﻿Frequency 
  and 
  Molecular 
  Number. 
  341 
  

  

  term 
  which 
  is 
  predominant 
  at 
  low 
  temperatures. 
  For 
  NaOl 
  

   he 
  finds 
  £i/ 
  = 
  229, 
  which 
  would 
  require 
  Nv=6ix 
  20' 
  6 
  X 
  10 
  12 
  . 
  

   As 
  Lindemann's 
  formula 
  gives 
  a 
  smaller 
  value 
  (215) 
  for 
  (3v, 
  

   it 
  may 
  be 
  suspected 
  that 
  the 
  true 
  value 
  for 
  Nv 
  at 
  very 
  low 
  

   temperatures 
  is 
  6 
  X 
  21 
  x 
  10 
  12 
  . 
  This 
  is 
  supported 
  by 
  the 
  

   value 
  for 
  KC1, 
  for 
  which 
  Nernst 
  gives 
  f3v 
  = 
  166, 
  so 
  that 
  

   Nv=6 
  x20'8 
  X 
  10 
  32 
  - 
  The 
  change 
  in 
  the 
  frequency 
  number 
  

   from 
  8 
  to 
  6 
  must 
  be 
  attributed 
  to 
  the 
  introduction 
  of 
  the 
  

   Einstein 
  term, 
  and 
  points 
  to 
  the 
  relation 
  ~Nv 
  = 
  nv 
  A 
  being 
  

   obeyed 
  by 
  the 
  corresponding 
  frequency. 
  This 
  is 
  actually 
  

   found 
  to 
  be 
  the 
  case, 
  as 
  is 
  shown 
  in 
  a 
  separate 
  paper 
  by 
  the 
  

   writer. 
  

  

  Nernst 
  also 
  gives 
  values 
  for 
  the 
  characteristic 
  frequency 
  

   of 
  chloride 
  of 
  mercury 
  and 
  chloride 
  of 
  silver. 
  For 
  HgCl 
  

   J3v 
  = 
  115, 
  from 
  which 
  we 
  find 
  Nv=ll 
  x 
  21'2x 
  10 
  12 
  , 
  and 
  for 
  

   AgCl 
  /3v=102, 
  giving 
  Nv=6ix21-0x 
  10 
  12 
  . 
  

  

  Experiments 
  by 
  Eucken 
  and 
  Schwers* 
  which 
  are 
  believed 
  

   to 
  be 
  very 
  accurate 
  give 
  the 
  characteristic 
  frequency 
  for 
  

   two 
  compounds 
  containing 
  three 
  atoms 
  in 
  the 
  molecule. 
  For 
  

   fluorite 
  (CaF 
  2 
  ) 
  £i/ 
  = 
  474, 
  resulting 
  in 
  Nv 
  = 
  18 
  x 
  20*9 
  x 
  10 
  12 
  . 
  

   For 
  pyrites 
  (FeS 
  2 
  ) 
  /3z> 
  = 
  645, 
  and 
  as 
  N 
  = 
  58 
  the 
  product 
  Nv 
  

   is 
  so 
  large 
  (782*6 
  x 
  10 
  12 
  ) 
  that 
  it 
  is 
  difficult 
  to 
  be 
  certain 
  of 
  

   the 
  value 
  to 
  be 
  assigned 
  to 
  n. 
  If 
  n 
  = 
  37 
  the 
  product 
  

   Nv 
  = 
  37x21*2x 
  10 
  12 
  ; 
  if, 
  as 
  is 
  more 
  probable, 
  ?i 
  = 
  36 
  the 
  

   product 
  Ni/= 
  36 
  x 
  21-8 
  X 
  10 
  12 
  . 
  

  

  Euckenf 
  found 
  for 
  carbon 
  dioxide 
  (C0 
  2 
  ) 
  in 
  the 
  solid 
  state 
  

   ^ 
  = 
  119, 
  giving 
  N^ 
  = 
  2£x21'9 
  x 
  10 
  12 
  . 
  This 
  is 
  of 
  interest 
  as 
  

   indicating 
  that 
  the 
  rule 
  applies 
  in 
  the 
  case 
  of 
  non-metallic 
  

   compounds. 
  

  

  § 
  4. 
  Characteristic 
  Frequency 
  from 
  Lindemann 
  s 
  Formula, 
  

  

  For 
  the 
  majority 
  of 
  compounds 
  no 
  measurements 
  of 
  the 
  

   specific 
  heat 
  at 
  low 
  temperatures 
  have 
  been 
  made, 
  and 
  in 
  such 
  

   cases 
  it 
  is 
  necessary 
  to 
  have 
  recourse 
  to 
  some 
  more 
  or 
  less 
  

   empirical 
  formula 
  such 
  as 
  that 
  of 
  Lindemann. 
  This 
  formula 
  

   gives 
  

  

  v=3'08xlOV(T*/MVt), 
  

  

  where 
  T 
  s 
  denotes 
  the 
  melting-point, 
  M 
  the 
  molecular 
  weight, 
  

   and 
  V 
  the 
  molecular 
  volume. 
  

  

  It 
  is 
  easy 
  to 
  understand 
  that 
  the 
  frequency 
  calculated 
  in 
  

   this 
  way 
  may 
  not 
  be 
  identical 
  with 
  the 
  frequency 
  deter- 
  

   mined 
  from 
  the 
  specific 
  heat 
  at 
  low 
  temperatures, 
  for 
  the 
  

  

  * 
  Eucken 
  & 
  Schwers, 
  D. 
  P. 
  G. 
  V. 
  vol. 
  xv. 
  p. 
  578 
  (1913). 
  

   t 
  Eucken, 
  i). 
  P. 
  G. 
  V. 
  vol. 
  xyiii. 
  p. 
  4 
  (1916). 
  

  

  Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  208. 
  April 
  1918. 
  2 
  B 
  

  

  