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perly the portion of loose fire which augments
the gether; whereas the particles of a solid cohere to. volume ofbodies that renders them fluid: their fui: gether, and gravitate as one maks. It is clear from dity is occafioned by a certain quantity of fire, this principle, that if a hole be made in a vessel which then disappears, with regard to any other full of water, the power necessary to prevent the sensible or perceptible effect.
Ruid from running out, must be able to overcome Sect. II. Of the Gravity of the PARTICLES that the weight to be overcome is the same,
the column of the Auid pressing on the hole, and of Fluids, and its Effects on the FLUIDS whether there is only this column of the fluid themselves.
acting on the part stopping the hole, or whetber ALTHOUGH no one finds any difficulty in al- the vessel be füll. lowing that water and other fluids are really pon This will be rendered clearer by an experiment, derous, and do actually gravitate when confider- made with the cylindrical glass veel A B C DÉg. ed as a whole body, being convinced by their s.pl.CLXXXV. which has a hole at bottom. A cy. own senses, that a vessel weighs less when empty, lindrical tube of glass pafter through, and is fitted than when it is filled with any fluid, and weighs to this hole; a small piston, or plug, is 'fitted to heavier the more it contains; yet, in the early this tube; and, being well greased, dides easily times of philofophy, there were persons who be- up and down ; a long wire is fixed to this piftor, lieved fluids did not gravitate in proprio loco, as to be hooked on to one arm of the balance E F. they termed it ; that is, when immersed in the On the upper part of this short tube may be ocfame, or a different fluid. A simple experiment casionally fitted a glass tube, G H, which is ex. will shew that they were mistaken, and that Auids actly of the fame diameter as the brass tube, and lose nothing in their weight in proprio loco. of the same height with the large vessel.
Take a hollow glass ball, such as is represented Having fitted the glass tube in its place, and in Plate CLXXXV. fig. 2. furnished with a brass poured in water up to the mark, put weights into stop.cock, and made fo heavy as to fink in water. the scale, at the opposite arm of the balance, till Exhaust it of its air, and then shut the cock. Ex- the piston just begins to rise; then take away the hausting the air from it, gives room to a quantity glass tube, and fill the large vessel with water to of water equal in bulk to the exhausted air. Sul- the same height, and it will be evident that the pend it now from the end of the balance, so that same weight as before 'overcomes the pressure. the bottle and the stop-cock may be under the sur. Now as the same weight overcomes the pressure, face of the water in the jar, and then counterpoise whether a column of water be only the fize of the it by a weight in the opposite scale. If we now piston, or whether the vessel be full of water, it open the cock, that the water may run into the is clear that particles of water exercise their gravi. bottle, the water will rush in, and the ball will ty independent of each other; but if the mass of preponderate, and bear down the beam on which water contained in the outer vessel was changed it hangs; clearly proving, that the parts of water into ice, to raise the piston we must use a weight retain their gravity in water, so as to press and equal to the weight of the whole column of ice. bear down upon the parts beneath them, other. The SURFACE of a FLUID which is contained wife the phial would not become heavier upon the in an open vessel, and free from all external impe. admission of the water ; and it will appear that diments, will be LEVEL, or parallel to the borithe ball overbalances the counterpoise, as much zon. No part of a fuid can stand higher than as the weight of the quantity of water in the ball. the reft : for, if any part be raised, it muft des
To facilitate the explanation of hydrostatic phe- scend by the force of gravity, and, in so doing, nomena, it has been usual for the writers on this will spread and diffuse itself till it is on a level with subject to consider the fluid in a vessel as cut into the other parts ; for, having gravity, and yielding feveral horizontal planes, or imaginary surfaces, easily to every impression, they obey the force of and to consist of a vast number of small, equal, gravity, and flip down till they come to a level. lubricious, spherical globules. Thus, fig. 3, pl. As the gravity of the particles reduces the upCLXXXV. A B C Dmay represent a vesel confift. per surface to a level, so likewise it occasions a prefing of such globules, a b c d e f, imaginary hori. sure on the lower part, greater or less in propor. zontal surfaces. Besides this imaginary horizontal tion to their depths below the surface, each part division of a fluid, they often conlider it as divided containing a pressure equal to the weight of all into perpendicular columns, from the top to the those that lie above it ; consequently, the parti. bottom of the fluid, as at fig. 4. Though fluids cles which are at equal depths below the surface are subject to the laws of gravity as well as solids, are equally presied. In other words, as the upper yet their Huidity occasions some peculiarities ne furface of the fluid is parallel to the horizon, and cessary to be noticed. The parts of a solid are so as the lower parts sustain the upper, and are preflconnected together as to form but one whole; ed by them, this pressure will be in proportion to their effort is as it were concentrated in a simple the incumbent matter, that is, to tbe height of point, called the centre of gravity. This is not the fluid above the particle that is pressed: but as the case with fluids; the particles here are all in- the upper surface of the Auid is parallel to the hodependent of each other, are extremely moveable, rizon, all the points of any furface that you may yielding to the least effort that tends to separate conceive within the fluid, parallel to the horizon, the one from the other.
