1152 
Physics. — “The coefficient of diffusion for gases according to 
O. E. Meyer.” By Prof. J. P. Kugnen. 
(Communicated in the meeting of January 25, 1913). 
Among the various methods of deriving an expression for the 
coefficient of diffusion from the kinetic theory on the assumption 
that the molecules behave like elastic spheres there is one — that 
of O. E. Meyer’), — which leads to a result differing largely from 
the others and from observation, although the fundamental assump- 
tions are essentially the same. 
The deduction of Mryegr’s formula is shortly as follows’): a plane 
of unit area is considered at right angles to the gradient of concen- 
tration and therefore to the diffusion stream, and the numbers of 
molecules of each kind are calculated which cross the plane per 
second. It is assumed that the molecules have on the average had 
their last collision at a distance / (mean free path) from the point 
where they cross the plane and that their number in each direction 
is proportional to their density at the point where the last collision 
has taken place. The numbers in question of both kinds of molecules 
are found to be 
1 dn 1 dn 
Se te and a, = — —u,l, —, 
3 3 dx 
where wu is the mean molecular velocity, m the number of molecules 
in unit volume and z the direction of the diffusion stream ; obviously 
dn, dn, : ; 
ae ae for 7, and /,, the mean free paths of the two kinds of mole- 
LT & 
cules in the mixture, we have 
bas 2 amen +n, 26° ve 
m 
2 
| oO 2 9 m,+m, 
and le va nrs dn, KO: pay 
1 
where s is the diameter of the molecule and e=} (s, + 5,). 
Owing to this double stream of molecules a total number a, + a, 
pass through the plane: this would in general represent a motion 
of the gas. As the gas considered as a whole is supposed to be at 
rest, the stream a, + a, will produce a pressure gradient by which 
a stream of the gas as a whole of the same amount in the opposite 
1) O. E Meyer, Die kin. Theorie der Gase p. 252 seq. 1899. 
2) e. g. L. Bourzmann, Kin. Theorie. J. p. 89 seq. 1896. 
