﻿208 
  

  

  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  ECONOMY 
  OF 
  

  

  That 
  is 
  to 
  say 
  : 
  when 
  no 
  heat 
  is 
  employed 
  in 
  producing 
  variations 
  of 
  tempera- 
  

   ture, 
  the 
  ratio 
  of 
  the 
  heat 
  received 
  to 
  the 
  heat 
  emitted 
  by 
  the 
  working 
  body 
  of 
  an 
  

   expansive 
  machine, 
  is 
  equal 
  to 
  that 
  of 
  the 
  absolute 
  temperatures 
  of 
  reception 
  and 
  

   emission, 
  each 
  diminished 
  by 
  the 
  constant 
  k, 
  which 
  is 
  the 
  same 
  for 
  all 
  substaiices. 
  

  

  Hence 
  let 
  

  

  n=-Q' 
  1 
  -Q' 
  =H 
  1 
  -H 
  

  

  denote 
  the 
  maximum 
  amount 
  of 
  power 
  which 
  can 
  be 
  obtained 
  out 
  of 
  the 
  total 
  

   heat 
  H 
  1? 
  in 
  an 
  expansive 
  machine 
  working 
  between 
  the 
  temperatures 
  r 
  1 
  and 
  t 
  . 
  

   Then 
  

  

  £ 
  = 
  T 
  0i 
  w 
  

  

  being 
  the 
  law 
  which 
  has 
  been 
  enunciated 
  in 
  Article 
  42, 
  and 
  which 
  is 
  deduced 
  

   entirely 
  from 
  the 
  principles 
  already 
  laid 
  down 
  in 
  the 
  Introduction 
  and 
  First 
  

   Section 
  of 
  this 
  paper. 
  

  

  The 
  value 
  of 
  the 
  constant 
  k 
  is 
  unknown 
  ; 
  and 
  the 
  nearest 
  approximation 
  to 
  

   accuracy 
  which 
  we 
  can 
  at 
  present 
  make, 
  is 
  to 
  neglect 
  it 
  in 
  calculation, 
  as 
  being 
  

   very 
  small 
  as 
  compared 
  with 
  t. 
  

  

  (44.) 
  This 
  approximation 
  having 
  been 
  adopted, 
  I 
  believe 
  it 
  will 
  be 
  found 
  that 
  

   the 
  formula 
  {66.), 
  although 
  very 
  different 
  in 
  appearance 
  from 
  that 
  arrived 
  at 
  by 
  

   Professor 
  Thomson, 
  gives 
  nearly 
  the 
  same 
  numerical 
  results. 
  For 
  example 
  : 
  let 
  the 
  

   machine 
  work 
  between 
  the 
  temperatures 
  140° 
  and 
  30° 
  centigrade 
  : 
  then 
  t 
  1= 
  414°-6, 
  

   t 
  = 
  304°-6, 
  and 
  

  

  £ 
  =0-2653 
  

   H 
  i 
  

  

  Professor 
  Thomson 
  has 
  informed 
  me, 
  that 
  for 
  the 
  same 
  temperatures 
  he 
  finds 
  

   this 
  ratio 
  to 
  be 
  02713 
  * 
  

  

  (45.) 
  To 
  make 
  a 
  steam-engine 
  work 
  according 
  to 
  the 
  conditions 
  of 
  maximum 
  

   effect 
  here 
  laid 
  down, 
  the 
  steam 
  must 
  enter 
  the 
  cylinder 
  from 
  the 
  boiler 
  without 
  

   diminishing 
  in 
  pressure, 
  and 
  must 
  be 
  worked 
  expansively 
  down 
  to 
  the 
  pressure 
  

   and 
  temperature 
  of 
  condensation. 
  It 
  must 
  then 
  be 
  so 
  far 
  liquefied 
  by 
  conduc- 
  

   tion 
  alone, 
  that 
  on 
  the 
  liquefaction 
  being 
  completed 
  by 
  compression, 
  it 
  may 
  be 
  

   restored 
  to 
  the 
  temperature 
  of 
  the 
  boiler 
  by 
  means 
  of 
  that 
  compression 
  alone. 
  

   These 
  conditions 
  are 
  unattainable 
  in 
  steam-engines 
  as 
  at 
  present 
  constructed, 
  and 
  

   different 
  from 
  those 
  which 
  form 
  the 
  basis 
  of 
  the 
  formulae 
  and 
  tables 
  in 
  the 
  Fourth 
  

   Section 
  of 
  this 
  paper 
  ; 
  hence 
  it 
  is 
  found, 
  both 
  by 
  experiment 
  and 
  by 
  calculation 
  

  

  * 
  Prom 
  information 
  which 
  I 
  have 
  received 
  from 
  Professor 
  Thomson 
  subsequently 
  to 
  the 
  com- 
  

   pletion 
  of 
  this 
  paper, 
  it 
  appears 
  that 
  his 
  formula 
  becomes 
  identical 
  with 
  the 
  approximate 
  formula 
  here 
  

  

  proposed, 
  on 
  making 
  the 
  function 
  called 
  by 
  him 
  u. 
  = 
  -, 
  J 
  being 
  Joule's 
  equivalent. 
  

  

  T 
  

  

  Mr 
  Joule 
  also, 
  some 
  time 
  since, 
  arrived 
  at 
  this 
  approximate 
  formula 
  in 
  the 
  particular 
  case 
  of 
  

   a 
  perfect 
  gas. 
  

  

  

  