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veral lower countries. This he makes to be one of the great ufes of mountains in the economy of the universe.

would in a great measure be avoided as people verfant in that bufinefs would feldom err fo far as to the whole amount of the difference previous to making any trial. Hence alfo the ftem may be・ HYDROPHYLAX, in botany, a genus of the made small enough, and the fcale graduated fo monogynia order, belonging to the tetrandria class nicely as to make the inftrument fufficiently accu- of plants. The calyx is tetrapartite; the corolla rate. According to this arrangement, it would funnel-shaped; the fruit two-edged and one-feeded. be proper to have the weights adapted to the hy- HYDROPHYLUM, WATER LEAF: a genus drometer marked with the different specific gravi- of the monogynia order, belonging to the pentanties which they are intended to indicate; zero dria clafs of plants; and in the natural method on the top of the ftem without a weight being ranking with thofe of which the order is doubtful. fuppofed to mean 800, and 20 at the bottom to The corolla is campanulated, with five melliferous fignify 820, which number the first weight would longitudinal ftria on the infide; the ftigma is bifid; carry; the fucceffive weights being marked, 846, the capfule globofe and bivalved. There is only 860, &c.; and the divifion on the ftem cut by the one fpecies, viz. fluid under trial, would be a number always to be added to that on the weight; the fum of the two fhowing the true fpecific gravity. The weights should undoubtedly be made to apply on the top of the stem, fo as never to come in contact with the liquor; and in ufing the hydrometer, its ftem fhould always be preffed down lower than the point at which it will ultimately reft, that by being wetted it may occafion no refiftance to the fluid. The inftrument itself fhould be of as regular a fhape and with as few inequalities as poffible, that all impediments to its motions may be avoided. * HYDROMETRY. n. f. [ùfwę and pergov.] The art of meafuring the extent of water.

HYDROMPHALUS, in medicine and furgery, a tumor in the navel arifing from a collection of water.

HYDROPHANES, OCULUS MUNDI, or LAPIS MUTABILIS, a kind of precious ftone highly efteemned among the ancients, but little known to the moderns till Mr Boyle made his observations upon it. Its fpecific gravity is about 2048; its colour of an opaque whitish brown; it is not foluble in acids nor affected by alkalies, but is eafily cut and polished. Sometimes it gives fire with fteel, fometimes not. It is infufible per fe; but when urged by a blowpipe, changes to a brownifh brittle fubftance. It is found in beds over the opals in Hungary, Silefia, and Saxony, and over the chalcedonies and agates in Iceland. Thefe ftones in general are either of a yellowish green, milky grey, or of a yellow like that of amber. The moft remarkable property of this ftone is, that it becomes tranfparent by mere immersion in any aqueous fluid; but gradually refumes its opacity when dry. See LAPIS MUTABILIS.

HYDROPHLOGE, a word ufed by Mr Wie gleb, for one of the component parts of water. See his Gen. Syft. of Chem.tranil. by Hopfon, p. 39. (1.)* HYDROPHOBIA. #. f. [¿¿gopoßia; hydrophobie, Fr. Dread of water-Among thofe difmal Tymptoms that follow the bite of a mad dog, the bydrophobia, or dread of water, is the most remark able. Quincy.

(2.) HYDROPHOBIA has likewife been fometimes found to take place in violent inflammations of the ftomach, and in hysteric fits. See MEDICINE, Ind. . HYDROPHYLACIA, a word used by Kircher and fome others who have written in the fame iyftem, to express thofe great refervoirs of water which he places in the Alps and other mountains for the fupply of rivers which run through the fe

HYDROPHYLLUM VIRGINIANUM, the water leaf of Morinus. It grows naturally in Canada and many other parts of America on moift spongy ground. The root is compofed of many ftrong fleshy fibres, from which arife many leaves with foot-ftalks 5 or 6 inches long, jagged into three, five, or feven lobes, almoft to the midrib, indented on their edges. The flowers are produced in loofe clufters hanging downwards, are bell-fhaped, and of a dirty white colour. It may be propagated by parting the roots; which ought to be done in autumn, that the plants may be well rooted before spring, otherwise they will require a great deal of water./

