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* In experiments with wire cloth over crest .004 ft. is deducted from observed depth, to compensate for thickness of wire.

Experiments 9 to 43 excluded because of doubt about air in piezometer--gauges subsequently changed.
Experiments 65 to 70 not of interest and omitted (timber on E).
Experiments 79 to 86 not reported by Prof. Williams.--See his letter of Dec. II, p. 4.--Head on model uncertain.
Experiments 44 to 47 not of interest-(Apron carried off by current).

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(See "Lowell Hydraulic Experiments" pp. 252-259 for formula and tables for computing discharge.)

§ Francis' Formula (English Units). Q = (Lo.1 nH) [3.33 (H+ h) — 3.33 h3]

L= length of weir.

H = head on weir.

h = head due velocity of approach. number of end contractions = zero, for these experiments. Trap open. ¶Trap closed.

n

The quantities taken from the curves of Diagram No. 34 were used in constructing a table of the quantities wasting over the actual dam at various depths up to 2.5 feet in height, which was the limit of these experiments. These total quantities at given depths were then again plotted on logarithmic cross section paper and the line of flow produced at the same slope indicated by the experiments up to a height as great as the largest depth ever observed over the dam. This diagram, Figure 35, photo reduced to a smaller scale, is given opposite.

Difference in the degree of roughness of surface of these wide crests was found by the Cornell experiments to make less difference in the discharge of water than might have been expected. Examples of this effect will be found noted on Diagram No. 34. For example, the change from a crest of smoothly planed plank to a crest covered and made rough with wire cloth lessened the discharge 3 per cent. at 0.47 feet depth; 2 per cent. at 0.8 feet depth; 0.8 per cent. at 1.35 feet depth; 1.3 per cent. at 2.1 feet depth.

From personal inspection of smoothness of surface of the stone crests of the dams before and after these Cornell experiments, I was led to adopt a mean between the lines of experiments with the wooden surface and that with the wire cloth over the surface, as fairly representing the actual conditions and for values to be used in our final diagram of discharge over the Croton Dam have adhered to those experiments in which the sloping surface of the model, upstream from the cut stone portion, was roughened with blocks and broken stone.

For the southerly 29.8 feet of angular crest, where obstructed by ledge (including the step), after making a second inspection of the length, position and roughness of the ledge subsequent to the Cornell experiments, I concluded to call the resistance of the ledge, which was actually about 30 feet long, double that found caused on our model E by a more regular obstruction 16 feet long, but used the normal angular crest experiments for the other 40 feet, and of course made due allowance for the decreased depth over the 8-inch step-10.5 feet long--at the southerly end of dam. Possibly this allowance, deducted for effect of ledge, was a little too large. On February 13, 1900, I had the opportunity to inspect this part of the dam while water was flowing over it 3.0 feet in depth, and found sufficient disturbance in the approaching water in the portion above this ledge due to certain wooden steps, direction of approach and other matters, to justify in large

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