above process yielded, under favorable circumstances, results not likely
to differ more than 5 per cent. The sequel showed that in a channel with
variable regimen, a discharge table for a given site must be of at least
double entry, as dependent on the local gauge-reading, and on the
velocity or surface-slope.

Special attention was paid to rapid approximations to mean sectional
velocity. The mean velocity past the central vertical, the central
surface velocity, and Chézy's quasi-velocity--i.e.,

100 x Sqrt (R x S)

where R = the hydraulic mean depth, and S = surface slope--were tried in
detail; thus 100, 76, and 83 average values thereof respectively were
taken from 581, 313, and 363 detail values. The ratios of these three
velocities to the mean velocity were taken out, and compared in detail
with Bazin's and Cutter's coefficients. Other formulæ were contrasted
also in slight detail. Kutter's alone seemed to be of general
applicability; when the surface slope measurement is good, and the
rugosity coefficient known for the site--both doubtful matters--it would
probably give results within 7½ per cent. of error. Improvement in
formulæ could at present be obtained only by increased complexity, and
the tentative research would be excessively laborious. Now the first two
ratios varied far less than the third; thus their use would probably
involve less error than the third, or approximation would be more likely
from direct velocity measurement than from any use of surface slope. The
connection between velocities was probably a closer one than between
velocity and slope; the former being perhaps only a geometric, and the
latter a physical one. The mean velocity past the central vertical was
recommended for use, as not being affected by wind; the reduction