﻿174 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  Now 
  this 
  quantity, 
  which 
  I 
  shall 
  denote 
  by 
  H, 
  is 
  the 
  total 
  heat 
  required 
  to 
  

   raise 
  unity 
  of 
  weight 
  of 
  liquid 
  from 
  t 
  c 
  to 
  r 
  x 
  of 
  absolute 
  temperature, 
  and 
  to 
  evapo- 
  

   rate 
  it 
  at 
  the 
  latter 
  temperature. 
  Therefore 
  the 
  total 
  heat 
  of 
  evaporation, 
  where 
  the 
  

   vapour 
  may 
  be 
  treated 
  as 
  a 
  perfect 
  gas, 
  increases 
  sensibly 
  at 
  an 
  uniform 
  rate 
  with 
  the 
  

   temperature 
  of 
  evaporation 
  ; 
  and 
  the 
  coefficient 
  oj 
  its 
  increase 
  with 
  temperature 
  is 
  

   equal 
  to 
  the 
  apparent 
  specific 
  heat 
  of 
  the 
  vapour 
  at 
  constant 
  pressure, 
  ft 
  (1 
  + 
  N). 
  

  

  (20.) 
  There 
  have 
  never 
  been 
  any 
  experiments 
  from 
  which 
  the 
  apparent 
  spe- 
  

   cific 
  heat 
  of 
  steam 
  under 
  constant 
  pressure 
  can 
  be 
  deduced 
  in 
  the 
  manner 
  in 
  which 
  

   that 
  of 
  permanent 
  gases 
  has 
  been 
  ascertained. 
  

  

  The 
  experiments 
  of 
  M. 
  Regnault, 
  however, 
  prove 
  that 
  the 
  total 
  heat 
  of 
  

   evaporation 
  of 
  water 
  increases 
  uniformly 
  with 
  the 
  temperature 
  from 
  C 
  to 
  200 
  J 
  

   centigrade, 
  and 
  thus 
  far 
  fully 
  confirm 
  the 
  results 
  of 
  this 
  theory. 
  

  

  The 
  coefficient 
  of 
  increase 
  is 
  equal 
  to 
  

  

  K 
  w 
  x 
  0-305 
  v 
  

  

  Its 
  mechanical 
  value 
  is 
  consequently 
  - 
  ,„ 
  , 
  . 
  

  

  116 
  - 
  4 
  metres 
  = 
  382 
  feet 
  per 
  centigrade 
  degree, 
  or 
  

   212 
  feet 
  per 
  degree 
  of 
  Fahrenheit. 
  

  

  Although 
  the 
  principle 
  of 
  the 
  conservation 
  of 
  vis 
  viva 
  has 
  thus 
  enabled 
  us 
  to 
  

   ascertain 
  the 
  law 
  of 
  increase 
  of 
  the 
  total 
  heat 
  of 
  evaporation, 
  it 
  does 
  not 
  enable 
  us 
  

   to 
  calculate 
  a 
  priori 
  the 
  constant 
  L 
  of 
  the 
  formula, 
  being 
  the 
  latent 
  heat 
  of 
  eva- 
  

   poration 
  at 
  the 
  fixed 
  temperature 
  from 
  which 
  the 
  total 
  heat 
  is 
  measured 
  ; 
  for 
  the 
  

   changes 
  of 
  molecular 
  arrangement 
  which 
  constitute 
  evaporation 
  are 
  unknown. 
  

  

  When 
  the 
  fixed 
  temperature 
  is 
  that 
  of 
  melting 
  ice, 
  M. 
  Regnauxt's 
  experi- 
  

   ments 
  give 
  606-5 
  centigrade 
  degrees, 
  applied 
  to 
  liquid 
  water 
  as 
  the 
  value 
  of 
  this 
  

   constant 
  ; 
  so 
  that 
  

  

  H 
  = 
  K 
  w 
  (606°-5 
  + 
  -305T°) 
  \ 
  

  

  For 
  the 
  centigrade 
  scale, 
  

  

  H=K 
  W 
  (1091°-7 
  + 
  -305 
  (T°-32°)) 
  

  

  For 
  Fahrenheit's 
  scale. 
  J 
  

  

  is 
  the 
  complete 
  expression 
  for 
  the 
  heat 
  required 
  to 
  raise 
  unity 
  of 
  weight 
  of 
  water 
  

   from 
  the 
  temperature 
  of 
  melting 
  ice 
  to 
  T° 
  above 
  the 
  ordinary 
  zero, 
  and 
  to 
  evapo- 
  

   rate 
  it 
  at 
  the 
  latter 
  temperature. 
  This 
  formula 
  has 
  been 
  given 
  by 
  M. 
  Regnault 
  

   as 
  merely 
  empirical 
  ; 
  but 
  we 
  have 
  seen 
  that 
  it 
  closely 
  represents 
  the 
  physical 
  law, 
  

   when 
  quantities 
  depending 
  on 
  the 
  expansion 
  of 
  water 
  are 
  neglected. 
  

  

  It 
  must 
  be 
  remarked, 
  that 
  the 
  unit 
  of 
  heat 
  in 
  M. 
  Regnauxt's 
  tables 
  is 
  not 
  

   precisely 
  the 
  specific 
  heat 
  of 
  water 
  at 
  0° 
  centigrade, 
  but 
  its 
  mean 
  specific 
  heat 
  

   between 
  the 
  initial 
  and 
  final 
  temperatures 
  of 
  the 
  water 
  in 
  the 
  calorimeter. 
  The 
  

   utmost 
  error, 
  however, 
  which 
  can 
  arise 
  from 
  this 
  circumstance, 
  is 
  less 
  than 
  12O0 
  

   of 
  the 
  total 
  heat 
  of 
  evaporation, 
  so 
  that 
  it 
  may 
  safely 
  be 
  neglected. 
  

  

  