﻿586 
  

  

  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  = 
  ¥*{ 
  

  

  A 
  i 
  

  

  The 
  following 
  will 
  be 
  the 
  values 
  of 
  the 
  functions 
  of 
  the 
  pressure 
  which 
  enter 
  

   into 
  the 
  above 
  equation 
  : 
  — 
  

  

  dP 
  

  

  d 
  t 
  

  

  P 
  V 
  

  

  X 
  v 
  

  

  V 
  

  

  ih 
  + 
  ^} 
  

  

  d 
  2 
  V 
  P 
  V 
  

  

  _!__ 
  — 
  _ 
  9 
  _ 
  

  

  <Zt 
  2 
  ~ 
  V 
  

  

  P 
  V 
  

  

  Q 
  ***■*■ 
  A 
  * 
  A 
  "<S~ 
  

  

  ♦^ 
  « 
  y 
  

  

  dP_. 
  n8 
  <ZP 
  _ 
  p 
  v 
  ^ 
  f 
  t 
  d. 
  A 
  D 
  1^ 
  d.A.B) 
  

  

  dV 
  dD 
  ° 
  • 
  It/ 
  dD 
  r 
  ' 
  ~d 
  1 
  D~ 
  \ 
  

  

  V^ 
  T 
  / 
  _ 
  T> 
  Tf 
  V 
  T 
  T 
  2 
  J 
  

  

  dv 
  

  

  - 
  P 
  V 
  

  

  — 
  ^O 
  v 
  

  

  + 
  

  

  d. 
  A 
  D 
  

  

  rf 
  . 
  A 
  t 
  D 
  

  

  (111 
  B.) 
  

  

  To 
  illustrate 
  the 
  application 
  of 
  these 
  formulae, 
  let 
  us 
  calculate 
  the 
  difference 
  

   between 
  the 
  real 
  specific 
  heat, 
  and 
  the 
  apparent 
  specific 
  heat, 
  at 
  constant 
  pressure, 
  

   of 
  carbonic 
  acid 
  gas, 
  at 
  the 
  temperature 
  of 
  melting 
  ice, 
  and 
  at 
  the 
  density 
  which, 
  

   if 
  the 
  gas 
  were 
  perfect, 
  would 
  correspond 
  to 
  a 
  pressure 
  of 
  one 
  atmosphere 
  at 
  the 
  

   temperature 
  of 
  melting 
  ice. 
  Let 
  this 
  density 
  be 
  denoted 
  by 
  D 
  (1 
  , 
  and 
  its 
  reciprocal 
  

   by 
  V 
  . 
  As 
  the 
  constants 
  have 
  been 
  deduced 
  from 
  M. 
  Regnault's 
  experiments, 
  

   the 
  calculations 
  will 
  be 
  made 
  in 
  French 
  measures 
  and 
  for 
  the 
  latitude 
  of 
  Paris. 
  

  

  The 
  actual 
  density 
  of 
  carbonic 
  acid 
  at 
  0° 
  centigrade, 
  and 
  under 
  one 
  atmosphere 
  

   of 
  pressure, 
  exceeds 
  the 
  theoretical 
  density, 
  in 
  the 
  perfectly 
  gaseous 
  state, 
  in 
  the 
  

   ratio 
  of 
  1*0065 
  to 
  1 
  nearly. 
  Hence 
  the 
  height 
  of 
  a 
  homogeneous 
  atmosphere 
  of 
  

   actual 
  carbonic 
  acid 
  at 
  0° 
  centigrade 
  being 
  .... 
  5225*5 
  metres 
  

   the 
  corresponding 
  height 
  in 
  the 
  state 
  of 
  perfect 
  gas 
  is 
  P 
  V 
  = 
  5259 
  5 
  „ 
  

  

  P 
  V 
  

  

  and 
  - 
  Q 
  — 
  - 
  = 
  19-53 
  metres 
  per 
  centigrade 
  degree 
  = 
  62-84 
  feet. 
  

  

  The 
  functions 
  which 
  express 
  the 
  influence 
  of 
  density 
  on 
  the 
  deviation 
  of 
  car- 
  

   bonic 
  acid 
  gas 
  from 
  the 
  perfectly 
  gaseous 
  state, 
  have 
  the 
  following 
  values 
  : 
  — 
  

  

  A 
  = 
  b 
  . 
  ^-; 
  A 
  1 
  = 
  a 
  

  

  when 
  

  

  Com. 
  log 
  b 
  = 
  3-1083932 
  ; 
  Com. 
  log 
  a 
  = 
  0-3344538 
  

   b 
  = 
  0-00128349 
  a 
  = 
  2-16 
  ; 
  

  

  = 
  26 
  

  

  D_ 
  

  

  d.l 
  

  

  ' 
  D 
  

  

  ) 
  

   = 
  a 
  

  

  D 
  

  

  ' 
  Do'' 
  

  

  d 
  

  

  dD 
  

  

  d 
  

   dD 
  ' 
  

  

  A,D 
  = 
  

  

  :2a 
  T) 
  

  

  

  A 
  D 
  

  

  (111 
  C.) 
  

  

  For 
  the 
  purposes 
  of 
  a 
  first 
  approximation, 
  we 
  may 
  assume 
  that 
  the 
  value 
  of 
  k 
  

  

  