ARule to equilibrate Solids in the water.
It followes, moreover, that a Solid less grave than the water, being put into a Vessell of any imaginable greatness, and water being circumfused about it to such a height, that as much water in Mass, as is the part of the Solid submerged, do weigh absolutely as much as the whole Solid; it shall by that water be justly sustained, be the circumfused Water in quantity greater or lesser.
For, if the Cylinder or Prisme M, less grave than the water,v. gra.in Subsequiteriall proportion, shall be put into the capacious Vessell A B C D, and the water raised about it, to three quarters of itsheight, namely, to its Levell A D: it shall be sustained and exactly poysed inEquilibrium. The same will happen;if the Vessell E N S Fwere very small, so, that between the Vessell and the Solid M, there were but a very narrow space, and only capable of so much water, as the hundredth part of the Mass M, by which it should be likewise raised and erected, as before it had been elevated to three fourths of the height of the Solid: which to many at the first sight, may seem a notable Paradox, and beget a conceit, that the Demonstration of these effects, were sophisticall and fallacious: but, for those who so repute it, the Experiment is a means that may fully satisfie them. But he that shall but comprehend of what Importance Velocity of Motion is, and how it exactly compensates the defect and want of Gravity, will cease to wonder, in considering that at the elevation of the Solid M, the great Mass of water A B C D abateth very little, but the little Mass of water E N S F decreaseth very much, and in an instant, as the Solid M before did rise, howbeit for a very short space: Whereupon the Moment, compounded of the small Absolute Gravity of the water E N S F, and of its great Velocity in ebbing,equalizeth the Force and and Moment,that results from the composition of the immense Gravity of the water A B C D, with its great slownesse of ebbing; since that in the Elevation of the Sollid M, the abasement of the lesser water E S, is performed just so much more swiftly than the great Mass of water A C, as this is more in Mass than that which we thus demonstrate.
The proportion according to which water riseth and falls in different Vessels at the Immersion and Elevation of Solids.
In the rising of the Solid M, its elevation hath the same proportion to the circumfused water E N S F, that the Surface of the said water, hath to the Superficies or Base of the said Solid M; which Base hath the same proportion to the Surface of the water A D, that theabasement or ebbing of the water A C, hath to the rise or elevation of the said Solid M. Therefore, by Perturbation of proportion, in the ascent of the said Solid M, the abasement of the water A B C D, to the abasement of the water E N S F, hath the same proportion, that the Surface of the water E F, hath to the Surface of the water A D; that is, that the whole Mass of the water E N S F, hath to the whole Mass A B C D, being equally high: It is manifest, therefore, that in the expulsion and elevation of the Solid M, the water E N S F shall exceed in Velocity ofMotion the water A B C D, asmuch as it on the other side is exceeded by that in quantity: whereupon their Moments in such operations, are mutually equall.
And, for ampler confirmation, and clearer explication of this, let us consider the present Figure, (which if I be not deceived, may serve to detect the errors of some Practick Mechanitians who upon a false foundation some times attempt impossible enterprizes,) in which, unto the large Vessell E I D F, the narrow Funnell or Pipe I C A B is continued, and suppose water infused into them, unto the Levell L G H, which water shall rest in this position, not without admiration in some, who cannot conceive how it can be, that theheavie charge of the great Mass of water G D, pressing downwards, should not elevate and repulse the little quantity of the other, contained in the Funnell or Pipe C L, by which the descent of it is resisted and hindered: But such wonder shall cease, if we begin to suppose the water G D to be abased only to Q D, and shall afterwards consider, what the water C L hath done, which to give place to the other, which is descended from the Levell G H, to the Levell Q O, shall of necessity have ascended in the same time, from the Levell L unto A B. And the ascent L B, shall be so much greater than the descent G Q, by how much the breadth of the Vessell G D, is greater than that of the Funnell I C; which, in summe, is as much as the water G D, is more than the water L C: but in regard that the Moment of the Velocity of the Motion, in one Moveable, compensates that of the Gravity of another what wonder is it, if the swift ascent of the lesser Water C L, shall resist the slow descent of the greater G D?
The same, therefore, happens in this operation,as in rhe Stilliard,in which a weight of two pounds counterpoyseth an other of 200,asoften as thatshall move in the same time, a space 100 times greater than this: which falleth out when one Arme of the Beam is an hundredtimes as long as the other. Let the erroneous opinion of those therefore cease, who hold that a Ship is better, and easier born up inA ship flotes as well in ten Tun of Water as in an Ocean.a great abundance of water, then in a lesser quantity, (this was believed byAristotlein his Problems, Sect. 23, Probl. 2.) it being on the contrary true, that its possible, that a Ship may as well float in ten Tun of water, as in an Ocean.
