128 MEASUREMENT OF FLOWING WATER.
have been compelled to rely for correctness of calculated results on
the application of a combination of a few known laws with experimental
data, which latter, though all-important, have been too restricted for
the deduction of a reliable mathematical theory.
formulas, in terms of dimensions of cross section and slope, are based
upon the supposition of either " permanent " or " uniform " motion.
Permanent motion approaches the condition of streams, permits changes
of cross section and slope of the water-surface, excepting sudden
bends, causing eddies and undulations, but demands that the discharge
from the different sections should be identical. Uniform motion, in
addition, requires an invariable cross section and constant slope of
the fluid-surface. The general formulas based on permanent motion
differ from those restricted to uniform motion, " by taking into
account changes of living force produced by changes of cross section at
the different points." * If there are no variations, the difference
between the formulas disappears.
considered that the resistances encountered by water in uniform motion
were in direct proportion to the length of the wetted perimeter, to the
length of the channel, and to the square of the mean velocity ; from
which he deduced the formula,