Hydrostatical paradoxes made out by new experiments, for the most physical and easie / by Robert Boyle ...

PARADOX XI.

That a solid Body, as ponderous as any yet known, though near the Top of the water it will sinck by its own weight; yet if it be plac'd at a greater depth then that of twenty times its own thickness, it will not sinck, if its descent be not assisted by the weight of the incumbent water.

THis Paradox, having never been (that I know of) propos'd as yet by any, has seem'd so little credible to those to whom I have mention'd it, (without excepting Mathematicians themselves,) that I can scarce hope it should be readily and generally recei∣ved in this Illustrious Company, upon

less clear Testimony, then that of Ex∣perience. And therefore, though (if I mistake not) some part of this propo∣sition may be plausibly deduc'd by the help of an Instrument ingeniously thought upon by Monsieur Paschal; Yet I shall have recourse to my own Method for the making of it out, for these two Reasons. The one, That a great part of the Paradox must be Explicated, as well as prov'd, by the Doctrine already setled in this paper. The other, That the Experiment pro∣pos'd by Monsieur Paschal, being to be done in a deep River, and requiring a Tube 20 foot long, whose Bottome must be fitted with a Brass Cylinder, made with an exactness, scarce (if at all) to be hoped for from our Work∣men: If I should build any thing on this so difficult an Experiment, (which himself does not affirm to have ever been actually tryed,) I fear most men

would rather reject the Experiment as a Chimaerical thing, then receive for its sake a Doctrine that appears to them very Extravagant.

Let us then, to imploy in this case also the method we have hitherto made use of, Fill a Glass vessel, A B C D, almost full of water; only, in regard that there is a great depth of water requisite to some Cir∣cumstances of the Experiment, This last must not be so shallow as those hi∣therto imploy'd: but a deep Cylin∣der, or Tube seal'd at one end, whose depth must be at least two or three foot, though its breadth need not be a∣bove 2 or 3 Inches; and, to keep it up∣right, it may be plac'd in a socket of metal or wood, of a size and weight convenient for such a purpose. This Glass being thus fitted in water, let us suppose E F, to be a round and flat piece of solid Brass, having about an

Inch in Diameter, and a fourth or sixth part of an inch in thickness. This Cy∣linder, being immers'd under water till it be just cover'd by the uppermost Surface of that Liquor, and being let go, must necessarily fall downwards in it; because if we suppose the imagi∣nary Superficies, G H, to pass along the Circle F, which is the lower part of the Brass Body, that metal being in specie far heavier then water, the Brass that leans upon the part F, must far more gravitate upon the said part F, then the incumbent water does upon any other part of the Superficies G H; and, consequently, the subjacent water at F will be thrust out of place by the descending Body. And because that, in what part soever of the water, not exceeding nine times its thickness mea∣sured from the Top of the water A C, the ponderous Body, E F, shall hap∣pen to be; there will be still, by rea∣son

of the specifick gravity of the Me∣tal, a greater pressure upon that part of the imaginary Superficies that passes along the bottome of the Body on which the part F shall happen to lean, then upon any other part of the same imaginary Superficies; the Brass Body would still descend by vertue of its own weight, though it were not as∣sisted by the weight of the water that is over it. But let us suppose it to be plac'd under water on the design∣able plain J K; and let this plain, which (as all other imaginary plains) is, as well as the real Surface of the wa∣ter, to be conceiv'd parallel to the Horizon; and let the depth or di∣stance of this plaine, from the up∣permost Surface of the water, be (some what) above nine times the thick∣ness of the Brass Body: I say that, in this case, the body would not descend, if it were not press'd downwards by

the weight of the water it has over it. For Brass being but a∣bout nine times as heavy as water of an e∣qual bulk to it, the Bo∣dy E F alone would press upon the part F, but as much as a Cy∣linder of water would, which having an equal Basis were 8 or 9 times as high as the Brass is thick. But now all the other parts of the I∣maginary surfaces, I K, being press'd upon by the incumbent water, which is as high above them as the newly mention'd Cylinder of water would be; there is no reason why the part F should be depress'd, rather then any o∣ther part of the Superficies J K: But because it is true, which we formerly taught; namely, that water retains its gravity in water; and that too, though a body, heavier in specie then it, be plac'd

immediately under it; it will necessa∣rily happen, That in what part soe∣ver the solid body be plac'd, provided it be every way environ'd with the wa∣ter, it must, for the Reason newly given, be made to move downwards, partly by its own weight, and partly by that of the incumbent water; and must continue to sinck, till it come to the bottom, or some other body that hinders its farther descent.