A Solidspecifiacllygraver than the water, cannot be born up by any quantity of it.
But following our matter, I say, that by what hath been hitherto demonstrated, we may understand how, that
One of the above named Solids, when more gravein speciethan the water, can never be sustained, by any whatever quantity of it.
For having seen how that the Moment wherewith such a Solid, as gravein specieas the water, contrasts with the Moment of any Mass of water whatsoever, is able to retain it, even to its totall Submersion, without its ever ascending; it remaineth, manifest, that the water is far less able to raise it up, when it exceeds the samein specie: so, that though you infuse water till its totall Submersion, it shall still stay at the Bottome, and with such Gravity, and Resistance to Elevation, as is the excess of its Absolute Gravity, above the Absolute Gravity of a Mass equall to it, made of water, or of a Matterin specieequally grave with the water: and, though you should moreover adde never so much water above the Levell of that which equalizeth the Altitude of the Solid, it shall not, for all that, encrease the Pression, or Gravitation, of the parts circumfused about the said Solid, by which greater pression, it might come to be repulsed; because, the Resistance is not made, but only by those parts of the water, which at the Motion of the said Solid do also move, and these are those only, which are comprehended by the two Superficies equidistant to the Horizon, and their parallels, that comprehend the Altitude of the Solid immerged in the water.
I conceive, I have by this time sufficiently declared and opened the way to the contemplation of the true, intrinsecall and proper Causes of diverse Motions, and of the Rest of many Solid Bodies in diverseMediums, and particularly in the water, shewing how all in effect, depend on the mutuall excesses of the Gravity of the Moveables and of theMediums: and, that which did highly import, removing the Objection, which peradventure would have begotten much doubting, and scruple in some, about the verity of my Conclusion, namely, how that notwithstanding, that the excess of the Gravity of the water, above the Gravity of the Solid, demitted into it, be the cause of its floating and rising from the Bottom to the Surface, yet a quantity of water, that weighs not ten pounds, can raise a Solid that weighs above100 pounds: in that we have demonstrated, That it sufficeth, that such difference be found between the Specificall Gravities of theMediumsand Moveables, let the particular and absolute Gravities be what they will: insomuch, that a Solid, provided that it be Specifically less grave than the water, although its absolute weight were 1000 pounds, yet may it be born up and elevated by ten pounds of water, and less: and on the contrary, another Solid, so that it be Specifically more grave than the water, though in absolute Gravity it were not above a pound, yet all the water in the Sea, cannot raise it from the Bottom, or float it. This sufficeth me, for my present occasion, to have, by the above declared Examples, discovered and demonstrated, without extending such matters farther, and, as I might have done, into a long Treatise: yea, but that there was a necessity of resolving the above proposed doubt, I should have contented my self with that only, which is demonstrated byArchimedes, in his firstBook De Insidentibus humido: where in generall termes he infers and confirms the sameOf Natation(a)Lib. 1, Prop. 4.(b)Id. Lib. 1. Prop. 3.(c)Id. Lib. 1. Prop. 3.Conclusions, namely, that Solids (a) less grave than water, swim or float upon it, the (b) more grave go to the Bottom, and the (c) equally grave rest indifferently in all places, yea, though they should be wholly under water.
The Authors defence ofArchimedeshis Doctrine, against the oppositions ofBuonamico.
But, because that this Doctrine of Archimedes, perused, transcribed and examined bySignor Francesco Buonamico, in hisfifth Book of Motion, Chap. 29, and afterwards by him confuted, might by the Authority of so renowned, and famous a Philosopher, be rendered dubious, and suspected of falsity; I have judged it necessary to defend it, if I am able so to do, and to clearArchimedes, from those censures, with which he appeareth to be charged.Buonamicorejecteth the Doctrine ofArchimedes, first, as not consentaneousHis first Objection against the Doctrine ofArchimedes.with the Opinion ofAristotle, adding, that it was a strange thing to him, that the Water should exceed the Earth in Gravity, seeing onHis Second Objection.the contrary, that the Gravity of water, increaseth, by means of the participation of Earth. And he subjoyns presently after, that he wasHis third Objection.not satisfied with the Reasons ofArchimedes, as not being able with that Doctrine, to assign the cause whence it comes, that a Boat and a Vessell, which otherwise, floats above the water, doth sink to the Bottom, if once it be filled with water; that by reason of the equality of Gravity, between the water within it, and the other water without, it should stay a top; but yet, nevertheless, we see it to go to the Bottom.
