Discourse on Floating Bodies Part 5

[50] Neither Figure, nor the breadth of Figure, is the Cause of Natation.

Some peradventure, by way of defence, may say, that wetting the Board of Ebony, and that in the superiour Superficies, it would, though of it self unable to pierce and penetrate the water, be born downwards, if not by the weight of the additionall water, at least by that desire and propension that the superiour parts of the water have to re-unite and rejoyn themselves: by the Motion of which parts, the said Board cometh in a certain manner, to be depressed downwards.

[Sidenote: The Bathed Solid descends not out of any affectation of union in the upper parts of the water.]

This weak Refuge will be removed, if we do but consider, that the repugnancy of the inferiour parts of the water, is as great against Dis-union, as the Inclination of its superiour parts is to union: nor can the uper unite themselves without depressing the board, nor can it descend without disuniting the parts of the nether Water: so that it doth follow, by necessary consequence, that for those respects, it shall not descend. Moreover, the same that may be said of the upper parts of the water, may with equall reason be said of the nether, namely, that desiring to unite, they shall force the said Board upwards.

Happily, some of these Gentlemen that dissent from me, will wonder, that I affirm, that the contiguous superiour Air is able to sustain that Plate of Bra.s.s or of Silver, that stayeth above water; as if I would in a certain sence allow the Air[51], a kind of Magnetick vertue of sustaining the grave Bodies, with which it is contiguous. To satisfie all I may, to all doubts, I have been considering how by some other sensible Experiment I might demonstrate, how truly that little contiguous and superiour Air sustaines those Solids, which being by nature apt to descend to the Bottom, being placed lightly on the water submerge not, unless they be first thorowly bathed; and have found, that one of these Bodies having descended to the Bottom, by conveighing to it (without touching it in the least) a little Air, which conjoyneth with the top of the same, it becometh sufficient, not only, as before to sustain it, but also to raise it, and to carry it back to the top, where it stays and abideth in the same manner, till such time, as the a.s.sistance of the conjoyned Air is taken away. And to this effect, I have taken a Ball of Wax, and made it with a little Lead, so grave, that it leasurely descends to the Bottom, making with all its Superficies very smooth and pollite: and this being put gently into the water, almost wholly submergeth, there remaining vissible only a little of the very top[52], the which so long as it is conjoyned with the Air, shall retain the Ball a-top, but the Contiguity of the Air taken away by wetting it, it shall descend to the Bottom and there remain. Now to make it by vertue of the Air, that before sustained it to return again to the top, and stay there, thrust into the water a Gla.s.s reversed with the mouth downwards, the which shall carry with it the Air it contains, and move this towards the Ball, abasing it till such time that you see, by the transparency of the Gla.s.s, that the contained Air do arrive to the summity of the _B_all[53]: then gently withdraw the Gla.s.s upwards, and you shall see the _B_all to rise, and afterwards stay on the top of the water[54], if you carefully part the Gla.s.s and the water without overmuch commoving and disturbing it.

There is, therefore, a certain affinity between the Air and other Bodies, which holds them unied, so, that they seperate not without a kind of violence. The same likewise is seen in the water[55]; for if we shall wholly submerge some Body in it, so that it be thorowly bathed, in the drawing of it afterwards gently out again, we shall see the water follow it, and rise notably above its Surface, before it seperates from it. Solid Bodies, also[56], if they be equall and alike in Superficies, so, that they make an exact Contact without the interposition of the least Air, that may part them in the seperation and yield untill that the ambient _Medium_ succeeds to replenish the place, do hold very firmly conjoyned, and are not to be seperated without great force but, because, the Air, Water, and other Liquids, very expeditiously shape themselves to contact with any Solid _B_odies, so that their Superficies do exquisitely adopt themselves to that of the Solids, without any thing remaining between them, therefore, the effect of this Conjunction and Adherence is more manifestly and frequently observed in them, than in hard and inflexible Bodies, whose Superficies do very rarely conjoyn with exactness of Contact[57]. This is therefore that Magnetick vertue, which with firm Connection conjoyneth all Bodies, that do touch without the interposition of flexible fluids; and, who knows, but that that a Contact, when it is very exact, may be a sufficient Cause of the Union and Continuity of the parts of a naturall _B_ody?

[51] _A_ Magnetisme in the _A_ir, by which it bears up those Solids in the water, that are contiguous with it.

[52] The Effect of the Airs Contiguity in the Natation of Solids.

[53] The force of Contact.

[54] _A_n Affectation of Conjunction betwixt Solids and the Air contiguous to them.

