﻿Motion 
  of 
  Electrons 
  in 
  Solids, 
  225 
  

  

  alike, 
  the 
  radiation 
  proceeds 
  from 
  electrons 
  describing 
  orbits 
  

   about 
  centres 
  repelling 
  as 
  the 
  inverse 
  cube 
  of 
  the 
  distance, 
  

   these 
  centres 
  being 
  of 
  equal 
  strength 
  in 
  all 
  kinds 
  of 
  matter. 
  

   The 
  influence 
  of 
  forces 
  varying 
  as 
  other 
  powers 
  of 
  the 
  dis- 
  

   tance, 
  and 
  of 
  the 
  presence 
  of 
  centres 
  of 
  force 
  other 
  than 
  that 
  

   primarily 
  involved, 
  must 
  be 
  looked 
  for 
  in 
  departures 
  from 
  

   the 
  laws 
  of 
  Stefan 
  and 
  Wien. 
  

  

  It 
  will 
  be 
  remembered 
  that 
  Sir 
  J. 
  J. 
  Thomson, 
  in 
  his 
  paper 
  

   already 
  referred 
  to, 
  comes 
  to 
  the 
  conclusion 
  that 
  Stefan's 
  

   and 
  Wien's 
  laws 
  point 
  to 
  collisions 
  with 
  molecules 
  which 
  

   have 
  to 
  be 
  similar 
  for 
  all 
  matter, 
  and 
  repel 
  according 
  to 
  the 
  

   law 
  fjLJr^. 
  The 
  present 
  writer 
  ventures 
  to 
  think 
  that 
  the 
  

   similar 
  centres 
  of 
  force 
  may 
  be 
  found 
  to 
  be 
  the 
  positive 
  

   electrons. 
  The 
  ultimate 
  test 
  of 
  any 
  such 
  conjecture 
  must, 
  

   however, 
  be 
  the 
  calculation 
  of 
  the 
  radiation 
  function 
  and 
  

   comparison 
  with 
  experiment. 
  

  

  Conclusion. 
  

   46. 
  It 
  may 
  be 
  of 
  value 
  to 
  collect 
  and 
  summarize 
  those 
  of 
  

   the 
  results 
  obtained 
  which 
  have 
  reference 
  to 
  the 
  radiation 
  

   problem, 
  arranging 
  them 
  in 
  their 
  logical 
  order. 
  

  

  I. 
  It 
  has 
  been 
  verified, 
  by 
  analysing 
  the 
  motion 
  of 
  the 
  

   electrons, 
  that 
  radiation 
  in 
  a 
  perfectly 
  reflecting 
  enclosure, 
  

   when 
  in 
  a 
  steady 
  state, 
  must 
  be 
  distributed 
  between 
  the 
  

   different 
  wave-lengths 
  according 
  to 
  the 
  law 
  of 
  equipartition 
  

   (§ 
  34). 
  We 
  have 
  found 
  formulae 
  for 
  the 
  rate 
  of 
  progress 
  

   towards 
  this 
  state, 
  and 
  for 
  the 
  " 
  time 
  of 
  relaxation 
  " 
  (§ 
  35). 
  

  

  II. 
  It 
  has 
  been 
  shown 
  that 
  when 
  the 
  walls 
  of 
  the 
  enclosure 
  

   are 
  incapable 
  of 
  retaining 
  radiation 
  of 
  short 
  wave-length 
  (as 
  

   all 
  actual 
  substances 
  are) 
  an 
  entirely 
  different 
  partition 
  of 
  

   energy 
  is 
  to 
  be 
  looked 
  for. 
  We 
  have 
  supposed 
  this 
  new 
  

   partition 
  to 
  be 
  such 
  that 
  the 
  energy 
  of 
  frequency 
  p 
  has 
  

   ®p 
  times 
  its 
  equipartition 
  value. 
  

  

  III. 
  It 
  has 
  been 
  verified, 
  by 
  analysing 
  the 
  motion 
  of 
  the 
  

   electrons, 
  that 
  6^=1 
  when 
  p 
  is 
  small, 
  and 
  that 
  Sp 
  must 
  fall 
  

   off 
  exponentially 
  with 
  p 
  when 
  p 
  is 
  great. 
  Both 
  these 
  results 
  

   are 
  in 
  agreement 
  with 
  experiment. 
  

  

  [The 
  first 
  result 
  Sp=l 
  had 
  been 
  obtained 
  by 
  Lorentz* 
  on 
  

   the 
  suppositions 
  of 
  undisturbed 
  free-paths 
  and 
  instantaneous 
  

   collisions, 
  but 
  it 
  seemed 
  desirable 
  to 
  have 
  a 
  further 
  calculation 
  

   free 
  from 
  these 
  suppositions 
  t-] 
  

  

  IV. 
  The 
  various 
  results 
  obtained 
  have 
  given 
  some 
  insight 
  

   as 
  to 
  why 
  ©^ 
  starts 
  with 
  unit 
  value 
  and 
  gradually 
  falls 
  off 
  

   as 
  p 
  increases. 
  We 
  have 
  found 
  t 
  (^26) 
  that 
  the 
  irregular 
  

  

  * 
  Amsterdam 
  Proceedings, 
  1902-3, 
  p. 
  666. 
  

  

  t 
  Phil. 
  Mag. 
  xvii. 
  p. 
  253. 
  

  

  t 
  Cf. 
  also 
  Phil. 
  Mag. 
  xvii. 
  p. 
  254. 
  

  

  Fhil 
  Mag. 
  S. 
  6. 
  Vol. 
  18. 
  No. 
  103. 
  July 
  1909. 
  Q 
  

  

  