﻿The 
  Unit-Stere 
  llieory. 
  61 
  

  

  are 
  approximately 
  in 
  arithmetical 
  series, 
  sometimes 
  exactly 
  so. 
  

   If 
  this 
  series 
  divided 
  by 
  a 
  second, 
  necessarily 
  arithmetical, 
  

   that 
  o£ 
  the 
  valency 
  numbers, 
  the 
  respective 
  ratios 
  are 
  constant 
  

   or 
  nearly 
  so. 
  

   Thus, 
  

  

  a 
  constant, 
  which 
  has 
  already 
  been 
  referred 
  to. 
  

  

  By 
  simple 
  arithmetical 
  processes 
  it 
  is 
  usually 
  possible 
  to 
  

   prove 
  that 
  the 
  apparent 
  atomic 
  volume 
  of 
  H 
  is 
  equal 
  to 
  the 
  

   volume 
  of 
  the 
  unit-stere, 
  and 
  the 
  volume 
  of 
  carbon 
  equal 
  

   to 
  4S. 
  This 
  method 
  is 
  important, 
  because 
  it 
  is 
  the 
  most 
  

   direct 
  method 
  of 
  proving 
  the 
  relation 
  

  

  It 
  is, 
  however, 
  sometimes 
  not 
  possible 
  to 
  obtain 
  very 
  

   exact 
  values 
  of 
  small 
  numbers 
  by 
  the 
  method 
  of 
  differences, 
  

   and 
  it 
  is 
  also 
  necessary 
  to 
  exclude 
  other 
  relations. 
  The 
  

   following 
  method 
  has 
  been 
  devised 
  to 
  supplement 
  that 
  given 
  

   above. 
  

  

  Let 
  it 
  be 
  supposed 
  that 
  the 
  apparent 
  volumes 
  of 
  a 
  series 
  

   of 
  homologous 
  compounds 
  like 
  the 
  paraffin 
  hydrocarbons 
  

   under 
  a 
  number 
  of 
  physical 
  conditions 
  be 
  obtained, 
  then, 
  

   assuming 
  that 
  the 
  relation 
  Y 
  = 
  WS 
  is 
  true 
  for 
  a 
  single 
  

   compound, 
  

  

  v„ 
  v» 
  v„ 
  = 
  w,s, 
  w 
  a 
  s, 
  W 
  3 
  S, 
  

  

  V/, 
  V/, 
  V,', 
  = 
  W, 
  S', 
  W 
  2 
  S', 
  W 
  3 
  8', 
  

  

  If 
  the 
  volumes 
  in 
  each 
  series 
  be 
  successively 
  divided 
  by 
  

   those 
  of 
  the 
  first 
  members, 
  then 
  

  

  V 
  Vi' 
  Vi' 
  

  

  Li 
  w, 
  w 
  3 
  

  

  v/ 
  v 
  s 
  ' 
  v 
  8 
  ' 
  v 
  = 
  i, 
  ^ 
  2 
  , 
  w 
  

  

  Vx" 
  Y/' 
  Y+" 
  

  

  W/ 
  Wi' 
  

  

  The 
  ratios 
  so 
  obtained 
  must 
  be 
  additive, 
  that 
  is, 
  the 
  differ- 
  

   ences 
  must 
  be 
  equal 
  or 
  nearly 
  so, 
  and 
  also 
  they 
  should 
  be 
  

   reproduced 
  by 
  dividing 
  the 
  valencies 
  of 
  the 
  successive 
  com- 
  

   pounds 
  by 
  the 
  valency 
  of 
  the 
  first. 
  

  

  Both 
  of 
  these 
  conditions 
  are 
  fulfilled 
  under 
  corresponding- 
  

   conditions 
  in 
  a 
  surprising 
  manner, 
  although 
  sometimes 
  not 
  

   quite 
  strictly. 
  

  

  