driven up by calking-irons.  The pipe was laid under the bed of the Big Canon Creek, a large stream when in freshet, where the head below the hydraulic grade line was 760 feet.  Some of the lead joints leaked slightly at first, but this was soon remedied by more careful calking.  No man-holes or escape-gates were used.  The pipe for the larger part of the year is not filled at its upper end; when such is the case, the water at the inlet carries down the pipe a great quantity of air, for which escapes must be provided to prevent a jarring or throbbing, which would soon destroy the pipe.  The escape air-valves used are shown by Fig. 16.  They consist simply of a heavy 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};]