immerfed part thereof, it must fink lower, because the fubjacent part at V, STATICS. would then be more charged than the reft. On the contrary, if the cube were lighter than the water, whofe place the immerfed part poffeffes, it muft, by the greater preffure of the water upon the other parts of the plain XW, than upon that contiguous to the wood at V, be impell'd upwards, till the preffure of the whole cube upon the part that fuftains it be equal to that of the water upon the reft of the plain, and confequently be the fame with the water whofe place the immerfed part poffeffes; the lightness of that part, in refpect of fo much water, being compensated by the weight of what remains unimmersed above the level of the water. Thus, when a piece of wood is thrown into water, tho' the moment it acquires in falling carries it thro' many imaginary plains below its proper ftation; yet the fuperior preffure to which each of thofe plains is expofed in all other parts, but in that contiguous to the bottom of the wood, presently impels it up again, till at length it refts in the place we have affign'd it.

SCHOLIUM.

This ingenious and ufeful propofition, relating to floating bodies, is mathematically demonftrated by Archimedes and his commentators, and may be farther manifefted to the eye by the following experiment. Having poured a convenient quantity of water into a large deep glafs, and placed another deeper, that was properly fhaped for fwimming, within it; we furnish'd the latter with balaft, a deck, and other parts of a fhip, till it funk down to fome particular marks we had placed on the outfide. Then obferving how high the water reach'd in the larger veffel, we carefully placed two or three marks in a level with the horizontal furface of the water; and taking out the floating glafs, we wiped the outfide dry, and weigh'd it, with all its rigging, in an exact pair of fcales, and afterwards pour'd an equal weight of water into the large glafs, which we found reach'd up to the marks whereto our counterfeit fhip had raised it. This experiment we several times repeated in veffels of different fizes, fhapes, and lading. From whence it appears, that the floating veffel, with all it contained and supported, was equal in weight to the water whofe bulk equall'd the immerfed part of the veffel, had it been cut off from the other, by a plain continu'd from the horizontal furface of the water. This theorem, with what we have brought to confirm or illuftrate it, may be apply'd, mutatis mutandis, to a fhip with all her rigging and lading; for 'tis univerfal, that the weight of a floating body equals that of the water whose fpace the immerfed part poffeffes. And hence the learned Stevinus fomewhere fays, that a whole fhip, with whatever belongs to it, preffes no more upon the bottom it floats over, than a bulk of water equal to the immerfed part of its hull.

STATICS.

PARA DOX IV.

A competent preffure of an external fluid is, alone, fufficient to raise the water in pumps.

The truth of this propofition may appear from the preceding experiments; however, we shall give it a farther illuftration and proof, as follows. Suck deeply tinged water into a flender glafs-pipe, to the height of an inch; and nimbly ftopping the upper orifice, immerfe the lower end into a glafs half fill'd with the fame tinged liquor, till the furface of that in the pipe be an inch below the top of the external fluid; next, pour oil of turpentine thereon, till it fwim three or four inches above the water; when eafing your finger, gently, from the upper orifice of the pipe, to admit a communication between the internal and external air, the liquor in the tube will be impell'd up almost as high as the furface of the external oil. Now, it cannot here be pretended, that the afcent of the liquor, in the pipe, is owing to nature's abhorrence of a Vacuum; fince, as the pipe is full of air, and its orifice open, there's no danger of a Vacuum, tho' the water did not rife; the air and water remaining contiguous as before. The true reason, then, of this afcent, is, that upon all the other parts of the imaginary plain cutting the immerfed end of the tube, there is a preffure of water and oil fwimming thereon, equal to four or five inches height of water; whilft, upon that part where the liquor contain'd in the pipe refts, there is only the preffure of one inch of water; whence the parts near the immerfed orifice, must be neceffarily thruft out of their places by those of the water that are more preffed, till fo much liquor be forced up into the pipe, as makes the preffure on that part of the imaginary plain equal to that of every other fuch part; when the water will rife no farther, but by reafon of the equilibrium, reft a little below the furface of the oil; the fpecific gravity of this being less than that of water. In like manner, it may happen in pumps; for as the oil of turpentine, tho' lighter than water, by refting upon the furface of the external fluid, forces up the liquor, within the pipe, far above the external water; fo the air, tho lighter than oil of turpentine, reaching to the height of many miles, and refting upon the water in a well, will prefs that water up the cylindrical cavity of a pump much higher, if all impediments were removed, than the furrounding water. Now the obftacle here is either the fucker, or the preffure of the external air; the whole ufe of the fucker is, therefore, to free the water in the pipe from any impediment to its afcent; as, in our experiment, the fides of the tube fufficiently defend the water therein from any preffure of the external oil that might obftruct its rifing. Laftly, as the liquor in our pipe was forced up, till the cylinder raised, became a ba lance to the preffure of the water and oil on the outfide; fo in pumps, the water rifes but to a certain height, viz. thirty-three, or thirty-four feet, beyond which it cannot be impell'd; because at that standard the preffure of the water in the pump upon that part of the imaginary plain wherein its