He farther addes, thatAristotlehad clearly confuted the Ancients,His fourth Objection.who said, that light Bodies moved upwards, driven by the impulse ofTheAncients denyedAbsolute Levity.the more grave Ambient: which if it were so, it should seem of necessity to follow, that all naturall Bodies are by nature heavy, andnone light: For that the same would befall the Fire and Air, if put in the Bottom of the water. And, howbeit,Aristotlegrants a Pulsion in the Elements, by which the Earth is reduced into a Sphericall Figure, yet nevertheless, in his judgement; it is not such that it can remove grave Bodies from their naturall places, but rather, that it send them toward the Centre, to which (as he somewhat obscurely continues to say,) the water principally moves, if it in the interim meet not with something that resists it, and, by its Gravity, thrusts it out of its place: in which case, if it cannot directly, yet at least as well as it can, it tends to the Centre: but it happens, that light Bodies by such Impulsion, do all ascend upward:but this properly they haveby nature, as also, that other of swimming. He concludes, lastly, that heThe causes of Natation & Submersion, according to the Peripateticks.concurs withArchimedesin his Conclusions; but not in the Causes, which he would referre to the facile and difficult Separation of theMedium, and to the predominance of the Elements, so that when the Moveable superates the power of theMedium; as for example, Lead doth the Continuity of water, it shall move thorow it, else not.
This is all that I have been able to collect, as produced againstArchimedesbySignor Buonamico: who hath not well observed the Principles and Suppositions ofArchimedes; which yet must be false, if the Doctrine be false, which depends upon them; but is contented to alledge therein some Inconveniences, and some Repugnances to the Doctrine and Opinion ofAristotle. In answer to which Objections, I say, first, That the being ofArchimedesDoctrine, simply differentThe Authors answer to the first Objection.from the Doctrine ofAristotle, ought not to move any to suspect it, there being no cause, why the Authority of this should be preferred to the Authority of the other: but, because, where the decrees of Nature are indifferently exposed to the intellectuall eyes of each, the Authority of the one and the other,loseth all a{u}thenticalnessof Perswasion, the absolute power residing in Reason; therefore I pass to that which he alledgeth in the second place, as an absurd consequentThe Authors answer to the second Objection.of the Doctrine ofArchimedes, namely, That water should be more grave than Earth. But I really find not, that everArchimedessaid such a thing, or that it can be rationally deduced from his Conclusions: and if that were manifest unto me, I verily believe, I should renounce his Doctrine, as most erroneous. Perhaps this Deduction ofBuonamico, is founded upon that which he citeth of the Vessel, which swims as long as its voyd of water, but once full it sinks to the Bottom, and understanding it of a Vessel of Earth, he infers againstArchimedesthus: Thou sayst that the Solids which swim, are less grave than water: this Vessell swimmeth: therefore, this Vessell is lesse grave than water. If this be the Illation. Ieasily answer, granting that this Vessell is lesse grave than water, and denying the other consequence, namely, that Earth is less Grave than Water. The Vessel that swims occupieth in the water, not only a place equall to the Mass of the Earth, of which it is formed; but equall to the Earth and to the Air together, contained in its concavity. And, if such a Mass compounded of Earth and Air, shall be less grave than such another quantity of water, it shall swim, and shall accord with the Doctrine ofArchimedes; but if, again, removing the Air, the Vessell shall be filled with water, so that the Solid put in the water, be nothing but Earth, nor occupieth other place, than that which is only possest by Earth, it shall then go to the Bottom, by reason that the Earth is heavier than the water: and this corresponds well with the meaning ofArchimedes. See the same effect illustrated, with such another Experiment, In pressing a Viall Glass to the Bottom of the water, when it is full of Air, it will meet with great resistance, because it is not the Glass alone, that is pressed under water, but together with the Glass a great Mass of Air, and such, that if you should take as much water, as the Mass of the Glass, and of the Air contained in it, you would have a weight much greater than that of the Viall, and of its Air: and, therefore, it will not submerge without great violence: but if we demit only the Glass into the water, which shall be when you shall fill the Glass with water, then shall the Glass descend to the Bottom; as superiour in Gravity to the water.
Returning, therefore, to our first purpose; I say, that Earth is more grave than water, and that therefore, a Solid of Earth goeth to the bottom of it; but one may possibly make a composition of Earth and Air, which shall be less grave than a like Mass of Water; and this shall swim: and yet both this and the other experiment shall very well accord with the Doctrine ofArchimedes. But because that in my judgment it hath nothing of difficulty in it, I will not positively affirme thatSignor Buonamico, would by such a discourse object untoArchimedesthe absurdity of inferring by his doctrine, that Earth was less grave than Water, though I know not how to conceive what other accident he could have induced thence.
