﻿196 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  POWER 
  AND 
  ECONOMY 
  

  

  express 
  them 
  in 
  a 
  form 
  more 
  convenient 
  for 
  practical 
  use, 
  the 
  notation 
  being 
  as 
  

   follows 
  : 
  — 
  

  

  Let 
  A 
  be 
  the 
  area 
  of 
  the 
  piston. 
  

  

  /, 
  the 
  length 
  of 
  stroke. 
  

  

  n, 
  the 
  number 
  of 
  double 
  strokes 
  in 
  unity 
  of 
  time. 
  

  

  c, 
  the 
  fraction 
  of 
  the 
  total 
  bulk 
  of 
  steam 
  above 
  the 
  piston 
  when 
  down, 
  allowed 
  

   for 
  clearance, 
  and 
  for 
  filling 
  steam-passages 
  ; 
  so 
  that 
  the 
  total 
  bulk 
  of 
  steam 
  at 
  

   the 
  end 
  of 
  the 
  effective 
  stroke 
  is 
  

  

  («) 
  

  

  1-c 
  

  

  I', 
  the 
  length 
  of 
  the 
  portion 
  of 
  the 
  stroke 
  performed 
  when 
  the 
  steam 
  is 
  cut 
  off. 
  

   s, 
  the 
  ratio 
  of 
  expansion 
  of 
  the 
  steam, 
  so 
  that 
  

  

  1 
  /-. 
  ^ 
  l 
  ' 
  

  

  \ 
  

  

  i 
  

  

  F 
  7~ 
  e 
  

  

  • 
  • 
  . 
  - 
  (p) 
  

  

  Let 
  W 
  be 
  the 
  weight 
  of 
  steam 
  expended 
  in 
  unity 
  of 
  time. 
  

  

  P 
  x 
  , 
  the 
  pressure 
  at 
  which 
  it 
  enters 
  the 
  cylinder. 
  

  

  Y 
  lt 
  the 
  volume 
  of 
  unity 
  of 
  weight 
  of 
  steam 
  at 
  saturation 
  at 
  the 
  pressure 
  P 
  t 
  ; 
  

   which 
  may 
  be 
  found 
  from 
  Table 
  I. 
  of 
  the 
  Appendix 
  to 
  the 
  original 
  paper. 
  

  

  F. 
  the 
  sum 
  of 
  all 
  the 
  resistances 
  not 
  depending 
  on 
  the 
  useful 
  load, 
  reduced 
  to 
  

   a 
  pressure 
  per 
  unit 
  of 
  area 
  of 
  piston 
  ; 
  whether 
  arising 
  from 
  imperfect 
  vacuum 
  in 
  

   the 
  condenser, 
  resistance 
  of 
  the 
  air-pump, 
  feed-pump, 
  and 
  cold-water 
  pump, 
  fric- 
  

   tion, 
  or 
  any 
  other 
  cause. 
  

  

  R, 
  the 
  resistance 
  arising 
  from 
  the 
  useful 
  load, 
  reduced 
  to 
  a 
  pressure 
  per 
  unit 
  

   of 
  area 
  of 
  piston. 
  

  

  Z, 
  the 
  ratio 
  of 
  the 
  total 
  action 
  of 
  steam 
  working 
  at 
  the 
  expansion 
  s, 
  to 
  its 
  

   action 
  without 
  expansion. 
  Values 
  of 
  this 
  ratio 
  are 
  given 
  in 
  the 
  second 
  Table 
  of 
  

   the 
  Appendix 
  to 
  the 
  original 
  paper. 
  

  

  Then 
  the 
  following 
  are 
  the 
  two 
  fundamental 
  equations 
  of 
  the 
  motion 
  of 
  the 
  

   steam-engine, 
  as 
  comprehended 
  in 
  equation 
  (50) 
  of 
  the 
  original 
  paper. 
  

  

  First, 
  Equality 
  of 
  power 
  and 
  effect, 
  — 
  

  

  RA/n=WV 
  1 
  {P 
  1 
  (Z-c*)-F(l-c)*} 
  . 
  . 
  (c) 
  

  

  Secondly, 
  Equality 
  of 
  two 
  expressions 
  for 
  the 
  weight 
  of 
  steam 
  expended 
  in 
  

   unity 
  of 
  time, 
  — 
  

  

  W= 
  v 
  ^ 
  n 
  . 
  . 
  . 
  . 
  . 
  (d) 
  

  

  