﻿Interionic 
  Force 
  in 
  Electrolytes. 
  355 
  

  

  The 
  essential 
  feature 
  of 
  the 
  ionic 
  distribution 
  represented 
  

   by 
  (6) 
  is 
  of 
  course 
  its 
  permanence, 
  that 
  is, 
  that 
  it 
  is 
  un- 
  

   disturbed 
  by 
  the 
  thermal 
  motions 
  of 
  the 
  ions. 
  Let 
  us 
  suppose 
  

   that 
  the 
  n 
  views 
  were 
  taken 
  at 
  certain 
  times 
  #!....£». 
  If 
  we 
  

   were 
  to 
  take 
  another 
  set 
  of 
  views 
  at 
  times 
  ti 
  + 
  T,....t 
  n 
  |-t, 
  

   where 
  r 
  is 
  a 
  very 
  small 
  time, 
  we 
  should 
  find 
  the 
  same 
  number 
  

   of 
  views 
  in 
  which 
  the 
  ions 
  have 
  the 
  configuration 
  P 
  ; 
  the 
  

   actual 
  views 
  will 
  not 
  be 
  identical 
  in 
  the 
  two 
  cases, 
  in 
  some 
  

   of 
  the 
  n 
  views 
  at 
  t 
  the 
  ions 
  will 
  have 
  left 
  the 
  volumes 
  dv, 
  

   but 
  in 
  an 
  equal 
  number 
  of 
  other 
  cases 
  ions 
  will 
  have 
  come 
  

   into 
  them. 
  

  

  Now 
  suppose 
  that 
  the 
  electrolyte 
  is 
  under 
  the 
  influence 
  of 
  

   an 
  external 
  electric 
  field 
  when 
  these 
  two 
  sets 
  of 
  views 
  are 
  

   being 
  taken. 
  In 
  addition 
  to 
  the 
  thermal 
  displacement 
  

   which 
  each 
  ion 
  undergoes 
  in 
  each 
  of 
  the 
  times 
  t, 
  it 
  will 
  be 
  

   dragged 
  by 
  the 
  electric 
  field 
  a 
  certain 
  distance 
  to 
  the 
  right 
  

   or 
  left. 
  We 
  can 
  effect 
  a 
  considerable 
  simplification 
  by 
  

   observing 
  that, 
  since 
  the 
  thermal 
  displacements 
  do 
  not 
  affect 
  

   the 
  distribution, 
  we 
  can 
  imagine 
  them 
  to 
  be 
  non-existent 
  

   without 
  affecting 
  in 
  any 
  way 
  the 
  result 
  of 
  reasoning- 
  con- 
  

   cerning 
  the 
  effect 
  on 
  the 
  distribution 
  of 
  the 
  displacements 
  

   due 
  to 
  the 
  electric 
  field. 
  With 
  this 
  simplification 
  the 
  

   problem 
  to 
  be 
  solved 
  becomes 
  this 
  : 
  — 
  A 
  set 
  of 
  views 
  at 
  times 
  

   ti,...t 
  n 
  , 
  and 
  another 
  set 
  at 
  £i 
  + 
  t,..A 
  + 
  t, 
  being 
  taken 
  of 
  a 
  

   system 
  of 
  ions 
  existing 
  in 
  configurations 
  the 
  probability 
  of 
  

   which 
  is 
  given 
  by 
  (6) 
  and 
  at 
  rest 
  during 
  the 
  intervals 
  r 
  so 
  

   far 
  as 
  thermal 
  motions 
  are 
  concerned, 
  but 
  in 
  which 
  each 
  ion 
  

   is 
  dragged 
  during 
  the 
  intervals 
  by 
  an 
  external 
  force 
  to 
  right 
  

   or 
  left 
  according 
  as 
  it 
  is 
  positive 
  or 
  negative, 
  what 
  is 
  the 
  

   average 
  velocity 
  with 
  which 
  an 
  ion 
  such 
  as 
  A 
  x 
  in 
  a 
  given 
  

   position 
  must 
  move 
  in 
  order 
  that 
  the 
  distribution 
  may 
  not 
  

   be 
  disturbed 
  ? 
  By 
  the 
  average 
  velocity 
  is 
  meant 
  the 
  average 
  

   for 
  all 
  the 
  views 
  which 
  show 
  the 
  ion 
  in 
  the 
  given 
  position, 
  

   but 
  as 
  it 
  makes 
  no 
  difference 
  whether 
  it 
  varies 
  from 
  view 
  to 
  

   view 
  or 
  is 
  uniform, 
  we 
  may 
  in 
  the 
  calculation 
  treat 
  it 
  as 
  

   uniform. 
  

  

  Let 
  w 
  x 
  , 
  . 
  . 
  ,u 
  m 
  be 
  the 
  velocities 
  of 
  each 
  ion 
  A 
  lv 
  . 
  . 
  A 
  m 
  . 
  Describe 
  

   small 
  cylinders 
  of 
  area 
  a 
  and 
  of 
  arbitrary 
  lengths 
  d% 
  1} 
  ...da 
  m 
  

   near 
  each 
  of 
  the 
  points 
  P 
  lv 
  ..P 
  TO 
  to 
  the 
  right 
  or 
  left 
  of 
  the 
  

   points 
  according 
  to 
  the 
  sign 
  of 
  the 
  ion. 
  The 
  number 
  of 
  

   cases 
  in 
  which 
  an 
  ion 
  is 
  to 
  be 
  found 
  in 
  each 
  of 
  these 
  cylinders 
  

   will 
  be 
  the 
  same 
  in 
  the 
  views 
  at 
  t 
  + 
  r 
  as 
  it 
  is 
  in 
  the 
  views 
  at 
  t. 
  

   Consequently 
  the 
  number 
  v 
  l 
  of 
  views 
  in 
  which 
  an 
  ion 
  

   will 
  enter 
  each 
  cylinder 
  during 
  the 
  intervals 
  t 
  is 
  the 
  same 
  

   as 
  the 
  number 
  v 
  2 
  in 
  which 
  an 
  ion 
  will 
  leave 
  each 
  cylinder. 
  

   But 
  vi 
  comprises 
  all 
  those 
  views 
  in 
  which 
  the 
  m 
  ions 
  are 
  

  

  