1008 
1 
o€ = Erin) Aen setten) 
If B is known, then € can be calculated. 
According to (3) we may write (4a) as: 
4x0" (0 — dg ORE okey ee 
o is the density of the particle, d that of the medium, g the accele- 
ration of gravity. | 
From (6) we can calculate a. 
SCHRÖDINGER *) showed that: 
in which ¢, is the mean of the times required by the particle to 
fall over the distance ZL. The Brownian movement namely causes 
the measured times to differ somewhat inter se. 
The measurement of A? took place in the following way: I ob- 
served a great many times the time in which the particle covers a 
certain distance in horizontal direction, when the gravity is neutral- 
ized by an electric force. To find A? from these times of displace- 
ment we ask: what is the chance that the particle after a time ¢ 
crosses for the first time a dividing line at a distance /, no matter 
on which side? We confine ourselves to the X-movement. I have 
made use of the method which ScHrOpiNGER *) uses for a similar 
problem. ; 
When at a time ‘=O a great number N of particles start from 
the point Oj»), the number with coordinates between r and z + dx 
at the moment ¢ will be: 
We see the meaning of a by calculating the mean value of a’, 
It then appears that: 
1 
2 A? 
Calling the points that lie at a distance / on the right and on 
the left of O, A and B (fig. 1), we shall calculate how many 
particles have passed neither of the points in the time ¢. 
eN 
5 4 Oma A C 
1) E. Scnröpincer. Phys. Zeitschr. 16, 1915, p. 289. 
