vy flap valve of cast-iron, with recess for lead filling to give
greater weight set on top the pipe, seating on a vulcanized rubber
cushion, and swinging on a loose hinge. When the pipe is only partly
filled with water, the valves drop down by their own weight, allowing the
air to freely escape; when the water rises above the level of a valve, it
is tightly closed by the resulting pressure. There are fourteen of these
valves, those on the lower end being designed to allow air to freely enter
the pipe in case it should burst in the deeper portion, and thus prevent
any collapse from atmospheric pressure. The valves have answered the
desired purposes most effectually. The pipe was hauled over a road built
to the inlet end, and shot down the mountain side by means of a V-shaped
trough of wood. For the lower end, the joints were hauled up the cliff
side into place by a crab worked by horse-power. On steep inclinations,
the pipe was held firmly in place by wire ropes fastened to iron pins in
the solid rock, as shown by the sketch. The covering of earth and stone
was 1 foot to 2 feet in depth; with steep slopes, the earth was kept from
sliding by rough dry walls, or by cedar plank placed crosswise. The pipe
was laid in 1878; the first year it broke twice, owing to the wretched
quality of the iron; since then, it has given no trouble, and has required
practically no attention. The cost of this work--ditch and flume 4,000
feet, and pipe 4,440 feet--was $23,779.53.

A comparison of the relative values of n, in the formula v = n (r s)^{1/2},
for the foregoing ditch, flume, and pipe will be instructive. The ditch
has a width on the bottom of 3 feet, on the top of 6 feet, with a depth of
3 feet, and an inclination of 20 feet per mile; its sides are rough, being
cut in part through the rock and with sharp curves, although fairly
regular; with a flow of about 1,300 miner's inches (32.8 cubic feet per
second) the ditch runs about full.

Therefore:

6 + 3
a = ----- x 3 = 13.5 ;
2

[TEX: a = \frac{6+3}{2} \times 3 = 13.5;]

a
r = ------------- = 1.41 ;
3.3 + 3 + 3.3

[TEX: r = \frac{a}{3.3 + 3 + 3.3} = 1.41;]

20 1
s = ------ = ----- ;
5280 264

[TEX: s = \frac{20}{5280} = \frac{1}{264};]

Q = 32.8, hence

Q
v = --- = 2.43;
a

[TEX: v = \frac{Q}{a} = 2.43;]

and

/ {1/2} \
n ( in v = n (r s)^ ) = 33.
\