﻿Motion 
  of 
  Electrons 
  in 
  Solids. 
  21D 
  

  

  same 
  for 
  all 
  kinds 
  of 
  matter. 
  Any 
  other 
  form 
  for 
  0^ 
  would 
  

   be 
  contrary 
  to 
  experience 
  : 
  a 
  form 
  in 
  which 
  T 
  and 
  p 
  entered 
  

   otherwise 
  thnn 
  through 
  the 
  single 
  variiible 
  T/p 
  would 
  be 
  in 
  

   opposition 
  to 
  Stefan's 
  law 
  and 
  to 
  Wien^s 
  displacement-law, 
  

   while 
  a 
  form 
  of 
  ©^ 
  which 
  varied 
  for 
  ditFe 
  rent 
  kinds 
  of 
  matter 
  

   would 
  contradict 
  the 
  fact 
  that 
  the 
  radiation 
  in 
  a 
  cavity 
  is 
  

   independent 
  of 
  the 
  substance 
  of 
  the 
  walls. 
  It 
  should 
  be 
  

   noticed 
  that 
  we 
  are 
  at 
  present 
  concerned 
  only 
  with 
  facts 
  

   about 
  Sp 
  which 
  are 
  deducible 
  from 
  experiment 
  ; 
  these 
  facts 
  

   are 
  undoubtedly 
  true, 
  quite 
  apart 
  from 
  any 
  theories 
  we 
  may 
  

   hold 
  as 
  to 
  why 
  they 
  are 
  true. 
  

  

  38. 
  We 
  shall 
  first 
  consider 
  what 
  are 
  the 
  conditions, 
  in 
  

   terms 
  of 
  the 
  electron-theory, 
  that 
  Sp 
  shall 
  have 
  the 
  required 
  

   functional 
  form. 
  If 
  these 
  conditions 
  are 
  found 
  to 
  be 
  such 
  as 
  

   we 
  can 
  readily 
  believe 
  to 
  be 
  satisfied 
  in 
  actual 
  matter, 
  then 
  

   we 
  shall 
  be 
  able 
  to 
  apply 
  a 
  further 
  test 
  to 
  the 
  electron 
  theory 
  

   by 
  actually 
  evaluating 
  the 
  function 
  Sp 
  and 
  comparing 
  the 
  

   value 
  so 
  found 
  with 
  experiment. 
  

  

  The 
  functional 
  form 
  required 
  for 
  0^ 
  can 
  be 
  expressed 
  by 
  

   the 
  equation 
  

  

  e 
  

  

  ^(f), 
  (72) 
  

  

  in 
  which 
  a 
  is 
  a 
  constant, 
  the 
  same 
  for 
  all 
  matter, 
  of 
  which 
  the 
  

   physical 
  dimensions 
  are 
  those 
  of 
  T/p, 
  and 
  </> 
  is 
  a 
  function 
  

   which 
  may 
  involve 
  other 
  constants, 
  but 
  must 
  be 
  the 
  same 
  

   for 
  all 
  kinds 
  of 
  matter. 
  Let 
  us 
  assume 
  &p 
  to 
  be 
  of 
  this 
  form 
  

   and 
  examine 
  what 
  inferences 
  can 
  be 
  drawn 
  from 
  equation 
  (72). 
  

   Let 
  us 
  put 
  

  

  ap 
  = 
  uT, 
  

   so 
  that 
  If 
  is 
  a 
  pure 
  number, 
  and 
  0;; 
  is 
  a 
  function 
  of 
  ii 
  only. 
  

   Expression 
  (GS), 
  which 
  represents 
  the 
  total 
  emission 
  per 
  unit 
  

   volume 
  per 
  unit 
  time, 
  now 
  becomes 
  

  

  KumT 
  

  

  4RT3/iXf'- 
  [• 
  ^e'a 
  ^ 
  , 
  ^ 
  , 
  

  

  2 
  (i>(ii)mlu 
  

  

  Yma^ 
  J 
  ^ 
  lKnmT\^ 
  

  

  

  (KmT\ 
  

  

  TT 
  V 
  mcr 
  

  

  where 
  ^ 
  is 
  a 
  new 
  function 
  which 
  is 
  the 
  same 
  for 
  all 
  matter. 
  

   The 
  total 
  emission 
  per 
  unit 
  volume 
  per 
  unit 
  time 
  is, 
  

   however, 
  known 
  to 
  be 
  (cj\ 
  equation 
  (GO)) 
  

  

  3V 
  -^ 
  ' 
  

   where 
  f^ 
  is 
  the 
  mean 
  value, 
  at 
  any 
  instant, 
  of 
  the 
  squares 
  of 
  

  

  