﻿tlie 
  Ions 
  of 
  Gases. 
  361 
  

  

  We 
  have 
  already 
  seen 
  that 
  the 
  experiments 
  of 
  Barns 
  by 
  the 
  

   entirely 
  independent 
  condensation 
  method 
  yield 
  6 
  and 
  4*5 
  

   for 
  10'^ 
  X 
  2A/3, 
  so 
  that 
  the 
  mean 
  value 
  of 
  A 
  is 
  0-0000787, 
  

   with 
  which 
  the 
  result 
  obtained 
  from 
  Townsend^s 
  work 
  is 
  in 
  

   excellent 
  agreement. 
  With 
  the 
  N- 
  formula 
  Barus 
  found 
  

   that 
  in 
  his 
  experiments 
  ol 
  ranged 
  from 
  3 
  to 
  10 
  times 
  that 
  

   given 
  by 
  Townsend's 
  and 
  similar 
  experiments. 
  McClung 
  

   and 
  Lano;evin 
  found 
  values 
  for 
  a 
  in 
  air 
  in 
  close 
  aoreement 
  

   with 
  that 
  of 
  Townsend, 
  though 
  they 
  used 
  entirely 
  different 
  

   electrical 
  methods. 
  The 
  experiments 
  of 
  McClung 
  when 
  used 
  

   to 
  give 
  A 
  yield 
  for 
  air 
  the 
  value 
  0*000176, 
  which 
  is 
  about 
  

   double 
  those 
  just 
  calculated. 
  The 
  data 
  of 
  Langevin 
  do 
  not 
  

   contain 
  all 
  the 
  particulars 
  necessary 
  for 
  a 
  calculation 
  of 
  A 
  

   absolutely. 
  We 
  shall 
  now 
  consider 
  the 
  values 
  of 
  A 
  for 
  the 
  

   four 
  gases 
  of 
  Townsend's 
  experiments, 
  obtained 
  from 
  his 
  

   data 
  

  

  

  Air. 
  

  

  O2. 
  

  

  CO2. 
  

  

  H2. 
  

  

  uje 
  

  

  .. 
  3420 
  

  

  3380 
  

  

  3500 
  

  

  3020 
  

  

  lO^A 
  . 
  . 
  . 
  . 
  

  

  .. 
  832 
  

  

  769 
  

  

  800 
  

  

  922 
  

  

  It 
  is 
  remarkable 
  that 
  each 
  parameter 
  has 
  a 
  value 
  that 
  

   changes 
  but 
  little 
  from 
  one 
  gas 
  to 
  another. 
  McClung 
  and 
  

   Langevin 
  by 
  their 
  independent 
  methods 
  get 
  nearly 
  the 
  same 
  

   value 
  as 
  Townsend 
  for 
  a 
  for 
  CO2, 
  aad 
  McClung's 
  value 
  in 
  

   the 
  case 
  of 
  Hg 
  agrees 
  with 
  that 
  of 
  Townsend. 
  We 
  have 
  

   now 
  to 
  see 
  how 
  the 
  values 
  just 
  given 
  for 
  A 
  accord 
  with 
  the 
  

   theory 
  of 
  it. 
  In 
  (23) 
  the 
  coefficient 
  of 
  1/p 
  is 
  to 
  be 
  propor- 
  

   tional 
  to 
  the 
  mean 
  free 
  path 
  of 
  an 
  ion 
  through 
  the 
  gas 
  at 
  a 
  

   pressure 
  of 
  760 
  mm., 
  which 
  is 
  inversely 
  proportional 
  to 
  the 
  

   square 
  of 
  the 
  molecular 
  diameter 
  with 
  appropriate 
  allowance 
  

   for 
  the 
  attraction 
  between 
  ion 
  and 
  molecule. 
  Thus 
  we 
  have 
  

   the 
  coefficient 
  of 
  1/p 
  in 
  (23) 
  inversely 
  proportional 
  to 
  

  

  (2a)2(H-C7288X 
  

  

  which 
  can 
  be 
  calculated 
  from 
  the 
  data 
  of 
  Table 
  II., 
  which 
  

   vield 
  the 
  following 
  value 
  for 
  the 
  coefficient 
  : 
  — 
  air 
  745, 
  

   O2 
  860, 
  CO2 
  462, 
  and 
  H2 
  908. 
  The 
  value 
  462 
  thus 
  obtained 
  

   for 
  CO2 
  is 
  to 
  be 
  compared 
  with 
  509 
  obtained 
  in 
  (23) 
  from 
  

   Langevin's 
  experiments. 
  These 
  enable 
  us 
  to 
  calculate 
  for 
  

   each 
  gas 
  at 
  760 
  mm. 
  this 
  coefficient 
  divided 
  by 
  760 
  which 
  is 
  

   the 
  part 
  of 
  log 
  ep^''^ 
  we 
  require. 
  The 
  corresponding 
  factor 
  of 
  

   ep^'^ 
  multiplied 
  by 
  ^1+1^2 
  or 
  by 
  u 
  from 
  Table 
  II., 
  according 
  

   to 
  the 
  theory 
  of 
  A, 
  is 
  to 
  be 
  proportional 
  to 
  A. 
  Here 
  are 
  the 
  

   values 
  of 
  A 
  divided 
  by 
  this 
  product 
  :— 
  air 
  50, 
  O2 
  65, 
  CO24I, 
  

  

  