A Discourse Presented to the Most Serene Don Cosimo II., Great Duke of Tuscany, Concerning the Natation of Bodies Vpon, and Submersion In, t · Galileo Galilei
THEOREME V.
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.
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.
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.
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._
It is now to be noted, that the Board of Ebany and the Ball, put into the water, both sink, but the Ball more swiftly, and the Board more slowly; and slower and slower, according as it shall be more broad and thin, and of this Tardity the breadth of the Figure is the true Cause: But these broad Boards that slowly descend, are the same, that being put lightly upon the water, do swimm: Therefore, if that were true which the Adversaries affirm, the same numerical Figure, would in the same numericall water, cause one while Rest, and another while Tardity of Motion, which is impossible: for every perticular Figure which descends to the Bottom[43], hath of necessity its own determinate Tardity and slowness, proper and naturall unto it, according to which it moveth, so that every other Tardity, greater or lesser is improper to its nature: if, therefore, a Board, as suppose of a foot square, descendeth naturally with six degrees of Tardity, it is impossible, that it should descend with ten or twenty, unless some new impediment do arrest it. Much less can it, by reason of the same Figure rest, and wholly cease to move; but it is necessary, that when ever it resteth, there do some greater impediment intervene than the breadth of the Figure.
Therefore, it must be somewhat else, and not the Figure, that stayeth the Board of Ebany above water, of which Figure the only Effect is the retardment of the Motion, according to which it descendeth more slowly than the Ball. Let it be confessed, therefore, rationally discoursing, that the true and sole Cause of the Ebanys going to the Bottom, is the excess of its Gravity above the Gravity of the water: and the Cause of the greater or less Tardity, the breadth of this Figure, or the contractedness of that: but of its Rest, it can by no means be allowed, that the quallity of the Figure, is the Cause thereof: aswell, because, making the Tardity greater, according as the Figure more dilateth, there cannot be so immense a Dilatation, to which there may not be found a correspondent immence Tardity without redusing it to Nullity of Motion; as, because the Figures produced by the Antagonists for effecters of Rest, are the self same that do also go to the Bottom. [43] Every perticular Figure hath its own peculiar Tardity.
I will not omit another reason, founded also upon Experience, and if I deceive not my self, manifestly concluding, how that the Introduction of the breadth or amplitude of Figure, and the Resistance of the water against penetration, have nothing to do in the Effect of descending, or ascending, or resting in the water. [D]Take a piece of wood or other Matter, of which a Ball ascends from the Bottom of the water to the Surface, more slowly than a Ball of Ebony of the same bignesse, so that it is manifest, that the Ball of Ebony more readily divideth the water in descending, than the other in ascending; as for Example, let the Wood be Walnut-tree. Then take a Board of Walnut-tree, like and equall to that of Ebony of the Antagonists, which swims; and if it be true, that this floats above water, by reason of the Figure, unable through its breadth, to pierce the Crassitude of the same, the other of Wallnut-tree, without all question, being thrust unto the Bottom, will stay there, as less apt, through the same impediment of Figure, to divide the said Resistance of the water. But if we shall find, and by experience see, that not only the thin Board, but every other Figure of the same Wallnut-tree will return to float, as undoubtedly we shall, then I must desier my opposers to forbear to attribute the floating of the Ebony, unto the Figure of the Board, in regard that the Resistance of the water is the same, as well to the ascent, as to the descent, and the force of the Wallnut-trees ascension, is lesse than the Ebonys force in going to the Bottom.
And, because, that the excess of their Gravity above the Gravity of the water, is questionless the Cause of the sinking of the flat piece of Ebony, and the thin Plate of Gold, when they go to the Bottom, therefore, of necessity, when they float, the Cause of their staying above water, proceeds from Levity, which in that case, by some Accident, peradventure not hitherto observed, cometh to meet with the said Board, rendering it no longer as it was before, whilst it did sink more ponderous than the water, but less. Now, let us return to take the thin Plate of Gold, or of Silver, or the thin Board of Ebony, and let us lay it lightly upon the water, so that it stay there without sinking, and diligently observe its effect. And first, see how false the assertion of _Aristotle_, and our oponents is, to wit, that it stayeth above water, through its unability to pierce and penetrate the Resistance of the waters Crassitude: for it will manifestly appear, not only that the said Plates have penetrated the water, but also that they are a considerable matter lower than the Surface of the same, the which continueth eminent, and maketh as it were a Rampert on all sides, round about the said Plates, the profundity of which they stay swimming: and, according as the said Plates shall be more grave than the water, two, four, ten or twenty times, it is necessary, that their Superficies do stay below the universall Surface of the water, so much more, than the thickness of those Plates, as we shal more distinctly shew anon. In the mean space, for the more easie understanding of what I say, observe with me a little the present Scheme: in which let us suppose the Surface of the water to be distended, according to the Lines F L D B, upon which if one shall put a board of matter specifically more grave than water, but so lightly that it submerge not, it shall not rest any thing above, but shall enter with its whole thickness into the water: and, moreover, shall sink also, as we see by the Board A I, O I, whose breadth is wholly sunk into the water, the little Ramperts of water L A and D O incompassing it, whose Superficies is notably higher than the Superficies of the Board. See now whether it be true, that the said Board goes not to the Bottom, as being of Figure unapt to penetrate the Crassitude of the water.
