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OR, A

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VOL. IX.

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EDINBURGH,

PRINTED FOR A. BELL AND C. MACFARQUHAR

MDCCXCVII.

Entered in Stationers Hall in Terms of the Aft of Parliament.

ENCYCLOPEDIA BRITANNICA.

I

Fluid de

A

HYDROSTATICS;

SCIENCE which treats of the weight, motion, and equilibria of liquid bodies. Under this head, not only accounts of the nature and properties of fluids in general are introduced, and the laws by which they act; but also the art of weighing folid bodies in fluids, in order to difcover their specific gravities.

SECT. I. Of FLUIDS in general.

SIR Ifaac Newton's definition of a fluid is, That it is fined, &c. a body yielding to any force impreffed, and which hath its parts very eafily moved one among another. See FLUIDITY.

This definition fuppofes the motion fpoken of produced by a partial preffure; for in the cafe of an incompreffible fluid, it is demonftrated by Dr Keil, that under a total or an equal preffure, it would be impoffible that the yielding body should move.

The original and conftituent parts of fluids are by the moderns conceived to be particles fmall, fmooth, hard, and fpherical: according to which opinion, every particle is of itself a solid or a fixed body; and, when confidered fingly, is no fluid, but becomes fo only by being joined with other particles of the fame kind. From this definition, it hath been concluded by fome philofophers, that fome fubftances, fuch as mercury, are effentially fluid, on account of the particular configuration of their particles; but later difcoveries have evinced the fallacy of this opinion, and that fluidity is truly to be reckoned an effect of heat. See FLUIDITY.

That fluids have vacuities, will appear upon mixing falt with water, a certain quantity whereof will be diffolved, and thereby imbibed, without enlarging the dimenfions. A fluid's becoming more buoyant, is a certain proof that its fpecific gravity is increased, and of confequence that many of its vacuities are thereby filled: after which it may ftill receive a certain quantity of other diffoluble bodies, the particles whereof are adapted to the vacancies remaining, without adding any thing to its bulk, though the abfolute weight of the whole fluid be thereby increased.

This might be demonstrated, by weighing a phial of rain-water critically, with a nice balance: pour this water into a cup, and add falt to it; refund of the clear liquor what will again fill the phial; an increafe of weight will be found under the fame dimenfions, from a repletion, as has been faid, of the vacuities of the fresh water with faline particles.

VOL. IX. Part I.

And as fluids have vacuities, or are not perfectly denfe; it is also probable, that they are compounded of fmall fpheres of different diameters, whofe interftices may be fucceffively filled with apt materials for that purpose: and the fmaller these interftices are, the greater will the gravity of the fluid always be.

For instance, fuppofe a barrel be filled with bullets in the most compact manner, a great many small-shot may afterwards be placed in the interstices of those balls, the vacuities of the shot may then be replenished with a certain quantity of fea-fand; the interstices of the grains of the fand may again be filled with water; and thus may the weight of the barrel be greatly augmented, without increafing the general bulk.Now this being true with regard to folids, is appli- and procable alfo to fluids. For inftance, river-water will perties. diffolve a certain quantity of falt; after which it will receive a certain quantity of fugar; and after that, a certain quantity of alum, and perhaps other diffoluble bodies, and not increafe its firft dimenfions.

The more perfect a fluid is, the more eafily will it yield to all impreflions, and the more easily will the parts unite and coalefce when feparated. A perfect fluid is that whofe parts are put into motion by the leaft force imaginable: an imperfect one is that whofe parts yield to a fmall force, not the leaf. It is probable, that in nature there is no perfect fluid, the element of fire perhaps excepted; fince we fee that the mutual attraction of the parts of all the fluids, fubject to our experiments, renders them cohesive in fome degree; and the more they cling together, the lefs perfect their fluidity is. If, for inftance, a glafs be filled with water above the brim, it will vifibly rife to a convex fu face, which, was it a perfect fluid, free from either tenacity or cohesion, would be impoffible.