are equally pressed. Should this equality of prélThe PARTS of a FLUID GRAVITATE independ- sure be at any time destroyed, and there be a leis ently of each other, and this is a natural conse- pressure on one part of the surface than on the quence of their duidity, or their not adhering to other parts, the Ruid yielding to any impression,
part will be moved, that is, will ascend till the From a cursory view of the subject, fome may preffure becomes equal.
consider it as a kind of mechanical paradox, that the We may confirm this by a simple experiment pressure of a Auid upward, or in a direction conwith a glass tube. Stopping one end with your trary to that of gravity, should benothing more than finger, immerge the other in water. The water a consequence of gravity itself; but it is very easy will rise in the tube; but the tube being full to shew, from mechanical principles, that a force of air, while you keep your finger upon the orifice, acting in a given direction may communicate prefthe rise is but Imall; but if you take away your sure through a number of intermediate bodies, su finger, that the air which compressed may escape, that the last body shall be impelled in any direction the water will rise up into the tube, and not be whatever even in that which is directly contrary at rest till it attains the fame height with the ex. to the original impulse ; and this is the cafe in rem ternal water.
spect of the particles which compofe fluids. SOLIDS make no effort but in the direction of From the foregoing experiments it very clearly gravity, or perpendicularly downwards; but appears, that the PERPENDICULAR PRESSURE of FLUIDS exert a force of pressure EQUAL to their any fluid column, is, from some UNKNOWN connecGRAVITY, in all directions, and in all EQUALLY. tion of the parts, diffused laterally in every direcThis follows from the nature of a fluid, for its tion; and at the same depth, the pressures, estimated particles yield to any impreffion, and are easily in any direction, are equal to each other. What has moved; therefore no drop will remain in its place, been proved of water obtains in all other subkances if, whilft it is pressed by a superincumbent fluid, it that are fluid, and under the influence of gravity. be not equally pressed on all fides; because being sect. I. Of the Action of Pevids againff the a fluid itself, it will yield to every impreffion, and begin to move, unless it be acted upon by equal
BOTTOMS, SIDES, and TOPS, of the VESSELS forces, in all possible directions. But it cannot
which CONTAIN tbem. move, because the surrounding drops resist on all It is evident, that the bottom and fides of a verfidesits motionwith the same force thatitendeavours sel containing a fluid (and the top also, when the to move, and consequently the drop mult remain fluid is raised above it in a tube) are pressed by the at reft; what is thus proved of one drop, holds parts of the fluids which immediately touch them; equally true of all; confequently all the parts of and as action and re-action are equal, these parts all a huid, at equal depths below the surface, are ftuftain an equal degree of pressure. As the pressure pressed equally in all directions,
of fluids is equal every way, the bottoms and fides Let us take the several glass tubes, A, B, C, D, fig. of the vessels are pressed as much as the neighbour6, pl. CLXXXV. which are open at both ends ; im. ‘ing parts of the fluid ; but it has been shewn that merge them in water to the same depth, their up- this action increases in proportion to the height of per orifice being stopped by the finger. Upon the fluid, but is every way equal at the same depth. taking away the finger, the water will rise to the This pressure depends on the height, not the quanfame height in all the tubes, though it enters the tity of the fluid, consequently, when the height lower end in very different directions: in A the of the fluid, and the area or surface pressed, repressure is directed upwards, in B downwards, in main the same, the action upon this surface will C fideways, and in D obliquely, but the pressure always be equal, however the figure of the vessel is equal in each. If we pour a greater quantity be changed. In other words, the pressure which of water into the vetfel, it will rise equally in the the bottom of the vessel sustains from the fluid tubes; so that fluids press in all directions, with contained in it, whatever be the fhape of the ves. a force proportionable to their heights.