HYDROPICAL.) adj. [i♪gowixos; hydropique, * HYDROPICK. from hydrops, Latin.] 1. Dropfical; diseased with extravafated water.— Cantharides heat the watery parts of the body, as urine, and hydropical water. Bacon's Nat. Hiftory. The world's whole fap is funk:

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The general balm the hydropick earth hath drunk. Donne. -Hydropical fwellings, if they be pure, are pellucid. Wiseman.

Hydropick wretches by degrees decay, Growing the more, the more they waste away; By their own ruins they augmented lie, With thirst and heat amidst a deluge fry. Blackm. One fort of remedy he uses in dropfies, the water of the hydropicks. Arbuthnot. 2. Refembling dropfy. Some men's hydropick insatiableness learned to thirft the more, by how much more they drank. King Charles.-Every luft is a kind of hydropick diftemper, and the more we drink the more we fhall thirst. Tillotson.

HYDROPS, in medicine, the DROPSY.

HYDROSCOPE, an inftrument anciently used for the measuring of time. It was a kind of water clock, confifting of a cylindrical tube, conical at bottom: the cylinder was graduated, or marked out with divifions, to which the top of the wa ter becoming fucceflively contiguous, as it trickled out, the vertex of the cone pointed out the hour. See HYDROSTATICS, Part II. Sec. XII.

*HYDROSTATICAL. adj. [ö♪wg and satin.] Relating to hydroftaticks; taught by hydroftaticks. A human body forming in fuch a fluid, will ne ver be reconcileable to this bydrostatical law: there will be always fomething lighter beneath, and fomething heavier above; because the bone, the heaviest in fpecie, will be ever in the midft. Bentley.

* HYDRO

* HYDROSTATICALLY. adv. [from hydroAatical.] According to hydroftaticks.-The weight of all bodies around the earth is ever proportional to the quantity of their matter: for instance, a

pound weight, examined bydrostatically, doth always contain an equal quantity of folid mass. Bentley. HYDROSTATIC BALANCE. See BALANCE, 5.

HYDROSTATIC S.

DEFINITIONS and DIVISION of the SCIENCE.

"H

YDROSTATICKS. n. S. [üdwg, and rain; hydroftatique, Fr.] The fcience of weigh ing fluids; weighing bodies in fluids.

THIS fcience not only treats of the weighing of fluids, and of folid bodies in them (as Dr JOHNSON obferves above), but comprehends their nature and properties in general, particularly their preffure, gravity, equilibrium, and motions.

This laft branch of the fubject, when treated of by itself, forms a diftinét fcience, entitled HYDRAULICS; but it is fo neceffarily connected with the other branches of HYDROSTATICS, that it would be improper to feparate them, farther than by defcribing the former as the ft part, and the latter as the 2d part of this treatise.

PART I. HYDROSTATICS.

SECT. I. Of FLUIDITY.

By HYDROSTATICS, properly fo called, in contradiftinction from HYDRAULICS, we are taught how to determine the gravity or preffure of fluids upon folids, or upon each other, in veffels where water is not allowed to efcape or run off, but remains at reft.

