1154 
he had to make in order to carry out the required integrations 
was, that in ordinary slow diffusion Maxwurr’s law of distribution 
may be taken as fulfilled. The want of rigour which this implies 
may perhaps account for the small difference between the formula 
and observation mentioned. 
The question arises, what causes the great difference between 
Meyrr’s result and the others. Gross’) criticised the superposition 
of the gas current on the diffusion current: he tried to improve 
the theory by leaving out the former and by taking 3(a@,--a,) as 
the real diffusion stream; but this is certainly illegitimate, as the 
definition of D presupposes the gas to be at rest or the plane 
through which the diffusion stream is calculated to move with 
the gas. 
LANGEVIN ®) pointed out, that the dynamical action between the 
two kinds of molecules is lost sight of altogether in Meyer’s method, 
but he failed to indicate, how to modify or supplement it in order 
to take this action into account. Neither does BoLTZMANN explain the 
striking contradiction between the two methods. 
It is possible to remove this contradiction for the greater part by 
making use of the notion of persistence of molecular velocity which 
Jeans?) introduces into the kinetie theory and which also plays an 
important part in the theory of the Brownian movement. This 
quantity depends on the principle that, when a molecule collides 
with other molecules, it will after a collision on the average have 
retained a component of velocity in the original direction. Jrans has 
calculated what fraction of the original velocity this component 
is on the average: he calls this fraction the persistence 9 and finds 
1 1 
S= t zz gL +2) = 0.406. 
Jeans shows that the usual calculations in the kinetic theory of 
the various transport-phenomena of which diffusion is an example 
have to be corrected for this persistence. For the sake of simplicity 
it is assumed that a molecule describes the same distance / between 
suecessive collisions. Owing to persistence a molecule will on the 
average after describing a path / travel on in the same direction 
over distances successively of /9, /9* ete., therefore altogether describe 
a distance //(1—®) before its motion in the given direction is exhausted 
and similarly a molecule which reaches a plane from a distance / 
will not on the average have had a component 0 in the given 
. 1) G. Gross. Wied. Ann. 40 p, 424 1890. 
2) Le. 
3) J. H. Jeans. The dynamical theory of gases p. 236 sqq. 1904, 