But in case the water above the so∣lid body did not gravitate upon it, and thereby assist its descent; or, in case that the incumbent water were by some Artifice or other, so remov'd, That none of the lateral water (if I may so call it) could succeed in its place to lean upon the solid; then it will follow, from what we have newly shown, that the solid would be kept suspended. And in case it were plac'd much deep∣er in the water, as over against the

point L or M; Then, if we conceive the incumbent water to be remov'd or fenc'd off from it, the pressure of the solid alone upon the part F, of the ima∣ginary Superficies L M, being very much inferior to that of the water up∣on the other parts of the same Surface, the part F would be strongly impell'd upwards, by a force proportionate to the difference of those two pressures. And therefore, since I have found by tryals, purposely made in scales mar∣vellously exact, and with refined Gold, (purer then perhaps any that was ever weighed in water) That Gold, though much the ponderoufest of bodies yet known in the world, is not full 20 times as heavy as water of the same Bulk; I kept within compass (as well as im∣ploy'd a round number, as they call it) when I said, That no body (yet known,) how ponderous soever, will subside in water by its own weight alone, if it

were so plac'd under water, that the depth of the water did above twenty times exceed the height of the Body; (not to mention here, that though gold and water being weigh'd in the aire, their proportion is above 19 to one, yet in the water, gold does, as other sincking bodies, loose as much of its weight, as that of an equal bulk of wa∣ter amounts too.)

I was saying just now, that in case the Brazen body were plac'd low e∣enough beneath the Surface of the water, and kept from being depress'd by any incumbent water, it would be supported by the subjacent water. And this is that very thing that I am now to shew by an Experiment.

Let then the Brass body E F, be the cover of a brass Valve; (as in the annexed figure:) and let the Valve be fastned with some strong and close Cement

to a Glass pipe, O P, (open at both ends) and of a competent length and wideness. For then the Body, E F, being the undermost part of the In∣strument, and not sticking to any other part of it, will fall by its own weight if it be not supported. Now then, ty∣ing a thred to a Button Q, (that is wont to be made in the middle of the doors of Brass valves) you must, by pulling that string streight and up∣wards, make the Body, E F, shut the orifice of the Valve, as close as you can; (which is easily and presently done.) Then thrusting the Valve under water, to the depth of a foot or more; the Ce∣ment and the sides of the Glass, O P, (which reaches far above the top of the water X Y) will keep the water from coming to beare upon the upper part of the body E F; and consequent∣ly the imaginary Surface, V W, (that passes by the lower part of the said

body) will, where it is contiguous there∣unto, be press'd upon only by the pro∣per weight of the body E F; but in its other parts, by the much greater weight of the incumbent water. So that, though you let go the string, (that held the body, E F, close to the rest of the Instrument) the said body will not at all sinck, though there be no∣thing but water beneath it to support it.

And to manifest that 'tis onely the pressure of the water, of a competent depth, that keeps the solid suspended; if you slowly lift up the instrument to∣wards (X Y) the top of the water; you shall find, that, though for a while the parts of the Valve will continue u∣nited, as they were before; yet, when once it is rais'd so near the Surface, (as between the plain J K, and X Y) that the single weight of E F, upon the sub∣jacent part of the imaginary plain that

passes by it, is greater then the pressure of the incumbent water upon other parts of the same plain; that Body, being no more supported as formerly, will fall down, and the water will get into the pipe, and ascend therein, to the level of the External water.

But if, when the Valve is first thrust under water, and before you let go the thred that keeps its parts together, you thrust it down to a good depth, as to the Superficies R S: then, though you should hang a considerable weight, as L, to the Valve E F, (as I am going to shew you a Tryal with a Massy Cy∣linder of stone broader then the Valve, and of divers inches in length) the sur∣plusage of pressure on the other parts of the plain, V W, (now in R S) over and above what the weight of the body E F, and that of the Cylindrical stone, L, to boot, can amount to, on that part of the Surface vvhich is contigu∣ous

to the said body E F, will be great enough to press so hard against the lower part of the Valve, that its own weight, though assisted with that of the stone, will not be able to disjoyne them.

By which (to note that by the way) you may see, that though, when two flat and polish'd marbles are joyn'd together, we find it is impossible to se∣ver them without force; we need not have recourse to a fuga vacui, to Ex∣plicate the cause of their Cohaesion, whilst they are environ'd by the Aire, which is a Fluid not devoid of Gravi∣ty, and reaching above the Marbles no body knows how high.

And to evince, That 'tis only such a pressure of the water, as I have been declaring, that causes the Cohaesion of the parts of the Valve; if you gently lift it up towards the top of the water, you will quickly find the Brass body,

E F, drawn down by the stone (L) that hangs at it; as you will perceive by the waters getting in between the parts of the Valve, and ascending into the pipe.

To which I shall only add, what you will quickly see, That, in perfect Conformity to our Doctrine, the pres∣sure of the body, E F, upon the sub∣jacent water, being very much increa∣sed by the weight of the stone that hangs at it, the Valve needs not, as be∣fore, be lifted up above the plain J K, to overcome the resistance of the wa∣ter, being now enabled to do it before it is rais'd near so high.

Notes

• Fig. 19.
• The word, about, is added, because indeed the Author, as he else∣where delivers, did by exact scales find Brass to weigh between eight or nine times as much as water; but judg'd it needless to his pre∣sent Argument, and in∣convenient to take no∣tice of the fraction.
• Fig. 20.