2. Pressure of Liquids on Surfaces.—The general proposition on this point may be stated thus: The pressure of a liquid on any surface immersed in it, is equal to the weight of a column of the liquid whose base is the solface pressed. and whose height is the perptn dicular depth of the center of gravity of the surface below the surface of the liquid. See article CENTER OF PRESSURE. The pressure thus exerted is independent of the shape or size of the vessel or cavity containing the liquid.
• 3. Buoyancy and Flotation.—As a consequence of the proposition regarding the pressure of liquids on surfaces, it can be shown that when a solid body is immersed in a liquid, it loses as much weight at that of an equal bulk of the liquid weighs. it fol lows that, if a cubic_ foot of the liquid and of the solid have equal weights, the solid will lose all its weight, or will remain in the liquid 'wherever it is put; if a cubic foot of the liquid weigh more than one of the solid, the solid will not only lose all its weight, but will rise up, and that with a force equal to the difference; if a cubic foot of the liquid weigh less than one of the solid, the solid will lose weight, but will sink.
'When a solid swims, or rises and floats on the surface of a liquid, the next problem of hydrostatics is to determine how much of it will be below the surface. We have already seen that any solid in a liquid is pressed upward with a force equal to the weight of the water whose room it occupies. Now, a floating body must be pressed up with a force equal to its own weight, otherwise it would sink lower; hence, a float ing body displaces its own weight of the liquid. A solid, as AB in Fig. 4, sinks until the space occupied by the part B immersed would contain an amount of water equal in weight to the whole solid As the buoyancy of a body thus depends on the relation between its weight and the weight of an equal bulk of the liquid, the same body will be more or less buoyant, according to the density of the liquid in which it is immersed. A piece of wood that sinks a foot in water, will sink barely an inch in mercury. Mercury buoys up even iron. Also a body which would sink of itself, is buoyed up by attaching to it a lighter body; the bulk is thus increased without proportionally increasing the weight. This is the principle of life-preservers of all kinds. The heaviest substances may be made to float by shaping them so as to make them displace more than their own weight of water. A flat plate of iron sinks; the same plate, made concave like a cup or boat, floats. It may be noted that the buoyant property of liquids is independent at their depth or expanse, if there be only enough to surround the object. A few pounds of water might be made to bear up a body of a ton weight; a ship floats as high in a small dock as in the ocean. , 4. Stability of _bloating abd (Fig. 5) to be a portion of a liquid turned solid, but unchanged in bulk; it will evidently remain at rest, as if it were still liquid.
Its weight may be represented by the force cg, act ing on its center of gravity c; but that force is bal anced by the upward pressure of the water on the different parts of the under surface; therefore. the resultant of all these elementary pressures must be a force, cs, exactly equal and opposite to cg, and acting on the same point c, for if it acted on any other point, the body would not be at rest. Now,
whatever other body of the same size and shape we suppose substituted for the mass of solid water abd, the supporting pressure or buoyancy of the water around it must be the same; hence we conclude that when a body is immersed r..t a liquid, the buoyant pressure is a force equal to the weight of the liquid displaced, and having its point of applica tion in the center of gravity of the space from which the liquid is displaced. This point may be called the center of buoyancy.
We may suppose that the space abd is occupied by the immersed part of a floating body aebd (Fig. 5). The supporting force, cb, is still the same as in the former case, and acts at c, the center of gravity of the displaced water; the weight of the body must also be the same; but its point of application is now c', the center of gravity of the whole body. When the body is floating at rest or in a state of equilibrium, this point must evidently be in the same verti cal line with c; for if the two forces were in the position of cs, c'g (Fig. 6), they would tend to make the body roll over. The line passing through the center of gravity of a floating body and the center of gravity of the displaced water, is called the axis of flotation.
The equilibrium of a floating body is said to be stable, when, on suffering a slight displacement, it tends to regain its original position. The conditions of stability will be understood from the accompanying figures. Fig. 7 represents a body floating in equilibrium, G being its center of its center of buoyancy, and A GB the axis of flotation, which is of course vertical. In Fig. 8 the same body is represented as pushed or drawn slightly from the perpendicular.
The shape of the immersed portion being now altered, the center of buoyancy is no longer in the axis of figure, but to one side, as at B.
Now, it is evident that if the line of direction of the upward pressure—that is, a vertical line through B—meets the axis above the center of gravity, as at M, the tendency of the two forces is to bring the axis into its original position, and in that case the equilibrium of the body is stable. But if B_li meet the axis below G, the tendency is to bring the axis further and further front, the vertical, until the body get into some new position of equilibrium. There iS still another case; the line of support or buoyancy may,meet the axis in G, and then the two forces counteract one another, and the body remains in any position in which it is put; this is called indip rent equilibrium. In a floating cylinder of wood, for instance, B is always right under G, in whatever way the cylinder is turned. When the angles through which a floating body is made to roll are small, the point M is nearly constant. It is called the metacenter; and its position may be calculated for a body of given weight and dimen sions. In the construction and lading of ships, it is an object to have the center of gravity as low as possible, in order that it may be always below the metacenter. With this view, heavy materials, in the shape of ballast, are placed in the bottom, and the heaviest portions of the cargo are stowed low in the hold. See SPECIFIC GRAVITY and AllEOKETER.