also give this mean with more accuracy and convenience than any
instrument of its class; this instrument is new. Measurement of the
velocity at five eighths depth would also afford a fair approximation.

One hundred and fourteen average transverse velocity curves were
prepared from 714 separate curves. These average curves were all very
flat, and were convex down stream--over a level or concave bed--and
nearly symmetric in a symmetric section. The velocity was greatest near
the center, or deepest channel, decreased very slowly at first toward
both banks, more rapidly with approach to the banks or with shallowing
of the depth, very rapidly close to the banks, and was very small at the
edges, possibly zero. The figure of the curve was found to be determined
by the figure of the bed, a convexity in the bed producing a concavity
in the curve and _vice versa_, and more markedly in shallow than in deep
water. Curves on the same transversal, at the same site, and with
similar conditions, but differing in general velocity, were nearly
parallel projections. At the edges there was a strong transverse surface
flow from the edge toward mid-channel, decreasing rapidly with distance
from the edge. The discussion showed that it was almost hopeless to seek
the geometric figure of the curves from mere experiment.

Five hundred and eighty-one cubic discharges were measured under very
varied conditions. The process adopted contained three steps: (1)
Sounding along about fifteen float courses, scattered across the site in
eight cross sections; time, say four hours. (2) Measurement of the mean
velocities through the full depths in those float courses, each thrice
repeated; time, say four hours. (3) Computation, say two hours. This
process was direct and wholly experimental; each step was done in a time
which gave some chance of a constant state of water. From an extended
comparison of all results under similar conditions, it appeared that the