HYDROSTATICS. 





balance of upward pressure. This balance or 

 result must be exactly equal to the weight of the 

 conceived isolated body, otherwise it could not 

 keep it at rest. The upward pressure, then, on 

 any separate portion AB, say a cubic foot, within 

 a mass of liquid, is equal to the weight of that 

 portion. This is true, whatever be the shape of 

 the isolated body. If we now suppose the mass 

 of water, AB, to become solid ice without change 

 of bulk, the same pressure will act upon it as 

 before ; and if we further conceive the cubic foot 

 of ice to become a cubic foot of gold, the upward 

 pressure upon it will remain the same namely, 

 the weight of a cubic foot of water, or the weight 

 of the water it displaces. To this extent the water 

 supports it, and renders it lighter. 



It appears, then, that a solid body in a liquid 

 loses as much weight as an equal bulk of the 

 liquid weighs. 



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 still sink. 



It follows that, when two liquids, or, generally, 

 when two fluids (for the principle is true of gases 

 as well as of liquids) of different specific gravity 

 are put together into the same vessel, the lighter 

 will float on the top of the heavier, provided they 

 are of a kind that do not intermix. For if we 

 suppose AB (fig. 1 6) to be a mass of oil sur- 

 rounded by water, being lighter than the same 

 bulk of water, it must rise up ; and as it cannot 

 remain in a heap at the top, it diffuses itself in 

 a horizontal stratum. 



A body of alcohol or spirits in similar circum- 

 stances would take the same position for an 

 instant ; but the attraction existing between 

 alcohol and water, soon causes a mutual and 

 equal diffusion of the one through the other. 



When a solid swims, or rises and floats on the 

 surface of a liquid, the next problem of hydro- 

 statics 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 floating body dis- 

 places its own weight of the liquid. 



By measuring how many cubic feet of water a 

 floating body, such as a ship, displaces, we can 

 thus know its weight, by allowing 1000 ounces, or 

 62*5 Ibs. for every cubic foot. 



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. 

 Sea-water is denser than fresh water, in the pro- 

 portion of 1026 to 1000. A ship, then, that carries 

 1026 tons on the sea, would carry only 1000 tons 

 on a fresh-water lake. 



The human body has almost the same weight 

 as an equal bulk of water. When the lungs are 



full of air, it is slightly lighter, and will float with 

 a bulk of about half the head above water. A 

 person, then, that cannot swim, but has presence 

 of mind to lie flat on the back, with the back part 

 of the head submerged, may, by keeping the lunjjs 

 full, continue to float with the face above water ; 

 but if any other part of the body, as a hand, is 

 raised above the surface, the whole head goes 

 immediately under. Swimmers, by the action of 

 hands and feet against the water, keep the whole 

 head, and often more, above the surface. 



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 most common are those which 

 consist of pieces of cork, or other very light mate- 

 rial, attached to the upper part of the body. But 

 air-tight bags are preferable, as they may be said 

 scarcely to encumber the body when empty, and, 

 as danger approaches, they can be inflated with 

 ease by being blown into. Life-boats have large 

 quantities of cork in their structure, and also air- 

 tight vessels made of thin metallic plates ; so that, 

 even when the boat is filled with water, a con- 

 siderable portion of it still floats above the general 

 surface. The bodies of some animals, as sea-fowl, 

 and many other species of birds, are considerably 

 lighter than water. The feathers with which they 

 are covered add very much to their buoyancy. 

 Fishes are enabled to alter their buoyancy by 

 means of an air-bag, which they can inflate at 

 pleasure by an apparatus for generating gases. 



The buoyant property of liquids is independent 

 of 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. 



Stability of Floating Bodies. Conceive abd 

 (fig. 17) 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 eg, acting on its centre 

 of gravity c ; but that force is balanced by the 



Fig. 17. 



9 

 Fig. 18. 



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 eg, 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 in a liquid, the 

 buoyant pressure is a force equal to the weight of 

 the liquid displaced, and having its point of 



