﻿360 
  Dr. 
  S. 
  R. 
  Milner 
  on 
  tie 
  Efect 
  of 
  

  

  Part 
  III. 
  

  

  The 
  theorem 
  thus 
  proved 
  can 
  be 
  applied 
  to 
  throw 
  some 
  

   light 
  on 
  the 
  nature 
  of 
  the 
  interionic 
  forces 
  in 
  strong 
  electro- 
  

   lytes, 
  but 
  before 
  applying 
  it 
  it 
  is 
  necessary 
  to 
  identify 
  u 
  

   and 
  p 
  clearly 
  with 
  measured 
  physical 
  quantities. 
  As 
  regards 
  

   u 
  there 
  is 
  no 
  difficulty 
  : 
  it 
  represents 
  the 
  mobility 
  of 
  an 
  ion 
  

   in 
  a 
  region 
  where 
  it 
  is 
  free 
  from 
  interionic 
  force. 
  u 
  is 
  

   there 
  conditioned 
  only 
  b} 
  T 
  the 
  friction 
  of 
  the 
  water, 
  and 
  can 
  

   thus 
  be 
  identified 
  with 
  the 
  experimentally 
  determined 
  

   mobility 
  at 
  zero 
  concentration 
  to 
  which 
  the 
  same 
  condition 
  

   applies. 
  The 
  case 
  is 
  different 
  for 
  p 
  the 
  free 
  ionic 
  pressure. 
  

   In 
  what 
  relation 
  does 
  this 
  stand 
  to 
  the 
  measured 
  osmotic 
  

   pressure 
  ? 
  It 
  will 
  be 
  useful 
  to 
  consider 
  this 
  point 
  in 
  

   connexion 
  with 
  three 
  possible 
  theories 
  of 
  the 
  constitution 
  of 
  

   electrolytes. 
  

  

  (1) 
  In 
  the 
  original 
  theory 
  of 
  Arrhenius 
  electric 
  interionic 
  

   forces 
  are 
  neglected, 
  and 
  an 
  ion 
  is 
  assumed 
  to 
  be 
  definitely 
  

   either 
  associated 
  (when 
  it 
  contributes 
  nothing 
  to 
  the 
  free 
  

   ionic 
  pressure 
  p) 
  or 
  free. 
  Although 
  p 
  is 
  not 
  susceptible 
  

   to 
  direct 
  measurement, 
  a 
  clear 
  conception 
  of 
  it 
  can 
  

   be 
  got. 
  

  

  The 
  general 
  theorem 
  is 
  of 
  course 
  independent 
  of 
  the 
  law 
  

   of 
  force 
  between 
  the 
  ions 
  and 
  applies 
  to 
  this 
  theory 
  equally 
  

   with 
  others. 
  Interionic 
  forces 
  (of 
  the 
  kind 
  referred 
  to 
  

   below 
  as 
  u 
  chemical 
  " 
  forces) 
  produce 
  an 
  increase 
  in 
  the 
  

   frequency 
  of 
  occurrence 
  of 
  ions 
  in 
  an 
  associated 
  state 
  with 
  a 
  

   consequent 
  reduction 
  in 
  the 
  pressure 
  of 
  the 
  free 
  ions 
  in 
  the 
  

   ratio 
  of 
  1-/8:1. 
  The 
  average 
  mobility 
  of 
  an 
  ion, 
  taken 
  

   over 
  a 
  period 
  long 
  enough 
  to 
  include 
  its 
  being 
  combined 
  as 
  

   well 
  as 
  free, 
  is 
  reduced 
  in 
  the 
  same 
  ratio. 
  This 
  agrees 
  with 
  

   the 
  experimental 
  requirement 
  of 
  an 
  equality 
  in 
  the 
  freezing- 
  

   point 
  and 
  conductivity 
  variations, 
  for 
  in 
  calculating 
  the 
  

   complete 
  osmotic 
  pressure 
  P, 
  allowance 
  must 
  be 
  made 
  for 
  

   the 
  molecular 
  pressure 
  of 
  the 
  fraction 
  /3/2 
  of 
  associated 
  ions. 
  

  

  The 
  reduction 
  in 
  P 
  is 
  thus 
  in 
  the 
  ratio 
  11-/3+^) 
  : 
  1, 
  and 
  

   consequently 
  

  

  To 
  A 
  

  

  in 
  agreement 
  with 
  the 
  experimental 
  results 
  (v. 
  Part 
  I.). 
  

  

  The 
  difficulty 
  here, 
  as 
  already 
  mentioned, 
  is 
  the 
  failure 
  of 
  

   the 
  mass 
  action 
  law 
  (4) 
  to 
  represent 
  correctly 
  the 
  variation 
  

   of 
  /3. 
  When 
  we 
  consider 
  the 
  dynamical 
  assumptions 
  on 
  

   which 
  (4) 
  is 
  based, 
  we 
  find 
  it 
  essential 
  that 
  the 
  forces 
  which 
  

   tend 
  to 
  produce 
  association 
  of 
  the 
  ions 
  must 
  fall 
  off 
  very 
  

  

  