HYDROSTATICS.
1 6
their primary particles. There is nothing more different in ac-curacy and truth, than that apprehension which is adequate to thepurposes of human life, and that which ought to satisfy the investi-gation of a philosopher. Thus there is nothing more obvious tocommon observers, than fluidity, yet the philosopher tinds it a pro-perty difficult to be conceived, and which he could not give cre-dit to, if it were not rendered familiar to him try custom and ex-perience. It is a physical phenomenon which has not yet beenexplained, and of which it is very difficult to give a clear account.It is, indeed, impossible to comprehend, how a material and in-compressible substance can be composed of parts so elementary,so moveable among themselves, and yet with so little adherence,as to assume immediately the form of any vessel into which it ispoured; that its surface is always parallel to the horizon, or per-fectly level ; that, in syphons, or when agitated by the wind, itmakes isochrone vibrations, or undulations like a pendulum; thatit runs off where favoured by the smallest descent; &c. ?:r. Yetall these facts, being common and familiar, occasion no surpriseto-nrunkind in general. However, the cause of fluidity appears tobe heat, or caloric, acting in some way or other on the componentparts of fluids, probably by a repulsive force, by means'of whichthe cohesion is destroyed. See Physics. Although no one findsany difficulty in allowing that water and other fluids are reallyponderous, and do actually gravitate when considered as a wholebody, being convinced by their own senses, that a vessel weighsless when empty, than when it is filled with any fluid, and weighsheavier the more it contains ; yet, in the early times of philoso-phy, there were persons who believed lluids did not gravitate inproprio loco, as they termed it; that is, when immersed in theSame, or a different fluid. A simple experiment will shew that theywere mistaken, and that fluids lose nothing in their weight in pro-prio loco. r I ake a glass-vessel or bottle furnished with a hrass-♦itop-eock, and made so heavy as to sink in water. Exhaust it ofits air, and then shut the cock. Suspend it now from the end ofa balance, so that the bottle and the stop-cock may lie under tlu-eurface of the water, and then counterpoise it by a weight in theopposite scale. If we now open the cock, the water will run intothe bottle, which then will preponderate, and hoar down the beamon which it hangs; clearly proving, that the parts of water retaintheir gravity in water, sons to press and bear down upon the partsbeneath them, otherwise the phial would not become heavier uponthe admission of the water ; and it will appear that the vessel over-balances the counterpoise, as much as the weight of the quantityof water in the vessel. To facilitate the explanation of hydrosta-tic phenomena, it has been usual for the writers on this subject toconsider the fluid in a vessel as cut into several horizontal planes,or imaginary surfaces, and to consist of a vast number of small,equal, lubricous, spherical globules. See fig. 1, Plate X.CIH.And though we are ignorant of the true figure of the constituentparticles, yet, because we know that they easily glide one amonganother, this supposition will not affect the argument, being onlymade by way of illustration. A 11 C D may represent a vesselconsisting of such globules. Besides this imaginary horizontal di-vision of a lluid, they often consider it as divided into perpendicu-lar columns, from the top to the bottom of the fluid, as at figs. 1,2.Though fluids are subject to the laws of gravity as well as solids,vet their fluidity occasions some peculiarities necessary (o be no-ticed. The parts of a solid are so connected together as to formbut one whole ; their effort is as it were concentrated in a simplepoint, called the centre of gravity. 'Phis is not the case with•fluids; tlie particles here are all independent oi each oilier, areextremely moveable, yielding to the least effort that tends to se-parate the one from tfie othi-r. 'Die parts of a lluid gravitate in-dependently of each other, and this is a natural consequence oftheir fluidity, or their not adhering together; whereas the particlesof a solid cohere together, and gravitate as one mass.
Prop. I. Any particle of a fluid, at rest in any vessel, pressesequally in every direction. For if an aperture be made in thevessel on any side, the fluid will run out, and that in whatever di-rection the aperture he made, whether horizontally, as at G, fig.
or perpendicularly, as at B, anti the same would take place, ifthe aperture proceeded by means of a tube from any point withinUie vessel; lienee there is a pressure on every particle of the fluid,ami on every side of it ; and since the fluid is at rest, tlie pressureLs equal on every side ; otherwise motion would ensue, (def. of afluid) hence Uftn each particle by its re-action presses equally in
every direction. Hence, if tubes, open at botii ends, and bent inany direction, be immersed in water, it will rise to the same heightin each, which is an ocular demonstration of the proposition.