SIR ISAAC NEWTON's definition of a fluid is much the fame with that of the late Mr George Adams, whofe writings on this fubject we shall chiefly quote in the prefent treatife. He defines a fluid to be a body whofe parts are fo loosely connected together, that they eafily yield to any force impreffed upon them, and move freely amongft each other. In this sense, fire, air, &c. are confider. ed as fluids. In almost every phyfical fpeculation, where experiment can reach, the fubject admits of fome illustration; where that is denied, the reasonings are in general vain and conjectural. We do not know the form of the parts of which fluids are compofed, and can make no experiments to reduce them into their primary particles. There is nothing more different in accuracy and truth, than that apprehenfion which is adequate to the purposes of human life, and that which ought to fatisfy the investigation of a philofopher. Thus there is nothing more obvious to common obfervers than fluidity, yet the philofopher finds it a property difficult to be conceived, and which he could not give credit to, if it was not rendered familiar to him by custom and experience. It is a physical phenomenon which has not yet been explained, and of which it is very difficult to give a clear account. It is, indeed, impoffible to comprehend, how a material and incompreffible fubftance can be compofed of parts fo elementary, fo moveable among themfelves, and yet with fo little adherence, as to affume immediately the form of any vessel into which it is poured; that its fur

face is always parallel to the horizon, or perfectly level; that, in fyphons, or when agitated by the wind, it makes ifochrone vibrations, or undulations like a pendulum; that it runs off where favoured by the smallest defcent, &c. &c. Yet all thefe facts, being common and familiar, occafion no furprise to mankind in general.

FLUIDITY is caufed by a certain degree of fire, which, when employed for this purpose, difappears with refpect to any other fenfible or perceptible effect. It does not dilate the volume, but refifts the particular attachment of the parts. Some have endeavoured to give mechanical ideas of a fluid body, by comparing it to a heap of fand: but the impoffibility of giving fluidity by any kind of mechanical comminution, will appear by confidering two of the circumftances neceffary to conftitute a fluid body: 1. That the parts, notwithftanding the greateft compreffion, may be moved, in relation to each other, with the fmalleft conceivable force, or will give no fenfible refiftance to motion within the mass in any direction. 2. That the parts fhall gravitate to each other, whereby there is a conftant tendency to arrange themselves about a common centre, and form a spherical body; which, as the parts do not refift motion, is eafily executed in fmall bodies. Hence the appearance of drops always takes place when a fluid is in proper circumftances.

Let us now fee how far thefe qualities may be procured by mechanical operations, even executed without thofe imperfections that neceffarily attend human performance. A body of fand, the par ticles of which fhould be perfectly fpherical and polished, or smooth, would only imitate a fluid in being able to spread itself upon a smooth plane inftead of lying in a heap, but would poffefs neither of the two qualities effential to a fluid body. For a heap of fpherical bodies, if compreffed, could not move by relation to each other, except by a force fufficient to balance that by which, in this cafe, they are neceffarily retained in their places. Neither can the parts of the supposed body of fand cohere, either to themselves or to other bodies, in the manner of fluids, as in each particle the mafs of gravitating matter must be great in proportion to the point of contact by which they thould cohere. If the cohefion of the particles of fand increased, the spreading quality would be diminished.

Many other differences might be pointed out; but fuppofing every thing elfe favourable to the mechanical theory, yet ftill there would remain to be explained the operation of fire, which is fo effential to fluidity. This would lead us too far, as it would render it neceffary for us to inveftigate the nature of that refiftance by which the figure of bodies is preferved in their hardness. By fire hard bodies are made foft; but it is not proBbbb 2

perly

perly the portion of loofe fire which augments the volume of bodies that renders them fluid: their fluidity is occafioned by a certain quantity of fire, which then disappears, with regard to any other fenfible or perceptible effect.

SECT. II. Of the GRAVITY of the PARTICLES of FLUIDS, and its EFFECTS on the FLUIDS themfelves.

ALTHOUGH no one finds any difficulty in allowing that water and other fluids are really ponderous, and do actually gravitate when confidered as a whole body, being convinced by their own fenfes, that a veffel weighs lefs when empty, than when it is filled with any fluid, and weighs heavier the more it contains; yet, in the early times of philofophy, there were perfons who believed fluids did not gravitate in proprio loco, as they termed it; that is, when immerfed in the fame, or a different fluid. A fimple experiment will fhew that they were mistaken, and that fluids lofe nothing in their weight in proprio loco.