fel, is equal to the weight of a pillar of the suid, The fame experiment is perhaps rendered ftill whose base is equal to the area of the bottom, and clearer by pouring some mercury into tubes. The whose height is the same with the perpendicular tubes for this purpose are smaller than those to be height of the fluid. used in the former experiment: some of them are That this is the case, in vefsels that are equally straight, and others bent at various angles. Though wide from top to bottom, is obvious, because the the tubes are open at both ends, one of the ex. bottom of such a vessel does actually sustain such tremities should be closed till after the immersion, a column of Auid, a column in this case equal to to prevent the mercury from falling out. On the whole weight of the fluid. Here the whole immerging the lover end of these tubes in water, weight of the huid contained in the vessel, and no the mercury will afcend toward the upper end of other force besides, presses upon the bottom, and the tubes. It is to be remarked, concerning this is consequently proportional to the quantity of experiment, that whatever be the angles at which matter contained in the vessel, which quantity is the tubes are bent, and howerer they are inclined as the surface of the bottom, and the perpendicuto the horizon, if before immersion the mercury lar height above it. But that the case should be in all the tubes be on a level, it will continue so the fame in irregular vefsels, is not so easy to conafter immersion, provided all the tubes are im- ceive ; for inftance, that in a vessel which from a merfed to the same depth. Consequently, when large bottom grows narrower as it rises, the botit has been proved that the pressures of a fuid are tom hould bear the same pressure when the vessel as the surface pressed, and their dept s from the is filled, as it would were the veffel equally wide furface of the incumbent fluid, it will follow that throughout from bottom to top, seems strange, the pressure of a Ruid is not only propagated in . yet is what neceffarily follows from the nature of all directions, but that the quantities of the pres- Auidity. fare at the same depths, and on a given furface, Before we proceed to illuftrate this proposition are equal in all directions.
by experiment, it inay not be improper to explain
it by diagrams; considering it, 1. when the vessel equal to the pressure upon the bottom of a cylinis narrower at the top than the bottom; 2. when drical one of the same BASE AND HEIGHT. it is wider at the top than the bottom.
The same mode of reasoning may be applied to 1. If the vessel MNFT, fig., pl. CLXXXV. is the vessel D BLP, fg. 9, which confifts of two smaller at the top than at the bottom, the pressure cylindrical parts N MLP, a great cylinder at the upon the bottom, ET, is as great as the prefiure bottom, and D BIV, a lesier one at the top.upon the bottom of a cylindrical vessel, ABCD, For the pressure upon LP, when the vessel is full fs. 8, of equal base and height, when they are of water, will be as great as if the veel was as both filled with water, or any other fluid, not- wide at top as at bottom; that is, as great as it withstanding there will be considerably more would be upon the same bottom L P, fuppofing water in the cylinder than the cone. Make F G, the vessel was an uniform cylinder, whose base OR, in the cylinder, fig. 8, equal to OR, the was L P, and height LF. L A and OR, two base of the column MNOR of the cone, fig. 7. equal drops at the same depth, are pressed equal. Now, as these columns of water are equal, it is ly; and OR having as much water to sustain, is evident that O R in the cylinder and OR in the as much pressed as if the vessel was an uniform cone fustain an equal weight, and consequently an cylinder. Therefore L A, or CP, or any other equal pressure. It is also evident, from what has equal part at the bottom, and consequently the been explained at the beginning of this article, whole bottom, is as mucii preffed in one case as that every part equal to OR, at the bottom of the it would be in the other. Indeed L A or CP cylinder, is pressed just as much as O R. But it is have less water to suftain than OR; but the corequisite to prove, that every part at the bottom luma NTL A presses upwards against N T with of the cone is equal to O R at the bottom of the a force equal