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  205 
  ) 
  

  

  X. 
  — 
  On 
  the 
  Economy 
  of 
  Heat 
  in 
  Expansive 
  Machines, 
  forming 
  the 
  Fifth 
  Section 
  of 
  

   a 
  Paper 
  On 
  the 
  Mechanical 
  Action 
  of 
  Heat. 
  By 
  William 
  John 
  Macquorn 
  

   Rankine, 
  Civil 
  Engineer, 
  F.R.S.E., 
  F.R.S.S.A., 
  &c. 
  

  

  (Read 
  21st 
  April 
  1851.) 
  

  

  (39.) 
  A 
  machine 
  working 
  by 
  expansive 
  power 
  consists 
  essentially 
  of 
  a 
  portion 
  

   of 
  some 
  substance 
  to 
  which 
  heat 
  is 
  communicated, 
  so 
  as 
  to 
  expand 
  it, 
  at 
  a 
  higher 
  

   temperature, 
  being 
  abstracted 
  from 
  it, 
  so 
  as 
  to 
  condense 
  it 
  to 
  its 
  original 
  volume, 
  

   at 
  a 
  lower 
  temperature. 
  The 
  quantity 
  of 
  heat 
  given 
  out 
  by 
  the 
  substance 
  is 
  less 
  

   than 
  the 
  quantity 
  received 
  ; 
  the 
  difference 
  disappearing 
  as 
  heat 
  to 
  appear 
  in 
  the 
  

   form 
  of 
  expansive 
  power. 
  

  

  The 
  heat 
  originally 
  received 
  by 
  the 
  working 
  body 
  may 
  act 
  in 
  two 
  ways 
  : 
  to 
  

   raise 
  its 
  temperature, 
  and 
  to 
  expand 
  it. 
  The 
  heat 
  given 
  out 
  may 
  also 
  act 
  in 
  two 
  

   ways 
  : 
  to 
  lower 
  the 
  temperature, 
  and 
  to 
  contract 
  the 
  body. 
  Now, 
  as 
  the 
  conver- 
  

   sion 
  of 
  heat 
  into 
  expansive 
  power 
  arises 
  from 
  changes 
  of 
  volume 
  only, 
  and 
  not 
  

   from 
  changes 
  of 
  temperature, 
  it 
  is 
  obvious, 
  that 
  the 
  proportion 
  of 
  the 
  heat 
  re- 
  

   ceived 
  which 
  is 
  converted 
  into 
  expansive 
  power 
  will 
  be 
  the 
  greatest 
  possible, 
  

   when 
  the 
  reception 
  of 
  heat, 
  and 
  its 
  emission, 
  each 
  take 
  place 
  at 
  a 
  constant 
  tem- 
  

   perature. 
  

  

  (40.) 
  Carnot 
  was 
  the 
  first 
  to 
  assert 
  the 
  law, 
  that 
  the 
  ratio 
  of 
  the 
  maximum 
  me- 
  

   chanical 
  effect, 
  to 
  the 
  whole 
  heat 
  expended 
  in 
  an 
  expansive 
  machine, 
  is 
  a 
  function 
  

   solely 
  of 
  the 
  two 
  temperatures 
  at 
  which 
  the 
  heat 
  is 
  respectively 
  received 
  and 
  emitted, 
  

   and 
  is 
  independent 
  of 
  the 
  nature 
  of 
  the 
  working 
  substance. 
  But 
  his 
  investigations 
  

   not 
  being 
  based 
  on 
  the 
  principle 
  of 
  the 
  dynamical 
  convertibility 
  of 
  heat, 
  involve 
  

   the 
  fallacy 
  that 
  power 
  can 
  be 
  produced 
  out 
  of 
  nothing. 
  

  

  (41.) 
  The 
  merit 
  of 
  combining 
  Carnot's 
  Law, 
  as 
  it 
  is 
  termed, 
  with 
  that 
  of 
  the 
  

   convertibility 
  of 
  heat 
  and 
  power, 
  belongs 
  to 
  Mr 
  Clausius 
  and 
  Professor 
  William 
  

   Thomson; 
  and 
  in 
  the 
  shape 
  into 
  which 
  they 
  have 
  brought 
  it, 
  it 
  may 
  be 
  stated 
  thus: 
  — 
  

  

  The 
  maximum 
  proportion 
  of 
  heat 
  converted 
  into 
  expansive 
  power 
  by 
  any 
  ma- 
  

   chine, 
  is 
  a 
  function 
  solely 
  of 
  the 
  temperatures 
  at 
  which 
  heat 
  is 
  received 
  and 
  emitted 
  

   by 
  the 
  working 
  substance 
  ; 
  which 
  function, 
  for 
  each 
  pair 
  of 
  temperatures, 
  is 
  the 
  same 
  

   for 
  all 
  substances 
  in 
  nature. 
  

  

  This 
  law 
  is 
  laid 
  down 
  by 
  Mr 
  Clausius, 
  as 
  it 
  originally 
  had 
  been 
  by 
  Carnot, 
  

   as 
  an 
  independent 
  axiom 
  ; 
  and 
  I 
  had 
  at 
  first 
  doubts 
  as 
  to 
  the 
  soundness 
  of 
  the 
  

   reasoning 
  by 
  which 
  he 
  maintained 
  it. 
  Having 
  stated 
  those 
  doubts 
  to 
  Professor 
  

   Thomson, 
  I 
  am 
  indebted 
  to 
  him 
  for 
  having 
  induced 
  me 
  to 
  investigate 
  the 
  subject 
  

   thoroughly; 
  for 
  although 
  I 
  have 
  not 
  yet 
  seen 
  his 
  paper, 
  nor 
  become 
  acquainted 
  with 
  

  

  VOL. 
  XX. 
  PART 
  II. 
  3 
  I 
  

  

  