STATICS. holding the longer leg of our tube in a perpendicular pofture, it be varioufly inclined to different angles with the furface of the water A B, fo that the orifice of the fhorter leg FG, may fometimes tend towards the top, and, at others, towards the bottom of the glafs; the oblique preffure of the water depends fo intirely upon its height above the orifice G, that the oil in the longer leg will ftill continue with its furface I K, but little higher than that of A B.

Fig. 19.

SCHOLI A.

1. We once attempted to discover the quantity of this lateral preffure by the following experiment. Having obtain'd a glass bubble X, with a flender neck, whofe gravity fell very little fhort of that of water; and provided a large wide-mouth'd glafs, exactly fitted with a cork, perforated in the middle, to receive, perpendicularly, a long, flender, glafs pipe, that defcended confiderably below the cork, wherein, alfo, was another hole, near its edge, for a fecond fmall pipe to pafs thro', whofe upper end reaching only two or three inches into the air, was firmly closed; then the veffel being filled with water, and the bubble fuffer'd to float thereon, the cork was applied, and well cemented to the mouth of the glafs, fo that nothing could pafs in or out of the veffel, except thro' the long flender pipe; all the other vents being carefully ftopp'd with cement. When things were thus prepared, and the bubble was made to float at a confiderable diftance from the deeply immterfed end of the long tube, we poured water thro' its upper orifice E, which, for want of other vent, afcended back again into the fame cavity; and if the water therein was only permitted to rife as high as I, for inftance, the bubble X, would still continue a-float: but if the water rofe to K, the bubble prefently fell to the bottom of the veffel, and remain'd thereat while the water ftood to the fame height in the pipe EF; but if the height were diminifh'd, by pouring fome of the water off, the bubble would re-afcend. Hence we fee, that the upper parts of water gravitate on the lower; and that, in a full veffel, the fame thing happens, tho' the former be not directly incumbent on the latter, but at a confiderable distance from the line of their direction; for the additional cylinder of water KI, acting like any other heavy body upon the water, caufes the bubble X, to fubfide. And, fince the air included in this bubble, was remarkably condenfed, it follows, that the cylinder of water K I, preffed upon the fubjacent fluid in the veffel; for otherwife the air in the bubble could not have been comprefs'd: and as this bubble floated on one fide, at a tolerable distance from the pipe E F, and above its lower orifice F; 'tis evident, that the cylinder of water IK, preffes as well laterally, as directly, upon all the bodies that lie beneath its furface. And thus every affignable part of the fides of the veffel, fuftains a preffure proportionable to its depth under water, and its own magnitude: if, therefore, any part were fo weak, as to yield to the weight of the cylinder IK (due allowance being made for the obliquity of the preffure) 'twere unfit to enter the compofition of our glass. Even the cork itself, refifts a preffure proportionable to the

breadth

breadth of its under furface, and the height of the cylinder K I; and might, STATICS.. therefore, if not too ftrongly faften'd, be raifed thereby; fo that if the cement fhould fail, the water would forcibly iffue out of its vents. Thus, alfo, the ftopple G, of the fhort pipe GH, may, by this means, be violently thruft out of its place, as will more fatisfactorily appear, by stopping the orifice at G, with your finger, which will, there, be strongly prefs'd upwards.

2. To fhew that the very oblique preffure fuftain'd by the bubble, from the water in the long tube, differ'd not confiderably from that of water placed directly over it, I fet two fuch bubbles feparately a-float in long cylindrical glaffes of water, when, if they were plunged but to a small depth, they would rife again to the top; fo that I was obliged to immerfe them to a confiderable depth, before the preffure of the incumbent water would fink them.

3. We may here, alfo, obferve, how the preffures of fuch different fluids, as air and water, will communicate. For, having fometimes left a fmall part of our veffel A B CD, unfill'd with water, fo that air remain'd between the furface L M, and the cork; the preffure of the water in the pipe from I, to K, would, if the cork were tight, caufe the bubble to fink, as if the veffel had been wholly fill'd with water; the comprefs'd and imprifon'd air above LM, communicating the preffure it receiv'd to the contiguous water.

PARADOX VIII.

Water will as well deprefs, as fupport a body Specifically lighter than itself.

