1155 
direction at that distance before it collided there, but at a distance 
I/A—9). We can also say, that the molecules which have had a 
collision at a distance //(1—®) succeed on the average in getting to 
the plane before their velocity in the given direction is reduced to 0. 
In the calculation of the numbers that cross the plane it was assumed 
that the velocities were evenly distributed in all directions at a 
distance /: as it now appears that this condition does not hold for 
a distance / but for the distance //(1—®), the correct result is obtained 
by replacing 7 by //(1—®) in the final formula. 
In this manner JrANs corrects Mryer’s formula’), but it is clear 
that by this means no improvement is effected, as D is multiplied 
by a constant factor and the anomalous dependence on n, and n, 
remains. An important point has however been overlooked by Jnans 
viz. that the persistence obtains a different value when one deals 
with a mixture of two kinds of molecules of different mass. 
When the calculation of 9 is carried out for a molecule m, amongst 
molecules m, one finds 
m,+m,\— i ai than Ae PEE Ey m, — 0.188 m, 
ie 
ie m, +m, = om, + mM, 
For m,—=m, this expression reduces to the one given by Jmans. 
As a molecule m, collides not only with molecules m, but also 
with molecules of its own kind, the correct expression for the 
persistence is obtained by multiplying the average number of collisions 
of the latter kind by 0.406 and that of the former by the above 
fraction. In this manner the factor 1/(1—%) becomes 
5 man, — 0.188 
ip =1: | Ln, srs,° V21,<0.406—n, XO” Ante, My zl 
m, m,+m, 
for the molecules m, and 
5 Fm, m,—0.188m, 
je [ror 1,X0.406 —n, 10° Bee Tali 9 Pie = 
2 
m, m,+m, 
for the molecules m,. 
Repeating Mryer’s argument we find for D 
1 
Da me i a: Ny Ugly f,)- 
If we now put n= 0, we obtain 
1) Jeans Lc. p. 278. Comp. M. v. Smorvenowskr, Bull. de l’Ac. d. Se. de Cracovie 
1906, p. 202. 
