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  LVI. 
  The 
  Thomson 
  Effect 
  in 
  a 
  Binary 
  Electrolyte. 
  

   By 
  F. 
  G. 
  Donnan, 
  M.A., 
  Ph.D.* 
  

  

  THE 
  coefficient 
  a 
  in 
  the 
  equation 
  de=adt 
  for 
  an 
  unequally 
  

   heated 
  homogeneous 
  conductor 
  may 
  be 
  calculated 
  for 
  an 
  

   aqueous 
  solution 
  by 
  means 
  of 
  the 
  theory 
  of 
  electrolytic 
  con- 
  

   vection 
  developed 
  by 
  Nernst 
  and 
  Planck. 
  Although 
  the 
  

   expression 
  for 
  a 
  is 
  a 
  simple 
  deduction 
  from 
  this 
  theory, 
  the 
  

   calculation 
  has 
  not 
  yet 
  been 
  explicitly 
  made, 
  so 
  far 
  as 
  I 
  am 
  

   aware 
  ; 
  and 
  it 
  may 
  therefore 
  be 
  of 
  some 
  interest 
  to 
  examine 
  

   the 
  matter 
  somewhat 
  more 
  closely. 
  For 
  simplicity's 
  sake 
  we 
  

   shall 
  consider 
  a 
  binary 
  electrolyte, 
  the 
  valency 
  of 
  each 
  ion 
  

   being 
  a>. 
  

  

  Let 
  e 
  = 
  potential 
  of 
  the 
  free 
  electricity 
  in 
  the 
  system, 
  

  

  t 
  = 
  temperature 
  (absolute), 
  

  

  p 
  = 
  osmotic 
  pressure 
  due 
  to 
  positive 
  plus 
  negative 
  ions, 
  

  

  x= 
  distance 
  measured 
  in 
  direction 
  of 
  maximum 
  tem- 
  

   perature-gradient, 
  

  

  c 
  = 
  concentration 
  expressed 
  in 
  gram-molecules 
  of 
  salt 
  

   per 
  litre, 
  

  

  a 
  = 
  degree 
  of 
  electrolytic 
  dissociation. 
  

  

  The 
  flow 
  of 
  heat 
  is 
  supposed 
  to 
  be 
  rectilinear, 
  and 
  e, 
  x 
  y 
  

   and 
  p 
  are 
  measured 
  as 
  increasing 
  with 
  t, 
  i. 
  e. 
  from 
  cold 
  to 
  

   hot. 
  We 
  have 
  p 
  = 
  2acRt, 
  and 
  the 
  number 
  of 
  gram-ions 
  in 
  

   volume 
  element 
  dv 
  equal 
  to 
  2acdv 
  f 
  . 
  The 
  osmotic 
  force 
  on 
  

   the 
  ionized 
  matter 
  in 
  volume 
  element 
  in 
  the 
  positive 
  direction 
  

  

  of 
  «2? 
  is 
  f-dv. 
  Thus 
  the 
  osmotic 
  force 
  per 
  grani-ion 
  in 
  the 
  

  

  dx 
  . 
  1 
  dp 
  . 
  . 
  

  

  element 
  dv 
  is 
  — 
  ~ 
  — 
  • 
  -~. 
  The 
  electrical 
  force 
  in 
  the 
  same 
  

   "Lac 
  dx 
  7 
  

  

  direction 
  per 
  positive 
  gram-ion 
  is 
  —we 
  -7-, 
  where 
  e 
  is 
  the 
  

  

  quantity 
  of 
  electricity 
  associated 
  with 
  a 
  monovalent 
  gram- 
  ion. 
  

   Hence 
  we 
  obtain: 
  — 
  

  

  Total 
  force 
  per 
  gram-kation 
  = 
  — 
  ^ 
  7- 
  — 
  coe 
  -j-. 
  

  

  x 
  ° 
  lac 
  ax 
  ax 
  

  

  Total 
  force 
  per 
  gram- 
  anion 
  = 
  — 
  ~ 
  + 
  we 
  -*-. 
  

  

  lac 
  dx 
  dx 
  

  

  If 
  u 
  and 
  v 
  denote 
  the 
  velocities 
  acquired 
  by 
  the 
  kation 
  and 
  

   anion 
  respectively 
  under 
  unit 
  force, 
  then 
  the 
  number 
  of 
  gram- 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  t 
  Concentration-changes 
  due 
  to 
  expansion 
  of 
  the 
  solution 
  by 
  heat 
  are 
  

   neglected. 
  

  

  