150 FLUIDITY AND PLASTICITY
rebound is exactly opposite in direction, although diminished in
amount. For paths between A and B a particle would collide
with M on rebounding from N but the component of the velocity
in the direction NP is diminished. Also for paths between D and
E, as well as between F and G, the component of the velocity
in the direction NP will be diminished. Only between E and F
is the component in the direction of the flow greater after collision
than before. But the distance EF becomes zero when 0 = 90°
and it has its maximum value when 8 = 0°, i.e., when the trans-
lational motion is zero. Since all of the paths between A and G
are equally likely, it is clear that for this section at least the
average translational velocity is diminished by collision, irrespec-
tive of the size of the angle or of the velocity of the particle, and
the same would be true even if the particle were of considerable
size. The same must be true a fortiori for sections other than the
one passing through the centers of the spheres, for then there
must, after collision, be a component velocity at right angles
to the plane of the paper and therefore to the direction of flow.
The section would be similar to the one given except that the
circles would not touch, the spaces between them corresponding
to the pores of the surface in which the translational velocity
would quite certainly be changed to disordered motion.
It follows from the above that a fluid in contact with a rough
surface tends to have a translational velocity identical with that
of the surface1. Reverting to our model, the theorem explains
how molecules striking the surface A receive its translational
velocity and how this translational velocity becomes trans-
formed into disordered motion at the surface B. If the motion
of the surface A were suddenly stopped, all of the flow would
cease in a time which, for gases made up of particles whose
velocity is expressed in kilometers per minute, must be quite
inappreciable. • It is to be particularly noted that collisions
between molecules of a gas are unnecessary for this type of viscous
resistance. This type of resistance is caused solely by the diffu-
sion of the molecules and it therefore may be appropriately
referred to as diffusional viscosity.
For the opposite extreme we may take for consideration a
very viscous liquid. The molecular free path is so greatly reduced
1 Cf. Jeans (1904) and Dushman (1921).