﻿182 
  On 
  the 
  Connexion 
  between 
  Cathode 
  and 
  Rontgen 
  Rays. 
  

  

  which 
  the 
  particle 
  was 
  originally 
  moving. 
  It 
  is 
  these 
  pulses 
  

   which 
  I 
  believe 
  constitute 
  the 
  Rontgen 
  rays. 
  As 
  they 
  con- 
  

   sist 
  of 
  electric 
  and 
  magnetic 
  disturbances, 
  they 
  might 
  be 
  

   expected 
  to 
  produce 
  some 
  effects 
  analogous 
  to 
  those 
  of 
  light. 
  

   If 
  they 
  were 
  so 
  thin 
  that 
  the 
  time 
  taken 
  by 
  them 
  to 
  pass 
  over 
  

   a 
  molecule 
  of 
  a 
  substance 
  were 
  small 
  compared 
  with 
  the 
  time 
  

   of 
  vibration 
  of 
  the 
  molecule, 
  there 
  would 
  be 
  no 
  refraction, 
  

   and 
  the 
  thinness 
  of 
  the 
  pulse 
  would 
  also 
  account 
  for 
  the 
  

   absence 
  of 
  diffraction. 
  

  

  In 
  the 
  preceding 
  investigation 
  we 
  have 
  supposed 
  that 
  the 
  

   stoppage 
  of 
  the 
  particle 
  is 
  instantaneous 
  ; 
  if 
  the 
  impact 
  lasts 
  

   for 
  a 
  finite 
  time 
  T 
  the 
  negative 
  pulse 
  will 
  be 
  broadened 
  out, 
  so 
  

   that 
  its 
  thickness, 
  instead 
  of 
  being 
  2a, 
  will 
  be 
  2a 
  + 
  VT, 
  where 
  

   V 
  is 
  the 
  velocity 
  of 
  light. 
  The 
  intensity 
  of 
  the 
  magnetic 
  

   force 
  in 
  the 
  pulse 
  will 
  vary 
  inversely 
  as 
  the 
  thickness 
  of 
  the 
  

   pulse, 
  so 
  that 
  when 
  the 
  collision 
  lasts 
  for 
  the 
  time 
  T, 
  the 
  

   magnetic 
  force 
  in 
  the 
  negative 
  pulse 
  will 
  be 
  2a/(2a 
  + 
  VT) 
  of 
  

   the 
  value 
  given 
  above. 
  The 
  more 
  sudden 
  the 
  collision, 
  the 
  

   thinner 
  the 
  pulse 
  and 
  the 
  greater 
  the 
  magnetic 
  force 
  and 
  the 
  

   energy 
  in 
  the 
  pulse 
  ; 
  the 
  pulse 
  will, 
  however, 
  possess 
  the 
  pro- 
  

   perties 
  of 
  the 
  Rontgen 
  rays 
  until 
  T 
  is 
  comparable 
  to 
  one 
  of 
  

   the 
  times 
  of 
  vibration 
  of 
  a 
  substance 
  through 
  which 
  it 
  has 
  to 
  

   pass. 
  In 
  the 
  case 
  of 
  the 
  cathode 
  rays 
  all 
  the 
  circumstances 
  

   seem 
  favourable 
  to 
  a 
  very 
  sudden 
  collision, 
  as 
  the 
  mass 
  of 
  the 
  

   moving 
  particles 
  is 
  very 
  small 
  and 
  their 
  velocity 
  exceedingly 
  

   great. 
  In 
  some 
  experiments 
  which 
  I 
  described 
  in 
  the 
  Philo- 
  

   sophical 
  Magazine 
  for 
  Oct. 
  1897 
  on 
  cathode 
  rays, 
  the 
  velocity 
  

   of 
  the 
  negative 
  particles 
  was 
  about 
  one 
  third 
  of 
  that 
  of 
  light, 
  

   and 
  in 
  some 
  more 
  recent 
  experiments 
  made 
  on 
  the 
  Lenard 
  rays, 
  

   with 
  the 
  apparatus 
  described 
  by 
  Des 
  Coudres, 
  considerably 
  

   higher 
  velocities 
  were 
  found. 
  A 
  change 
  in 
  the 
  time 
  of 
  the 
  

   collision 
  will 
  alter 
  the 
  thickness 
  of 
  the 
  pulse 
  and 
  so 
  change 
  

   the 
  nature 
  of 
  the 
  ray. 
  

  

  If 
  we 
  suppose 
  that 
  part 
  of 
  the 
  absorption 
  of 
  the 
  rays 
  is 
  due 
  

   to 
  the 
  communication 
  of 
  energy 
  to 
  charged 
  ions 
  in 
  their 
  path, 
  

   we 
  find 
  that 
  the 
  thicker 
  the 
  pulse 
  the 
  greater 
  the 
  absorption. 
  

   For 
  suppose 
  that 
  E 
  is 
  the 
  electric 
  intensity 
  in 
  the 
  pulse, 
  m 
  the 
  

   mass, 
  and 
  e 
  the 
  charge 
  on 
  an 
  ion 
  ; 
  then 
  if 
  u 
  is 
  the 
  velocity 
  

   communicated 
  to 
  the 
  ion 
  when 
  the 
  pulse 
  passes 
  over 
  it, 
  t 
  the 
  

   time 
  taken 
  by 
  the 
  pulse 
  to 
  pass 
  over 
  it, 
  

  

  mu 
  = 
  J$e 
  . 
  t, 
  

   or 
  if 
  d 
  is 
  the 
  thickness 
  of 
  the 
  pulse 
  

  

  ™ 
  d 
  

  

  mu 
  = 
  Hie 
  . 
  ^ 
  ; 
  

  

  