﻿354 
  Dr. 
  S. 
  R. 
  Milner 
  on 
  the 
  Effect 
  oj 
  

  

  that, 
  if 
  the 
  distribution 
  is 
  to 
  remain 
  permanent 
  when 
  the 
  

   electrolyte 
  is 
  carrying 
  a 
  current, 
  the 
  velocity 
  with 
  which 
  

   each 
  ion 
  must 
  be 
  supposed 
  to 
  move 
  under 
  the 
  influence 
  of 
  

   the 
  applied 
  electric 
  field 
  must 
  be 
  a 
  function 
  at 
  each 
  instant 
  

   of 
  the 
  mutual 
  potential 
  energy 
  which 
  the 
  ion 
  possesses 
  with 
  

   the 
  others. 
  

  

  The 
  way 
  in 
  which 
  the 
  random 
  distribution 
  will 
  be 
  modified 
  

   when 
  the 
  ions 
  are 
  subject 
  to 
  interionic 
  force 
  is 
  given 
  by 
  a 
  

   theorem 
  due 
  to 
  Boltzmann. 
  Let 
  us 
  suppose 
  that 
  we 
  take 
  

   a 
  large 
  number 
  of 
  instantaneous 
  views 
  of 
  a 
  certain 
  region 
  

   of 
  the 
  liquid, 
  and 
  that 
  in 
  each 
  view 
  we 
  observe 
  the 
  positions 
  

   and 
  signs 
  of 
  all 
  the 
  ions 
  which 
  are 
  present 
  in 
  it. 
  We 
  

   will 
  confine 
  our 
  attention 
  in 
  the 
  first 
  place 
  to 
  those 
  views 
  

   alone, 
  n 
  in 
  number, 
  in 
  which 
  the 
  region 
  contains 
  m 
  ions, 
  

   Aj.^Am, 
  and 
  no 
  more, 
  and 
  we 
  will 
  suppose 
  that 
  these 
  are 
  

   all 
  so 
  far 
  away 
  from 
  the 
  ions 
  outside 
  the 
  region 
  that 
  the 
  

   forces 
  between 
  the 
  ions 
  inside 
  and 
  outside 
  are 
  negligible. 
  

   This 
  will 
  simplify 
  the 
  statement 
  of 
  the 
  argument 
  without 
  

   affecting 
  the 
  generality 
  of 
  it 
  in 
  any 
  way, 
  since 
  the 
  region 
  

   may, 
  if 
  necessary, 
  comprise 
  the 
  whole 
  of 
  the 
  liquid. 
  In 
  a 
  

   certain 
  number, 
  say 
  v, 
  of 
  the 
  n 
  views, 
  the 
  m 
  ions 
  will 
  be 
  

   found 
  in 
  small 
  equal 
  volumes 
  dv 
  l 
  ...dv 
  m 
  , 
  situated 
  at 
  the 
  

   points 
  P!...P 
  TO 
  . 
  For 
  shortness 
  we 
  will 
  call 
  this 
  the 
  P 
  confi- 
  

   guration, 
  and 
  speak 
  of 
  the 
  ion 
  A! 
  as 
  " 
  occupying 
  the 
  position 
  " 
  

   P 
  x 
  , 
  the 
  uniform 
  size 
  of 
  the 
  elementary 
  volumes 
  being 
  under- 
  

   stood. 
  In 
  another 
  number 
  v' 
  of 
  views 
  the 
  ions 
  will 
  be 
  found 
  

   in 
  positions 
  P/. 
  . 
  .P 
  m 
  ' 
  (P' 
  configuration). 
  On 
  a 
  purely 
  random 
  

   distribution 
  we 
  should 
  have 
  

  

  v=v', 
  

  

  but 
  in 
  the 
  modification 
  caused 
  by 
  the 
  presence 
  of 
  interionic 
  

   force, 
  

  

  FsrJ 
  ^-»-«W* 
  . 
  . 
  . 
  , 
  (5) 
  

  

  v/v' 
  here 
  stands 
  for 
  the 
  probability 
  of 
  the 
  P 
  configuration 
  

   relative 
  to 
  that 
  of 
  the 
  P'. 
  <£ 
  and 
  <j)' 
  are 
  the 
  respective 
  

   mutual 
  potential 
  energies 
  of 
  the 
  ions 
  in 
  each 
  configuration, 
  

   i. 
  e. 
  the 
  work 
  done 
  by 
  the 
  system 
  when 
  the 
  ions 
  are 
  moved 
  

   to 
  infinite 
  distances 
  apart. 
  When 
  the 
  forces 
  are 
  attractive 
  

   <f> 
  and 
  (j> 
  f 
  are 
  negative 
  quantities. 
  kT 
  = 
  § 
  X 
  average 
  translatory 
  

   kinetic 
  energy 
  of 
  an 
  ion. 
  

  

  Equation 
  (5) 
  can 
  easily 
  be 
  transformed 
  so 
  as 
  to 
  represent 
  

   the 
  absolute 
  probability 
  of 
  a 
  given 
  configuration 
  (estimated 
  

   under 
  the 
  special 
  conditions 
  attached 
  to 
  the 
  total 
  number 
  of 
  

   views 
  n) 
  by 
  writing 
  it 
  in 
  the 
  form 
  

  

  v=Kne-* 
  /kT 
  dv 
  v 
  .Jv 
  m 
  (6) 
  

  

  