﻿202 
  Mr. 
  E. 
  Haigh 
  on 
  Orthobaric 
  Volumes 
  in 
  

  

  only 
  reference 
  to 
  that 
  class 
  of 
  substances 
  in 
  which 
  no 
  marked 
  

   degree 
  of 
  polymerization 
  is 
  apparent. 
  

  

  § 
  1. 
  On 
  a 
  Reduced 
  Equation 
  connecting 
  

   Orthobaric 
  Volumes 
  with 
  Pressure 
  and 
  Temperature. 
  

   The 
  fundamental 
  proposition 
  which 
  it 
  is 
  the 
  object 
  of 
  this 
  

   article 
  to 
  establish 
  may 
  be 
  stated 
  as 
  follows 
  : 
  — 
  

  

  The 
  orthobaric 
  volumes 
  of 
  all 
  " 
  normal 
  " 
  substances 
  are 
  

   connected 
  with 
  vapour-pressures 
  and 
  temperatures 
  of 
  ebullition 
  

   by 
  the 
  reduced 
  equation 
  

  

  {-H 
  i 
  -'X»-WK*-'). 
  

  

  + 
  {' 
  + 
  ( 
  i 
  -")(*V—) 
  + 
  y}( 
  3 
  +- 
  1 
  ) 
  

  

  = 
  160 
  (1) 
  

  

  In 
  the 
  above 
  equation 
  7r, 
  represent 
  reduced 
  vapour- 
  

   pressure 
  and 
  temperature, 
  <p, 
  yjr 
  are 
  respectively 
  the 
  reduced 
  

   volumes 
  of 
  the 
  saturated 
  vapour 
  and 
  of 
  the 
  liquid. 
  

  

  Essentially, 
  the 
  equation 
  is 
  a 
  dual 
  form 
  of 
  van 
  der 
  Waals's 
  

  

  reduced 
  

   is 
  removec 
  

  

  equation, 
  for 
  if 
  the 
  function 
  (l 
  — 
  0\ 
  l— 
  7r\ 
  

  

  eel, 
  it 
  becomes 
  ^ 
  ' 
  \<PY 
  

  

  (2) 
  

  

  (w 
  + 
  1 
  2 
  ) 
  (a* 
  - 
  1) 
  + 
  (- 
  + 
  £) 
  (W 
  - 
  1) 
  = 
  is* 
  ■ 
  

  

  This 
  latter 
  equation, 
  though 
  approximately 
  true, 
  does 
  not 
  

   exhibit 
  the 
  close 
  agreement 
  with 
  experimental 
  results 
  which 
  

   will 
  be 
  shown 
  to 
  be 
  a 
  characteristic 
  feature 
  of 
  equation 
  (1). 
  

  

  At 
  the 
  critical 
  point 
  (1 
  — 
  6)(-7-j 
  — 
  7r) 
  vanishes, 
  and 
  

  

  since 
  </> 
  = 
  i/r 
  the 
  equation 
  reduces 
  to 
  van 
  der 
  Waals's 
  well 
  

   known 
  form. 
  

  

  Since 
  equation 
  (1), 
  or 
  any 
  of 
  the 
  forms 
  in 
  which 
  it 
  can 
  be 
  

   expressed, 
  connects 
  the 
  properties 
  of 
  two 
  phases 
  of 
  the 
  same 
  

   substance, 
  it 
  will 
  be 
  referred 
  to 
  as 
  the 
  6< 
  dual 
  " 
  equation. 
  

  

  The 
  introduction 
  of 
  the 
  function 
  (l~"^)(i, 
  — 
  tt) 
  

  

  is 
  due 
  to 
  an 
  attempt 
  to 
  take 
  account 
  of 
  the 
  interacting 
  forces 
  

   between 
  a 
  liquid 
  and 
  its 
  saturated 
  vapour 
  at 
  the 
  surface 
  of 
  

   separation. 
  It 
  may 
  be 
  well 
  to 
  state 
  at 
  once 
  that 
  the 
  equation 
  

   obtained 
  must 
  be 
  regarded 
  as 
  an 
  empirical 
  result, 
  since 
  the 
  

   method 
  of 
  investigation 
  has 
  been 
  necossirily 
  tentative, 
  though 
  

   with 
  some 
  guidance 
  from 
  theoretical 
  considerations 
  in 
  the 
  

  

  selection 
  of 
  the 
  functions 
  employed. 
  

  

  * 
  See 
  paper 
  "On 
  the 
  Variation 
  of 
  Molecular 
  Surface 
  Energy 
  with 
  

   Temperature,!' 
  fan 
  W. 
  Ramsay, 
  F.R.S., 
  and 
  Dr. 
  J. 
  Shields, 
  Phil. 
  Trans, 
  

   vol. 
  1.84 
  A. 
  p. 
  (il7. 
  (The 
  fader 
  1 
  — 
  corresponds 
  to 
  r, 
  the 
  temperature 
  

   from 
  the 
  critical 
  poinl 
  measured 
  downwards.) 
  

  

  