Perhaps such a Probleme (in my judgement false) was read bySignor Buonamicoin some other Author, by whom peradventure it was attributed as a singular propertie, of some particular Water, and so comes now to be used with a double errour in confutation ofArchimedes, since he saith no such thing, nor by him that did say it was it meant of the common Element of Water.
The Authors answer to the third Objection.
The third difficulty in the doctrine ofArchimedeswas, that he could not render a reason whence it arose, that a piece of Wood, and a Vessell of Wood, which otherwise floats, goeth to the bottom, if filled with Water.Signor Buonamicohath supposed that a Vessell of Wood, and of Wood that by nature swims, as before is said, goes to thebottom, if it be filled with water; of which he in the following Chapter, which is the 30 of the fifth Book copiously discourseth: but I (speaking alwayes without diminution of his singular Learning) dare in defence ofArchimedesdeny this experiment, being certain that a piece of Wood which by its nature sinks not in Water, shall not sinke though it be turned and converted into the forme of any Vessell whatsoever, and then filled with Water: and he that would readily see the Experiment in some other tractable Matter, and that is easily reduced into several Figures, may take pure Wax, and making it first into a Ball or other solid Figure, let him adde to it so much Lead as shall just carry it to the bottome, so that being a graine less it could not be able to sinke it, and making it afterwards into the forme of a Dish, and filling it with Water, he shall finde that without the said Lead it shall not sinke, and that with the Lead it shall descend with much slowness: & in short he shall satisfie himself, that the Water included makes no alteration. I say not all this while, but that its possible of Wood to make Barkes, which being filled with water, sinke; but that proceeds not through its Gravity, encreased by the Water, but rather from the Nailes and other Iron Workes, so that it no longer hath a Body less grave than Water, but one mixt of Iron and Wood, more grave than a like Masse of Water. Therefore letSignor Buonamicodesist from desiring a reason of an effect, that is not in nature: yea if the sinking of the Woodden Vessell when its full of Water, may call in question the Doctrine ofArchimedes, which he would not have you to follow, is on the contrary consonant and agreeable to the Doctrine of the Peripateticks, since it aptly assignes a reason why such a Vessell must, when its full of Water, descend to the bottom; converting the Argument the other way, we may with safety say that the Doctrine ofArchimedesis true, since it aptly agreeth with true experiments, and question the other, whose Deductions are fastened upon erroneouss Conclusions. As for the other point hinted in this same Instance, where itseemes thatBenonamicounderstands the same not only of a piece of wood, shaped in the forme of a Vessell, but also of massie Wood, which filled,scilicet, as I believe, he would say, soaked and steeped in Water, goes finally to the bottom that happens in some porose Woods, which, while their Porosity is replenished with Air, or other Matter less grave than Water, are Masses specificially less grave than the said Water, like as is that Viall of Glass whilest it is full of Air: but when, such light Matter departing, there succeedeth Water into the same Porosities and Cavities, there results a compound of Water and Glass more grave than a like Mass of Water: but the excess of its Gravity consists in the Matter of the Glass, and not in the Water, which cannot be graver than it self: so that which remaines of the Wood, theAir of its Cavities departing, if it shall be more gravein speciethan Water, fil but its Porosities with Water, and you shall have a Compost of Water and of Wood more grave than Water, but not by vertue of the Water received into and imbibed by the Porosities, but of that Matter of the Wood which remains when the Air is departed: and being such it shall, according to the Doctrine ofArchimedes, goe to the bottom, like as before, according to the same Doctrine it did swim.
The Authors answer to the fourth Objection.
