﻿Theory 
  of 
  the 
  Thermoelectric 
  Forces. 
  769 
  

  

  open 
  to 
  this 
  objection, 
  which 
  makes 
  the 
  ratio 
  of 
  the 
  con- 
  

   ductivities 
  for 
  heat 
  and 
  electricity 
  of 
  the 
  right 
  magnitude, 
  

   and 
  gives 
  an 
  account 
  of 
  the 
  radiation 
  of 
  heat 
  and 
  of 
  the 
  

   different 
  effects 
  called 
  after 
  Hall, 
  Peltier, 
  and 
  Thomson. 
  

   I 
  shall, 
  however, 
  begin 
  with 
  the 
  first 
  method, 
  supposing 
  the 
  

   corpuscles 
  to 
  be 
  free 
  and 
  in 
  temperature 
  equilibrium 
  with 
  

   their 
  surroundings 
  like 
  a 
  very 
  rarefied 
  gas 
  in 
  a 
  porous 
  body. 
  

   The 
  following 
  considerations 
  apply 
  to 
  the 
  first 
  as 
  well 
  as 
  to 
  

   the 
  second 
  theory. 
  

  

  § 
  1. 
  Potential-Differences 
  between 
  Metals 
  in 
  Contact. 
  

  

  When 
  two 
  metals 
  A 
  and 
  B 
  at 
  the 
  same 
  temperature 
  are 
  

   placed 
  in 
  perfect 
  contact, 
  if 
  the 
  number 
  Nj 
  of 
  corpuscles 
  in 
  

   unit 
  volume 
  in 
  the 
  metal 
  A 
  is 
  greater 
  than 
  that 
  in 
  B, 
  then 
  

   corpuscles 
  will 
  flow 
  from 
  A 
  to 
  B. 
  There 
  is 
  evaporation 
  of 
  

   negative 
  electricity 
  in 
  the 
  first 
  metal 
  and 
  condensation 
  in 
  

   the 
  second. 
  After 
  a 
  very 
  short 
  time, 
  however, 
  this 
  distil- 
  

   lation 
  will 
  be 
  stopped, 
  the 
  metal 
  A 
  getting 
  charged 
  positively 
  

   and 
  the 
  metal 
  B 
  negatively. 
  These 
  charges 
  produce 
  an 
  

   electric 
  force 
  X 
  directed 
  from 
  A 
  to 
  B. 
  The 
  attraction 
  of 
  the 
  

   positive 
  electricity 
  in 
  A 
  will 
  tend 
  to 
  prevent 
  the 
  corpuscles 
  

   escaping 
  from 
  it, 
  and 
  the 
  flow 
  will 
  cease, 
  when 
  the 
  attraction 
  

   of 
  the 
  positive 
  electricity 
  in 
  A 
  and 
  the 
  repulsion 
  of 
  the 
  

   negative 
  in 
  B 
  just 
  balances 
  the 
  effect 
  of 
  the 
  difference 
  in 
  

   pressure. 
  The 
  positive 
  electrification 
  in 
  A 
  and 
  the 
  negative 
  

   in 
  B 
  will 
  be 
  close 
  to 
  the 
  surface 
  of 
  separation, 
  and 
  these 
  two 
  

   electrifications 
  will 
  produce 
  a 
  difference 
  in 
  electric 
  potential 
  

   between 
  A 
  and 
  B, 
  which 
  we 
  can 
  calculate 
  in 
  the 
  following 
  way. 
  

  

  Let 
  N 
  be 
  the 
  number 
  of 
  corpuscles 
  per 
  unit 
  volume 
  in 
  A 
  

   at 
  a 
  point 
  distant 
  x 
  from 
  the 
  boundary 
  between 
  the 
  two 
  metals. 
  

   Then 
  the 
  number 
  of 
  corpuscles 
  crossing 
  unit 
  surface 
  at 
  x 
  in 
  

   unit 
  time 
  according 
  to 
  the 
  law 
  of 
  diffusion 
  is 
  equal 
  to 
  ^ 
  

   vl 
  . 
  "d^fdx, 
  where 
  v 
  denotes 
  the 
  mean 
  velocity 
  and 
  I 
  the 
  

   mean 
  free 
  path 
  of 
  the 
  corpuscles 
  at 
  the 
  temperature 
  T. 
  Let 
  

   e 
  be 
  the 
  negative 
  charge 
  of 
  a 
  corpuscle 
  and 
  X 
  the 
  electric 
  

   force 
  at 
  the 
  point 
  x, 
  then 
  the 
  number 
  of 
  corpuscles 
  acted 
  on 
  

   by 
  the 
  force 
  X, 
  passing 
  through 
  unit 
  surface 
  in 
  unit 
  time, 
  is 
  

   equal 
  to 
  N^vX/4aT, 
  a 
  being 
  the 
  universal 
  constant 
  of 
  the 
  

   kinetic 
  theory 
  of 
  gases. 
  The 
  number 
  of 
  corpuscles, 
  flowing 
  

   in 
  unit 
  time 
  through 
  unit 
  surface 
  from 
  A 
  to 
  B, 
  is 
  equal 
  to 
  

   1 
  7 
  dN 
  _ 
  NgZvX 
  

   3" 
  55 
  4«T 
  : 
  

   in 
  the 
  case 
  of 
  equilibrium 
  this 
  flux 
  must 
  vanish. 
  Therefore 
  

  

  3e 
  -dx 
  N' 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  16. 
  No. 
  95. 
  Nov. 
  1908. 
  3 
  E 
  

  

  