﻿202 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  POWER 
  AND 
  ECONOMY 
  

  

  graphic 
  solution, 
  on 
  the 
  other 
  hand, 
  is 
  very 
  simple 
  and 
  rapid, 
  and 
  sufficiently 
  

   accurate 
  for 
  all 
  practical 
  purposes 
  ; 
  and 
  I 
  have 
  therefore 
  adopted 
  it. 
  

  

  In 
  the 
  annexed 
  diagram, 
  Plate 
  VIIL, 
  fig. 
  1, 
  the 
  axis 
  of 
  abscissae, 
  -XO 
  + 
  X, 
  is 
  

   graduated 
  from 
  towards 
  +X 
  into 
  divisions 
  representing 
  ratios 
  of 
  expansion, 
  or 
  

   values 
  of 
  s. 
  The 
  divisions 
  of 
  the 
  axis 
  of 
  ordinates, 
  Y, 
  represent 
  values 
  of 
  Z. 
  

   The 
  curve 
  marked 
  " 
  locus 
  of 
  Z," 
  is 
  laid 
  down 
  from 
  the 
  third 
  column 
  of 
  Table 
  II. 
  

   of 
  the 
  Appendix 
  to 
  the 
  original 
  paper, 
  being 
  applicable 
  to 
  initial 
  pressures 
  not 
  

   exceeding 
  four 
  atmospheres. 
  

  

  Through 
  the 
  origin 
  draw 
  a 
  straight 
  line 
  BOA, 
  at 
  such 
  an 
  inclination 
  to 
  

  

  F 
  

   —XO 
  + 
  X 
  that 
  its 
  ordinates 
  are 
  represented 
  by 
  p-s. 
  Then 
  the 
  ordinates 
  measured 
  

  

  from 
  this 
  inclined 
  line 
  to 
  the 
  locus 
  of 
  Z 
  represent 
  the 
  value 
  of 
  the 
  numerator 
  

  

  -p 
  

   Z 
  — 
  p-s, 
  of 
  the 
  ratio 
  (62), 
  corresponding 
  to 
  the 
  various 
  values 
  of 
  s. 
  

  

  Take 
  a 
  point 
  at 
  C 
  on 
  the 
  line 
  BOA, 
  whose 
  abscissa, 
  measured 
  along 
  O 
  — 
  X, 
  re- 
  

   presents 
  - 
  =4p 
  Then 
  the 
  ordinates, 
  measured 
  from 
  BOA, 
  of 
  any 
  straight 
  line 
  

  

  drawn 
  through 
  C, 
  vary 
  proportionally 
  to 
  the 
  denominator 
  jr-y- 
  +s 
  of 
  the 
  ratio 
  (62). 
  

  

  Through 
  the 
  point 
  C, 
  therefore, 
  draw 
  a 
  straight 
  line 
  CT, 
  touching 
  the 
  locus 
  of 
  

   Z 
  : 
  Then 
  the 
  ratio 
  (62) 
  is 
  a 
  maximum 
  at 
  the 
  point 
  of 
  contact 
  T, 
  and 
  the 
  abscissa 
  

   at 
  that 
  point 
  represents 
  the 
  ratio 
  of 
  expansion 
  required. 
  

  

  Example. 
  

  

  (38.) 
  To 
  exemplify 
  this 
  method, 
  let 
  us 
  take 
  the 
  following 
  data. 
  

  

  Greatest 
  pressure 
  in 
  the 
  cylinder 
  P 
  l 
  = 
  201b. 
  per 
  square 
  inch, 
  =2880 
  lb. 
  per 
  

   square 
  foot. 
  

  

  The 
  corresponding 
  value 
  of 
  Y 
  1 
  is 
  20*248 
  cubic 
  feet 
  per 
  pound 
  of 
  steam. 
  

  

  To 
  obtain 
  this 
  initial 
  pressure 
  in 
  the 
  cylinder, 
  it 
  will 
  be 
  necessary 
  to 
  have 
  

   a 
  pressure 
  of 
  about 
  50 
  lbs. 
  per 
  square 
  inch 
  in 
  the 
  boiler. 
  

  

  F, 
  resistance 
  not 
  depending 
  on 
  the 
  useful 
  load 
  =2 
  lb. 
  per 
  square 
  inch, 
  

   =288 
  lb. 
  per 
  square 
  foot, 
  =^ 
  P 
  x 
  . 
  

  

  In, 
  amount 
  of 
  down 
  strokes, 
  =4800 
  feet 
  per 
  hour; 
  being 
  the 
  average 
  speed 
  

   found 
  to 
  answer 
  best 
  in 
  practice. 
  

  

  To 
  estimate 
  h, 
  the 
  annual 
  cost 
  of 
  producing 
  one 
  pound 
  of 
  steam 
  per 
  hour, 
  I 
  

   shall 
  suppose 
  that 
  the 
  engine 
  works 
  6000 
  hours 
  per 
  annum 
  ; 
  that 
  the 
  cost 
  of 
  

   fuel 
  is 
  one 
  penny 
  per 
  100 
  lb. 
  of 
  steam;* 
  that 
  the 
  cost 
  of 
  boiler 
  for 
  each 
  pound 
  

   of 
  steam 
  per 
  hour 
  is 
  0*016 
  ton, 
  at 
  £27, 
  =£0*432 
  ; 
  and 
  that 
  the 
  interest 
  of 
  capital 
  

   is 
  five 
  per 
  cent, 
  per 
  annum. 
  Hence 
  h 
  is 
  thus 
  made 
  up 
  — 
  

  

  * 
  This 
  estimate 
  is 
  made 
  on 
  the 
  supposition 
  that 
  coals 
  capable 
  of 
  producing 
  nine 
  times 
  their 
  

   weight 
  of 
  steam 
  are 
  worth 
  about 
  16s. 
  9d. 
  per 
  ton. 
  

  

  