﻿62 
  Mr. 
  Gervaise 
  Le 
  Bas 
  on 
  

  

  Divide 
  the 
  volumes 
  o£ 
  the 
  members 
  of 
  the 
  successive 
  

   series 
  by 
  the 
  corresponding 
  members 
  of 
  the 
  first 
  ; 
  then 
  

  

  Vx'/V,, 
  v//v 
  2 
  , 
  v//v 
  3 
  , 
  = 
  S'/S, 
  

  

  Vi7v„ 
  v 
  2 
  "/v 
  2) 
  v 
  3 
  "/v 
  3 
  , 
  = 
  s"/s, 
  

  

  a 
  series 
  of 
  

   . 
  constants. 
  

  

  = 
  &7S, 
  

  

  The 
  reference 
  points 
  are 
  generally 
  the 
  critical 
  temperatures 
  

   or 
  pressures, 
  but 
  it 
  has 
  been 
  found 
  convenient 
  to 
  utilize 
  the 
  

   melting-points 
  in 
  the 
  case 
  of 
  the 
  more 
  complex 
  hydrocarbons. 
  

  

  It 
  is 
  no 
  doubt 
  a 
  fact 
  that 
  the 
  apparent 
  molecular 
  volumes 
  

   under 
  corresponding 
  conditions 
  are 
  proportional 
  to 
  their 
  real 
  

   volumes, 
  approximately 
  at 
  any 
  rate. 
  Let 
  it 
  be 
  supposed 
  that 
  

   these 
  are 
  respectively 
  equal 
  to 
  V^ 
  Y 
  2 
  °, 
  V 
  3 
  °, 
  .... 
  

  

  Then 
  

  

  Ji_ 
  Vj_ 
  Y± 
  _s 
  ) 
  

  

  vr°' 
  v 
  2 
  °' 
  v 
  8 
  o' 
  - 
  s 
  > 
  . 
  

  

  I 
  a 
  series 
  or 
  constants 
  

   y.i 
  "vV 
  Yl 
  _ 
  ^ 
  *" 
  °^ 
  increasing 
  mag- 
  

  

  ■fp 
  yv 
  y"5> 
  - 
  gr> 
  | 
  nitu 
  d 
  e 
  . 
  

  

  - 
  • 
  - 
  • 
  ; 
  

  

  The 
  real 
  volumes 
  are 
  known 
  to 
  be 
  about 
  £ 
  of 
  the 
  molecular 
  

   critical 
  volumes, 
  and 
  no 
  doubt 
  are 
  equal 
  fractions 
  • 
  of 
  the 
  

   apparent 
  volumes 
  under 
  corresponding 
  conditions. 
  In 
  sup- 
  

   port 
  of 
  this 
  conclusion 
  one 
  finds 
  that 
  the 
  molecular 
  refractions 
  

   are 
  equal 
  fractions 
  of 
  the 
  apparent 
  volumes 
  of 
  the 
  compounds 
  

   under 
  coincident 
  conditions. 
  

  

  In 
  consequence 
  of 
  this 
  proportionality 
  the 
  molecular 
  

   refractions 
  themselves 
  are 
  subject 
  to 
  additive 
  relations 
  similar 
  

   to 
  those 
  of 
  the 
  apparent 
  molecular 
  volumes 
  of 
  the 
  compounds 
  

   under 
  such 
  conditions. 
  

  

  Unsaturated 
  Compounds. 
  

   The 
  Olefines 
  and 
  the 
  Acetylenes. 
  

  

  Ju 
  view 
  of 
  the 
  very 
  interesting 
  relations 
  found 
  among 
  the 
  

   saturated 
  paraffins 
  under 
  corresponding 
  conditions, 
  the 
  pos- 
  

   sible 
  extension 
  of 
  the 
  theory 
  to 
  other 
  series 
  is 
  a 
  matter 
  of 
  

   peculiar 
  interest. 
  Attention 
  will 
  be 
  directed 
  in 
  this 
  section 
  

   to 
  unsaturated 
  hydrocarbons, 
  (1) 
  the 
  olefines 
  C 
  n 
  H 
  2 
  J 
  = 
  | 
  and 
  

   the 
  acetylenes 
  C 
  n 
  P 
  2w-2 
  |=j, 
  (2) 
  aromatic 
  compounds. 
  

  

  In 
  spite 
  of 
  the 
  very 
  great 
  amount 
  of 
  experimental 
  mate- 
  

   rial 
  very 
  little 
  of 
  it 
  is 
  suitable 
  Tor 
  our 
  present 
  purpose, 
  since 
  

   most 
  of 
  the 
  observations 
  refer 
  to 
  some 
  common 
  temperature 
  

   like 
  0° 
  or 
  20°. 
  In 
  the 
  ca.se 
  of 
  compounds 
  belonging 
  to 
  the 
  

  

  