Part 4

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[31]: Therefore, we must of necessity conclude, that the said Exhalations do much more expeditiously ascend through the Water, than through the Air; and that, consequently, they are moved by the Impulse of the Ambient _Medium_, and not by an intrinsick Principle that is in them, of avoiding the Centre of the Earth; to which other grave Bodies tend.

[31] Fiery Exhalations ascend thorow the Water more swiftly than doth the Air; & the Air ascends more swiftly thorow the Water, than Fire thorow the Air.

[Sidenote: _T_he Authors confutation of the Peripateticks Causes of Natation & Submersion.]

To that which for a finall conclusion, _Signor Buonamico_ produceth of going about to reduce the descending or not descending, to the easie and uneasie Division of the _Medium_, 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 Fluid _Mediums_, as the Air, the Water, and other Liquids, there is any Resistance against Division[32], but all by every the least Force, are 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[33], is to be considered, as far as to the excesse or defect of Gravity, in relation to the _Medium_: 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[34]: and it being under the predominancy of the Air, is the 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[35]? Moreover, he that alledgeth Gravity, brings a Cause most perspicuous to Sence[36]: 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.

[32] Water & other fluids void of Resistance against Division.

[33] _T_he predominancy of Elements in Moveables to be considered only in relation to their excess or defect of Gravity in reference to the _Medium_.

[34] _T_he immediate Cause of Natation is that the Moveable is less grave than the Water.

[35] _T_he Peripateticks alledge for the reason of Natation the Cause of the Cause.

[36] Gravity a Cause most perspicuous to sence.

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 by _Archimedes_, that then any Body shall submerge in water[37], when it shall be specifically more grave than it, and that if it shall be less grave[38], it shall of necessity swim, and that it will rest indifferently in any place under water, if its Gravity be perfectly like to that of the water.

[37] Lib 1. of Natation Prop. 7

[38] Id. Lib. 1. Prop. 4.

These things explained and proved[39], I come to consider that which 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,

[39] Id. Lib 1. Prop. 3.

THEOREME V.

[Sidenote: 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.

[Sidenote: 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 of _Aristotle_, confirmed themselves in their Opinions, that the Cause of that Rest was the breadth of the Figure, u{n}able by its small weight to 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 the _Medium_ is the cause of Descent or Ascent: when ever we would make proof 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.

[Sidenote: 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 being _in Specie_ a 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.

Me thinkes I hear some of the Adversaries to raise a doubt upon my produced Experiment[40]. 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.

[40] An objection against the Experiment in 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[41], 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.

[41] An Experiment in Ebany, brought to disprove the Experiment in Wax.

Beginning, therefore, to examine one by one, all the particulars that have 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[42]: nor have I ever alledged them stript of 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} about to 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.

[42] Figure is unseperable from Corporeall Substance.

[Sidenote: 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 the Figures 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 of _Damascus_ Steel: 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 of _Aristotle_ move me, who in more than one place, affirmeth the contrary to this, which Experience shews me.

[Sidenote: No Solid of such Levity, nor of such Figure, but that it doth penetrate the Crassitude of the Water.]

[Sidenote: Bodies of all Figures, laid upon the water, do penetrate its Crassitude, and in what proportion.]

I return, therefore, to assert, that there is not any Solid of such Levity, nor of such Figure, that being put upon the water, doth not divide and penetrate its Crassitude: yea if any with a more perspicatious eye, shall return to observe more exactly the thin Boards of Wood, he shall see them to be with part of their thickness under water, and not only with their inferiour Superficies, to kisse the Superiour of the water, as they of necessity must have believed, who have said, that such Boards submerge not, as not being able to divide the Tenacity of the parts of the water: and, moreover, he shall see, that subtle shivers of Ebony, Stone or Metall, when they float, have not only broak the Continuity of the water, but are with all their thickness, under the Surface of it; and more and more, according as the Matters are more grave: so that a thin Plate of Lead, shall be lower than the Surface of the circumfused water, by at least twelve times the thickness of the Plate, and Gold shall dive below the Levell of the water, almost twenty times the thickness of the Plate, as I shall anon declare.

