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  IV. 
  The 
  Unit-Stere 
  Theory 
  : 
  The 
  Demonstration 
  of 
  a 
  Natural 
  

   Relation 
  between 
  the 
  Volumes 
  of 
  the 
  Atoms 
  in 
  Compounds 
  

   under 
  Corresponding 
  Conditions 
  and 
  that 
  of 
  Combined 
  Hy- 
  

   drogen. 
  By 
  Gervaise 
  Le 
  Bas, 
  B.Sc* 
  

  

  ]/ 
  Part 
  II. 
  

  

  The 
  Relative 
  Volumes 
  of 
  Carbon 
  and 
  Hydrogen 
  (a) 
  in 
  

   the 
  Liquid 
  Olefines 
  C 
  2 
  H 
  2>1 
  1 
  = 
  | 
  and 
  the 
  Acetylenes 
  

   (J 
  ? 
  H 
  2n 
  _ 
  2 
  |E|, 
  (b) 
  in 
  Aromatic 
  and 
  Hydroaromatic 
  

   Compounds. 
  

  

  IN 
  a 
  former 
  paper 
  (Phil. 
  Mag. 
  ser. 
  6, 
  vol. 
  xiv. 
  No. 
  81, 
  

   pp. 
  324-350) 
  the 
  normal 
  paraffin 
  hydrocarbons 
  C. 
  n 
  H 
  2n+2 
  . 
  

   were 
  dealt 
  with. 
  The 
  apparent 
  volume 
  of 
  a 
  particular 
  hydro- 
  

   carbon 
  under 
  all 
  physical 
  conditions, 
  from 
  the 
  melting 
  to 
  the 
  

   critical 
  point, 
  was 
  considered 
  to 
  be 
  measured 
  by 
  the 
  product 
  

   of 
  a 
  number 
  W, 
  which 
  represents 
  the 
  number 
  of 
  valencies, 
  

   and 
  a 
  variable 
  S, 
  called 
  the 
  unit-stere, 
  the 
  magnitude 
  of 
  

   which 
  depends 
  upon 
  the 
  physical 
  circumstances 
  of 
  the 
  

   experiment. 
  The 
  unit-stere 
  S 
  is 
  equal 
  to 
  the 
  apparent 
  

   volume 
  of 
  hydrogen 
  in 
  the 
  combined 
  state 
  ; 
  the 
  apparent 
  

   atomic 
  volume 
  of 
  carbon 
  being 
  equal 
  to 
  IS. 
  The 
  relation 
  

   C 
  = 
  4S 
  thus 
  connects 
  the 
  apparent 
  volumes 
  of 
  the 
  atoms 
  in 
  

   the 
  individual 
  hydrocarbons 
  under 
  the 
  circumstances 
  already 
  

   mentioned, 
  and 
  as 
  a 
  result 
  the 
  equation 
  

  

  Mol. 
  vol. 
  of 
  C 
  w 
  H 
  2n+2 
  =(6w 
  + 
  2)S 
  = 
  WS 
  

  

  is 
  always 
  true, 
  at 
  least 
  approximately. 
  

  

  It 
  is 
  obvious 
  that 
  no 
  direct 
  comparison 
  of 
  the 
  apparent 
  

   volumes 
  of 
  the 
  atoms 
  in 
  each 
  compound 
  is 
  possible, 
  but 
  the 
  

   validity 
  of 
  the 
  above 
  equation 
  can 
  be 
  demonstrated 
  from 
  a 
  

   consideration 
  of 
  the 
  volumes 
  of 
  successive 
  members 
  of 
  the 
  

   paraffin 
  series 
  under 
  coincident 
  conditions. 
  The 
  relation 
  is 
  

   however, 
  not 
  always 
  quite 
  strictly 
  followed 
  in 
  such 
  a 
  series, 
  

   and 
  this 
  constitutes 
  the 
  first 
  limitation 
  of 
  the 
  principle 
  of 
  

   strict 
  additivity 
  to 
  be 
  met 
  with. 
  The 
  explanation 
  given 
  of 
  

   this 
  is 
  that 
  the 
  relative 
  volumes 
  of 
  the 
  carbon 
  and 
  hydrogen 
  

   atoms 
  are 
  very 
  closely 
  in 
  the 
  ratio 
  of 
  4 
  : 
  1 
  in 
  a 
  single 
  

   compound, 
  but 
  that 
  the 
  apparent 
  volumes 
  of 
  like 
  atoms 
  

   may 
  change 
  very 
  slightly 
  from 
  compound 
  to 
  compound 
  

   under 
  most 
  physical 
  conditions. 
  Another 
  way 
  of 
  stating 
  this 
  

   is 
  that 
  there 
  is 
  no 
  one 
  physical 
  condition 
  except 
  perhaps 
  

   absolute 
  zero 
  at 
  which 
  all 
  the 
  compounds 
  of 
  a 
  series 
  are 
  

   really 
  comparable. 
  Thus 
  the 
  molecular 
  volumes 
  of 
  a 
  series 
  

   of 
  homologous 
  hydrocarbons 
  under 
  corresponding 
  conditions 
  

   * 
  Communicated 
  by 
  Prof. 
  W. 
  J. 
  Pope, 
  F.R.S. 
  

  

  