﻿Theory 
  of 
  the 
  Thermoelectric 
  Forces. 
  115 
  

  

  substances. 
  The 
  potential-difference 
  arising 
  in 
  this 
  way 
  is 
  

   equal 
  to 
  

  

  V„-V,= 
  ^Tlog|. 
  

  

  I£ 
  a 
  current 
  i 
  is 
  flowing 
  through 
  the 
  metals 
  in 
  a 
  direction 
  

   opposite 
  to 
  the 
  electric 
  force 
  

  

  x= 
  4a 
  dlo-ffN 
  

   3 
  e 
  d.2' 
  ' 
  

  

  a 
  corpuscle 
  in 
  travelling 
  from 
  B 
  to 
  A, 
  and 
  acted 
  on 
  by 
  the 
  

   force 
  Xe, 
  will 
  increase 
  its 
  kinetic 
  energy, 
  and 
  therefore 
  

   abstract 
  from 
  the 
  metal 
  an 
  amount 
  of 
  heat 
  whose 
  mechanical 
  

   equivalent 
  is 
  X# 
  dx. 
  If 
  the 
  current 
  i 
  is 
  flowing 
  in 
  the 
  direc- 
  

   tion 
  opposite 
  to 
  X, 
  the 
  number 
  of 
  corpuscles 
  which 
  cross 
  

  

  unit 
  area 
  in 
  unit 
  time 
  is 
  - 
  , 
  and 
  the 
  mechanical 
  equivalent 
  of 
  

  

  the 
  heat 
  they 
  abstract 
  from 
  the 
  metals 
  passing 
  through 
  the 
  

   junction 
  is 
  

  

  The 
  heat 
  absorbed 
  in 
  unit 
  time 
  and 
  per 
  unit 
  current, 
  i. 
  e. 
  

   the 
  Peltier 
  effect, 
  will 
  be 
  : 
  

  

  If 
  the 
  current 
  were 
  to 
  flow 
  in 
  the 
  opposite 
  direction 
  the 
  

   same 
  amount 
  of 
  heat 
  would 
  be 
  communicated 
  to 
  the 
  metal. 
  

   The 
  Peltier 
  effect 
  is 
  a 
  real 
  measure 
  of 
  the 
  potential-differences 
  

   between 
  metals 
  in 
  contact. 
  From 
  the 
  Peltier 
  effect 
  we 
  may 
  

   derive 
  the 
  ratio 
  of 
  the 
  number 
  of 
  corpuscles 
  in 
  two 
  metals. 
  

   Thus 
  to 
  take 
  the 
  case 
  of 
  antimony 
  and 
  bismuth, 
  whose 
  

   Peltier 
  effect 
  is 
  exceptionally 
  large, 
  

  

  log| 
  = 
  l-33: 
  or 
  |=3-8. 
  

  

  Thus, 
  if 
  the 
  number 
  of 
  corpuscles 
  in 
  the 
  unit 
  volume 
  of 
  

   antimony 
  were 
  about 
  four 
  times 
  that 
  in 
  bismuth 
  we 
  should, 
  

   on 
  this 
  theory, 
  get 
  Peltier 
  effects 
  of 
  about 
  the 
  right 
  amount. 
  

   The 
  Peltier 
  effect 
  for 
  antimony 
  and 
  bismuth 
  being 
  very 
  much 
  

   larger 
  than 
  that 
  for 
  most 
  pairs 
  of 
  metals, 
  we 
  see 
  that 
  the 
  

   theory 
  indicates 
  that 
  the 
  number 
  of 
  free 
  corpuscles 
  per 
  unit 
  

   volume 
  does 
  not 
  vary 
  much 
  from 
  one 
  metal 
  to 
  another. 
  

  

  