The works of the Honourable Robert Boyle, Esq., epitomiz'd by Richard Boulton ... ; illustrated with copper plates.

PARADOX VI. If a Body placed under Water, [paradox VI] with its upper∣most Surface parallel to the Horrizon, how much Water soever there may be on this or that side above the Body, the direct Pressure sustained by the Body (for we now consider not the La∣teral or the recoiling Pressure, to which the Body may be exposed, if quite environed with Water) is no more than that of a Column of Water, having the Horizontal superficies of the Body for its Basis, and the Perpendicular depth of the Water for its height.

And so likewise, If the Water that leans upon the Body be contained in Pipes open at both ends, the Pressure of the Water is to be estimated by the weight of a Pil∣lar of Water, whose Basis is equal to the lower Orifice of a Pipe, (which we suppose to be pa∣rallel to the Horizon) and its height equal to a Perpendicular, reaching thence to the top of the Water; tho' the Pipe be much inclined towards the Horizon, or tho' it be irregularly shaped, and much broader in some Parts, than the said Orifice.

As for the first part of our Paradox, it is proposed by Stevinus in more general Terms, and thus demonstrated, (See Fig. 7. Plate the second) where, supposing A B C D to be a solid Rectangular figure of Water, whose Ba∣sis E F is parallel to the Horizon, and whose

height G E is a Perpendicular from the Surface of that Water, the bottom D E, E F, and F C cannot be charged with a greater weight than what is respectively Perpendicular, be∣cause none of them can receive an Additional weight from the Water Collaterally, but it must diminish the weight of Water Per∣pendicularly incumbent on that other bottom, else there must be a greater weight upon the Basis D E F C, than is contained in the Surface A B. C D, which is impossible.

To which instance of the learned Stevinus I shall add the following. For if Oyl be suck'd up into the Pipe represented by Fig. 8 Plate the second, and when it is at a convenient height in the longer Leg, you nimbly stop the upper Orifice, till it be depressed so low into the Wa∣ter, that the Oyl is but little above the Surface of the Water, it will rest near that station, when the upper Orifice is unstopped; and if it be depressed lower than that, the weight of the incumbent Pillar of Water will force its way into the Pipe, so far as answers the weight of a Cylinder of Water of an equal Bore with the Oyl contained in the Pipe, and on the con∣trary, if the Pipe be elevated above its first station, as much Oyl will rise out of the Pipe and emerge, as answers in weight to the part of the incumbent Pillar of Water removed by that means from gravitating upon it. And to this I shall add, that tho' Water is not con∣tained in Pipes, yet it presses as regularly upon subjacent Bodies as if it were; which will be e∣vident, if a Vessel of the shape of the Funnel de∣lineated in Fig. the 6th be imployed, for

the Liquor contained in the small Stem of that will be able to sustain the whole incumbent Wa∣ter: In confirmation of which, we made use of such a Vessel, as Plate the third, figure the first represents,* 1.1 and filling the parallel Leg with Oyl, and the other as well as the Ball with Water, the Oyl was elevated no higher in the longer Leg, than if the less Leg had been an uniform Tube of the same Diameter; and when the Ex∣periment was reiterated with Oyl in the Ball, and Water in the long Leg, the weight of that Oyl was not able to raise the Water in the long Leg to an equal superficies with it self; the Liquors in both these Experiments which was contained in the capacity of the Ball, being sustained by the concave sides of the Glass. And the like Experiment being tryed with Quick-silver, which was poured into the shor∣ter Leg C D, till it rought almost to the bottom of the Ball, and as high in the longer Tube A B, upon an affusion of Water into the long∣er Leg, the Mercury was buoyed up into the Ball, till it rought to H E G, where if more than what was Perpendicularly incumbent on the Tube C had pressed upon it, the Water would not have been able to keep it at such a height.

But to confirm the second part of our Para∣dox,* 1.2 we made use of a Glass, such as Plate the third Fig. the second represents, and having filled the Glass half full of Water, we stop∣ped it with a Cork, in which the Pipes there delineated were fixed, and likewise the Tun∣nel, the bottom of each of the Pipes, being each immersed considerably in Water, and

then pouring in Oyl through the Tunnel, we observed, that the Water was elevated to an equal height from the lower superficies of the Oyl which pressed on the Water; in which Ex∣periment, tho' the Pipes contained more Wa∣ter by being included, yet that Water pressed no more upon the imaginary Plain, than an e∣rect Pipe of equal Bore with the lower super∣ficies of the Water contained in it would have done. And if Oyl of Turpentine be poised in a Pipe in an erect Posture, and then by inclination a greater portion of it brought under Water, yet the external Water will raise the Oyl con∣tained in it; and the same was evident, when Oyl of Turpentine being contained in three Pipes of such figures as Plate the third Fig. the third represents, for in all such cases,* 1.3 where the Pipes are in an inclined Posture, or some Parts of them larger than ordinary, part of the weight of the Liquors contained weigh upon the sides of the Vessel, and no more presses up∣on the subjacent Liquor, than is answerable to an erect Pipe of equal Bore with the lower Orifice, and of equal height with an erect Tube, answerable to the length of one end of that Pipe from the other.

To make out what Stevinus hath asserted, viz. That if a Cylinder of Water be placed upon a subjacent Body, the Basis will sustain a weight equal to that Circular Basis, and to the Perpendicular height of it, we provided a Vessel of Laton,* 1.4 of the figure represented by Fig. twelve Plate the third, which being furnished with a close bottom C D, made of a flat piece of Wood, covered with a soft Bladder,

and greased on the lower side near the edges, that leaned on the rim of Wood G H, contigu∣ous every where to the inside of the Latten, that it might be easily lifted up from off the rim, and yet at other times lye so close upon it, that the Water should not be able to get out between them. To the midst of this bottom was fastned a long string, for a use to be here∣after mention'd; the Instrument being thus prepared, the Water was poured in at the top of the Pipe A B, which pressing upon the false bottom C D, against the subjacent rim G H, con∣tributed to render the Vessel more close, and to obstruct its own passage, whereupon we tyed the upper end of the string I K to a beam, and put so many weights into the opposite Scale, as were sufficient to raise the false bottom C D from the rim G H. And then deducting from that weight, the weight of the false bottom, and the Water contained in the broad Cylindri∣cal Box B E C H. G D F, we found that the Pres∣sure, which was made upon C D was much greater than what reading Stevinus would make one expect, and than all the Water contained both in the Pipe and Cylinder would have been, had it been contained in an uniform Cylin∣der.

Notes

• * 1.1

  See Plate 3. Fig. 1.
• * 1.2

  See Plate 3. Fig. 2.
• * 1.3

  See Fig. 3. Plate 3.
• * 1.4

  See Fig. 4. Plate 3.