Of these scale-hydrometers we have several different kinds, according as they are to determine different liquids. Among them may be mentioned Beaume's hydrometer, an instrument of constant use in chemistry. In the finer kinds of aërometers the weighted sphere, B, Fig. 56, forms the bulb of a delicate thermometer, the stem of which rises into the cavity, A. This enables us to determine the temperature of the liquid at the same time with its specific gravity.

Nicholson's gavimeter is a hydrometer which enables us to determine the density either of solids or liquids. It is represented by Fig. 57.

CHAPTER XII.

HYDROSTATIC PRESSURES AND FORMATION OF FOUNTAINS.

Fundamental Fact of Hydrostatics-holds also for Gases-Illustrations of Upward Pressure-Determination of Specific Gravities of Liquids on these principles-Theory of Fountains-Cause of Natural Springs-Artesian

Wells.

THE fundamental fact in hydrostatics thus appears to be, that as each atom of a liquid yields to the influence of gravity without being restrained by any cohesive force, all the particles of such a mass must press upon those which are immediately beneath them, and, therefore, the pressure of a liquid must be as its depth.

The same fact has already been recognised for elastic fluids, in speaking of the mechanical properties of the earth's atmosphere, which, for this very reason, and also from the circumstance that it is a highly compressible body, possesses different densities at different heights. The lower regions have to sustain or bear up the weight of all above them; but as we go higher and higher this weight becomes less and less, until at the surface it ceases to exist at all. We have already shown, from the nature of a fluid, such pressures are

propagated equally in all directions, upward and laterally, as well as downward. This important principle deserves, however, a still further illustration from the consequences we have now to draw from it. Let a tube of glass, a b, Fig. 58, have its lower end, b, closed with a valve slightly weighted and opening upward, the end, a, being open. On holding the tube in a vertical position, the valve is kept shut by its own weight. But if we depress it in a vessel of water, as soon as a certain depth is reached the upward pressure of the water forces the valve, and the tube begins to fill. Still further, if before immersing the tube we fill it to the height of a few inches with water, we shall find that it must now be depressed to a greater depth than before, because the downward pressure of the included water tends to keep the valve shut.

Fig. 58.

From the same principles it follows, that whenever a liquid has freedom of motion, it will tend to arrange itself, so that all parts of its surface shall

be equi-distant from the centre of the earth. For this reason the surface of water in basins, and other reservoirs of limited extent, is always in a horizontal plane; but when those surfaces are of greater extent, as in the case of lakes and the sea, they necessarily exhibit a rounded form, conforming to the figure of the earth. It is also to be remembered that, when liquids are included in narrow tubes, the phenomena of capillary attraction disturb both their level and surface-figure.

Fig. 59.

All liquids, therefore, tend to find their own level. This fact is well illustrated by the instrument, Fig. 59, consisting of a cylinder of glass, a, connected by means of a horizontal branch with the tube b, which moves at a tight joint at c. By this joint, b can be set parallel to a, or in any other position. If a is filled with water to a given height, the liquid immediately flows through the horizontal connecting-pipe, and rises to the same height in b that it occupies in a. Nor does it

matter whether b be parallel to a, or set at any inclined position; the liquid spontaneously adjusts itself to an equal altitude.

The same liquid always occupies the same level. But when in the branches of a tube we have liquids, the specific gravities of which are different, then, as

[13

10

has already been stated in Chapter X., they rise to different heights. The law which determines this is, "The heights of different fluids are inversely as their specific gravities.' If, therefore, in one of the branches of a tube, a b, Fig. 60, some quicksilver is poured so as to rise to a height of one inch, it will require in the other tube, bc, a column of water 13 inches long to equilibrate it, because the specific gravities of quicksilver and water are as 13 to 1.