Prop. 2. The surface of a fluid at rest, which is contained inan open vessel, and free from all external impediments, will belevel, or parallel to the horizon. For let the surface EB, fig. 3.not be horizontal, then the particle a is pressed perpendicularlydownward by its own weight, as is every other particle ; it is alsopressed by means of the particles above it, on the side towardsBF, and lias not a counterbalancing pressure on tiie other side,since the particle b is - lower than it, and is pressed downward bygravity; therefore, when the surface is not horizontal, the fluidwill be in motion, and therefore when it is at rest, the surfacewill be horizontal.
Prop. 3. The pressure on any part of an uniform fluid will heas the perpendicular distance from its surface. For, let ABC D,tig. 1, be a vessel filled with such a fluid. Then, since the pres-sure is occasioned by the gravity of the incumbent particles, thepressure on any particles, as s and r, will be as the number ofparticles lying upon them, that is, since tiie fluid is uniform, as theperpendicular distances from the surface, 3 s and 3 r. The samewill hold good if the sides of the vessel, be not perpendicular tothe horizon ; for tiie pressure on s, fig.4, is as AS, or its equal m n <ami since tiie pressure is entirely caused by gravity, the particleswill not he afflicted by it in tiie direction Sn, and "tiie pressure ona particle at n will be the same as that on s ; hence tiie pressureon r will be as m n -j- nr ; that is, m r, tiie perpendicular distancefrom the surface.
Cor. Hence all the parts of a fluid, at equal distances from thesurface, produce every where an equal pressure. This also ap-pears from experiment; for if the fluid he made to spout perpen-dicularly, as through B m, fig. 5, it will rise nearly to tiie level oftiie surface of tiie fluid in the vessel, tiie small difference beinf}occasioned by the resistance of the air.
Prop. 4. if a column of a fluid extend from the bottom of lh®vessel containing it to the surface of the fluid, its pressure on thebase of the column will be equal to tiie weight of tiie column.For let a 3, fig. 1, he a column extending to the surface AB, andhaving an indefinitely small base; then tiie pressure of the highestparticle is that of its own weight; also tiie pressure of the next par-ticle is that of its own weight added to the weight of the iirst; andin like manner it may be shewn that tiie pressure of any particle inthe column is that ot its own weight together with the weight of adthe incumbent particles, and therefore tiie pressure of the columnon a is equal to the weight of the whole column. And since anycolumn may be conceived to be made up of such small column 5the proposition is manifest.
Cor. 1. 'l’lie whole pressure of a fluid downwards, against lh®bottom and sides of a vessel is equal to tlie whole weight! of tl’ efluid, if over every part of tiie bottom and sides a perpendicularcolumn extends to the surface. For the fluid in such a vessc*may be conceived to be made of an indefinite number of small co-lumns mr, ns, oh, fig. 15, and the pressure of each downward’’equal to its weight; hence the whole pressure downwards is eqi’ a *to tiie whole weight.
Cor. 2. Hence tiie whole pressure has the same effect as th®whole gravity, if it had been solid, and therefore the same as if tb cwhole had been concentrated in tiie centre of gravity. .
Cor. 3. Since the effect of ah c, any part G, lig. lfi, of a fl”’..is the same as if it took place at its centre of gravity ; and since it ”kept in equilibrium by tiie remaining part of tiie fluid II, the r®'action of tiie part II must be the same as if it took place at tl’ esame point.
Cor. 4. 'Flip pressure on any surface downward is equal to Jcolumn of the fluid having that surface for its base, and its topcoinciding with (lie plane of the surface of the fluid. This*’ 1 *shewn above when the column extends to the surface of the flu' £ ‘Jthus the pressure downward on Gil, lig. 21, is equal to theot the column GIljw, F.BCD being tiie vessel; but the press’’^'on Gil is the same if AC be tin: side of the vessel, since its dep 1 ! 1is the same ; hence tiie corollary is manifest.
Cor. 5. The same is true of the pressure on any surface i'P,ward. For since tiie pressure of the fluid on the'surface *-* .downward is exactly sustained by tiie pressure upward, these pr® 5slircs are equal.
i’ROi*. 3. Tin* pressure of a fluid against any surface, in a ditf^