
  The 
  

   theory 
  1 
  wish 
  to 
  put 
  forward 
  is 
  that 
  the 
  Rontgen 
  rays 
  are 
  

   these 
  thin 
  pulses 
  of 
  electric 
  and 
  magnetic 
  disturbance 
  which 
  

   are 
  started 
  when 
  the 
  small 
  negatively 
  charged 
  particles 
  which 
  

   constitute 
  the 
  cathode 
  rays 
  are 
  stopped. 
  

  

  We 
  shall 
  now 
  proceed 
  to 
  calculate 
  the 
  disturbance 
  propa- 
  

   gated 
  through 
  the 
  dielectric 
  when 
  a 
  charged 
  particle 
  is 
  

   suddenly 
  stopped. 
  

  

  The 
  components 
  of 
  the 
  magnetic 
  force 
  and 
  the 
  electric 
  

   intensity 
  all 
  satisfy 
  Poisson's 
  equation 
  

  

  dt* 
  \dx* 
  dy* 
  T 
  dz 
  2 
  J 
  ' 
  

  

  the 
  solution 
  of 
  this 
  equation 
  was 
  shown 
  by 
  Poisson 
  to 
  be 
  

  

  where 
  <f> 
  is 
  the 
  value 
  of 
  the 
  function 
  at 
  a 
  point 
  P 
  at 
  the 
  

   time 
  t 
  ; 
  &>! 
  the 
  mean 
  value 
  of 
  <£ 
  when 
  £ 
  = 
  over 
  the 
  surface 
  

   Phil. 
  Mag. 
  S. 
  5. 
  Vol. 
  45. 
  No. 
  273. 
  Feb. 
  1898. 
  

  

  