﻿656 
  On 
  the 
  Change 
  of 
  Electrical 
  Resistance 
  of 
  Metals. 
  

  

  the 
  corpuscles 
  must 
  be 
  equal 
  to 
  the 
  force 
  tending 
  to 
  keep 
  

   them 
  in. 
  Taking 
  the 
  axis 
  of 
  x 
  as 
  perpendicular 
  to 
  the 
  

   surface 
  of 
  the 
  metal, 
  then 
  at 
  any 
  point 
  x 
  if 
  p 
  is 
  the 
  pressure, 
  

   X 
  the 
  force, 
  and 
  n 
  the 
  number 
  of 
  corpuscles 
  per 
  unit 
  volume, 
  

  

  -* 
  = 
  X*. 
  

  

  ax 
  

  

  But 
  p 
  is 
  proportional 
  to 
  the 
  absolute 
  temperature, 
  and 
  the 
  

   number 
  of 
  corpuscles 
  therefore 
  

  

  ndn 
  Y 
  

  

  — 
  cv 
  — 
  — 
  Xne. 
  

  

  ax 
  

  

  or 
  

  

  _£_[lo 
  gw 
  ] 
  =jXdx, 
  

  

  where 
  W 
  is 
  the 
  work 
  required 
  to 
  take 
  the 
  corpuscle 
  from 
  the 
  

   inside 
  to 
  the 
  outside 
  of 
  the 
  metal. 
  

  

  On 
  the 
  assumption 
  that 
  the 
  work 
  is 
  all 
  electrical, 
  W 
  would 
  

   be 
  the 
  difference 
  of 
  potential, 
  and 
  in 
  the 
  case 
  of 
  two 
  metals 
  

   in 
  contact 
  it 
  would 
  be 
  equal 
  to 
  Y 
  the 
  contact-difference 
  of 
  

   potential. 
  If 
  n 
  x 
  and 
  1% 
  are 
  the 
  number 
  of 
  corpuscles 
  per 
  

   unit 
  volume 
  in 
  each 
  metal, 
  then 
  on 
  the 
  above 
  assumption 
  we 
  

   have 
  

  

  V=^logA 
  . 
  (A) 
  

  

  e 
  *n 
  2 
  

  

  Taking 
  Maxwell's 
  value 
  of 
  2 
  x 
  10 
  19 
  for 
  the 
  number 
  of 
  

   molecules 
  per 
  c.c. 
  of 
  a 
  gas 
  at 
  standard 
  temperature 
  and 
  

   pressure, 
  we 
  have 
  

  

  - 
  = 
  0-027 
  volt. 
  

   e 
  

  

  Substituting 
  the 
  values 
  of 
  n 
  obtained 
  for 
  the 
  different 
  metals 
  

   in 
  (A), 
  the 
  values 
  tabulated 
  below 
  are 
  obtained, 
  on 
  making 
  

   the 
  assumption 
  stated 
  above, 
  for 
  the 
  contact-difference 
  of 
  

   potential 
  in 
  volts 
  : 
  

  

  Cu-Pt. 
  Cu-Au. 
  Cu-Ag. 
  Cu-Cd. 
  Cu-Zn. 
  Cu-Sn. 
  Cu-C. 
  

   0-0239 
  0-0117 
  -0-0015 
  0-0684 
  0-0478 
  0-0546 
  0-2176 
  

  

  In 
  conclusion 
  I 
  wish 
  to 
  acknowledge 
  my 
  indebtedness 
  to 
  

   Prof. 
  Thomson 
  for 
  his 
  kindly 
  interest 
  and 
  valuable 
  suggestions 
  

   throughout 
  the 
  course 
  of 
  the 
  investigation. 
  

  

  Cavendish 
  Laboratory, 
  

   March 
  14th 
  , 
  1902/ 
  

  

  