FLUIDITY AND PLASTICITY
cation, "so far agree with the results of previous investigators as
to show the want of any regularity." He perceived that this
difficulty was due to irregularity in the supply of lubricant, so
he conducted experiments in an oil bath. Not only was he thus
able to obtain a high degree of regularity but he proved that the
journal and bearing are completely and continuously separated
by a film of oil. This film is maintained by the motion of the
journal against a hydrostatic pressure in the oil, which at the crown
of the bearing was shown by actual measurement to be 625 Ib.
per square inch greater than the pressure in the oil bath.
Tower demonstrated that even with an oily pad in contact
with the journal, the results were regular although the results
were different from those with the oil bath. Of lubrication less
than that afforded by the oil pad he says: "The results, generally
speaking, were so uncertain and irregular that they may be sum-
med up in a few words. The friction depends on the quantity
and uniform distribution of the oil, and may be anything between
the oil bath results and seizing, according to the perfection or
imperfection of the lubrication."
These experiments of Tower are indeed a landmark in the
development of the theory of lubrication for they stimulated
various investigators such as Osborne Reynolds, Stokes, and Lord
Rayleigh to apply the fundamental hydrodynamical equations
to the results obtained. And the labors of Reynolds, continued
by Sommerfeld (1904) and Michell (1905), have in fact enabled
us to reach a complete solution of the problem of lubrication in
certain very special cases. The mathematical integrations have
generally proved very difficult.
REYNOLDS' THEORY OF LUBRICATION
The model of viscous flow which we have considered, page 5,
does not give rise to any pressure at right angles to the direction
of flow, hence it is unable to sustain a load permanently and will
not serve for practical lubrication.
Case I. Parallel Surfaces Approaching with Tangential Motion.
Let AB in Fig. 83 represent the section of a surface which is
moving with the uniform velocity U in respect to the bearing
block CD, each being of indefinite length ia the direction perpen-