Mercury, the most perfect fluid we know, is not exempt from this attraction; for fhould the bottom of a flat glafs, having a gentle rifing toward the middle, be covered thin with quickfilver, a little motion of the machine will cause the fluid foon to feparate from the middle, and lie round it like a ring, having edges of a confiderable thickness.

But if a like quantity thereof be poured into a golden cup, it will, on the contrary, appear higher confiderably on the fides than in the middle. Which may proceed in part, perhaps, from the gold's being of great dentity, and therefore capable of exerting thereon a greater degree of attraction than other metals. Probably too it may happen from its having pores of

A

an

2

Its nature

Fluids.

Fluids.

part or fide in which the preffure is leaft. And hence, Preffure of no particle or quantity of a fluid can be at rest till it is every way equally preffed.

Preffure of an apter difpofition and magnitude to receive the minute mercurial particles, than those of iron and fome other metals; and therefore the attraction of cohesion in this experiment may obtain alfo: and every one knows how easily these two bodies incorporate, and make a perfe& amalgama. But the reafon commonly given for the two phenomena is, thats mercury, in the firft cafe, attracts itself more than it does glafs; and, in the last case, mercury attracts gold more than it does itself.

Sir Ifaac Newton held all matter to be originally homogeneous; and that from the different modifications and texture of it alone, all bodies receive their various ftructure, compofition, and form. In his definition of a fluid, he feems to imply, that he thought fluids to be compofed of primary folids; and, in the beginning of his Principia, he speaks of fand and powders as of imperfect fluids.

Borelli has demonftrated, that the conftituent parts of fluids are not fluid, but confiftent bodies; and that 3 the elements of all bodies are perfectly firm and hard. Florentine The incompreffibility of water, proved by the Floexperiment. rentine experiment, is a fufficient evidence alfo, that each primary particle or fpherule thereof is a perfect and impenetrable folid. Mr Locke too, in his Efay on Human Underflanding, admits this to be fo.

Fluids prefs as much

This famous experiment was first attempted by the great lord Verulam, who inclofed a quantity of water in lead, and found that it inclined rather to make its way through the pores of the metal, than be reduced into lefs compafs by any force that could be applied. The academics of Florence made this experiment afterwards more accurately with a globe of filver, as being a metal lefs yielding and ductile than gold. This being filled with water, and well clofed, they found, by hammering gently thereon, that the fphericity of the globe was altered to a lefs capacious figure (as might geometrically be proved); but a part of the water always like dew came through its fides before this could be obtained. This has been attempted by Sir Ifaac Newton, and fo many competent judges, on gold and several other metals fince, with equal fuccefs, that we do not hold any fluid in its natural ftate, except the air, to be either compreffible or elaftic.In fome experiments by Mr Canton, it hath been obferved, that water is more or lefs compreffed according to the different conftitution of the atmosphere; whence it hath been concluded that the Florentine experiment was erroneous: but it will not follow, that water can be compreffed by any artificial force, becaufe nature hath a method of compreffing it; any more than that folid metal can be compreffed artificially, though we know that very flight degrees of heat and cold will expand or contract its dimenfions. See WATER.

SECT. II. Of the Gravity and Preffure of Fluids.

ALL bodies, both fluid and folid, prefs downwards by the force of gravity: but fluids have this wonderupward as ful property, that their preffure upwards and fidewife downward. is equal to their preffure downwards; and this is always in proportion to their perpendicular height, without any regard to their quantity: for, as each particle is quite free to move, it will move towards that

To fhow by experiment that fluids prefs upward as Plate well as downward, let A B be a long upright tube ccxxxIX filled with water near to its top; and CD a finall tube fig. 2. open at both ends, and immerfed into the water in the large one: if the immerfion be quick, you will fee the water rife in the fmall tube to the fame height that it ftands in the great one, or until the furfaces of the water in both are on the fame level: which fhows that the water is pressed upward into the small tube by the weight of what is in the great one; otherwife it could never rife therein, contrary to its natural gravity, unless the diameter of the bore were so fmall, that the attraction of the tube would raise the water; which will never happen, if the tube be as wide as that in a common barometer. And, as the water rifes no higher in the fall tube than till its furface be on a level with the furface of the water in the great one, this shows that the preffure is not in proportion to the quantity of water in the great tube, but in proportion to its perpendicular height therein : for there is much more water in the great tube all around the fmall one, than what is raised to the same height in the fmall one as it ftands in the great.

