﻿460 
  On 
  Molecular 
  Frequency 
  and 
  Molecular 
  Number. 
  

  

  In 
  consequence 
  of 
  the 
  presence 
  of 
  traces 
  of 
  impurity, 
  or 
  

   through 
  imperfect 
  crystallization, 
  it 
  is 
  at 
  least 
  possible 
  that 
  

   fusion 
  may 
  sometimes 
  occur 
  when 
  the 
  number 
  of 
  valency 
  

   electrons 
  is 
  smaller 
  than 
  the 
  normal 
  value. 
  

  

  It 
  is 
  noticeable 
  that 
  for 
  a 
  large 
  number 
  of 
  compounds 
  the 
  

  

  frequency 
  number 
  is 
  one 
  of 
  the 
  series 
  4J, 
  6, 
  7J, 
  9, 
  ; 
  

  

  suggesting 
  that 
  the 
  factor 
  3 
  plays 
  an 
  important 
  part 
  in 
  the 
  

   determination 
  of 
  its 
  value. 
  It 
  may 
  not 
  be 
  entirely 
  accidental 
  

   that 
  a 
  number 
  belonging 
  to 
  this 
  series 
  frequently 
  occurs 
  when 
  

   the 
  compound 
  contains 
  an 
  element 
  of 
  valency 
  3 
  (e. 
  g. 
  amongst 
  

   the 
  compounds 
  of 
  As, 
  Sb, 
  Bi, 
  and 
  Fe). 
  It 
  is 
  not 
  unlikely 
  

   that 
  the 
  factor 
  3 
  should 
  occur 
  in 
  such 
  cases 
  if 
  it 
  is 
  supposed 
  

   that 
  the 
  chemical 
  valency 
  is 
  associated 
  with 
  a 
  certain 
  number 
  

   of 
  valency 
  electrons. 
  

  

  The 
  facts 
  recorded 
  in 
  this 
  paper 
  are 
  regarded 
  as 
  proving 
  

   that 
  the 
  characteristic 
  frequency 
  calculated 
  for 
  a 
  metallic 
  

   compound 
  by 
  means 
  of 
  Lindemann's 
  formula 
  can, 
  in 
  general, 
  

   be 
  expressed 
  in 
  the 
  form 
  nv 
  A 
  or 
  in 
  the 
  form 
  (n 
  4 
  i)^A, 
  where 
  n 
  

   is 
  an 
  integer 
  and 
  v 
  K 
  is 
  approximately 
  21 
  X 
  10 
  12 
  sec. 
  -1 
  . 
  The 
  

   evidence 
  for 
  this 
  may 
  not 
  be 
  considered 
  conclusive 
  when 
  com- 
  

   pounds 
  of 
  one 
  single 
  metal 
  are 
  examined, 
  but 
  the 
  evidence 
  in 
  

   the 
  present 
  case 
  is 
  cumulative. 
  The 
  degree 
  of 
  probability 
  

   of 
  this 
  result 
  may 
  be 
  small 
  when 
  compounds 
  of 
  a 
  single 
  

   element 
  are 
  found 
  to 
  conform 
  to 
  the 
  rule; 
  but 
  it 
  is 
  larger 
  

   when 
  the 
  compounds 
  of 
  all 
  the 
  elements 
  in 
  a 
  group 
  are 
  found 
  

   to 
  give 
  concordant 
  values 
  for 
  v 
  A 
  , 
  and 
  becomes 
  very 
  great 
  

   when 
  the 
  number 
  of 
  compounds 
  is 
  extended 
  to 
  include 
  all 
  the 
  

   groups 
  in 
  MendeleefFs 
  classification. 
  Further, 
  these 
  results 
  

   for 
  compounds 
  and 
  those 
  recorded 
  previously 
  for 
  the 
  elements 
  

   mutually 
  support 
  one 
  another, 
  and 
  lead 
  to 
  the 
  conclusion 
  that 
  

   we 
  have 
  to 
  deal 
  with 
  a 
  property 
  that 
  is 
  fundamental 
  and 
  

   characteristic 
  of 
  the 
  solid 
  state 
  of 
  matter. 
  It 
  is 
  to 
  be 
  borne 
  

   in 
  mind 
  that 
  the 
  formula 
  of 
  Lindemann 
  is 
  looked 
  upon 
  as 
  

   giving 
  only 
  an 
  approximate 
  value 
  for 
  the 
  characteristic 
  

   frequency, 
  and 
  the 
  final 
  justification 
  for 
  the 
  proposed 
  

   relation 
  must 
  come 
  from 
  observations 
  on 
  the 
  specific 
  heat 
  

   of 
  compounds 
  at 
  low 
  temperatures. 
  

  

  