And, if we exactly consider, what, and how great the Solid is, that in this Experiment enters into the water, and contrasts with the Gravity of the same, it will be found to be all that which we find to be beneath the Surface of the water, the which is an aggregate and Compound of a Board of Ebony, and of almost the like quantity of Air, or a Mass compounded of a Plate of Lead, and ten or twelve times as much Air. But, Gentlemen, you that are my Antagonists in our Question, we require the Identity of Matter, and the alteration only of the Figure; therefore, you must remove that Air, which being conjoyned with the Board, makes it become another Body less grave than the Water, and put only the Ebony into the Water, and you shall certainly see the Board descend to the Bottom; and, if that do not happen, you have got the day. And to seperate the Air from the Ebony[44], there needs no more but only to bath the Superficies of the said Board with the same Water: for the Water being thus interposed between the Board and the Air, the other circumfused Water shall run together without any impediment, and shall receive into it the sole and bare Ebony, as it was to do.
Moreover, it is untrue, that the Board sinks by vertue of the new Weight added to it by the Water, in the single and slight bathing of it: for I will put ten or twenty drops of Water upon the same Board, whilst it is sustained upon the water; which drops, because not conjoyned with the other Water circumfused, shall not so encrease the weight of it, as to make it sink: but if the Board being taken out, and all the water wiped off that was added thereto, I should bath all its Superficies with one only very small drop, and put it again upon the water, without doubt it shall sink, the other Water running to cover it, not being retained by the superiour Air; which Air by the interposition of the thin vail of water, that takes away its Contiguity unto the Ebony, shall without Renitence be seperated, nor doth it in the least oppose the succession of the other Water: but rather, to speak better, it shall descend freely; because it shall be all invironed and covered with water, as soon as its superiour Superficies, before vailed with water, doth arrive to the Levell of the universall Surface of the said water.
To say, in the next place, that water can encrease the weight of things that are demitted into it, is most false; for water hath no Gravity in water[45], since it descends not: yea, if we would well consider what any immense Mass of water doth put upon a grave Body; that is placed in it, we shall find experimentally, that it, on the contrary, will rather in a great part deminish the weight of it[46], and that we may be able to lift an huge Stone from the Bottom of the water, which the water being removed, we are not able to stir. Nor let them tell me by way of reply, that although the superposed water augment not the Gravity of things that are in it, yet it increaseth the ponderosity of those that swim, and are part in the water and part in the Air, as is seen, for Example, in a Brass Ketle[47], which whilst it is empty of water, and replenished only with Air shall swim, but pouring of Water therein, it shall become so grave, that it shall sink to the Bottom, and that by reason of the new weight added thereto. To this I will return answer, as above, that the Gravity of the Water, contained in the Vessel is not that which sinks it to the Bottom, but the proper Gravity of the Brass, superiour to the Specificall Gravity of the Water: for if the Vessel were less grave than water, the Ocean would not suffice to submerge it[48].
And, give me leave to repeat it again, as the fundamentall and principall point in this Case, that the Air contained in this Vessel before the infusion of the Water, was that which kept it a-float[49], since that there was made of it, and of the Brass, a Composition less grave than an equall quantity of Water: and the place that the Vessel occupyeth in the Water whilst it floats, is not equall to the Brass alone, but to the Brass and to the Air together, which filleth that part of the Vessel that is below the Levell of the water: Moreover, when the Water is infused, the Air is removed, and there is a composition made of Brass and of water, more grave _in specie_ than the simple water, but not by vertue of the water infused, as having greater Specifick Gravity than the other water, but through the proper Gravity of the Brass, and through the alienation of the Air.
Text from Project Gutenberg, public domain in the United States.