Take out the fmall tube, and let the water run out of it; then it will be filled with air. Stop its upper end with the cork C, and it will be full of air all below the cork: this done, plunge it again to the bottom of the water in the great tube, and you will fee the water rife up in it to the height E. Which shows that the air is a body, otherwife it could not hinder the water from rifing up to the fame height as it did before, namely, to A; and in fo doing, it drove the air out at the top; but now the air is confined by the cork C: And it also fhows that the air is a compreffible body; for if it were not fo, a drop of water could not enter into the tube.

The picffure of fluids being equal in all directions, it follows, that the fides of a veffel are as much preffed by a fluid in it, all around in any given ring of points, as the fluid below that ring is preffed by the weight of all that ftands above it. Hence the preffure upon every point in the fides, immediately above the bottom, is equal to the preffure upon every point of the bottom.

To fhow this by experiment, let a hole be made at e Fig. 3. in the fide of the tube A B clofe by the bottom, and another hole of the fame fize in the bottom at C; then pour your water into the tube, keeping it full as long as you choose the holes fhould run, and have two bafons ready to receive the water that runs through the two holes, until you think there is enough in each bafon; and you will find by measuring the quantities, that they are equal. Which shows that the water run with equal fpeed through both holes; which it could not have done, if it had not been equally preffed through them both. For, if a hole of the fame fize be made in the fide of the tube, as about ƒ, and if all three are permitted to run together, you will find that the quantity run through the hole at ƒ is much lefs than what has run in the fame time through either of the holes C or e.

In the fame figure, let the tube be re curved from the bottom at C into the fhape DE, and the hole at C

Fluids.

Preffure of C be topt with a cork. Then pour water into the tube to any height, as Ag, and it will spout up in a jet EFG, nearly as high as it is kept in the tube AB, by continuing to pour in as much there as runs through the hole E; which will be the cafe whilft the furface Ag keeps at the fame height. And if a little ball of cork G be laid upon the top of the jet, it will be fupported thereby, and dance upon it. The reafon why the jet rifes not quite fo high as the furface of the water Ag, is owing to the refiftance it meets with in the open air for if a tube, either great or small, was fcrewed upon the pipe at E, the water would rife in it until the furfaces of the water in both tubes were on the fame level; as will be shown by the next expe

dox.

Plate

riment.

:

5 Any quantity of a fluid, how small foever, may be ftatic para- made to balance and fupport any quantity, how great foever. This is defervedly termed the hydroflatical paradox; which we fhall firft fhow by an experiment, and then account for it upon the principle above mentioned, namely, that the preffure of fluids is directly as their perpendicular height, without any regard to their quantity. Let a fmall glafs tube DCG, open at both ends, ccxxxix. and bended at B, be joined to the end of a great one fig. 4. AI at cd, where the great one is alfo open; fo that these tubes in their openings may freely communicate with each other. Then pour water through a small necked funnel into the fmall tube at H; this water will run through the joining of the tubes at cd, and rife up into the great tube; and if you continue pouring until the furface of the water comes to any part, as A, in the great tube, and then leave off, you will fee that the furface of the water in the small tube will be juft as high at D; fo that the perpendicular altitude of the water will be the fame in both tubes, however fmall the one be in proportion to the other. This fhows, that the small column DCG balances and fupports the great column Acd; which it could not do if their preffures were not equal against one another in the recurved bottom at B.-If the fmall tube be made longer, and inclined in the fituation GEF, the furface of the water in it will stand at F, on the fame level with the furface A in the great tube: that is, the water will have the fame perpendicular height in both tubes, although the column in the small tube is longer than that in the great one; the former being oblique, and the latter perpendicular.

