﻿218 
  Prof. 
  J. 
  H. 
  Jeans 
  on 
  the 
  

  

  The 
  symbol 
  k 
  has 
  ah^eady 
  been 
  regarded 
  as 
  dependent 
  on 
  

   the 
  pjirtition 
  of 
  radiant 
  energy. 
  In 
  passing 
  to 
  the 
  new 
  

   conditions 
  now 
  under 
  consideration, 
  k 
  acquires 
  a 
  new 
  value 
  

   but 
  not 
  a 
  new 
  meaning 
  ; 
  it 
  stands 
  in 
  the 
  analysis 
  just 
  as 
  

   before, 
  and 
  equation 
  (62) 
  remains 
  true 
  for 
  the 
  new 
  value 
  

   of 
  K 
  as 
  well 
  as 
  for 
  the 
  old, 
  except 
  that, 
  as 
  in 
  Part 
  I., 
  its 
  validity 
  

   is 
  confined 
  to 
  small 
  values 
  of 
  p. 
  

  

  Equation 
  (63) 
  also 
  is 
  no 
  longer 
  true 
  except 
  for 
  certain 
  

   sufficiently 
  great 
  values 
  of 
  the 
  time-interval 
  ^2~^i« 
  -^^ 
  ^ 
  con- 
  

   sequence, 
  equation 
  (64) 
  no 
  longer 
  expresses 
  the 
  emission 
  of 
  

   radiation 
  except 
  for 
  waves 
  of 
  great 
  wave-length. 
  

  

  Let 
  us 
  replace 
  this 
  formula 
  for 
  the 
  emission 
  by 
  the 
  perfectly 
  

   general 
  formula 
  

  

  r 
  4^>^^ 
  .... 
  (68) 
  

  

  which 
  will 
  be 
  supposed 
  true 
  from 
  /) 
  = 
  to 
  p 
  = 
  co 
  , 
  Here 
  

   @p 
  is 
  a 
  function 
  of 
  p 
  and 
  of 
  T, 
  and 
  the 
  constants 
  of 
  matter. 
  

   The 
  formula 
  (6S) 
  is 
  perfectly 
  general 
  because 
  (i^p 
  may 
  be 
  

   a 
  perfectly 
  general 
  function 
  of 
  p 
  and 
  of 
  these 
  other 
  

   quantities. 
  

  

  Our 
  analysis 
  has 
  already 
  proved 
  that 
  ®p 
  must 
  become 
  

   equal 
  to 
  unity 
  when 
  p 
  is 
  small, 
  and 
  must 
  fall 
  off 
  exponentially 
  

   with 
  p 
  when 
  p 
  is 
  great. 
  

  

  Formula 
  (65) 
  will 
  give 
  the 
  absorption 
  provided 
  p 
  is 
  small. 
  

   Thus 
  at 
  sufficiently 
  low 
  temperatures 
  the 
  formula 
  will 
  give 
  

   the 
  absorption 
  accurately 
  through 
  those 
  parts 
  of 
  the 
  spectrum 
  

   in 
  which 
  the 
  energy 
  is 
  appreciable. 
  To 
  avoid 
  too 
  great 
  com- 
  

   plication, 
  we 
  shall 
  assume 
  formula 
  (65) 
  to 
  be 
  accurate 
  for 
  all 
  

   values 
  of 
  JO 
  with 
  which 
  we 
  are 
  concerned. 
  Our 
  results 
  will 
  

   therefore 
  be 
  strictly 
  true 
  for 
  low 
  temperatures, 
  but 
  will 
  be 
  

   only 
  approximations 
  for 
  higher 
  temperatures. 
  

  

  37. 
  Using 
  Ihe 
  assumed 
  value 
  (GS) 
  for 
  the 
  emission, 
  it 
  is 
  

   found 
  that 
  equation 
  (66) 
  must 
  be 
  replaced 
  by 
  

  

  so 
  that 
  instead 
  of 
  equation 
  (67) 
  for 
  the 
  steady 
  state, 
  we 
  have 
  

  

  :Epdp=^,nTp'epdp 
  (70) 
  

  

  = 
  S7r:RTX-^@pdX 
  (71) 
  

  

  From 
  what 
  has 
  already 
  gone 
  before 
  (§ 
  16), 
  it 
  will 
  be 
  

   clear 
  that 
  the 
  known 
  qualitative 
  properties 
  of 
  radiation 
  

   will 
  be 
  accounted 
  for 
  if, 
  on 
  actual 
  calculation, 
  Sp 
  is 
  found 
  to 
  

   be 
  a 
  function 
  only 
  of 
  T/p 
  and 
  of 
  constants 
  which 
  are 
  the 
  

  

  