﻿Processes 
  and 
  Planck 
  3 
  s 
  Tlieory. 
  237 
  

  

  Further, 
  from 
  the 
  equations 
  

  

  K 
  x 
  = 
  K 
  sin 
  2 
  1» 
  + 
  K' 
  cos 
  2 
  ft), 
  

  

  K 
  2 
  = 
  K 
  cos 
  2 
  &> 
  4- 
  K' 
  sin 
  2 
  &% 
  

  

  K 
  and 
  K' 
  may 
  be 
  expressed 
  as 
  linear 
  functions 
  of 
  K 
  l 
  

   and 
  K 
  2 
  . 
  And 
  since 
  BK 
  2 
  = 
  0, 
  and 
  BKi 
  is 
  proportional 
  to 
  

  

  3 
  J_^ 
  by 
  (36), 
  it 
  follows 
  that 
  dK 
  and 
  BK', 
  and 
  therefore 
  also 
  

  

  4-7TV 
  

  

  B(L 
  + 
  L/), 
  and 
  therefore 
  also 
  the 
  quantity 
  in 
  brackets 
  in 
  

  

  (46), 
  is 
  proportional 
  to 
  -7 
  — 
  . 
  The 
  factor 
  7 
  — 
  is 
  then 
  not 
  

  

  wanted 
  outside 
  of 
  the 
  bracket, 
  and 
  has 
  no 
  right 
  to 
  be 
  there. 
  

  

  It 
  is 
  true 
  that 
  since 
  L/c 
  denotes 
  entropy 
  per 
  unit 
  of 
  volume, 
  

  

  the 
  quantity 
  in 
  brackets 
  requires 
  some 
  factor 
  to 
  make 
  it 
  

  

  express 
  an 
  actual 
  amount 
  of 
  entropy. 
  But 
  such 
  factor 
  must 
  

  

  3cV 
  

   be 
  independent 
  of 
  cr, 
  and 
  therefore 
  cannot 
  be 
  -r—. 
  The 
  

  

  above 
  are 
  the 
  difficulties 
  which 
  I 
  have 
  found. 
  Very 
  pro- 
  

   bably 
  they 
  are 
  capable 
  of 
  explanation. 
  

  

  On 
  Planck's 
  'Theory 
  in 
  relation 
  to 
  the 
  Distribution 
  of 
  

   Energy 
  in 
  the 
  Spectrum. 
  

  

  19. 
  Planck 
  has 
  given 
  no 
  account 
  of 
  interchanges 
  of 
  energy 
  

   between 
  systems 
  of 
  different 
  vibration 
  periods. 
  His 
  method 
  

   is 
  in 
  fact 
  based 
  on 
  the 
  assumption 
  or 
  proof 
  (art. 
  6) 
  that 
  waves 
  

   of 
  different 
  period 
  from 
  that 
  of 
  a 
  resonator 
  pass 
  the 
  resonator 
  

   unaffected, 
  so 
  that 
  no 
  interchange 
  of 
  energy 
  takes 
  place. 
  

   This, 
  however, 
  is 
  not 
  quite 
  rigorous. 
  If 
  the 
  difference 
  of 
  

   periods, 
  though 
  not 
  zero, 
  be 
  very 
  small, 
  some 
  very 
  small 
  

   interchange 
  of 
  energy 
  between 
  the 
  wave 
  and 
  the 
  resonator 
  

   will 
  consistently 
  with 
  the 
  equation 
  of 
  p. 
  443 
  take 
  place. 
  We 
  

   may 
  admit, 
  therefore, 
  that 
  if 
  all 
  values 
  of 
  v 
  are 
  represented, 
  

   v 
  varying 
  continuously 
  between 
  different 
  systems, 
  energy 
  

  

  will 
  pass 
  indirectly 
  from 
  systems 
  of 
  period 
  - 
  to 
  s} 
  T 
  stems 
  of 
  

  

  period 
  -7, 
  though 
  the 
  rate 
  of 
  interchange 
  will 
  be 
  much 
  slower 
  

  

  than 
  between 
  systems 
  of 
  the 
  same 
  period. 
  

  

  20. 
  Now 
  Planck 
  does 
  not 
  investigate 
  the 
  law 
  of 
  these 
  slow 
  

   interchanges. 
  He 
  assumes 
  that 
  an 
  entropy 
  function 
  exists 
  

   for 
  them, 
  and 
  that 
  it 
  is 
  precisely 
  the 
  same 
  function 
  (but 
  with 
  

   variable 
  v) 
  which 
  has 
  been 
  defined 
  above 
  for 
  systems 
  having 
  

   the 
  same 
  period. 
  That 
  may 
  be 
  true, 
  but 
  it 
  cannot, 
  I 
  think, 
  

   be 
  accepted 
  as 
  an 
  axiom. 
  It 
  seems 
  to 
  me 
  that 
  this 
  branch 
  of 
  

   the 
  subject 
  requires 
  further 
  elucidation. 
  

  

  