﻿produced 
  in 
  Air 
  by 
  the 
  Motion 
  of 
  Negative 
  Ions, 
  221 
  

  

  quantities 
  so 
  long 
  as 
  R 
  is 
  small. 
  But 
  as 
  the 
  multiplying 
  

   space 
  is 
  expanded 
  on 
  diminishing 
  the 
  pressure, 
  the 
  limits 
  

   assigned 
  by 
  the 
  method 
  to 
  the 
  positive 
  current 
  far 
  exceed 
  its 
  

   actual 
  value. 
  

  

  12. 
  There 
  is, 
  however, 
  another 
  simple 
  test 
  which 
  may 
  be 
  

   mentioned, 
  and 
  which 
  serves 
  to 
  define 
  the 
  voltage 
  o£ 
  the 
  

   outer 
  cylinder 
  for 
  which 
  the 
  negative 
  current 
  just 
  begins 
  

   perceptibly 
  to 
  increase 
  owing 
  to 
  the 
  ionizing 
  effects 
  of 
  

   collisions. 
  

  

  Referring 
  to 
  the 
  curve 
  for 
  air 
  (Phil. 
  Mag. 
  Feb. 
  1901, 
  

   p. 
  213) 
  connecting 
  a 
  Y 
  with 
  X 
  1? 
  it 
  is 
  easy 
  to 
  show 
  that 
  from 
  

   Xj 
  = 
  440 
  and 
  onwards 
  the 
  equation 
  

  

  _440 
  

  

  a 
  { 
  = 
  20e 
  *F 
  (5) 
  

  

  represents 
  the 
  curve 
  with 
  accuracy. 
  It 
  is 
  necessary, 
  before 
  

   proceeding, 
  to 
  give 
  a 
  physical 
  interpretation 
  of 
  this 
  equation. 
  

   Out 
  -of 
  n 
  free 
  paths 
  which 
  a 
  molecule 
  of 
  gas 
  traverses 
  

  

  exceed 
  m 
  times 
  the 
  mean 
  path. 
  Now 
  if 
  one 
  supposes 
  that 
  

   every 
  ion 
  starts 
  from 
  rest 
  and 
  that 
  every 
  ion 
  which 
  has 
  fallen 
  

   through 
  more 
  than 
  U 
  volts 
  after 
  its 
  previous 
  collision 
  has 
  

   sufficient 
  velocity 
  to 
  produce 
  another 
  pair 
  of 
  ions 
  by 
  its 
  impact, 
  

   then 
  every 
  ionizing 
  impact 
  must 
  terminate 
  a 
  path 
  greater 
  than 
  

  

  ^ 
  , 
  where 
  X 
  is 
  the 
  force 
  in 
  the 
  neighbourhood 
  of 
  the 
  

   X 
  7 
  e 
  

  

  collision. 
  Let 
  L 
  be 
  the 
  mean 
  free 
  path 
  of 
  a 
  negative 
  ion 
  

   for 
  a 
  pressure 
  of 
  1 
  mm. 
  Then 
  — 
  is 
  its 
  mean 
  path 
  for 
  the 
  

   pressure 
  p 
  millimetres. 
  Therefore 
  in 
  traversing 
  a 
  centimetre 
  

  

  it 
  makes 
  t 
  collisions 
  and 
  of 
  these 
  

   Li 
  

  

  -E 
  / 
  L 
  

  

  will 
  be 
  ionizing 
  collisions. 
  

  

  Now 
  if 
  L 
  = 
  2 
  1 
  -o 
  cm., 
  the 
  previous 
  equation 
  becomes 
  

  

  _20U 
  

  

  20 
  pe 
  Xi 
  where 
  Xj 
  = 
  X/^. 
  

   The 
  statistical 
  meaning 
  of 
  the 
  equation 
  (o) 
  

  

  _ 
  440 
  

  

  a^ZQe 
  x, 
  

   is 
  therefore 
  this 
  : 
  when 
  Xi 
  exceeds 
  440, 
  L 
  e. 
  when 
  X 
  exceeds 
  

  

  