We have proved, that the upper parts of fluids gravitate upon the lower, or bodies immerfed therein. Now, when a body is unequally preffed, it muft neceffarily move from that place where the preffure is greateft, to where it is leaft; whence, if a quantity of oil, hath its upper furface alone, exposed to the preffure of water, and nothing be in the way to hinder its defcent, the oil must neceffarily be deprefs'd, and not buoy'd up thereby. To illuftrate this by an an experiment; take a small glass fyphon E F GH, Fig. 20. with its fhorter leg GH, 3 or 4 inches long, and parallel to the other E F; plunge the shorter into oil of turpentine, till it be quite filled, and the fluid reaches to an equal height in the longer, as from F, to I; then stopping, with your finger, the orifice E, of the longer leg, immerfe them both a little under water: remove your finger, and as you gradually plunge the fyphon deeper, the oil, in its fhorter leg, will fink, and, at length, wholly rife into the longer; which fufficiently proves and illuftrates our propo

fition.

SCHOLIUM.

At once to confirm the prefent paradox, the feventh, and the fecond, I took a slender glass pipe OP N ML, and fuck'd oil of turpentine into Fig. 23+

STATICS. its lower orifice L, till it reach'd to P, in the longer leg, in a level with L;, and, ftopping the upper end O, with my finger, I plunged the tube to a convenient depth under water; when, removing my finger, the external fluid firft drove away the oil in LM, then depreffed it from M to N; and lastly, wholly impelled it into the longer leg NPO; fo that the oil was, here, evidently prefled not only laterally, but alfo downwards, and upwards.

Fig. 22.

Fig. 23.

PARADOX IX.

Notwithstanding the doctrine of pofitive levity, an oil, lighter than water, may be kept immerfed in that fluid.

Since the furface of ftagnant water is, phyfically fpeaking, horizontal; that part which preffes against the lower fuperficies of an immerfed body, must be deeper than that which preffes upon the upper: if, therefore, the water incumbent on the upper part of a body, can be made to stand at a greater height than the reft of the fluid wherein 'tis immerfed, fo as to balance what preffes against the lower; oil may be fufpended betwixt two parcels of water. To reduce this theory to practice, I fuck'd water into a ftrait, flender glafs pipe TP, to the height of an inch, and there held it fufpended, by topping the upper orifice with my finger; then plunging the lower end of the tube, two inches below the furface of fome oil of turpentine, deeply tinged with copper, whereby the oil, driving up the water, afcended to the height of an inch in the lower end of the pipe; when, I again clofed its upper end, to keep both liquors fufpended. In the next place, I plunged the tube into a glafs of water, three or four inches below its furface; fo that the water, upon the removal of my finger, was preffed into the lower end of the pipe P, to Q, impelling up the oil QR, to R, and the incumbent water to TS; at which ftations, the three feveral parts of oil and water together, prefs upon P, as much as the external water upon the other parts of the fame plain G H; yet the cil QR, afcends not, because the water RS, is kept from defcending below it, by the fides of the tube; whilft its upper furface TS, ftands higher than AD, that of the reft of the water: by which means, the incumbent fluid may be made to prefs upon the upper furface R, of the cylinder of oil, as forcibly as the water preffes againft Q, the lower furface of the fame; whence the oil will remain fufpended.

PARADOX X.

The afcent and flux of water in Syphons, are explicable, without fuppofing a
Fuga vacui.

Provide a cylindrical glafs A B C D, both wide and deep, as alfo, a fyphon F K G, with unequal legs, communicating with a long cylindrical pipe K E; to each leg of this fyphon, fix a cylindrical glafs I, and H, filled with water, as in the fcheme, that the water may run from the higher