[55] The like affectation of Conjunction betwixt Solids & the water.

[56] Also the like affectation and Conjunction betwixt Solids themselves.

[57] Contact may be the Cause of the Continuity of Naturall Bodies.

Now, pursuing my purpose, I say; that it needs not, that we have recourse to the Tenacity, that the parts of the water have amongst themselves, by which they resist and oppose Division, Distraction, and Seperation, because there is no such Coherence and Resistance of Division for if there were, it would be no less in the internall parts than in those nearer the superiour or externall Surface, so that the same Board, finding alwayes the same Resistance and Renitence, would no less stop in the middle of the water than about the Surface, which is false. Moreover, what Resistance can we place in the Continuity of the water, if we see that it is impossible to find any Body of whatsoever Matter, Figure or Magnitude, which being put into the water, shall be obstructed and impeded by the Tenacity of the parts of the water to one another, so, but that it is moved upwards or downwards, according as the Cause of their Motion transports it? And, what greater proof of it can we desier, than that which we daily see in Muddy waters, which being put into Vessels to be drunk, and being, after some hours setling[58], still, as we say, thick in the end, after four or six dayes they are wholly setled, and become pure and clear?

Nor can their Resistance of Penetration stay those impalpable and insensible Atomes of Sand, which by reason of their exceeding small force, spend six dayes in descending the s.p.a.ce of half a yard.

[58] The settlement of _M_uddy Water, proveth that that Element hath no aversion to Division.

_Nor let them say, that the seeing of such small Bodies, consume six dayes in descending so little a way, is a sufficient Argument of the Waters Resistance of Division; because that is no resisting of Division, but a r.e.t.a.r.ding of Motion; and it would be simplicity to say, that a thing opposeth Division[59], and that in the same instant, it permits it self to be divided: nor doth the r.e.t.a.r.dation of Motion at all favour the Adversaries cause, for that they are to instance in a thing that wholly prohibiteth Motion, and procureth Rest; it is necessary, therefore, to find out Bodies that stay in the water, if one would shew its repugnancy to Division, and not such as move in it, howbeit but slowly._

[59] Water cannot oppose division, and at the same time permit it self to be divided.

What then is this Cra.s.situde of the water, with which it resisteth Division? What, I beseech you, should it be, if we (as we have said above) with all diligence attempting the reduction of a Matter into so like a Gravity with the water, that forming it into a dilated Plate it rests suspended as we have said, between the two waters, it be impossible to effect it, though we bring them to such an Equiponderance, that as much Lead as the fourth part of a Grain of Musterd-seed, added to the same expanded Plate, that in Air [_i. e.

out of the water_] shall weigh four or six pounds, sinketh it to the Bottom, and being substracted, it ascends to the Surface of the water?

I cannot see, (if what I say be true, as it is most certain) what minute vertue and force we can possibly find or imagine, to which the Resistance of the water against Division and Penetration is not inferiour; whereupon, we must of necessity conclude that it is nothing: because, if it were of any sensible power, some large Plate might be found or compounded of a Matter alike in Gravity to the water, which not only would stay between the two waters; but, moreover, should not be able to descend or ascend without notable force. We may likewise collect the same from an other Experiment[60], shewing that the Water gives way also in the same manner to transversall Division; for if in a setled and standing water we should place any great Ma.s.s that goeth not to the bottom, drawing it with a single Womans Hair, we might carry it from place to place without any opposition, and this whatever Figure it hath, though that it possess a great s.p.a.ce of water, as for instance, a great Beam would do moved side-ways. Perhaps some might oppose me and say, that if the Resistance of water against Division, as I affirm, were nothing; s.h.i.+ps should not need such a force of Oars and Sayles for the moving of them from place to place in a tranquile Sea, or standing Lake. To him that should make such an objection, I would reply[61], that the water contrasteth not against, nor simply resisteth Division, but a sudden Division, and with so much greater Renitence, by how much greater the Velocity is: and the Cause of this Resistance depends not on Cra.s.situde, or any other thing that absolutely opposeth Division, but because that the parts of the water divided, in giving way to that Solid that is moved in it, are themselves also necessitated locally to move, some to the one side, and some to the other, and some downwards: and this must no less be done by the waves before the s.h.i.+p, or other Body swimming through the water, than by the posteriour and subsequent; because, the s.h.i.+p proceeding forwards, to make it self a way to receive its Bulk, it is requisite, that with the Prow it repulse the adjacent parts of the water, as well on one hand as on the other, and that it move them as much transversly, as is the half of the breadth of the Hull: and the like removall must those waves make, that succeeding the Poump do run from the remoter parts of the s.h.i.+p towards those of the middle, successively to replenish the places, which the s.h.i.+p in advancing forwards, goeth, leaving vacant. Now, because, all Mot.i.tions are made in Time[62], and the longer in greater time: and it being moreover true, that those Bodies that in a certain time are moved by a certain power such a certain s.p.a.ce, shall not be moved the same s.p.a.ce, and in a shorter Time, unless by a greater Power: therefore, the broader s.h.i.+ps move slower than the narrower, being put on by an equall Force: and the same Vessel requires so much greater force of Wind, or Oars, the faster it is to move.

