1326 
this z did not exist, the gas would really spread uniformly in the 
space, in which 2* would increase. 
Exactly the same thing as we saw for the distribution of the 2’s, 
applies also to that of the w’s. Here too we must assume that the 
ws are independent of the w’s, but that there is a w=— pw, 
which brings about that the distribution of the 7v’s is stationary. If 
Ss 
we write p=, we see that the simple supposition introduced into 
m 
equation (1) is exactly that which warrants a stationary distribution 
of velocity. 
: gi a : GA en 5 
Of course this holds only for the mean force. will consist of 
dt 
two terms, one of which is — sw, and the other can assume all 
kinds of values independently of 1 and 2, equally probably positive 
ones as negative ones. Moreover the same holds in the analogous 
case of the distribution of the 2’s. Besides the z= — Ly other 2’s 
mn 
will exist there too, which are due to the collisions of the molecules 
inter se, and which can assume all kinds of values independent of 
the z’s and 2’s, equally probably positive ones as negative ones. 
In the calenlus of probability it is proved that a quantity will 
be distributed according to Gauss’ law of probability, when its value 
is determined by a great many mutuaily independent causes. We 
now see that in physics, when we consider the many collisions of 
the molecules as the many causes, the existence of these many 
causes is not sufficient to account for the actually existing stationary 
distribution according to the law in question. We must moreover 
assume that the second time derivative of the quantity distributed 
according to Gauss’ law is proportional to that quantity, but of 
opposed sign. 
§ 2. In connection with the above sketched views we shall now 
try to find a formula for the mean deviation of a suspended 
particle. We have not succeeded in finding a derivation of such a 
formula which satisfies high demands of accuracy and certainty. 
We hope to have found a not too inaccurate approximation in the 
following calculation. 
We start from the relation: 
u=—pu+tq Moe SRS eee hes (2) 
multiply both members by df, and integrate with respect to {during 