lower orifice lies, is the fame with that the other equal parts thereof fuftain, STATICS. from fo much of the external water and atmosphere as refts thereon. And this may fuffice to fhew, that nothing more than a competent weight of an external fluid, such as the air, is requifite to raise the water in pumps.

SCHOLIUM.

For a farther confirmation of this propofition, and, at the fame time, to fhew that a small quantity of quick-filver may be fufpended in an open tube; I fhall here offer another experiment. Having fuck'd into the lower end of an open glafs- tube, the diameter of whofe bore was above the fixth of an inch, near half an inch height of quick-filver, and nimbly stopped the upper end with my finger; I plunged the mercury into a deep glafs of oil of turpentine, being careful not to open the upper orifice, till the quickfilver was funk eighteen or twenty times its own height below the furface of the oil; after which, it remain'd fufpended, while the tube continued unftopped: and as if I raised it towards the upper furface of the oil, it would drop out; fo if I depreffed it deeper into that fluid, it would be impelled higher up into the pipe: and, by this means, fo ponderous a body as mercury was made fometimes to rife, and fometimes to fall, but ftill to continue fupported by a liquor fpecifically lighter than common fpirit of wine. This experiment, however, may eafily mifcarry, unless great care be used; and, after all, the oil will foon infinuate itself between the fides of the pipe, and so short a cylinder of mercury; for which reafon, I here prefer water to oil of turpentine.

COROLLARY.

Since a cylinder of mercury, about thirty inches high, is equal in weight to one of water, about the height of thirty-three, or thirty-four feet; 'tis evident, that the preffure of the external air, which can raise and fufpend that height of water, will do the fame to the proportionable one of mercury, in the Torricellian experiment.

PARADOX. V.

The preffure of an external fluid will keep an beterogeneous liquor fufpended at the fame height, in tubes of very different bores.

Pour a fufficient quantity of deeply tinged water into a clear, deep, wide-mouth'd glafs, and close it with a broad, thin cork, wherein various round holes, of different magnitudes, have been burnt; into each of which you may thruft an open glafs-tube of a correfponding fize, fo that they may ftand parallel to one another, and perpendicular to the furface of the fluid, wherein they are immerfed. Befides thefe holes, another aperture must be made in the cork, to receive the fmall end of a glafs-funnel, by means whereof, oil may be conveyed into the veffel, when stopped; and in the fender part of this funnel, 'tis proper to place fome cotton, to break the force of the defcending oil, which might otherwife fruftrate the expe

2

riment,

Fig. 9.