[60] An hair will draw a great Ma.s.s thorow the Water; which proveth, that it hath no Resistance against transversall Division.

[61] How s.h.i.+ps are moved in the water.

[62] Bodies moved a certain s.p.a.ce in a certain Time, by a certain power, cannot be moved the same s.p.a.ce and in a shorter time, but by a greater power.

_But yet for all this, any great Ma.s.s swimming in a standing Lake, may be moved by any pet.i.t force; only it is true, that a lesser force more slowly moves it: but if the waters Resistance of Division, were in any manner sensible, it would follow, that the said Ma.s.s, should, notwithstanding the percussion of some sensible force, continue immoveable, which is not so[63]. Yea, I will say farther, that should we retire our selves into the more internall contemplation of the Nature of water and other Fluids, perhaps we should discover the Const.i.tution of their parts to be such, that they not only do not oppose Division, but that they have not any thing in them to be divided: so that the Resistance that is observed in moving through the water[64], is like to that which we meet with in pa.s.sing through a great Throng of People, wherein we find impediment, and not by any difficulty in the Division, for that none of those persons are divided whereof the Croud is composed, but only in moving of those persons side-ways which were before divided and disjoyned: and thus we find Resistance in thrusting a Stick into an heap of Sand, not because any part of the Sand is to be cut in pieces, but only to be moved and raised[65]. Two manners of Penetration, therefore, offer themselves to us, one in Bodies, whose parts were continuall, and here Division seemeth necessary, the other in the aggregates of parts not continuall, but contiguous only[66], and here there is no necessity of dividing but of moving only. Now, I am not well resolved, whether water and other Fluids may be esteemed to be of parts continuall or contiguous only[67]; yet I find my self indeed inclined to think that they are rather contiguous (if there be in Nature no other manner of aggregating, than by the union, or by the touching of the extreams:) and I am induced thereto by the great difference that I see between the Conjunction of the parts of an hard or Solid Body[68], and the Conjunction of the same parts when the same Body shall be made Liquid and Fluid: for if, for example, I take a Ma.s.s of Silver or other Solid and hard Mettall, I shall in dividing it into two parts, find not only the resistance that is found in the moving of it only[69], but an other incomparably greater, dependent on that vertue, whatever it be, which holds the parts united: and so if we would divide again those two parts into other two, and successively into others and others, we should still find a like Resistance, but ever less by how much smaller the parts to be divided shall be; but if, lastly, employing most subtile and acute Instruments, such as are the most tenuous parts of the Fire, we shall resolve it (perhaps) into its last and least Particles, there shall not be left in them any longer either Resistance of Division, or so much as a capacity of being farther divided, especially by Instruments more grosse than the acuities of Fire: and what Knife or Rasor put into well melted Silver can we finde, that will divide a thing which surpa.s.seth the separating power of Fire? Certainly none: because either the whole shall be reduced to the most minute and ultimate Divisions, or if there remain parts capable still of other Subdidivisions, they cannot receive them, but only from acuter Divisors than Fire; but a Stick or Rod of Iron, moved in the melted Metall, is not such a one. Of a like Const.i.tution and Consistence, I account the parts of Water[70], and other Liquids to be, namely, incapable of Division by reason of their Ienuity; or if not absolutely indivisible, yet at least not to be divided by a Board, or other Solid Body, palpable unto the hand, the Sector being alwayes required to be more sharp than the Solid to be cut. Solid Bodies, therefore, do only move, and not divide the Water[71], when put into it; whose parts being before divided to the extreamest minuity, and therefore capable of being moved, either many of them at once, or few, or very few, they soon give place to every small Corpuscle, that descends in the same: for that, it being little and light, descending in the Air, and arriving to the Surface of the Water, it meets with Particles of Water more small, and of less Resistance against Motion and Extrusion, than is its own prement and extrusive force; whereupon it submergeth, and moveth such a portion of them, as is proportionate to its Power. There is not, therefore, any Resistance in Water against Division, nay, there is not in it any divisible parts. I adde; moreover, that in case yet there should be any small Resistance found (which is absolutely false)[72] haply in attempting with an Hair to move a very great natant Machine, or in essaying by the addition of one small Grain of Lead to sink, or by removall of it to raise a very broad Plate of Matter, equall in Gravity with Water, (which likewise will not happen, in case we proceed with dexterity) we may observe that that Resistance is a very different thing from that which the Adversaries produce for the Cause of the Natation of the Plate of Lead or Board of Ebony, for that one may make a Board of Ebony, which being put upon the Water swimmeth, and cannot be submerged, no not by the addition of an hundred Grains of Lead put upon the same, and afterwards being bathed, not only sinks, though the said Lead be taken away, but though moreover a quant.i.ty of Cork, or of some other light Body fastened to it, sufficeth not to hinder it from sinking unto the bottome: so that you see, that although it were granted that there is a certain small Resistance of Division found in the substance of the Water, yet this hath nothing to do with that Cause which supports the Board above the Water, with a Resistance an hundred times greater than that which men can find in the parts of the Water: nor let them tell me, that only the Surface of the Water hath such Resistance[73], and not the internall parts, or that such Resistance is found greatest in the beginning of the Submersion, as it also seems that in the beginning, Motion meets with greater opposition, than in the continuance of it; because, first, I will permit, that the Water be stirred, and that the superiour parts be mingled with the middle[74], and inferiour parts, or that those above be wholly removed, and those in the middle only made use off, and yet you shall see the effect for all that, to be still the same: Moreover, that Hair which draws a Beam through the Water, is likewise to divide the upperparts, and is also to begin the Motion, and yet it begins it, and yet it divides it: and finally, let the Board of Ebony be put in the midway, betwixt the bottome and the top of the Water, and let it there for awhile be suspended and setled, and afterwards let it be left at liberty, and it will instantly begin its Motion, and will continue it unto the bottome. Nay, more, the Board so soon as it is dimitted upon the Water, hath not only begun to move and divide it, but is for a good s.p.a.ce dimerged into it._

