1324 
forces are determined by the mutual position of the molecules, it 
follows that also the forces must be independent of the velocities, 
and that a formula of the form ® = — py cannot be valid. 
Now it is true that it has appeared that the laws of classical 
mechanics, hence also those of Gisps’s statistical mechanics, are not 
applicable to all processes of nature. But we have nevertheless every 
reason to assume that for the heat’ motion of molecules and of 
suspended particles these laws hold with a sufficient degree of approxi- 
mation, so that it seems to us that the result that the forces acting 
on these particles, are independent of the velocities in case of sta- 
tistical equilibrium, is beyond doubt. 
Yet at first sight the supposition of friction seems very plausible, 
and there are different considerations which seem to show its vali- 
dity. We shall examine some of these considerations somewhat more 
closely. 
1. In the first place it is clear that a moving particle will more 
probably collide with another particle on its front side (the side 
being foremost in the motion) than on its back side, and that it 
then will be acted upon by a force opposite to the velocity with 
which it arrives. 
But it is just a closer consideration of these collisions that is very 
suitable to give us a good insight into what really happens. Let us 
consider a collision of a molecule against a wall. Before the impact 
the velocity was directed towards the wall. The force at the impact 
is Opposite to this velocity. But if we consider the force in connec: 
tion with the velocity existing simultaneously, we can divide the 
collision into two parts. During the first part the velocity directed 
towards the wall is exhausted. The force is then directed opposite 
to the velocity. During the second part, however, the molecule 
obtains a velocity directed from the wall. Then the velocity obtained 
already and the force have the same direction. On an average the 
product of force and velocity is zero, at least in case of perfectly 
elastic collision. If we finally consider the force at the collision in 
_eonneetion with the vetocity after the collision, we see that force 
and velocity have the same direction. 
For collisions of molecules inter se the same thing holds for the 
mean values as we saw here for collisions of molecules against a wall. 
Summarising we may say that every velocity v has been brought 
about by a force which some time before acted in the direction of 
this velocity, hence e.g. $ _a,/= + q». At the moment itself that the 
velocity v, exists, the force is independent of »,, so on an average 
zero; &, = 0. And after some time a force will act which exhausts 
