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stretched out to an extent of several miles, that the convexity becomes conspicuous. It is very perceptible on the ocean when a ship is seen approaching on the horizon; first the masts and sails of the ship are seen, and lastly the hull. In order to catch the first glimpse of vessels at sea, the point of outlook for them is placed high above the water. By this means, the person who looks is able to see over a part of the convexity, and give information of the approach of vessels to those placed below.

which is made. Thus, the weight of a lump of lead is greater than an equal bulk of cork; therefore its specific gravity is greater; and so on with all other substances, when compared together. For the sake of convenience, pure distilled water, at a temperature of 62 degrees, has been established as a standard by which to compare the specific gravity or relative weight of solid and liquid bodies. Every such body is said to be of either a greater or less specific gravity than water, bulk for bulk.

The convexity of the land is not so conspicuous, in We have an example of a difference in the specific consequence of the many risings and fallings in the sur-gravities of liquids, in mercury, water, oil, and spirits. face. It is only in some extensive alluvial plains in Mercury is considerably more dense or heavy than any different parts of the world that the convexity can be of the others; the next in density is water, then oil, perceived in the same manner as at sea. and lastly spirits. If we put a quantity of each of these In forming roads, railways, and canals, it is neces-liquids into a glass vessel, one after the other, in the sary to make allowance for the convexity of the earth's surface. The first thing done in such cases is to survey the land by means of an instrument called a theodolite. One of the varieties of the theodolite is a small telescope fixed on a stand, which must, when looked through, be placed perfectly horizontal, or in a true level. To find a true level, an instrument is fixed below it, called a spirit level, and by that it is regulated.

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A spirit level is in universal request in works of art requiring levelness of foundation or surface. It consists of a cylindrical glass a b tube, as in fig. 10, containing a quantity of spirits of wine sufficient to fill it, except a small part, in which

Fig. 10.

the air is left. The tube being completely closed or
sealed, the small vacancy where the air is left shows an
air-bubble at whatever part of the tube is uppermost.
The tube being set in a small wooden case with a level
bottom, this case is laid upon the block of stone, wood,
or other object to be levelled, and when the air bubble
is seen to rest in the middle of the upper side, it signi-
fies that the object on which the instrument lies is a
true level. In the accompanying figure, the air-bubble
is seen at the middle at b; the slightest unevenness
would cause the bubble to proceed to a at one end, or
c at the other.

A true level being found for the theodolite, the surveyor looks through the glass or telescope towards a pole, the lower end of which rests on the ground, and is held in a perpendicular position by a man at (we shall suppose) the distance of a mile, previously measured. The pole having figures marked upon it, a certain figure on a level with the eye is ascertained; 7 inches and 9-10ths are then reckoned down the pole from the figure, and at that depth we have the natural level from which the surveyor makes his subsequent calculations. If a road were to be made on the plan of preserving a true level, it would proceed in its course at a tangent from the earth's convexity, like the line TL in fig. 9, and, consequently, would reach a point above that to which it was destined to go. It would impossible to make the water in a canal pursue a true level; in the attempt to do so, the water would not remain at rest in the channel prepared for it, but

would rush towards the lower end.

As most countries are less or more irregular in surface, canals are usually constructed with different levels, 80 much of the length being on one level, and so much on another, as the case may be. At every change of level there is a lock, or portion enclosed with gateways, to keep the water at the proper level, and to allow the passage of vessels. The locks of a canal, therefore, are like steps of a stair, one at a greater height than another, and by their means vessels may be made to proceed up

or down hill.

SPECIFIC GRAVITY.

The more dense in substance that a body is, it is the more heavy or weighty, because it contains the more particles to be operated upon by attraction of gravita tion. In reference to the density of bodies, the term specific gravity is employed to denote the comparison

order here mentioned, we shall observe that all keep their respective places, without intermixture, the heaviest at the bottom and the lightest at the top. Should they even be jumbled together in the vessel, it will be noticed that they in time rectify the disturbauce, each assuming its own position.