Take a hollow glafs ball, fuch as is represented in Plate CLXXXV. fig. 2. furnished with a brafs ftop-cock, and made fo heavy as to fink in water. Exhauft it of its air, and then shut the cock. Exhaufting the air from it, gives room to a quantity of water equal in bulk to the exhaufted air. Sufpend it now from the end of the balance, fo that the bottle and the ftop-cock may be under the furface of the water in the jar, and then counterpoife it by a weight in the oppofite fcale. If we now open the cock, that the water may run into the bottle, the water will rufh in, and the ball will preponderate, and bear down the beam on which it hangs; clearly proving, that the parts of water retain their gravity in water, fo as to prefs and bear down upon the parts beneath them, otherwife the phial would not become heavier upon the admiffion of the water; and it will appear that the ball overbalances the counterpoife, as much as the weight of the quantity of water in the ball. To facilitate the explanation of hydroftatic phenomena, it has been usual for the writers on this fubject to confider the fluid in a veffel as cut into feveral horizontal planes, or imaginary furfaces, and to confift of a vaft number of fmall, equal, lubricious, fpherical globules. Thus, fig. 3, pl. CLXXXV. A BCD may reprefent a veflel confifting of fuch globules, a b, c d, e f, imaginary horizontal furfaces. Befides this imaginary horizontal divifion of a fluid, they often confider it as divided into perpendicular columns, from the top to the bottom of the fluid, as at fig. 4. Though fluids are fubject to the laws of gravity as well as folids, yet their fluidity occafions fome peculiarities neceffary to be noticed. The parts of a folid are fo connected together as to form but one whole; their effort is as it were concentrated in a fimple point, called the centre of gravity. This is not the cafe with fluids; the particles here are all independent of each other, are extremely moveable, yielding to the least effort that tends to feparate the one from the other.

The PARTS of a FLUID GRAVITATE independently of each other, and this is a natural confequence of their fluidity, or their not adhering to

gether; whereas the particles of a folid cohere to. gether, and gravitate as one mafs. It is clear from this principle, that if a hole be made in a vessel full of water, the power neceffary to prevent the fluid from running out, must be able to overcome the column of the fluid preffing on the hole, and whether there is only this column of the fluid that the weight to be overcome is the fame, acting on the part stopping the hole, or whether the veffel be full.

This will be rendered clearer by an experiment, made with the cylindrical glass vessel A B C D, fg. 5.pl. CLXXXV. which has a hole at bottom. A cy. lindrical tube of glass paffe through, and is fitted to this hole; a small piston, or plug, is fitted to this tube; and, being well greafed, flides eafily up and down; a long wire is fixed to this pifton, to be hooked on to one arm of the balance E F. On the upper part of this short tube may be occafionally fitted a glass tube, G H, which is exactly of the fame diameter as the brass tube, and of the fame height with the large vessel.

Having fitted the glafs tube in its place, and poured in water up to the mark, put weights into the scale, at the oppofite arm of the balance, till the pifton juft begins to rife; then take away the glafs tube, and fill the large veffel with water to the fame height, and it will be evident that the fame weight as before overcomes the preffure. Now as the same weight overcomes the pressure, whether a column of water be only the fize of the pifton, or whether the veffel be full of water, it is clear that particles of water exercise their gravity independent of each other; but if the mafs of water contained in the outer veffel was changed into ice, to raise the pifton we must use a weight equal to the weight of the whole column of ice.

The SURFACE of a FLUID which is contained in an open veffel, and free from all external impediments, will be LEVEL, or parallel to the hori zon. No part of a fluid can ftand higher than the reft: for, if any part be raised, it muft defcend by the force of gravity, and, in so doing, will spread and diffuse itself till it is on a level with the other parts; for, having gravity, and yielding easily to every impreffion, they obey the force or gravity, and flip down till they come to a level.

