
MECHANICAL ACTION OF HEAT. 151 
I have integrated the differential equation which results from this condition, 
for substances in the gaseous state, in which the forces that interfere with the 
centrifugal force and atmospheric elasticity are comparatively small; and the 
result is 
: p=04 D (2541) 0-F+s/0) he viey 
P is the entire elasticity of the gas, and D its mean density. M represents 
the total mass of an atom, measured by weight, and pm that of its atmospheric 
part ; so that FD is the mean density of the atomic atmospheres. 
J (D) denotes the effect of the mutual actions of separate atoms. 
The first term represents the superficial-atomic elasticity. F denotes the 
effect of the attraction of the nucleus in modifying that elasticity, and can be 
eee approximately by a converging series, in terms of the negative powers 
of x55 b 
of the density D. 
By using the first term of such a series, and determining its coefficient, and 
the quantity f(D) empirically, I have obtained formule agreeing closely with the 
results of M. REGNAULT’s experiments on the Expansion of Atmospheric Air, 
Carbonic Acid, and Hydrogen. 
In a perfect gas, the above expression is reduced to 
+1, commencing with the inverse square, the coefficients being functions 
ie vv (25+1) Pa Rs GUILE) 
Let 7, as before, denote the number of atoms of a substance which, in the 
state of perfect gas, occupy unity of volume under unity of pressure at the tem- 
perature of melting ice, so that  M is its specific gravity in that state: then 
P=aynus (so 5+1) ‘scabs Sih OVE) 
The . by which _ is here multiplied fulfils the condition of being a 
function of 7 ae “and of constants which are the same for all substances, and is 
therefore fitted for a measure of temperature. It obviously varies proportionally 
to the pressure of a perfect gas of a given density, or its volume under a given 
pressure. | 
j Let 7, therefore, denote temperature, as measured from an imaginary zero, 
_ C degrees of the scale adopted, below the temperature of melting ice, at which 
wt ox 
‘age eg 
VOL. XX. PART I. 28 
