﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  179 
  

  

  we 
  obtain 
  for 
  the 
  value 
  of 
  the 
  expansive 
  action 
  of 
  unity 
  of 
  weight 
  of 
  steam, 
  

  

  

  (45.) 
  

  

  s 
  being 
  used 
  to 
  denote 
  ^A 
  or 
  the 
  ratio 
  of 
  the 
  volumes 
  occupied 
  by 
  steam 
  at 
  the 
  

  

  V, 
  

  

  end 
  and 
  at 
  the 
  beginning 
  of 
  the 
  expansion 
  respectively. 
  

  

  A 
  table 
  to 
  facilitate 
  the 
  computation 
  is 
  given 
  in 
  the 
  Appendix. 
  

  

  The 
  gross 
  mechanical 
  action 
  of 
  unity 
  of 
  weight 
  of 
  steam 
  on 
  one 
  side 
  of 
  the 
  

   piston 
  is 
  found 
  by 
  adding 
  to 
  the 
  above 
  quantity 
  the 
  action 
  of 
  the 
  steam 
  before 
  it 
  

   begins 
  to 
  expand, 
  or 
  P 
  x 
  V 
  15 
  and 
  is 
  therefore 
  

  

  I-* 
  

  

  ^(i^-iV) 
  • 
  • 
  • 
  <«■> 
  

  

  The 
  values 
  of 
  the 
  coefficients 
  and 
  exponent 
  being 
  

  

  1 
  

  

  0" 
  

  

  1 
  

  

  1 
  

  

  l-o- 
  

  

  l-o- 
  

  

  cr 
  

  

  

  

  

  1 
  

  

  7 
  

  

  6 
  

  

  

  '6 
  

   1 
  

  

  6 
  

  

  5 
  

  

  

  "5 
  

  

  For 
  initial 
  pressures 
  between 
  

  

  1 
  and 
  4 
  atmospheres, 
  . 
  

  

  4 
  and 
  8 
  atmospheres, 
  . 
  

  

  (24.) 
  The 
  following 
  deductions 
  have 
  to 
  be 
  made 
  from 
  the 
  gross 
  action, 
  in 
  

   order 
  to 
  obtain 
  the 
  action 
  effective 
  in 
  overcoming 
  resistance. 
  

  

  First, 
  For 
  loss 
  of 
  power 
  owing 
  to 
  a 
  portion 
  of 
  the 
  steam 
  being 
  employed 
  in 
  

   filling 
  steam-passages, 
  and 
  the 
  space 
  called 
  the 
  clearance 
  of 
  the 
  cylinder 
  at 
  one 
  

   end. 
  Let 
  the 
  bulk 
  of 
  steam 
  so 
  employed 
  be 
  the 
  fraction 
  c 
  S 
  2 
  of 
  the 
  space 
  filled 
  

   by 
  steam 
  at 
  the 
  end 
  of 
  the 
  expansion 
  ; 
  then 
  the 
  loss 
  of 
  power 
  from 
  this 
  cause 
  is 
  

  

  Secondly, 
  For 
  the 
  pressure 
  on 
  the 
  opposite 
  side 
  of 
  the 
  piston, 
  of 
  the 
  steam 
  

   which 
  escapes 
  into 
  the 
  condenser, 
  or 
  into 
  the 
  atmosphere, 
  as 
  the 
  case 
  may 
  be. 
  

   Let 
  P 
  3 
  be 
  the 
  pressure 
  of 
  this 
  steam 
  ; 
  the 
  deduction 
  to 
  be 
  made 
  for 
  its 
  action 
  is 
  

  

  P 
  3 
  S 
  2 
  (l-,)=:P 
  3 
  V 
  l 
  (l- 
  C 
  ),. 
  

  

  These 
  deductions 
  having 
  been 
  made, 
  there 
  is 
  obtained 
  for 
  the 
  effect 
  of 
  unity 
  

   of 
  weight 
  of 
  water 
  evaporated, 
  

  

  V 
  i 
  { 
  p 
  i 
  (i4^-i^* 
  1 
  " 
  7 
  - 
  cs 
  )- 
  p 
  3( 
  1 
  - 
  c 
  )*} 
  • 
  • 
  (47.) 
  

  

  (25.) 
  The 
  effect 
  of 
  the 
  engine 
  in 
  unity 
  of 
  time 
  is 
  found 
  by 
  multiplying 
  the 
  

   vol. 
  xx. 
  paet 
  i. 
  3 
  b 
  

  

  