As to that finally which presents itself in the fourth place, namely, that theAncientshave been heretofore confuted byAristotle, who denying Positive and Absolute Levity, and truely esteeming all Bodies to be grave, said, that that which moved upward was driven by the circumambient Air, and therefore that also the Doctrine ofArchimedes, as an adherent to such an Opinion was convicted and confuted: I answer first, thatSignor Buonamicoin my judgement hath imposed uponArchimedes, and deduced from his words more than ever he intended by them, or may from his Propositions be collected, in regard thatArchimedesneither denies, nor admitteth Positive Levity, nor doth he so much as mention it: so that much less oughtBuonamicoto inferre, that he hath denyed that it might be the Cause and Principle of the Ascension of Fire, and other Light Bodies:Of Natation, Lib. 1. Prop. 7.having but only demonstrated, that Solid Bodies more grave than Water descend in it, according to the excess of their Gravity above the Gravity of that, he demonstrates likewise, how the less grave ascend in the same Water,accordng to its excessof Gravity, above theOf Natation, Lib. 1. Prop. 4.Gravity of them. So that the most that can be gathered from the Demonstration ofArchimedesis, that like as the excess of the Gravity of the Moveable above the Gravity of the Water, is the Cause that it descends therein, so the excess of the Gravity of the water above that of the Moveable, is a sufficient Cause why it descends not, but rather betakes it self to swim: not enquiring whether of moving upwards there is, or is not any other Cause contrary to Gravity: nor dothArchimedesdiscourse less properly than if one should say: If the South Winde shall assault the Barke with greaterImpetusthan is the violence with which the Streame of the River carries it towards the South, the motion of it shall be towards the North: but if theImpetusof the Water shall overcome that of the Winde, its motion shall be towards the South. The discourse is excellent and would be unworthily contradicted by such as should oppose it, saying: Thou mis-alledgest as Cause of the motion of the Bark towards the South, theImpetusof the Stream of the Water above that of the South Winde; mis-alledgest I say, for it is the Force of the North Winde opposite to the South, that is able to drive the Bark towards the South. Such an Objection would be superfluous, because he which alledgeth for Cause of the Motion the Stream of the Water, denies notbut that the Winde opposite to the South may do the same, but only affirmeth that the force of the Water prevailing over the South Wind, the Bark shall move towards the South: and saith no more than is true. And just thus whenArchimedessaith, that the Gravity of the Water prevailing over that by which the moveable descends to the Bottom, such moveable shall be raised from the Bottom to the Surface alledgeth a very true Cause of such an Accident, nor doth he affirm or deny that there is, or is not, a vertue contrary to Gravity, called by some Levity, that hath also a power of moving some Matters upwards. Let therefore the Weapons ofSignor Buonamicobe directed againstPlato, and otherAncients, who totally denyingLevity, andPlatodenyeth Positive Levity.taking all Bodies to be grave, say that the Motion upwards is made, not from an intrinsecal Principle of the Moveable, but only by the Impulse of theMedium; and letArchimedesand his Doctrine escape him, since he hath given him no Cause of quarelling with him. But if this Apologie, produced in defence ofArchimedes, should seem to some insufficient to free him from the Objections and Arguments, produced byAristotleagainstPlato, and the otherAncients, as if they did also fight againstArchimedes, alledging the Impulse of the Water as the Cause of the swimming of some Bodies less grave than it,The Authors defence of the doctrine ofPlatoand theAncients, who absolutely deny Levity:I would not question, but that I should be able to maintaine the Doctrine ofPlatoand those others to be most true, who absolutely deny Levity, and affirm no other Intrinsecal Principle of Motion to be in Elementary Bodies save only that towards the Centre of the Earth,According toPlatothere is no Principle of the Motion, of descent in Naturall Bodies, save that to the Centre.nor no other Cause of moving upwards, speaking of that which hath the resemblance of natural Motion, but only the repulse of theMedium, fluid, and exceeding the Gravity of the Moveable: and as to theNo cause of the motion of Ascent, save the Impulse of theMedium, exceeding the Moveable in Gravitie.Reasons ofAristotleon the contrary, I believe that I could be able fully to answer them, and I would assay to do it, if it were absolutely necessary to the present Matter, or were it not too long a Digression for this short Treatise. I will only say, that if there were in some of our Ellementary Bodies an Intrinsecall Principle and Naturall Inclination to shun the Centre of the Earth, and to move towards the Concave of the Moon, such Bodies, without doubt, would more swiftly ascend through thoseMediumsthat least oppose the Velocity of the Moveable, and these are the more tenuous and subtle; as is, for example, the Air in comparison of the Water, we daily proving that we can with farre more expeditious Velocity move a Hand or a Board to and again in one than in the other: nevertheless, weBodies ascend much swifter in the Water, than in the Air.never could finde any Body, that did not ascend much more swiftly in the water than in the Air. Yea of Bodies which we see continually to ascend in the Water, there is none that having arrived to the confines of the Air, do not wholly lose their Motion; even the Air it self,All Bodies ascending through Water, lose their Motion, comming to the confines of the Air.which rising with great Celerity through the Water, being once come toits Region it loseth all
The lighter Bodies ascend more swiftly through Water.
And, howbeit, Experience shewes, that the Bodies, successively less grave, do most expeditiously ascend in water, it cannot be doubted, but that the Ignean Exhalations do ascend more swiftly through the water, than doth the Air: which Air is seen by Experience to ascend more swiftly through the Water, than the Fiery Exhalations through the Air: Therefore, we must of necessity conclude, that the saidFiery Exhalations ascend thorow the Water more swiftly than doth the Air; & the Air ascends more swiftly thorow the Water, than Fire thorow the Air.Exhalations do much more expeditiously ascend through the Water, than through the Air; and that, consequently, they are moved by the Impulse of the AmbientMedium, and not by an intrinsick Principle that is in them, of avoiding the Centre of the Earth; to which other grave Bodies tend.