to the difference between this cocylinder; for instance, the part F1 is pressed just lumo and D BOR, or to the weight of as much as much as O R is. It has been shewn, that all water as would fill the space FENT; for if a equal parts of a fluid, at equal depths from the sur. hole was made at NT, and a tube, FENT, fol. faces, are pressed equally; but the drops contigu- dered into it, the pressure against the bottom of ous to FI and OR are at equal depths from the the tube would support water in it to the height surfaces; therefore these drops, and consequently NT, the faine height it stands at in the tube D the parts F I and O R, are equally pressed. Now, BIV. Now, as the re-action of N T downwards as cvery part equal to OR, in the bottom both of is equal to the action upwards against it, that is, the cone and cylinder, is pressed as much as OR, the force with which NT keeps the water below and since one bottom is equal to the other, it fol- it, down against L A, is equal to the force with lows, that the whole prefiure upon F T is equal which this water presses against NT; L A is to the whole pressure upon CD.
therefore pressed down not only with the weight But although it appears, that the proposition is of the water NTLA, but likewise by the re-actrue, some persons have a difficulty in discovering tion of NT, which is equal to the weight of as the reason why it is true; for it certainly does not much water as would fill FENT, and make secm likely, at first view, that Fl, with no more NTLA equal to DBRO; whence it follows, that water over it than fills the space F EI, should be the weight and re-action together on LA, are equal pressed as much as OR, which fuftains the whole to the weight on DBR O, by which OR is prefied; column MNOR. But it mult be remembered, and the same may be proved of every other equal that the water F E I preffes upwards against FE, portion of the whole bottom and cover; and, as well as downwards against Fl; and if a hole therefore, by the weight and re-action, L P is as was made at F E, and a tube soldered therein, the much pressed as if it was the bottom of a cylinwater, by the pressure upwards, would be fuf- drical vessel FHLP, having the fame dimenfions tained in the tube at the same height that it stands at the top as at the bottom, and filled with water in the vessel; therefore this pressure is equal to to the height LF. But to proceed : the weight of as much water as would fill the tube. Though the pressure upon FT, fig. 7, is equal CAFE.
to the pressure upon CD, when both vessels are Now, the same pressure which would support filled with water to the same perpendicular height; the water in such a tube acts upon FE; but the yet if they were filled with ice, or any other solid re-action of F E downwards is equal to the action substance, instead of water, CD would be more "upwards against it: that is, E F keeps the water pressed than FT. For CD, whether the vesel down with a force equal to that with which it en. be filled with ice or water, fuftains the whole deavours to rise, equal to the difference of weight weight of the body which refts upon it, and do between F E I and MNOR; and as F I sustains more; but F T, which, besides the weight MN both the weight of the water FEI, and the ac- FT, sustains the re-action of the sides M NFT, tion or force with which the water is kept from when the vessel is filled with water, has only rising, but OR fustains only the weight of water the weight to sustain when it is filled with ice ; MNOR, the preffure upon F I will be equal to for ice, or any other solid body, does not press the pressure upon O R, and the fame may be upwards. This is a property, which, as it only proved of any other column. Therefore the bot. arises from the nature of a fluid, belongs to fluids tom of the cone is as much pressed by the weight only; FT will therefore be only pressed by the of water which fills the conė, and this re-action weight of the ice, and consequently will be less together, as the fame bottom would be pressed by pretied than CD, in proportion as the cone is less the weight of as much water as would fill up the than the cylinder, when their bases and heights whole cylindrical space CBFT; that is, the, are equal. For the same reason LP, fig. 9, if it prellure upon the bottom of a conical yelrel'is were full of ice, would be as much less pressed