with water, so that it will sink to its neck, with a small flag projecting answers very well; or the number of revolutions of a wheel accommodated with float-boards may be counted.

In any stream, the velocity is greatest in the middle (where the water is deepest), and at a certain distance from the surface. From this point it diminishes toward the banks. Investigations of this kind are best made by Pictot's streammeasurer, Fig. 66. It consists of a vertical tube, with a trumpet-shaped extremity, bent at a right angle. When plunged in motionless water the level in the tube corresponds with that outside, but the impulse of a stream causes the water to rise in the tube until its vertical pressure counterpoises

the force.

The force of flowing water is often employed for various purposes in the arts. Wehave several different kinds of water-wheels, as the undershot, the overshot, and the breast-wheel. The first of these consists of a wheel or drum revolving upon an axis, and on the periphery there are placed float-boards, a b c d e, &c. It is to be fixed so that its lower floats are immersed in a running stream or tide, and is driven round by the momentum of the current.

Fig. 66.

Fig. 67.

[It is obvious that we may make the diameter of an undershot wheel as great as we please; and that, the greater the diameter, the larger will be the gain of power. But in this, as in all previous instances, what is gained in power is lost in velocity; since a given amount of movement in the water, which would carry a wheel of 12 feet in diameter through a whole revolution, will only carry a wheel of 24 feet through half a revolution.-Dr. Carpenter's Mechanical Philosophy," page 262.]

66

The overshot-wheel, in like manner, consists of a cylinder or drum, with

a series of cells or buckets, so arranged that the water which is delivered by a trough, A B, on the uppermost part of the wheel, may be held by the descending buckets as long as possible. It is the weight of this water that gives motion to the wheel on its axis.

The breast-wheel, in like manner, consists of a drum working on an axis,

and having float-boards on its periphery. It is placed against a wall of a circular form, and the water brought to it fills the buckets at the point A, and turns the wheel, partly by its momentum, and partly by its weight.

[The most advantageous diameter of the breast-wheel will depend, like that of the overshot-wheel, upon the height of the fall. It is obvious that the water does not act equally in moving the wheel during the whole of its descent; for, as the power produced by its weight always acts in lines perpendicular to the earth's surface, its action at A is in the direction A a, and therefore the length of leverage is only Cc. By the time that the wheel

D
a c

E

F

Fig. 70.

has moved round, so that the weight is at B, it will act in the direction B b, and therefore with the lever power Cd; and when it has arrived at D, it will act with the power of the full radius DC. It is obvious that no weight of water at E will have any influence in turning the wheel, since its pressure is in the downward direction, EF; but as soon as it is acting, to the least degree, on one side of this, it will begin to exert a power which continually increases until it reaches D, after which it will diminish in the same proportion.-Dr. Carpenter's "Mechanical Philosophy," page 263.]

a

Fig. 73.

Fig. 71.

Fig. 72.

Of these three forms the overshot-wheel is the most powerful. There are a great many contrivances for the purpose of raising water to a higher level. These constitute the different varieties of pumps.

The common pump is represented in Fig. 71. It consists of three parts: the suction-pipe, the barrel, and the piston. The suction-pipe, a 6, is of sufficient length to reach down to the water, A, proposed to be raised from the reservoir, R. The barrel, C B, is a perfectly cylindrical cavity, in which the piston, P, moves, air-tight, up and down, by the rod, d. It is commonly moved by a lever, but in the figure a rod and handle, DE, are represented. On one side is the spout, S. At the top of the suction-pipe, at O, there is a valve, v, and also one on the piston, at c. They both open upward. When the piston is raised from the bottom of the barrel, and again depressed, it exhausts the air in the suction-pipe, and the water rises from the reservoir, pressed up by the atmosphere. After a few movements of the piston the barrel becomes full of water, which, at each successive lift, is thrown out of the spout, S. The action of this machine is readily understood, after what has been said of the air-pump, which it closely resembles in structure. In the forcing-pump the suction-pipe, e R, is commonly short, and the piston, g, has no valve. On the box at O there is a valve, v, as in the former machine, and when the piston is moved upward in the barrel, C B, by the handle, E, and rod, D d, the water, A, rises from the reservoir, R, and enters the barrel. During the downward movement of the piston the valve, v, shuts, and the water passes by a channel round m, through the lateral pipe, MT M N, into the air-vessel, K K. The entrance to this airvessel, at P, is closed by a valve, a, and there proceeds from it a vertical tube, H G, open at both ends. After a few movements of the piston, the lower end, I, of this tube becomes covered with water, and any further

Fig. 74.

quantity now thrown in compresses the air
in the space, H G, which, exerting its elastic
force, drives out the water in a continuous
jet, S.
The reciprocating motion of the
piston may, therefore, be made to give rise
to a continuous and unintermitting stream
by the aid of the air-vessel, K K.