Sea or salt water, in consequence of being loaded with foreign matter, is of greater density or specific gravity than pure fresh water of the same temperature. If we therefore pour a quantity of salt water into a glass vessel, and then gently place some fresh water above it, we shall observe the same phenomenon, of each kind of liquid retaining its position, the heaviest to the bottom, and the lightest to the top. After being jumbled together, the two liquids will, as far as possible, return to their former relative position.

If we fill a bottle with water, and dip it with the open mouth downwards into a jar or barrel of spirits, the water, in virtue of its density, will be emptied and sink into the spirits, and the spirits will immediately rush up into the empty bottle, and supply the place of the water.

A

C

The force which liquids exert in opposing each other in a state of equilibrium, corresponds to their specific gravities; in other words, a small quantity of a heavy liquid will balance a much greater quantity of a lighter liquid. For example, take a bent glass tube, as in fig. 11, and pour as much water into it as will extend from the bottom at E to A. This quantity of water will be balanced or kept to its summit level at A by a quantity of mercury measuring from E to B, or by a quantity of oil from E to C, or by a quantity of spirits from E to D. Each of these experiments may be performed one after the other. The pressure of liquids being as the vertical height, and not as breadth, it would make no difference in the result of the experiments, if the limb of the tube for the mercury, oil, or spirits, were increased to a foot, a mile, or any other diameter.

E

bd

B

Fig. 11.

Alcohol

Water, at its ordinary temperature of 62 degrees, has a specific gravity of 1000 ounces to the cubic foot. Platinum is 224 times heavier, or 224 times the specific gravity of water; gold is 191, mercury 13, copper 84, iron 8, common stone about 24, and brick 2. is a little more than 8-10ths of the heaviness or specific gravity of water, or 0-815; and oil of almonds is a little more than 9-10ths, or 0-913. Atmospheric air at the earth's surface is 1-800th part, or 000125; in other words, while a cubic foot of water weighs 1000 ounces, a cubic foot of air weighs one ounce and a quarter.

Sea-water generally possesses a specific gravity of 1.035-that is, to 1000 parts of fresh water there are in addition 35 parts of saline substances.* Sea-water being, therefore, 35 parts for every 1000 of water more dense than fresh water, it possesses a proportionally greater power of buoying up bodies. A vessel which will carry 1000 tons on fresh water, will thus carry 1035 tons on the sea.

* This is given only as a general rule. The sea is not uniformly

salt.

FLUID SUPPORT.

The immersion of solid bodies in liquids develops some important principles in hydrostatics.

Any body of greater specific gravity than water, bulk for bulk, will sink on being thrown into water; but a body will float if its specific gravity be less than that of water.

The mode of stating the law in reference to the immersion and floating of solid bodies in any kind of fluids, is as follows:

First.-Any solid body immersed in a fluid displaces exactly its own bulk of fluid, and the force with which the body is buoyed up is equal to the weight of the fluid which is displaced; therefore, the body will sink or swim, according as its own weight is greater or less than the bulk of displaced fluid. This refers to bodies of less density than water.

Second. Any solid body of a greater density than water, when wholly immersed in that fluid, loses exactly as much of its weight as the weight of an equal bulk of the water-that is, of the water which it displaces.

tion to its weight, its displacement of water depends exclusively on its weight, so long as it is not heavier than water. A vessel of cork, wood, or any substance lighter than water, weighing a thousand tons, displaces exactly the same weight of water, or is buoyed up with the same degree of force.

From these circumstances, it appears that the entire weight of any floating body may be calculated by measuring the quantity of water which it displaces.

On immersing a stone or any other solid object in water, it is found to be buoyed up in proportion as its specific gravity is less than that of water. If its specific gravity be greater than water, it will sink to the bottom, and if less, it will swim. As the water of the ocean becomes of greater specific gravity the greater the depth, it may happen that an object which sinks at the top of the water, will remain suspended in equilibrium when it descends to a point at which the specific gravity of the water is equal to its own.

