Chapter V: Part 5

But _Democritus_ notes, that this Cause only takes place when we treat of raising and sustaining of Plates of Matters, but very little heavier than the water, or extreamly thin: but in Matters very grave, and of some thickness, as Plates of Lead or other Mettal, that same Effect wholly ceaseth: In Testimony of which, let's observe that such Plates, being raised by the Fiery Atomes, ascend through all the depth of the water, and stop at the Confines of the Air, still staying under water: but the Plates of the Opponents stay not, but only when they have their upper Superficies dry, nor is there any means to be used, that when they are within the water, they may not sink to the bottom. The cause, therefore, of the Supernatation of the things of which _Democritus_ speaks is one, and that of the Supernatation of the things of which we speak is another. But, returning to _Aristotle_[86], methinks that he hath more weakly confuted _Democritus_, than _Democritus_ himself hath done: For _Aristotle_ having propounded the Objection which he maketh against him, and opposed him with saying, that if the calid ascendent Corpuscles were those that raised the thin Plate, much more then would such a Solid be raised and born upwards through the Air, it sheweth that the desire in _Aristotle_ to detect _Democritus_, was predominate over the exquisiteness of Solid Philosophizing: which desire of his he hath discovered in other occasions, and that we may not digress too far from this place, in the Text precedent to this Chapter which we have in hand[87]; where he attempts to confute the same _Democritus_ for that he, not contenting himself with names only, had essayed more particularly to declare what things Gravity and Levity were; that is, the Causes of descending and ascending, (and had introduced Repletion and Vacuity) ascribing this to Fire, by which it moves upwards, and that to the Earth, by which it descends; afterwards attributing to the Air more of Fire, and to the water more of Earth. But _Aristotle_ desiring a positive Cause, even of ascending Motion, and not as _Plato_, or these others, a simple negation, or privation, such as Vacuity would be in reference to Repletion[88], argueth against _Democritus_ and saith: If it be true, as you suppose, then there shall be a great Mass of water, which shall have more of Fire, than a small Mass of Air, and a great Mass of Air, which shall have more of Earth than a little Mass of water, whereby it would ensue, that a great Mass of Air, should come more swiftly downwards, than a little quantity of water: But that is never in any case soever: Therefore _Democritus_ discourseth erroneously.

[86] _Aristotle_ shews his desire of finding _Democritus_ in an
Error, to exceed that of discovering Truth.

[87] Cap. 5. Text 41.

[88] Id. ibid.

But in my opinion, the Doctrine of _Democritus_ is not by this allegation overthrown, but if I erre not, the manner of _Aristotle_ deduction either concludes not, or if it do conclude any thing, it may with equall force be restored against himself. _Democritus_ will grant to _Aristotle_, that there may be a great Mass of Air taken, which contains more Earth, than a small quantity of water, but yet will deny, that such a Mass of Air, shall go faster downwards than a little water, and that for many reasons. First, because if the greater quantity of Earth, contained in the great Mass of Air, ought to cause a greater Velocity than a less quantity of Earth, contained in a little quantity of water, it would be necessary, first, that it were true, that a greater Mass of pure Earth, should move more swiftly than a less: But this is false, though _Aristotle_ in many places affirms it to be true: because not the greater absolute, but the greater specificall Gravity, is the cause of greater Velocity[89]: nor doth a Ball of Wood, weighing ten pounds, descend more swiftly than one weighing ten Ounces, and that is of the same Matter: but indeed a Bullet of Lead of four Ounces, descendeth more swiftly than a Ball of Wood of twenty Pounds: because the Lead is more _grave in specie_ than the Wood. Therefore, its not necessary, that a great Mass of Air, by reason of the much Earth contained in it, do descend more swiftly than a little Mass of water[90], but on the contrary, any whatsoever Mass of water, shall move more swiftly than any other of Air, by reason the participation of the terrene parts _in specie_ is greater in the water, than in the Air. Let us note, in the second place, how that in multiplying the Mass of the Air, we not only multiply that which is therein of terrene, but its Fire also: whence the Cause of ascending, no less encreaseth, by vertue of the Fire, than that of descending on the account of its multiplied Earth. It was requisite in increasing the greatness of the Air, to multiply that which it hath of terrene only, leaving its Fire in its first state, for then the terrene parts of the augmented Air, overcoming the terrene parts of the small quantity of water, it might with more probability have been pretended, that the great quantity of Air, ought to descend with a greater _Impetus_, than the little quantity of water.

