﻿Frequency 
  and 
  Molecular 
  Number. 
  409 
  

  

  where 
  M 
  1? 
  M 
  2 
  are 
  the 
  masses 
  of 
  the 
  atoms, 
  K 
  is 
  the 
  com- 
  

   pressibility, 
  and 
  D 
  the 
  density. 
  This 
  may 
  be 
  compared 
  

   with 
  Einstein's 
  formula. 
  Rubens 
  and 
  Wartenberg 
  have 
  

   shown 
  that 
  this 
  formula 
  gives 
  results 
  in 
  moderately 
  good 
  

   agreement 
  with 
  their 
  observations. 
  

  

  They 
  have 
  also 
  obtained 
  fair 
  agreement 
  by 
  employing 
  a 
  

   modified 
  form 
  of 
  the 
  equation 
  of 
  Lindemann, 
  viz. 
  

  

  // 
  M,M 
  2 
  YH 
  

  

  where 
  V 
  is 
  the 
  molecular 
  volume 
  and 
  T 
  s 
  the 
  melting- 
  

   point. 
  

  

  In 
  both 
  formulae 
  the 
  constant 
  must 
  be 
  determined 
  em- 
  

   pirically. 
  

  

  The 
  results 
  of 
  this 
  and 
  preceding 
  papers 
  support 
  the 
  

   following 
  conclusions: 
  — 
  

  

  (1) 
  The 
  forces 
  binding 
  the 
  atoms 
  in 
  the 
  molecule 
  are 
  

   similar 
  in 
  character 
  to 
  those 
  which 
  bind 
  the 
  molecules 
  of 
  

   the 
  solid, 
  that 
  is 
  the 
  forces 
  of 
  chemical 
  affinity 
  are 
  of 
  the 
  

   same 
  nature 
  as 
  the 
  forces 
  of 
  molecular 
  cohesion*. 
  

  

  (2) 
  There 
  must 
  be 
  something 
  of 
  a 
  discrete 
  character 
  in 
  

   the 
  nature 
  of 
  these 
  forces, 
  in 
  order 
  to 
  account 
  for 
  the 
  

   occurrence 
  of 
  integral 
  values 
  of 
  n. 
  The 
  simplest 
  hypothesis 
  

   is 
  to 
  assume 
  that 
  the 
  forces 
  arise 
  from 
  the 
  presence 
  of 
  

   valency 
  electrons. 
  As 
  it 
  is 
  probable 
  that 
  these 
  forces 
  act 
  

   only 
  in 
  definite 
  directions, 
  it 
  is 
  a 
  plausible 
  suggestion 
  that 
  

   the 
  linkages 
  between 
  the 
  atoms 
  are 
  constituted 
  by 
  Faraday 
  

   tubes 
  of 
  force, 
  which 
  would 
  then 
  be 
  regarded 
  as 
  physical 
  

   entities. 
  The 
  fundamental 
  frequencies, 
  v 
  A 
  and 
  i/ 
  E 
  , 
  would 
  

   depend 
  on 
  the 
  properties 
  of 
  the 
  unit 
  tube 
  of 
  force. 
  It 
  has 
  

   been 
  pointed 
  out 
  by 
  Prof. 
  Nicholson 
  f 
  that 
  such 
  a 
  view 
  seems 
  

   to 
  be 
  required 
  in 
  order 
  to 
  explain 
  the 
  relations 
  between 
  the 
  

   frequencies 
  of 
  spectral 
  series. 
  Attention 
  may 
  also 
  be 
  drawn 
  

   to 
  an 
  important 
  article 
  by 
  Sir 
  J. 
  J. 
  Thomson 
  on 
  the 
  Forces 
  

   between 
  Atoms 
  and 
  Chemical 
  Affinity!, 
  in 
  which 
  chemical 
  

   valency 
  is 
  discussed 
  from 
  the 
  same 
  standpoint. 
  

  

  * 
  Compare 
  Nernst, 
  'The 
  Theory 
  of 
  the 
  Solid 
  State,' 
  pp. 
  4-9 
  (1914) 
  ; 
  

   Langmuir, 
  Arm. 
  Chem. 
  Soc. 
  Journ. 
  vol. 
  xxxviii. 
  p. 
  2221 
  (1916). 
  

   + 
  Nicholson, 
  Phil. 
  Mag. 
  vol. 
  xxvii. 
  p. 
  541, 
  vol. 
  xxviii. 
  p. 
  90 
  (1914). 
  

   t 
  J. 
  J. 
  Thomson, 
  Phil. 
  Mag. 
  vol. 
  xxvii. 
  p. 
  757 
  (1914). 
  

  

  