﻿238 
  Mr. 
  S. 
  H. 
  Bur 
  bury 
  on 
  Irreversible 
  

  

  21. 
  According 
  to 
  Planck, 
  if 
  the 
  entropy 
  has 
  the 
  general 
  

  

  form 
  p\J 
  log 
  q 
  — 
  for 
  the 
  resonator, 
  and 
  pK 
  log-2— 
  for 
  the 
  wave, 
  

   we 
  have 
  e 
  

  

  1 
  1 
  , 
  c 
  2 
  1 
  

  

  where 
  v 
  is 
  now 
  a 
  variable. 
  As 
  he 
  himself 
  explains, 
  the 
  

   constants 
  p, 
  q, 
  q 
  1 
  are 
  not 
  determined 
  by 
  the 
  analysis 
  (which 
  

   appears 
  to 
  determine 
  the 
  ratio 
  q'/q 
  but 
  no 
  more), 
  but 
  are 
  

   chosen 
  to 
  make 
  the 
  results 
  of 
  analysis 
  agree 
  with 
  those 
  of 
  

   experiment. 
  

  

  22. 
  For 
  any 
  infinitely 
  small 
  " 
  virtual 
  " 
  change 
  of 
  state 
  the 
  

   variation 
  of 
  the 
  total 
  entropy 
  must 
  in 
  the 
  stationary 
  state 
  

   vanish. 
  The 
  " 
  virtual 
  " 
  change 
  of 
  state 
  supposed 
  is 
  that 
  a 
  

   small 
  quantity 
  of 
  energy 
  proportional 
  to 
  "dK 
  x 
  is 
  added 
  to 
  one 
  

  

  system 
  of 
  period 
  — 
  , 
  and 
  another 
  small 
  quantity 
  proportional 
  

  

  Vl 
  1 
  

  

  to^Kgis 
  added 
  to 
  another 
  system 
  of 
  period 
  -, 
  cceteris 
  paribus. 
  

  

  Now 
  a 
  " 
  virtual 
  " 
  change 
  — 
  if 
  there 
  is 
  any 
  virtue 
  in 
  the 
  term 
  

   — 
  means 
  a 
  change 
  consistent 
  with 
  the 
  conditions 
  of 
  our 
  

   system. 
  In 
  this 
  supposition, 
  therefore, 
  we 
  have 
  definitely 
  

   thrown 
  overboard 
  the 
  restriction 
  that 
  energy 
  can 
  only 
  be 
  

   interchanged 
  between 
  systems 
  of 
  the 
  same 
  period. 
  

  

  However, 
  given 
  that 
  the 
  above 
  change 
  takes 
  place, 
  we 
  have 
  

   by 
  conservation 
  of 
  energy 
  

  

  BKx 
  + 
  dK^O. 
  

  

  And 
  by 
  conservation 
  of 
  entropy 
  in 
  the 
  stationary 
  state, 
  

  

  i>ilog 
  (q 
  1 
  K 
  l 
  )'dK 
  1 
  +p 
  2 
  \og 
  feK 
  2 
  )3K 
  2 
  = 
  0. 
  

  

  From 
  which 
  it 
  follows 
  that 
  in 
  the 
  stationary 
  state 
  p 
  log 
  (qK) 
  

   is 
  an 
  absolute 
  constant, 
  independent 
  of 
  v. 
  

   Assume 
  -. 
  

  

  p 
  log 
  (gK) 
  = 
  -tf 
  

  

  whence 
  ,, 
  1-1 
  

  

  K 
  = 
  e 
  pe. 
  

   9 
  

  

  Instead 
  of 
  v 
  Planck 
  now 
  introduces 
  the 
  new 
  variable 
  X, 
  the 
  

   wave-length, 
  by 
  the 
  formula 
  

  

  v 
  

  

  A, 
  

  

  