THEORY OF VISCOSITY AND THERMAL CONDUCTION, IN A MONATOMIC GAS. 343 
The Thermal Conductivity of Monatomic Gases. 
§ 12 (C) It is convenient to discuss the thermal conductivity of gases in terms of the 
constant f in the formula 3- = fp C„, as this eliminates the necessity for a separate 
discussion of the dependence of 3- on pressure and temperature ; this is parallel with 
that of p, andjf is nearly or quite independent of pressure and temperature in normal 
conditions. As we have seen in § 11 (F), the value of f has been a matter of some 
uncertainty ; so long as its value for rigid elastic spheres was supposed to be 1'6027, 
while for Maxwellian molecules it was known to be f, it seemed to offer a means of 
testing the suitability of different molecular models. On the ground of the 
discrepancy between the theoretical and observed relation between p and T, 
Maxwellian molecules were known to be unsatisfactory representations of actual 
molecules. Until about 1900 no reliable determinations of /had been made for mona¬ 
tomic gases, and those found for diatomic gases agreed fairly well with Meyer’s value 
of f (i.e., 1'6027 or, more accurately, 1'416) ; at the time this was regarded as a 
confirmation of the rigid elastic spherical model of the molecule, and as indicating 
that the internal molecular energy, which is not taken into account in these theories of 
a monatomic gas, is transmitted at the same rate as the translational energy. When, 
in 1902, Schwarze obtained the values of f for argon and helium, and found them 
nearly equal to f, the conclusion to be drawn was not obvious. It certainly 
contradicted Meyer’s theory, but left the question open as to whether the analysis, or 
the assumption of the rigid elastic spherical model, was at fault; also if f — -§ indicated 
that the molecules are Maxwellian, the failure of the corresponding law connecting 
p and T remained unexplained. It should be remembered, moreover, that the law 
p oc T’ /2 for rigid elastic spherical molecules is equally contradictory to experiment. 
These difficulties were removed by the theorem of my former paper, according to 
which f is an invariable constant -§ for all monatomic molecules. This is now seen to 
be incorrect as a general theorem, but the deviations found for the various particular 
molecular models discussed leaves little room for doubt that f is very nearly equal to 
-4 in the case of all likely models. The fact simply is, therefore, that f is very 
unsuitable as a means of discrimination between different models, and Schwarze’s 
observations indicate some mathematical fallacy in Meyer’s theory, without supporting 
any particular molecular model. The observed values of f are hardly known with 
sufficient accuracy to enable any conclusion to be drawn from a slight divergence 
from the value ■§, within the limits prescribed in (249) to (251). They are important, 
however, as confirming the general validity of the kinetic theory, apart from any 
hypothesis as to the nature of the molecules. 
The following table contains all the available data concerning the value of / for 
monatomic gases. Only very recently has the conductivity of neon been deter¬ 
mined, owing to the scarcity of the gas ; for krypton and xenon its value is still 
unknown. 
3 A 
VOL. CCXYI.-A. 
