Thus the body is in a perpetual state of oscillation up and down; the body in sinking falls a little below its equilibrium position, and in rising ascends a little above it. When a man uses his hands to assist himself in swimming or in floating, his proceeding resembles that of a bird when flying; the reaction of the water for the man, and of the air for the bird, is a force which is perpetually urging the body upwards.

407. The buoyancy afforded by water is obvious to persons wading or bathing. In deep water so much is the weight diminished that the feet are scarcely sensible of any pressure. Stones and rocks may be trodden on without inconvenience, which by their sharpness or roughness would cause great pain to a person walking barefoot on them without the support of the water. In trying to ford a river where there is a current men and animals have sometimes been thrown down by a comparatively slight stream, on account of their small pressure on the ground, and consequently the small sustaining friction. Salt water is denser than fresh water, and therefore it is easier to swim and float in seas than in rivers. A cubic

foot of salt water weighs about 1027 ounces. An experiment is sometimes performed which shews the difference in buoyancy between salt water and fresh water. An egg will sink to the bottom in a vessel of fresh water, and will float in a vessel of salt water. Let fresh water be poured gently on some salt water in a vessel; then a mixture of the two takes place where they are in contact. Put an egg carefully into the upper part; then it will descend, and after a little oscillation it will rest in a position where it displaces liquid in weight equal to its own. position of the egg is one of stable equilibrium; for if the egg be depressed a little it comes into the place of somewhat denser liquid, and is urged up again; and if the egg is elevated a little it comes into the place of somewhat rarer liquid, and is urged down again.

This

408. It is possible to give to a body composed of any material such a form that it will float upon water. Thus a basin composed of metal or china will float with the convex side downwards. In this case the body dis

places as much water as a body of the same shape and weight would do, if instead of being hollow it were completely closed up; at least such is the case if we neglect the insignificant weight of the air which the hollow body holds. A tea-cup may be put into water with its convex part downwards, and it will be observed to float, and it will continue to float if some water be poured into it; by gradually increasing the water we find that before the cup is full it will sink, namely when the weight of the cup and of the contained water is greater than the weight of the water which the whole cup would displace.

409. A ship which is formed of wood might float even if filled with water; for wood in general is lighter bulk for bulk, than water. But some wood is heavier, bulk for bulk, than water; and in all cases, taking into account the metal used in the construction, the whole weight of a ship may be greater than the weight of an equal bulk of water, so that the ship would sink if filled with water. But as long as the water is kept out the ship floats with a part above the surface of the water. Ships can be made of iron, as we know by constant observation; for increased safety they should be divided into water-tight compartments, so that if the water enters one compartment by a leak or any accident, the water displaced by the other compartments may still keep the vessel afloat. The buoyancy of fluids is seen in a remarkable degree in the case of the great ironclads which are now constructed. Notwithstanding the weight of the armour, several inches thick, which covers the sides, and the additional burden of the enormous guns, the vessels float. The fact is that they are of vast size, and so the weight of the displaced water is very considerable.

410. We may weigh a ship by means of the principle that the weight of the ship is equal to the weight of the displaced water. For the form of the ship is in general sufficiently regular to enable us to determine the volume of the displaced water by the aid of rules given for the purpose: see Mensuration, Chapter XXXI. And when we know the volume of the displaced water we can immediately find its weight. A simpler calculation of the same

kind will tell us how much more freight can be put on a ship, when it already floats in a certain position. The area of the plane of flotation means the area of a horizontal section of the ship made at the surface of the water. Now suppose this area is 1000 square feet in the case of a certain ship, and that it is safe to sink the ship an additional foot in the water; then the additional water displaced will be about 1000 cubic feet, and consequently the ship will bear an additional weight equal to that of 1000 cubic feet of water. If this is salt water the weight is about 1027000 ounces, that is 64137 pounds.

411. The use of bladders and corks to enable persons to float is well known. The bladder filled with air is practically of no weight, so that when it is attached to the person and kept below the surface an upward force is obtained equal to the weight of the water which the inflated bladder displaces. In the case of the cork the upward force is equal to the weight of the water displaced diminished by the weight of the cork itself; and the weight of the cork is appreciable, though small.

