﻿Frequency 
  and 
  Molecular 
  JS 
  umber. 
  405 
  

  

  atoms 
  contained 
  in 
  the 
  compound. 
  The 
  writer 
  has 
  shown* 
  

   that 
  the 
  characteristic 
  frequency, 
  v 
  % 
  o£ 
  the 
  atom 
  of 
  a 
  solid 
  

   element 
  is 
  connected 
  with 
  the 
  atomic 
  number 
  N 
  by 
  the 
  

   relation 
  

  

  Nv 
  = 
  ?w 
  A 
  or 
  Ni>= 
  (71 
  + 
  i)^' 
  

   where 
  n 
  is 
  an 
  integer, 
  and 
  v 
  A 
  a 
  constant 
  frequency 
  having 
  a 
  

   value 
  not 
  far 
  from 
  21 
  X 
  10 
  12 
  sec. 
  -1 
  . 
  Seeing 
  that 
  the 
  forces 
  

   which 
  control 
  the 
  vibrations 
  of 
  the 
  atoms 
  in 
  solids 
  are 
  the 
  

   same 
  whether 
  it 
  be 
  a 
  question 
  of 
  the 
  specific 
  heat 
  of 
  the 
  solid 
  

   or 
  the 
  reflexion 
  of 
  radiation, 
  it 
  might 
  be 
  anticipated 
  that 
  the 
  

   same 
  relation 
  would 
  hold 
  in 
  connexion 
  with 
  the 
  residual 
  

   rays. 
  

  

  According 
  to 
  the 
  theory 
  developed 
  by 
  Nernst 
  f 
  the 
  heat 
  

   energy 
  of 
  a 
  compound 
  in 
  the 
  solid 
  state 
  is 
  made 
  up 
  of 
  the 
  

   energy 
  due 
  to 
  the 
  motion 
  of 
  the 
  molecules 
  relative 
  to 
  one 
  

   another 
  and 
  that 
  due 
  to 
  the 
  vibrations 
  of 
  the 
  atoms 
  in 
  the 
  

   molecule. 
  The 
  first 
  contribution 
  is 
  calculated 
  by 
  the 
  formula 
  

   of 
  Debye, 
  the 
  second 
  by 
  the 
  formula 
  of 
  Einstein. 
  Each 
  

   calculation 
  involves 
  a 
  knowledge 
  of 
  the 
  corresponding 
  

   characteristic 
  frequency 
  ; 
  the 
  first, 
  v\, 
  is 
  given, 
  approxi- 
  

   mately 
  at 
  least, 
  by 
  Lindemann's 
  formula 
  ; 
  the 
  second, 
  v 
  2 
  , 
  

   is 
  found 
  from 
  the 
  residual 
  rays 
  of 
  Rubens. 
  Nernst 
  has 
  

   pointed 
  out 
  that 
  in 
  the 
  case 
  of 
  KOI 
  and 
  NaCl, 
  the 
  value 
  of 
  v 
  x 
  

   is 
  almost 
  0*75 
  times 
  the 
  value 
  of 
  v 
  2 
  ; 
  and 
  in 
  other 
  cases, 
  

   although 
  the 
  molecular 
  frequency 
  is 
  slower 
  than 
  the 
  internal 
  

   frequency, 
  the 
  two 
  are 
  not 
  very 
  different. 
  Indeed, 
  in 
  

   his 
  earlier 
  work 
  Nernst 
  obtained 
  fairly 
  good 
  agreement 
  by 
  

   calculating 
  the 
  values 
  of 
  the 
  atomic 
  heat 
  on 
  the 
  assumption 
  

   of 
  only 
  one 
  frequency, 
  v. 
  The 
  writer 
  has 
  ghownj 
  that 
  the 
  

   molecular 
  frequency 
  is 
  connected 
  with 
  the 
  " 
  molecular 
  

   number" 
  by 
  a 
  relation 
  of 
  the 
  same 
  form 
  as 
  that 
  already 
  

   quoted 
  for 
  the 
  atomic 
  frequency 
  and 
  the 
  atomic 
  number. 
  The 
  

   collective 
  results 
  suggest 
  that 
  the 
  internal 
  frequency 
  may 
  

   conform 
  to 
  the 
  same 
  relation. 
  In 
  the 
  following 
  pages 
  the 
  

   experimental 
  results 
  are 
  examined 
  for 
  a 
  number 
  of 
  com- 
  

   pounds, 
  and 
  it 
  is 
  found 
  that 
  there 
  is 
  a 
  strong 
  presumption 
  in 
  

   favour 
  of 
  the 
  establishment 
  of 
  the 
  relation 
  suggested. 
  

  

  NaCl. 
  In 
  the 
  case 
  of 
  rock 
  salt§ 
  two 
  rays 
  of 
  different 
  

   strengths 
  were 
  observed, 
  a 
  stronger 
  at 
  53*6 
  fx 
  and 
  a 
  

   weaker 
  at 
  46'9 
  /jl. 
  The 
  corresponding 
  frequencies 
  are 
  

   5-60 
  xlO 
  12 
  and 
  6'40xl0 
  12 
  sec." 
  1 
  . 
  Assuming 
  the 
  former 
  

  

  * 
  H. 
  S. 
  Allen, 
  Roy. 
  Soc. 
  Proc. 
  vol. 
  xciv. 
  p. 
  100 
  (1917) 
  ; 
  Phil. 
  Mag. 
  

   vol. 
  xxxiv. 
  p. 
  478 
  (1917). 
  

  

  t 
  Nernst, 
  < 
  The 
  Theory 
  of 
  the 
  Solid 
  State 
  ' 
  (London, 
  1914). 
  

  

  % 
  H. 
  S. 
  Allen, 
  Phil. 
  Mag. 
  vol. 
  xxxv., 
  April 
  1918. 
  

  

  § 
  Rubens 
  and 
  Hollnagel, 
  Preuss. 
  Akad. 
  Berlin, 
  vol. 
  iv. 
  p. 
  2Q 
  (1910). 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  209. 
  May 
  1918. 
  2 
  F 
  

  

  