﻿Radiation 
  and 
  Specific 
  Heat. 
  789 
  

  

  If 
  the 
  values 
  given 
  in 
  (1) 
  and 
  (2) 
  for 
  the 
  partial 
  pressure 
  

   and 
  energy-density 
  in 
  equal 
  intervals 
  dvjv 
  (or 
  dX/X) 
  are 
  

   integrated 
  from 
  to 
  infinity 
  at 
  constant 
  temperature, 
  we 
  

   obtain 
  for 
  the 
  total 
  pressure 
  and 
  energy-density 
  of 
  full 
  

   radiation 
  the 
  expressions 
  

  

  P=2CTV& 
  3 
  , 
  and 
  E/V=6CT76 
  3 
  , 
  ... 
  (5) 
  

  

  or 
  the 
  pressure 
  of 
  fall 
  radiation 
  is 
  one-third 
  of 
  the 
  intrinsic 
  

   energy-density, 
  which 
  is 
  the 
  relation 
  generally 
  assumed 
  in 
  

   deducing 
  the 
  fourth-power 
  law, 
  but 
  this 
  cannot 
  be 
  true 
  for 
  

   each 
  component 
  separately. 
  

  

  According 
  to 
  the 
  theory 
  of 
  exchanges, 
  the 
  total 
  stream 
  

   Q 
  = 
  <jT 
  4 
  , 
  which 
  issues 
  per 
  sq. 
  cm. 
  per 
  sec. 
  from 
  a 
  black 
  

   surface 
  at 
  a 
  temperature 
  T, 
  is 
  3c/4 
  of 
  the 
  pressure, 
  or 
  c/4 
  of 
  

   the 
  energy-density, 
  in 
  the 
  case 
  of 
  full 
  radiation. 
  Whence 
  

   the 
  value 
  of 
  the 
  constant 
  is 
  26 
  3 
  cr/3c, 
  in 
  terms 
  of 
  the 
  radia- 
  

   tion 
  constant 
  a, 
  the 
  probable 
  value 
  of 
  which 
  is 
  5*60 
  x 
  10~ 
  5 
  

  

  C.G.S. 
  

  

  It 
  will 
  be 
  observed 
  that, 
  in 
  the 
  case 
  of 
  long 
  waves 
  and 
  

   high 
  temperatures, 
  according 
  to 
  formula 
  (4), 
  neglecting 
  the 
  

   square 
  of 
  the 
  small 
  quantity 
  be/XT, 
  the 
  total 
  energy 
  reduces 
  

   to 
  the 
  pressure 
  term, 
  namely, 
  Cg' 
  s 
  A-~ 
  4 
  T. 
  If 
  the 
  external 
  

   energy 
  pv 
  is 
  equally 
  divided 
  among 
  the 
  molecules 
  as 
  already 
  

   assumed, 
  the 
  value 
  of 
  the 
  constant 
  Cc 
  3 
  should 
  be 
  87rR/N, 
  

   according 
  to 
  the 
  reasoning 
  of 
  Lord 
  Rayleigh 
  (' 
  Nature,' 
  

   vol. 
  lxxii. 
  p. 
  54) 
  based 
  on 
  the 
  equipartition 
  of 
  energy. 
  The 
  

   value 
  of 
  ST 
  deduced 
  from 
  that 
  of 
  C 
  on 
  this 
  assumption 
  is 
  

   6 
  12 
  x 
  10 
  23 
  , 
  which 
  agrees 
  closely 
  with 
  Planck's 
  * 
  value, 
  and 
  

   with 
  the 
  latest 
  estimates 
  based 
  on 
  the 
  phenomena 
  of 
  radio- 
  

   activity. 
  But 
  according 
  to 
  my 
  view, 
  equipartition 
  applies 
  

   only 
  to 
  the 
  pressure-energy. 
  The 
  intrinsic 
  energy, 
  depend- 
  

   ing 
  on 
  the 
  frequency, 
  should 
  not 
  be 
  equally 
  divided, 
  because 
  

   the 
  frequencies 
  are 
  mutually 
  independent, 
  and 
  incapable 
  of 
  

   directly 
  affecting 
  each 
  other 
  in 
  free 
  aether. 
  There 
  is, 
  how- 
  

   ever, 
  an 
  analogous 
  relation 
  for 
  the 
  partition 
  of 
  energy 
  of 
  a 
  

   given 
  frequency 
  between 
  the 
  aether 
  and 
  a 
  material 
  molecule 
  

   of 
  the 
  same 
  frequency. 
  

  

  According 
  to 
  Planck's 
  well-known 
  relation, 
  the 
  intrinsic 
  

   energy 
  U 
  A 
  of 
  a 
  resonator 
  of 
  frequency 
  cjX 
  in 
  equilibrium 
  

  

  * 
  It 
  may 
  be 
  remarked 
  that 
  Planck's 
  quantum 
  h 
  is 
  the 
  same 
  as 
  the 
  

   molecular 
  unit 
  of 
  caloric 
  Hb/~N, 
  namely 
  the 
  intrinsic 
  energy 
  Hbv 
  per 
  gm. 
  

   mol. 
  divided 
  by 
  the 
  number 
  of 
  molecules 
  N 
  and 
  by 
  the 
  frequency 
  v. 
  

   The 
  difference 
  between 
  the 
  present 
  theory 
  and 
  Planck's 
  appears 
  to 
  

   originate 
  mainly 
  from 
  his 
  assumption 
  for 
  the 
  entropy 
  relation, 
  TdS 
  — 
  dE, 
  

   in 
  place 
  of 
  the 
  usual 
  dE+pdv. 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  154. 
  Oct. 
  1913. 
  3 
  G 
  

  

  