it to rise on the left hand 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 face parallel to the horizon; let it be depressed very gently until the weight of the displaced water is equal to the weight of the solid, and then be left to itself. The solid most probably will not remain in equilibrium, but will turn over. 425. In order that a solid may be in equilibrium when floating on a liquid two conditions must be satisfied. (1) The weight of the solid must be equal to the weight of the liquid displaced. (2) The centre of gravity of the solid and the centre of gravity of the liquid displaced must be in the same vertical straight line. The first of these two conditions has been already explained. If a solid be wholly or partially immersed in a liquid it is acted on by two forces, its own weight vertically downwards, which may be supposed to act at its centre of gravity, and a force equal to the weight of the displaced liquid vertically upwards, which may be supposed to act at the centre of gravity of the displaced liquid. If these two forces are not equal the solid will move downwards or upwards according as the former or the latter force preponderates. But suppose that the two centres of gravity are not in the same vertical straight line, then even if the two forces are equal they do not keep the solid in equilibrium because they are not directly opposed to each other; they will turn the body round. 426. If a solid composed of materials lighter than water, bulk for bulk, is put into still water we know as an experimental fact that it will at last come to a position of equilibrium. There may be for a time a movement up and down, or a rocking to and fro; but the friction at last stops the motion, and the solid remains at rest. Also even if a body is composed of material which is heavier than water, bulk for bulk, yet by giving to it a hollow form we can in general secure for it a position of equilibrium when put on water. The subject is very important, and is connected with that of the stability and instability of equilibrium noticed in Art. 182. 427. If we suppose the floating solid to be symmetrical in shape, like a sphere, then it is easy to see that the centre of gravity of the floating solid and the centre of gravity of the water displaced do lie in the same vertical straight line whatever may be the depth of immersion; and thus if this depth be suitably taken the solid will remain in equilibrium. The same remark applies to the brick-shaped solid when one face is kept horizontal. In such cases the equilibrium is stable so far as regards any movement up and down. For if the solid is pushed down a little the weight of the water displaced is greater than in the position of equilibrium; and so the upward force preponderates, and the solid rises when left to itself. In like manner if the solid be drawn up a little the weight displaced is less than in the position of equilibrium; and so the downward force predominates, and the solid descends when left to itself. 428. Let us suppose a ship or such like body floating in equilibrium on water. Let it be tilted by the wind or some other force sideways. Let ABC represent a vertical section of the ship, taken at right angles to the length, passing through G, the centre of gravity of the ship, and cutting the keel at B. Let H be the centre of gravity of the water displaced by the ship in its tilted position. Then the ship is acted on by its own weight downwards at G, and by a force vertically upwards at H equal to the weight of the water displaced. If these forces are not equal there will be motion upwards or downwards; but this is of small consequence, because by such motion there is a tendency to promote the required adjustment for equilibrium, as explained at the end of the preceding Article. The important question is as to the direction in T. P. 12 which the ship will turn round. Draw a vertical straight line through H, and let it meet BG produced, if necessary, at M. This point M is called the metacentre, and in books which discuss the theory of the subject it is shewn how the position of this point may be determined when the amount of tilting is very slight; but the process is not sufficiently elementary for our purpose. We may however easily see the importance which attaches to the position of the point M. Suppose M to be, as in the diagram, above G. Then it may be taken as tolerably obvious that the joint effect of the upward force at M and the downward force at G is to turn the ship back again so as to bring BG to be vertical as at first. Thus the original position of the ship is one of stable equilibrium with respect to this tilting. Suppose however that M falls below &; then in the same way we see that the joint effect of the upward force at M and the downward force at G is to turn the ship further away from the position in which BG is vertical. Thus the original position of the ship is one of unstable equilibrium with respect to this tilting. See Art. 345. 429. Hence we see that it is essential for the safety of a ship that the centre of gravity should not be too high up. The proper situation is secured by putting the heavy goods which the ship carries as low in the hold as possible. After a ship has discharged the cargo it is found necessary to put into the hold sand or stones or such things for the sake of bringing down the centre of gravity of the whole as low as possible; these things are called ballast. So also if people go on the water in a small boat they must be careful to remain sitting down so as to keep the centre of gravity low; and especially they should avoid any sudden rising, which may elevate the centre of gravity, and tilt the boat at the same time, 430. We may observe that we have not taken the most general form of the investigation. We have assumed that the body is of the nature of a ship so as to have its two sides symmetrical, and we have supposed that the tilting is from side to side. Under these circumstances G and H remain always in the same vertical plane in which the tilting takes place; otherwise the matter becomes too |