﻿182 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  in 
  fact, 
  the 
  resistance 
  of 
  the 
  engine 
  when 
  unloaded. 
  Now 
  it 
  is 
  evident, 
  that 
  the 
  

   maximum 
  useful 
  effect 
  of 
  the 
  steam 
  has 
  been 
  attained, 
  as 
  soon 
  as 
  it 
  has 
  expanded 
  

   to 
  a 
  pressure 
  which 
  is 
  in 
  equilibrio 
  with 
  the 
  pressure 
  of 
  the 
  waste 
  steam 
  added 
  

   to 
  the 
  resistance 
  of 
  the 
  engine 
  when 
  unloaded 
  ; 
  for 
  any 
  further 
  expansion, 
  though 
  

   increasing 
  the 
  total 
  effect, 
  diminishes 
  the 
  useful 
  effect. 
  Therefore 
  if 
  we 
  make 
  

  

  R=R'+/, 
  

  

  R' 
  being 
  the 
  resistance 
  arising 
  from 
  the 
  useful 
  work, 
  and 
  / 
  the 
  resistance 
  of 
  the 
  

   engine 
  when 
  unloaded, 
  both 
  expressed 
  in 
  the 
  form 
  of 
  pressure 
  on 
  the 
  piston, 
  the 
  

   expansion 
  corresponding 
  to 
  the 
  maximum 
  of 
  useful 
  effect 
  will 
  take 
  place 
  when 
  

  

  P 
  2 
  =P 
  3 
  +/ 
  . 
  . 
  

  

  the 
  corresponding 
  ratio 
  of 
  expansion 
  being 
  

  

  P, 
  

  

  ~Gfc) 
  

  

  (53.) 
  

  

  The 
  maximum 
  useful 
  effect 
  with 
  a 
  given 
  pressure 
  on 
  the 
  safety-valve 
  has 
  

   been 
  so 
  fully 
  discussed 
  by 
  M. 
  de 
  Pambour, 
  that 
  it 
  is 
  unnecessary 
  to 
  do 
  more 
  than 
  

   to 
  state 
  that 
  it 
  takes 
  place 
  when 
  the 
  initial 
  pressure 
  in 
  the 
  cylinder 
  is 
  equal 
  to 
  

   that 
  at 
  the 
  safety-valve 
  : 
  that 
  is 
  to 
  say, 
  when 
  it 
  and 
  the 
  useful 
  resistance 
  are 
  the 
  

   greatest 
  that 
  the 
  safety-valve 
  will 
  permit. 
  

  

  (30.) 
  Annexed 
  is 
  a 
  table 
  of 
  the 
  values 
  of 
  some 
  of 
  the 
  quantities 
  which 
  enter 
  

   into 
  the 
  preceding 
  equations 
  in 
  the 
  notation 
  of 
  the 
  Count 
  de 
  Pambour's 
  works. 
  

  

  Expression 
  in 
  the 
  Notation 
  Equivalent 
  Expression 
  in 
  

  

  of 
  this 
  paper. 
  M. 
  de 
  Pambouk's 
  Notation. 
  

  

  R 
  = 
  R'+/ 
  .... 
  (L 
  + 
  S)r+f 
  

  

  Au 
  .... 
  av 
  

  

  W 
  . 
  . 
  . 
  . 
  S 
  x 
  weight 
  of 
  one 
  cubic 
  

  

  foot 
  of 
  water. 
  

  

  P 
  3 
  .... 
  p 
  

  

  I 
  +c 
  

  

  S 
  .... 
  T 
  , 
  

  

  I' 
  + 
  c 
  

   c 
  

  

  I' 
  + 
  c 
  

  

  (31.) 
  As 
  an 
  illustration, 
  I 
  shall 
  calculate 
  the 
  maximum 
  useful 
  effect 
  of 
  one 
  

   pound, 
  and 
  of 
  one 
  cubic 
  foot 
  of 
  water, 
  in 
  a 
  Cornish 
  double-acting 
  engine, 
  in 
  the 
  

   circumstances 
  taken 
  by 
  M. 
  de 
  Pambour 
  as 
  an 
  example 
  for 
  that 
  kind 
  of 
  engine 
  : 
  

   that 
  is 
  to 
  say, 
  — 
  

  

  1 
  

  

  Clearance 
  one-twentieth 
  of 
  the 
  stroke, 
  or 
  c 
  =ht 
  

  

  Resistance 
  not 
  depending 
  on 
  the 
  useful 
  load, 
  /= 
  72 
  lb. 
  per 
  square 
  foot. 
  

  

  Pressure 
  of 
  condensation, 
  . 
  . 
  . 
  P 
  3 
  = 
  5761b. 
  

  

  