﻿154 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  The 
  equilibrium 
  of 
  a 
  vapour 
  in 
  contact 
  with 
  its 
  liquid 
  depends 
  on 
  three 
  con- 
  

   ditions. 
  

  

  First, 
  The 
  total 
  elasticity 
  of 
  the 
  substance 
  in 
  the 
  two 
  states 
  must 
  be 
  the 
  

   same. 
  

  

  Secondly, 
  The 
  superficial 
  atomic 
  elasticity 
  must 
  vary 
  continuously 
  ; 
  so 
  that 
  

   if 
  at 
  the 
  surface 
  which 
  reflects 
  light 
  there 
  is 
  an 
  abrupt 
  change 
  of 
  density 
  (which 
  

   seems 
  almost 
  certain), 
  there 
  must 
  there 
  be 
  two 
  densities 
  corresponding 
  to 
  the 
  

   same 
  superficial-atomic 
  elasticity. 
  

  

  Thirdly, 
  The 
  two 
  forces, 
  which 
  act 
  on 
  each 
  stratum 
  of 
  vapour 
  parallel 
  to 
  the 
  

   surface 
  of 
  the 
  liquid, 
  namely, 
  the 
  preponderance 
  of 
  molecular 
  attraction 
  towards 
  

   the 
  liquid, 
  and 
  the 
  difference 
  of 
  the 
  superficial-atomic 
  elasticities 
  at 
  the 
  two 
  sides 
  

   of 
  the 
  stratum, 
  must 
  be 
  in 
  equilibrio. 
  

  

  Close 
  to 
  the 
  surface 
  of 
  the 
  liquid, 
  therefore, 
  the 
  vapour 
  is 
  highly 
  condensed. 
  

   The 
  density 
  diminishes 
  rapidly 
  as 
  the 
  distance 
  from 
  the 
  liquid 
  increases, 
  and 
  at 
  

   all 
  appreciable 
  distances 
  has 
  a 
  sensibly 
  uniform 
  value, 
  which 
  is 
  a 
  function 
  of 
  the 
  

   temperature 
  and 
  of 
  certain 
  unknown 
  molecular 
  forces. 
  

  

  The 
  integration 
  of 
  a 
  differential 
  equation 
  representing 
  the 
  third 
  condition 
  of 
  

   equilibrium, 
  indicates 
  the 
  form 
  of 
  the 
  approximate 
  equation. 
  

  

  LogP 
  = 
  a-^-^ 
  . 
  . 
  . 
  (XIV.) 
  

  

  The 
  coefficients 
  of 
  which 
  have 
  been 
  determined 
  empirically 
  by 
  three 
  experi- 
  

   mental 
  data 
  for 
  each 
  fluid. 
  For 
  proofs 
  of 
  the 
  extreme 
  closeness 
  with 
  which 
  the 
  

   formulae 
  thus 
  obtained 
  agree 
  with 
  experiment, 
  I 
  refer 
  to 
  the 
  Journal 
  in 
  which 
  

   they 
  first 
  appeared. 
  

  

  I 
  annex 
  a 
  table 
  of 
  the 
  coefficients 
  for 
  water, 
  alcohol, 
  ether, 
  turpentine, 
  petro- 
  

   leum, 
  and 
  mercury, 
  in 
  the 
  direct 
  equation, 
  and 
  also 
  in 
  the 
  inverse 
  formula. 
  

  

  l-J* 
  

  

  -^A-A 
  ■ 
  ■ 
  (xv.) 
  

  

  7 
  4 
  y 
  2 
  27 
  

  

  by 
  which 
  the 
  temperature 
  of 
  vapour 
  at 
  saturation 
  may 
  be 
  calculated 
  from 
  the 
  

   pressure. 
  In 
  the 
  ninth 
  and 
  tenth 
  columns 
  are 
  stated 
  the 
  limits 
  between 
  which 
  the 
  

   formulae 
  have 
  been 
  compared 
  with 
  experiment. 
  

  

  For 
  turpentine, 
  petroleum, 
  and 
  mercury, 
  the 
  formula 
  consists 
  of 
  two 
  terms 
  

   only, 
  

  

  LogP=a— 
  £ 
  . 
  . 
  . 
  (XVI.) 
  

   the 
  small 
  range 
  of 
  the 
  experiments 
  rendering 
  the 
  determination 
  of 
  7 
  impossible. 
  

  

  

  