
MECHANICAL ACTION OF HEAT. 581 
Bay V, P : 
ieee ey Hyp. ee p, nearly (7 being nearly constant), 

and K, nearly = k. 
The value of the integral in the numerator is found as follows :— 
The Centrifugal Theory of Elasticity indicates that the pressure of an imper- 
fect gas may be represented by the following formula :— 
Vv 
P_P, {= +4,— >= 3s — be. | ats mee -(L043 
where V, is the volume in the perfectly gaseous state, at a standard pressure P,, 
and absolute temperature +,, and A,, A,, &c., are a series of functions of the den- 
sity, to be determined empirically. From this formula it is easily seen that 
V, A, 2 
ge =p, {4+ a + de. } ee | ae Pe (i 5 
so that the first term in the numerator of the expression (103) has the following 
value :— 
xf (7-2) avatavef mirror | he SZ avtée.}. “ae GIG,) 
Vv 
*as = Nz, nearly. 

in which 

In order to represent correctly the result of M. ReaNnautt’s experiments on 
the elasticity and expansion of gases, it was found sufficient to use, in the for- 
mula for the pressure (104), the first three terms; and the functions of the den- 
sity which occur in these terms, as determined empirically from the experiments, 
were found to have the following values, in which the unit of volume is the 
theoretical volume of unity of weight of air under the pressure of one atmosphere, 
at the temperature of melting ice,* and the values of the constants are given for 
the centigrade scale. 
A ADF 2 tA NG 
v=? (¥) ; Gaa =) relink o3 at eneueliay 
Com. log b = 38181545; Com. log a = 0:3176168. 
Hence it appears that the integrals in the formula (106) have the following 
values :— 
Vo AG A; 1\34 , 2 MA 2 A, se 10 a T, 1\ x% 
tf yav=20.a. (+) a ae ) . (107 A.) 

Vv, 
in which the common logarithms of the constants are 
* This unit of volume is greater than the actual volume of air, under the circumstances described, 
in the ratio of 1:00085 to 1. 
VOL. XX. PART IV. 78 
