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  PROFESSOR 
  WILLIAM 
  THOMSON 
  ON 
  THE 
  

  

  produce 
  more 
  mechanical 
  effect 
  from 
  a 
  given 
  quantity 
  of 
  heat, 
  with 
  a 
  given 
  

   available 
  range 
  of 
  temperatures, 
  than 
  an 
  engine 
  satisfying 
  the 
  criterion 
  stated 
  in 
  

   the 
  enunciation 
  of 
  the 
  proposition. 
  

  

  29. 
  The 
  mechanical 
  equivalent 
  of 
  a 
  thermal 
  unit 
  Fahrenheit, 
  or 
  the 
  quantity 
  of 
  

   heat 
  necessary 
  to 
  raise 
  the 
  temperature 
  of 
  a 
  pound 
  of 
  water 
  from 
  32° 
  to 
  33° 
  Fahr., 
  

   has 
  been 
  determined 
  by 
  Joule 
  in 
  foot-pounds 
  at 
  Manchester, 
  and 
  the 
  value 
  

   which 
  he 
  gives 
  as 
  his 
  best 
  determination 
  is 
  772-69. 
  Mr 
  Rankine 
  takes, 
  as 
  the 
  

   result 
  of 
  Joule's 
  determination, 
  772, 
  which 
  he 
  estimates 
  must 
  be 
  within 
  3^ 
  of 
  its 
  

   own 
  amount, 
  of 
  the 
  truth. 
  If 
  we 
  take 
  772| 
  as 
  the 
  number, 
  we 
  find, 
  by 
  mul- 
  

   tiplying 
  it 
  by 
  f 
  , 
  1 
  390 
  as 
  the 
  equivalent 
  of 
  the 
  thermal 
  unit 
  centigrade, 
  which 
  is 
  

   taken 
  as 
  the 
  value 
  of 
  J 
  in 
  the 
  numerical 
  applications 
  contained 
  in 
  the 
  present 
  

   paper. 
  

  

  30. 
  With 
  regard 
  to 
  the 
  determination 
  of 
  the 
  values 
  of 
  /z 
  for 
  different 
  tem- 
  

   peratures, 
  it 
  is 
  to 
  be 
  remarked 
  that 
  equation 
  (4) 
  shews 
  that 
  this 
  might 
  be 
  done 
  

   by 
  experiments 
  upon 
  any 
  substance 
  whatever 
  of 
  indestructible 
  texture, 
  and 
  indi- 
  

   cates 
  exactly 
  the 
  experimental 
  data 
  required 
  in 
  each 
  case. 
  For 
  instance, 
  by 
  first 
  

   supposing 
  the 
  medium 
  to 
  be 
  air 
  ; 
  and 
  again, 
  by 
  supposing 
  it 
  to 
  consist 
  partly 
  of 
  

   liquid 
  water 
  and 
  partly 
  of 
  saturated 
  vapour, 
  we 
  deduce, 
  as 
  is 
  shewn 
  in 
  Part 
  III. 
  

   of 
  this 
  paper, 
  the 
  two 
  expressions 
  (6), 
  given 
  in 
  § 
  30 
  of 
  my 
  former 
  paper, 
  for 
  the 
  

   value 
  of 
  fi 
  at 
  any 
  temperature. 
  As 
  yet 
  no 
  experiments 
  have 
  been 
  made 
  upon 
  

   air 
  which 
  afford 
  the 
  required 
  data 
  for 
  calculating 
  the 
  value 
  of 
  fx 
  through 
  any 
  

   extensive 
  range 
  of 
  temperature; 
  but 
  for 
  temperatures 
  between 
  50° 
  and 
  60° 
  

   Fahrenheit, 
  Joule's 
  experiments* 
  on 
  the 
  heat 
  evolved 
  by 
  the 
  expenditure 
  of 
  a 
  

   given 
  amount 
  of 
  work 
  on 
  the 
  compression 
  of 
  air 
  kept 
  at 
  a 
  constant 
  temperature, 
  

   afford 
  the 
  most 
  direct 
  data 
  for 
  this 
  object 
  which 
  have 
  yet 
  been 
  obtained 
  ; 
  since, 
  

   if 
  Q 
  be 
  the 
  quantity 
  of 
  heat 
  evolved 
  by 
  the 
  compression 
  of 
  a 
  fluid 
  subject 
  to 
  " 
  the 
  

   gaseous 
  laws" 
  of 
  expansion 
  and 
  compressibility, 
  W 
  the 
  amount 
  of 
  mechanical 
  

   work 
  spent, 
  and 
  t 
  the 
  constant 
  temperature 
  of 
  the 
  fluid, 
  we 
  have, 
  by 
  (11) 
  of 
  § 
  49 
  

   of 
  my 
  former 
  paper, 
  

  

  W.E 
  

   M 
  = 
  Q(1 
  + 
  E,) 
  ( 
  10 
  )> 
  

  

  which 
  is 
  in 
  reality 
  a 
  simple 
  consequence 
  of 
  the 
  other 
  expression 
  for 
  fx 
  in 
  terms 
  

  

  of 
  data 
  with 
  reference 
  to 
  air. 
  Remarks 
  upon 
  the 
  determination 
  of 
  ll 
  by 
  such 
  

  

  experiments, 
  and 
  by 
  another 
  class 
  of 
  experiments 
  on 
  air 
  originated 
  by 
  Joule, 
  

  

  are 
  reserved 
  for 
  a 
  separate 
  communication, 
  which 
  I 
  hope 
  to 
  be 
  able 
  to 
  make 
  to 
  the 
  

  

  Royal 
  Society 
  on 
  another 
  occasion. 
  

  

  31. 
  The 
  second 
  of 
  the 
  expressions 
  (6), 
  in 
  § 
  30 
  of 
  my 
  former 
  paper, 
  or 
  the 
  

   equivalent 
  expression 
  (32), 
  given 
  below 
  in 
  the 
  present 
  paper, 
  shews 
  that 
  /jl 
  may 
  

   be 
  determined 
  for 
  any 
  temperature 
  from 
  determinations 
  for 
  that 
  temperature 
  of; 
  

  

  * 
  " 
  On 
  the 
  Changes 
  of 
  Temperature 
  produced 
  by 
  the 
  Rarefaction 
  and 
  Condensation 
  of 
  Air," 
  

   Phil. 
  Mag., 
  vol. 
  xxvi. 
  May 
  1845. 
  

  

  