large dimensions." (pp. 222, 223, vol. i.) Now it is certain that, all other circumstances being alike, the quantities of water discharged from large are proportionally greater than those discharged from small outlets. Hence the oncia magistrale, as determined by experiments with the former, has a decidedly higher value than when determined by the latter.

The cause of this is clear. To give a discharge of, say, six water-inches, the breadth of the outlet is made six times that for one inch, the height and the pressure remaining in both cases the same. The proportion between the sectional area and perimeter of the outlets becomes, however, materially altered, and the influence of the perimeter in effecting the contraction of the vein diminishes gradually as the size of the outlet increases; and in a similar proportion the discharge becomes greater. To elucidate this, it may be remarked, that in an outlet for one oncia magistrale the ratio of the section to the perimeter is as 1 to 23.33; for two, as 1 to 16.66; for four, as 1 to 13.33; for eight, as 1 to 11.66; for ten, as 1 to 11.33, or about half what is for one oncia; for twenty oncia, as 1 to 10.66, and so on; and there are real differences of discharge due to the variable ratios now given.

Very serious pecuniary loss may consequently be the result to the proprietors of the canal or the consumers of the water. It appears (vol. i., pp. 226, 227) that for summer irrigation each cubic foot per second is capable of irrigating 61.8 acres, and that the annual rent of this quantity, summer and winter, is £13 5s.; the difference of 0.43 cb. ft. between the highest and lowest estimate of the discharge of the modulo magistrale is worth £5 135., and would irrigate 26 acres at the above rate.

The recognition of the differences between the discharges of large and small outlets was very early made in Lombardy. In the module of Cremona, invented in

1561, no single outlet was allowed to exceed 1.31 ft. high by 3.18 ft. broad, equal to about 12 or 13 water-inches. In the Milanese single outlets have been restricted for nearly three centuries and a half to discharges of from 9 to 12 once. In Piedmont they have been more careful, and have there limited single outlets to 6 once, which, by general consent, seems to be the most approved size for diminishing to the utmost the error due to the inequality of discharges from large and small openings. For practical purposes, therefore, and taking the mean of the various estimates of the value of the oncia magistrale just adverted to, it may be considered as equal to very nearly 1 cb. ft. per sec.

107. Another mode of insuring a constant discharge through an orifice having a charge subject to variation has been brought into use by the late Mr. Thom, an hydraulic engineer of great eminence. It attains this

the reservoir is on the right-hand side. If the quantity drawn off by the town or mill to be supplied should increase, then the level of the surface, will descend; and the apparatus must be such that it may permit a larger quantity to pass through the pipe, and vice versa. Again, if the level of, I should remain constant, and, from an increased or diminished rainfall, that of the reservoir rise or fall, then this apparatus should be so constructed as to adjust the orifice of the discharging main pipe that it deliver only that constant quantity carried off from the receiving basin, and needed for the town or millworks.

Fig. 41 gives a longitudinal section of the detail of the regulator: d is a moveable cast-iron cylinder or float attached at top to a chain passing over the pulley or wheel c, and surrounded by a fixed cylinder of a diameter slightly larger, containing water, and represented in section at e. The other end of this chain is fixed to the bent lever b, working freely on a stud carried by two cast iron brackets screwed to the extremity of the pipe passing through the base of the embankment of the reservoir, and terminating in a square mouth-piece, faced to receive a square hinged flap-valve, a, which is retained in any desired position by the lower and shorter arm of the bent lever which works against the back of the valve by an anti-friction roller at v; the inner cylinder d must be loaded with weights sufficient to keep the flap-valve quite closed when the outer cylinder e is empty.

Now if we suppose the water in the outer cylinder e to stand at the level ss, the cast-iron float being immersed to a certain depth below this surface, part only of its weight, acting by the chain upon the bent lever b, will press against the square flap-valve and thus partially open the mouth of the main-pipe, restricting the discharge through it to the desired quantity. Suppose, then, that from any

circumstances this discharge should become too small, and therefore the surface 1, I descend, it will then be necessary that the self-acting apparatus should be such as to permit the valve to open, and therefore, also, the castiron float to rise, which it will do if the water-level in the outer cylinder be made to rise; for then the cast-iron float becomes specifically lighter, and presses with a less force upon the valve a, which immediately yields to the pressure of the water issuing through the discharge-pipe, and thus permits a greater quantity to escape.

If, on the other hand, the quantity discharged had been too great, and thus the surface l, I rise, it will be necessary that the cast-iron float descend, and thus press the flap-valve closer upon the square face of the discharge-pipe. This it will do if the water in the outer cylinder be made to fall; for thus the float becomes specifically heavier, and sinks, closing the flap-valve a : so that we have to devise such mechanical arrangements that when the discharge is too small, the water surface in the cylinder e shall rise, and when too great that it shall descend.

This is effected in the following manner :-A small closed cistern, g, is placed at the side of the portico of the entrance door of the building; this is supplied with water by a horizontal pipe, r, in communication with the vertical pipe, h, placed on the discharging main for the escape of air, which would otherwise collect within it, and greatly impede the discharge.

In all cases of discharge of water through pipes, care must be taken that the air which may collect be readily let off.-Vide Buck's Account of the Montgomeryshire Canal Lock; Simms on Public Works in England, p. 8. The pipe, h, must necessarily be carried up the slope of the embankment, and communicate with the air above the level of the highest water in the reservoir. The cis

L

tern, g, is thus kept constantly supplied with water, and a communication is formed by the pipe k between it and the cylinder e. In the vertical part of this pipe are fixed two double-beat valves-described below-whose common spindle is fixed to the float n, placed in the receiving basin 7, 7; now if the surface of the water upon which n rests should rise beyond the proper level, then this float, n, also rises, and, forcing up the spindle, closes up the upper or discharge valve from the cistern, g, and, as the valves are fixed on one spindle, of course simultaneously opens the lower one, so that the water which buoys up the float d, in the cylinder e, begins to flow out, and the consequent depression of the surface s, s, causing d to descend, partially closes the flap-valve, a; and therefore the surface /, / begins to descend, and with it the float n, which necessarily opens the valve which had shut off the water from the cistern g, and it, again receiving a supply, d, rises, and consequently the flapvalve opens, and thus very soon arrives at a position giving nearly perfect equality between the supply and consumption of water.

In cases when the pressure upon a sluice is not great, the float n may be directly connected with the lever which works the sluice. Fig. 42 represents this simple apparatus : a, a is the

transverse section of the conduit, in which the sluice moves vertically, and is connected by an adjustable link with an oscillating beam c, jointed to the top of the short pillar d. The other

extremity of this beam

Fig. 42.

is similarly connected to a hollow wrought-iron float