﻿[ 
  912 
  ] 
  

  

  LXXIX. 
  A 
  Special 
  Case 
  of 
  Gaseous 
  Conduction. 
  

   By 
  Norman 
  Campbell, 
  Sc.D.* 
  

  

  I. 
  Theoretical. 
  

  

  1. 
  npHE 
  relation 
  o£ 
  the 
  current 
  through 
  a 
  gas 
  contained 
  in 
  a 
  

   JL 
  parallel 
  plate 
  condenser 
  and 
  uniformly 
  ionized 
  to 
  the 
  

   electric 
  field 
  acting 
  upon 
  it 
  has 
  been 
  studied 
  by 
  J. 
  J. 
  Thomson, 
  

   Mie, 
  Seeliger, 
  and 
  Greinacher. 
  Seeman 
  f 
  , 
  in 
  an 
  elaborate 
  

   series 
  of 
  observations, 
  has 
  shown 
  that 
  the 
  theoretical 
  formulae 
  

   are 
  satisfactorily 
  in 
  accordance 
  with 
  experiment 
  when 
  the 
  

   ionization 
  is 
  produced 
  by 
  X 
  rays. 
  In 
  the 
  circumstances 
  

   contemplated 
  by 
  the 
  theory 
  and 
  realized 
  in 
  the 
  experiments, 
  

   the 
  only 
  process 
  which 
  limits 
  the 
  proportion 
  of 
  the 
  saturation 
  

   current 
  which 
  can 
  be 
  obtained 
  with 
  small 
  fields 
  is 
  that 
  of 
  

   the 
  recombination 
  of 
  the 
  ions. 
  But 
  even 
  if 
  there 
  were 
  no 
  

   recombination, 
  another 
  process, 
  diffusion, 
  would 
  make 
  it 
  

   impossible 
  to 
  obtain 
  the 
  saturation 
  current 
  with 
  infinitely 
  

   small 
  fields 
  ; 
  for 
  the 
  diffusion 
  of 
  the 
  ions 
  involves 
  the 
  possi- 
  

   bility 
  that 
  they 
  may 
  travel 
  against 
  the 
  field 
  to 
  the 
  similarly 
  

   charged, 
  and 
  not 
  to 
  the 
  oppositely 
  charged, 
  electrode. 
  The 
  

   theory 
  developed 
  hitherto 
  considers 
  only 
  those 
  cases 
  where 
  

   the 
  effects 
  of 
  diffusion 
  may 
  be 
  neglected 
  compared 
  with 
  those 
  

   of 
  recombination 
  ; 
  some 
  recent 
  experiments, 
  to 
  be 
  described 
  

   below, 
  seem 
  to 
  show 
  that 
  cases 
  may 
  occur 
  in 
  practice 
  in 
  which 
  

   the 
  relative 
  importance 
  of 
  the 
  two 
  processes 
  is 
  reversed. 
  

  

  2. 
  Let 
  us 
  consider, 
  then, 
  the 
  equations 
  determining 
  the 
  

   motion 
  of 
  the 
  ions 
  in 
  a 
  parallel 
  plate 
  condenser, 
  neglecting 
  

   recombination 
  but 
  taking 
  diffusion 
  into 
  account. 
  

  

  Let 
  the 
  plane 
  of 
  x 
  = 
  be 
  parallel 
  to 
  the 
  plates 
  and 
  distant 
  I 
  

   from 
  each 
  of 
  them. 
  Let 
  V 
  be 
  the 
  potential 
  difference 
  

   between 
  the 
  plates, 
  X 
  the 
  electric 
  intensity, 
  q 
  the 
  number 
  of 
  

   ions 
  produced 
  in 
  unit 
  time 
  in 
  unit 
  volume, 
  A^X, 
  & 
  2 
  X 
  the 
  

   velocities 
  of 
  the 
  positive 
  and 
  negative 
  ions, 
  D 
  lt 
  D 
  2 
  their 
  

   diffusion 
  coefficients, 
  n 
  l9 
  n 
  2 
  the 
  concentrations 
  of 
  the 
  ions 
  in 
  

   the 
  gas, 
  i 
  the 
  current 
  density, 
  and 
  I 
  the 
  saturation-current 
  

   density. 
  The 
  fundamental 
  equations 
  expressed 
  in 
  electro- 
  

   static 
  units 
  are 
  : 
  — 
  

  

  «=c(«^*£) 
  d) 
  

  

  = 
  -£(v 
  2 
  X 
  + 
  D 
  2 
  g) 
  (2) 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  t 
  Ann. 
  d. 
  Phys. 
  vol. 
  xxxviii. 
  p. 
  781 
  (1912) 
  ; 
  references 
  are 
  given 
  in 
  this 
  

   paper 
  to 
  the 
  theoretical 
  discussions. 
  

  

  