﻿■Theory 
  of 
  the 
  Thermoelectric 
  Forces. 
  785 
  

  

  the 
  junction. 
  Thus, 
  when 
  the 
  current 
  passes 
  through 
  the 
  

   system 
  of 
  alternate 
  layers 
  o£ 
  the 
  two 
  metals, 
  one 
  face 
  of 
  each 
  

   layer 
  will 
  be 
  cooled 
  and 
  the 
  other 
  heated, 
  and 
  thus 
  in 
  the 
  

   pile 
  of 
  layers 
  differences 
  of 
  temperature 
  proportional 
  to 
  the 
  

   current 
  will 
  be 
  established. 
  This 
  will 
  give 
  rise 
  to 
  a 
  thermo- 
  

   electric 
  force 
  tending 
  to 
  oppose 
  the 
  current. 
  Such 
  a 
  force 
  

   would 
  produce 
  exactly 
  the 
  same 
  effect 
  as 
  a 
  resistance. 
  

  

  If 
  At 
  is 
  the 
  difference 
  of 
  temperature 
  between 
  two 
  

   junctions, 
  the 
  electromotive 
  force 
  of 
  an 
  elementary 
  couple 
  

   will 
  be 
  equal 
  to 
  

  

  e= 
  - 
  -loo-— 
  Ac. 
  

   de 
  & 
  JS 
  6 
  

  

  The 
  amount 
  of 
  heat 
  developed 
  in 
  unit 
  time 
  and 
  per 
  unit 
  

   area 
  of 
  the 
  cross-section 
  in 
  each 
  couple 
  is 
  equal 
  to 
  

  

  zQi 
  + 
  io-xAr. 
  

  

  This 
  amount 
  is 
  to 
  be 
  equated 
  to 
  the 
  heat 
  conducted 
  per 
  

   second 
  towards 
  the 
  cold 
  junctions 
  on 
  the 
  two 
  sides. 
  Let 
  

   k 
  u 
  k 
  2 
  be 
  the 
  conductivities 
  for 
  heat 
  of 
  the 
  two 
  metals, 
  l 
  x 
  and 
  

   Z 
  2 
  the 
  corresponding 
  lengths 
  ; 
  the 
  heat 
  conducted 
  per 
  second 
  

   towards 
  the 
  cold 
  junctions 
  is 
  

  

  At 
  

   h 
  

  

  h 
  + 
  

  

  At 
  , 
  K 
  /k 
  x 
  k 
  2 
  \ 
  1 
  Aj 
  /&, 
  k 
  2 
  \ 
  

  

  ~-k 
  2 
  -At 
  - 
  r 
  1 
  + 
  - 
  2 
  )— 
  — 
  = 
  At. 
  ?i 
  A— 
  + 
  — 
  I, 
  

  

  if 
  there 
  are 
  n 
  similar 
  couples 
  per 
  unit 
  of 
  length, 
  

   and 
  if 
  we 
  put 
  

  

  * 
  - 
  and 
  

  

  "2 
  

  

  when 
  a 
  stationary 
  state 
  is 
  reached, 
  

  

  i(Q 
  1 
  + 
  «r 
  1 
  A0=nA/^ 
  + 
  M. 
  

  

  \Pl 
  ft) 
  

  

  The 
  whole 
  electromotive 
  force~per 
  unit 
  of 
  length 
  is 
  equal 
  to 
  

  

  \ 
  Pi 
  pJ 
  

  

  nAti 
  

  

  / 
  • 
  / 
  V 
  Pi 
  

   ne 
  = 
  co 
  / 
  i 
  = 
  co' 
  ■ 
  ~ 
  ' 
  — 
  A 
  -:—, 
  

  

  <o' 
  denoting 
  the 
  false 
  resistance 
  due 
  to 
  thermoelectric 
  causes, 
  

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

  

  