The Authors confutation of the Peripateticks Causes of Natation & Submersion.
To that which for a finall conclusion,Signor Buonamicoproduceth of going about to reduce the descending or not descending, to the easie and uneasie Division of theMedium, and to the predominancy of the Elements: I answer, as to the first part, that that cannot in any manner be admitted as a Cause, being that in none of the FluidMediums, as the Air, the Water, and other Liquids, there is any Resistance against Division, but all by every the least Force, areWater & other fluids void of Resistance against Division.divided and penetrated, as I will anon demonstrate: so, that of such Resistance of Division there can be no Act, since it self is not in being. As to the other part, I say, that the predominancy of the Elements in Moveables, is to be considered, as far as to the excesseThe predominancy of Elements in Moveables to be considered only in relation to their excess or defect of Gravity in reference to theMedium.or defect of Gravity, in relation to theMedium: for in that Action, the Elements operate not, but only, so far as they are grave or light: therefore, to say that the Wood of the Firre sinks not, because Air predominateth in it, is no more than to say, because it is less grave than the Water. Yea, even the immediate Cause, is its being less grave than the Water: and it being under the predominancy of the Air, is theThe immediate Cause of Natation is that the Moveable is less grave than the Water.Cause of its less Gravity: Therefore, he that alledgeth the predominancy of the Element for a Cause, brings the Cause of the Cause, and not the neerest and immediate Cause. Now, who knows not that the true Cause is the immediate, and not the mediate? Moreover,The Peripateticks alledge for the reason of Natation the Cause of the Cause.he that alledgeth Gravity, brings a Cause most perspicuous to Sence:Gravity a Cause most perspicuous to sence.The cause we may very easily assertain our selves; whether Ebony, for example, and Firre, be more or less grave than water: but whether Earth or Air predominates in them, who shall make that manifest? Certainly, no Experiment can better do it than to observe whether they swim or sink. So, that he who knows, not whether such a Solid swims, unless when he knows that Air predominates in it, knows not whether it swim, unless he sees it swim, for then he knows that it swims, when he knows that it is Air that predominates, but knows not that Air hath the predominance, unless he sees it swim: therefore, he knows not if it swims, till such time as he hath seen it swim.
Let us not then despise those Hints, though very dark, which Reason, after some contemplation, offereth to our Intelligence, and lets be content to be taught byArchimedes, that then any Body shall submerge in water, when it shall be specifically more grave than it,Lib 1. of Natation Prop. 7and that if it shall be less grave, it shall of necessity swim, andId. Lib. 1. Prop. 4.that it will rest indifferently in any place under water, if its Gravity be perfectly like to that of the water.
These things explained and proved, I come to consider that whichId. Lib 1. Prop. 3.offers it self, touching what the Diversity of figure given unto the said Moveable hath to do with these Motions and Rests; and proceed to affirme, that,
Diversity of Figure no Cause of its absolute Natation or Submersion.
The diversity of Figures given to this or that Solid, cannot any way be a Cause of its absolute Sinking or Swimming.
So that if a Solid being formed, for example, into a Sphericall Figure, doth sink or swim in the water, I say, that being formed into any other Figure, the same figure in the same water, shall sink or swim: nor can such its Motion by the Expansion or by other mutation of Figure, be impeded or taken away.
The Expansion of Figure, retards the Velocity of the ascent or descent of the Moveable in the water; but doth not deprive it of all Motion.
The Expansion of the Figure may indeed retard its Velocity, aswell of ascent as descent, and more and more according as the said Figure is reduced to a greater breadth and thinness: but that it may be reduced to such a form as that that same matter be wholly hindred from moving in the same water, that I hold to be impossible. In this I have met with great contradictors, who producing some Experiments, and in perticular a thin Board of Ebony, and a Ball of the same Wood, and shewing how the Ball in Water descended to the bottom, and the Board being put lightly upon the Water submerged not, but rested; have held, and with the Authority ofAristotle, confirmed themselves in their Opinions, that the Cause of that Rest was the breadth of the Figure,u{n}able by its small weightto pierce and penetrate the Resistance of the Waters Crassitude, which Resistance is readily overcome by the other Sphericall Figure.
This is the Principal point in the present Question, in which I perswade my self to be on the right side.