[63] The parts of Liquids, so farre from resisting Division, that they contain not any thing that may be divided.

[64] The Resistance a Solid findeth in moving through the water, like to that we meet with in pa.s.sing through a throng of people:

[65] Or in thrusting a Stick into an heap of Sand.

[66] Two kinds of Penetration, one in Bodies continuall, the other in Bodies only contiguous.

[67] Water consists not of continuall, but only of contiguous parts.

[68] _Se{e} what satisfaction he hath given, as to this point, in Lib. de Motu. Dial. 2._

[69] Great difference betwixt the Conjunction of the parts of a Body when Solid, and when fluid.

[70] Water consists of parts that admit of no farther division.

[71] Solids dimitted into the water, do onely move, and not divide it.

[72] If there were any Resistance of Division in water, it must needs be small, in that it is overcome by an Hair, a Grain of Lead, or a slight bathing of the Solid.

[73] The uper parts of the Water, do no more resist Division than the middle or lower parts.

[74] Waters Resistance of division, not greater in the beginning of the Submersion.

Let us receive it, therefore, for a true and undoubted Conclusion, That the Water hath not any Renitence against simple Division, and that it is not possible to find any Solid Body, be it of what Figure it will, which being put into the Water, its Motion upwards or downwards, according as it exceedeth, or shall be exceeded by the Water in Gravity (although such excesse and difference be insensible) shall be prohibited, and taken away, by the Cra.s.situde of the said Water. When, therefore, we see the Board of Ebony, or of other Matter, more grave than the Water, to stay in the Confines of the Water and Air, without submerging, we must have recourse to some other Originall, for the investing the Cause of that Effect, than to the breadth of the Figure, unable to overcome the Renitence with which the Water opposeth Division, since there is no Resistance; and from that which is not in being, we can expect no Action. It remains most true, therefore, as we have said before, that this so succeds, for that that which in such manner put upon the water, not the same Body with that which is put _into_ the Water: because this which is put _into_ the Water, is the pure Board of Ebony, which for that it is more grave than the Water, sinketh, and that which is put _upon_ the Water, is a Composition of Ebony, and of so much Air, that both together are specifically less grave than the Water, and therefore they do not descend.

I will farther confirm this which I say. Gentlemen, my Antagonists, we are agreed, that the excess or defect of the Gravity of the Solid, unto the Gravity of the Water, is the true and proper Cause of Natation or Submersion.

[Sidenote: Great Caution to be had in experimenting the operation of Figure in Natation.]

