﻿the 
  Ions 
  of 
  Gases. 
  345 
  

  

  from 
  the 
  corresponding 
  parameters 
  in 
  the 
  similar 
  equation 
  

   for 
  the 
  viscosity 
  of 
  a 
  gas. 
  We 
  can 
  test 
  the 
  validity 
  of 
  (9) 
  

   by 
  means 
  of 
  the 
  experiments 
  of 
  Phillips 
  (loc. 
  cit.). 
  In 
  air 
  

   for 
  the 
  positive 
  ion 
  A^ 
  = 
  0*222 
  and 
  C' 
  = 
  509*6, 
  and 
  for 
  the 
  

   negative 
  ion 
  A' 
  = 
  0-222 
  and 
  C' 
  = 
  333-3. 
  These 
  give 
  the 
  

   follo^^•ing 
  calculated 
  mobilities 
  for 
  comparison 
  with 
  the 
  ex- 
  

   perimental. 
  

  

  Table 
  I. 
  

  

  T 
  411 
  399 
  383 
  373 
  348 
  333 
  285 
  209 
  94 
  

  

  Pos. 
  fwexp. 
  ... 
  2-00 
  1-95 
  1-85 
  I'Sl 
  1-67 
  1-60 
  1-39 
  0-945 
  0-235 
  

  

  ion. 
  [ucal. 
  ... 
  201 
  1-95 
  1-86 
  1-81 
  1-68 
  1-60 
  1-34 
  0*934 
  0-336 
  

  

  Reg- 
  

   ion. 
  

  

  u 
  esp. 
  ... 
  2-495 
  240 
  230 
  2-21 
  2-125 
  200 
  1-785 
  1*23 
  0-235 
  

   h^cal. 
  ... 
  2-487 
  2-42 
  2-33 
  2-27 
  2-12 
  2-03 
  1-73 
  1-24 
  0-474 
  

  

  Down 
  to 
  T 
  = 
  209° 
  the 
  mobilities 
  of 
  both 
  ions 
  are 
  given 
  

   with 
  satisfactory 
  accuracy 
  by 
  the 
  theoretical 
  formula 
  (9), 
  

   but 
  at 
  94^ 
  the 
  formula 
  fails, 
  as 
  theoretical 
  considerations 
  led 
  

   ns 
  to 
  expect 
  that 
  it 
  would, 
  because 
  94 
  is 
  about 
  30 
  below 
  the 
  

   critical 
  temperature 
  of 
  air. 
  It 
  is 
  notable 
  that 
  at 
  this 
  lowest 
  

   temperature 
  the 
  experimental 
  mobility 
  is 
  the 
  same 
  for 
  both 
  

   ions. 
  This 
  shows 
  that 
  at 
  this 
  temperature 
  some 
  rather 
  

   profound 
  change 
  has 
  occurred 
  in 
  the 
  conditions 
  of 
  movement 
  

   of 
  the 
  two 
  ions. 
  From 
  the 
  values 
  of 
  A' 
  and 
  C 
  it 
  appears 
  

   that 
  at 
  high 
  temperatures 
  the 
  mobilities 
  of 
  the 
  two 
  ions 
  will 
  

   tend 
  to 
  become 
  equal 
  again. 
  It 
  appears 
  also 
  that 
  the 
  differ- 
  

   ence 
  in 
  the 
  mobilities 
  is 
  caused 
  by 
  the 
  difference 
  in 
  the 
  

   values 
  of 
  (V 
  which 
  are 
  proportional 
  to 
  the 
  potential 
  energy 
  

   of 
  ion 
  and 
  molecule 
  in 
  contact. 
  If 
  we 
  compare 
  these 
  values, 
  

   namely 
  509-6 
  and 
  333-3, 
  with 
  113 
  the 
  value 
  of 
  C 
  the 
  similar 
  

   parameter 
  in 
  the 
  viscosity 
  of 
  air, 
  which 
  is 
  proportional 
  to 
  

   the 
  potential 
  energy 
  of 
  two 
  molecules 
  of 
  air 
  in 
  contact, 
  we 
  

   see 
  that 
  in 
  both 
  cases 
  the 
  potential 
  energv 
  of 
  ion 
  and 
  molecule 
  

   is 
  larger 
  than 
  that 
  of 
  molecule 
  and 
  molecule. 
  This 
  is 
  what 
  

   we 
  should 
  expect 
  from 
  our 
  knowledge 
  that 
  the 
  potential 
  

   energy 
  of 
  molecule 
  and 
  molecule 
  is 
  like 
  that 
  of 
  two 
  electric 
  

   doublets 
  of 
  charges 
  e 
  and 
  moment 
  es 
  in 
  which 
  s 
  is 
  less 
  than 
  

   the 
  diameter 
  of 
  a 
  molecule. 
  It 
  seems 
  then 
  we 
  must 
  trace 
  

   the 
  remarkable 
  difference 
  in 
  the 
  mobilities 
  of 
  the 
  two 
  ions 
  

   to 
  differences 
  of 
  their 
  potential 
  energies 
  when 
  in 
  contact 
  

   with 
  a 
  molecule 
  of 
  air. 
  Unfortunately 
  we 
  do 
  not 
  know 
  

   experimentally 
  what 
  the 
  ions 
  are. 
  In 
  pure 
  gases 
  we 
  may 
  

   infer 
  that 
  the 
  ions 
  are 
  atoms 
  charged 
  with 
  a 
  positive 
  or 
  a 
  

   negative 
  electron, 
  but 
  we 
  do 
  not 
  vet 
  know 
  whether 
  in 
  the 
  

  

  