﻿c. 
  

  

  produced 
  in 
  Air 
  by 
  the 
  Motion 
  of 
  Negative 
  Ions. 
  219 
  

  

  to 
  the 
  inner 
  axis, 
  the 
  intensity 
  at 
  the 
  wire 
  being 
  fifty 
  

   times 
  the 
  intensity 
  at 
  points 
  where 
  r=5 
  mm. 
  Thus, 
  for 
  

   moderate 
  values 
  of 
  V 
  the 
  region 
  where 
  ions 
  are 
  generated 
  by 
  

   collisions 
  is 
  a 
  small 
  cylindrical 
  volume 
  inclosing 
  the 
  wire. 
  

   Let 
  the 
  radius 
  of 
  this 
  multiplying 
  space 
  be 
  R. 
  Let 
  I 
  

   negative 
  ions 
  entering 
  this 
  cylindrical 
  space 
  from 
  regions 
  

   external 
  to 
  it 
  be 
  increased 
  by 
  multiplication 
  to 
  xl 
  ions 
  when 
  

   the 
  wire 
  is 
  reached. 
  Those 
  ions 
  which 
  are 
  generated 
  by 
  the 
  

   Rb'ntgen 
  rays 
  within 
  the 
  cylinder 
  R 
  will 
  be 
  multiplied 
  by 
  the 
  

   process 
  of 
  collision 
  to 
  a 
  lesser 
  extent. 
  Therefore 
  the 
  whole 
  

   negative 
  current 
  will 
  be 
  

  

  = 
  x 
  \ 
  C 
  «-V^ 
  C 
  U 
  +y 
  ¥=oJ 
  Q 
  * 
  . 
  . 
  (1) 
  

  

  where 
  y 
  < 
  x. 
  

  

  When 
  the 
  force 
  is 
  reversed, 
  the 
  only 
  ions 
  which 
  undergo 
  

   multiplication 
  are 
  those 
  which 
  start 
  within 
  the 
  cylinder 
  R, 
  

   so 
  that 
  the 
  corresponding 
  positive 
  current 
  will 
  be 
  

  

  in 
  which 
  z 
  is 
  plainly 
  < 
  y. 
  

  

  Now, 
  since 
  x>y>z>l,it 
  follows 
  that 
  the 
  negative 
  current 
  

   always 
  exceeds 
  the 
  positive, 
  the 
  secondary 
  radiation 
  being 
  

   neglected. 
  And 
  if 
  R 
  2 
  is 
  small 
  compared 
  with 
  b 
  2 
  , 
  the 
  negative 
  

   current 
  will 
  be 
  about 
  # 
  times 
  the 
  positive. 
  

  

  10. 
  As 
  an 
  illustration 
  we 
  may 
  suppose 
  in 
  particular 
  that 
  

   R 
  is 
  1 
  mm., 
  L 
  e. 
  about 
  twice 
  the 
  mean 
  free 
  path 
  of 
  a 
  negative 
  

   ion 
  in 
  air 
  at 
  a 
  pressure 
  of 
  1 
  mm. 
  Let 
  the 
  cylinder 
  R 
  be 
  

   divided 
  into 
  two 
  parts 
  by 
  means 
  of 
  a 
  coaxial 
  cylinder 
  of 
  

   radius 
  J 
  R=*5 
  mm. 
  Then 
  if 
  100 
  ions 
  are 
  uniformly 
  dis- 
  

   tributed 
  within 
  the 
  cylinder 
  R, 
  25 
  will 
  q. 
  p. 
  fall 
  within 
  the 
  

   inner 
  cylinder 
  R/2, 
  and 
  75 
  between 
  the 
  two 
  cylinders. 
  

   Further, 
  let 
  it 
  be 
  supposed 
  that 
  every 
  ion 
  executes 
  its 
  mean 
  

   path 
  R/2, 
  and 
  at 
  the 
  end 
  of 
  it 
  generates 
  another 
  negative 
  

   ion 
  by 
  collision. 
  Then, 
  when 
  the 
  negative 
  ions 
  are 
  driven 
  to 
  

   the 
  wire, 
  the 
  original 
  100 
  will 
  be 
  increased 
  to 
  25 
  -H 
  2 
  x 
  75 
  on 
  

   reaching 
  it. 
  Therefore 
  ?/ 
  = 
  l 
  # 
  75. 
  Now 
  let 
  the 
  force 
  be 
  re- 
  

   versed. 
  Then 
  the 
  same 
  100 
  ions 
  will 
  produce 
  a 
  total 
  flux 
  of 
  

   2 
  x 
  25 
  + 
  75 
  ions 
  across 
  the 
  cylinder 
  R. 
  Therefore 
  2 
  = 
  1*25. 
  

  

  Thus 
  y 
  = 
  l-±xz. 
  

  

  11. 
  To 
  apply 
  these 
  results 
  to 
  the 
  tables 
  above, 
  it 
  is 
  to 
  be 
  

   observed 
  that 
  a/p 
  is 
  negligible 
  unless 
  

  

  - 
  >30 
  (Curve, 
  Phil. 
  Mag. 
  Feb. 
  1901, 
  p. 
  212), 
  

  

  and 
  that 
  then 
  it 
  is 
  at 
  first 
  extremely 
  small. 
  

  

  