STATICS. riment. Things being thus prepared, pour oil of turpentine thro' the funnel, till the tinged water be preffed up into all the pipes, and rife to a confiderable height therein, above the lower furface of the oil; when you'll plainly perceive the liquor to ftand at the fame level, both in the greater and fmaller tubes, while in each it is plainly fuftain'd at that height above the other water, by the preffure of the external oil; which being specifically lighter than water, its furface will remain fomewhat higher on the outfide of the tubes, than the tinged water they contain. And if, by means of a fyphon, apply'd in the place of the funnel, the oil be gradually drawn off from the water; as the depth and preffure of the fame decreases, the liquor in all the pipes, both great and fmall, will gradually fubfide. For, fuppofe E F, the furface of the water within-fide of the tubes, as well as without them, before any oil fwims upon it; the lightness of that fluid, compared to water, will prevent it, when pour'd thereon, from getting into the cavity of the pipes L, M, N: and, therefore, rifing on the outfide thereof, it must, by its gravity, prefs the water, and impel it up into them. And if the upper furface of the oil reach to GH, and that of the water defcend to IK; by means of the quantity of oil made ufe of, the liquor in the pipes ought to have its feveral upper furfaces in the fame level with each other, notwithstanding the great inequality of their bores; fince that part of the plain I K, whereon refts the circular orifice of the largest tube L, is no more preffed by the incumbent water, than any other equal part of the fame is by the oil it fuftains; the oil having only an additional height on the plain I K, to balance the preffure of the liquor in the pipe. And tho' the tube L were twice its present bigness, 'twould but prefs the fubjacent plain I K, equally with the oil on the other equal parts. Nor ought this preffure of the external oil to raise the water in the flender pipe N, above the surface Q, in the fame level with O; for were the liquor higher in the fmall pipe, it must prefs that part of the plain IK, whereon it refts with a force fuperior to that of the oil upon the other parts of IK, which is greater than the oil could refift; whence, confequently, the liquor in the fender pipe muft fubfide, till its surface fall below that of the external oil; for, till then, the different fluids cannot reft in equilibrium. In a word, it matters not how wide the cylinder of water be, which the oil is to fupport, provided it rife no higher than the difference in the specific gravities of the two fluids will admit of; for in this cafe, the preffure of water on the fuftaining part of the plain, will be equal to the preffure of the external oil on all the other parts thereof; and, confequently, the two liquors must remain perfectly balanced.

SCHOLIA.

1. It may here be obferv'd, that there's no neceffity the glass-tubes L, M, N, fhould be of the fame length; fince, as their lower orifices are open, the liquor will rife to the fame height within them, tho' they lie not in the fame plain below the water.

2. We all along fuppofe, and particularly in the laft experiment, that STATICS. the smallest glass tubes employ'd are of a moderate fize, and not exceeding narrow; or, in cafe they are, that allowance be made for the property of water's rifing in them to a greater height, than can be attributed to the balance either of water or oil, that keeps it there fufpended.

PARADOX VI.

The direct preffure fuftain'd by a body, placed any where under water, with its upper furface parallel to the horizon, is that of a column of water, whose base is the horizontal fuperficies of the body, and height the perpendicular depth of the water; and if the water preffing upon a body, be contained in open tubes, its preffure is to be estimated by a column of the fame, the bafe whereof equals the lower orifice of the pipe, and height a perpendicular from thence to the top of the water and this, tho' the pipes ftand obliquely, be irregularly shaped, or wider in fome parts than the faid orifice.

The former part of our propofition we might, with Stevinus, make more general, and thus demonftrate. Suppofe ABCD, a folid rectangular fi- Fig. 10. gure of water, whose base DC, is parallel to the horizon, and height GE, a perpendicular let fall from the upper to the lower furface of the water; if that part of the bafe E F, be charged with more water than GEFH, the overplus muft come from the adjacent water; fuppofe it then, if poffible, to come from A GED, and HBCF: then, for the fame reason, the bafe DE, will have more water incumbent thereon than AGED; and the like may be faid of F C, whence the whole bafe DC will sustain a greater weight than that of the whole water ABCD, which is abfurd. By the like reafoning we prove that the base DC, fuftains no lefs a weight than that of the water GHFE; fince, then, it fuftains neither a greater weight nor a lefs, than the column of water GHFE, it must exactly fuftain the fame.

To this demonftration we fhall annex fenfible experiments, to confirm and illuftrate each part of our propofition. First then, fuck oil of turpen- Fig. 11 tine into a flender glafs fyphon, till it fill the fhorter leg, and rife two or three inches high in the longer; then nimbly ftop the upper orifice with your finger, and plunge the lower part of the fyphon into a deep glafs of water, till the furface of the oil in the longer leg rifes but little higher than that of the external water, and upon removing your finger, the furface of the oil will either entirely, or almoft, preferve its former station; when if the fyphon be immerfed deeper, the oil in the fhorter leg will be deprefs'd; but upon gently raifing the fyphon towards the top of the water, it will exceed its former ftation, gradually flow out in drops, and emerge to the furface. Now, fince the water, at first, kept the oil in the longer leg, fufpended no higher than it would have been by a cylinder of water, equal in bafis to the orifice of the fhorter leg, and reaching, in length, from thence to the top of the water, as may be eafily feen in a fyphon with legs fufficiently long; and fince, when by raifing the fyphon,