A very neat instrument for illustrating these facts is shown in Fig. 61. It consists of two long glass tubes, a b, which are connected with a small exhausting syringe, c, their lower ends being open dip into the cups w á, in which the liquids whose specific gravities are to be tried, Fig. 60. are placed. Let us suppose they are water and alcohol. The syringe produces the same degree of partial exhaustion in both the tubes, and the two liquids, equally pressed up by the atmospheric air, begin to rise. But it will be found that the alcohol rises much higher than the waterto a height which is inversely proportional to its specific gravity.

When in the instrument, Fig. 59, we bend the tube b upon its joint, so that its end is below the water-level in a, the liquid now begins to spirt out; or if, instead of the jointed tube, we have a shorter tube, C e D, Fig. 62, proceeding from the reservoir A B, the water spouts from its termination and forms a fountain, E F, which rises nearly to the same height as the water-level. The resistance of the air and the descent of the falling drops

Fig. 61.

shorten the altitude to which the jet rises to a certain extent. On the top of the fountain a cork ball, G, may be suspended by the playing water.

A

B

The same instrument may be used to show the equality of the vertical and lateral pressures at any point. For let the tube D E, be removed so as to leave a circular aperture at e; also let C be a plug closing an aperture in the bottom of exactly the same size as e,-now, if the reservoir, A B, be filled to the height g, and kept at that point by continually pouring in water, and the quantities of liquid flowing out through the lateral aperture e, and the vertical one, C, be measured, they will be found precisely the same, showing therefore the equality of the pressures; but if an aperture of the same size were made at f, the quantity would be found correspondingly less.

It is upon these principles that fountains often depend. The water in a reservoir at a distance is brought by pipes to the jet of the fountain, and there suffered to escape. The vertical height to which it can be thrown is as the height of the reservoir, and by having several jets variously arranged in respect of one another, the fountain can be made to give rise to different fanciful forms, as is the case with many public fountains.

Fig. 62. A simple method of exhibiting the fountain is shown in Fig. 63. A jar, G, is filled with water, and a tube, bent as at a bc, is dipped in it. By sucking with the mouth at a, the water may be made to fill the tube, and then, on being left to itself, will play as a fountain.

On similar principles we account for the occurrence of springs, natural fountains, and artesian wells. The strata composing the crust of the earth are, in most cases, in positions inclined to the horizon. They also differ very greatly in permeability to water-sandy and loamy strata readily allowing it to percolate through them, while its passage is more perfectly resisted by tenacious clays. On the side of a hill, the superficial strata of which are pervious, but which rest on an impervious bed below, the rain water penetrates, and being guided along the inclination, bursts out on the sides of the hill or in the valley below, wherever there is a weak Fig. 63. place, as where its vertical pressure has become sufficiently powerful to force a way. This constitutes a common spring. The general principle of the artesian or overflowing wells is illustrated

in Fig. 64. Let b' b c d, be the surface of a region of country the strata of which, b' b, and d, are more or less impervious to water, while the intermediate one, c, of a sandy or porous constitution, allows it a freer passage. When in the distant sandy country, at c, the rain falls, it percolates readily, and is guided by the resisting stratum d. Now if

Fig. 64.

at a a boring is made deep enough to strike into c, or near to d, on the principle which we have been explaining, the water will tend to rise in that boring to its proper hydrostatic level, and therefore, in many instances, will overflow at its mouth. The region of country in which this water originally fell may have been many miles distant.

[London stands in a hollow, of which the first or innermost layer is a basin of clay, placed over chalk, and on boring through the clay (sometimes of 300 feet in thickness) the water issues, and in many places rises considerably above the surface of the ground, showing that there is a higher source or level somewhere.-Dr. Arnott's "Elements of Physics," 3rd edition, page 275.]

It follows, from the action of gravity on liquids, that if we have several which differ in specific gravity in the same vessel, they will arrange them-selves according to their densities. Thus, if into a deep jar we pour quicksilver, solution of sulphate of copper, water, and alcohol, they will arrange themselves in the order in which they have been named.

CHAPTER XIII.

OF FLOWING LIQUIDS AND HYDRAULIC MACHINES.

