﻿232 
  Mr. 
  S. 
  H. 
  Burbury 
  on 
  Irreversible 
  

  

  3cV 
  

   be 
  very 
  small. 
  Therefore 
  -r 
  — 
  is 
  a 
  quantity 
  whose 
  square 
  

  

  may 
  be 
  neglected. 
  7rv 
  

  

  The 
  result 
  stated 
  above 
  for 
  the 
  absorbed 
  energy 
  involves 
  a 
  

   relation 
  between 
  the 
  magnitude 
  of 
  the 
  elementary 
  area 
  r' 
  2 
  d£l, 
  

   that 
  is 
  the 
  section 
  of 
  the 
  wave 
  which 
  we 
  are 
  considering, 
  and 
  

   the 
  cross 
  section 
  of 
  the 
  resonator. 
  For 
  the 
  quantity 
  of 
  

   energy 
  absorbed 
  by 
  the 
  resonator 
  will 
  depend 
  on 
  the 
  cross 
  

   section, 
  so 
  therefore 
  must 
  dCl. 
  I 
  understand 
  Planck 
  to 
  state 
  

   this, 
  p. 
  461. 
  

  

  11. 
  Again, 
  the 
  energy 
  emitted 
  by 
  the 
  resonator 
  per 
  unit 
  of 
  

   time 
  is 
  2avTJ 
  (art. 
  8). 
  It 
  is 
  emitted 
  uniformly 
  in 
  all 
  

   directions, 
  making 
  with 
  the 
  axis 
  angles 
  between 
  6 
  and 
  

   + 
  d0. 
  But 
  the 
  energy 
  emitted 
  in 
  such 
  directions 
  is 
  pro- 
  

   portional 
  to 
  sin 
  2 
  0. 
  Therefore 
  the 
  energy 
  emitted 
  in 
  any 
  

   direction 
  d£l 
  is 
  per 
  unit 
  of 
  time 
  

  

  2<7vUsin 
  2 
  <9dn 
  3<rvU 
  

  

  sir 
  0dlL, 
  

  

  J« 
  

  

  4.7T 
  

  

  because 
  \ 
  sin 
  2 
  0d£l 
  = 
  ~ 
  . 
  

   J 
  3 
  

  

  12. 
  The 
  energy 
  thus 
  emitted 
  by 
  the 
  resonator 
  is 
  absorbed 
  

   by 
  the 
  waves 
  of 
  the 
  same 
  period 
  -. 
  It 
  follows 
  that 
  if 
  

  

  fKidfl 
  dt 
  denotes 
  the 
  energy 
  of 
  the 
  wave 
  of 
  period 
  - 
  which 
  

   passes 
  the 
  elementary 
  area 
  r 
  2 
  d£l 
  in 
  time 
  dt, 
  

  

  dt 
  ^ 
  =/ 
  W 
  = 
  - 
  47TV 
  Kl 
  Sm 
  $ 
  + 
  to 
  U 
  Sm 
  6 
  

  

  But 
  dJJ 
  3c*v/ 
  v 
  v 
  2 
  U\ 
  . 
  2 
  . 
  

  

  Therefore 
  d(f%) 
  dU__ 
  

  

  dr 
  + 
  dt~ 
  

  

  expresses 
  the 
  conservation 
  of 
  energy. 
  

  

  13. 
  The 
  conditions 
  of 
  the 
  transfer 
  of 
  energy 
  between 
  

   resonator 
  and 
  wave 
  are 
  precisely 
  the 
  conditions 
  necessary 
  for 
  

   application 
  of 
  the 
  theorem 
  of 
  art. 
  3. 
  Each 
  system 
  emits 
  to 
  

   the 
  other 
  per 
  unit 
  of 
  time 
  an 
  amount 
  of 
  energy 
  proportional 
  

   to 
  the 
  energy 
  which 
  the 
  emitting 
  system 
  has 
  for 
  the 
  time 
  

   being. 
  Further, 
  the 
  ratio 
  k 
  i2 
  /k 
  21 
  of 
  art. 
  2 
  is 
  here 
  c 
  2 
  /y 
  2 
  . 
  We 
  

   expect 
  then 
  to 
  find 
  that 
  an 
  entropy 
  function 
  exists. 
  

  

  