Whatever be the weight of any solid object when weighed in air, its apparent weight is lessened when weighed in water. Thus, a stone may be moved with comparative ease in water, which cannot be lifted withIt is of great importance that these propositions out considerable difficulty on land. The apparent dishould be fully comprehended, for they explain innu- minution of weight in these cases is caused by the supmerable phenomena in nature, in reference to the float-port afforded by the liquid. Attraction of gravitation, ing or swimming of bodies in water or in the atmo- which is the cause of what we call weight, is countersphere. acted more in water than in air, because the water has Water, as has been explained, consists of innumer- a tendency to buoy up the object. The weight of any able small particles, pressing in all directions, or up-object in water is thereby lessened to the extent of the wards as well as downwards. Let us fix our attention weight of a bulk of liquid equal to the size of the object. on a supposed single particle in the mass: while the If the object displace a pound of water, will weigh a liquid is in a condition of repose, we may imagine the pound lighter in water than in air. particle to be sustained between contending forces-the The circumstance of any solid object displacing its force of a column of particles above, and the equally own bulk of liquid, and losing exactly as much of its strong force of particles beneath, pushing to get up-weight as the weight of that bulk of liquid which it disward or away from this column.

A

C

places, has led to the use of the hydrostatic or water Let us now substitute any solid object for the sup- balance, for ascertainposed particle; for example, the quadrangular object ing the intrinsic value AB represented in a vessel of water, of gold and other prefig. 12. This object, supposed to be cious metals. For exof the same density as water, which ample, by knowing in we see is sunk in a buoyant condition the first place how in the water, has displaced a mass of much water a pound of particles, all of which were operated pure gold displaces, and upon in the manner of the supposed then weighing in water, single particle. This object, then, by as in fig. 14, an object taking the place of the mass of particles, has become said to be a pound of subject to the same contending forces, and is conse-gold, we should observe quently floated or sustained to the same extent as they

were.

B

Fig. 12.

If we suppose that the weight of the object is two pounds, liquid to the amount of two pounds is displaced, and the object is pressed upwards with the force of two pounds. Or, to vary the example, suppose that only the lower half beneath the line C is the solid object, and that the space occupied by the upper half is water, the object is still pressed upwards with a force of two pounds; but being one pound weight in itself, and having a pound of water above it, it remains suspended in equilibrium.

These examples refer to bodies which are of the same density or weight as water, bulk for bulk; we shall now take an example of a body specifically lighter than water, by which it will be observed that the buoyancy is governed by the same principle.

A

B

Fig. 13 represents a solid object A B half immersed in a vessel of water. In this, as in all cases in which there is a portion of the object above the water, the weight of that portion is borne by, and therefore conveyed to, the portion which is immersed. Thus, in the example before us, the portion B, though less than a pound weight in itself, by supporting A becomes, we shall say, a pound, and displaces a pound of water; it is therefore buoyed up with the corresponding force of a pound.

Fig. 13.

Whether a body be large or small in bulk, in propor

Fig. 14.

whether it displaced the proper quantity of water; if it displaced more than was proper, then we should be certain that it contained alloy or some inferior substance, being too bulky for a pound of gold. Such weights are used by goldsmiths.

Thus, if a piece of gold weigh 194 ounces in air, it would weigh only 184 ounces in water; the ounce of weight thus counteracted being just the weight of the water that the gold displaces. Therefore the weight of the gold would be to that of the water as 19 ounces to ounce; that is, the specific gravity of gold is 191, if

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water is taken for the standard.

We may cause an object, such as a light hollow ball, or bladder, to displace much more water than what is equal to its own weight; but in doing so, we must press the ball into the water, and that degree of pressure compensates the deficiency of weight in the ball. Thus, extraneous pressure on a floating body, and weight in the body itself, are the same thing as respects buoyancy.

The human body in a state of health, with the lungs full of air, is specifically lighter than water, and more so in the sea than in fresh water. Persons, therefore, on going or falling into water, cannot possibly sink, unless they struggle so as to prevent the liquid from buoying them up. The body will float with a bulk of about half the head above the surface; and thus a person who cannot swim may live and breathe, until chilled or otherwise paralysed, by simply stretching himself on his back, and lying with his face above the water. By throwing the arms out of the water, the body does not

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displace so much liquid; its weight is increased, and it
naturally sinks. Ignorance of these facts in hydrosta-
tics, and want of resolution, cause many deaths by
drowning.

