﻿340 
  Dr. 
  H. 
  S. 
  Allen 
  on 
  Molecular 
  

  

  expression 
  for 
  the 
  specific 
  heat, 
  C 
  v 
  , 
  which 
  is 
  reduced, 
  at 
  

   sufficiently 
  low 
  temperatures, 
  to 
  a 
  simple 
  law 
  of 
  propor- 
  

   tionality 
  between 
  G 
  v 
  and 
  T 
  3 
  . 
  That 
  this 
  is 
  also 
  true 
  for 
  certain 
  

   regular 
  polyatomic 
  substances 
  has 
  been 
  shown 
  experimentally 
  

   by 
  Eucken 
  and 
  Scbwers* 
  in 
  the 
  case 
  of 
  fluorite, 
  CaF 
  2 
  , 
  and 
  

   pyrites, 
  FeS 
  2 
  . 
  Thus 
  it 
  would 
  appear 
  that 
  near 
  the 
  absolute 
  

   zero 
  the 
  forces 
  uniting 
  the 
  atoms 
  in 
  the 
  molecule 
  are 
  suffi- 
  

   ciently 
  great;, 
  as 
  compared 
  with 
  the 
  forces 
  uniting 
  the 
  

   molecules, 
  to 
  compel 
  the 
  individual 
  atoms 
  to 
  follow 
  the 
  

   movements 
  of 
  the 
  molecule 
  of 
  which 
  each 
  forms 
  a 
  part. 
  At 
  

   low 
  temperatures 
  the 
  specific 
  heat 
  can 
  be 
  represented 
  by 
  

   Debye's 
  formula 
  assuming 
  a 
  single 
  characteristic 
  frequency. 
  

   At 
  higher 
  temperatures 
  Nernst 
  introduces 
  one 
  or 
  more 
  

   Einstein 
  terms, 
  with 
  appropriate 
  characteristic 
  frequencies, 
  

   to 
  include 
  the 
  vibrations 
  of 
  the 
  atoms 
  in 
  the 
  molecule. 
  It 
  

   will 
  be 
  shown 
  that 
  the 
  characteristic 
  frequency, 
  v, 
  for 
  the 
  

   molecular 
  movement 
  conforms 
  to 
  the 
  relation 
  previously 
  

   found 
  to 
  hold 
  for 
  the 
  elements, 
  viz. 
  

  

  Nv 
  = 
  w^a 
  or 
  Nv 
  = 
  (n 
  + 
  ^) 
  v 
  A 
  , 
  

  

  where 
  N 
  is 
  now 
  the 
  molecular 
  instead 
  of 
  the 
  atomic 
  number, 
  

   n 
  is 
  an 
  integer, 
  and 
  va 
  is 
  a 
  fundamental 
  frequency 
  having 
  a 
  

   value 
  very 
  near 
  to 
  21 
  x 
  10 
  12 
  sec. 
  -1 
  . 
  The 
  term 
  " 
  frequency 
  

   number 
  " 
  is 
  suggested 
  to 
  denote 
  the 
  numerical 
  factor, 
  n 
  or 
  

  

  It 
  would, 
  of 
  course, 
  be 
  possible 
  to 
  avoid 
  the 
  introduction 
  

   of 
  the 
  fraction 
  J 
  by 
  introducing 
  a 
  fundamental 
  frequency 
  

   which 
  is 
  -J 
  that 
  just 
  quoted, 
  but 
  as 
  the 
  number 
  of 
  cases 
  

   requiring 
  the 
  fractional 
  value 
  is 
  comparatively 
  small, 
  it 
  

   seems 
  better 
  to 
  retain 
  for 
  the 
  present 
  the 
  larger 
  value 
  for 
  v 
  K 
  . 
  

  

  § 
  3. 
  Characteristic 
  Frequency 
  from 
  Specific 
  Heat. 
  

  

  For 
  a 
  small 
  number 
  of 
  compounds 
  low-temperature 
  mea- 
  

   surements 
  are 
  available, 
  and 
  the 
  characteristic 
  frequency 
  

   can 
  be 
  deduced 
  from 
  the 
  specific 
  heat. 
  In 
  1912 
  Nernst 
  and 
  

   Lindemannf 
  published 
  observations 
  on 
  the 
  specific 
  heat 
  of 
  

   rock-salt 
  and 
  sylvin 
  at 
  temperatures 
  down 
  to 
  22° 
  K. 
  For 
  

   NaCl 
  the 
  characteristic 
  frequency, 
  v, 
  was 
  determined 
  by 
  

   the 
  equation 
  /3z> 
  = 
  287'3, 
  whilst 
  for 
  KC1 
  ^ 
  = 
  217-6, 
  where 
  

   £=4*78 
  xlO 
  -11 
  . 
  From 
  these 
  results 
  we 
  find 
  the 
  value 
  of 
  

   Ni> 
  for 
  rock-salt 
  to 
  be 
  8 
  x 
  21*0 
  x 
  10 
  12 
  , 
  whilst 
  for 
  sylvin 
  it 
  is 
  

   nearly 
  the 
  same, 
  8 
  x 
  20*5 
  x 
  10 
  12 
  . 
  In 
  his 
  address 
  on 
  the 
  

   Kinetic 
  Theory 
  Nernst 
  gives 
  different 
  values 
  for 
  the 
  Debye 
  

  

  * 
  Eucken 
  and 
  Schwers, 
  Btr. 
  deutsch.phys. 
  Gesell. 
  vol, 
  xv. 
  p. 
  578 
  (1913). 
  

   f 
  Freuss. 
  Akad. 
  Berlin, 
  p. 
  1160 
  (1912). 
  

  

  