FLUIDITY AND TEMPERATURE

149

to obtain a model of viscous flow it is therefore necessary to
assume that the surfaces are not perfectly smooth. In view of the
known discontinuity of matter, one could hardly assume a
smooth surface, and the least degree of roughness which one
could well assume would be one made up of equal spheres
whose centers lie in the same plane and as closely packed
together as possible. That there is a greater degree of roughness
in all ordinary surfaces is probable, but it suffices for our present
purposes to show in what follows that this simple assumption
in regard to the nature of the surfaces gives a workable model of
viscous flow.

It becomes necessary to show that momentum is being con-

FIG. 57.—A diagram illustrating how translational motion becomes changed into
vibrational motion by striking a rough surface.
tinually taken from the surface A and changed into heat. That
the model meets the requirements depends upon the truth of the
following theorem: When a series of elastic particles strike a
rough surface, the resultant component of velocity along the surface
will be diminished. Let M, N, and P in Fig. 57 represent the
section through the centers of three of the greatly magnified
spheres supposed to make up the surface. It is evident that if a
small particle were to strike such a surface at an angle 0, its
possible paths in striking the sphere N would all lie between A and
G. Considering the directions of the particle before and after
collision, assuming that the angle of rebound at any point of
the surface is equal to the angle of incidence, we find that for
possible paths between B and D the average resultant velocity on