﻿Theory 
  of 
  the 
  Thermoelectric 
  Forces. 
  Ill 
  

  

  If 
  the 
  current 
  i 
  is 
  flowing 
  in 
  the 
  direction 
  from 
  A 
  to 
  B, 
  t. 
  e. 
  

   in 
  the 
  direction 
  of 
  increasing 
  temperature, 
  the 
  number 
  of 
  

   corpuscles 
  which 
  cross 
  unit 
  area 
  in 
  unit 
  time 
  in 
  the 
  direction 
  

   from 
  B 
  to 
  A 
  is 
  i/e, 
  and 
  the 
  mechanical 
  equivalent 
  of 
  the 
  

   heat 
  they 
  communicate 
  to 
  the 
  metal 
  between 
  the 
  places 
  

   where 
  the 
  temperatures 
  are 
  respectively 
  T 
  and 
  T 
  + 
  dT 
  is 
  

   equal 
  to 
  

  

  i 
  

  

  i 
  4 
  dlogN\ 
  

  

  But 
  if 
  a 
  is 
  the 
  specific 
  heat 
  of 
  electricity 
  in 
  the 
  metal, 
  this 
  

   amount 
  of 
  heat 
  is 
  by 
  definition 
  equal 
  to 
  

  

  — 
  i&dT, 
  

  

  the 
  sign 
  minus 
  being 
  applied 
  because 
  the 
  electric 
  current 
  is 
  

   flowing 
  from 
  the 
  cold 
  to 
  the 
  hot 
  part 
  of 
  the 
  metal 
  ; 
  hence 
  

  

  rftr&W) 
  

  

  As 
  lead 
  has 
  no 
  Thomson 
  effect, 
  its 
  a- 
  is 
  zero. 
  If 
  the 
  current 
  

   is 
  flowing 
  in 
  the 
  direction 
  of 
  decreasing 
  temperature, 
  and 
  if 
  

   in 
  this 
  case 
  heat 
  is 
  developed, 
  we 
  consider 
  a 
  as 
  positive 
  ; 
  

   thus 
  a 
  would 
  be 
  positive 
  in 
  the 
  metals 
  Cu 
  commercial, 
  Sb 
  

   commercial, 
  Cd, 
  Zn, 
  Ag. 
  On 
  the 
  other 
  hand, 
  a 
  is 
  negative 
  

   in 
  the 
  metals 
  : 
  Fe, 
  Hg, 
  Sn, 
  Al, 
  Pt, 
  Sb 
  pure, 
  Bi 
  pure. 
  

  

  In 
  these 
  metals 
  heat 
  will 
  be 
  absorbed 
  when 
  an 
  electric 
  

   current 
  flows 
  from 
  hot 
  to 
  cold 
  parts. 
  When 
  the 
  specific 
  

   heat 
  a 
  in 
  the 
  lead 
  disappears 
  we 
  see 
  that 
  the 
  corpuscle 
  

   passing 
  from 
  T 
  + 
  dT 
  to 
  T 
  loses 
  the 
  same 
  amount 
  of 
  kinetic 
  

   energy 
  in 
  consequence 
  of 
  the 
  decreasing 
  temperature 
  as 
  it 
  

   gains 
  in 
  consequence 
  of 
  the 
  acceleration 
  produced 
  by 
  the 
  

   pressure 
  difference 
  due 
  to 
  the 
  increasing 
  number 
  of 
  cor- 
  

   puscles 
  with 
  increasing 
  temperature. 
  Consider 
  two 
  metals 
  

   a 
  and 
  b, 
  containing 
  at 
  the 
  same 
  temperature 
  T 
  the 
  numbers 
  

   N 
  a 
  and 
  N& 
  of 
  free 
  corpuscles, 
  the 
  corresponding 
  specific 
  heat 
  

   of 
  electricity 
  will 
  be 
  

  

  4 
  <* 
  T 
  d 
  log 
  N 
  a 
  « 
  

   °* 
  a 
  ~3e 
  dT_ 
  "' 
  

  

  4 
  a. 
  ~d 
  log 
  N^ 
  a 
  

   o 
  e 
  ol 
  e 
  

  

  . 
  . 
  Br. 
  

  

  4- 
  * 
  l0g 
  Si 
  

  

  