﻿342 
  Dr. 
  H. 
  S. 
  Allen 
  on 
  Molecular 
  

  

  molecule 
  of 
  the 
  solid 
  at 
  or 
  near 
  the 
  melting-point 
  may 
  not 
  

   have 
  the 
  same 
  constitution 
  as 
  the 
  molecule 
  near 
  the 
  absolute 
  

   zero 
  of 
  temperature. 
  The 
  frequency 
  as 
  given 
  by 
  Lindemann's 
  

   formula 
  must 
  be 
  taken 
  to 
  represent 
  the 
  characteristic 
  frequency 
  

   the 
  substance 
  would 
  take 
  at 
  low 
  temperatures, 
  on 
  the 
  assump- 
  

   tion 
  that 
  the 
  molecular 
  structure 
  remained 
  unchanged 
  in 
  

   cooling 
  from 
  the 
  melting-point 
  to 
  the 
  absolute 
  zero. 
  If 
  

   either 
  polymerization 
  or 
  dissociation 
  occur 
  in 
  the 
  process 
  of 
  

   cooling, 
  then 
  a 
  change 
  in 
  the 
  characteristic 
  frequency 
  is 
  to 
  

   be 
  anticipated. 
  

  

  A 
  definite 
  decision 
  as 
  to 
  whether 
  the 
  relation 
  between 
  N 
  

   and 
  v 
  is 
  exact 
  or 
  only 
  approximate 
  cannot 
  be 
  reached 
  until 
  

   further 
  accurate 
  determinations 
  of 
  the 
  specific 
  heat 
  of 
  com- 
  

   pounds 
  at 
  very 
  low 
  temperatures 
  are 
  available. 
  Empirical 
  

   formulae, 
  such 
  as 
  that 
  of 
  Lindemann, 
  may 
  be 
  employed 
  for 
  

   the 
  evaluation 
  of 
  v, 
  but 
  it 
  must 
  be 
  remembered 
  that 
  such 
  

   formulae 
  generally 
  give 
  only 
  approximations 
  to 
  the 
  true 
  

   value, 
  and 
  therefore 
  cannot 
  furnish 
  a 
  decisive 
  test. 
  It 
  has 
  

   been 
  suggested 
  that 
  to 
  render 
  Lindemann's 
  formula 
  accurate 
  

   an 
  additional 
  factor 
  is 
  required 
  depending 
  upon 
  the 
  relation 
  

   between 
  the 
  molecular 
  volume 
  at 
  absolute 
  zero 
  and 
  that 
  at 
  

   the 
  melting-point*. 
  It 
  may 
  be 
  anticipated 
  that 
  the 
  formula 
  

   in 
  its 
  present 
  form 
  should 
  give 
  comparable 
  results 
  for 
  

   chemical 
  compounds 
  of 
  similar 
  constitution. 
  This 
  would 
  

   be 
  shown 
  by 
  agreement 
  between 
  the 
  values 
  of 
  Nv, 
  or 
  by 
  

   concordant 
  values 
  of 
  v 
  A 
  ". 
  It 
  has, 
  in 
  fact, 
  been 
  shown 
  pre- 
  

   viously 
  that 
  such 
  agreement 
  exists 
  in 
  the 
  case 
  of 
  similar 
  

   elements, 
  and 
  evidence 
  is 
  now 
  put 
  forward 
  that 
  relations 
  of 
  

   the 
  same 
  kind 
  hold 
  for 
  similar 
  compounds. 
  

  

  It 
  must 
  be 
  borne 
  in 
  mind 
  in 
  considering 
  the 
  results 
  not 
  

   only 
  that 
  Lindemann's 
  formula 
  is 
  merely 
  an 
  approximate 
  

   one, 
  but 
  that 
  the 
  numerical 
  factor 
  is 
  purely 
  empirical. 
  

   Further, 
  it 
  is 
  to 
  be 
  noticed 
  that 
  the 
  molecular 
  volume 
  is 
  

   usually 
  found 
  from 
  determinations 
  of 
  the 
  density 
  made 
  at 
  

   ordinary 
  temperatures. 
  It 
  might 
  be 
  better 
  to 
  employ 
  the 
  

   density 
  of 
  the 
  solid 
  near 
  the 
  absolute 
  zero 
  of 
  temperature 
  or 
  

   at 
  the 
  melting-point. 
  

  

  The 
  data 
  employed 
  for 
  the 
  calculation 
  of 
  the 
  characteristic 
  

   frequencies 
  in 
  the 
  following 
  paragraphs 
  have 
  been 
  taken 
  

   mainly 
  from 
  Nostrand's 
  4 
  Chemical 
  Annual 
  ' 
  for 
  1913, 
  which 
  

   gives 
  Tables 
  convenient 
  for 
  this 
  purpose. 
  Kaye 
  and 
  Laby's 
  

   4 
  Physical 
  and 
  Chemical 
  Constants' 
  (1911), 
  and 
  the 
  Smith- 
  

   sonian 
  Physical 
  Tables 
  (1914) 
  have 
  also 
  been 
  made 
  use 
  of 
  

   for 
  certain 
  compounds. 
  In 
  cases 
  where 
  a 
  range 
  of 
  values 
  

  

  * 
  Cf. 
  Sutherland, 
  Phil. 
  Mag. 
  vol. 
  xxx. 
  p. 
  818 
  (1890); 
  vol. 
  xxxii. 
  

   p. 
  524 
  (1891) 
  ; 
  and 
  Gruneisen 
  ? 
  >4>m. 
  d. 
  Physik, 
  vol. 
  xxxix. 
  p. 
  298 
  (1912). 
  

  

  