﻿the 
  Ions 
  of 
  Gases. 
  367 
  

  

  namely 
  a 
  nucleus 
  of 
  (HoO)2 
  or 
  (H20)3 
  or 
  both 
  in 
  a 
  state 
  

   very 
  similar 
  to 
  that 
  of 
  a 
  liquid 
  surrounded 
  by 
  an 
  envelope 
  of 
  

   HoO 
  vapour 
  which 
  is 
  kept 
  highly 
  concentrated 
  close 
  to 
  the 
  

   nucleus. 
  This 
  envelope 
  is 
  similar 
  to 
  the 
  surface 
  film 
  of 
  

   vapour 
  o£ 
  HoO 
  deposited 
  on 
  the 
  grains 
  of 
  fine 
  powders. 
  The 
  

   number 
  of 
  H2O 
  molecules 
  per 
  cm.^ 
  close 
  to 
  the 
  nucleus 
  will 
  

   have 
  a 
  value 
  X2, 
  like 
  a 
  saturation 
  value, 
  and 
  the 
  number 
  will 
  

   diminish 
  with 
  increasing 
  distance 
  from 
  the 
  nucleus 
  till 
  it 
  

   becomes 
  Xj 
  where 
  its 
  influence 
  has 
  ceased. 
  The 
  thickness 
  o£ 
  

   this 
  transition 
  layer 
  may 
  be 
  taken 
  to 
  be 
  constant 
  for 
  a 
  given 
  

   value 
  ot 
  Xo, 
  or 
  we 
  can 
  replace 
  it 
  approximately 
  by 
  a 
  constant 
  

   length 
  I 
  such 
  that 
  'i.TrrH 
  is 
  the 
  volume 
  of 
  the 
  transition 
  layer, 
  

   in 
  which 
  the 
  mean 
  value 
  of 
  '^2 
  is 
  not 
  (N2s 
  + 
  i^2)/^ 
  but 
  

   E'Ns^ 
  + 
  H'Ns 
  where 
  E^ 
  and 
  H' 
  are 
  constants. 
  The 
  resistance 
  

   to 
  the 
  motion 
  of 
  all 
  the 
  vapour 
  with 
  unit 
  velocity 
  through 
  the 
  

   air 
  will 
  be 
  47rr"Z(E'N25-hH'i:s'2) 
  times 
  (26 
  a). 
  We 
  can 
  use 
  

   (26 
  a) 
  also 
  to 
  give 
  the 
  resistance 
  to 
  the 
  motion 
  of 
  the 
  nucleus 
  

   by 
  replacing 
  a2 
  + 
  «3 
  by 
  r. 
  We 
  neglect 
  the 
  resistance 
  of 
  the 
  

   nucleolus 
  and 
  write 
  the 
  total 
  resistance 
  to 
  unit 
  velocity 
  in 
  

   the 
  form 
  

  

  7'2Isr3TV2(E'N2, 
  + 
  G^ 
  + 
  H'N2) 
  . 
  . 
  . 
  (28) 
  

  

  where 
  Gr^ 
  is 
  the 
  constant 
  for 
  the 
  nucleus. 
  This 
  is 
  F, 
  and 
  

   neglecting 
  it 
  in 
  comparison 
  with 
  ^q~'^'^ 
  which 
  is 
  proportional 
  

   to 
  Yq-^ 
  we 
  obtain 
  from 
  (25) 
  

  

  e^^=7^(fim^TI\m^,,-^a^-B:^^)u 
  . 
  . 
  (29) 
  

  

  where 
  E, 
  G, 
  and 
  H 
  are 
  constants. 
  Thus 
  the 
  reciprocal 
  of 
  the 
  

   mobility 
  for 
  ^E/(i^ 
  = 
  volt/cm. 
  is 
  linear 
  in 
  N2 
  which 
  is 
  pro- 
  

   portional 
  to 
  the 
  humidity. 
  This 
  is 
  one 
  of 
  Pollock's 
  results 
  

   for 
  the 
  Langevin 
  ion. 
  He 
  finds 
  1/^=1200+107*5/^, 
  where 
  

   li 
  is 
  the 
  humidity 
  in 
  grams/m^. 
  The 
  constant 
  term 
  1200, 
  

   being 
  not 
  far 
  from 
  half 
  the 
  2500 
  to 
  3000 
  usually 
  found 
  for 
  

   the 
  Langevin 
  ion 
  in 
  ordinary 
  air, 
  shows 
  that 
  the 
  resistance 
  

   associated 
  with 
  N2S 
  is 
  about 
  equal 
  to 
  that 
  associated 
  with 
  N2, 
  

   a 
  result 
  which 
  necessitates 
  the 
  stipulation 
  above 
  that 
  the 
  mean 
  

   value 
  of 
  ^2 
  takes 
  the 
  form 
  E%,-f 
  H'N2. 
  Equation 
  (29) 
  

   shows 
  that 
  the 
  mobility 
  of 
  a 
  Langevin 
  ion 
  in 
  a 
  gas 
  should 
  be 
  

   inversely 
  proportional 
  to 
  the 
  density, 
  so 
  that 
  refined 
  observa- 
  

   tions 
  in 
  the 
  atmosphere 
  ought 
  to 
  be 
  reduced 
  to 
  values 
  for 
  

   standard 
  atmospheric 
  pressure. 
  But 
  the 
  most 
  striking 
  result 
  

   in 
  (29) 
  is 
  that 
  1/u 
  should 
  be 
  proportional 
  to 
  q^'^, 
  varying 
  

   rapidly 
  with 
  change 
  of 
  concentration 
  of 
  the 
  large 
  ions. 
  

   Moreover, 
  as 
  before 
  in 
  (27), 
  r^ 
  is 
  probably 
  proportional 
  to 
  

   1/(T 
  — 
  Tj), 
  so 
  that 
  (29) 
  gives 
  a 
  fairly 
  complicated 
  dependence 
  

   of 
  u 
  upon 
  the 
  natural 
  variables. 
  

  

  