﻿Thomson 
  Effect 
  in 
  a 
  Binary 
  Electrolyte. 
  531 
  

  

  If 
  — 
  be 
  small, 
  or 
  if 
  the 
  salt 
  be 
  completely 
  dissociated, 
  

   equation 
  (iv 
  ) 
  reduces 
  to 
  the 
  simple 
  form 
  

  

  <r=^(l-2») 
  (v.) 
  

  

  0)6 
  

  

  From 
  (v.) 
  we 
  see 
  that 
  the 
  electrolyte 
  will 
  have 
  a 
  positive 
  

   or 
  negative 
  " 
  specific 
  heat 
  of 
  electricity" 
  according 
  as 
  v 
  is 
  > 
  

   or 
  < 
  it, 
  i. 
  e. 
  as 
  n 
  < 
  or 
  >-^. 
  

  

  It 
  is 
  also 
  evident 
  from 
  (v.) 
  that 
  in 
  a 
  completely 
  dissociated 
  

   binary 
  electrolyte 
  the 
  Thomson 
  effect 
  will 
  be 
  independent 
  of 
  

   the 
  concentration, 
  as 
  Nernst 
  has 
  already 
  pointed 
  out. 
  As 
  a 
  

   matter 
  of 
  fact, 
  it 
  is 
  only 
  possible 
  to 
  speak 
  of 
  an 
  initial 
  Thomson 
  

   effect 
  ; 
  and 
  in 
  this 
  sense 
  the 
  foregoing 
  expressions 
  are 
  to 
  be 
  

   taken. 
  For 
  diffusion 
  sets 
  in 
  at 
  once 
  in 
  the 
  unequally 
  heated 
  

   solution, 
  and 
  the 
  conductor 
  thus 
  ceases 
  to 
  be 
  homogeneous. 
  

   The 
  result 
  will 
  be 
  that 
  the 
  P.D. 
  between 
  the 
  ends 
  of 
  the 
  

   unequally 
  heated 
  conductor 
  will 
  gradually 
  decrease, 
  becoming 
  

   zero 
  when 
  diffusion- 
  equilibrium 
  is 
  attained 
  if 
  the 
  electrolyte 
  

   be 
  completely 
  dissociated. 
  

  

  For 
  a 
  completely 
  dissociated 
  electrolyte 
  ^? 
  = 
  2cR£ 
  ; 
  and 
  

   therefore 
  

  

  "Lac 
  C 
  

  

  Accordingly, 
  integrating 
  from 
  t 
  x 
  to 
  t 
  2 
  , 
  we 
  obtain 
  

  

  R, 
  C^v 
  — 
  u 
  , 
  R 
  f^v 
  — 
  ut 
  7 
  

  

  eg 
  = 
  — 
  1 
  at 
  + 
  • 
  — 
  1 
  etc, 
  

  

  coe]. 
  v 
  + 
  u 
  coel, 
  v 
  + 
  uc 
  

  

  as 
  the 
  expression 
  for 
  the 
  total 
  P.D. 
  at 
  any 
  time 
  6, 
  and 
  for 
  its 
  

   rate 
  of 
  change 
  

  

  \eWJe 
  (oeJ 
  f) 
  v 
  + 
  u^d\ 
  ^ 
  ' 
  ' 
  

   where 
  c 
  = 
  -^r(^, 
  0), 
  with 
  the 
  conditions 
  that 
  -fy= 
  const. 
  = 
  c 
  for 
  

   0=0, 
  and 
  ^= 
  — 
  — 
  : 
  for 
  0=co 
  . 
  

  

  In 
  order 
  to 
  calculate 
  the 
  initial 
  Thomson 
  effect, 
  

  

  ■=|f 
  (1 
  - 
  2w),ff 
  ' 
  

  

  it 
  would 
  be 
  necessary 
  to 
  know 
  what 
  function 
  (1 
  — 
  2n) 
  is 
  of 
  the 
  

   temperature. 
  It 
  is 
  known, 
  however, 
  that 
  n 
  approaches 
  the 
  

   value 
  *5 
  as 
  the 
  temperature 
  increases, 
  so 
  that 
  the 
  numerical 
  

  

  