There are various kinds of apparatus for preventing
drowning, called life-preservers. The most common
are those which consist of pieces of cork or other very
light material attached to the upper part of the body.
But air-tight bags are preferable, as they may be said
scarcely to encumber the body when empty, and, as
danger approaches, they can be inflated with ease by
being blown into. Life-boats have large quantities of
cork in their structure, and also air-tight vessels made
of thin metallic plates; so that, even when the boat is
filled with water, a considerable portion of it still floats
above the general surface. The bodies of some animals,
as sea-fowl, and many other species of birds, are con-
siderably lighter than water. The feathers with which
they are covered add very much to their buoyancy.
Quadrupeds swim much easier than men, because the
natural motion of their legs in walking or running is
that which best fits them for swimming. Fishes are
enabled to change their specific gravity by means of an
air-bag with which they are provided. When the air-
bag is distended, they rise to the surface; and when it
is contracted, they descend to the bottom.

The buoyant property of liquids is independent of
their depth or expanse, for if there be only enough of
water to surround an object plunged into it, the object
will float as effectually as if it had been immersed in a
large mass of water. Thus, a few pounds of water may
float an object which is a ton in weight. We account
for these phenomena by the law of pressure in liquids
being as vertical height, not as width of column, and
by a body being buoyed up with a force exactly in pro-
portion to the weight of water which it displaces.
These important truths in hydrostatics teach the
practical lesson, that if canals be made only as deep or
wide as will afford water to surround the vessels placed
upon them, they will be sufficiently large for all pur-
poses of buoyancy and navigation. A ship floats no
better on the face of a sheet of water miles in width,
than it would do on a mill-pond, provided there be
enough of water in the pond to keep it off the bottom.
Every solid body possesses a centre of gravity, which
is the point upon or about which the body balances
itself, and remains in a state of rest, or equilibrium, in
any position.

The equilibrium of floating bodies is regulated in the same manner. The floating body has a centre of gravity, about which the whole mass will balance itself in the liquid; the heaviest side will sink lowest, and the more light will be uppermost.

In reference to floating bodies, there is a point called the centre of buoyancy; this is the centre of gravity of the liquid which is displaced. If the floating body be of the same specific gravity as water, then the centre of buoyancy will be at the same point in the floating body as it would have been in the water; but there is seldom this uniformity, at least not in vessels used for purposes of navigation. It is necessary that all such vessels should be of a less specific gravity than water, in order that a part of their weight may be composed of cargo, stores, passengers, &c., and that they may be sufficiently buoyant.

Heavy materials, called ballast, are usually placed in the bottom of the holds of vessels, to ensure a low centre of gravity. A ship of the largest capacity and burden, with its centre of gravity properly regulated, rests in the water with a stateliness and stability which cannot be destroyed except by some extraordinary violence.

HYDROMETERS.

If a substance be weighed in two fluids, the weights which it loses in each are as the specific gravities of those fluids. Thus, a cubic inch of lead loses 253 grains when weighed in water, and only 209 grains when weighed in rectified spirit; therefore, a cubic inch of

rectified spirit weighs 209 grains, an equal bulk of water weighing 253; and so the specific gravity of water is about a fourth greater than that of the spirit.

The instrument called a hydrometer is constructed upon this principle. Its name is derived from two Greek words, signifying measure of water; but it is of course used for ascertaining the density of all kinds of liquids. There are various kinds of hydrometers. One of them consists of a glass or copper ball with a stem, on which is marked a scale of equal parts or degrees. When immersed in any fluid, the stem sinks to a certain depth, which is indicated by the graduated scale. The length to which it sinks in the standard of comparison being known, we can thus easily ascertain how much it is specifically heavier or lighter than the fluid.

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Much in the same manner is constructed another hydrometer of great delicacy and exactness. It consists of a ball of glass about three inches diameter, with another joined to it, and opening into it, of one inch diameter, bc, fig. 15, and a brass neck d, into which is screwed a wire a e, divided into inches and tenths of an inch, about ten inches long and onefortieth of an inch in diameter. The whole weight of the instrument is 4000 grains when loaded with small weights, such as shot, in the lower ball c. When plunged into water in the jar, this instrument is found to sink an inch if a single grain be laid upon the top a; hence a tenth of a grain sinks it a tenth of an inch. So great is the delicacy of this hydrometer, that the difference in specific gravity of one part in 40,000 can be detected. Its total weight of Fig. 15. 4000 grains is convenient for comparing water; but the quantity of shot in the lower ball can be varied, so as to adapt the instrument to measure the specific gravities of fluids lighter or heavier than the standard of comparison.