Therefore, beginning to investigate with the examination of exquisite Experiments that really the Figure doth not a jot alter the descent or Ascent of the same Solids, and having already demonstrated that the greater or less Gravity of the Solid in relation to the Gravity of theMediumis the cause of Descent or Ascent: when ever we would makeproof of that, which about this Effect the diversity of Figure worketh, its necessary to make the Experiment with Matter wherein variety of Gravities hath no place. For making use of Matters which may be different in their Specifical Gravities, and meeting with varieties of effects of Ascending and Descending, we shall alwayes be left unsatisfied whether that diversity derive it self really from the sole Figure, or else from the divers Gravity also. We may remedy this by takeing one only Matter, that is tractable and easily reduceable into every sort of Figure. Moreover, it will be an excellent expedient to take a kinde of Matter, exactly alike in Gravity unto the Water: for that Matter, as far as pertaines to the Gravity, is indifferent either to Ascend or Descend; so that we may presently observe any the least difference that derives it self from the diversity of Figure.
An Experiment in Wax, that proveth Figure to have no Operation in Natation & Submersion.
Now to do this, Wax is most apt, which, besides its incapacity of receiveing any sensible alteration from its imbibing of Water, is ductile or pliant, and the same piece is easily reduceable into all Figures: and beingin Speciea very inconsiderable matter inferiour in Gravity to the Water, by mixing therewith a little of the fileings of Lead it is reduced to a Gravity exactly equall to that of the Water.
This Matter prepared, and, for example, a Ball being made thereof as bigge as an Orange or biger, and that made so grave as to sink to the bottom, but so lightly, that takeing thence one only Grain of Lead, it returns to the top, and being added, it submergeth to the bottom, let the same Wax afterwards be made into a very broad and thin Flake or Cake; and then, returning to make the same Experiment, you shall see that it being put to the bottom, it shall, with the Grain of Lead rest below, and that Grain deducted, it shall ascend to the very Surface, and added again it shall dive to the bottom. And this same effect shall happen alwaies in all sort of Figures, as wel regular as irregular: nor shall you ever finde any that will swim without the removall of the Grain of Lead, or sinke to the bottom unless it be added: and, in short, about the going or not going to the Bottom, you shall discover no diversity, although, indeed, you shall about the quick and slow descent: for the more expatiated and distended Figures move more slowly aswel in the diveing to the bottom as in the rising to the top; and the other more contracted and compact Figures, more speedily. Now I know not what may be expected from the diversity of Figures, if the most contrary to one another operate not so much as doth a very small Grain of Lead, added or removed.
An objection against the Experiment in Water.
Me thinkes I hear some of the Adversaries to raise a doubt upon my produced Experiment. And first that they offer to my consideration, that the Figure, as a Figure simply, and disjunct from the Matter workes not any effect, but requires to be conjoyned with the Matter;and, furthermore, not with every Matter, but with those only, wherewith it may be able to execute the desired operation. Like as we see it verified by Experience, that the Acute and sharp Angle is more apt to cut, than the Obtuse; yet alwaies provided, that both the one and the other, be joyned with a Matter apt to cut, as for example, with Steel. Therefore, a Knife with a fine and sharp edge, cuts Bread or Wood with much ease, which it will not do, if the edge be blunt and thick: but he that will instead of Steel, take Wax, and mould it into a Knife, undoubtedly shall never know the effects of sharp and blunt edges: because neither of them will cut, the Wax being unable by reason of its flexibility, to overcome the hardness of the Wood and Bread. And, therefore, applying the like discourse to our purpose, they say, that the difference of Figure will shew different effects, touching Natation and Submersion, but not conjoyned with any kind of Matter, but only with those Matters which, by their Gravity, are apt to resist the Velocity of the water, whence he that would elect for the Matter, Cork or other light wood, unable, through its Levity, to superate the Crassitude of the water, and of that Matter should forme Solids of divers Figures, would in vain seek to find out what operation Figure hath in Natation or Submersion; because all would swim, and that not through any property of this or that Figure, but through the debility of the Matter, wanting so much Gravity, as is requisite to superate and overcome the Density and Crassitude of the water.
Its needfull, therefore, if wee would see the effect wrought by the Diversity of Figure, first to make choice of a Matter of its nature apt to penetrate the Crassitude of the water. And, for this effect,An Experiment in Ebany, brought to disprove the Experiment in Wax.they have made choice of such a Matter, as fit, that being readily reduced into Sphericall Figure, goes to the Bottom; and it is Ebony, of which they afterwards making a small Board or Splinter, as thin as a Lath, have illustrated how that this, put upon the Surface of the water, rests there without descending to the Bottom: and making, on the otherside, of the same wood a Ball, no less than a hazell Nut, they shew, that this swims not, but descendes. From which Experiment, they think they may frankly conclude, that the Breadth of the Figure in the flat Lath or Board, is the cause of its not descending to the Bottom, for as much as a Ball of the same Matter, not different from the Board in any thing but in Figure, submergeth in the same water to the Bottom. The discourse and the Experiment hath really so much of probability and likelyhood of truth in it, that it would be no wonder, if many perswaded by a certain cursory observation, should yield credit to it; nevertheless, I think I am able to discover, how that it is not free from falacy.
