﻿344 
  Mr. 
  W. 
  Sutherland 
  on 
  

  

  minimum 
  value 
  of 
  r 
  by 
  the^ 
  condition 
  dz/dd 
  = 
  0. 
  Denote 
  

   the 
  reciprocal 
  o£ 
  this 
  distance 
  by 
  w 
  which 
  is 
  given 
  by 
  

  

  2 
  

  

  or 
  

  

  minis 
  l^ 
  ' 
  ^ 
  ) 
  

  

  There 
  must 
  be 
  a 
  collision 
  i£ 
  1/w 
  is 
  less 
  than 
  ai 
  + 
  a^. 
  Hence 
  

   the 
  greatest 
  value 
  o£ 
  h 
  'lor 
  which 
  a 
  collision 
  is 
  possible 
  is 
  

   given 
  by 
  

  

  or 
  

  

  Thus 
  it 
  is 
  proved 
  that 
  to 
  adapt 
  (2) 
  to 
  the 
  case 
  where 
  

   electric 
  and 
  cohesional 
  forces 
  are 
  operative 
  {ai 
  + 
  a^y 
  is 
  to 
  be 
  

   replaced 
  by 
  the 
  right 
  hand 
  of 
  (7). 
  Just 
  as 
  the 
  correspond- 
  

   ing 
  result 
  in 
  the 
  theory 
  of 
  the 
  viscosity 
  of 
  a 
  gas 
  applies 
  

   strictly 
  only 
  to 
  gases 
  above 
  their 
  critical 
  temperature 
  and 
  at 
  

   moderate 
  densities, 
  that 
  is 
  to 
  say, 
  under 
  conditions 
  which 
  

   allow 
  the 
  relative 
  orbit 
  of 
  a 
  pair 
  of 
  colliding 
  molecules 
  seldom 
  

   to 
  consist 
  of 
  a 
  curve 
  of 
  finite 
  range, 
  so 
  the 
  result 
  just 
  obtained 
  

   is 
  strictly 
  applicable 
  only 
  when 
  the 
  relative 
  orbit 
  of 
  ion 
  and 
  

   molecule 
  is 
  seldom 
  a 
  curve 
  of 
  finite 
  range. 
  For 
  the 
  resist- 
  

   ance 
  to 
  an 
  ion 
  we 
  now 
  get 
  from 
  (2) 
  with 
  m^Vi^ 
  — 
  rn^v^^, 
  

  

  '...(8) 
  

  

  To 
  adapt 
  this 
  for 
  comparison 
  with 
  experimental 
  results 
  we 
  

   put 
  m^v^ 
  proportional 
  to 
  T 
  the 
  absolute 
  temperature, 
  and 
  

   remembering 
  that 
  N3 
  varies 
  as 
  1/T, 
  we 
  get 
  F 
  proportional 
  to 
  

   T-*(1 
  + 
  C7T) 
  where 
  C' 
  is 
  proportional 
  to 
  

  

  If 
  then 
  in 
  (1) 
  we 
  make 
  dB/dx 
  a 
  volt 
  per 
  cm., 
  we 
  get 
  for 
  the 
  

   relation 
  between 
  ionic 
  mobility 
  u 
  and 
  temperature 
  T 
  the 
  

   equation 
  

  

  """ 
  1 
  + 
  C7T 
  ^^^ 
  

  

  in 
  which 
  A^ 
  and 
  C^ 
  are 
  parameters 
  having 
  values 
  character- 
  

   istic 
  of 
  each 
  gas, 
  the 
  dashes 
  being 
  used 
  to 
  distinguish 
  them 
  

  

  I 
  

  

  