﻿790 
  Prof. 
  H. 
  L. 
  Callendar 
  on 
  

  

  with 
  full 
  radiation 
  of 
  intrinsic 
  energy-density 
  u 
  K 
  per 
  unit 
  

   range 
  of 
  \ 
  at 
  X, 
  is 
  given 
  by 
  the 
  equation 
  

  

  U 
  x 
  =3A, 
  4 
  w 
  A 
  /87r; 
  (6) 
  

  

  this 
  appears 
  to 
  be 
  deducible 
  from 
  the 
  usual 
  differential 
  

   equation 
  of 
  forced 
  oscillations 
  on 
  the 
  assumption 
  that 
  the 
  

   only 
  damping 
  is 
  that 
  due 
  to 
  radiation, 
  and 
  may 
  be 
  applied 
  

   with 
  a 
  fair 
  degree 
  of 
  probability 
  to 
  the 
  equilibrium 
  between 
  

   the 
  intrinsic 
  energy 
  of 
  vibration 
  of 
  molecules 
  and 
  that 
  of 
  

   the 
  corresponding 
  frequencies 
  of 
  thermal 
  radiation. 
  

  

  Taking 
  the 
  value 
  of 
  u^ 
  as 
  that 
  given 
  by 
  the 
  intrinsic 
  energy 
  

   term 
  in 
  equation 
  (4), 
  with 
  87rR/N 
  for 
  Cc 
  3 
  , 
  the 
  intrinsic 
  

   energy 
  of 
  N 
  molecules 
  in 
  equilibrium 
  with 
  full 
  radiation 
  at 
  

   a 
  temperature 
  T 
  becomes 
  

  

  E-NU 
  x 
  =3E^ 
  &cMT 
  6c/X, 
  .... 
  (7) 
  

  

  the 
  limit 
  of 
  which, 
  when 
  T 
  is 
  infinite, 
  is 
  3R&V, 
  or 
  three 
  times 
  

   the 
  intrinsic 
  energy 
  of 
  a 
  gramme 
  molecule 
  of 
  radiation 
  of 
  

   the 
  same 
  frequency. 
  This 
  quantity 
  may 
  be 
  regarded 
  simply 
  

   as 
  the 
  intrinsic 
  energy 
  of 
  the 
  radiation 
  condensed 
  in 
  the 
  

   molecules, 
  which 
  is 
  independent 
  of 
  the 
  temperature 
  except 
  

   for 
  the 
  exponential 
  term. 
  

  

  The 
  corresponding 
  value 
  of 
  the 
  PV 
  of 
  the 
  condensed 
  

   radiation 
  is, 
  

  

  PV 
  = 
  3ftT<r* 
  c/XT 
  (8) 
  

  

  The 
  only 
  specific 
  heat 
  which 
  can 
  be 
  measured 
  experi- 
  

   mentally 
  in 
  the 
  majority 
  of 
  cases 
  is 
  the 
  rate 
  of 
  variation 
  

   of 
  the 
  total 
  heat 
  E 
  + 
  PV 
  when 
  the 
  substance 
  is 
  in 
  equi- 
  

   librium 
  with 
  full 
  radiation. 
  The 
  term 
  PV 
  here 
  represents 
  

   the 
  internal 
  pressure-energy 
  of 
  the 
  condensed 
  radiation. 
  

   The 
  external 
  pressure 
  may 
  generally 
  be 
  neglected 
  in 
  the 
  case 
  

   of 
  solids 
  or 
  liquids 
  in 
  comparison 
  with 
  the 
  internal 
  pressure 
  

   of 
  the 
  radiation. 
  

  

  Differentiating 
  the 
  sum 
  of 
  (7) 
  and 
  (8) 
  with 
  regard 
  to 
  T, 
  

   and 
  writing 
  z 
  as 
  an 
  abbreviation 
  for 
  be/XT 
  or 
  bv/T, 
  we 
  obtain 
  

   as 
  the 
  expression 
  for 
  the 
  variation 
  of 
  the 
  specific 
  heat 
  in 
  the 
  

   simple 
  case 
  of 
  a 
  gramme-atom 
  of 
  a 
  substance 
  possessing 
  only 
  

   a 
  single 
  frequency, 
  

  

  d(E 
  + 
  TY)/dT 
  = 
  3R(i 
  + 
  z 
  + 
  s*) 
  e 
  -'. 
  . 
  . 
  (9) 
  

  

  This 
  expression 
  gives 
  a 
  limit 
  3R, 
  as 
  it 
  should, 
  when 
  z 
  = 
  0, 
  

   but 
  has 
  a 
  maximum 
  9H/e, 
  when 
  0=1. 
  This 
  might 
  appear 
  

   at 
  first 
  sight 
  to 
  be 
  a 
  fatal 
  objection, 
  but 
  it 
  is 
  a 
  well 
  ascer- 
  

   tained 
  fact, 
  which 
  has 
  not 
  been 
  previously 
  explained 
  in 
  a 
  

   satisfactory 
  manner, 
  that 
  some 
  simple 
  substances, 
  such 
  as 
  

  

  