MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 179 
We may conclude from the above table that the calculated values of D 12 are in very 
satisfactory agreement with the observed data, the differences between the two being 
not greater than the experimental errors would render probable, if we may judge of 
these errors from the internal accordance of the observed results. It should also be 
remembered that the molecular model chosen for calculation is not the best 
representation of an actual gas molecule, though it is sufficiently good for the 
purpose, especially in view of its simplicity for numerical work. 
(j) The Absolute Magnitude of D 12 . 
We next consider the absolute magnitude of the coefficient of diffusion. A 
comparison of a theoretical expression for D 12 with the corresponding observed value 
involves not only the accuracy of the theory and experiment, but also the suitability 
of the molecular model adopted as the basis of the theory. If we choose the rigid 
elastic sphere as model (and for many purposes this very simple model is fairly 
satisfactory) we may deduce from the observed value of D 12 for a specified gas- 
mixture the corresponding value of o-i + (r 2 ( c f (13’01) and (9‘3l)). By doing this for 
three pairs of gases A-B, B-C, C-A we can obviously determine from the resulting 
values of cr a + a b , cr b + ar c , cr c + a- a die individual molecular radii <x a , a b , <r c . # By taking 
different sets of pairs we may obtain more than one determination of each molecular 
radius, and the mutual accordance of these affords some sort of check on the theory 
—mainly, I think, relating to the suitability of the molecular model. But we cannot 
in this way test whether the theoretical formula is in error by a factor which is 
nearly or quite constant, since this would merely alter the deduced values of the radii 
in a common ratio. 
[Revised June 2 , 1916. —By another method, as follows, we can to some extent 
check the absolute magnitude of the theoretical results. Having determined values 
of o- in the above manner, we can use <n (the radius for a particular gas) to calculate 
Du by the formula which expresses D 12 in the case of dissimilar molecules, putting 
m 2 = a 2 = ov In this way, practically by interpolation, we obtain a virtually 
experimental value of D n (which cannot be measured directly). But the theoretical 
expression for D n can also be written in the form D' n EE Jc —, ki and pi being 
Pi 
respectively the viscosity and density of the gas, while k is a numerical constant. If 
the correct theoretical expression for /q is used here, the theoretical value of k should 
agree with the experimentally measured value D u pJk v The former depends, of 
course, on the molecular hypothesis adopted, varying from IT20 for rigid elastic 
spheres to 1'504 for Maxwellian molecules. The following table gives several 
experimental values of k (taken from Jeans’ treatise!), which all lie between the 
* This method is due to Lord Kelvin, ‘Baltimore Lectures,’ p. 295. 
t Cf. Jeans’ ‘ Dynamical Theory of Gases,’ 2nd ed., §§ 447, 448. The value of k deduced from the 
corrected Meyer’s theory is D34 as against the value k = D20 given by the present theory (13-24). 
The formula for k there used is that given in my second memoir. 
VOL. CCXVII— A. 2 C 
