﻿Diffusion 
  to 
  Conducting 
  Gases. 
  475 
  

  

  Substituting 
  for 
  -f-(pu), 
  -j- 
  (pv), 
  and 
  j-(pw) 
  their 
  values 
  

  

  derived 
  by 
  differentiating 
  equations 
  (3), 
  we 
  arrive 
  at 
  the 
  

   equation 
  

  

  dp__ 
  S00Yp 
  Q 
  

   dt~~ 
  Ne 
  V 
  [P) 
  > 
  

  

  which 
  is 
  the 
  general 
  equation 
  we 
  assumed 
  in 
  Section 
  T. 
  

  

  Thus 
  the 
  value 
  of 
  the 
  constant 
  k 
  is 
  ' 
  — 
  AT 
  ^° 
  . 
  

  

  xse 
  

  

  5. 
  The 
  loss 
  of 
  conductivity 
  of 
  a 
  gas 
  is 
  due 
  partly 
  to 
  the 
  

   recombination 
  of 
  some 
  of 
  the 
  positively 
  charged 
  carriers 
  with 
  

   the 
  negatively 
  charged 
  ones, 
  and 
  partly 
  to 
  the 
  carriers 
  coming 
  

   into 
  contact 
  with 
  the 
  conductors. 
  It 
  is 
  with 
  this 
  latter 
  phe- 
  

   nomenon 
  that 
  we 
  are 
  here 
  chiefly 
  concerned. 
  By 
  substituting 
  

   the 
  above 
  value 
  of 
  k 
  in 
  the 
  three 
  solutions 
  obtained 
  in 
  Section 
  I. 
  

   we 
  obtain 
  expressions 
  which 
  give 
  the 
  loss 
  of 
  conductivity 
  of 
  a 
  

   gas 
  due 
  to 
  the 
  diffusion 
  of 
  the 
  carriers 
  towards 
  the 
  sides 
  of 
  

   the 
  vessel 
  which 
  contains 
  it. 
  This 
  loss 
  of 
  conductivity 
  takes 
  

   place 
  in 
  a 
  closed 
  vessel 
  without 
  any 
  electromotive 
  force 
  acting 
  

   on 
  the 
  gas. 
  

  

  When 
  a 
  carrier 
  comes 
  into 
  contact 
  with 
  a 
  conductor 
  it 
  

   either 
  gives 
  up 
  its 
  charge, 
  or 
  remains 
  in 
  contact 
  with 
  the 
  

   surface. 
  From 
  the 
  way 
  in 
  which 
  the 
  equations 
  in 
  Section 
  I. 
  

   were 
  solved, 
  it 
  is 
  clear 
  that 
  the 
  solutions 
  apply 
  to 
  the 
  case 
  

   where 
  the 
  carrier, 
  instead 
  of 
  giving 
  up 
  its 
  charge 
  to 
  the 
  side, 
  

   induces 
  an 
  opposite 
  charge 
  on 
  the 
  conductor, 
  and 
  is 
  held 
  

   attracted 
  to 
  the 
  surface 
  by 
  the 
  electric 
  force 
  arising 
  from 
  its 
  

   image. 
  The 
  solutions 
  apply 
  equally 
  well 
  on 
  the 
  hypothesis 
  

   that 
  the 
  carrier 
  discharges 
  and 
  comes 
  back 
  into 
  the 
  gas. 
  In 
  

   this 
  case 
  we 
  have 
  a 
  slight 
  increase 
  in 
  the 
  number 
  of 
  molecules 
  

   of 
  B, 
  less 
  than 
  one 
  part 
  in 
  10 
  10 
  ; 
  so 
  that 
  the 
  correction 
  to 
  be 
  

   applied 
  would 
  amount 
  to 
  calculating 
  the 
  difference 
  of 
  the 
  rate 
  

   of 
  diffusion 
  of 
  A 
  through 
  a 
  gas 
  having 
  a 
  density 
  greater 
  than 
  

   B 
  in 
  the 
  proportion 
  of 
  10 
  10 
  + 
  1 
  to 
  10 
  10 
  , 
  which 
  of 
  course 
  can 
  

   in 
  no 
  way 
  affect 
  the 
  original 
  solution. 
  

  

  If 
  we 
  leave 
  out 
  of 
  consideration 
  the 
  recombination 
  of 
  the 
  

   ions 
  or 
  charged 
  carriers, 
  we 
  see 
  that 
  the 
  conductivity 
  of 
  a 
  gas 
  

   will 
  fall 
  from 
  p 
  to 
  p 
  in 
  a 
  time 
  t, 
  where 
  the 
  ratio 
  of 
  p 
  to 
  p 
  is 
  

  

  -(2tt-l) 
  2 
  7T 
  2 
  /e* 
  

  

  