As the gravity of the particles reduces the upper furface to a level, fo likewife it occafions a preffure on the lower part, greater or lefs in proportion to their depths below the furface, each part containing a preffure equal to the weight of all thofe that lie above it; confequently, the particles which are at equal depths below the furface are equally preffed. In other words, as the upper furface of the fluid is parallel to the horizon, and as the lower parts fuftain the upper, and are preffed by them, this preffure will be in proportion to the incumbent matter, that is, to the height of the fluid above the particle that is preffed: but as the upper furface of the fluid is parallel to the horizon, all the points of any furface that you may conceive within the fluid, parallel to the horizon, are equally preffed. Should this equality of présfure be at any time deftroyed, and there be a leis preffure on one part of the furface than on the other parts, the fluid yielding to any impreffion,

this

this part will be moved, that is, will afcend till the preffure becomes equal.

We may confirm this by a fimple experiment with a glass tube. Stopping one end with your finger, immerge the other in water. The water will rife in the tube; but the tube being full of air, while you keep your finger upon the orifice, the rife is but Imall; but if you take away your finger, that the air which compreffed may efcape, the water will rife up into the tube, and not be at rest till it attains the fame height with the external water.

SOLIDS make no effort but in the direction of gravity, or perpendicularly downwards; but FLUIDS exert a force of preffure EQUAL to their GRAVITY, in all directions, and in all EQUALLY. This follows from the nature of a fluid, for its particles yield to any impreffion, and are eafily moved; therefore no drop will remain in its place, if, whilft it is preffed by a fuperincumbent fluid, it be not equally preffed on all fides; because being a fluid itself, it will yield to every impreffion, and begin to move, unless it be acted upon by equal forces, in all poffible directions. But it cannot move, because the furrounding drops refift on all fides its motion with the fame force that it endeavours to move, and consequently the drop must remain at reft; what is thus proved of one drop, holds equally true of all; confequently all the parts of a fluid, at equal depths below the furface, are preffed equally in all directions.

Let us take the feveral glass tubes, A, B, C, D,fig. 6, pl. CLXXXV. which are open at both ends; immerge them in water to the fame depth, their upper orifice being ftopped by the finger. Upon taking away the finger, the water will rife to the fame height in all the tubes, though it enters the lower end in very different directions: in A the preffure is directed upwards, in B downwards, in C fideways, and in D obliquely, but the preffure is equal in each. If we pour a greater quantity of water into the vetfel, it will rise equally in the tubes; fo that fluids prefs in all directions, with a force proportionable to their heights.

From a curfory view of the fubject, fome may confider it as a kind of mechanical paradox, that the preffure of a fluid upward, or in a direction contrary to that of gravity, fhould be nothing more than a confequence of gravity itself; but it is very easy to fhew, from mechanical principles, that a force acting in a given direction may communicate preffure through a number of intermediate bodies, fo that the last body shall be impelled in any direction whatever, even in that which is directly contrary to the original impulfe; and this is the cafe in re fpect of the particles which compofe fluids.

From the foregoing experiments it very clearly appears, that the PERPENDICULAR PRESSURE of any fluid column, is, from fome UNKNOWN Connection of the parts, diffused laterally in every direc tion; and at the fame depth, the preffures, estimated in any direction, are equal to each other. What has been proved of water obtains in all other fubftances that are fluid, and under the influence of gravity. SECT. III. Of the ACTION of FLUIDS against the BOTTOMS, SIDES, and TOPS, of the VESSELS which CONTAIN them.

