﻿226 
  Motion 
  of 
  Electrons 
  in 
  Solids. 
  

  

  motion 
  of 
  the 
  electrons 
  can 
  be 
  resolved 
  into 
  regular 
  trains 
  of 
  

   waves. 
  Only 
  those 
  waves 
  contribute 
  to 
  the 
  radiation 
  which 
  

   travel 
  with 
  the 
  velocity 
  of 
  light 
  (§27). 
  These 
  waves 
  emit 
  

   and 
  absorb 
  radiation 
  with 
  a 
  frequency 
  equal 
  to 
  their 
  own, 
  

   and 
  there 
  will 
  clearly 
  be 
  rapid 
  interchange 
  of 
  energy 
  between 
  

   the 
  waves 
  of 
  electrons 
  and 
  the 
  radiation 
  of 
  the 
  same 
  frequency 
  

   in 
  the 
  aether. 
  So 
  long 
  as 
  we 
  deal 
  only 
  with 
  waves 
  of 
  wave- 
  

   length 
  great 
  compared 
  with 
  the 
  distances 
  of 
  adjacent 
  electrons, 
  

   the 
  collection 
  of 
  electrons 
  can 
  be 
  treated 
  as 
  a 
  continuous 
  

   electric 
  medium. 
  The 
  degrees 
  of 
  freedom 
  of 
  the 
  electrons 
  

   may 
  be 
  supposed 
  to 
  be 
  the 
  waves 
  in 
  this 
  medium, 
  and 
  these 
  

   are 
  in 
  energy-equilibrinm 
  both 
  vrith 
  the 
  matter 
  and 
  with 
  the 
  

   waves 
  in 
  the 
  aether. 
  We 
  see 
  at 
  once 
  the 
  dynamical 
  necessity 
  

   for 
  the 
  result 
  that 
  ©^=1 
  whenp 
  is 
  small. 
  

  

  As 
  we 
  advance 
  up 
  the 
  spectrum 
  we 
  cannot 
  suppose 
  that 
  

   there 
  are 
  waves 
  of 
  the 
  electric 
  medium 
  for 
  all 
  values 
  of 
  p^ 
  

   for 
  if 
  this 
  were 
  so 
  the 
  finite 
  number 
  of 
  electrons 
  would 
  

   possess 
  an 
  infinite 
  number 
  of 
  degrees 
  of 
  freedom. 
  If 
  pi 
  and 
  

   ji?2 
  ai'e 
  two 
  adjacent 
  values 
  of 
  p, 
  there 
  may 
  be 
  only 
  one 
  degree 
  

   of 
  freedom 
  of 
  the 
  electric 
  medium 
  for 
  the 
  values 
  pi 
  and 
  p^ 
  

   of 
  p, 
  and 
  for 
  all 
  the 
  values 
  between. 
  The 
  vibrations 
  of 
  this 
  

   degree 
  of 
  freedom 
  may 
  at 
  one 
  instant 
  exchange 
  energy 
  with 
  

   the 
  vibrations 
  in 
  the 
  sether 
  of 
  frequency 
  pi, 
  at 
  another 
  

   instant 
  with 
  those 
  of 
  frequency 
  ^2, 
  and 
  so 
  on. 
  If 
  the 
  various 
  

   vibrations 
  of 
  the 
  aether 
  are 
  retained 
  indefinitely 
  there 
  must 
  

   ultimately 
  be 
  partition 
  of 
  energy 
  between 
  all 
  (result 
  I.), 
  but 
  

   if 
  not 
  there 
  must 
  be 
  a 
  falling 
  off 
  from 
  equipartition 
  values. 
  

  

  V. 
  The 
  dependence 
  of 
  ©^ 
  on 
  p 
  will 
  vary 
  with 
  difEerent 
  

   structures 
  of 
  matter. 
  All 
  the 
  known 
  phenomena 
  of 
  radiation 
  

   are 
  accounted 
  for 
  if 
  %p 
  is 
  a 
  function 
  only 
  of 
  T/p 
  and 
  of 
  

   universal 
  constants. 
  

  

  According 
  to 
  the 
  thermodynamical 
  theory, 
  %p 
  must 
  neces- 
  

   sarily 
  have 
  this 
  form. 
  The 
  thermodynamical 
  theory, 
  however, 
  

   applies 
  (if 
  at 
  all) 
  only 
  to 
  the 
  radiation 
  inside 
  a 
  perfectly 
  

   radiation-tight 
  enclosure. 
  Then 
  ©^ 
  has 
  the 
  required 
  form, 
  

   for 
  it 
  is 
  equal 
  to 
  unity 
  for 
  all 
  values 
  of 
  T 
  and 
  p 
  (result 
  I.), 
  

   but 
  this 
  does 
  not 
  give 
  any 
  assistance 
  towards 
  finding 
  a 
  

   formula 
  for 
  natural 
  radiation. 
  

  

  VI. 
  The 
  required 
  form 
  of 
  ©^ 
  is 
  obtained 
  only 
  if 
  the 
  law 
  

   of 
  force 
  acting 
  on 
  the 
  electrons 
  is 
  that 
  of 
  the 
  inverse 
  cube 
  

   of 
  the 
  distance. 
  

  

  VII. 
  Since 
  it 
  is 
  known 
  that 
  there 
  are 
  terms 
  in 
  the 
  law 
  of 
  

   force 
  which 
  fall 
  ofF 
  as 
  the 
  inverse 
  square, 
  and 
  since 
  the 
  

   electrons 
  must 
  always 
  be 
  acted 
  on 
  by 
  more 
  than 
  one 
  centre 
  

   of 
  force, 
  it 
  follows, 
  if 
  our 
  analysis 
  is 
  sound, 
  that 
  Stefan's 
  and 
  

   Wien's 
  laws 
  must 
  be 
  only 
  approximations. 
  

  

  April 
  28th, 
  1909. 
  

  

  