Laws of the Flowing of Liquids-Determination of the Quantity Discharged-Contracted Vein-Parabolic Jets-Relative Velocity of the parts of Streams Undershot, Overshot, and Breast-Wheels-Common Pump-Forcing-Pump-Vera's Pump-Chain-Pump.

IF a liquid, the particles of which have no cohesion, flows from an aperture in the bottom of its containing vessel, the particles so descending fall to the aperture with a velocity proportional to the height of the liquid.

The force and velocity with which a liquid issues depend, therefore, on the height of its level--the higher the level the greater the velocity.

As the pressures are equal in all directions, and as it is gravity which is the cause of the flow, "The velocity which the particles of a fluid acquire when issuing from an orifice, whether sideways, upward, or downward, is equal to that which they would have acquired in falling perpendicularly from the level of the fluid to that of the orifice."

When a liquid flows from a reservoir which is not replenished, but the level of which continually descends, the velocity is uniformly retarded; so that an unreplenished reservoir empties itself through a given aperture in twice the time which would have been required for the same quantity of water to have flowed through the same aperture, had the level been continually kept up to the same point.

The theoretical law for determining the quantity of water discharged from an orifice, and which is, that "the quantity discharged in each second may be obtained by multiplying the velocity by the area of the aperture," is not found to hold good in practice-a disturbance arising from the adhesion of the particles to one another, from their friction against the aperture, and from the formation of what is designated "the contracted vein." For when water flows through a circular aperture in a plate, the diameter of the

issuing stream is contracted, and reaches its minimum dimensions at a distance about equal to that of half the diameter of the aperture. This effect arises from the circumstance that the flowing water is not alone that which is situated perpendicularly above the orifice, but the lateral portions likewise move. These, therefore, going in oblique directions, make the stream depart from the cylindrical form, and contract it, as has been described.

By attachment of tubes of suitable shapes to the aperture, this effect may be avoided, and the quantity of flowing water greatly increased. A simple aperture and such a tube being compared together, the latter was found to discharge half as much more water in the same space of time.

As the motion of flowing liquids depends on the same laws as that of falling solids, and is determined by gravity, it is obvious that the path of a spouting jet, the direction of which is parallel or oblique to the horizon, will be a parabola; for, as we shall hereafter see, that is the path of a body projected under the influence of gravity in vacuo. When a liquid is suffered to escape in a horizontal direction through the side of a vessel, it may be easily shown to flow in a parabolic path. The maximum distance to which a jet can reach on a horizontal plane is, when the opening is half the height of the liquid.

H

C

E

B

A

[In consequence of the motion of water, or other liquids, being subject to the same laws as falling bodies, it is evident that the velocity and quantity of water discharged at various depths in rivers would be as the square roots of those depths, provided various mechanical causes did not exist to check its force. Let ABCD represent a tank of water, from which a channel, B D F I, slopes considerably. It will be found that the lower part of the water at D has a velocity as the square root of the depth BD; the water at F flows with a velocity proportioned to the square root of the depth E F; and the water at I as the square root G I. The top water at H has only a velocity equal to that of the bottom water at F, because it is the same depth from the line of level ABG; and, therefore, by the same rule, we may arrive at the velocity of any part of the channel.

Fig. 65.

[A very slight declivity suffices to give the running motion to water. Three inches per mile, in a smooth, straight channel, gives a velocity of about three miles per hour. The Ganges, which gathers the waters of the Himalaya mountains, the loftiest in the world, at 1,800 miles from its mouth, is only 800 feet above the level of the sea-that is, about twice the height of St. Paul's church in London; and to fall these 800 feet in its long course, the water requires more than a month. The great river Magdalena, in South America, running for 1,000 miles between two ridges of the Andes, falls only 500 feet in all that distance. Above the commencement of the thousand miles, it is seen descending in rapids and cataracts from the mountains.-Dr. Arnott's "Elements of Physics," page 260.]

To measure the velocity of flowing water, floating bodies are used: they drift, immersed in the stream under examination. A bottle partly filled,