﻿178 
  

  

  MR 
  W. 
  J. 
  M. 
  EANKINE 
  ON 
  THE 
  

  

  and 
  

  

  we 
  obtain 
  

  

  »«- 
  ?v 
  ? 
  

  

  T 
  T* 
  

  

  8 
  m 
  

   m 
  

  

  "T" 
  o 
  ■*- 
  

  

  V 
  

  

  (43.) 
  

  

  $V 
  

  

  and 
  denoting 
  the 
  coefficient 
  of 
  ^ 
  by 
  — 
  v, 
  

  

  dlogS 
  

  

  — 
  — 
  v 
  

  

  and 
  because 
  

  

  d 
  log 
  0! 
  _ 
  

  

  dlogV 
  

  

  dlogV 
  

   d 
  log 
  P 
  

  

  d 
  log 
  m 
  _ 
  

   rflogP 
  ~ 
  

  

  dlogV 
  

  

  l-u 
  

  

  = 
  -!+■ 
  

  

  + 
  v 
  

  

  £ 
  2y 
  

  

  T 
  T 
  J 
  

  

  V 
  1 
  /3' 
  2v) 
  

  

  (44.) 
  

  

  8' 
  2y 
  

  

  T 
  T* 
  

  

  rf 
  log 
  S 
  

   rflogP 
  

  

  = 
  -(!-,) 
  (l-__J__) 
  

  

  /3' 
  2 
  Y 
  

  

  + 
  

  

  As 
  the 
  mean 
  temperature 
  of 
  the 
  liquid 
  thus 
  produced 
  more 
  or 
  less 
  exceeds 
  

   that 
  of 
  the 
  remaining 
  vapour, 
  a 
  small 
  fraction 
  of 
  it 
  will 
  be 
  reconverted 
  into 
  

   vapour, 
  if 
  the 
  expansion 
  is 
  carried 
  on 
  slowly 
  enough 
  ; 
  but 
  its 
  amount 
  is 
  so 
  small, 
  

   that 
  to 
  take 
  it 
  into 
  account 
  would 
  needlessly 
  complicate 
  the 
  calculation, 
  without 
  

   making 
  it 
  to 
  any 
  material 
  extent 
  more 
  accurate. 
  

  

  (23.) 
  The 
  extreme 
  complexity 
  of 
  the 
  exponent 
  <r, 
  considered 
  as 
  a 
  function 
  of 
  

  

  the 
  pressure 
  P, 
  would 
  render 
  a 
  general 
  formula 
  for 
  the 
  expansive 
  action 
  J 
  Vd 
  S 
  very 
  

  

  cumbrous 
  in 
  its 
  application. 
  For 
  practical 
  purposes, 
  it 
  is 
  sufficient 
  to 
  consider 
  

   the 
  exponent 
  <r 
  as 
  constant 
  during 
  the 
  expansion 
  which 
  takes 
  place 
  in 
  any 
  given 
  

   engine, 
  assigning 
  it 
  an 
  average 
  value 
  suitable 
  to 
  the 
  part 
  of 
  the 
  scale 
  of 
  pressures 
  

   in 
  which 
  the 
  expansion 
  takes 
  place. 
  For 
  engines 
  in 
  which 
  the 
  steam 
  is 
  intro- 
  

   duced 
  at 
  pressures 
  not 
  exceeding 
  four 
  atmospheres, 
  I 
  conceive 
  that 
  it 
  will 
  be 
  suffi- 
  

   ciently 
  accurate 
  to 
  make 
  

  

  <r= 
  

  

  7' 
  

  

  while 
  for 
  engines 
  in 
  which 
  the 
  initial 
  pressure 
  lies 
  between 
  four 
  and 
  eight 
  atmo- 
  

   spheres, 
  the 
  suitable 
  value 
  is 
  

  

  5 
  

  

  The 
  utmost 
  error 
  which 
  can 
  arise 
  from 
  using 
  these 
  exponents 
  is 
  about 
  yj5o 
  °f 
  

   the 
  whole 
  power 
  of 
  the 
  engine, 
  and 
  that 
  only 
  in 
  extreme 
  cases. 
  

   Making, 
  therefore, 
  

  

  S\ 
  -; 
  

  

  -Mr) 
  

  

  