PREFACE
Our knowledge of the flow of electrical energy long ago de-
veloped into the science of Electricity but our knowledge of the
flow of matter has even yet not developed into a coordinate
science. In this respect the outcome of the labors of the hydro-
dynamicians has been disappointing. The names of Newton,
Navier, Poisson, Graham, Maxwell, Stokes and Helmholtz with
a thousand others testify that this field has been well and com-
petently tilled. Even from the first the flow of liquids has been
a subject of practical importance, yet the subject of Hydraulics
has never become more than an empirical subject of interest
merely to the engineer.
Unfortunately the theory is complicated in that the flow of
matter may be hydraulic (turbulent), viscous (linear), or plastic,
dependent upon the conditions. It was in 1842 that viscous
flow was first differentiated from hydraulic flow, and only now
are we coming to realize the important distinction between vis-
cous and plastic deformation. Considering the confusion which
has existed in regard to the character of flow, it is not surprising
that there has been uncertainty in regard to precise methods of
measurement and that exact methods have been discovered, only
to be forgotten, and rediscovered independently later. As a
result, the amount of really trustworthy data in the literature
on the flow of matter under reproducible conditions is limited,
often to an embarrassing extent.
If we are to have a theory of flow in general, we must consider
matter in its three states. No such general theory has appeared,
although one is manifestly needed to give the breath of life to
the dead facts about flow. The author offers the theory given
in the following pages with the utmost trepidation. Although
he has given several years to the pleasant task of supporting its
most important conclusions, a lifetime would be far too short to
complete the work unaided. The author makes no apology for
any lack of finality. Parts of the theory which have already