There is another very simple hydrometer, which consists of a number of glass beads of different weights, but whose proportions are known, and the beads marked accordingly. These are dropped into the fluid under examination, until one is found which neither sinks to the bottom nor swims upon the surface, but remains at rest wherever it is placed in the liquid; and this bead being numbered, indicates the specific gravity.

In making calculations of the strength and specific gravity of spirits, by the above or any other means, attention must be paid to the degree of temperature of the liquid. Heat expands the liquor, and renders it specifically lighter; all spirits are therefore more bulky, in proportion to their weight, in summer than in winter, and also apparently stronger, not really so.

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HYDRAULICS.

Having detailed the laws and properties of water in a state of rest or equilibrium, we have now to mention some of the more important results of these laws, and also the effects which are produced upon liquids by the application of forces, whether natural or artificial.

WATER A MECHANICAL AGENT.

Water, as already explained in the Laws of Matter and Motion, may be made a useful agent of power, merely by allowing it to act with the force of its own gravity, as in turning a mill; and in this manner it is extensively employed in all civilised countries possessing brooks which are sufficiently rapid in their descent.

But water may be rendered otherwise useful as an agent of force in the arts. Although subtile in substance, and eluding the grasp of those who desire to

Thus, the proportion is estimated between the small bore of the pump and the large bore of the cavity or barrel for the piston. Suppose that the pump has only one thousandth of the area of the barrel, and if a man, by means of its lever handle, press its rod down with a force of five hundred pounds, the piston of the barrel will rise with a force of one thousand times five hundred pounds, or more than two hundred tons. A boy working the pump by a long handle, and taking a sufficiency of time, will raise a pressure of thousands of tons. In the hydraulic press, a force-pump is employed for the sake of convenience; the same end could be attained by a small column of water of a great elevation, on the principle of pressure in liquids being as vertical height.

handle and hold it, it can, without alteration of tem- | press is analogous to that for calculating lever powers. perature, be made to act as a mechanical power, as conveniently and usefully as if it were a solid substance, like iron, stone, or wood. The lever, the screw, the inclined plane, or any of the ordinary mechanical powers, are not more remarkable as instruments of force than water, a single gallon of which may be made to perform what cannot be accomplished (except at enormous cost and labour) by the strongest metal. To render water serviceable as an instrument of force, it must be confined, and an attempt then made to compress it into less than its natural bulk. In making this attempt, the impressed force is freely communicated through the mass, and in the endeavour to avoid compression, the liquid will repel whatever moveable object is presented to it. The force with which water may be squirted from a boy's syringe, gives but a feeble idea of the power of liquids when subjected in a state of confinement to the impression of external force.

The mechanical force of water is exemplified by the hydraulic press. This is an engine employed by papermakers, printers, and manufacturers of various kinds of goods, for the purpose of giving a high degree of pressure or smooth glazed finish to their respective articles. It has generally superseded the screw press, on account of its much greater power, with a less degree of trouble and risk of injury to the mechanism.

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Fig. 16 represents the outline of a hydraulic press. AB is the frame, consisting of four upright pillars supporting a cross top of great strength, and against which the pressure takes place in an upward direction. C, the material to be pressed, is forced upward by D, a round iron piston. This piston is very nicely fitted into an iron case E, which has a cavity F for receiving the water: the neck of the case grasps the piston so tightly that no water can escape. A small pipe G conveys water into the hollow cavity from a forcing-pump H, which stands in a trough of water T. All that part of the apparatus below the base of the pillars is sunk out of sight in the ground. The pump apparatus is here represented as exceedingly simple, but in real machines it is very complex and of great power.

The pump, on being wrought, forces the water into the cavity. There the water, in endeavouring to escape, operates upon the moveable piston, which it causes slowly to rise with its burden. The pressure thus exerted by the liquid almost exceeds belief; unless the case for the water be of enormous strength, it will be rent in an instant as if made of the weakest material. When the weight has been raised to the required height, a stopcock is turned upon the pipe, and the apparatus remains at rest. The opening of the cock allows the water to gush out, and the weight accordingly sinks.

