﻿Theory 
  of 
  the 
  Thermoelectric 
  Forces, 
  

  

  771 
  

  

  keep 
  the 
  corpuscles 
  from 
  drifting 
  under 
  the 
  pressure 
  dif- 
  

   ferences. 
  Let 
  us 
  now 
  suppose 
  that 
  the 
  number 
  of 
  corpuscles 
  

   per 
  unit 
  volume 
  depends 
  on 
  the 
  temperature, 
  so 
  that 
  at 
  

   100° 
  C. 
  one 
  c.cm. 
  contains 
  a 
  larger 
  number 
  of 
  these 
  particles 
  

   than 
  one 
  c.cm. 
  at 
  0° 
  C. 
  

  

  Let 
  the 
  temperature 
  increase 
  from 
  A 
  to 
  B. 
  If 
  we 
  consider 
  

   in 
  a 
  distance 
  x 
  from 
  A 
  a 
  cross-section 
  of 
  unit 
  surface, 
  a 
  

   larger 
  number 
  of 
  corpuscles 
  will 
  drift 
  in 
  unit 
  time 
  from 
  

  

  Fior. 
  1. 
  

  

  too 
  

  

  

  + 
  x 
  

  

  T 
  / 
  rj 
  AV 
  T 
  * 
  N 
  2 
  V, 
  

  

  right 
  to 
  left 
  than 
  in 
  the 
  opposite 
  direction. 
  An 
  accumu- 
  

   lation 
  of 
  negative 
  charges 
  will 
  take 
  place 
  in 
  A 
  at 
  the 
  colder 
  

   end 
  of 
  the 
  bar 
  and 
  of 
  positive 
  charges 
  at 
  the 
  hotter 
  end 
  B. 
  

   These 
  charges 
  produce 
  a 
  certain 
  electromotive 
  force 
  X 
  at 
  a 
  

   point 
  distant 
  x 
  from 
  A, 
  tending 
  to 
  move 
  the 
  corpuscles 
  from 
  

   A 
  to 
  B. 
  The 
  attraction 
  of 
  the 
  positive 
  electricity 
  in 
  B 
  will 
  

   tend 
  to 
  prevent 
  the 
  corpuscles 
  escaping 
  from 
  it, 
  and 
  the 
  flow 
  

   will 
  cease 
  when 
  the 
  attraction 
  of 
  the 
  positive 
  electricity 
  in 
  B 
  

   and 
  the 
  repulsion 
  of 
  the 
  negative 
  in 
  A 
  just 
  balance 
  the 
  effect 
  

   of 
  the 
  difference 
  in 
  the 
  number 
  of 
  corpuscles 
  per 
  unit 
  volume 
  

   due 
  to 
  the 
  difference 
  of 
  the 
  temperature. 
  The 
  same 
  con- 
  

   siderations 
  as 
  in 
  the 
  first 
  paragraph, 
  applied 
  to 
  this 
  case, 
  

   lead 
  to 
  the 
  expression 
  of 
  the 
  electric 
  force 
  X 
  

  

  3 
  e 
  ~§x 
  

  

  N 
  is 
  the 
  number 
  of 
  corpuscles 
  in 
  unit 
  volume 
  at 
  #, 
  and 
  T 
  

   the 
  corresponding 
  temperature, 
  thus 
  

  

  v.-v 
  s 
  

  

  4 
  ?f 
  2 
  T 
  

  

  aiogN 
  

  

  ~dx 
  

  

  dx. 
  

  

  A 
  potential-difference 
  of 
  this 
  amount 
  will 
  be 
  found 
  between 
  

   the 
  two 
  ends 
  of 
  the 
  metallic 
  bar. 
  The 
  electric 
  force 
  X 
  will 
  

   account 
  for 
  the 
  Thomson 
  effect 
  and 
  for 
  one 
  part 
  of 
  the 
  

   electric 
  forces 
  of 
  thermoelectric 
  couples. 
  These 
  forces 
  X 
  

   may 
  be 
  used 
  for 
  the 
  performance 
  of 
  mechanical 
  work, 
  which 
  

   again 
  could 
  be 
  transformed 
  into 
  heat, 
  so 
  that 
  the 
  process 
  

   under 
  consideration 
  is 
  a 
  reversible 
  one. 
  

  

  ?E2 
  

  

  