But let us proceed to evince, that the water yields and suffers it self to be penetrated by every the lightest Body; and therewithall demonstrate, how, even by Matters that submerge not, we may come to know that Figure operates nothing about the going or not going to the Bottom, seeing that the water suffers it self to be penetrated equally by every Figure.

[Sidenote: The Experiment of a Cone, demitted with its Base, and after with its Point downwards.]

Make a Cone, or a Piramis of Cypress, of Firre, or of other Wood of like Gravity, or of pure Wax, and let its height be somewhat great, namely a handfull, or more, and put it into the water with the Base downwards: first, you shall see that it will penetrate the water, nor shall it be at all impeded by the largeness of the Base, nor yet shall it sink all under water, but the part towards the point shall lye above it: by which shall be manifest, first, that that Solid forbeares not to sink out of an inability to divide the Continuity of the water, having already divided it with its broad part, that in the opinion of the Adversaries is the less apt to make the division. The Piramid being thus fixed, note what part of it shall be submerged, and revert it afterwards with the point downwards, and you shall see that it shall not dive into the water more than before, but if you observe how far it shall sink, every person expert in Geometry, may measure, that those parts that remain out of the water, both in the one and in the other Experiment are equall to an hair: whence he may manifestly conclude, that the acute Figure which seemed most apt to part and penetrate the water, doth not part or penetrate it more than the large and spacious.

And he that would have a more easie Experiment, let him take two Cylinders of the same Matter, one long and small, and the other short, but very broad, and let him put them in the water, not distended, but erect and endways: he shall see, if he diligently measure the parts of the one and of the other, that in each of them the part submerged, retains exactly the same proportion to that out of the water, and that no greater part is submerged of that long and small one, than of the other more spacious and broad: howbeit, this rests upon a very large, and that upon a very little Superficies of water: therefore the diversity of Figure, occasioneth neither facility, nor difficulty, in parting and penetrating the Continuity of the water, and, consequently, cannot be the Cause of the Natation or Submersion. He may likewise discover the non operating of variety of Figures, in arising from the Bottom of the water, towards the Surface, by taking Wax, and tempering it with a competent quantity of the filings of Lead, so that it may become a considerable matter graver than the water: then let him make it into a Ball, and thrust it unto the Bottom of the water; and fasten to it as much Cork, or other light matter, as just serveth to raise it, and draw it towards the Surface: for afterwards changing the same Wax into a thin Cake, or into any other Figure, that same Cork shall raise it in the same manner to a hair.

This silenceth not my Antagonists, but they say, that all the discourse hitherto made by me little importeth to them, and that it serves their turn, that they have demonstrated in one only particular, and in what matter, and under what Figure pleaseth them, namely, in a Board and in a Ball of Ebony, that this put in the water, descends to the Bottom, and that stays atop to swim: and the Matter being the same, and the two Bodies differing in nothing but in Figure, they affirm, that they have with all perspicuity demonstrated and sensibly manifested what they undertook; and lastly, that they have obtained their intent. Nevertheless, I believe, and thinke, I can demonstrate, that that same Experiment proveth nothing against my Conclusion.

[Sidenote: In Experiments of Natation, the Solid is to be put into, not upon the water.]

And first, it is false, that the Ball descends, and the Board not: for the Board shall also descend, if you do to both the Figures, as the words of our Question requireth; that is, if you put them both into the water.

[Sidenote: The Question of Natation stated.]

_The words were these. That the Antagonists having an opinion, that the Figure would alter the Solid Bodies, in relation to the descending or not descending, ascending or not ascending in the same_ Medium, _as_ v. gr. _in the same water, in such sort, that, for Example, a Solid that being of a Sphericall Figure, shall descend to the Bottom, being reduced into some other Figure, shall not descend: I holding the contrary, do affirm, that a Corporeall Solid Body, which reduced into a Sphericall Figure, or any other, shall go to the Bottom, shall do the like under whatsoever other Figure, {&}c._

[Sidenote: Place defined according to Aristotle.]