22 Proceedings of Royal Society of Edinburgh. [dec. 6, 
be treated as a function of v. So long as the particles are of 
the same kind, or at least of equal mass if of different diameters, 
such integrals are easy to evaluate ; but it is very different when 
the masses differ in two mixed gases. In what follows, the merely 
numerical factor of the expression above will be denoted by C r , so 
that the value of the expression is, when the masses and diameters 
are equal, C r /^7r«s 2 A r/2 , and the introduction of different diameters 
merely introduces another factor. Here 3/2 h is the mean square 
speed, n the number of particles per cubic unit, and s their common 
diameter. 
When the masses are unequal there will, in general, be different 
mean free paths for particles of two different kinds, and the 
integrals cannot be simplified in the above way. In this case the 
integrals will be expressed as 1 (^ r , 9 (£ r . 
(1) In my former paper I showed that the Yirial equation is, for 
equal hard spheres exerting no molecular action other than the 
impacts, 
nPv 2 l 2 = | p(V — 2mrs s /3 ) , 
where n is the number of particles, P the mass of one, s its diameter, 
v ‘ 2 the mean-square speed, p the pressure, and V the volume. The 
quantity subtracted from the volume is four times the sum of the 
volumes of the spheres ; and I pointed out that this expression 
exactly agrees in form with Amagat’s experimental results for 
hydrogen, which were conducted through wide ranges of pressure 
and between 18° C. and 100° C. 
In a mixture of equal numbers of two kinds of particles, of 
diameters s 15 s 2 , I find that for s 3 in the above formula we must put 
iW + sw+tf), 
where s = (s 1 + s 2 )/2. Thus the “ultimate volume” is increased if 
the sizes of the particles differ, though the mean diameter is 
unaltered. 
(2) Por the coefficient of viscosity in a single gas the value found 
is 
jyCi = pA. 0 , 412 
37 ms 2 Jh fit 