Beginning, therefore, to examine one by one, all the particulars thathave been produced, I say, that Figures, as simple Figures, not only operate not in naturall things, but neither are they ever seperated from the Corporeall substance: nor have I ever alledged them stript ofFigure is unseperable from Corporeall Substance.sensible Matter, like as also I freely admit, that in our endeavouring to examine the Diversity of Accidents, dependant upon the variety of Figures, it is necessary to apply them to Matters, which obstruct not the various operations of those various Figures: and I admit and grant, that I should do very ill; if I would experiment the influence of Acutenesse of edge with a Knife of Wax, applying it to cut an Oak, because there is no Acuteness in Wax able to cut that very hard wood. But yet such an Experiment of this Knife, would not be besides the purpose, to cut curded Milk, or other very yielding Matter: yea, in such like Matters, the Wax is more commodious than Steel; for finding the diversity depending upon Angles, more or less Acute, for that Milk is indifferently cut with a Raisor, and with a Knife, that hath a blunt edge. It needs, therefore, that regard be had, not only to the hardness, solidity or Gravity of Bodies, which under divers figures, are to divide and penetrate some Matters, but it forceth also, that regard be had, on the other side, to the Resistance of the Matters, to be divided and penetrated. But since I have in making the Experiment concerning our Contest; chosen a Matter which penetrates the Resistance of the water; and in all figures descendes to the Bottome, the Adversaries can charge me with no defect; yea, I have propounded so much a more excellent Method than they, in as much as I have removed all other Causes, of descending or not descending to the Bottom, and retained the only sole and pure variety of Figures, demonstrating that the same Figures all descende with the only alteration of a Grain in weight: which Grain being removed, they return to float and swim; it is not true, therefore, (resuming the Example by them introduced)that I have gon{e} aboutto experiment the efficacy of Acuteness, in cutting with Matters unable to cut, but with Matters proportioned to our occasion, since they are subjected to no other variety, then that alone which depends on the Figure more or less acute.
The answer to the Objection against the Experiment of the Wax.
But let us proceed a little farther, and observe, how that indeed the Consideration, which, they say, ought to be had about the Election of the Matter, to the end, that it may be proportionate for the making of our experiment, is needlessly introduced, declaring by the example of Cutting, that like as Acuteness is inefficient to cut, unless when it is in a Matter hard and apt to superate the Resistance of the wood or other Matter, which we intend to cut; so the aptitude of descending or not descending in water, ought and can only be known in those Matters, that are able to overcome the Renitence, and superate the Crassitude of the water. Unto which, I say, that to make distinction and election, more of this than of that Matter, on which to impress theFigures for cutting or penetrating this or that Body, as the solidity or obdurateness of the said Bodies shall be greater or less, is very necessary: but withall I subjoyn, that such distinction, election and caution would be superfluous and unprofitable, if the Body to be cut or penetrated, should have no Resistance, or should not at all withstand the Cutting or Penitration: and if the Knife were to be used in cutting a Mist or Smoak, one of Paper would be equally serviceable with one ofDamascusSteel: and so by reason the water hath not any Resistance against the Penitration of any Solid Body, all choice of Matter is superfluous and needless, and the Election which I said above to have been well made of a Matter reciprocall in Gravity to water, was not because it was necessary, for the overcoming of the crassitude of the water, but its Gravity, with which only it resists the sinking of Solid Bodies: and for what concerneth the Resistance of the crassitude, if we narrowly consider it, we shall find that all Solid Bodies, as well those that sink, as those that swim, are indifferently accomodated and apt to bring us to the knowledge of the truth in question. Nor will I be frighted out of the belief of these Conclusions, by the Experiments which may be produced against me, of many severall Woods, Corks, Galls, and, moreover, of subtle slates and plates of all sorts of Stone and Mettall, apt by means of their Naturall Gravity, to move towards the Centre of the Earth, the which, nevertheless, being impotent, either through the Figure (as the Adversaries thinke) or through Levity, to break and penetrate the Continuity of the parts of the water, and to distract its union, do continue to swimm without submerging in the least: nor on the other side, shall the Authority ofAristotlemove me, who in more than one place, affirmeth the contrary to this, which Experience shews me.