﻿ISO 
  mr 
  w. 
  j. 
  m. 
  rankine 
  on 
  the 
  

  

  above 
  quantity 
  by 
  the 
  number 
  of 
  units 
  of 
  weight 
  of 
  water 
  evaporated 
  in 
  unity 
  of 
  

   time. 
  

  

  If 
  this 
  number 
  be 
  denoted 
  by 
  W, 
  

  

  WS. 
  2 
  (l-c) 
  = 
  WY 
  l 
  (l-c)s=Au 
  . 
  . 
  . 
  (48.) 
  

  

  will 
  represent 
  the 
  cubical 
  space 
  traversed 
  by 
  the 
  piston 
  in 
  unity 
  of 
  time, 
  A 
  denot- 
  

   ing 
  the 
  area 
  of 
  the 
  piston, 
  and 
  u 
  its 
  mean 
  Velocity. 
  

  

  Now 
  let 
  the 
  whole 
  resistance 
  to 
  be 
  overcome 
  by 
  the 
  engine 
  be 
  reduced 
  by 
  the 
  

   principles 
  of 
  statics 
  to 
  a 
  certain 
  equivalent 
  pressure 
  per 
  unit 
  of 
  area 
  of 
  piston, 
  

   and 
  let 
  this 
  pressure 
  be 
  denoted 
  by 
  R. 
  Then, 
  

  

  RAm=RWV 
  1 
  (1-c)* 
  . 
  . 
  . 
  (49.) 
  

   expresses 
  the 
  effect 
  of 
  the 
  engine 
  in 
  terms 
  of 
  the 
  gross 
  resistance. 
  

  

  We 
  have 
  now 
  the 
  means 
  of 
  calculating 
  the 
  circumstances 
  attending 
  the 
  work- 
  

   ing 
  of 
  a 
  steam-engine 
  according 
  to 
  the 
  principle 
  of 
  the 
  conservation 
  of 
  vis 
  viva, 
  

   or, 
  in 
  other 
  words, 
  of 
  the 
  equality 
  of 
  power 
  and 
  effect, 
  which 
  regulates 
  the 
  action 
  

   of 
  all 
  machines 
  that 
  move 
  with 
  an 
  uniform 
  or 
  periodical 
  velocity. 
  

  

  This 
  principle 
  was 
  first 
  applied 
  to 
  the 
  steam-engine 
  by 
  the 
  Count 
  de 
  Pam- 
  

   bour 
  ; 
  and 
  accordingly, 
  the 
  formulas 
  which 
  I 
  am 
  about 
  to 
  give 
  only 
  differ 
  from 
  

   those 
  of 
  his 
  work 
  in 
  the 
  expressions 
  for 
  the 
  maximum 
  pressure 
  at 
  a 
  given 
  tempe- 
  

   rature, 
  and 
  for 
  the 
  expansive 
  action 
  of 
  the 
  steam, 
  which 
  are 
  results 
  peculiar 
  to 
  

   the 
  theory 
  of 
  this 
  essay. 
  

  

  In 
  the 
  first 
  place, 
  the 
  effect, 
  as 
  expressed 
  in 
  terms 
  of 
  the 
  pressure, 
  is 
  to 
  be 
  

   equated 
  to 
  the 
  effect 
  as 
  expressed 
  in 
  terms 
  of 
  the 
  resistance, 
  as 
  follows 
  : 
  — 
  

  

  EAa=RWV 
  1 
  .(l-c)* 
  = 
  WV 
  ] 
  fPj 
  ^-1 
  J^ 
  s 
  ^'-*s\ 
  - 
  P 
  8 
  (l-c) 
  *] 
  . 
  . 
  (50.) 
  

  

  This 
  is 
  the 
  fundamental 
  equation 
  of 
  the 
  action 
  of 
  the 
  steam-engine, 
  and 
  

   corresponds 
  with 
  Equation 
  A. 
  of 
  M. 
  de 
  Pambour's 
  theory. 
  

  

  (260 
  Dividing 
  both 
  sides 
  of 
  Equation 
  (50.) 
  b}^ 
  the 
  space 
  traversed 
  by 
  the 
  piston 
  

   in 
  unity 
  of 
  time 
  WV, 
  (1 
  — 
  c) 
  s, 
  and 
  transferring 
  the 
  pressure 
  of 
  the 
  waste 
  steam, 
  

   P 
  3 
  , 
  to 
  the 
  first 
  side, 
  we 
  obtain 
  this 
  equation 
  : 
  — 
  

  

  1 
  <T 
  I- 
  1 
  - 
  

  

  — 
  s 
  * 
  — 
  cs 
  

  

  *+».-», 
  V 
  : 
  *)« 
  — 
  ■ 
  • 
  ' 
  (51 
  ° 
  

  

  which 
  gives 
  the 
  means 
  of 
  determining 
  the 
  pressure 
  P 
  x 
  at 
  which 
  the 
  steam 
  must 
  

   enter 
  the 
  cylinder, 
  in 
  order 
  to 
  overcome 
  a 
  given 
  resistance 
  and 
  counter-pressure 
  

   with 
  a 
  given 
  expansion 
  ; 
  or 
  supposing 
  the 
  expansion 
  5 
  to 
  be 
  variable 
  at 
  pleasure, 
  

   and 
  the 
  initial 
  pressure 
  P, 
  fixed, 
  the 
  equation 
  gives 
  the 
  means 
  of 
  finding, 
  by 
  

   approximation, 
  the 
  expansion 
  best 
  adapted 
  to 
  overcome 
  a 
  given 
  resistance 
  and 
  

   counter- 
  pressure. 
  

  

  The 
  next 
  step 
  is 
  to 
  determine, 
  from 
  Equations 
  XV* 
  of 
  the 
  Introduction 
  and 
  

  

  