﻿188 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  To 
  reduce 
  the 
  logarithm 
  of 
  the 
  number 
  of 
  cubic 
  metres 
  occupied 
  by 
  one 
  kilo- 
  

   gramme 
  to 
  that 
  of 
  the 
  number 
  of 
  cubic 
  feet 
  occupied 
  by 
  one 
  pound 
  avoirdupois, 
  

   add 
  1-20463. 
  

  

  The 
  logarithms 
  are 
  given 
  to 
  five 
  places 
  of 
  decimals 
  only, 
  as 
  a 
  greater 
  degree 
  

   of 
  precision 
  is 
  not 
  attainable 
  in 
  calculations 
  of 
  this 
  kind. 
  

  

  The 
  second 
  table 
  is 
  for 
  the 
  purpose 
  of 
  calculating 
  the 
  mechanical 
  action 
  of 
  

   steam 
  in 
  expansive 
  engines. 
  

  

  The 
  first 
  column 
  contains 
  values 
  of 
  the 
  fraction 
  of 
  the 
  entire 
  capacity 
  of 
  the 
  

   cylinder 
  which 
  is 
  filled 
  with 
  steam 
  before 
  the 
  expansion 
  commences 
  (being 
  the 
  

  

  quantity 
  - 
  of 
  the 
  formulae), 
  for 
  every 
  hundredth 
  part, 
  from 
  1-00, 
  or 
  the 
  whole 
  

  

  cylinder, 
  down 
  to 
  0*10, 
  or 
  one-tenth. 
  

  

  If 
  / 
  be 
  the 
  entire 
  length 
  of 
  stroke, 
  V 
  the 
  portion 
  performed 
  at 
  full 
  pressure, 
  

   and 
  c 
  the 
  fraction 
  of 
  the 
  entire 
  capacity 
  of 
  the 
  cylinder 
  allowed 
  for 
  clearance, 
  then 
  

  

  1 
  

   r 
  = 
  r 
  - 
  F 
  , 
  and 
  - 
  = 
  (\-c 
  )T 
  + 
  c. 
  

  

  The 
  entire 
  capacity 
  of 
  the 
  cylinder 
  is 
  to 
  be 
  understood 
  to 
  include 
  clearance 
  at 
  

   one 
  end 
  only. 
  

  

  The 
  second 
  column 
  gives 
  the 
  reciprocals 
  of 
  the 
  quantities 
  in 
  the 
  first, 
  or 
  the 
  

   values 
  of 
  the 
  ratio 
  of 
  expansion 
  s. 
  

  

  The 
  third 
  and 
  fourth 
  columns, 
  headed 
  Z, 
  give 
  the 
  values 
  of 
  the 
  quantity 
  

  

  s 
  ' 
  of 
  Article 
  23, 
  which 
  represents 
  the 
  ratio 
  of 
  the 
  entire 
  gross 
  action 
  

  

  l-o- 
  1-c- 
  

  

  of 
  the 
  steam 
  to 
  its 
  action 
  at 
  full 
  pressure, 
  without 
  allowing 
  for 
  clearance. 
  The 
  

   third 
  column 
  is 
  to 
  be 
  used 
  for 
  initial 
  pressures 
  of 
  from 
  one 
  to 
  four 
  atmospheres 
  ; 
  

   and 
  the 
  fourth 
  for 
  initial 
  pressures 
  of 
  from 
  four 
  to 
  eight 
  atmospheres. 
  

  

  The 
  deduction 
  to 
  be 
  made 
  from 
  the 
  quantity 
  Z 
  for 
  clearance 
  is 
  c 
  s, 
  or 
  the 
  

   product 
  of 
  the 
  fraction 
  of 
  the 
  cylinder 
  allowed 
  for 
  clearance 
  by 
  the 
  ratio 
  of 
  expan- 
  

   sion. 
  Hence, 
  to 
  calculate 
  from 
  the 
  tables 
  the 
  net 
  mechanical 
  action 
  of 
  unity 
  of 
  

   weight 
  of 
  steam, 
  allowing 
  for 
  the 
  counter-pressure 
  of 
  the 
  waste 
  steam 
  P 
  3 
  , 
  as 
  well 
  

   as 
  for 
  clearance, 
  we 
  have 
  the 
  formula 
  

  

  P 
  1 
  V 
  1 
  (Z- 
  C 
  ,)-P 
  3 
  V 
  1 
  (1- 
  C 
  ), 
  

   being 
  equivalent 
  to 
  the 
  formula 
  (47.) 
  of 
  this 
  paper. 
  

  

  