﻿tlie 
  Ions 
  of 
  Gases, 
  

  

  363 
  

  

  small 
  ion 
  in 
  <a 
  moist 
  gas 
  tends 
  to 
  attach 
  molecules 
  of 
  H2O 
  to 
  

   itself 
  as 
  satellites 
  and 
  to 
  surround 
  itself 
  with 
  an 
  envelope 
  of 
  

   vapour 
  of 
  H^O. 
  To 
  such 
  an 
  ion 
  we 
  shall 
  now 
  apply 
  equations 
  

   (11) 
  with 
  the 
  supposition 
  that 
  6u 
  can 
  be 
  neglected 
  and 
  also 
  

   Yu 
  as 
  a 
  separate 
  term, 
  though 
  F?f, 
  as 
  the 
  cause 
  of 
  ??/, 
  will 
  be 
  

   investigated 
  immediately. 
  

  

  In 
  large 
  ions 
  it 
  has 
  been 
  found 
  that 
  u^=- 
  —Ui=- 
  — 
  w, 
  so 
  that 
  

   the 
  two 
  equations 
  reduce 
  to 
  

  

  da 
  

  

  = 
  2Kuq- 
  

  

  -1/3 
  

  

  (25) 
  

  

  ? 
  is 
  proportional 
  to 
  q, 
  so 
  that 
  when 
  d'E/da; 
  = 
  volt/cm., 
  the 
  

   last 
  equation 
  makes 
  uq-^ 
  constant 
  for 
  different 
  values 
  of 
  q 
  at 
  

   a 
  given 
  temperature. 
  This 
  is 
  the 
  result 
  discovered 
  by 
  Moreau 
  

   in 
  his 
  experiments 
  on 
  the 
  cooled 
  gases 
  of 
  flames 
  sprayed 
  with 
  

   electrolytic 
  solutions 
  [Ann. 
  de 
  Ch. 
  et 
  de 
  Ph. 
  [8] 
  viii. 
  1906, 
  

   p. 
  201, 
  Compt. 
  Rend, 
  cxli. 
  1905, 
  p. 
  1225). 
  He 
  found 
  that 
  

   in 
  the 
  cooled 
  gases 
  the 
  number 
  of 
  ions 
  per 
  cm.^ 
  varies 
  as 
  the 
  

   square 
  root 
  of 
  the 
  concentration 
  of 
  the 
  electrolyte 
  in 
  the 
  

   solution, 
  in 
  agreement 
  with 
  the 
  law 
  of 
  Arrhenius 
  for 
  uncooled 
  

   gases 
  of 
  flames 
  at 
  ordinary 
  flame 
  temperatures. 
  H. 
  A. 
  Wilson 
  

   has 
  pushed 
  the 
  temperature 
  up 
  till 
  the 
  ionic 
  dissociation 
  in 
  

   gases 
  sprayed 
  with 
  electrolyte 
  is 
  complete. 
  

  

  If 
  in 
  Moreau's 
  experiments 
  we 
  denote 
  the 
  concentration 
  of 
  

   the 
  sprayed 
  electrolytic 
  solution 
  by 
  n, 
  we 
  have 
  q 
  cc 
  n}i'^ 
  and 
  

   so 
  from 
  (25) 
  we 
  get 
  un^'^ 
  constant 
  at 
  a 
  given 
  temperature. 
  

   He 
  found 
  Wi= 
  — 
  ^2 
  ^^d 
  q 
  of 
  the 
  order 
  10^. 
  We 
  shall 
  take 
  

   his 
  results 
  with 
  solutions 
  of 
  KCl 
  as 
  typical, 
  their 
  strengths 
  

   being 
  normal 
  X, 
  N/I, 
  and 
  N/16, 
  which 
  we 
  shall 
  express 
  by 
  

   putting 
  71 
  = 
  1, 
  l/I, 
  and 
  1/J6, 
  giving 
  his 
  values 
  of 
  u 
  in 
  

   cm./sec. 
  for 
  ^E/VZ.i" 
  = 
  volty^cm. 
  

  

  Table 
  IY. 
  

  

  Temp. 
  C. 
  170° 
  110° 
  

  

  100° 
  

  

  70° 
  

  

  30° 
  

  

  15° 
  

  

  100m 
  100«7«1/3 
  lOOi^ 
  100mw1/3 
  

  

  100?^ 
  lOOMni/3 
  

  

  lOOi* 
  lOOimV^ 
  

  

  lOOw 
  100w?ii/3 
  

  

  100?* 
  100?«ii/3 
  

  

  «=l 
  39 
  39 
  16 
  16 
  1 
  16 
  16 
  

  

  10 
  10 
  

  

  4-5 
  4-5 
  

  

  1-5 
  ]-5 
  

  

  «=l/4 
  65 
  41 
  27 
  17 
  i 
  24 
  15 
  

  

  15 
  9-4 
  

  

  — 
  — 
  

  

  2-4 
  1-5 
  

  

  n=l/16 
  90 
  36 
  47 
  19 
  40 
  16 
  24 
  9-5 
  

  

  1 
  

  

  7-2 
  2-9 
  

  

  5-1 
  20 
  

  

  The 
  departures 
  from 
  constancy 
  in 
  un^'^ 
  are 
  irregular. 
  

   Moreau 
  sought 
  to 
  give 
  a 
  different 
  explanation 
  for 
  the 
  origin 
  

   of 
  the 
  constancy 
  of 
  un^^ 
  in 
  his 
  various 
  solutions. 
  

  

  