A MODE OF REGULATING THE SUPPLY OF WATER BETWEEN INTERSECTING RIVULETS AND CANALS.

DEVISED BY THE LATE ROBERT ALMOND, Esq.
of Nottingham.

[Communicated by MARSHALL HALL, M.D.,F.R.S.E., &c. &c.]

THE Nottingham and Erewash canals diverge from the same

point, at Langley Mill, in the county of Derby, and are terminated at the distance of a few miles from each other, by the river Trent. In consequence of this relative situation, the Nottingham, which was cut most recently, intersected some of the rivulets which had previously fallen into the Erewash. To compensate for this injury, an eminent mathematician devised the following ingenious plan of delivering from a reservoir of the Nottingham Canal, a given quantity of water per minute, under every variation of the height of water in the reservoir.

The water is brought into a small cistern, of which A (Fig. 1.) represents part of the end. b is an aperture, parallel with the horizon, which would of itself deliver the stipulated quantity when the water in the cistern is at its greatest height. a is a vertical aperture, connected with the former, and is quite closed by the shuttle B, when the cistern is full. Its sides are of that peculiar curvature, that as the shuttle is raised by the action of the buoy C, descending with the surface of the water in the cistern, the additional part of the aperture disclosed exactly compensates for the diminution of pressure. This plan, however, though correct in theory, proved altogether abortive in practice, on account of the excessive friction which is produced, partly by the motion of the shuttle in a groove, and partly by the lateral pressure of that portion of the water which is above the disclosed part of the orifice*.

A dispute afterwards arising respecting the Gilt Brook, which the Erewash Company deemed valuable in the dry summer months, and which had formerly been one of their feeders, they demanded a regular supply of water, according to the average quantity which the brook should be found to deliver in the months of June, July, and August. This quan

* The investigation of the curve proper for the sides of the aperture, is furnished by the inventor in the Gents. Diary for 1799,'

tity proved to be 11.25 cubic feet per minute; but a great difficulty now arose respecting an impartial mode of supply, and this difficulty appeared greater in consequence of the failure of the former plan. At length the dispute was amicably adjusted by the following method, which was invented and carried into execution by Mr. Robert Almond, of Nottingham, then one of the proprietors of the Nottingham Canal.

a

A (Fig. 2.) represents a pipe placed under the haling path of the Nottingham Canal, having the end, which communicates with the canal, turned downwards to prevent stones and dirt from falling into it. Its other extremity is connected with a large cast iron vessel B, in which the water necessarily rises to the level of that in the canal. C is a copper syphon, balanced in such a manner, partly by means of hollow copper sphere, through which it passes, and partly by two weights passing over the wheels, as represented in the drawing, that it rises and falls freely with the water in the canal. By this contrivance, the discharging orifice of the syphon will always be at equal depths below the surface of the water in the canal, and must therefore constantly deliver equal quantities in equal times. D is a stone cistern, into which the water runs, after being discharged from the syphon, and which serves as a gauge, open to the inspection of passengers. On its interior side, a plate of copper is placed perpendicular to the plane of the section, and which is made visible by the stone being cut down to its edge. The water always remains level with this plate, whilst a discharge is taking place from the pipe P.

It must appear to every one versed in hydraulics, that, owing to the friction of the water against the sides of the syphon, its velocity must be retarded, and that the discharging leg must be longer than the theory of emptying vessels would lead us to suppose. This remark is verified by the case before us. The internal diameter of the syphon is 2.45 inches, and the lower orifice is 21.03 inches beneath the level of the canal; but, according to the theory, which supposes that the velocity at the orifice is that acquired by a body falling from rest through a space equal to half the depth of fluid above it, the quantity discharged per 1")2 depth of the lower orifice = area of orifice x 386

12.22, &c., each term being expressed in inches.

It is

therefore advisable, in the construction of such an apparatus, to make the difference of the legs of the syphon double that which the theory requires, and then to reduce the longer to its proper accuracy by absolute experiment.

The above equation is of more use in the construction of the gauge cistern. The depth above the pipe being assumed greater than is wished, the area of the pipe may be calculated, and the stone be afterwards cut down to the level at which the water is observed to remain.

When the apparatus is once regulated, the syphon and weights should preserve an exact balance in every point of ascent and descent; as the accuracy of the discharge depends in a great measure upon that circumstance. If strong catgut, or any light cord, be used to connect the syphon with the weights, the equilibrium may not be sensibly affected by the motion of the syphon. In the present case light chains are used; and, as the wheels are about two feet in diameter, half a revolution, or a variation of three feet in the level of the canal will take the weight of six feet of chain from one side of the axle, and add it to the other. To obviate this inconvenience, one of the wheels has a piece of lead attached to its side, which is narrower at its extremities than at its centre. W (Fig. 3.) represents the wheel thus loaded, and in its situation when the syphon is at its lowest point.

It only remains to observe, that this simple apparatus, which is so easily regulated by a little increase or diminution of the weights, has now been at work for more than fourteen years, without any alteration in its adjustment, and to the perfect satisfaction of all parties. A very intense frost has once or twice suspended its operation, but the succeeding thaw has enabled it to resume its function of a constant arbitrator.

Nottingham, 1826.

R. W. A.

Note. A floating syphon, with wheels and balance weights, is, we believe, fully described in the article Hydrodynamics,' in Brewster's Encyclopædia; but the date of the article is by much posterior to the first erection of the instrument described above, and which has the authority of twenty years constant use.-Editor.

ON THE GEOMETRIC PROPERTIES OF THE MAGNETIC CURVE, WITH AN ACCOUNT OF AN INSTRUMENT FOR ITS MECHANICAL DESCRIPTION.

By P. M. ROGET, M.D., SEC. R.S.

THE properties of the magnetic curve being interesting to the geometrician, as well as important in their connexion with the theory of magnetism, I am induced to offer the following demonstrations of the two fundamental propositions respecting them, derived directly from the law of magnetic forces, as being more simple than any of those given by Professors Robison, Playfair, or Leslie. I have also added an account of a method I have devised for the mechanical description of these curves.

The principal problem relating to the magnetic curves is to find the direction, CT, Fig. 1. of the tangent to the curve

which passes through any given point C, when the situations N and S of the two poles are given. This direction indicates the position which an infinitely small compass needle, placed at C, and at liberty to turn freely round its centre, in a plane passing through N and S, will assume by the action of the magnet N S. This position must be such, that the rotatory forces exerted on both poles of the needle by each pole of the magnet shall exactly balance one another.

The forces themselves, according to the established law of magnetic action, are inversely as the squares of the distances