HYDROSTATICS.

BOOK III.

SECTION I.

On the pressure of Fluids.

451. Defs. HYDROSTATICS is that branch of mechanics which treats of the pressure and equilibrium of fluids.

452. A fluid is a body whose parts easily yield to any force impressed on them, and that move freely among themselves as water, air, mercury, fire, &c. Principia, pa. 64. vol. 2.

Fluids are divided into two classes, compressible and incompressible, or elastic and non-elastic: this distinction is, however, strictly speaking inaccurate; for since all bodies are porous, their constituent parts may be brought nearer to each other, and as every fluid is an assemblage of solid bodies, it must be compressible.

The different kinds of air, vapours, &c. are called compres.. sible, or elastic; and water, wine, mercury, &c. incompressible, or non-elastic fluids. Mr. Canton has proved, in the Philoso phical Transactions for the years 1762 and 1764, that water is compressible: however its compressibility is so exceeding small that it may be, without much impropriety, still ranked among non-elastic fluids.

Some fluids have a very sensible degree of tenacity, and are called viscous, or imperfect fluids. Water and mercury are classed among the most perfect fluids.

Fluidity, according to the Newtonian system, arises from a want of any sensible cohesion between the constituent particles of the fluid. But so little is at present known concerning the essential nature and constitution of fluids, that, rather than bewilder the student with inadequate hypotheses, we shall proceed to those subjects which are better known, and which are more immediately connected with what is useful in practical mechanics.

PROPOSITION CVI.

453. Fluids gravitate, that is have weight, in their own element, or, as it is sometimes expressed, in proprio loco.

For, otherwise, the same fluid or substance being increased in magnitude would not be increased in weight; which is absurd. Let a quantity of fluid whose weight is W, be put into a vessel which contains a quantity of fluid, either of the same or of another kind, whose weight is w, and it is obvious that the weight of the whole is W+w.

Some persons, having found that a bucket of water in water weighed nothing, (or possessed no relative gravity, concluded that there was no absolute gravity of any particle of water anchite at remained in water; but, this mistake is easily corrected by the following experiment.

Put some shot into a bottle, só as to make it sink in water, and, when close corked and totally immersed, let it be hung to one end of a nice balance, and while thus hanging, let it be counterpoised very exactly by weights in the opposite scale, then, pulling out the cork, the water will rush into the bottle and destroy the equilibrium, and cause that end of the beam to which the bottle is appended, to descend: which plainly proves that water has weight in water.

Again, if by adding more weights to those in the scales, the equilibrium be once more restored; take the bottle out of the water in the vessel, and let the water in the bottle be poured out and weighed, and its weight will be found to be exactly equal to the weights made use of to procure the latter equili briumh; which shows that water, and all other fluids, weigh The same in their own elements as out of it.

PROPOSITION CVII.

454. The pressure of fluids is exerted equally in all directions.

Experiments prove that fluids are discharged from a vessel with the same velocity, at the same depth, whether they spout upwards, downwards, horizontally, or in any other direction.

But equal forces, or pressures, produce equal velocities; therefore, the proposition is evident.

Or, if any fluid be put into a vessel, and glass tubes either straight or bended in any angle, be put into it; the fluid will rise in all the tubes, to the height of the surface of the fluid in the vessel.

This is one of the most remarkable properties of fluids, and can be conceived to arise only from the perfect freedom with which the particles move among themselves; which is probably owing to the particles of the fluid being kept at a certain distance by a repulsive power inherent in there. This

also points out one remarkable difference between fluids and solids; for while fluids press equally in all directions, solids press only downwards, or in the direction of gravity.

455.

PROPOSITION CVIII.

Supposing the earth's surface to be a plane, the surface of every stagnant fluid is horizontal.

For, since fluids press equally in all directions, if any part of the surface were higher than another, the pressure in that place would be greater, and of course motion would ensue ; but, by hypothesis, the fluid is at rest; therefore, the surface must be horizontal.

456. Cor. 1. If there be two immiscible fluids in the same vessel, their surfaces will both of them be parallel to the horizon.

457. Cor. 2. As the particles of fluids gravitate towards the earth's centre, the surface of a fluid will in reality be spherical;-hence, the surface of the sea is nearly spherical ; but when the extent of surface is small, as in lakes, ponds, &c. the surface differs insensibly from a plane.

PROPOSITION CIX.

458. Fluids of the same density, press upon equal bases with forces which are as their perpendicular altitudes, whatever their quantities may be, or the shape of the containing vessels.

When the sides of the vessels are straight, and perpendicular to the horizon, the pressures upon the same bases must evidently be as the altitudes of the vessels.

Thus, let ACFE (fig. 153.) be the section of a vessel filled with a fluid, then it is plain that the pressure upon the whole base CF, is as CFX AC; but because the contained fluid is at rest, any portion of it as CDab, or CDno, may be taken, and