The mode of calculating the power of the hydraulic

AQUEDUCTS-FOUNTAINS.

The tendency in a liquid to find its level, has permitted the construction of apparatus, consisting of pipes and cisterns, for supplying towns with water. No species of hydraulic machine has been of such great use to mankind as this apparatus.

In ancient times, the fact of water rising to an uniform level in every part of its volume, was either not perfectly understood, or there was a deficiency of materials wherewith to construct the apparatus required for carrying water a great distance.

From whatever cause, towns were in these times supplied with water by means of open canals, either cut in the level ground, or supported on the top of arches built for the purpose. These structures, with their elevated channels, were called aqueducts. In Italy, and some other countries in the south of Europe, the remains of stupendous aqueducts, miles in length,

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still exist.

By a knowledge of the laws of fluids, and by possess. ing an abundance of lead and iron, we are enabled in the present day to construct apparatus for supplying towns with water in a manner the most effectual and simple; causing a cheap iron or leaden tube, sunk in the ground, to perform the office of the most expensive and magnificent aqueduct.

The method of supplying towns with water consists in leading a pipe of sufficient diameter from a lake, river, or fountain of fresh and pure water, to the place where the supply is required. The iron pipes used for this purpose are composed of a number of short pieces soldered together, and extending to any length, or in any direction. From these main pipes smaller tubes of lead are led into the houses requiring the supply of water; and by means of these minor tubes, the water may be carried to any point which is not of a higher level than the original fountain affording the supply.

[graphic]

Fig. 17.

Fig. 17 is a representation of the mode of supplying towns with water in this convenient manner. A pipe is observed to proceed from a lake on the top of a hill down into a valley, and thence to supply a house situated on the opposite rising ground. From the pipe, in its passage across the valley, a small tube is carried to supply an ornamental fountain or jet d'eau. The water spouts from this jet d'eau with a force corresponding to the height of the lake above.

In towns not commanding a supply of water from a

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sufficient height, the water is forced by an apparatus
of pumps to an elevated reservoir, and from that the
pipes are laid. When the water is impure, or loaded
with muddy particles, it is usual to purify it by filtra-
tion at the reservoir; it is made to filter or ooze through
a mass of find sand, in which the particles of mud are
deposited.

Springs in the ground are natural hydraulic opera-
tions, and are accounted for on principles connected
with the laws of fluids. One kind of springs is caused
by capillary attraction, or natural attractive force by
which liquids rise in small tubes, porous substances, or
between flat bodies closely laid towards each other.
This species of power is a remarkable variety of the
mutual attraction of matter, and is as unaccountable as
the attraction of gravitation, or the attraction exercised
by the lodestone.

Springs from capillary attraction are believed to be less common and of smaller importance than springs which originate from the obvious cause of water finding its level. The water which falls in the form of rain sinks into the ground in high situations, and finds an outlet at a lower level, though perhaps at a considerable distance. Some springs are also accounted for by a reference to atmospheric action, but these will form a subject of notice under the head Pneumatics.

FRICTION BETWEEN FLUIDS AND SOLIDS.

The flowing of water through pipes, or in natural channels, is liable to be materially affected by friction. Water flows smoothly, and with least retardation from friction, when the channel is perfectly smooth and straight. Every little inequality which is presented to the liquid, helps to retard it, and so likewise does every bend or angle in its path. A smooth leaden pipe will thus convey more water than a wooden pipe of the same capacity, Practically, an allowance is made in the magnitude of pipes for the loss of speed by friction. Where the length of the tube is considerable, and there are several bendings, it is not unusual to allow a third of the capacity for retardation.

By increasing the capacity of pipes, a prodigious gain is secured in the transmission of water. The loss from friction on a small tube of an inch diameter of bore is so great, that one of twice the capacity will deliver five times as much water.

The rate at which water flows from an orifice in a reservoir, or containing vessel, is affected by the situation and the shape of the orifice.

