﻿214 
  Prof. 
  J. 
  H. 
  Jeans 
  on 
  the 
  

  

  This 
  formula 
  can 
  be 
  used, 
  as 
  in 
  Part 
  I., 
  for 
  the 
  calculation 
  

   of 
  radiation. 
  It 
  is 
  of 
  interest 
  to 
  notice 
  that 
  it 
  can 
  be 
  readily 
  

   transformed 
  to 
  another 
  known 
  formula. 
  

  

  If 
  we 
  replace 
  cosp(^i 
  — 
  ^2) 
  ^J 
  Gosph 
  cosp^2 
  + 
  sinp^isin;)/2r 
  

   and 
  integrate 
  by 
  parts 
  with 
  respect 
  to 
  ^1 
  and 
  fg 
  simultaneously^ 
  

   w^e 
  obtain 
  for 
  the 
  emission 
  

  

  + 
  sin 
  pti 
  sin 
  pt2)dt 
  I 
  dt2 
  > 
  dp 
  

  

  p=o 
  

  

  p 
  

   _ 
  2//, 
  

  

  p=o 
  \ 
  

  

  which 
  is 
  the 
  formula 
  used 
  by 
  Sir 
  J. 
  J. 
  Thomson 
  *. 
  On 
  

   integration 
  wiih 
  respect 
  to 
  p, 
  the 
  total 
  radiation 
  per 
  unit 
  

   volume 
  per 
  unit 
  time 
  is 
  verified 
  to 
  be 
  

  

  2^«T 
  (60) 
  

  

  Radiation 
  in 
  a 
  Perfectly 
  Reflecting 
  Enclosure. 
  

  

  30. 
  Every 
  material 
  substance 
  ought, 
  on 
  the 
  electromagnetic 
  

   theory 
  of 
  light, 
  to 
  be 
  perfectly 
  reflecting 
  for 
  waves 
  of 
  infinite 
  

   wave-length, 
  while 
  all 
  actual 
  substances 
  are 
  transparent 
  for 
  

   waves 
  of 
  very 
  short 
  wave-length. 
  

  

  It 
  follows 
  that 
  in 
  any 
  actual 
  enclosure, 
  the 
  radiation 
  of 
  

   great 
  wave-length 
  will 
  be 
  retained 
  indefinitely, 
  so 
  that 
  equi~ 
  

   libiium 
  (i. 
  e, 
  equipartition) 
  of 
  energy 
  must 
  be 
  established 
  

   between 
  this 
  radiation 
  and 
  the 
  matter 
  in 
  the 
  enclosure 
  (a 
  

   consequence 
  of 
  general 
  dynamical 
  theory 
  which 
  we 
  have 
  

   already 
  verified), 
  but 
  the 
  radiation 
  of 
  short 
  wave-length 
  will 
  

   escape 
  without 
  ever 
  attaining 
  to 
  energy-equilibrium. 
  

  

  On 
  the 
  other 
  hand 
  in 
  an 
  ideal 
  (but 
  in 
  practice 
  unattain- 
  

   able) 
  enclosure, 
  from 
  which 
  no 
  radiant 
  energy 
  can 
  escapCj 
  

   no 
  matter 
  how 
  short 
  its 
  wave-length, 
  there 
  ought 
  to 
  be 
  equi- 
  

   librium 
  of 
  energy 
  between 
  matter 
  and 
  radiant 
  energy 
  of 
  all 
  

   wave-lengths. 
  The 
  law 
  of 
  partition 
  of 
  radiant 
  energy 
  in 
  

   such 
  an 
  enclosure 
  ought, 
  therefore, 
  to 
  be 
  that 
  given 
  by 
  the^ 
  

   theorem 
  of 
  equipartition 
  of 
  energy, 
  namely, 
  

  

  87rRTX-4^/\ 
  (()1) 
  

  

  * 
  Phil. 
  Mag-. 
  (6) 
  vol. 
  xiv. 
  p. 
  217. 
  

  

  