( 318 ) 
The group, the amplitudes of which have the same values, but 
all the opposite sign, will be about as numerous. These two groups 
together contain + 2Fd@ molecules. If the most probable distribution 
prevailed, these two groups would have exactly the same number 
of molecules and would furnish together a moment 0. 
If we have an event, which may take place in two directions, 
the probability for one direction being p and that for the other ¢ 
(where p +4 =1) and if this event occurs a very great number (n) 
of times, the calculus of probabilities teaches that the chance, that 
of these x events the number which occurs in one direction is 
between np +v and xp + v + dy, is represented by: 
1 ve 
ig MOT 
Uy 1a 
In this C is equal to y/2npg and is called modulus. 
If we apply this to the 2/dmdr molecules, then p=q7 =}. 
The probability that the deviation, which one of the groups shows 
from the most probable value, lies between v and v + dy, is: 
1 v 
e p dy 
PV 
where £ = /F do dr. 
Of the 2d molecules one group has a deviation of + 1, so 
that it amounts to Fdo +v, the other group has a deviation of 
— vy and amounts to Fdw —y. The difference between the two 
groups is then 2 y and the amount they contribute to the moment 
of the volume element is [2 vae:|. 
If we put: 
{2 Van == man | 
in which the brackets indicate that also a corresponding expression 
: Ant 
for the y and < components and for the coefficients of sin 
is meant, then we may represent the probability that the two groups 
in consideration contribute to the moment of the volume element 
an amount, the amplitudes of which lie between 
[mz] and [mor + dingy] 
by 
J 
2 
Mel 
e ye dm 
Vn 
