﻿On 
  Irreversible 
  Processes 
  and 
  Planck 
  3 
  s 
  Theory. 
  225 
  

  

  appears 
  also 
  to 
  be 
  reached 
  sooner 
  when 
  the 
  outer 
  cylinder 
  is 
  

   positive 
  than 
  when 
  it 
  is 
  negative. 
  It 
  follows 
  that 
  as 
  the 
  

   potential 
  of 
  the 
  cylinder 
  is 
  numerically 
  raised, 
  a 
  voltage 
  is 
  

   reached 
  at 
  which 
  the 
  positive 
  current 
  overtakes 
  the 
  negative; 
  

   an 
  event 
  which, 
  however, 
  only 
  happens 
  when 
  the 
  sparking 
  

   point 
  is 
  nearly 
  reached. 
  

  

  19. 
  These 
  phenomena 
  possibly 
  indicate 
  that 
  when 
  X/p 
  

   attains 
  a 
  certain 
  magnitude, 
  positive 
  ions 
  under 
  certain 
  cir- 
  

   cumstances 
  of 
  impact 
  are 
  capable 
  of 
  generating 
  others 
  by 
  

   collision, 
  and 
  such 
  an 
  hypothesis 
  would 
  easily 
  account 
  for 
  all 
  

   the 
  facts, 
  including 
  sparking. 
  But 
  experiments 
  will 
  be 
  

   undertaken 
  in 
  order, 
  if 
  possible, 
  to 
  throw 
  light 
  on 
  this 
  subject. 
  

   Another 
  series 
  of 
  experiments 
  are 
  being 
  undertaken 
  to 
  exhibit 
  

   the 
  difference 
  of 
  behaviour 
  between 
  positively 
  and 
  negatively 
  

   charged 
  ions 
  generated 
  from, 
  and 
  moving 
  in, 
  hydrogen 
  and 
  

   carbonic 
  acid 
  gas. 
  

  

  I 
  must 
  take 
  this 
  opportunity 
  of 
  thanking 
  both 
  Professor 
  

   Townsend, 
  who 
  suggested 
  this 
  research, 
  for 
  his 
  many 
  sug- 
  

   gestions, 
  and 
  Professor 
  Turner 
  for 
  his 
  kindness 
  in 
  providing 
  

   a 
  laboratory, 
  doubtless 
  at 
  great 
  personal 
  inconvenience, 
  in 
  

   the 
  University 
  Observatory, 
  Oxford, 
  where 
  the 
  experiments 
  

   were 
  carried 
  out. 
  

  

  XXIII. 
  On 
  Irreversible 
  Processes 
  and 
  Planck's 
  Theory 
  in 
  

   relation 
  thereto. 
  By 
  S. 
  H. 
  Burbury, 
  F.R.S* 
  

  

  PLANCK'S 
  theory 
  is 
  developed 
  in 
  his 
  treatise 
  " 
  Ueber 
  

   irreversible 
  Strahlungsvorgange 
  " 
  {Berlin. 
  Sitzungs- 
  

   berichte, 
  1897, 
  pp. 
  441-480), 
  and 
  is 
  modified 
  in 
  subsequent 
  

   papers 
  in 
  detail 
  only. 
  It 
  will 
  be 
  found 
  to 
  depend 
  on 
  some 
  

   well-known 
  algebraic 
  theorems, 
  and 
  on 
  a 
  certain 
  law 
  of 
  

   interchange 
  of 
  energy 
  between 
  the 
  parts 
  of 
  a 
  material 
  

   system. 
  

  

  1. 
  If 
  u, 
  v 
  be 
  two 
  quantities 
  necessarily 
  positive, 
  and 
  which 
  

   vary 
  subject 
  to 
  the 
  condition 
  that 
  u 
  + 
  v=2c, 
  a 
  constant, 
  the 
  

   least 
  possible 
  value 
  of 
  u 
  log 
  n 
  + 
  v 
  log 
  v 
  is 
  when 
  u 
  = 
  v, 
  and 
  the 
  

   greatest 
  is 
  when 
  either 
  u 
  = 
  or 
  v 
  = 
  0. 
  For 
  we 
  may 
  write 
  

   u 
  = 
  c-t-x, 
  v 
  = 
  c—x, 
  x 
  being 
  positive 
  and 
  less 
  than 
  c. 
  Then 
  

  

  — 
  (u 
  log 
  u 
  + 
  v 
  log 
  v) 
  = 
  j- 
  (c 
  + 
  x 
  log 
  c 
  + 
  x 
  + 
  c—x\og 
  c—x) 
  

  

  n 
  C 
  + 
  X 
  

  

  =lo 
  « 
  ^ 
  

  

  -and 
  as 
  this 
  is 
  necessarily 
  positive, 
  the 
  proposition 
  is 
  proved. 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  3. 
  No. 
  14. 
  Feb. 
  1902. 
  Q 
  

  

  