﻿Interionic 
  Force 
  in 
  Electrolytes. 
  357 
  

  

  molecule 
  when 
  in 
  a 
  certain 
  region 
  R 
  is 
  <f> 
  (a 
  negative 
  

   quantity) 
  and 
  zero 
  elsewhere. 
  The 
  distribution 
  will 
  be 
  such 
  

   that 
  the 
  chance 
  of 
  a 
  molecule 
  occupying 
  a 
  position 
  inside 
  R 
  is 
  

   to 
  that 
  of 
  its 
  occupying 
  one 
  outside 
  as 
  e~® 
  : 
  1, 
  and, 
  in 
  fact, 
  

   the 
  densities 
  in 
  the 
  two 
  parts 
  will 
  adjust 
  themselves 
  in 
  this 
  

   proportion. 
  If 
  we 
  imagine 
  a 
  unit 
  plane 
  situated 
  inside 
  R, 
  

   the 
  momentum 
  transferred 
  through 
  it 
  per 
  second 
  will 
  be 
  the 
  

   total 
  pressure 
  inside 
  R, 
  but 
  it 
  is 
  only 
  a 
  certain 
  fraction 
  — 
  

   e 
  +(t>kT 
  — 
  Q 
  £ 
  ^ 
  e 
  mo 
  i 
  ecu 
  i 
  es 
  passing 
  through 
  the 
  plane 
  which 
  

   are 
  capable 
  of 
  transferring 
  their 
  momentum 
  outside 
  the 
  

   region. 
  We 
  can 
  thus 
  divide 
  the 
  pressure 
  in 
  R 
  into 
  two 
  

   parts 
  — 
  the 
  external 
  pressure, 
  which 
  is 
  due 
  to 
  momentum 
  

   capable 
  of 
  being 
  transferred 
  outside 
  it, 
  and 
  which 
  is, 
  in 
  fact, 
  

   in 
  equilibrium 
  with 
  the 
  pressure 
  outside, 
  and 
  the 
  internal 
  

   pressure, 
  which 
  in 
  this 
  case 
  will 
  be 
  exerted 
  on 
  the 
  mechanical 
  

   constraints 
  which 
  cause 
  the 
  increased 
  density 
  in 
  R. 
  

  

  A 
  similar 
  state 
  of 
  things 
  occurs 
  when 
  we 
  deal 
  with 
  a 
  group 
  

   of 
  ions 
  existing 
  momentarily 
  in 
  a 
  liquid. 
  The 
  whole 
  

   momentum 
  passed 
  per 
  second 
  by 
  the 
  ions 
  of 
  the 
  group 
  

   through 
  a 
  unit 
  area 
  drawn 
  in 
  the 
  interior 
  of 
  the 
  group 
  will 
  

   not 
  be 
  delivered 
  to 
  places 
  of 
  zero 
  potential 
  energy, 
  and 
  the 
  

   fraction 
  of 
  it 
  that 
  is 
  so 
  delivered 
  will 
  be 
  in 
  statistical 
  

   equilibrium 
  with 
  the 
  pressure 
  exerted 
  by 
  those 
  ions 
  which 
  

   are 
  in 
  positions 
  of 
  zero 
  energy. 
  We 
  may 
  call 
  this 
  fraction 
  

   the 
  external 
  pressure 
  p 
  of 
  the 
  ions 
  in 
  the 
  group 
  or 
  the 
  

   pressure 
  of 
  the 
  " 
  free 
  " 
  ions 
  — 
  understanding 
  by 
  free 
  ions 
  

   those 
  which 
  momentarily 
  have 
  no 
  mutual 
  energy 
  with 
  any 
  

   others. 
  Let 
  us 
  inquire 
  how 
  much 
  of 
  the 
  momentum 
  of 
  an 
  

   ion 
  existing 
  in 
  a 
  group 
  such 
  as 
  that 
  considered 
  above 
  would, 
  

   on 
  the 
  average, 
  be 
  capable 
  of 
  being 
  transferred 
  to 
  a 
  place 
  of 
  

   zero 
  potential. 
  

  

  Consider 
  a 
  single 
  ion 
  of 
  mass 
  m 
  moving 
  in 
  a 
  random 
  

   direction 
  with 
  velocity 
  v. 
  The 
  average 
  rate 
  at 
  which 
  it 
  

   transfers, 
  parallel 
  to 
  a 
  given 
  direction, 
  the 
  component 
  in 
  

   that 
  direction 
  of 
  its 
  momentum 
  is 
  Jmv 
  2 
  , 
  or, 
  if 
  we 
  take 
  into 
  

   the 
  average 
  all 
  the 
  possible 
  velocities 
  which 
  it 
  may 
  have, 
  

   jmt) 
  2 
  or 
  JcT. 
  The 
  sum 
  of 
  this 
  quantity 
  for 
  every 
  ion 
  in 
  the 
  

   mixture 
  gives 
  the 
  total 
  (i. 
  e. 
  internal 
  + 
  external) 
  pressure 
  

   x 
  volume, 
  PV, 
  of 
  the 
  electrolyte. 
  The 
  contribution 
  of 
  each 
  

   ion 
  to 
  the 
  total 
  PV 
  is 
  thus 
  a 
  scalar 
  quantity 
  ^mv 
  2 
  associated 
  

   with 
  the 
  ion 
  — 
  these 
  contributions 
  will 
  therefore 
  obey 
  the 
  

   same 
  law 
  of 
  distribution 
  as 
  do 
  the 
  ions 
  themselves. 
  

  

  Consider 
  now 
  two 
  configurations 
  P 
  and 
  P' 
  of 
  the 
  group 
  

   of 
  m 
  ions 
  dealt 
  with 
  above. 
  In 
  P 
  the 
  ions 
  occupy 
  the 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  208. 
  April 
  1918. 
  2 
  C 
  

  

  