Now, if you will shew that besides the former Cause, there is another which is so powerfull, that it can hinder and remove the Submersion of those very Solids, that by their Gravity sink, and if you will say, that this is the breadth or ampleness of Figure, you are oblieged, when ever you would shew such an Experiment, first to make the circ.u.mstances certain, that that Solid which you put into the Water, be not less grave _in specie_ than it, for if you should not do so, any one might with reason say, that not the Figure, but the Levity was the cause of that Natation. But I say, that when you shall dimit a Board of Ebony into the Water, you do not put therein a Solid more grave _in specie_ than the Water, but one lighter, for besides the Ebony, there is in the Water a Ma.s.s of Air, united with the Ebony, and such, and so light, that of both there results a Composition less grave than the Water: See, therefore, that you remove the Air, and put the Ebony alone into the Water, for so you shall immerge a Solid more grave then the Water, and if this shall not go to the Bottom, you have well Philosophized and I ill.

Now, since we have found the true Cause of the Natation of those Bodies, which otherwise, as being graver than the Water, would descend to the bottom, I think, that for the perfect and distinct knowledge of this business, it would be good to proceed in a way of discovering demonstratively those particular Accidents that do attend these effects, and,

PROBL. I.

[Sidenote: To finde the proportion Figures ought to have to the waters Gravity, that by help of the contiguous Air, they may swim.]

_To finde what proportion severall Figures of different Matters ought to have, unto the Gravity of the Water, that so they may be able by vertue of the Contiguous Air to stay afloat._

[Ill.u.s.tration]

Let, therefore, for better ill.u.s.tration, D F N E be a Vessell, wherein the water is contained, and suppose a Plate or Board, whose thickness is comprehended between the Lines I C and O S, and let it be of Matter exceeding the water in Gravity, so that being put upon the water, it dimergeth and abaseth below the Levell of the said water, leaving the little Banks A I and B C, which are at the greatest height they can be, so that if the Plate I S should but descend any little s.p.a.ce farther, the little Banks or Ramparts would no longer consist, but expulsing the Air A I C B, they would diffuse themselves over the Superficies I C, and would submerge the Plate. The height A I B C is therefore the greatest profundity that the little Banks of water admit of. Now I say, that from this, and from the proportion in Gravity, that the Matter of the Plate hath to the water, we may easily finde of what thickness, at most, we may make the said Plates, to the end, they may be able to bear up above water: for if the Matter of the Plate or Board I S were, for Example, as heavy again as the water, a Board of that Matter shall be, at the most of a thickness equall to the greatest height of the Banks, that is, as thick as A I is high: which we will thus demonstrate. Let the Solid I S be double in Gravity to the water, and let it be a regular Prisme, or Cylinder, to wit, that hath its two flat Superficies, superiour and inferiour, alike and equall, and at Right Angles with the other laterall Superficies, and let its thickness I O be equall to the greatest Alt.i.tude of the Banks of water: I say, that if it be put upon the water, it will not submerge: for the Alt.i.tude A I being equall to the Alt.i.tude I O, the Ma.s.s of the Air A B C I shall be equall to the Ma.s.s of the Solid C I O S: and the whole Ma.s.s A O S B double to the Ma.s.s I S; And since the Ma.s.s of the Air A C, neither encreaseth nor diminisheth the Gravity of the Ma.s.s I S, and the Solid I S was supposed double in Gravity to the water; Therefore as much water as the Ma.s.s submerged A O S B, compounded of the Air A I C B, and of the Solid I O S C, weighs just as much as the same submerged Ma.s.s A O S B: but when such a Ma.s.s of water, as is the submerged part of the Solid, weighs as much as the said Solid, it descends not farther, but resteth, as by (_a_) _Archimedes_[75], and above by us, hath been demonstrated: Therefore, I S shall descend no farther, but shall rest. And if the Solid I S shall be Sesquialter in Gravity to the water, it shall float, as long as its thickness be not above twice as much as the greatest Alt.i.tude of the Ramparts of water, that is, of A I. For I S being Sesquialter in Gravity to the water, and the Alt.i.tude O I, being double to I A, the Solid submerged A O S B, shall be also Sesquialter in Ma.s.s to the Solid I S. And because the Air A C, neither increaseth nor diminisheth the ponderosity of the Solid I S: Therefore, as much water in quant.i.ty as the submerged Ma.s.s A O S B, weighs as much as the said Ma.s.s submerged: And, therefore, that Ma.s.s shall rest. And briefly in generall.

[75] Of Natation Lib. 1. Prop. 3.

[Ill.u.s.tration]