﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  181 
  

  

  (33.) 
  of 
  this 
  section, 
  the 
  volume 
  V 
  x 
  of 
  unity 
  of 
  weight 
  of 
  steam 
  corresponding 
  to 
  

   the 
  maximum 
  pressure 
  P 
  t 
  . 
  Then 
  Equation 
  (48.) 
  gives 
  the 
  space 
  traversed 
  by 
  the 
  

   piston 
  in 
  unity 
  of 
  time, 
  which, 
  being 
  multiplied 
  by 
  the 
  resistance 
  R 
  per 
  unit 
  of 
  

   area 
  of 
  piston, 
  gives 
  the 
  gross 
  effect 
  of 
  the 
  engine. 
  

  

  (27.) 
  If, 
  on 
  the 
  other 
  hand, 
  the 
  space 
  traversed 
  by 
  the 
  piston 
  in 
  unity 
  of 
  time 
  

   is 
  fixed, 
  Equation 
  (48.) 
  gives 
  the 
  means 
  of 
  determining, 
  from 
  the 
  evaporating 
  

   power 
  of 
  the 
  boiler 
  W, 
  either 
  the 
  volume 
  V 
  1 
  of 
  unity 
  of 
  weight 
  of 
  steam 
  required 
  

   to 
  work 
  the 
  engine 
  at 
  the 
  given 
  velocity 
  with 
  a 
  given 
  expansion, 
  or 
  the 
  expansion 
  

   s 
  proper 
  to 
  enable 
  steam 
  of 
  a 
  given 
  initial 
  density 
  to 
  work 
  the 
  engine 
  at 
  the 
  given 
  

   velocity. 
  The 
  initial 
  pressure 
  P 
  1 
  being 
  then 
  determined 
  from 
  the 
  volume 
  V 
  l5 
  the 
  

   resistance 
  which 
  the 
  engine 
  is 
  capable 
  of 
  overcoming 
  with 
  the 
  given 
  velocity 
  is 
  to 
  

   be 
  calculated 
  by 
  means 
  of 
  Equation 
  (51.) 
  

  

  (28.) 
  This 
  calculation 
  involves 
  the 
  determination 
  of 
  the 
  pressure 
  1 
  > 
  l 
  from 
  the 
  

   volume 
  Y 
  1 
  of 
  unity 
  of 
  weight 
  of 
  steam 
  at 
  saturation, 
  which 
  can 
  only 
  be 
  done 
  by 
  

   approximation. 
  The 
  following 
  formula 
  will 
  be 
  found 
  useful 
  for 
  this 
  purpose 
  : 
  — 
  

  

  -- 
  (v-:) 
  

  

  A11 
  . 
  . 
  . 
  (52.) 
  

  

  where 
  m 
  represents 
  the 
  pressure 
  of 
  one 
  atmosphere, 
  V 
  the 
  volume 
  of 
  steam 
  of 
  

   saturation 
  at 
  that 
  pressure 
  (being 
  1696 
  times 
  the 
  volume 
  of 
  water 
  at 
  4°'l 
  cent., 
  

   or 
  27*136 
  cubic 
  feet 
  per 
  pound 
  avoirdupois), 
  and 
  V 
  t 
  the 
  volume 
  of 
  steam 
  of 
  satu- 
  

   ration 
  at 
  the 
  pressure 
  P 
  r 
  This 
  formula 
  is 
  only 
  applicable 
  between 
  the 
  pressures 
  

   of 
  one 
  and 
  eight 
  atmospheres 
  : 
  that 
  is 
  to 
  say, 
  when 
  the 
  volume 
  of 
  steam 
  is 
  not 
  

   greater 
  than 
  27 
  cubic 
  feet 
  per 
  pound, 
  nor 
  less 
  than 
  4, 
  and 
  the 
  temperature 
  not 
  

   lower 
  than 
  100° 
  centigrade, 
  nor 
  higher 
  than 
  171° 
  centigrade 
  (which 
  correspond 
  to 
  

   212° 
  and 
  340° 
  Fahrenheit). 
  

  

  The 
  greatest 
  error 
  in 
  computing 
  the 
  pressure 
  by 
  means 
  of 
  this 
  formula 
  is 
  

   about 
  jo 
  of 
  an 
  atmosphere, 
  and 
  occurs 
  at 
  the 
  pressure 
  of 
  four 
  atmospheres, 
  so 
  

   that 
  it 
  is 
  2^5 
  of 
  the 
  whole 
  pressure. 
  This 
  is 
  sufficiently 
  accurate 
  for 
  practice, 
  in 
  

   calculating 
  the 
  power 
  of 
  steam-engines 
  ; 
  but 
  should 
  a 
  more 
  accurate 
  result 
  be 
  

   required, 
  the 
  approximate 
  value 
  of 
  the 
  pressure 
  may 
  be 
  used 
  to 
  calculate 
  the 
  

   temperature 
  by 
  means 
  of 
  Equation 
  XV. 
  ; 
  and 
  the 
  temperature 
  thus 
  determined 
  

   (which 
  will 
  be 
  correct 
  to 
  \ 
  of 
  a 
  centigrade 
  degree) 
  may 
  then 
  be 
  used 
  in 
  conjunc- 
  

   tion 
  with 
  the 
  volume 
  to 
  compute 
  a 
  corrected 
  value 
  of 
  the 
  pressure, 
  according 
  to 
  

   Equation 
  (38.) 
  The 
  pressure, 
  as 
  thus 
  ascertained, 
  will 
  be 
  correct 
  to 
  §500 
  of 
  its 
  

   amount, 
  which 
  may 
  be 
  considered 
  the 
  greatest 
  degree 
  of 
  accuracy 
  attainable. 
  

  

  The 
  most 
  convenient 
  and 
  expeditious 
  mode, 
  however, 
  of 
  computing 
  the 
  pres- 
  

   sure 
  from 
  the 
  volume, 
  or 
  vice 
  versa, 
  is 
  by 
  interpolation 
  from 
  the 
  table 
  given 
  in 
  the 
  

   Appendix 
  to 
  this 
  paper. 
  

  

  (29.) 
  The 
  resistance 
  denoted 
  by 
  R 
  may 
  be 
  divided 
  into 
  two 
  parts 
  ; 
  that 
  which 
  

   arises 
  from 
  the 
  useful 
  work 
  performed, 
  and 
  that 
  which 
  is 
  independent 
  of 
  it, 
  being, 
  

  

  