586 MR W. J. M. RANKINE ON THE 
Clan Fy os A} 
lz — Fas {= Ss Jal az ss 
The following will be the values of the functions of the pressure which enter 
into the above equation :— 









dBase PEWS fo AA? ee PAN ay A,D 
in The a Shue re ai aN Fey oe 
ae if Diy Rae LER Nin DA, : 
yy oS ee a ar : oa} 
7%) i q (111 B.) 
d P 2 i A, ? 
heey (a i =) 
o PV) = 
GE). COSTE a tA a gd RASA 
av 7, aD 7 ED 
To illustrate the application of these formule, 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,, and its reciprocal 
by V,. As the constants have been deduced from M. Reanautt’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 gasisP,V, = 52595 ,, 
and 

‘ 
= ® — 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 :— 
D D 
Ae = bs te eee Mabe 
Com. log b = 3:1083932 ; Com. log a = 0:3344538 
b = 0:00128349 a= 2-165 
® ‘ (111 C.) 
DA, Wf DiredaD Dead 
La D = A, = =a. >;-—-A,D 
S D by ae beh OF Dao yo 
D d D 
Te Dis ab 20> S27 ep, 
For the purposes of a first approximation, we may assume that the value of x 

a 



