﻿362 
  Dr. 
  S. 
  B, 
  Milner 
  on 
  the 
  Effect 
  of 
  

  

  between 
  the 
  freezing-point 
  and 
  conductivity 
  variations 
  will 
  

   result 
  from 
  the 
  proposition. 
  For 
  if 
  /3 
  is 
  the 
  fractional 
  

   alteration 
  of 
  pV 
  , 
  and 
  therefore 
  of 
  u, 
  and 
  if 
  further 
  p 
  = 
  P, 
  

   we 
  shall 
  get 
  

  

  t_PV_ 
  p 
  V_ 
  X. 
  

  

  7 
  -RT-Rf- 
  2(1 
  «' 
  T^- 
  1 
  -* 
  3 
  ' 
  

  

  which 
  is 
  in 
  conflict 
  with 
  the 
  experimental 
  result 
  (3) 
  

   (Part 
  I.). 
  

  

  p 
  and 
  P, 
  however, 
  cannot 
  be 
  the 
  same, 
  as 
  is 
  evident 
  from 
  

   the 
  following 
  consideration 
  : 
  — 
  Consider 
  a 
  pair 
  of 
  ions 
  which 
  

   happen 
  to 
  be 
  fairly 
  close 
  together 
  and 
  under 
  the 
  influence 
  

   of 
  each 
  other's 
  attraction, 
  and 
  let 
  a 
  number 
  of 
  representative 
  

   views 
  be 
  taken. 
  In 
  a 
  certain 
  fraction 
  — 
  e^ 
  — 
  of 
  the 
  cases 
  

   the 
  ions 
  contribute 
  to 
  the 
  free 
  ionic 
  jt?Y, 
  in 
  the 
  remainder 
  of 
  

   the 
  cases 
  the 
  ions 
  act 
  as 
  though 
  bound 
  together 
  and 
  contribute 
  

   nothing 
  to 
  pY, 
  but 
  in 
  these 
  cases 
  the 
  pair 
  will 
  make 
  to 
  the 
  

   measured 
  PY 
  exactly 
  the 
  same 
  contribution 
  as 
  if 
  the 
  ions 
  

   formed 
  an 
  actual 
  molecule. 
  The 
  effect 
  of 
  electrical 
  forces 
  is 
  

   in 
  this 
  respect 
  exactly 
  similar 
  to 
  that 
  produced 
  by 
  chemical 
  

   association. 
  The 
  electrical 
  bond 
  it 
  is 
  true 
  persists 
  when 
  the 
  

   ions 
  are 
  well 
  separated 
  from 
  each 
  other, 
  while 
  the 
  chemical 
  

   bond 
  acts 
  only 
  at 
  very 
  small 
  distances, 
  but 
  this 
  difference 
  is 
  

   immaterial 
  in 
  considering 
  the 
  molecular 
  pressure 
  which 
  a 
  

   pair 
  of 
  bound 
  ions 
  will 
  exert. 
  For 
  the 
  type 
  of 
  force 
  con- 
  

   sidered, 
  however, 
  the 
  bonds 
  are 
  not 
  confined 
  to 
  single 
  pairs 
  

   of 
  ions, 
  but 
  each 
  pair 
  must 
  be 
  considered 
  as 
  forming 
  part 
  of 
  

   a 
  large 
  group, 
  with 
  the 
  rest 
  of 
  the 
  ions 
  in 
  which 
  it 
  possesses 
  

   a 
  certain 
  mutual 
  energy, 
  and 
  so 
  is 
  not 
  free 
  to 
  exercise 
  its 
  

   full 
  molecular 
  pressure. 
  While 
  a 
  difference 
  between 
  p 
  and 
  

   P 
  may 
  on 
  these 
  lines 
  be 
  inferred 
  to 
  exist, 
  it 
  is 
  difficult 
  to 
  

   settle 
  exactly 
  what 
  it 
  is 
  *. 
  It 
  seems 
  doubtful 
  that 
  it 
  would 
  

   be 
  such 
  as 
  to 
  give 
  the 
  exact 
  equality 
  between 
  & 
  and 
  /3 
  2 
  

   which 
  experiment 
  suggests 
  unless 
  the 
  mutual 
  energy 
  between 
  

   each 
  pair 
  and 
  the 
  rest 
  of 
  the 
  group 
  is 
  negligible. 
  

  

  (3) 
  A 
  theory 
  which 
  is 
  to 
  some 
  extent 
  intermediate 
  

   between 
  (1) 
  and 
  (2) 
  has 
  much 
  to 
  recommend 
  it. 
  We 
  must 
  

   infer 
  from 
  the 
  preceding 
  comparisons 
  that 
  the 
  interionic 
  

   forces 
  must 
  extend 
  over 
  considerable 
  distances, 
  as 
  it 
  is 
  only 
  

  

  * 
  The 
  straightforward 
  way 
  to 
  settle 
  this 
  point 
  is 
  to 
  calculate 
  p 
  by 
  a 
  

   method 
  in 
  accordance 
  with 
  its 
  definition 
  on 
  p. 
  357 
  and 
  compare 
  it 
  with 
  P. 
  

   The 
  calculation 
  can 
  be 
  carried 
  out 
  strictly 
  by 
  exactly 
  the 
  same 
  method 
  

   as 
  that 
  by 
  which 
  P 
  was 
  originally 
  determined 
  (loc. 
  cit.). 
  It 
  has 
  been 
  

   done, 
  but 
  unfortunately 
  the 
  numerical 
  results 
  in 
  both 
  cases 
  can 
  only 
  be 
  

   obtained 
  in 
  an 
  approximate 
  form 
  which 
  is 
  not 
  sufficiently 
  accurate 
  to 
  

   determine 
  definitely 
  what 
  is 
  the 
  difference 
  between 
  them. 
  

  

  