Ir is evident, that the bottom and fides of a veffel containing a fluid (and the top alfo, when the fluid is raifed above it in a tube) are preffed by the parts of the fluids which immediately touch them; and as action and re-action are equal, these parts all ftuftain an equal degree of preffure. As the preffure of fluids is equal every way, the bottoms and fides of the veffels are preffed as much as the neighbouring parts of the fluid; but it has been fhewn that this action increases in proportion to the height of the fluid, but is every way equal at the fame depth. This preffure depends on the height, not the quantity of the fluid; confequently, when the height of the fluid, and the area or furface preffed, remain the fame, the action upon this surface will always be equal, however the figure of the veffel be changed. In other words, the preffure which the bottom of the vessel sustains from the fluid contained in it, whatever be the fhape of the vesfel, is equal to the weight of a pillar of the fluid, whofe bafe is equal to the area of the bottom, and whofe height is the fame with the perpendicular height of the fluid.

The fame experiment is perhaps rendered ftill clearer by pouring fome mercury into tubes. The fubes for this purpose are smaller than those to be used in the former experiment: some of them are That this is the cafe, in veffels 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 fuch a veffel does actually sustain such tremities should be clofed till after the immersion, a column of fluid, a column in this cafe equal to to prevent the mercury from falling out. On the whole weight of the fluid. Here the whole immerging the lower end of these tubes in water, weight of the fluid contained in the vessel, and no the mercury will afcend toward the upper end of other force befides, preffes upon the bottom, and the tubes. It is to be remarked, concerning this is confequently proportional to the quantity of experiment, that whatever be the angles at which matter contained in the veffel, which quantity is the tubes are bent, and however they are inclined as the furface of the bottom, and the perpendicu to the horizon, if before immerfion the mercury lar height above it. But that the cafe should be in all the tubes be on a level, it will continue fo the fame in irregular veffels, is not so easy to conafter immersion, provided all the tubes are im-ceive; for inftance, that in a veffel which from z merfed to the fame depth. Confequently, when it has been proved that the preffures of a fluid are as the furface preffed, and their depths from the furface of the incumbent fluid, it will follow that the preffure of a fluid is not only propagated in all directions, but that the quantities of the preffare at the fame depths, and on a given furface, are equal in all directions.

large bottom grows narrower as it rifes, the bottom should bear the fame preffure when the veffel is filled, as it would were the veffel equally wide throughout from bottom to top, feems strange, yet is what neceffarily follows from the nature of fluidity.

Before we proceed to illustrate this propofition by experiment, it may not be improper to explain

it by diagrams; confidering it, 1. when the veffel is narrower at the top than the bottom; 2. when it is wider at the top than the bottom.

1. If the veffel MNF T, fig. 7, pl. CLXXXV. is smaller at the top than at the bottom, the preffure upon the bottom, ET, is as great as the preffure upon the bottom of a cylindrical veffel, A B C D, fig. 8, of equal bafe and height, when they are both filled with water, or any other fluid, notwithstanding there will be confiderably more water in the cylinder than the cone. Make F G, OR, in the cylinder, fig. 8, equal to OR, the bafe of the column MNOR of the cone, fig. 7. Now, as thefe columns of water are equal, it is evident that O R in the cylinder and OR in the cone fuftain an equal weight, and consequently an equal preffure. It is alfo evident, from what has been explained at the beginning of this article, that every part equal to OR, at the bottom of the cylinder, is pressed just as much as O R. But it is requisite to prove, that every part at the bottom of the cone is equal to OR at the bottom of the cylinder; for inftance, the part F1 is preffed juft as much as OR is. It has been fhewn, that all equal parts of a fluid, at equal depths from the furfaces, are preffed equally; but the drops contiguous to FI and OR are at equal depths from the furfaces; therefore thefe drops, and confequently the parts F I and O R, are equally preffed. Now, as every part equal to OR, in the bottom both of the cone and cylinder, is preffed as much as OR, and fince one bottom is equal to the other, it follows, that the whole preffure upon FT is equal to the whole preffure upon C D.

