﻿the 
  Ions 
  of 
  Gases. 
  357 
  

  

  and 
  to 
  the 
  rate 
  at 
  which 
  unsymmetrical 
  distributions 
  arise 
  to 
  

   produce 
  the 
  motion 
  which 
  we 
  have 
  treated 
  as 
  a 
  leak. 
  This 
  

   equation 
  can 
  be 
  written 
  

  

  ^Ni2/3/^^=--fA(Ni2/3>)2 
  (13) 
  

  

  and 
  its 
  inteo-ral 
  is 
  

  

  o 
  

  

  ]Sri-'/3 
  = 
  Q 
  + 
  2A^/3, 
  . 
  . 
  . 
  . 
  (19) 
  

  

  where 
  C 
  is 
  a 
  constant. 
  Thus 
  we 
  have 
  Ni~^/^ 
  a 
  linear 
  func- 
  

   tion 
  of 
  the 
  time, 
  whereas 
  the 
  integral 
  o£ 
  (15) 
  makes 
  Ni~^ 
  a 
  

   linear 
  function 
  of 
  the 
  time. 
  From 
  the 
  tabulated 
  data 
  of 
  

   Barus 
  for 
  ions 
  in 
  air, 
  I 
  find 
  with 
  second 
  for 
  unit 
  t 
  

  

  105^1-2/3 
  = 
  52 
  + 
  6^ 
  (20) 
  

  

  with 
  the 
  following 
  comparison 
  : 
  — 
  

  

  30 
  60 
  120 
  

   9 
  5 
  1 
  

   9 
  4 
  1-5 
  

  

  Seconds 
  

  

  ... 
  

  

  5 
  

  

  10 
  

  

  20 
  

  

  lO-^N^exp. 
  ... 
  

  

  ... 
  83 
  

  

  38 
  

  

  27 
  

  

  14 
  

  

  10-%,cal 
  

  

  ... 
  84 
  

  

  35 
  

  

  27 
  

  

  14 
  

  

  Barus 
  gives 
  five 
  other 
  sets 
  of 
  data 
  in 
  graph 
  form, 
  and 
  in 
  

   these 
  10^ 
  x 
  2A/3 
  has 
  a 
  value 
  about 
  4'5. 
  The 
  comparison 
  just 
  

   given 
  covers 
  a 
  range 
  of 
  N^ 
  large 
  enough 
  to 
  show 
  that 
  (17) 
  

   is 
  to 
  be 
  preferred 
  to 
  (15). 
  But 
  as 
  (15) 
  has 
  been 
  taken 
  by 
  

   J. 
  J. 
  Thomson 
  to 
  be 
  proved 
  by 
  various 
  experiments 
  origi- 
  

   nating 
  in 
  the 
  Cavendish 
  laboratory, 
  it 
  is 
  necessary 
  to 
  look 
  

   rather 
  more 
  closely 
  into 
  the 
  evidence. 
  In 
  the 
  paper 
  of 
  

   J. 
  J. 
  Thomson 
  and 
  Rutherford 
  on 
  the 
  passage 
  of 
  electricity 
  

   through 
  gases 
  exposed 
  to 
  Rontgen 
  rays 
  (Phil. 
  Mag. 
  [5] 
  xlii. 
  

   1896, 
  p. 
  392), 
  the 
  experimental 
  results 
  can 
  be 
  expressed 
  with 
  

   a 
  slightly 
  smaller 
  average 
  error 
  by 
  the 
  ^i 
  formula 
  than 
  by 
  

   the 
  Nj-^'^ 
  one, 
  but 
  they 
  can 
  be 
  expressed 
  with 
  a 
  still 
  smaller 
  

   average 
  error 
  by 
  a 
  formula 
  using 
  Ni^/^. 
  These 
  early 
  experi- 
  

   ments 
  are 
  therefore 
  not 
  suitable 
  for 
  deciding 
  between 
  the 
  

   two 
  formulae. 
  In 
  Rutherford's 
  paper 
  on 
  the 
  rate 
  of 
  recom- 
  

   bination 
  (Phil. 
  Mag. 
  [5] 
  xliv. 
  1897, 
  p. 
  422) 
  the 
  experi- 
  

   mental 
  results 
  are 
  represented 
  with 
  the 
  following 
  average 
  

   errors 
  per 
  cent. 
  : 
  — 
  

  

  On 
  page 
  423 
  

   With 
  the 
  Ni2 
  formula 
  5-7 
  

  

  IVJ 
  5/3 
  O.O 
  

  

  The 
  theoretical 
  handling 
  of 
  McClung's 
  experiments 
  (Phil. 
  

   Mag. 
  [6] 
  iii. 
  1902, 
  p. 
  283) 
  on 
  the 
  rate 
  of 
  recombination 
  of 
  

   FldL 
  Mag. 
  S. 
  6. 
  Vol. 
  18. 
  No. 
  105. 
  Sept. 
  1909. 
  2 
  B 
  

  

  427 
  

  

  429 
  

  

  6-0 
  

  

  6-7 
  

  

  3-5 
  

  

  7-7 
  

  

  