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  LXVI. 
  Note 
  on 
  Radiation 
  and 
  Specific 
  Heat. 
  

   By 
  H. 
  L. 
  Callendar 
  *. 
  

  

  I^HE 
  following 
  note 
  is 
  communicated 
  in 
  explanation 
  of 
  

   some 
  points 
  raised 
  in 
  my 
  address 
  to 
  Section 
  A 
  of 
  the 
  

   British 
  Association 
  last 
  year. 
  

  

  When 
  a 
  given 
  quantity 
  of 
  full 
  radiation 
  is 
  compressed 
  in 
  a 
  

   reflecting 
  enclosure 
  the 
  wave-length 
  of 
  each 
  component 
  is 
  

   altered 
  by 
  the 
  Doppler 
  effect 
  in 
  proportion 
  to 
  the 
  cube 
  root 
  

   of 
  the 
  volume, 
  and 
  the 
  intrinsic 
  energy 
  of 
  each 
  varies 
  

   directly 
  as 
  the 
  frequency. 
  The 
  measure 
  of 
  the 
  temperature 
  

   is 
  the 
  common 
  ratio 
  in 
  which 
  the 
  energy 
  and 
  frequency 
  of 
  

   all 
  the 
  components 
  is 
  changed 
  ; 
  and 
  the 
  measure 
  of 
  the 
  

   quantity 
  of 
  each 
  component 
  which 
  remains 
  constant 
  is 
  the 
  

   energy 
  divided 
  by 
  the 
  frequency, 
  or 
  in 
  the 
  case 
  of 
  full 
  

   radiation 
  by 
  the 
  temperature. 
  

  

  A 
  quantity 
  of 
  radiation 
  such 
  that 
  the 
  product 
  of 
  its 
  pressure 
  

   and 
  volume 
  pv 
  is 
  equal 
  to 
  RT 
  (the 
  same 
  as 
  that 
  of 
  a 
  gramme 
  

   molecule 
  of 
  a 
  gas 
  at 
  the 
  same 
  temperature) 
  may 
  conveniently 
  

   be 
  called 
  a 
  gramme-molecule, 
  and 
  regarded 
  as 
  consisting 
  of 
  

   N 
  separate 
  molecules 
  (molecules 
  of 
  caloric) 
  for 
  descriptive 
  

   purposes. 
  If 
  the 
  frequencies 
  of 
  the 
  components 
  are 
  included 
  

   between 
  the 
  limits 
  v 
  and 
  v 
  + 
  dv 
  at 
  the 
  temperature 
  T, 
  the 
  

   intrinsic 
  energy 
  E 
  per 
  gm. 
  mol. 
  may 
  be 
  represented 
  by 
  B.bv, 
  

   where 
  b 
  is 
  a 
  constant, 
  and 
  will 
  be 
  included 
  in 
  an 
  equal 
  

   interval 
  dvjv 
  of 
  frequency 
  when 
  v 
  is 
  varied 
  by 
  adiabatic 
  

   compression 
  in 
  the 
  same 
  ratio 
  as 
  T, 
  the 
  quantity 
  remaining 
  

   constant. 
  The 
  ratio 
  E/jdi> 
  of 
  the 
  energy-density 
  E/i? 
  to 
  the 
  

   pressure 
  p 
  } 
  will 
  be 
  of 
  the 
  form 
  ftv/T, 
  and 
  the 
  latent 
  heat, 
  

   L 
  = 
  E/t' 
  + 
  p, 
  absorbed 
  in 
  the 
  production 
  of 
  unit 
  volume 
  will 
  

   be 
  represented 
  by 
  p(l 
  + 
  bv/T), 
  

  

  It 
  is 
  assumed 
  on 
  the 
  molecular 
  theory 
  that 
  the 
  condition 
  

   of 
  equilibrium 
  between 
  different 
  frequencies 
  at 
  the 
  same 
  

   temperature 
  is 
  the 
  same 
  as 
  that 
  between 
  molecules, 
  namely, 
  

   that 
  the 
  product 
  pv 
  for 
  N 
  molecules 
  of 
  any 
  frequency 
  is 
  equal 
  

   to 
  RT, 
  in 
  which 
  case 
  the 
  expression 
  bv/T 
  for 
  the 
  ratio 
  ~E/pv 
  

   applies 
  generally 
  when 
  v 
  and 
  T 
  vary 
  independently. 
  The 
  

   variation 
  of 
  the 
  saturation 
  pressure 
  jt? 
  of 
  a 
  particular 
  frequency 
  

   v 
  follows 
  immediately 
  by 
  Carnot's 
  principle,, 
  since 
  the 
  latent 
  

   heat 
  per 
  unit 
  volume 
  Fj/v+p 
  must 
  be 
  equal 
  to 
  T(dp/dT). 
  

   The 
  integration 
  of 
  this 
  equation 
  at 
  constant 
  v 
  gives 
  an 
  

   expression 
  of 
  the 
  form, 
  

  

  p^WTe'W, 
  (1) 
  

  

  in 
  which 
  the 
  constant 
  of 
  integration 
  Cv 
  d 
  i 
  as 
  a 
  function 
  of 
  v, 
  

  

  * 
  Communicated 
  bv 
  the 
  Author. 
  

  

  