﻿Diffusion 
  to 
  Conducting 
  Gases, 
  477 
  

  

  so 
  that 
  the 
  time 
  that 
  any 
  portion 
  of 
  the 
  gas 
  will 
  be 
  in 
  the 
  

   tube 
  will 
  be 
  T 
  J 
  o 
  of 
  a 
  second. 
  

  

  The 
  ratio 
  of 
  the 
  conductivity 
  of 
  the 
  gas 
  entering 
  the 
  tubing 
  

   to 
  the 
  conductivity 
  of 
  the 
  gas 
  as 
  it 
  escapes 
  will, 
  therefore, 
  be 
  

  

  [ 
  e 
  —a 
  x 
  2 
  Kt 
  6 
  —a. 
  2 
  2 
  Kt 
  -| 
  

  

  a 
  2 
  et 
  x 
  2 
  a 
  l 
  a£ 
  J 
  

  

  The 
  values 
  of 
  aa 
  1? 
  aa 
  2 
  , 
  &c. 
  which 
  are 
  the 
  positive 
  roots 
  of 
  

   J 
  (a«) 
  =0 
  are 
  2'404, 
  5*520, 
  8'654, 
  &o. 
  (Lord 
  Rayleigh, 
  ' 
  Theory 
  

   of 
  Sound/ 
  section 
  206). 
  

  

  Substituting 
  for 
  a, 
  a 
  1? 
  a 
  2 
  , 
  &c. 
  their 
  values 
  we 
  obtain 
  

  

  — 
  (2-4)2H 
  — 
  (5'5) 
  2 
  H 
  

  

  where 
  a 
  = 
  T 
  ^ 
  ^ 
  = 
  ^ 
  * 
  = 
  . 
  

  

  So 
  that 
  :±» 
  t^ 
  

  

  R=4 
  [Hr 
  + 
  W2" 
  + 
  &c 
  -] 
  = 
  A^P" 
  

  

  If 
  # 
  were 
  unity, 
  in 
  other 
  words 
  if 
  the 
  ion 
  in 
  the 
  oxygen 
  

   which 
  is 
  conducting 
  under 
  Rontgen 
  rays 
  were 
  to 
  carry 
  the 
  

   same 
  charge 
  as 
  it 
  does 
  in 
  electrolysis, 
  then 
  the 
  conductivity 
  

   of 
  the 
  gas 
  would 
  be 
  reduced 
  to 
  ^ 
  of 
  its 
  value 
  by 
  passing- 
  

   it 
  along 
  a 
  tube 
  10 
  centimetres 
  long 
  and 
  1 
  millimetre 
  radius 
  

   at 
  the 
  rate 
  of 
  100 
  centimetres 
  per 
  second. 
  

  

  It 
  is 
  interesting 
  to 
  find 
  what 
  would 
  be 
  the 
  effect 
  of 
  the 
  

  

  attraction, 
  towards 
  the 
  sides 
  of 
  a 
  tube 
  made 
  of 
  conducting 
  

  

  material, 
  of 
  each 
  individual 
  carrier 
  by 
  its 
  own 
  image 
  in 
  the 
  

  

  conductor. 
  It 
  is 
  quite 
  evident 
  that 
  this 
  effect 
  only 
  comes 
  in 
  

  

  when 
  the 
  carrier 
  is 
  near 
  the 
  surface, 
  so 
  that 
  we 
  can 
  regard 
  

  

  the 
  radius 
  of 
  curvature 
  of 
  the 
  tube 
  as 
  large 
  in 
  comparison 
  

  

  with 
  the 
  distance 
  of 
  the 
  carrier 
  from 
  the 
  surface. 
  When 
  this 
  

  

  e 
  2 
  

   distance 
  is 
  ,v. 
  the 
  force 
  on 
  the 
  carrier 
  will 
  be 
  — 
  — 
  r 
  , 
  and 
  under 
  

  

  e 
  l'Q 
  

   this 
  force 
  it 
  would 
  travel 
  at 
  the 
  rate 
  of 
  -j—^ 
  x 
  — 
  =— 
  , 
  since 
  

  

  ..it 
  3 
  °o 
  

  

  under 
  a 
  volt 
  a 
  centimetre 
  it 
  travels 
  at 
  tne 
  rate 
  of 
  1*6 
  centi- 
  

   metres 
  per 
  second. 
  

   Hence 
  we 
  have 
  

  

  _ 
  10- 
  10 
  x 
  120 
  _ 
  dx 
  

   U 
  ~ 
  x* 
  ~ 
  dt 
  ' 
  

  

  assuming 
  that 
  the 
  atomic 
  charge 
  on 
  oxygen 
  is 
  10 
  -10 
  ; 
  therefore 
  

  

  10 
  9 
  

   dt 
  = 
  — 
  — 
  r- 
  a?dx. 
  

   12 
  

  

  