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. XXXIV. DIFFERENT LIQUIDS. 416. 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 it to rise on the left hand G H AB and CD will not be in the same horizontal plane; CD will be higher than AB. We may easily state the relation between the two levels. Let EF be in the same horizontal plane as GH; thus CG represents the height of the oil, and AE the height of the water, above the level of their common boundary GH. It is found that CG is in the same proportion to AE as the specific gravity of water is to the specific gravity of oil. The specific gravity of olive oil is about 9, so that in this case AE is of CG. 9 10 This important result can be fully verified by experiment, but the verification is almost unnecessary because the result is an obvious consequence of principles already established. For the pressure at E is measured by the weight of a column of water of the height EA; and the pressure at G is measured by the weight of a column of oil of the height GC; see Art. 359. And the pressure at G is equal to the pressure at E, by Art. 418. Thus finally the weight of a column of water of the height EA must be equal to the weight of a column of oil on a base of the same size and of the height GC. Then since the weights are equal, the height GC must be to the height EĂ in the same proportion as the specific gravity of water is to the specific gravity of oil. 421. Various illustrations of the principle involved in Art. 417 present themselves. A simple case is the way in which cream is formed by the lighter particles of milk rising to the upper part of the vessel containing it. Again by the application of heat a substance is in general expanded, so that it becomes lighter, bulk for bulk, than it was originally. Let us suppose that heat is applied at the bottom of a vessel of water; then as the lower layer of water gains heat it expands, and so becomes lighter and rises to the surface. The heavier and colder water on the other hand descends, and thus in time the heat is communicated to the whole mass of water. The motion may be easily watched, if the vessel be made of glass, by throwing in some coloured particles of about the same specific gravity as the water: for these are carried up and down by the moving fluid. If, however, the heat is applied at the top of the vessel the water at the top is rendered lighter than the rest and so does not descend; in this case although the heat is ultimately communicated to the whole mass of water, yet it is a much slower process than in the former case. On the contrary if we wish to cool a liquid the lowering of the temperature should be effected at the top; for then the cooler liquid, being heavier than the rest, descends, and other liquid comes to the top to be exposed to the same cooling influence. 422. When heat is continually applied to water it is found that if the water is in an open vessel its heat cannot be raised beyond a certain point. At this point the water becomes changed into vapour called steam. If the heat is applied at the bottom of the vessel the steam is formed there first in the shape of bubbles. Steam is several hundred times lighter than water, bulk for bulk, so that the bubbles rise rapidly to the surface and escape; this is the well-known process called boiling. XXXV. EQUILIBRIUM OF FLOATING BODIES. 423. We have already paid some attention to the equilibrium of floating bodies, but we must now consider the subject more fully. We have shewn that when a solid floats in equilibrium on a liquid the weight of the solid is always equal to the weight of the liquid which it displaces; but as we shall now see something more is requisite to ensure the equilibrium of the solid. 424. Take in the first place a sphere of wood, and depress it very gently in water until it has reached a suitable depth; then it will remain at rest. Next take a solid in the shape of a brick, made of wood, and depress it very gently, keeping the upper face always horizontal; the same result will happen. But take this brick-shaped solid, and put it into the water obliquely, so that it has no |