﻿Frequency 
  and 
  Molecular 
  Number. 
  343 
  

  

  is 
  given 
  for 
  the 
  melting-point, 
  the 
  highest 
  value 
  quoted 
  has 
  

   been 
  used 
  ; 
  similarly 
  the 
  largest 
  value 
  of 
  the 
  density 
  has 
  been 
  

   taken 
  in 
  calculating 
  the 
  molecular 
  volume. 
  

  

  § 
  5. 
  Inorganic 
  Compounds 
  (Lindemann's 
  Formula). 
  

  

  It 
  may 
  be 
  pointed 
  out 
  in 
  the 
  first 
  place 
  that 
  the 
  product 
  

   Nv 
  frequently 
  has 
  the 
  same 
  value 
  for 
  compounds 
  which 
  are 
  

   similar 
  in 
  their 
  chemical 
  constitution 
  and 
  behaviour. 
  Thus 
  

   in 
  the 
  case 
  of 
  the 
  alkali 
  metals 
  we 
  find 
  for 
  the 
  chlorides 
  

   of 
  sodium, 
  potassium, 
  and 
  rubidium 
  the 
  values 
  : 
  — 
  

  

  JSTaCl, 
  123-2 
  x 
  10 
  12 
  ; 
  KC1, 
  125*8 
  x 
  10 
  12 
  ; 
  RbCl, 
  124-7 
  x 
  10 
  12 
  , 
  

  

  Similarly 
  for 
  the 
  iodides 
  of 
  the 
  same 
  metals 
  : 
  — 
  

  

  Nal, 
  145-2 
  x 
  10 
  12 
  ; 
  KI, 
  143*1 
  x 
  10 
  12 
  ; 
  Rbl, 
  145*4 
  x 
  10 
  12 
  . 
  

  

  Further 
  it 
  may 
  be 
  noted 
  that 
  the 
  product 
  for 
  the 
  iodide 
  

   exceeds 
  that 
  for 
  the 
  chloride 
  by 
  an 
  amount 
  which 
  is 
  approxi- 
  

   mately 
  constant, 
  and 
  equal 
  to 
  about 
  20 
  x 
  10 
  12 
  . 
  Similarly 
  

   the 
  difference 
  between 
  the 
  product 
  for 
  sodium 
  chloride 
  

   (123-2 
  x 
  10 
  12 
  ) 
  and 
  that 
  for 
  lithium 
  chloride 
  (101*6 
  X 
  10 
  12 
  ) 
  is 
  

   21*6 
  xlO 
  12 
  , 
  whilst 
  the 
  difference 
  between 
  the 
  product 
  for 
  

   sodium 
  iodide 
  (145*2 
  x 
  10 
  12 
  ) 
  and 
  that 
  for 
  lithium 
  iodide 
  

   (124-7 
  X 
  10 
  12 
  ) 
  is 
  20-5 
  x 
  10 
  12 
  . 
  All 
  such 
  relations, 
  and 
  their 
  

   number 
  is 
  far 
  too 
  great 
  for 
  them 
  to 
  be 
  fortuitous, 
  may 
  be 
  

   included 
  in 
  the 
  formulae 
  

  

  Nj/=nj> 
  A 
  and 
  Nv 
  = 
  (n 
  + 
  J)i> 
  A 
  , 
  

  

  where 
  v 
  A 
  is 
  approximately 
  21 
  X 
  10 
  12 
  sec." 
  1 
  . 
  

  

  These 
  formulae 
  have 
  now 
  been 
  tested 
  for 
  those 
  inorganic 
  

   compounds 
  for 
  which 
  the 
  necessary 
  data 
  are 
  recorded, 
  and 
  

   it 
  has 
  been 
  found 
  that 
  the 
  number 
  of 
  cases 
  in 
  which 
  one 
  or 
  

   other 
  of 
  the 
  formulae 
  cannot 
  be 
  applied 
  is 
  small. 
  It 
  is 
  hoped 
  

   to 
  publish 
  details 
  of 
  these 
  results 
  later 
  ; 
  at 
  present 
  it 
  will 
  

   suffice 
  to 
  quote 
  the 
  figures 
  for 
  two 
  series 
  of 
  compounds. 
  In 
  

   Table 
  I. 
  are 
  given 
  the 
  results 
  for 
  all 
  the 
  lithium 
  compounds 
  

   for 
  which 
  data 
  are 
  available. 
  This 
  element 
  has 
  been 
  selected 
  

   on 
  account 
  of 
  the 
  small 
  atomic 
  number 
  (N 
  = 
  3) 
  rendering 
  the 
  

   product 
  Nz> 
  comparatively 
  small 
  ; 
  consequently 
  it 
  is 
  not 
  

   necessary 
  to 
  employ 
  large 
  values 
  for 
  n, 
  and 
  a 
  more 
  satis- 
  

   factory 
  test 
  of 
  the 
  new 
  relation 
  can 
  be 
  obtained. 
  The 
  

   frequency 
  number 
  in 
  the 
  last 
  column 
  of 
  the 
  Table 
  falls 
  

   between 
  3^ 
  and 
  8, 
  whilst 
  the 
  extreme 
  values 
  for 
  v 
  K 
  are 
  

   20*1 
  x 
  10 
  12 
  sec. 
  -1 
  and 
  21*3 
  X 
  10 
  12 
  sec. 
  -1 
  Application 
  of 
  the 
  

   theory 
  of 
  probability 
  to 
  the 
  figures 
  shows 
  that 
  there 
  is 
  only 
  

   1 
  chance 
  in 
  282 
  that 
  these 
  results 
  should 
  occur 
  by 
  accident, 
  

  

  2B2 
  

  

  