412. The pontoons used in military operations may be noticed. These are simply water-tight casks which are usually made of metal for greater strength. They are put into a river in sufficient number and connected together; they float, and will continue to do so even when laden with heavy weights, so that they can be used as a temporary bridge for the passage of an army and its artillery. The same principle is applied to life-boats; they have round them a hollow metallic tube which by itself would float, and so when fastened to the boat below the surface of the water it gives buoyancy to the boat.

413. A contrivance called a camel has been used in Holland for enabling ships to pass over a spot in the water which would otherwise be too shallow. Large chests full of water are fastened to the sides of the ships; the water is then removed and the increased buoyancy enables the ship to float over the shallow spot. The water may be removed from the vessels in various ways. Pumps may be employed; or if the vessels have no tops and their upper parts are above the surface, the water may be drawn out in buckets.

414. The principle of floating bodies is used to regulate the supply of liquids to reservoirs or other vessels. For instance, water is admitted to a tank, and it is required to keep the water always at or below a certain level in the tank. For this a ball-tap is the usual contrivance. A hollow ball of metal floats on the surface, and therefore rises as the level of the water rises. This ball can be connected by a wire or a lever with a tap or valve placed at the pipe through which the water enters the tank; and the wire or lever is so adjusted as to close the valve when the water has risen to the prescribed level. A valve is a contrivance much used in machines which are connected with fluids; it is a little door which can open or shut so as to allow passage to a fluid through a pipe in one direction, but not in the contrary direction.

415. The Diving Bell is an instrument which we shall describe hereafter; but the reader perhaps already knows that by means of it work may be done under water. For instance, the contents of a sunken ship may be examined and recovered, and the foundations of buildings may be laid in the sea. The workmen find that their power of moving objects seems to be vastly increased under the water; the weight of most stones is little more than half the weight on dry land, so that a man can move a stone nearly twice as great as the largest he could move on dry land.

416.

XXXIV. DIFFERENT LIQUIDS.

We have hitherto considered only one kind of liquid at a time, but there are various phenomena connected with the presence of two or more liquids in communication.

417. Suppose that oil and water are mixed together in a vessel; it will be found that after a little time has elapsed the water which is the heavier liquid will occupy the lower part, and the oil which is the lighter liquid will occupy the upper part, and that the boundary between the two liquids will be a horizontal plane. It might be possible with great care to get the oil into the lower part of the vessel and the water over it, but the

equilibrium would be unstable; any accidental blow would derange the system, and the water would finally get to the bottom. In a similar manner if water be mixed with mercury the mercury will go to the bottom, and the water to the top. If oil, water, and mercury be mixed together the mercury goes to the bottom, the water takes the middle position, and the oil goes to the top; and the boundary between two different liquids is a horizontal plane.

418. It is easy to see that when we have thus two or more liquids in a vessel some modification must be made in the verbal statement of results obtained in the case of a single liquid. We must not say universally, as in Art. 364, that the pressure is proportional to the depth; though this will be true so long as we take points within the highest layer of liquid. The pressure at any point will be measured by the weight of a column consisting of portions of different liquids, namely, of the liquids which occur between the level of the point and the level of the topmost surface. It will still be true that the pressure is the same at all points in the same horizontal plane; and from this we deduce by reasoning that the boundary between two different liquids is a horizontal plane.

419. We suppose that when different liquids are put together they form what is called a mechanical mixture, and not a chemical combination. The reader may probably know that when two liquids are put together they sometimes form a compound possessing distinct properties of its own, and which cannot be easily separated again into the two liquids from which it arose. An example, though not a very striking one, may be seen in the mixture of wine and water; when such a mixture is made it will not very readily separate itself again like the mixture of oil and water considered in Art. 417.

420. The principle that liquids stand at a level, which was explained in Chapter XXX, must now receive a little limitation when different liquids communicate.

Suppose we have oil and water in different vessels, but still in communication. For example, let there be a bent tube; let water occupy the lower part, and suppose