﻿Processes 
  and 
  Planck's 
  Theory; 
  23# 
  

  

  And 
  thence 
  using 
  his 
  own 
  form 
  for 
  p 
  and 
  q, 
  namely 
  p 
  = 
  — 
  ,, 
  

   q 
  = 
  — 
  v 
  he 
  obtains 
  for 
  the 
  intensity 
  E 
  x 
  , 
  of 
  the 
  wave-length 
  \. 
  

  

  which 
  is 
  Wien's 
  law. 
  And 
  this 
  at 
  the 
  date 
  of 
  Planck's' 
  

   paper 
  now 
  under 
  discussion 
  was 
  considered 
  to 
  be 
  sufficiently 
  

   accurate. 
  

  

  23. 
  Later 
  researches 
  of 
  Beckmann, 
  Pringsheim, 
  and 
  others, 
  

   throw 
  doubt 
  on 
  the 
  accuracy 
  of 
  "Wien's 
  law. 
  It 
  becomes, 
  

   then 
  necessary, 
  in 
  order 
  to 
  make 
  the 
  results 
  of 
  Planck's 
  

   analysis 
  agree 
  with 
  experiments, 
  either 
  to 
  vary 
  the 
  constants 
  

   p, 
  q, 
  q', 
  or 
  else 
  to 
  vary 
  the 
  form 
  of 
  the 
  function 
  S. 
  And 
  this 
  

   Planck 
  does 
  in 
  his 
  paper 
  " 
  Ueber 
  irreversible 
  Strahlungs- 
  

   vorgange 
  " 
  ( 
  Preuss. 
  Akad. 
  Wiss. 
  Berlin, 
  Sitzungsberichte, 
  xxv. 
  

   pp. 
  544-555, 
  May 
  9, 
  1901). 
  He 
  there, 
  without 
  altering 
  the 
  

   general 
  theory 
  as 
  developed 
  in 
  the 
  former 
  treatise, 
  assumes, 
  

   for 
  the 
  entropy 
  of 
  the 
  resonator 
  

  

  »-'{(>+ 
  £M>+£)-NE}. 
  

  

  where 
  k 
  and 
  h 
  are 
  constants, 
  and 
  obtains 
  results 
  in 
  accordance- 
  

   with 
  the 
  later 
  experiments. 
  

  

  Is 
  Planck's 
  a 
  true 
  irreversible 
  process 
  ? 
  

  

  24. 
  According 
  to 
  the 
  theorems 
  of 
  art. 
  2, 
  every 
  interchange- 
  

   of 
  energy 
  between 
  the 
  parts 
  of 
  a 
  material 
  system, 
  if 
  such 
  

   interchanges 
  are 
  made 
  in 
  accordance 
  with 
  the 
  law 
  there 
  

   assumed, 
  is 
  an 
  irreversible 
  process, 
  just 
  as, 
  and 
  for 
  the 
  same 
  

   reason 
  that, 
  interchanges 
  of 
  heat 
  between 
  hot 
  and 
  cold 
  bodies, 
  

   are 
  irreversible. 
  Now 
  according 
  to 
  Planck 
  the 
  interchanges 
  of 
  

   energy 
  between 
  different 
  parts 
  of 
  his 
  system 
  do 
  take 
  place 
  

   according 
  to 
  the 
  law 
  assumed 
  in 
  art. 
  2. 
  The 
  process, 
  if 
  it 
  

   exists 
  in 
  nature, 
  is 
  therefore 
  an 
  irreversible 
  process. 
  

  

  But 
  the 
  existence 
  of 
  such 
  a 
  machine 
  as 
  Planck's 
  resonator 
  

   cannot 
  be 
  proved 
  by 
  experiment. 
  For 
  any 
  actual 
  electric 
  

   vibration 
  such 
  as 
  he 
  supposes 
  must 
  be 
  accompanied 
  by 
  dissi- 
  

   pation 
  of 
  energy. 
  It 
  may 
  be 
  that 
  aether, 
  the 
  universal 
  solvent 
  

   of 
  mathematical 
  difficulties, 
  supplies 
  us 
  with 
  the 
  instrument 
  

   required. 
  But 
  if 
  not, 
  Planck's 
  process 
  is 
  non-existent. 
  And 
  

   can 
  a 
  non-existent 
  process 
  be 
  irreversible? 
  

  

  25. 
  It 
  seems 
  to 
  me 
  that 
  if 
  at 
  any 
  instant 
  all 
  the 
  velocities 
  in 
  

   Planck's 
  problem 
  were 
  reversed, 
  the 
  system 
  would 
  not 
  retrace 
  

  

  