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  PKOFESSOR 
  WILLIAM 
  THOMSON 
  ON 
  THE 
  

  

  57. 
  If 
  we 
  suppose 
  /j. 
  and 
  L 
  to 
  be 
  known 
  for 
  any 
  temperature, 
  equation 
  (32) 
  

   enables 
  us 
  to 
  determine 
  the 
  value 
  of 
  -*- 
  for 
  that 
  temperature 
  ; 
  and 
  thence 
  de- 
  

   ducing 
  a 
  value 
  of 
  d 
  t, 
  we 
  have 
  

  

  dt=^~d 
  P 
  (35); 
  

  

  which 
  shews 
  the 
  effect 
  of 
  pressure 
  in 
  altering 
  the 
  " 
  boiling 
  point" 
  if 
  the 
  mixed 
  

   medium 
  be 
  a 
  liquid 
  and 
  its 
  vapour, 
  or 
  the 
  melting 
  point 
  if 
  it 
  be 
  a 
  solid 
  in 
  contact 
  

   Avith 
  the 
  same 
  substance 
  in 
  the 
  liquid 
  state. 
  This 
  agrees 
  with 
  the 
  conclusion 
  

   arrived 
  at 
  by 
  my 
  elder 
  brother 
  in 
  his 
  Theoretical 
  Investigation 
  of 
  the 
  Effect 
  of 
  

   Pressure 
  in 
  Lowering 
  the 
  Freezing 
  Point 
  of 
  Water.* 
  His 
  result, 
  obtained 
  by 
  taking 
  

   as 
  the 
  value 
  for 
  /jl, 
  that 
  derived 
  from 
  Table 
  I. 
  of 
  my 
  former 
  paper 
  for 
  the 
  tem- 
  

   perature 
  0°, 
  is 
  that 
  the 
  freezing 
  point 
  is 
  lowered 
  by 
  -0075 
  3 
  cent, 
  by 
  an 
  additional 
  

   atmosphere 
  of 
  pressure. 
  Clausius, 
  with 
  the 
  other 
  data 
  the 
  same, 
  obtains 
  00733° 
  

   as 
  the 
  lowering 
  of 
  temperature 
  produced 
  by 
  the 
  same 
  additional 
  pressure, 
  which 
  

   differs 
  from 
  my 
  brother's 
  result 
  only 
  from 
  having 
  been 
  calculated 
  from 
  a 
  formula 
  

  

  E 
  

   which 
  implies 
  the 
  hypothetical 
  expression 
  J 
  j— 
  ^- 
  for 
  fx. 
  It 
  was 
  by 
  applying 
  equa- 
  

   tion 
  (33) 
  to 
  determine 
  -r- 
  for 
  the 
  same 
  case, 
  that 
  Clausius 
  arrived 
  at 
  the 
  curious 
  

  

  result 
  regarding 
  the 
  latent 
  heat 
  of 
  water 
  under 
  pressure, 
  mentioned 
  above 
  {§ 
  45). 
  

  

  58. 
  Lastly, 
  it 
  may 
  be 
  remarked 
  that 
  every 
  quantity 
  except 
  h, 
  which 
  appears 
  

  

  in 
  equation 
  (33), 
  is 
  known 
  with 
  tolerable 
  accuracy 
  for 
  saturated 
  steam 
  through 
  a 
  

  

  wide 
  range 
  of 
  temperature 
  ; 
  and 
  we 
  may 
  therefore 
  use 
  this 
  equation 
  to 
  find 
  h, 
  

  

  which 
  has 
  never 
  yet 
  been 
  made 
  an 
  object 
  of 
  experimental 
  research. 
  Thus 
  we 
  

  

  have 
  

  

  7— 
  A 
  dp 
  (d\j 
  

  

  _ 
  h= 
  ?-± 
  dp 
  _ 
  td_L, 
  \ 
  

  

  J 
  dt 
  \dt 
  ) 
  

  

  For 
  the 
  value 
  of 
  7 
  the 
  best 
  data 
  regarding 
  the 
  density 
  of 
  saturated 
  steam 
  

   that 
  can 
  be 
  had 
  must 
  be 
  taken. 
  If 
  for 
  different 
  temperatures 
  we 
  use 
  the 
  same 
  

   values 
  for 
  the 
  density 
  of 
  saturated 
  steam 
  (calculated 
  according 
  to 
  the 
  gaseous 
  

  

  laws, 
  and 
  Regnault's 
  observed 
  pressure 
  from 
  j^^, 
  taken 
  as 
  the 
  density 
  at 
  100°), 
  

   the 
  values 
  obtained 
  for 
  the 
  first 
  term 
  of 
  the 
  second 
  member 
  of 
  the 
  preceding 
  

   equation 
  are 
  the 
  same 
  as 
  if 
  we 
  take 
  the 
  form 
  

  

  . 
  L 
  ix 
  (d 
  L 
  \ 
  

  

  — 
  h— 
  -4-— 
  (-— 
  + 
  c 
  ) 
  

  

  J 
  \dt 
  ) 
  

  

  derived 
  from 
  (34), 
  and 
  use 
  the 
  values 
  of 
  fx 
  shewn 
  in 
  Table 
  I. 
  of 
  my 
  former 
  paper. 
  

   The 
  values 
  of 
  —h 
  in 
  the 
  second 
  column 
  in 
  the 
  following 
  table 
  have 
  been 
  so 
  calcu- 
  

  

  * 
  Transactions, 
  Vol. 
  xvi., 
  Part 
  v. 
  His 
  paper 
  was 
  republished, 
  with 
  some 
  slight 
  modifications, 
  in 
  

   the 
  Cambridge 
  and 
  Dublin 
  Mathematical 
  Journal, 
  New 
  Series, 
  Vol. 
  V. 
  — 
  Nov. 
  1850. 
  

  

  