glafs

glafs I, into the lower H; then, while the pipe E K, is held ftill, pour STATICS. oil of turpentine, gently, into the cylinder. A B C D, till it rife above the top of the fyphon F KG; when, the oil preffing on the water, will raise it into the legs of the fyphon, and force it out of the vellel I, into H: in which cafe, 'tis manifeft, the water runs thro' the fyphon, whilft the air has free admiffion thereinto, at the orifice E; fo that nature's abhorrence of a vacuum, cannot be the caufe of this flux. A juft folution of the phenomenon may be had from confidering the preffure of the oil, and the fituation of the veffels; for, that fluid afcending higher than K, preffes upon the furface of the external water, in the glaffes I, and H, wherein the legs of the fyphon are plunged, and forces it up into them; but as the excels of water in the glafs I, proves an over-balance for the greater depth of oil in the glafs H, the water is obliged to run from the shorter leg into the longer. Thus it happens in fyphons; when once the water is brought to run thro' them, the air gravitates upon the furface of the external fluid, wherein their legs are plunged, and not upon that which they contain; and, therefore, tho' the incumbent air, ftands a little higher over the fluid in the lower veffel, than in the upper, yet the water in the longer leg, greatly over-balancing that in the fhorter, it must needs flow out at the latter. And the preffure of the external air being able to raife water to a much greater height than that of the fhorter leg, the efflux will continue till fome other caufe put a ftop thereto. But if the legs of a fyphon exceed 35 feet in perpendicular altitude, the water will not flow thro' them; because the preffure of the external air is unable to raise water to that height. So, likewife, were an hole made in the top of a fyphon, whilst water was flowing thro' it, the flux would prefently ceafe; for the air, then preffing, as well within as without the fyphon, would return the water in each leg to its proper veffel. To confirm this particular, I procured two fyphons, the one of tin, the other of glafs, each of which had in the upper part of its bend, a fmall perforation, which I could stop with my finger, or open at pleafure; wherein I frequently perform'd the experiment. And having once carefully ftopp'd one of the above-mention'd holes, with oiled paper and cement, and found the water to run freely thro' the fyphon; yet a puncture made in the paper, by the point of a needle, admitted air fufficient to make the water in the legs fall back, before I could poffibly ftop the needle quick enough into the hole to prevent it.

PARADOX XI.

The most ponderous folid body we know, immerfed in water to a depth exceeding that of twenty times its own thickness, will float, if it be there fenced from the direct preffure of the incumbent fluid.

Let a deep glafs veffel A B C D, be almoft fill'd with water; wherein if a Fig. 24 fmall cylinder of brafs EF, be immerfed, till its upper furface is juft cover'd, and then let go; it muft, by reafon of its greater fpecific gravity,

necefla

STATICS. neceffarily fall to the bottom. But, were it placed on the plain IK, which lies at above the depth of nine times the body's thickness below the upper furface of the fluid; I affert that it would not defcend, unless it were preffed downwards by the weight of the incumbent fluid. For brafs being nearly nine times fpecifically heavier than water; the body EF, alone, would prefs upon the part F, as much as a cylinder of water, of an equal bafis, but about nine times the height of the brafs; and, confequently, the part F, will be no more depreffed, than any other part of the plain IK. But finee water gravitates on water, and alfo upon bodies heavier in Specie than itself, if immerfed therein; the brafs-cylinder EF, wherever it refts in the fluid, must be forced downwards, both by its own weight, and that of the incumbent water. But were the incumbent water prevented from gravitating thereon, it follows, that the body would, at that depth, be kept fufpended. And, in cafe the body refted, in like manner, upon the plain LM; the much greater preffure of the water on the other parts of the fame furface, would impel it upwards, with a force proportionable to the difference of their refpective weights.

Fig. 25.

of

And having found, by exact tryals, that the pureft gold, the moft ponderous body we know, is not quite twenty-times fo heavy as an equal bulk of water; if this metal, alfo, were immerfed into a greater depth than that of twenty times its own thickness, and there fenced from the pressure of the incumbent water; it muft neceffarily float. To confirm this by an experiment. Suppofe the brafs-body EF, to be the cover of a brafsvalve, and the valve itfelf ftrongly cemented to an open glafs-pipe OP; when, the body EF, being the lower part of the inftrument, and every way detached therefrom, would fall by its own weight, if unfupported. Then to the button Q, faften a thread, which, by being pulled upwards, may cause EF, to close the orifice of the valve: the valve being now plunged under water, to the depth of a foot, the cement, and the fides of the pipe OP, will prevent the fluid from preffing upon the upper part the body EF; and, confequently, that part of the plain V W, contiguous to its furface, will be prefs'd upon only by the weight of the body EF, but in its other parts by that of the incumbent water; fo that, letting go the ftring which held the body EF, close to the inftrument, that body will remain fufpended by the bare preffure of the water beneath it. And that this alone is the cause of the phenomenon, appears by gently raifing the inftrument towards the top of the water; for when it has afcended near the furface, fuppofe between the plains I K, and XY, the body EF, will fall down, and the water rife in the pipe OP, to a level with that in the containing veffel. But if the valve be at firft plunged much deeper under water, before the ftring be relaxed, for inftance, to the plain SR, the valve EF, will require a confiderable weight, as L, befides its own, to disjoin it: but if the weight prove infufficient for the purpofe, it may foon be render'd effectual, by raifing the inftrument, far lefs than before, towards the top of the water.

CO