HYDROSTATICS treats of the equilibrium of liquids, and of their pressures on the walls of vessels containing them; the science depends on the way in which the molecules of a liquid form a mass under the action of gravity and molecular attraction. the latter of which is so modified in liquids as to give them their state of liquidity. While the particles of a liquid cohere, they are free to slide upon one another witbout time least apparent friction; and it is this perfect mobility that gives them time mechanical properties concidered in hydrostatics.
The fundamental property may be thus stated: WHEN A PRESSURE IS EXERTED ON ANY PART OF THE SURFACE OF A Ligon), THAT PRESSURE IS TRANSMITTED UNDIMIN ISHED TO ALL PARTS OF THE MASS, AND IN ALL DIRECTIONS. Most of the other propositions of hydrostatics are only differentlorms or direct consequences of this truth. This is a physical axiom, but its truth may be experimentally proved. Suppose a close box B filled with water, and having a tube a inserted into the upper cover, of an inch in area, and with a plug or piston fitting into it. If the piston a is now pressed down upon the water with a force equal to a pound-weight, the water, being unable to escape, will react upon the piston with the same force; but it obviously will not press more against a than against any other part of the box, therefore every square inch of the interior surface of the box is pressed outward with the force of a pound. If, then, there is another tube inserted in any part of the box with a plug of the same area, as at b, it will require a force of a pound to keep this plug in its place. (We leave out of account at present the pressure upon b arising from the weight of the water in the box above it, and consider only the pressure propagated by the forcing down of the plug a.) However many plugs of the same size there were, each would be pressed out with the same force of a pound; and if there were a large plug of four times the area, as at e, it would be pressed out with a force' of 4 lbs. We have only, then, to enlarge•the area of the piston c to obtain any multiplication of the force exerted at a. If the area of c is 1000 in., that of a being 1 in., a pressure of 1 lb. on a becomes a pressure of 1000 lbs. on c; and if we make the pressure on a 1 ton, that on c will be 1000 tons. This seemingly wonderful multiplication of power has received the name of the hydrostatic paradox, it is, however, nothing more than what takes place in the lever, when 1 lb. on the long
arm is made to balance 100 lbs. on the short arm.
If the pressure we have supposed exerted on the piston a arose from a pound of water poured into the tube above it, it would continue the same though the piston were removed. The pound of water in the tube is then pressing with its whole weight on every square inch of the inner surface of the box—downwards, sidewise, and upwards. The apparatus called the hydrostatic bellows acts on this principle (see Fig. 2). It consists of two stout circular boards connected together by leather in the manner of a bellows; B. The tube A is connected with the interior; and a person standing on the upper board, and pouring water into the tube; may lift himself up. If the area of the upper board is 1000 times that of the tube, an ounce of water in the tube will support 1000 ounces at W. It is on the sante principle that the hydraulic press (q.v.) depends.
1. Equilibrium of Liquids.—After this explanation of the fundamental properties of liquids, it may be enough to state the two conditions of fluid equilibrium which directly flow from it. (1.) Every molecule of the liquid must be solicited by equal and contrary pressures in every direction. This is a corollary from liquid mobility. (2.) The upper molecules of a liquid, which are free, must form a surface perpendicular to the impressed force. The truth of this will sufficiently appear from the proof that the surface of a liquid at rest under gravity must be what is called horizontal. It can be shown to be a con sequence of the primary property of " pressing equally in all directions." For let da and eb be vertical lines, or lines in the direction of gravity; and ab a plane tit right angles to that direction, or horizontal. A particle of the liquid at a is pressed by the column of particles above it front a to d; and the like is the case at b. Now, since the liquid is at rest, these pressures must be equal; for if the pressure at b, for instance, were greater than at a, there would he a flow of the water from a towards b. It follows that the line ad is equal to be, and hence that de is parallel to ab, and therefore horizontal. The state might be proved of any two points in the surface; therefore the whole is in the same horizontal plane.