﻿the 
  Unit-Steve 
  Theory. 
  91 
  

  

  critical 
  volumes 
  are 
  proportional 
  to 
  the 
  critical 
  coefficients 
  and 
  

   are 
  thus 
  subject 
  to 
  similar 
  additive 
  relations. 
  It 
  is, 
  however, 
  

   highly 
  probable 
  that 
  these 
  would 
  be 
  still 
  more 
  clearly 
  shown 
  

   in 
  the 
  molecular 
  critical 
  volumes. 
  The 
  volumes 
  of 
  the 
  side- 
  

   chains 
  in 
  the 
  benzene 
  homologues 
  are 
  thus 
  equal 
  to 
  corre- 
  

   sponding 
  paraffinoid 
  residues, 
  while 
  the 
  nucleus 
  undergoes 
  a 
  

   contraction. 
  

  

  M.Y. 
  of 
  C 
  6 
  H 
  12 
  at 
  B.P. 
  116-3. 
  M.V 
  K 
  . 
  of 
  C 
  6 
  H 
  lo 
  = 
  306-7. 
  

  

  Ratio 
  2-64. 
  

  

  M.Y. 
  of 
  C 
  7 
  H 
  10 
  (Toluene) 
  at 
  B.P. 
  118-3. 
  Calculated 
  M. 
  V 
  K 
  . 
  of 
  

  

  C 
  7 
  H 
  10 
  = 
  11 
  8-3 
  x 
  2-64 
  = 
  313-3, 
  

  

  Yol. 
  of 
  CH 
  2 
  at 
  the 
  Critical 
  Poinfc= 
  Vol. 
  of 
  CH 
  8 
  - 
  Vol. 
  of 
  C 
  6 
  H 
  6 
  

  

  = 
  313-3-256-3 
  = 
  57. 
  

  

  - 
  57 
  

   Yol. 
  of 
  H 
  in 
  side-chain 
  = 
  — 
  =9*5, 
  

  

  which 
  is 
  about 
  equal 
  to 
  that 
  in 
  the 
  paraffin 
  hydrocarbons. 
  

  

  Summary. 
  

  

  It 
  has 
  been 
  found 
  that 
  at 
  the 
  melting-point 
  and 
  at 
  equal 
  

   intervals 
  of 
  temperature 
  therefrom 
  the 
  molecular 
  volumes 
  

   of 
  the 
  oh 
  'fines 
  may 
  be 
  expressed 
  by 
  the 
  following 
  formula 
  : 
  

  

  M. 
  vol. 
  C 
  n 
  H 
  2 
  „! 
  = 
  | 
  = 
  6nS-2-62 
  = 
  WS-! 
  = 
  | 
  

  

  the 
  acetylenes 
  by 
  the 
  following 
  : 
  

  

  M. 
  vol. 
  C 
  n 
  H 
  2n 
  _ 
  2 
  |=| 
  = 
  6nS-2S~3=WS-[EE:|; 
  

  

  the 
  specific 
  gravities 
  of 
  the 
  above 
  compounds 
  are 
  at 
  equal 
  

   intervals 
  of 
  temperature 
  from 
  the 
  melting-points 
  equal 
  

   fractions 
  of 
  the 
  specific 
  gravities 
  at 
  those 
  points. 
  

  

  The 
  molecular 
  volume 
  of 
  a 
  single 
  olefine 
  and 
  acetylene 
  is 
  

   at 
  the 
  boiling-point 
  expressed 
  by 
  the 
  following 
  formulae 
  : 
  — 
  

  

  M. 
  vol. 
  of 
  C»H 
  2n 
  =6nS 
  (defines). 
  

  

  M. 
  vol. 
  of 
  C 
  n 
  H 
  2?l 
  _ 
  2 
  = 
  6>iS-2S 
  (Acetylenes). 
  

  

  The 
  value 
  of 
  S 
  is 
  usually 
  about 
  3*7, 
  but 
  may 
  vary 
  slightly 
  

   from 
  compound 
  to 
  compound. 
  In 
  so 
  far 
  as 
  3*7 
  is 
  constant 
  

   the 
  above 
  formulae 
  are 
  general 
  for 
  a 
  series. 
  

  

  3*7 
  is 
  the 
  atomic 
  volume 
  of 
  H. 
  The 
  atomic 
  volume 
  of 
  

   carbon 
  is 
  14*8, 
  which 
  numbers 
  are 
  also 
  those 
  of 
  similar 
  atoms 
  

   in 
  the 
  paraffins. 
  

  

  Thus 
  C 
  = 
  4S 
  = 
  4^, 
  the 
  symbols 
  having 
  the 
  same 
  meaning 
  

   as 
  before. 
  

  

  