Page:The American Cyclopædia (1879) Volume IX.djvu/128

120 HYDROMECHANICS Fio. 11. Cartesian Diver. of it8 weight equal to that of an equal bulk of water is proved by filling the vessel a with water, when the equilibrium of the balance will be restored. It is by means of a similar apparatus that the specific gravities of solids is ascertained (see GRAVITY, SPECIFIC); and upon the principles already laid down hy- drometers, or instruments for ascertaining the specific gravity of liquids, are constructed. (See HYDROMETEK.) It is thus also shown why it is easier to raise weights in water than in air, and why fat persons sustain them- selves in water more easily than those who are lean. The air bladder in fishes is for the purpose of enabling them to rise or descend in the element in which they live. This rise and fall by varying the specific gravity is beautifully illustrated by means of the little toy called the bottle imp or Cartesian diver, fig. 11. A bottle is near- ly filled with water, and a hol- low image of glass or metal and lighter than water, or several little balloons of glass, each of them having an opening below through which water may flow in and out, are introduced into the bottle or jar, which then has its mouth cov- ered with a sheet of caoutchouc, or some elastic membrane. Pressure upon this will compress the air beneath it, and to the same degree the air which is contained in the upper part of the image or the balloons, so that their specific gravity is increased enough to make them sink. Removal of pressure will allow the confined air to resume its former bulk, by which the specific gravity will again become less than that of the water, and they will again ascend. If their surfaces have oblique or spiral directions, and the air is properly distributed, the images may be made to perform various curious evo- lutions. Stability of Floating Bodies. There are certain points to be observed in determining the stability of floating bodies; these are: 1, the centre of gravity of the floating body ; 2, the centre of buoyancy ; and 3, the metacentre. When a body floats upon water it is acted on by two forces : 1, its own weight, acting verti- cally downward through its centre of gravity ; 2, the resultant force produced by the upward pressure of the liquid, which acts through the centre of gravity of the fluid that is displaced, which point is called the centre of buoyancy of the body. It follows, therefore, that these t vro points, the centre of gravity and the centre of buoyancy, must be in the same vertical line for the body to be in a state of equilibrium ; for otherwise the two forces, one acting downward and the other upward, would form a couple which would cause the body to turn. When these two centres are in the same vertical lino, but the centre of gravity is above, the body, except in some cases to be noted presently, is in a state of unstable equilibrium ; but when the centre of gravity is beneath, the body is in a state of stable equilibrium. If a body is floating in a liquid and is entirely immersed, it will not come to a state of stable equilibrium until the centre of gravity is vertically below the centre of buoy- ancy. This is shown in fig. 12, in the case of bodies which are less dense at one end than at the other, where B and B' are the centres of buoy- ancy and G and G' those of gravity. But in many cases, when a body is only partially immersed, the centre of gravity may be above that of buoyancy, and yet the action of turn- ing cannot take place, so that a condition of stable equilibrium will be attained under these circumstances. If a flat body, such as a light wooden plank, is placed in water, it will float, and a portion will be above the surface, as Flo . Fio. 13. FIG. 14. shown in fig. 13 ; and therefore, if the cen- tre of gravity is not below the centre of vol- ume, it will be above the centre of buoyancy, and yet the body will be in a state of stable equilibrium. For if it be tipped as represent- ed in fig. 14, the centre of buoyancy will be brought to the position B', on the depressed side of the vertical passing through the centre of gravity, and this will cause the body to re- turn to its former position. But if the body has such a shape that when it is displaced the centre of buoyancy is brought to that side of the vertical passing through the centre of gravity, which is elevated as represented in fig. 15, then the body will turn over. When the body is in the new position, a vertical drawn through the changed position of the centre of buoyancy will intersect the line which in the first position passed vertically through the cen- tre of gravity, and this point of intersection is called the metacentre, represented at M in figs. 15 and 16. When the metacentre is above the centre of gravity, as in fig. 1 0, the body will tend, by the action of the centre of buoyancy, to return to its former position ; but when it is below, as in fig. 15, the action of the centre of buoyancy, being upward on the elevated side, will tend to turn the body over. Its proper place therefore, as its name would indicate, is above the centre of gravity, but it cannot be a fixed point. In all well built ships, however, its position is pretty nearly constant for all inclinations. For example, in fig. 16, as long as increase of inclination of the vessel carried