﻿the 
  Ions 
  of 
  Gases. 
  365 
  

  

  tional 
  to 
  N2 
  the 
  number 
  per 
  unit 
  volume 
  in 
  the 
  air. 
  The 
  

   total 
  number 
  on 
  the 
  sphere 
  is 
  proportional 
  to 
  N2r^, 
  say 
  equal 
  

   to 
  AXa?*". 
  We 
  wish 
  to 
  find 
  the 
  resistance 
  F 
  to 
  the 
  motion 
  o£ 
  

   this 
  sphere 
  through 
  the 
  air 
  with 
  unit 
  velocity. 
  Just 
  as 
  in 
  

   the 
  theory 
  o£ 
  the 
  viscosity 
  oi: 
  gases 
  we 
  may 
  say 
  that 
  on 
  

   account 
  of 
  the 
  electric 
  force 
  o£ 
  the 
  nucleolus 
  and 
  the 
  

   cohesional 
  force 
  of 
  the 
  sphere, 
  the 
  number 
  of 
  molecules 
  of 
  

   air 
  encountered 
  by 
  the 
  sphere 
  will 
  be 
  increased 
  in 
  the 
  propor- 
  

   tion 
  1+ 
  {2e^S2/r^m2 
  + 
  W2^)/v2^ 
  : 
  1. 
  Unless 
  the 
  number 
  of 
  H2O 
  

   molecules 
  in 
  the 
  sphere 
  is 
  great, 
  the 
  tendency 
  will 
  be 
  for 
  

   each 
  molecule 
  to 
  experience 
  as 
  much 
  resistance 
  as 
  if 
  the 
  

   others 
  were 
  absent. 
  It 
  is 
  not 
  a 
  case 
  of 
  a 
  compact 
  sphere 
  of 
  

   radius 
  r, 
  but 
  of 
  AN2?'^ 
  spheres 
  of 
  radius 
  ag. 
  If 
  the 
  H2O 
  

   liquefies 
  into 
  something 
  like 
  water, 
  we 
  shall 
  have 
  to 
  deal 
  

   rather 
  with 
  a 
  single 
  large 
  sphere 
  formed 
  by 
  the 
  liquid. 
  For 
  

   the 
  resistance 
  to 
  one 
  molecule 
  of 
  II2O 
  moving 
  with 
  unit 
  

   velocity 
  through 
  the 
  air 
  we 
  get 
  from 
  the 
  kinetic 
  theory 
  of 
  

   diffusion 
  

  

  |N3(a2 
  + 
  a,y{2'Tr(v2^ 
  + 
  v^')/3 
  \^n2msl{m2 
  + 
  m,) 
  (26 
  a) 
  

  

  Strictly 
  we 
  ought 
  to 
  write 
  down 
  the 
  resistance 
  offered 
  to 
  the 
  

   nucleolus, 
  but, 
  as 
  it 
  would 
  be 
  quite 
  similar 
  to 
  this, 
  v/e 
  shall 
  

   merge 
  it 
  in 
  the 
  resistance 
  offered 
  to 
  the 
  ANg^^ 
  molecules. 
  

   Thus 
  

  

  F 
  = 
  lANgNsr^l 
  1 
  + 
  {2e\lr^m2 
  + 
  io/)/v2' 
  \ 
  (^2 
  + 
  a.Y 
  

  

  X 
  { 
  27r 
  (^2^ 
  + 
  ^''s^) 
  /3 
  pm2m3/(m2 
  4- 
  m^) 
  . 
  

  

  Replacing 
  m2V2^l2 
  by 
  T 
  the 
  temperature 
  and 
  m2W2^/2 
  by 
  Ta 
  

   a 
  constant 
  temperature, 
  we 
  find 
  from 
  {26) 
  that 
  r^ 
  cc 
  1/(T 
  — 
  TJ 
  

   and 
  1 
  + 
  [2e\[r^mr, 
  + 
  W2^) 
  /v/ 
  = 
  2, 
  while 
  (vg' 
  + 
  ^3^)* 
  oc 
  T*. 
  Re- 
  

   turning 
  to 
  (25) 
  remembering 
  that 
  ?is 
  proportional 
  to 
  F^-, 
  we 
  

   get 
  

  

  e^=Cq'^^^2^,Th/(T-Ta) 
  . 
  . 
  . 
  (27) 
  

  

  where 
  C 
  is 
  constant. 
  This 
  is 
  the 
  general 
  equation 
  for 
  the 
  

   motion 
  of 
  an 
  ion 
  consisting 
  of 
  nucleolus 
  and 
  H2O 
  molecules 
  

   in 
  an 
  electric 
  field. 
  To 
  apply 
  it 
  to 
  the 
  case 
  of 
  Moreau's 
  

   experiments 
  we 
  put 
  n^^ 
  for 
  9^/^, 
  and 
  have 
  N2, 
  N3, 
  and 
  n 
  all 
  

   varying 
  inversely 
  as 
  T, 
  so 
  that 
  u 
  the 
  mobility 
  when 
  d^/dx 
  

   = 
  volt/cm. 
  cc 
  Tii/«(T-Ta). 
  From 
  Table 
  IV. 
  the 
  mean 
  value 
  

   of 
  un}'^ 
  at 
  each 
  temperature 
  gives 
  a 
  useful 
  mean 
  value 
  of 
  v 
  

   for 
  the 
  case 
  in 
  which 
  the 
  solution 
  sprayed 
  into 
  the 
  flame 
  

   was 
  normal, 
  and 
  from 
  these 
  I 
  find 
  that 
  Ta 
  = 
  270. 
  In 
  the 
  

   next 
  Table 
  the 
  first 
  row 
  gives 
  temperatures, 
  the 
  second 
  

  

  