﻿788 
  Prof. 
  H. 
  L. 
  Callendar 
  on 
  

  

  is 
  determined 
  by 
  the 
  condition 
  that 
  p 
  must 
  vary 
  as 
  v* 
  or 
  T 
  4 
  

   when 
  z//T 
  is 
  constant, 
  since 
  full 
  radiation 
  remains 
  saturated 
  

   in 
  adiabatic 
  compression. 
  

  

  The 
  corresponding 
  expression 
  for 
  the 
  intrinsic 
  energy- 
  

   density 
  E/v 
  is 
  

  

  E/v 
  = 
  G% 
  4 
  *- 
  6 
  "/ 
  T 
  (2) 
  

  

  Expressions 
  (1) 
  and 
  (2) 
  apply 
  to 
  the 
  variation 
  of 
  the 
  

   pressure 
  and 
  energy-density 
  of 
  components 
  or 
  molecules 
  

   included 
  in 
  a 
  frequency 
  interval 
  dv/v, 
  which 
  remains 
  constant 
  

   when 
  v 
  is 
  varied. 
  The 
  quantity 
  observed 
  in 
  experimental 
  

   measurements 
  is 
  proportional 
  to 
  the 
  latent 
  heat 
  per 
  unit 
  

   volume, 
  which 
  is 
  the 
  sum 
  of 
  (1) 
  and 
  (2). 
  The 
  isochromatics, 
  

   or 
  the 
  curves 
  representing 
  the 
  variation 
  with 
  temperature 
  

   of 
  the 
  latent 
  energy-density 
  of 
  a 
  particular 
  wave-length 
  or 
  

   frequency, 
  are 
  of 
  the 
  form, 
  

  

  E/v+p 
  = 
  Cp 
  3 
  {T 
  + 
  bv)e-^ 
  T 
  , 
  .... 
  (3) 
  

  

  which 
  agrees 
  somewhat 
  better 
  than 
  Planck's 
  well-known 
  

   formula 
  with 
  the 
  observations 
  of 
  Pubens 
  on 
  the 
  Re 
  ststr 
  allien 
  

   of 
  quartz, 
  fluorite, 
  and 
  rocksalt. 
  

  

  The 
  curve 
  of 
  variation 
  of 
  latent 
  heat 
  with 
  frequency 
  at 
  

   constant 
  temperature, 
  or 
  the 
  distribution 
  of 
  energy 
  in 
  the 
  

   spectrum, 
  is 
  most 
  familiarly 
  expressed 
  in 
  terms 
  of 
  the 
  wave- 
  

   length 
  X 
  = 
  c/v, 
  where 
  c 
  is 
  the 
  velocity 
  of 
  light. 
  The 
  latent 
  

   energy-density 
  L 
  per 
  unit 
  range 
  of 
  X 
  is 
  given 
  by 
  the 
  

   equation 
  

  

  Ld\ 
  = 
  W\- 
  5 
  {\T 
  + 
  bc)e- 
  bc 
  * 
  T 
  d\. 
  ... 
  (4) 
  

  

  This 
  curve 
  has 
  a 
  maximum 
  when 
  \T 
  = 
  *2071 
  be, 
  whence 
  

   the 
  value 
  of 
  the 
  constant 
  be 
  is 
  1*400, 
  if 
  X 
  is 
  measured 
  in 
  

   cms. 
  and 
  the 
  position 
  of 
  the 
  maximum 
  is 
  taken 
  at 
  XT 
  = 
  '2900 
  

   from 
  experimental 
  data. 
  Formula 
  (4) 
  reduces, 
  like 
  Planck's 
  

   equation, 
  to 
  Rayleigh's 
  formula 
  for 
  large 
  values 
  of 
  XT, 
  and 
  

   to 
  Wien's 
  formula 
  for 
  small 
  values. 
  The 
  relative 
  values 
  

   given 
  by 
  equation 
  (4) 
  for 
  the 
  distribution 
  throughout 
  the 
  

   observational 
  range 
  on 
  either 
  side 
  of 
  the 
  maximum, 
  agree 
  so 
  

   closely 
  with 
  tbose 
  given 
  by 
  Planck's 
  formula 
  that 
  a 
  special 
  

   null 
  method 
  was 
  devised 
  with 
  the 
  object 
  of 
  testing 
  the 
  

   formulae 
  by 
  experiment. 
  Unfortunately, 
  the 
  somewhat 
  

   elaborate 
  apparatus 
  required 
  for 
  this 
  purpose, 
  though 
  com- 
  

   menced 
  in 
  1908, 
  has 
  not 
  yet 
  been 
  completed 
  owing 
  to 
  

   pressure 
  of 
  other 
  work. 
  In 
  the 
  meantime 
  the 
  approximate 
  

   agreement 
  with 
  Planck's 
  formula 
  may 
  be 
  taken 
  as 
  an 
  indi- 
  

   cation 
  of 
  the 
  possible 
  correctness 
  of 
  (4), 
  which 
  appears 
  to 
  

   harmonize 
  better 
  than 
  Planck's 
  formula 
  with 
  the 
  " 
  classical 
  

   thermodynamics.'' 
  

  

  