Since then the preffure of fluids is directly as their perpendicular heights, without any regard to their quantities, it appears, that whatever the figure or fize of veffels be, if they are of equal heights, and if the areas of their bottoms are equal, the preffures of equal heights of water are equal upon the bottoms of these veffels; even though the one fhould hold a thousand or ten thousand times as much water as would fill the Fig. 5, 6. other. To confirm this part of the hydroftatical paradox by an experiment, let two veffels be prepared of equal heights, but very unequal contents, fuch as AB fig. 5. and AB in fig. 6. Let each veffel be open at both ends, and their bottoms Dd, Dd be of equal widths. Let a brass bottom CC be exactly fitted to each veffel, not to go into it, but for it to ftand upon; and let a piece of wet leather be put between each veffel and its brafs bottom, for the fake of clofeness.

Join each bottom to its veffel by a hinge D, fo that Preffure of
it may lie open like the lid of a box; and let each bor- Fluids.
tom be kept up to its veffel by equal weights E and E
hung to lines which go over the pulleys F and F
(whofe blocks are fixed to the fides of the veffels at ƒ),
and the lines tied to hooks at d and d, fixed in brass
bottoms oppofite to the hinges D and D. Things
being thus prepared and fitted, hold the veffel AB
(fig. 6.) upright in your hands over a bafon on a
table, and caufe water to be poured into the vessel
flowly, till the preffure of the water bears down its
bottom at the fide d, and raises the weight E; and
then part of the water will run out at d. Mark the
height at which the surface H of the water stood in
the veffel, when the bottom began to give way at d;
and then, holding up the other veffel AB (fig. 5.) in
the fame manner, cause water to be poured into it at
H and you will fee, that when the water rises to A
in this veffel, just as high as it did in the former, its
bottom will alfo give way at d, and it will lofe part of

:

the water.

The natural reafon of this furprising phenomenon is, that fince all parts of a fluid at equal depths below the furface are equally preffed in all manner of directions, the water immediately below the fixed part Bf (fig. 5.) will be preffed as much upward againft its lower furface within the veffel, by the action of the column Ag, as it would be by a column of the fame height, and of any diameter whatever; (as was evident by the experiment with the tube, fig. 4.) and therefore, fince action and reaction are equal and contrary to each other, the water immediately below the furface Bf will be preffed as much downward by it, as if it was immediately touched and preffed by a column of the height g A, and of the diameter Bf: and therefore the water in the cavity BD df will be preffed as much downward upon its bottom CC, as the bottom of the other veffel (fig. 6.) is preffed by all the water above it.

To illuftrate this a little farther, let a hole be made Fig. 5. at f in the fixed top Bf, and let a tube G be put into it; then, if water be poured into the tube A, it will (after filling the cavity B d) rife up into the tube G, until it comes to a level with that in the tube A; which is manifeftly owing to the preffure of the water in the tube A, upon that in the cavity of the vessel below it. Confequently, that part of the top Bf, in which the hole is now made, would, if corked up, be preffed upward with a force equal to the whole weight of all the water which is fupported in the tube G: and the fame thing would hold at g, if a hole were made there. And fo, if the whole cover or top Bf were full of holes, and had tubes as high as the middle one Ag put into them, the water in each tube would rife to the fame height as it is kept in the tube A, by pouring more into it, to make up the deficiency that it fuftains by fupplying the others, until they are all full; and then the water in the tube A would fupport equal heights of water in all the reft of the tubes. Or, if all the tubes except A, or any other one, were taken away, and a large tube equal in diameter to the whole top Bf were placed upon it and cemented to it, and then if water were poured into the tube that was left in either of the holes, it would afcend through all the reft of the holes, until itfilled the large tube to the A 2

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