﻿Radiation 
  and 
  Specific 
  Heat. 
  791 
  

  

  water 
  and 
  mercury, 
  show 
  a 
  diminution 
  of 
  specific 
  heat 
  with 
  

   rise 
  of 
  temperature. 
  

  

  IE 
  the 
  mean 
  frequencies 
  given 
  by 
  the 
  Peststrahlen 
  for 
  rock- 
  

   salt 
  and 
  sylvine 
  are 
  inserted 
  in 
  this 
  formula, 
  the 
  values 
  ob- 
  

   tained 
  for 
  the 
  specific 
  heats 
  are 
  in 
  good 
  agreement 
  with 
  

   those 
  found 
  experimentally 
  at 
  the 
  temperature 
  of 
  liquid 
  air, 
  

   but 
  are 
  somewhat 
  lower 
  than 
  those 
  found 
  in 
  liquid 
  hydrogen, 
  

   and 
  slightly 
  higher 
  than 
  those 
  found 
  at 
  ordinary 
  tempera- 
  

   tures. 
  This 
  may 
  be 
  explained 
  by 
  supposing 
  that 
  the 
  resonance 
  

   is 
  not 
  sharply 
  confined 
  to 
  a 
  single 
  frequency, 
  but 
  extends 
  

   over 
  an 
  appreciable 
  range. 
  The 
  effect 
  of 
  this 
  would 
  be 
  to 
  

   flatten 
  out 
  the 
  curve, 
  improving 
  the 
  agreement 
  at 
  high 
  and 
  

   low 
  temperatures, 
  without 
  materially 
  affecting 
  Ihe 
  agree- 
  

   ment 
  at 
  the 
  mean 
  point 
  where 
  z 
  = 
  3, 
  which 
  corresponds 
  

   approximately 
  in 
  the 
  case 
  of 
  rocksalt 
  and 
  sylvine 
  to 
  the 
  tem- 
  

   perature 
  of 
  liquid 
  air. 
  The 
  same 
  type 
  of 
  curve 
  represents 
  

   many 
  other 
  isotropic 
  substances 
  qualitatively, 
  but 
  the 
  appro- 
  

   priate 
  frequencies 
  cannot, 
  as 
  a 
  rule, 
  be 
  determined 
  by 
  

   independent 
  experiments. 
  For 
  anisotropic 
  substances, 
  such 
  

   as 
  ice 
  and 
  quartz, 
  possessing 
  different 
  frequencies 
  in 
  different 
  

   directions, 
  a 
  different 
  type 
  of 
  formula 
  would 
  no 
  doubt 
  be 
  

   required, 
  although 
  such 
  cases 
  might 
  be 
  represented 
  empiri- 
  

   cally 
  by 
  an 
  arbitrary 
  selection 
  of 
  frequencies. 
  

  

  It 
  is 
  well 
  known 
  that 
  the 
  formula 
  deduced 
  by 
  Einstein 
  

   from 
  Planck's 
  equation 
  by 
  somewhat 
  similar 
  reasoning, 
  does 
  

   not 
  give 
  correct 
  values 
  of 
  the 
  specific 
  heats 
  when 
  the 
  Rest- 
  

   strahlen 
  frequencies 
  are 
  assumed, 
  although 
  Planck's 
  formula 
  

   would 
  be 
  very 
  difficult 
  to 
  distinguish 
  from 
  that 
  here 
  pro- 
  

   posed 
  by 
  radiation 
  methods. 
  The 
  reason 
  may 
  possibty 
  be 
  

   that 
  the 
  Planck-Einstein 
  formulae 
  do 
  not 
  take 
  any 
  account 
  

   explicitly 
  of 
  the 
  pv 
  term 
  in 
  the 
  total 
  energy, 
  which, 
  for 
  the 
  

   matter 
  of 
  that, 
  is 
  seldom 
  or 
  never 
  mentioned 
  in 
  the 
  theory 
  oE 
  

   radiation, 
  except 
  in 
  the 
  deduction 
  of 
  the 
  fourth-power 
  law, 
  

   where 
  it 
  is 
  universally 
  admitted. 
  

  

  The 
  theory 
  above 
  sketched 
  differs 
  in 
  so 
  many 
  fundamental 
  

   points 
  from 
  that 
  commonly 
  accepted, 
  that 
  it 
  may 
  naturally 
  

   be 
  regarded 
  with 
  hesitation. 
  It 
  may 
  be 
  urged 
  in 
  apology 
  

   that 
  all 
  such 
  theories 
  are 
  necessarily 
  based 
  in 
  the 
  first 
  

   instance 
  on 
  somewhat 
  speculative 
  analogies. 
  The 
  analogy 
  

   assumed 
  in 
  the 
  present 
  case 
  is 
  very 
  simple, 
  and 
  the 
  results 
  

   to 
  which 
  it 
  leads 
  are 
  in 
  good 
  agreement 
  with 
  experiment. 
  

   The 
  same 
  relations 
  may 
  be 
  decruced 
  and 
  presented 
  in 
  many 
  

   other 
  ways, 
  and 
  the 
  theory 
  admits 
  of 
  many 
  obvious 
  exten- 
  

   sions. 
  But 
  it 
  seems 
  best 
  to 
  reserve 
  further 
  details 
  until 
  the 
  

   possibility 
  of 
  the 
  fundamental 
  assumption 
  has 
  been 
  discussed 
  

   by 
  capable 
  judges. 
  

  

  