﻿228 
  Wellisch 
  and 
  Woodrow 
  — 
  Columnar 
  Ionization. 
  

  

  produce 
  0-112 
  X 
  164,000 
  = 
  18,368 
  pairs 
  of 
  ions 
  in 
  the 
  ioniza- 
  

   tion 
  vessel 
  employed 
  in 
  the 
  experiments 
  described 
  above, 
  where 
  

   the 
  polonium 
  was 
  2 
  - 
  6 
  cm 
  from 
  the 
  center 
  of 
  the 
  vessel. 
  Let 
  S 
  

   be 
  the 
  cross-sectional 
  area 
  of 
  a 
  column 
  ; 
  then 
  assuming 
  uniform 
  

   ionization 
  within 
  the 
  column 
  the 
  total 
  charge 
  liberated 
  by 
  a 
  

   single 
  alpha 
  particle 
  in 
  the 
  region 
  considered 
  is 
  

  

  3 
  00 
  27*4 
  

  

  ^-SQ 
  = 
  — 
  S 
  = 
  18368 
  X 
  4-65 
  X 
  10" 
  10 
  , 
  

  

  whence 
  

  

  S 
  = 
  8-10 
  X 
  10- 
  6cm2 
  

  

  and 
  the 
  radius 
  of 
  the 
  cross-section 
  becomes 
  

  

  B, 
  = 
  0-0016 
  cm 
  . 
  

  

  In 
  the 
  application 
  of 
  the 
  theory 
  to 
  C0 
  2 
  , 
  as 
  the 
  saturation 
  

   current 
  could 
  not 
  be 
  obtained 
  experimentally, 
  recourse 
  was 
  had 
  

   to 
  the 
  method 
  described 
  by 
  Langevin* 
  in 
  his 
  original 
  paper. 
  

   The 
  ionization 
  curve 
  for 
  C0 
  2 
  was 
  drawn 
  with 
  electric 
  field 
  as 
  

   abscissae 
  and 
  current 
  as 
  ordinates 
  : 
  the 
  curve 
  was 
  then 
  pro- 
  

   duced 
  to 
  intersect 
  the 
  axis 
  of 
  ordinates. 
  The 
  straight 
  line 
  

   through 
  this 
  point 
  parallel 
  to 
  the 
  X-axis 
  was 
  taken 
  as 
  the 
  new 
  

   axis 
  and 
  the 
  method 
  of 
  Langevin 
  for 
  finding 
  e 
  was 
  then 
  applied. 
  

  

  A 
  large 
  curve 
  given 
  by 
  the 
  equation 
  y 
  = 
  — 
  log 
  (1 
  + 
  x) 
  

  

  X 
  

  

  was 
  plotted 
  with 
  log 
  (x) 
  as 
  abscissae 
  and 
  log 
  (y) 
  as 
  ordinates. 
  

   The 
  value 
  of 
  the 
  current 
  (measured 
  from 
  the 
  new 
  axis) 
  for 
  an 
  

   electric 
  field 
  of 
  1,575 
  volts 
  per 
  cm. 
  was 
  taken 
  as 
  Q' 
  and 
  then 
  

   from 
  different 
  values 
  of 
  log 
  (Q 
  7 
  /Q) 
  corresponding 
  to 
  values 
  of 
  

   log 
  (XyX) 
  = 
  log 
  {a' 
  /a\ 
  log 
  (x) 
  and 
  log 
  (y) 
  could 
  be 
  read 
  off 
  

   on 
  this 
  curve. 
  The 
  determinations 
  thus 
  made 
  of 
  e 
  from 
  the 
  

  

  equation 
  e 
  = 
  xy 
  ^ 
  (in 
  arbitrary 
  units), 
  for 
  different 
  values 
  of 
  X 
  

  

  are 
  given 
  in 
  Table 
  IX. 
  From 
  this 
  mean 
  value 
  of 
  e 
  = 
  2,032, 
  it 
  

  

  the 
  

  

  was 
  possible 
  to 
  determine 
  by 
  

   value 
  of 
  the 
  saturation 
  current. 
  

  

  the 
  use 
  of 
  equation 
  (1) 
  

   The 
  value 
  given 
  in 
  Table 
  IX 
  

  

  Table 
  IX. 
  

  

  X 
  

  

  200 
  

  

  400 
  

  

  600 
  

  

  800 
  

  

  1000 
  

  

  00 
  

  

  Q 
  

  

  0-181 
  

  

  0-260 
  

  

  0-301 
  

  

  0-331 
  

  

  0356 
  

  

  0-525 
  

  

  € 
  

  

  2030 
  

  

  1930 
  

  

  2050 
  

  

  1960 
  

  

  2190 
  

  

  

  for 
  X 
  = 
  co 
  was 
  obtained 
  in 
  this 
  way 
  ; 
  and 
  this 
  value 
  was 
  

   employed 
  in 
  plotting 
  the 
  curve 
  C, 
  fig. 
  5, 
  which 
  is 
  seen 
  to 
  inter- 
  

   sect 
  the 
  axis 
  of 
  ordinates 
  at 
  the 
  point 
  corresponding 
  to 
  the 
  

   fraction 
  0*41. 
  

   * 
  Langevin, 
  Ann. 
  Chim. 
  Phys. 
  (7), 
  xxviii, 
  p. 
  458, 
  1903. 
  

  

  