But although it appears, that the propofition is true, fome perfons have a difficulty in discovering the reafon why it is true; for it certainly does not feem likely, at firft view, that F I, with no more water over it than fills the space FE I, fhould be preffed as much as OR, which fuftains the whole column MNO R. But it must be remembered, that the water FEI preffes upwards against F E, as well as downwards against FI; and if a hole was made at F E, and a tube foldered therein, the water, by the preffure upwards, would be fuftained in the tube at the fame height that it ftands in the veffel; therefore this preffure is equal to the weight of as much water as would fill the tube CAFE.

Now, the fame preffure which would fupport the water in fuch a tube acts upon FE; but the re-action of F E downwards is equal to the action upwards against it: that is, E F keeps the water down with a force equal to that with which it endeavours to rife, equal to the difference of weight between F EI and MNOR; and as FI fuftains both the weight of the water FEI, and the action or force with which the water is kept from rifing, but OR fuftains only the weight of water MNOR, the preffure upon FI will be equal to the preffure upon OR, and the fame may be proved of any other column. Therefore the bottom of the cone is as much preffed by the weight of water which fills the cone, and this re-action together, as the fame bottom would be preffed by the weight of as much water as would fill up the whole cylindrical space CBFT; that is, the preffure upon the bottom of a conical veffel is

equal to the preflure upon the bottom of a cylin drical one of the fame BASE AND HEIGHT.

The fame mode of reasoning may be applied to the veffel DBLP, fig. 9, which confifts of two cylindrical parts N M L P, a great cylinder at the bottom, and D BIV, a leffer one at the top.For the preffure upon L P, when the veffel is full of water, will be as great as if the vessel was as wide at top as at bottom; that is, as great as it would be upon the fame bottom L P, fuppofing the veffel was an uniform cylinder, whofe base was LP, and height LF. LA and OR, two equal drops at the fame depth, are preffed equally; and OR having as much water to sustain, is as much preffed as if the veffel was an uniform cylinder. Therefore LA, or CP, or any other equal part at the bottom, and confequently the whole bottom, is as much preffed in one cafe as it would be in the other. Indeed LA or CP have less water to sustain thàn OR; but the column NT LA presses upwards against NT with a force equal to the difference between this column and D BOR, or to the weight of as much water as would fill the space FENT; for if a hole was made at N T, and a tube, F ENT, foldered into it, the preffure against the bottom of the tube would fupport water in it to the height NT, the fame height it stands at in the tube D BIV. Now, as the re-action of N T downwards is equal to the action upwards against it, that is, the force with which N T keeps the water below it, down againft L A, is equal to the force with which this water preffes againft NT; LA is therefore preffed down not only with the weight of the water N TLA, but likewife by the re-action of N T, which is equal to the weight of as much water as would fill FENT, and make NTLA equal to DBRO; whence it follows, that the weight and re-action together on LA, are equal to the weight on DBR O, by which OR is preffed; and the fame may be proved of every other equal portion of the whole bottom and cover; and, therefore, by the weight and re-action, LP is as much preffed as if it was the bottom of a cylindrical veffel F HLP, having the fame dimenfions at the top as at the bottom, and filled with water to the height LF. But to proceed:

Though the preffure upon FT, fig. 7, is equal to the preffure upon CD, when both veffels are filled with water to the fame perpendicular height; yet if they were filled with ice, or any other folid fubftance, inftead of water, CD would be more preffed than FT. For CD, whether the vessel be filled with ice or water, fuftains the whole weight of the body which refts upon it, and no more; but FT, which, befides the weight M N FT, fuftains the re-action of the fides M NFT, when the veffel is filled with water, has only the weight to fuftain when it is filled with ice; for ice, or any other folid body, does not prefs upwards. This is a property, which, as it only arifes from the nature of a fluid, belongs to fluids only; FT will therefore be only preffed by the weight of the ice, and consequently will be lefs preffed than CD, in proportion as the cone is lefs than the cylinder, when their bafes and heights are equal. For the fame reafon LP, fig. 9, if it were full of ice, would be as much leis preffed

than

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