The most favourable situation for the orifice is at the bottom of the vessel; but the velocity of the emission is not in the ratio of the height of the liquid, or of a perpendicular column of particles; for as the water presses in all directions alike, there is from all parts of the vessel a general rush as it were to the outlet, thus putting the whole mass in motion.

Although the rush of water at the outlet is not as the ratio of the depth, it depends upon the depth. Thus, if a vessel ten feet high be penetrated at the side on a level with the bottom, and the water stand at two feet and a half within, it will issue outwards with a certain degree of velocity. If the height of the water be quadrupled, that is, if the vessel be filled, the velocity will be doubled. In order to obtain a threefold velocity, a ninefold depth is necessary; for a fourfold velocity, sixteen times the depth is required, and so on. In fact, in whatever proportion the velocity of efflux is increased, the quantity of liquid discharged in a given time must be also increased in the same proportion; hence the quantity of water discharged conjointly with its degree of velocity will be increased in proportion to the pressure. There is here a striking coincidence between the descent of water and the relation which exists between the height from which a body falls, and the velocity acquired at the end of the fall.

It has been ascertained that water rushes with most advantage from an orifice, when the orifice is in the form of a short round tube inserted into the vessel, and of a length equal to twice its diameter.

It has also been found, that if the pipe, instead of being flush or level with the bottom of the reservoir, entered into it to some distance, it had the effect of making the flow of water even less than that which issued through the simple hole without any pipe. The singular fact of a pipe and hole of the same diameter discharging different quantities of water under different circumstances, whilst the head or pressure remains the same, must be accounted for by cross or opposing currents being created by the rush which all fluids make to the orifice. Currents will thus form from the top and sides of the containing vessel, and by their inertia they will cross each other, and thus impede the descent of the perpendicular column, causing the water which issues to run in a screw-like form; this, however, is in a great measure obviated by the application of a short tube from the aperture. That the projection of the tube too far into the interior of the vessel should make the flow less than if there were no pipe at all, may be thus explained:-The columns which descend from near the outside of the vessel, by turning up again to reach the discharging orifice, come into more direct opposi tion to the motion of the central descending columns, whilst they are at the same time themselves compelled to turn suddenly in opposition to their own inertia, before they can enter the pipe. Thus, the discharge is more effectually impeded than if it were proceeding from a mere opening in the bottom of the vessel.

The tube for the discharge of water should not only be short and round, but also trumpet-mouthed or funnel-shaped, both internally and externally, that being the form which admits the flow of liquid with the least possible retardation.

The effects of friction between liquids and solids are nowhere so conspicuous as in the flowing of rivers. The natural tendency in the water to descend at a certain speed, is limited by the roughness of the bottom, bends in the course of the stream, and small projections on the banks. From these causes, the water in a river flows with different velocities at different parts in any vertical section across the current. It flows at a slower rate of speed at and near the bottom than at the surface, and also slower at the sides than at the middle.

The resistance which a body moving in liquid meets with, when it comes in contact with a solid, is as the square of the velocity of the moving body; in other words, the resistance is not twice but four times with a double rate of speed. This is easily explained :

A vessel moving at the rate of one mile per hour displaces a certain quantity of water, and with a certain velocity; if it move twice as fast, it of course displaces twice as many particles in the same time, and requires to be moved by twice the force on that account; but it also displaces every particle with a double velocity, and requires another doubling of the power on this account; the power thus twice doubled, becomes a power of four. When the body is moved with a speed of three or four, a force of nine or sixteen is wanted, and so on. Thus, the resistance increases as the square of the speed.

This important law suggests practical hints of considerable importance. For instance, in steam navigation, if an engine of fifty horse power impel a vessel at the rate of seven miles an hour, it would require two of the same power to drive her ten miles an hour, and three such to drive her twelve miles an hour. Hence the enormous expense of fuel attending the gaining of a high degree of velocity.

ACTION OF WATER IN RIVERS.

In cases where it is desirable to preserve the banks of rivers from injury, either from the regular action of the current or from floods, the water ought to be allowed a free open channel, with banks of a very gradual descent. The utmost violence of water in a state of motion may be rendered comparatively harmless, by allowing the flood or torrent to expend itself on a sloping or shelving shore. Inattention to this simple fact in hydraulics frequently causes much destruction to pro perty on the banks of rivers.

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