﻿OF 
  SINGLE-ACTING 
  EXPANSIVE 
  STEAM-ENGINES. 
  197 
  

  

  From 
  these 
  two 
  equations 
  is 
  deduced 
  the 
  following, 
  expressing 
  the 
  ratio 
  of 
  the 
  

   mean 
  load 
  on 
  the 
  piston 
  to 
  the 
  initial 
  pressure 
  of 
  the 
  steam: 
  — 
  

  

  R 
  + 
  F 
  Z-cs 
  

   P 
  1 
  ~ 
  (l-c)s 
  ■••_•(«; 
  

  

  being 
  equivalent 
  to 
  equation 
  (51). 
  

  

  In 
  computing 
  the 
  effect 
  of 
  Cornish 
  engines 
  these 
  formulse 
  require 
  to 
  be 
  modi- 
  

   fied, 
  owing 
  to 
  the 
  following 
  circumstances. 
  

  

  The 
  terms 
  depending 
  on 
  the 
  clearance 
  c 
  have 
  been 
  introduced 
  into 
  equations 
  

   (c), 
  (d), 
  on 
  the 
  supposition 
  that 
  the 
  steam 
  employed 
  in 
  filling 
  the 
  space 
  above 
  the 
  

   piston 
  at 
  the 
  top 
  of 
  its 
  stroke 
  is 
  lost, 
  being 
  allowed 
  to 
  escape 
  into 
  the 
  condenser, 
  

   without 
  having 
  effected 
  any 
  work 
  ; 
  so 
  that 
  a 
  weight 
  of 
  steam 
  W 
  c 
  s 
  is 
  wasted, 
  

   and 
  an 
  amount 
  of 
  power 
  WV 
  t 
  (P 
  1 
  -F)cs 
  lost, 
  in 
  unity 
  of 
  time. 
  But 
  in 
  Cornish 
  

   engines 
  this 
  is 
  not 
  the 
  case 
  ; 
  for 
  by 
  closing 
  the 
  equilibrium- 
  valve 
  at 
  the 
  proper 
  

   point 
  of 
  the 
  up 
  or 
  out-door 
  stroke, 
  nearly 
  the 
  whole 
  quantity 
  of 
  steam 
  necessary 
  

   to 
  fill 
  the 
  clearance 
  and 
  valve-boxes 
  may 
  be 
  kept 
  imprisoned 
  above 
  the 
  piston 
  so 
  

   as 
  to 
  make 
  the 
  loss 
  of 
  power 
  depending 
  on 
  it 
  insensible 
  in 
  practice. 
  This 
  portion 
  

   of 
  steam 
  is 
  called 
  a 
  cushion, 
  from 
  its 
  preventing 
  a 
  shock 
  at 
  the 
  end 
  of 
  the 
  up- 
  

   stroke 
  ; 
  and 
  as 
  Mr 
  Pole 
  in 
  his 
  valuable 
  work 
  on 
  the 
  Cornish 
  engine 
  has 
  observed, 
  

   its 
  alternate 
  compression 
  and 
  expansion 
  compensate 
  each 
  other, 
  and 
  have 
  no 
  

   effect 
  on 
  the 
  duty 
  of 
  the 
  engine. 
  The 
  proper 
  moment 
  of 
  closing 
  the 
  equilibrium- 
  

   valve 
  is 
  fixed 
  by 
  trial, 
  which 
  is, 
  perhaps, 
  the 
  best 
  way 
  ; 
  but 
  if 
  it 
  is 
  to 
  be 
  fixed 
  by 
  

   theory, 
  the 
  following 
  is 
  the 
  proper 
  formula. 
  Let 
  I" 
  be 
  the 
  length 
  of 
  the 
  portion 
  of 
  

   the 
  up-stroke 
  remaining 
  to 
  be 
  performed 
  after 
  the 
  equilibrium-valve 
  has 
  been 
  

  

  closed 
  : 
  then 
  — 
  

  

  l"_ 
  c(s-l) 
  

  

  l~ 
  1-c 
  UJ 
  

  

  A 
  slight 
  deviation 
  from 
  this 
  adjustment 
  will 
  produce 
  little 
  effect 
  in 
  practice, 
  if 
  the 
  

  

  fraction 
  c 
  is 
  small. 
  

  

  In 
  forming 
  the 
  equations 
  of 
  motion, 
  therefore, 
  of 
  the 
  Cornish 
  engine, 
  we 
  may, 
  

   without 
  material 
  error 
  in 
  practice, 
  omit 
  the 
  terms 
  denoting 
  a 
  waste 
  of 
  steam 
  and 
  

   loss 
  of 
  power 
  due 
  to 
  clearance 
  and 
  filling 
  of 
  steam-passages 
  ; 
  and 
  the 
  results 
  are 
  

   the 
  following 
  : 
  — 
  

  

  Equation 
  of 
  effect 
  and 
  power 
  in 
  unity 
  of 
  time 
  : 
  — 
  

  

  Useful 
  effect 
  E=RA/«=WV 
  1 
  {P 
  1 
  Z-F} 
  . 
  (57.) 
  

  

  Weight 
  of 
  steam 
  expended 
  in 
  unity 
  of 
  time 
  : 
  — 
  

  

  W=^ 
  .... 
  (58.) 
  

  

  From 
  those 
  two 
  fundamental 
  equations 
  the 
  following 
  are 
  deduced 
  : 
  — 
  

   Ratio 
  of 
  mean 
  load 
  on 
  piston 
  to 
  maximum 
  pressure, 
  — 
  

  

  B+F,_Z 
  

  

  