578 MR W. J. M. RANKINE ON THE 
Equilibrium of heat and pressure between portions of two different perfect 
gases in contact requires that the pressures independent of heat, and the pres- 
sures caused by heat, shall separately be in equilibrio. Let the suffixes a and 6} 
be used to distinguish quantities relative to two different substances in the per- 
fectly gaseous condition. Then the first condition of equilibrium is expressed as 
follows :— 
h h 
(+) (a) = 7) cay alt ten Shin oa tere 
that is to say, the densities of two perfect gases in equilibrio are inversely propor- 
tional to the coefficients of elasticity of their atomic atmospheres. 
The second condition is expressed as follows :— 
F)o=A)o 
which, being taken in connection with the first condition, gives 
N N 
(F2)@=GQ@ . 2 so. + 0% 
Now by Equation 90, we have 

N ID WE 
vip aneens 
Hence the condition of equilibrium of heat between two perfect gases is 
(=) OM (=) (Bn stee oe A athe ane ee 
consequently, temperature may be measured by the product of the pressure and vo- 
lume of a perfect gas, divided by a coefficient, which is proportional to the volume of 
the gas at a standard pressure and temperature. 
Temperatures thus measured are reckoned from the point known as the zero 
of gaseous tension, or absolute zero of a perfect gas thermometer, 274-6 centigrade 
below the temperature of melting ice. 
Let V, denote the volume of unity of weight of a perfect gas, at a standard 
pressure P,, and absolute temperature 7,; then any other absolute temperature 
has the following value :-— 
IPA T, ‘ 
T=7, PV, =P.V, (N Q+h) Lod a ph oie ae 
while the absolute temperature of total privation of heat is 
h 
ae 94.A. 
70 BV, (94 A.) 
Hence it appears that quantity of heat in unity of weight bears the following 
relation to temperature,— 
Le ee et 
T) 

Q=yev-mH=% 
