﻿370 
  Mr. 
  W. 
  Sutherland 
  on 
  the 
  Ions 
  of 
  Gases. 
  

  

  o£ 
  gases. 
  In 
  a 
  gas 
  above 
  the 
  critical 
  temperature 
  and 
  at 
  

   ordinary 
  pressures 
  the 
  mobility 
  of 
  a 
  small 
  ion 
  varies 
  with 
  

   temperature 
  according 
  to 
  the 
  formula 
  u 
  = 
  AJT^I^ 
  j 
  (1 
  + 
  Q' 
  fl.) 
  in 
  

   which 
  A^ 
  is 
  a 
  parameter 
  characteristic 
  of 
  each 
  gas, 
  and 
  C^ 
  is 
  

   proportional 
  to 
  the 
  mutual 
  potential 
  energy 
  of 
  ion 
  and 
  

   molecule 
  when 
  in 
  contact 
  during 
  a 
  collision, 
  being 
  similar 
  to 
  

   C, 
  the 
  corresponding 
  quantity 
  in 
  the 
  theory 
  of 
  the 
  viscosit}^ 
  

   of 
  gases. 
  On 
  the 
  principles 
  of 
  the 
  kinetic 
  theory 
  of 
  gases 
  A' 
  

   is 
  found 
  for 
  any 
  gas 
  in 
  terms 
  of 
  the 
  number, 
  diameter, 
  mass, 
  

   and 
  velocity 
  of 
  its 
  molecules, 
  by 
  an 
  analysis 
  which 
  leads 
  

   finally 
  to 
  (12). 
  The 
  theory 
  is 
  verified 
  by 
  means 
  of 
  the 
  

   experiments 
  of 
  Phillips 
  on 
  the 
  effect 
  of 
  temperature 
  on 
  the 
  

   mobility 
  of 
  small 
  ions 
  in 
  air, 
  and 
  by 
  means 
  of 
  the 
  data 
  so 
  far 
  

   obtained 
  experimentally 
  for 
  the 
  mobility 
  of 
  small 
  ions 
  in 
  gases 
  

   and 
  vapours. 
  It 
  leads 
  to 
  values 
  of 
  the 
  potential 
  energy 
  of 
  

   ion 
  and 
  molecule 
  in 
  contact 
  which 
  are 
  given 
  in 
  Tables 
  II. 
  and 
  

   III., 
  and 
  these 
  furnish 
  evidence 
  of 
  the 
  presence 
  in 
  H2, 
  He, 
  

   N2, 
  and 
  O2 
  of 
  an 
  electric 
  doublet 
  of 
  constant 
  electric 
  moment. 
  

   By 
  taking 
  account 
  of 
  the 
  new 
  induced 
  type 
  of 
  viscosity 
  and 
  

   also 
  of 
  C' 
  it 
  is 
  shown 
  that 
  the 
  small 
  ion 
  has 
  no 
  molecules 
  

   attached 
  to 
  it. 
  It 
  is 
  like 
  the 
  ion 
  of 
  electrolytic 
  solutions. 
  

   The 
  smallness 
  of 
  the 
  coefficients 
  of 
  diffusion 
  of 
  ions 
  is 
  traced 
  

   to 
  the 
  induced 
  viscosity, 
  the 
  hypothesis 
  of 
  molecular 
  clusters 
  

   being 
  unnecessary. 
  As 
  regards 
  the 
  rate 
  of 
  recombination 
  of 
  

   small 
  ions 
  in 
  gases 
  it 
  is 
  necessary 
  to 
  replace 
  the 
  first 
  approxi- 
  

   mation 
  expressed 
  in 
  the 
  formula 
  of 
  J. 
  J. 
  Thomson, 
  namely 
  

   d^/dl= 
  — 
  uN^, 
  by 
  a 
  second 
  approximation 
  dN/dt= 
  —A'N^^'^^ 
  

   which 
  is 
  deduced 
  theoretically 
  by 
  regarding 
  recombination 
  

   as 
  a 
  leak 
  in 
  laminar 
  distribution 
  of 
  the 
  ionic 
  charges. 
  This 
  

   formula 
  is 
  verified 
  over 
  a 
  wide 
  range 
  of 
  values 
  of 
  N 
  by 
  the 
  

   experiments 
  of 
  Barus 
  and 
  also 
  by 
  the 
  experiments 
  adduced 
  by 
  

   J. 
  J. 
  Thomson 
  in 
  support 
  of 
  the 
  N^ 
  formula. 
  From 
  

   statistical 
  considerations 
  formula 
  (24) 
  is 
  established 
  for 
  A 
  and 
  

   verified 
  by 
  the 
  experiments 
  of 
  Langevin 
  on 
  the 
  effect 
  of 
  

   pressure 
  on 
  the 
  rate 
  of 
  recombination 
  of 
  ions 
  in 
  air 
  and 
  COg. 
  

   But 
  although 
  the 
  small 
  ion 
  is 
  not 
  associated 
  with 
  molecular 
  

   clusters, 
  there 
  are 
  cases 
  in 
  which 
  the 
  small 
  ion 
  attaches 
  

   molecules 
  to 
  itself 
  and 
  becomes 
  a 
  large 
  ion. 
  These 
  are 
  

   divided 
  into 
  two 
  classes, 
  the 
  large 
  ion 
  consisting 
  of 
  an 
  

   envelope 
  of 
  vapour, 
  such 
  as 
  that 
  of 
  HgO, 
  surrounding 
  a 
  small 
  

   ion 
  which 
  is 
  the 
  central 
  nucleolus, 
  and 
  the 
  larger 
  ion 
  in 
  which 
  

   a 
  liquid 
  or 
  solid 
  nucleus 
  forms 
  round 
  the 
  ionic 
  nucleolus, 
  the 
  

   whole 
  being 
  surrounded 
  by 
  an 
  envelope. 
  With 
  these 
  large 
  

   ions 
  the 
  induced 
  viscosity 
  becomes 
  of 
  negligible 
  importance, 
  

   because 
  the 
  moving 
  electric 
  charge 
  is 
  too 
  far 
  from 
  the 
  

   molecules 
  of 
  the 
  surrounding 
  gas. 
  But 
  the 
  direct 
  electric 
  

  

  