1325 
the velocity in that direction, so that then #4; — yv,. In con- 
nection with this we may probably put: 
d$ 
en Se en tas) wee en oe (2) 
Not the force, but its time derivative is opposite to the velocity. 
8 ES ALA dx ; 
From the foregoing it follows only that and » are opposite. That 
: . at 
the relation between these two quantities is represented by the simple 
formula (1) with s = constant, cannot yet be derived from it. We 
shall, however, find this confirmed in what follows. 
2. Another consideration, which apparently furnishes an argument 
in favour of the existence of a friction is the following: 
We call w the z-component of the velocity. Every molecule has 
a certain w at any moment, and the amount of it increases by 
wt in the time At. When the distribution of the w’s at first fol- 
lowed Gauss’ probability law, and the w’s are independent of the 
existing w’s, then it is clear that after some interval Gauss’ law of 
probability will again hold, with continually increasing modulus, 
however. It seems, indeed, necessary now to assume a friction which 
reduces the increased average velocity to the initial value, or ex- 
pressed better, which prevents the increase of the average velocity. 
This is, in fact, the way followed by EiNsrei and Hoer in the 
derivation of their formula. 
But yet we shall prove that the conclusion that now a force 
K:—=— pw must act, is erroneous. For this purpose we consider 
the following analogon. In a gas there is a plane z= 0. The mole- 
cules of the gas are subjected to forces directed towards this plane 
according to the law S.—=— fz. According to BoLTZMANN’'s well- 
known formula they will be distributed in space according to the law: 
=r als Wes 
ay 
Oe OR? RI 
in which n- represents the density in a plane z= 2,, 7, that of 
the plane z= 
Now the z-coordinate of every molecule will increase by zAt in 
the time Af. The value of 2 is then independent of z. For in every 
plane z== constant the same distribution of velocity prevails inde- 
pendent of the value of z. This would give rise to an increase of 
the modulus of the distribution of the zs. That this increase fails 
to appear is a consequence of the existence of a im If 
