﻿Motion 
  of 
  Electrons 
  in 
  Solids. 
  223 
  

  

  Since 
  ^ 
  is 
  to 
  be 
  the 
  same 
  for 
  all 
  substances, 
  ^ 
  must 
  be 
  the 
  

   same 
  for 
  all 
  substances. 
  

  

  41. 
  Going 
  back 
  to 
  equation 
  (73), 
  and 
  substituting 
  this 
  

   form 
  for 
  ^, 
  we 
  lind 
  that 
  we 
  must 
  have 
  (writing 
  v 
  for 
  

  

  KumT/:Se\i) 
  

  

  xT=0 
  

  

  The 
  fraction 
  v/u 
  does 
  not 
  depend 
  on 
  p, 
  and 
  is 
  therefore 
  

   independent 
  of 
  u. 
  Callhig 
  it 
  7, 
  tlie 
  equation 
  becomes 
  

  

  J 
  TT^^^Q^^'^i^' 
  • 
  • 
  

  

  (86) 
  

  

  and 
  since 
  </> 
  is 
  the 
  same 
  for 
  all 
  substances, 
  this 
  can 
  only 
  be 
  

   satisfied 
  if 
  7 
  is 
  the 
  same 
  for 
  all 
  substances. 
  It 
  must 
  clearly 
  

   be 
  a 
  pure 
  numerical 
  constant. 
  

   We 
  now 
  have 
  

  

  V 
  KmT 
  

  

  so 
  that 
  

  

  or, 
  in 
  simpler 
  form, 
  

  

  

  f^=~Y' 
  ^^^^ 
  

  

  where 
  h 
  is 
  a 
  universal 
  constant. 
  

  

  42. 
  For 
  pure 
  metals 
  k 
  is 
  known 
  from 
  experiment 
  to 
  be 
  

   approximately 
  proportional 
  to 
  the 
  inverse 
  temperature, 
  and 
  

   it 
  is 
  natural 
  to 
  expect 
  k 
  to 
  be 
  proportional 
  to 
  N. 
  There 
  is, 
  

   therefore, 
  nothing 
  inherently 
  improbable 
  in 
  equation 
  (88). 
  

   We 
  see 
  that 
  the 
  observed 
  differences 
  between 
  the 
  temperature 
  

   coefficients 
  of 
  k 
  and 
  the 
  values 
  which 
  they 
  would 
  have 
  if 
  k 
  

   varied 
  exactly 
  as 
  T~^ 
  must 
  be 
  attributed 
  either 
  to 
  variations 
  

   in 
  N 
  as 
  the 
  temperature 
  changes, 
  or 
  to 
  differences 
  between 
  

   the 
  value 
  of 
  k 
  measured 
  and 
  the 
  value 
  with 
  which 
  we 
  are 
  

   here 
  concerned. 
  Such 
  a 
  difference 
  would 
  arise, 
  for 
  instance, 
  

   if 
  the 
  resistance 
  of 
  a 
  solid 
  was 
  not 
  entirely 
  made 
  up 
  of 
  

   resistances 
  such 
  as 
  we 
  have 
  been 
  concerned 
  with 
  — 
  as, 
  for 
  

   example, 
  if 
  the 
  solid 
  were 
  not 
  homogeneous, 
  but 
  had 
  a 
  

   crystalline 
  structure. 
  In 
  any 
  case 
  equation 
  (88) 
  ought 
  only 
  

   to 
  be 
  true 
  for 
  very 
  low 
  values 
  of 
  T. 
  

  

  