﻿138 
  Mr. 
  John 
  S. 
  Townsend 
  on 
  Electrical 
  

  

  and 
  4*p£ 
  = 
  . 
  00255) 
  where 
  ft=8 
  10 
  _ 
  3 
  . 
  

  

  Hence 
  ^=5-6, 
  and 
  i°=15 
  (3) 
  

  

  P. 
  P 
  

  

  From 
  the 
  equation 
  kY 
  = 
  Fe, 
  which 
  is 
  similar 
  to 
  the 
  equa- 
  

   tions 
  (1) 
  (§ 
  9), 
  V 
  being 
  the 
  velocity 
  due 
  to 
  an 
  electromotive 
  

   force 
  F, 
  we 
  obtain 
  for 
  the 
  motion 
  of 
  the 
  charged 
  carrier 
  in 
  

  

  F 
  

  

  hydrogen 
  V 
  = 
  s— 
  ^ 
  , 
  and 
  for 
  the 
  motion 
  of 
  the 
  charged 
  carrier 
  

  

  F 
  

  

  in 
  oxygen 
  V=y-^. 
  Hence 
  under 
  an 
  electromotive 
  force 
  of 
  

  

  one 
  volt 
  per 
  centimetre, 
  the 
  hydrogen 
  carrier 
  travels 
  at 
  the 
  

  

  rate 
  of 
  r^r-: 
  — 
  ^-77 
  centimetres 
  per 
  second, 
  and 
  the 
  oxygen 
  

   300x5*6 
  -^ 
  1 
  r 
  • 
  /fc> 
  

  

  carrier 
  at 
  the 
  rate 
  of 
  -7- 
  x 
  —? 
  centimetres 
  per 
  second. 
  These 
  

  

  oOO 
  15 
  r 
  

  

  results 
  do 
  not 
  require 
  a 
  knowledge 
  of 
  e. 
  

  

  The 
  conclusions 
  arrived 
  at 
  from 
  the 
  above 
  investigations 
  

   are 
  based 
  on 
  the 
  assumption 
  that 
  in 
  each 
  case 
  we 
  are 
  dealing 
  

   with 
  a 
  gas 
  containing 
  carriers 
  all 
  charged 
  with 
  the 
  same 
  

   sign, 
  either 
  positive 
  or 
  negative. 
  Experiments 
  on 
  conduc- 
  

   tivity 
  have 
  been 
  carried 
  out 
  in 
  order 
  to 
  test 
  this 
  point, 
  and 
  it 
  

   has 
  been 
  found 
  that 
  we 
  are 
  in 
  reality 
  dealing 
  with 
  mixtures. 
  

   Thus 
  in 
  the 
  case 
  of 
  oxygen, 
  or 
  hydrogen, 
  from 
  a 
  sulphuric- 
  

   acid 
  cell 
  having 
  a 
  positive 
  charge 
  equal 
  to 
  3 
  0, 
  it 
  is 
  possible 
  

   to 
  obtain 
  from 
  the 
  gas 
  a 
  positive 
  charge 
  of 
  4 
  e 
  and 
  a 
  negative 
  

   charge 
  of 
  e. 
  If 
  we 
  suppose 
  the 
  positive 
  and 
  negative 
  to 
  act 
  

   independently 
  the 
  charge 
  on 
  the 
  oxygen 
  carrier 
  would 
  be 
  

   5 
  . 
  10 
  -10 
  instead 
  of 
  3 
  . 
  10 
  -10 
  , 
  also 
  the 
  velocities 
  under 
  a 
  volt 
  

   per 
  centimetre 
  would 
  be 
  smaller 
  in 
  the 
  ratio 
  of 
  3 
  : 
  4 
  than 
  

   those 
  given 
  above. 
  

  

  We 
  can 
  arrive 
  at 
  an 
  approximate 
  value 
  for 
  the 
  size 
  of 
  the 
  

   carrier 
  if 
  we 
  assume 
  that 
  the 
  viscosity 
  of 
  a 
  gas 
  affects 
  the 
  

   motion 
  of 
  a 
  small 
  sphere 
  and 
  a 
  large 
  one 
  according 
  to 
  the 
  

   same 
  law 
  ^irfia 
  V 
  = 
  P 
  (Lamb, 
  loc. 
  cit.) 
  ; 
  substituting 
  

  

  V= 
  300^6' 
  " 
  =10 
  ~ 
  4 
  

   for 
  hydrogen 
  and 
  

  

  P= 
  — 
  x 
  - 
  10~ 
  l0 
  = 
  -10~ 
  12 
  

   r 
  300 
  2 
  2 
  ' 
  

  

  we 
  get 
  for 
  the 
  radius, 
  a, 
  of 
  the 
  hydrogen 
  carrier 
  4*5 
  . 
  10~ 
  7 
  . 
  

   Similar 
  substitutions 
  give 
  the 
  radius 
  of 
  the 
  oxygen 
  carrier 
  

  

  