practical objection against any measure whose outlet is level with the supplying surface arises from the fact that this surface is always changing, not only from the variations in the level of the river supplying the canal, but from the hourly changes in the demand for water from the canal by the various land-owners along its length.

(XVII.) Calculate the discharge which would be given by Nos. 1, 3, 5, and 6, of the above Table,—m being taken equal to 0.62, the foot being 1.6702 feet English, we have × 0.62 × 8.024 = 3.315, and 1 × H≈ 2.789 sq. ft. common to each; and thus

For No. 1, we have 3.315 x 2.789 x 1.6702

Or generally, the discharge varying as 1. H.√H, and 1. H being constant, it is evident that it increases as √H; so that, by increasing the depth indefinitely at the expense of the width /, we increase the discharge. Thus, let H = 16, the log. of 3mlH√2g, that is, of (3.315 × 2.789=) 9.2455 being 0.9659304, we must add to it half the log. of H for the log of the discharge: half the log. of 16 is 0.6020600, and adding, we have 1.5679904 36.982 cb. ft.

=

log. of

102. Questions on 3 ml √2g. (H√H− h√h) = Q, the Italian dimensions being all reduced to English mea

sures.

(XVIII.) Ignazio Michellotti having determined to modify the mode of measuring a ruota introduced by his father, F. D. Michellotti, which had the upper edge level with the surface of the supplying canal, and was estimated to give a discharge equal to 11.83 cb. ft. per sec. defined

the uncia or inch of water to be that flowing through an orifice 0.5567 feet high, 0.41755 ft. wide, and having a pressure on the upper edge of 0.5567 ft. This he supposed would give the twelfth part of 11.832 cb. ft., or 0.986. Calculate its true value: m being 0.600, we have then H = 0.5567 + 0.5567 = 1.1134 feet, and l = 0.41755 feet. Ans. 1.02 cb ft.

(XIX.) The measure used on the Canal Lodi was defined to be 1.12 ft. by 0.12416' ft. wide, with a charge on the upper edge 0.32 ft., and these dimensions were supposed to give 0.77 cb. ft. per sec. Here H = 1.12 +0.32 = 1.44 ft., and /= 0.12416' ft. Ans. 0.6165 cb. ft. per sec.

(xx.) That used on the canal of Cremona was 1.31816' ft. high by 0.131 ft. wide, having a head also 0.131 ft., and estimated to discharge 0.88 cb. ft. Hence

30.6×0.131(1.449√1.449-0.131√0.131) 8.024=0.715 cb.ft.

(XXI.) That of Crema was 1.276 ft. high, 0.1275 ft. wide, a charge of 0.255 ft.: calculate the discharge.

Ans. 0.7225 cb. ft. per sec.

(XXII.) The Sardinian Civil Code determines the unit in which all grants of water should be expressed thus :— "The measure or modulo (Fig. 35) is that quantity of water which, under simple pressure, and with a free fall, issues from a rectangular quadrilateral opening, so placed that two of its sides shall be vertical, having a breadth of 0.6562 ft. (English measure), and a height also of

0.6562 FT

-><----- 0.6562

0.6562

Fig. 35.

1-3124

0.6562 ft. It shall be opened in a thin wall (or plateparete), against which the water stands, with its upper

surface perfectly free, at a constant height of 1.3124 ft. (= 2 x 0.6562) above the lower edge of the outlet." It is required to calculate the value of this unit in cubic feet per second. We have therefore /= 0.6562, and H and h being 1.3124 and 0.6562 respectively—

× 0.6 × 0.6562 (1.3124 √1.3124 -0.6562✓0.6562) 8.024 2.046 cb. ft. per sec.

=

When grants are made for more than one module, the only dimension which varies is the breadth of the outlet, the height and pressure remaining in all cases invariable: two modules would have a breadth of outlet of 1.3124 ft., three would have 1.9686 ft., and so on.

103. Description of a Piedmontese Outlet (“Italian Irrigation," pp. 21, 22, vol. ii.).-" AB (Fig. 36) is a portion of the transverse section of the supplying canal; the first part of the measuring apparatus is the sluice, which

B

D C

Fig. 36.

consists of masonry side-walls, and a gate of wood, working vertically. The dimensions of this primary outlet are not rigidly fixed, its object being merely to admit a larger or smaller supply into the chamber CD. The sluice is established in the bank of the canal, at such point as may be fixed upon by the canal authorities, or most convenient for the land-owner. Its sill is sometimes on the same level as the canal bed, sometimes above it, and very frequently as represented in the diagram.

There is a fall in front of the outlet, so as to draw the water towards it. For a length of from 40 to 50 feet from the sluice, the bed of the channel is made perfectly horizontal, paved with masonry or cut stone, the upper surface of which is on the same level as the sill of the sluice. At a distance from the outlet, ranging from 16 to 32 feet, is fixed the partition or slab of stone cd in which the regulating or measuring outlet ef is cut, the height of which is fixed at 0.56 ft., while the breadth varies with the number of units or inches to be given, each inch being represented by 0.42 ft. of breadth. The lower edge of the measuring outlet is ordinarily placed at 0.819 feet above the level of the flooring of the chamber CD. A small return cut in the inner face of the slab, at a height of 0.28 ft. above the upper edge of the outlet, indicates the constant level of the water necessary to insure the established pressure. This height is maintained by the raising or lowering, as may be requisite, of the sluice at the entrance of the chamber.

(XXIII.) Calculate the value of a grant of three inches of water from this structure. We have H = 0.56 + 0.28 0.84; hence

=

3 × 3 × 0.6 × 0.42 × (0.84 √0.84 – 0.28 ≤0.28) 8.024

= 2.514 cb. ft per sec.

104. Description of the Modulo Magistrale of Milan.— This module, as applied upon the Naviglio Grande, which in a course of 31 miles from its head on the River Ticino to the city of Milan, distributes 1851 cb. ft. per second, is in its principle identical with that already described (§ 103). For the interesting history of this canal, and the gradual improvements in the management of the grants of water, we refer to "Italian Irrigation,” vol. i., pp. 203, 228; vol. ii., pp. 36, 56. The honour of the discovery is due to Soldati, of Milan, about the year 1571,

who invented it in answer to an invitation from the magistracy of that city to architects and engineers to design a measuring apparatus.

The unit fixed upon, called the oncia magistrale, had the following dimensions (Fig. 37):—Height, 0.655 ft.; breadth, 0.3426' ft.; with a constant pressure of 0.32944

When one out

ft. above the upper edge of the outlet. let is designed for the discharge of several water-inches, the breadth only varies, in the proportion of 0.3426' ft. for each additional water-inch, the height and pressure remaining constant, as in Fig 38, which shows an outlet for six water-inches. The outlet is cut with care in a

+7986.0

-0.3426

2.0556.

·655-------0·329.

Fig. 38.

single slab of stone. To preserve it from being tampered with, an iron rim is fixed upon it, of the exact di