﻿198 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  POWER 
  AND 
  ECONOMY 
  

  

  Duty 
  of 
  unity 
  of 
  weight 
  of 
  steam, 
  — 
  

  

  Ihv^Z-F) 
  .... 
  (60.) 
  

  

  which, 
  being 
  multiplied 
  by 
  the 
  number 
  of 
  units 
  of 
  weight 
  of 
  steam 
  produced 
  by 
  a 
  

   given 
  weight 
  of 
  fuel, 
  gives 
  the 
  duty 
  of 
  that 
  weight 
  of 
  fuel. 
  

   Weight 
  of 
  steam 
  expended 
  per 
  stroke, 
  — 
  

  

  ^ 
  = 
  ^ 
  .... 
  (61.) 
  

  

  n 
  \ 
  1 
  s 
  K 
  ' 
  

  

  In 
  fact, 
  it 
  is 
  clear 
  that 
  if 
  any 
  five 
  quantities 
  out 
  of 
  the 
  following 
  seven 
  be 
  

   given, 
  the 
  other 
  two 
  may 
  be 
  determined 
  by 
  means 
  of 
  the 
  equations 
  : 
  

   R 
  + 
  F, 
  the 
  mean 
  load 
  on 
  unit 
  of 
  area 
  of 
  piston. 
  

   P 
  a 
  , 
  the 
  maximum 
  pressure 
  of 
  steam 
  in 
  the 
  cylinder. 
  

   s, 
  the 
  ratio 
  of 
  expansion. 
  

  

  W, 
  the 
  weight 
  of 
  steam 
  produced 
  in 
  unity 
  of 
  time. 
  

   A, 
  the 
  area 
  of 
  the 
  piston. 
  

   I, 
  the 
  length 
  of 
  stroke. 
  

   n, 
  the 
  number 
  of 
  strokes 
  in 
  unity 
  of 
  time. 
  

   The 
  other 
  quantities, 
  E, 
  Y 
  v 
  Z, 
  are 
  functions 
  of 
  those 
  seven. 
  

  

  Comparison 
  of 
  the 
  Theory 
  with 
  Mr 
  Wicksteed's 
  Experiments. 
  

  

  (36.) 
  In 
  order 
  to 
  test 
  the 
  practical 
  value 
  of 
  this 
  theory, 
  I 
  shall 
  compare 
  its 
  

   results 
  with 
  those 
  of 
  the 
  experiments 
  which 
  were 
  made 
  by 
  Mr 
  Wicksteed 
  on 
  the 
  

   large 
  Cornish 
  pumping 
  engine 
  built 
  under 
  the 
  direction 
  of 
  that 
  eminent 
  engineer 
  

   by 
  Messrs 
  Harvey 
  and 
  West, 
  for 
  the 
  East 
  London 
  Water- 
  Works 
  at 
  Old 
  Ford, 
  and 
  

   which 
  were 
  published 
  in 
  1841. 
  The 
  dimensions 
  and 
  structure 
  of 
  the 
  engine, 
  and 
  

   the 
  details 
  of 
  the 
  experiments, 
  are 
  stated 
  with 
  such 
  minuteness 
  and 
  precision, 
  that 
  

   there 
  is 
  none 
  of 
  that 
  uncertainty 
  respecting 
  the 
  circumstances 
  of 
  particular 
  cases, 
  

   which 
  is 
  the 
  most 
  frequent 
  cause 
  of 
  failure 
  in 
  the 
  attempt 
  to 
  apply 
  theoretical 
  

   principles 
  to 
  practice. 
  

  

  The 
  engine 
  was 
  worked 
  under 
  a 
  uniform 
  load 
  at 
  five 
  different 
  rates 
  of 
  ex- 
  

   pansion 
  successively. 
  The 
  number 
  of 
  strokes, 
  and 
  the 
  consumption 
  of 
  steam 
  

   during 
  each 
  trial, 
  having 
  been 
  accurately 
  registered, 
  Mr 
  Wicksteed 
  gives 
  a 
  table 
  

   shewing 
  the 
  weight 
  of 
  steam 
  consumed 
  per 
  stroke 
  for 
  each 
  of 
  the 
  five 
  rates 
  of 
  

   expansion. 
  I 
  shall 
  now 
  compute 
  the 
  weight 
  of 
  steam 
  per 
  stroke 
  theoretically, 
  

   and 
  compare 
  the 
  results. 
  

  

  Throughout 
  these 
  calculations 
  I 
  shall 
  uniformly 
  use 
  the 
  foot 
  as 
  the 
  unit 
  of 
  

   length, 
  the 
  avoirdupois 
  pound 
  as 
  that 
  of 
  weight, 
  and 
  the 
  hour 
  as 
  that 
  of 
  time. 
  

   Pressures 
  are 
  consequently 
  expressed 
  in 
  pounds 
  per 
  square 
  foot 
  for 
  the 
  purpose 
  of 
  

   calculation 
  ; 
  although 
  in 
  the 
  table 
  of 
  experiments 
  I 
  have 
  reduced 
  them 
  to 
  pounds 
  

   per 
  square 
  inch, 
  as 
  being 
  the 
  more 
  familiar 
  denomination. 
  

  

  