﻿168 
  .Mr. 
  W. 
  Sutherland 
  on 
  Ionization, 
  

  

  This 
  introduces 
  some 
  interesting 
  considerations. 
  In 
  the 
  firs,t 
  

   place 
  it 
  shows 
  that 
  the 
  dielectric 
  capacity 
  of 
  each 
  electrolytic 
  

   solution 
  must 
  be 
  taken 
  into 
  account 
  in 
  a 
  complete 
  investiga- 
  

   tion 
  of 
  ionization. 
  It 
  should 
  be 
  noticed 
  that 
  t/D 
  is 
  pro- 
  

   portional 
  to 
  the 
  strength 
  of 
  the 
  solution. 
  The 
  dielectric 
  

   capacity 
  of 
  solutions 
  demands 
  special 
  investigation. 
  But 
  if 
  

   we 
  consider 
  only 
  solutions 
  so 
  dilute 
  that 
  t/D 
  may 
  be 
  neglected, 
  

   we 
  find 
  from 
  (9) 
  that 
  in 
  different 
  solvents 
  the 
  specific 
  velocity 
  

   of 
  a 
  given 
  ion 
  must 
  vary 
  as 
  K 
  /?7. 
  Now 
  Whetham 
  has 
  pointed 
  

   out 
  (Phil. 
  Mag. 
  [5] 
  xxxviii., 
  xliv.) 
  that 
  with 
  water, 
  methyl 
  

   alcohol, 
  and 
  ethyl 
  alcohol 
  as 
  solvents, 
  the 
  conductivities 
  for 
  a 
  

   given 
  electrolyte 
  are 
  approximately 
  as 
  K 
  /?;, 
  one 
  estimate 
  of 
  

   \?7/K 
  for 
  the 
  three 
  substances 
  in 
  an 
  arbitrary 
  unit 
  giving 
  the 
  

   relative 
  values 
  1, 
  0*9, 
  and 
  1*1, 
  and 
  another 
  giving 
  1, 
  1*2, 
  and 
  

   1*3, 
  the 
  conductivities 
  standing 
  in 
  the 
  ratios 
  of 
  1 
  to 
  *73 
  and 
  

   *34. 
  Whetham 
  considers 
  the 
  dielectric 
  capacity 
  of 
  the 
  solvent 
  

   to 
  have 
  most 
  bearing 
  on 
  its 
  ionizing 
  power, 
  in 
  accordance 
  

   with 
  the 
  suggestion 
  of 
  J. 
  J. 
  Thomson, 
  but 
  according 
  to 
  our 
  

   reasoning 
  the 
  effect 
  of 
  dielectric 
  capacity 
  on 
  ionization 
  is 
  

   secondary 
  to 
  its 
  immediate 
  effect 
  on 
  ionic 
  velocities. 
  But 
  

   Whetham's 
  results 
  verify 
  in 
  a 
  broad 
  way 
  our 
  equation 
  (9) 
  

   when 
  applied 
  to 
  very 
  dilute 
  solutions. 
  

  

  It 
  is 
  important 
  to 
  remark 
  that 
  this 
  equation 
  might 
  appear 
  

   to 
  violate 
  the 
  law 
  of 
  the 
  conservation 
  of 
  energy 
  by 
  seeming 
  

   to 
  make 
  the 
  work 
  done 
  in 
  carrying 
  a 
  charge 
  e 
  from 
  potential 
  

   Ei 
  to 
  E 
  2 
  in 
  a 
  very 
  dilute 
  solution 
  to 
  be 
  K^Ex— 
  E 
  2 
  )/K 
  

   instead 
  of 
  ^(Ej 
  — 
  E 
  2 
  ). 
  But 
  the 
  difficulty 
  disappears 
  if 
  energy 
  

   (K 
  /K 
  — 
  1)^(E 
  1 
  — 
  E 
  2 
  ) 
  is 
  assumed 
  to 
  be 
  taken 
  from 
  ihe 
  

   dielectric. 
  The 
  total 
  energy 
  ultimately 
  given 
  to 
  the 
  dielectric 
  

   is 
  e(E 
  l 
  — 
  E 
  2 
  ) 
  in 
  the 
  form 
  of 
  the 
  heat 
  generated 
  by 
  the 
  friction 
  

   of 
  the 
  ion 
  carrying 
  the 
  charge 
  e. 
  Evidently 
  the 
  dielectric 
  

   has 
  a 
  profound 
  role 
  to 
  play 
  in 
  ionic 
  matters. 
  It 
  should 
  be 
  

   noticed 
  that 
  the 
  introduction 
  of 
  K 
  the 
  dielectric 
  capacity 
  

   of 
  the 
  atom 
  into 
  the 
  expression 
  for 
  ionic 
  velocity 
  is 
  important, 
  

   and 
  is 
  to 
  be 
  returned 
  to 
  in 
  the 
  final 
  section. 
  

  

  From 
  equation 
  (9) 
  with 
  the 
  assumption 
  that 
  at 
  infinite 
  

   dilution 
  i 
  = 
  l 
  we 
  can 
  write 
  the 
  general 
  value 
  of 
  i 
  thus 
  : 
  — 
  

  

  i- 
  ^ 
  (l-a-K/K^/D-Cl-Ko/K^/D}. 
  . 
  (10 
  

  

  /V 
  oV 
  

  

  To 
  realize 
  the 
  order 
  of 
  magnitude 
  of 
  the 
  effect 
  of 
  dielectric 
  

   capacity 
  here, 
  let 
  us 
  consider 
  the 
  case 
  of 
  an 
  electrolytic 
  ion 
  

   having 
  the 
  same 
  volume 
  as 
  a 
  molecule 
  of 
  H 
  2 
  in 
  a 
  solution 
  

   containing 
  0*1 
  gramme-equivalent 
  of 
  it 
  per 
  litre, 
  then, 
  in 
  

   round 
  numbers, 
  we 
  can 
  say 
  that 
  we 
  have 
  10 
  4 
  /18 
  = 
  555 
  mole- 
  

   cules 
  of 
  H 
  2 
  to 
  each 
  ion, 
  so 
  t/D 
  = 
  1/555. 
  For 
  an 
  ordinary 
  

  

  