﻿Frequency 
  and 
  Molecular 
  Number. 
  339 
  

  

  example, 
  the 
  molecular 
  number 
  of 
  water 
  (H 
  2 
  0, 
  hydrol) 
  is 
  

   10*, 
  for[the 
  nuclear 
  charge 
  of 
  hydrogen 
  is 
  1, 
  and 
  of 
  oxygen 
  

   is 
  8. 
  

  

  It 
  may 
  be 
  remarked 
  that 
  the 
  molecular 
  number 
  is 
  usually 
  

   even. 
  This 
  arises 
  from 
  the 
  fact 
  that 
  when 
  the 
  valency 
  is 
  

   odd, 
  the 
  atomic 
  number 
  is 
  usually 
  odd 
  also. 
  But 
  in 
  the 
  case 
  

   of 
  an 
  element 
  such 
  as 
  copper, 
  which 
  may 
  be 
  either 
  univalent 
  

   or 
  divalent, 
  or 
  in 
  the 
  case 
  of 
  some 
  of 
  the 
  metals 
  of 
  the 
  eighth 
  

   group, 
  the 
  molecular 
  number 
  may 
  be 
  odd. 
  

  

  In 
  former 
  papers 
  f 
  it 
  has 
  been 
  shown 
  that 
  simple 
  relations 
  

   exist 
  between 
  the 
  atomic 
  number 
  of 
  an 
  element 
  and 
  the 
  

   characteristic 
  frequency 
  deduced 
  from 
  observations 
  of 
  the 
  

   specific 
  heat 
  in 
  the 
  solid 
  state. 
  In 
  the 
  present 
  communication 
  

   similar 
  results 
  are 
  found 
  in 
  connexion 
  with 
  the 
  molecular 
  

   number 
  of 
  a 
  compound 
  and 
  its 
  characteristic 
  frequency. 
  

   So 
  far 
  as 
  the 
  writer 
  is 
  aware, 
  this 
  is 
  the 
  first 
  attempt 
  to 
  

   establish 
  a 
  relationship 
  involving 
  molecular 
  number, 
  previous 
  

   work 
  in 
  different 
  branches 
  of 
  physics 
  having 
  been 
  restricted 
  

   to 
  considerations 
  of 
  atomic 
  number 
  only. 
  

  

  § 
  2. 
  Characteristic 
  Molecular 
  Frequency. 
  

  

  At 
  high 
  temperatures 
  the 
  law 
  as 
  to 
  the 
  specific 
  heat 
  of 
  

   compounds 
  enunciated 
  by 
  Joule 
  J 
  and 
  verified 
  by 
  Kopp 
  § 
  

   shows 
  that, 
  as 
  the 
  specific 
  heat 
  is 
  then 
  mainly 
  additive, 
  the 
  

   heat 
  energy 
  arises 
  for 
  the 
  most 
  part 
  from 
  the 
  vibrations 
  of 
  

   the 
  individual 
  atoms 
  || 
  . 
  At 
  sufficiently 
  high 
  temperatures 
  the 
  

   vibrational 
  energy 
  of 
  each 
  atom 
  approaches 
  the 
  value 
  3RT. 
  

   At 
  low 
  temperatures, 
  on 
  the 
  other 
  hand, 
  NernstH 
  supposes 
  

   that 
  the 
  vibrations 
  of 
  the 
  molecules 
  play 
  a 
  more 
  important 
  

   part 
  than 
  the 
  vibrations 
  of 
  the 
  atoms 
  in 
  the 
  molecule. 
  In 
  

   the 
  case 
  of 
  regular 
  monatomic 
  solids 
  Debye 
  has 
  deduced 
  an 
  

  

  * 
  This 
  fact 
  is 
  probably 
  at 
  the 
  bottom 
  of 
  the 
  remarkable 
  numerical 
  

   relations 
  involving' 
  powers 
  of 
  10, 
  pointed 
  out 
  by 
  the 
  author 
  in 
  a 
  paper 
  

   read 
  before 
  the 
  Physical 
  Society 
  of 
  London 
  (Proceedings, 
  vol. 
  xxvii. 
  

   p. 
  425, 
  1915). 
  It 
  was 
  shown 
  that 
  there 
  must 
  be 
  a 
  numerical 
  connexion 
  

   between 
  the 
  unit 
  of 
  length 
  and 
  the 
  unit 
  of 
  mass 
  in 
  the 
  C.G.S. 
  system, 
  

   " 
  and 
  there 
  is 
  no 
  reason 
  why 
  it 
  should 
  not 
  involve 
  'the 
  number 
  10.'* 
  

   This 
  negative 
  statement 
  may 
  now 
  be 
  changed 
  to 
  a 
  positive 
  one. 
  There 
  

   is 
  a 
  reason, 
  in 
  the 
  constitution 
  of 
  water 
  itself, 
  why 
  the 
  number 
  10 
  should 
  

   be 
  introduced. 
  

  

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

   vol. 
  xxxiv. 
  p. 
  478, 
  p. 
  488 
  (1917). 
  

  

  X 
  Joule, 
  Phil. 
  Mag. 
  [3] 
  vol, 
  xxv. 
  p. 
  334 
  (1844). 
  

  

  § 
  Kopp, 
  IAeb. 
  Ann. 
  vol. 
  iii. 
  pp. 
  1 
  & 
  289 
  (1864). 
  

  

  || 
  Cf. 
  Sutherland, 
  Phil. 
  Mag. 
  [5] 
  vol. 
  xxxii. 
  p. 
  550 
  (1891). 
  

  

  51 
  Nernst, 
  Tortrage 
  iiber 
  die 
  Kinetische 
  Theorie, 
  1 
  ^. 
  79(1914). 
  'The 
  

   Theory 
  of 
  the 
  Solid 
  State,' 
  p. 
  81 
  (1914). 
  

  

  