﻿frequency 
  and 
  Molecular 
  Number. 
  349 
  

  

  reached 
  by 
  Sutherland*, 
  who 
  emphasized 
  the 
  fact 
  that 
  water 
  

   crystallizes 
  in 
  the 
  hexagonal 
  system, 
  whilst 
  trihydrol 
  can 
  

   be 
  represented 
  by 
  three 
  linked 
  oxygen 
  atoms 
  at 
  the 
  corner 
  

   of 
  an 
  equilateral 
  triangle 
  with 
  the 
  six 
  hydrogen 
  atoms 
  

   arranged 
  symmetrically 
  round 
  them. 
  . 
  

  

  It 
  is 
  easy 
  to 
  examine 
  the 
  effect 
  of 
  association 
  on 
  the 
  

   frequency 
  as 
  determined 
  by 
  Lindemamr's 
  formula. 
  If 
  M 
  

   denote 
  the 
  molecular 
  weight 
  of 
  the 
  simplest 
  molecule, 
  that 
  

   of 
  the 
  associated 
  molecule 
  maybe 
  written 
  xM, 
  The 
  molecular 
  

   volume 
  V 
  will 
  also 
  be 
  increased 
  x 
  times. 
  Hence 
  the 
  frequency, 
  

   determined 
  by 
  the 
  equation 
  

  

  V3 
  V 
  (m/ 
  

  

  will 
  be 
  divided 
  by 
  x* 
  + 
  2 
  = 
  x 
  s 
  \ 
  The 
  atomic 
  number 
  will 
  be 
  

   increased 
  x 
  times, 
  and 
  consequently 
  the 
  value 
  of 
  Nv 
  will 
  

   be 
  multiplied 
  by 
  #«. 
  It 
  is, 
  then, 
  a 
  simple 
  matter 
  to 
  find 
  an 
  

   integral 
  value 
  for 
  x 
  so 
  as 
  to 
  satisfy 
  the 
  relation 
  Nv 
  = 
  ?w 
  A 
  . 
  As 
  

   in 
  most 
  cases 
  there 
  is 
  no 
  independent 
  check 
  on 
  the 
  degree 
  

   of 
  association 
  of 
  a 
  solid, 
  it 
  does 
  not 
  seem 
  desirable 
  in 
  the 
  

   present 
  state 
  of 
  our 
  knowledge 
  to 
  attempt 
  to 
  apply 
  this 
  

   method 
  in 
  detail. 
  

  

  § 
  8. 
  Conclusion. 
  

  

  In 
  this 
  preliminary 
  survey 
  of 
  the 
  subject 
  of 
  the 
  relation 
  

   between 
  molecular 
  frequency, 
  v, 
  and 
  the 
  molecular 
  number, 
  

   N, 
  it 
  has 
  been 
  proved 
  that 
  the 
  product 
  Nv 
  frequently 
  shows 
  

   related 
  values 
  for 
  analogous 
  compounds. 
  There 
  is 
  considerable 
  

   evidence 
  for 
  the 
  validity 
  of 
  a 
  formula 
  of 
  the 
  type 
  NV 
  = 
  ny 
  A 
  in 
  

   the 
  case 
  of 
  most 
  inorganic 
  solid 
  compounds 
  and 
  of 
  a 
  number 
  

   of 
  organic 
  compounds. 
  To 
  what 
  extent 
  the 
  formula 
  is 
  to 
  be 
  

   considered 
  approximate 
  can 
  be 
  decided 
  only 
  when 
  further 
  

   data 
  as 
  to 
  the 
  specific 
  heat 
  of 
  solids 
  at 
  low 
  temperatures 
  are 
  

   available. 
  The 
  physical 
  significance 
  of 
  such 
  a 
  formula 
  has 
  

   been 
  discussed 
  in 
  an 
  earlier 
  paper. 
  Perhaps 
  the 
  simplest 
  

   interpretation 
  that 
  can 
  be 
  suggested 
  for 
  the 
  " 
  frequency 
  

   number/' 
  n, 
  is 
  that 
  it 
  is 
  related 
  to 
  the 
  number 
  of 
  valency 
  

   electrons 
  concerned 
  in 
  imparting 
  to 
  the 
  solid 
  its 
  crystalline 
  

   structure. 
  Further 
  investigation 
  on 
  these 
  lines 
  may 
  serve 
  

   to 
  throw 
  more 
  light 
  on 
  the 
  nature 
  of 
  the 
  forces 
  connecting 
  

   the 
  molecules, 
  and 
  the 
  problem 
  of 
  molecular 
  association, 
  in 
  

   crystalline 
  solids. 
  

  

  * 
  Sutherland, 
  Phil. 
  Mag. 
  vol. 
  1. 
  p. 
  460 
  (1900) 
  ; 
  Faraday 
  Soc. 
  vol. 
  vi. 
  

   (1910). 
  

  

  