Among other hydraulic machines may be mentioned Vera's pump, more, however, from its peculiar construction than for any real value it possesses. It consists of a pair of pulleys, over which a rope is made to run rapidly; the lower one is immersed in the water to be raised. By adhesion a portion of the water follows the rope in its movements, and is discharged into a receptacle placed above. (Fig 73.)

The chain-pump consists of a series of flat-plates, d, held together by pieces of metal, so arranged that, by turning an upper wheel, e, the whole chain is made to revolve, on one side ascending and on the other descending and passing over a lower wheel. As the flat plates pass upward they move through a trunk of suitable shape, ab, and therefore continually lift in it a column of water. The chain-pump requires

deep water to work in, and cannot completely empty its reservoir, but it has the advantage of not being liable to be choked.

CHAPTER XIV.

HYDRAULIC MACHINES.

Archimedes' Screw--The Syphon acts by the Pressure of Air-The Descent, Ascent, and Floating of Solids in Liquids--Quantity of Water displaced by a Floating Solid-Case where fluids of different densities are usedEquilibrium of Floating Solids.

THE screw of Archimedes is an ancient contrivance, invented by the philosopher whose name it bears, for the purpose of raising water in Egypt. It consists of a hollow screw-thread wound round an axis, upon which it can be worked by means of a handle. The lower end of this spiral tube dips in the reservoir from which the water is to be raised, and by turning the handle the water continually ascends the spire and flows out at its upper extremity.

E

The syphon is a tube with two branches, CE, DE, Fig. 75, of unequal length, often employed in the arts for the purpose of raising or decanting liquids. The method of using it is first to fill it, and then placing the shorter branch in the vessel, B, to be decanted, the liquid ascends to the bend and runs down the longer branch. It is obvious that this motion arises from the inequality of weight of the columns in the two branches. The long column over-balances the short one, and determines the flow; but this cannot take place without fresh quantities rising through the short branch, impelled by the pressure of the air. The syphon, therefore, is kept full by the pressure of the air, and kept running by the inequality of the lengths of the columns in its branches.

Fig. 75.

This inequality is not to be measured by the actual lengths of the glass branches themselves, but it is to be estimated by the difference of level, A, of the liquid in the vessel to be decanted and the free end, D, of the syphon.

That this instrument acts in consequence of the pressure of the air is shown by making a small one discharge quicksilver under an air-pump receiver. Its action will cease as soon as the air is removed.

By the aid of a syphon liquids of different specific gravities may be drawn out of a reservoir without disturbing one another, and those that are in the lower part without first removing those above. Upon the same principle water may be also conducted in pipes over elevated grounds.

Of the Floating of Bodies in Liquids.

A solid substance will remain motionless in the interior of a liquid mass when it is of the same specific gravity. Under these circumstances the

forces which tend to make it sink are its own weight and the weight of the column of water which is above it. But as its weight is the same as that of an equal volume of the liquid in which it is immersed, this downward tendency is counteracted and precisely equilibrated by the upward pressure of the surrounding liquid. Consequently the solid remains motionless in any position, precisely as a similar mass of the liquid itself would be.

But if the density of the immersed body is greater than that of an equal bulk of the liquid, then the downward forces preponderate over the upward pressure, and the solid descends.

If, on the other hand, the solid is lighter than an equal volume of the liquid, the upward pressure of the surrounding liquid overcomes the downward tendency, and the body rises to the surface and floats.

SPECIFIC GRAVITY.

In the act of floating, the body is divided into two regions: one is immersed in the liquid and the rest is in the air. The part which is immersed under the surface of the liquid is such as displaces a quantity of that liquid as is precisely equal in weight to the floating solid. This may be proved experimentally. Fill a glass, A, with water until B it runs off through the spout, a, then immerse in it a floating body, such as a wooden ball; the ball will displace a quantity of water, which, if it be collected in the receiver, B, and weighed, will be found precisely equal to the weight of the wood. In any fluid, a solid body will therefore sink to a depth which is greater as its specific gravity more nearly approaches that of the liquid. As soon as the two are equal, the solid becomes wholly immersed.

Fig. 76.

In fluids of different densities any floating body sinks deeper in that which has the smallest density. It will be recollected that these are the principles which are involved in the action of hy drometers. They are also applied in the case of specific-gravity bulbs, which are small glass bulbs, with solid handles, adjusted by the maker so as to be of different densities. When a number of these are put into a liquid, some will float and some will sink; but the one which remains suspended, neither floating nor sinking, has the same specific gravity as the liquid. That specific gravity is determined by the mark engraved on the bulb.

When a body floats on the surface of water it tends to take a position of stable equilibrium. The principles brought in operation here will be more fully described when we come to the study of the centre of gravity of bodies. For the present, it is sufficient to state, that stable equilibrium ensues when the centre of gravity of the floating solid is in the same vertical line as the centre of gravity of the portion of fluid displaced, and as respects position beneath it. These considerations are of great importance in the art of ship-building, and also in the right distribution of the cargo or ballast of a ship.

The principle of flotation is ingeniously applied in the ball-cock, an instrument for keeping cisterns or boilers filled with a regulated amount of water.

E