[89] The greater Specificall, not the greater absolute Gravity,
is the Cause of Velocity.

[90] Any Mass of water shal move more swiftly, than any of Air,
and why.

Therefore, the Fallacy lyes more in the Discourse of _Aristotle_, than in that of _Democritus_, who with severall other Reasons might oppose _Aristotle_, and alledge; If it be true, that the extreame Elements be one simply grave, and the other simply light, and that the mean Elements participate of the one, and of the other Nature; but the Air more of Levity, and the water more of Gravity, then there shall be a great Mass of Air, whose Gravity shall exceed the Gravity of a little quantity of water, and therefore such a Mass of Air shall descend more swiftly than that little water: But that is never seen to occurr: Therefore its not true, that the mean Elements do participate of the one, and the other quality. This argument is fallacious, no less than the other against _Democritus_.

Lastly, _Aristotle_ having said, that if the Position of _Democritus_ were true, it would follow, that a great Mass of Air should move more swiftly than a small Mass of water, and afterwards subjoyned, that that is never seen in any Case: methinks others may become desirous to know of him in what place this should evene, which he deduceth against _Democritus_, and what Experiment teacheth us, that it never falls out so. To suppose to see it in the Element of water, or in that of the Air is vain, because neither doth water through water, nor Air through Air move, nor would they ever by any whatever participation others assign them, of Earth or of Fire: the Earth, in that it is not a Body fluid, and yielding to the mobility of other Bodies, is a most improper place and _Medium_ for such an Experiment: _Vacuum_, according to the same _Aristotle_ himself, there is none, and were there, nothing would move in it: there remains the Region of Fire, but being so far distant from us, what Experiment can assure us, or hath assertained _Aristotle_ in such sort, that he should as of a thing most obvious to sence, affirm what he produceth in confutation of _Democritus_, to wit, that a great Mass of Air, is moved no swifter than a little one of water? But I will dwell no longer upon this matter, whereon I have spoke sufficiently: but leaving _Democritus_, I return to the Text of _Aristotle_, wherein he goes about to render the true reason, how it comes to pass, that the thin Plates of Iron or Lead do swim on the water; and, moreover, that Gold it self being beaten into thin Leaves, not only swims in water, but flyeth too and again in the Air. He supposeth that of Continualls[91], some are easily divisible, others not: and that of the easily divisible, some are more so, and some less: and these he affirms we should esteem the Causes. He addes that that is easily divisible, which is well terminated, and the more the more divisible, and that the Air is more so, than the water, and the water than the Earth. And, lastly, supposeth that in each kind, the lesse quantity is easlyer divided and broken than the greater.

[91] _De Caelo_ l. 4. c. 6. t. 44.

Here I note, that the Conclusions of _Aristotle_ in generall are all true, but methinks, that he applyeth them to particulars, in which they have no place, as indeed they have in others, as for Example, Wax is more easily divisible than Lead, and Lead than Silver, inasmuch as Wax receives all the terms more easlier than Lead, and Lead than Silver. Its true, moreover, that a little quantity of Silver is easlier divided than a great Mass: and all these Propositions are true, because true it is, that in Silver, Lead and Wax, there is simply a Resistance against Division, and where there is the absolute, there is also the respective. But if as well in water as in Air, there be no Renitence against simple Division, how can we say, that the water is easlier divided than the Air? We know not how to extricate our selves from the Equivocation: whereupon I return to answer, that Resistance of absolute Division is one thing, and Resistance of Division made with such and such Velocity is another. But to produce Rest, and to abate the Motion, the Resistance of absolute Division is necessary; and the Resistance of speedy Division, causeth not Rest, but slowness of Motion. But that as well in the Air, as in water, there is no Resistance of simple Division, is manifest, for that there is not found any Solid Body which divides not the Air, and also the water: and that beaten Gold, or small dust, are not able to superate the Resistance of the Air, is contrary to that which Experience shews us, for we see Gold and Dust to go waving to and again in the Air, and at last to descend downwards, and to do the same in the water, if it be put therein, and separated from the Air. And, because, as I say, neither the water, nor the Air do resist simple Division, it cannot be said, that the water resists more than the Air. Nor let any object unto me, the Example of most light Bodies, as a Feather, or a little of the pith of Elder, or water-reed that divides the Air and not the water, and from this infer, that the Air is easlier divisible than the water; for I say unto them, that if they do well observe, they shall see the same Body likewise divide the Continuity of the water[92], and submerge in part, and in such a part, as that so much water in Mass would weigh as much as the whole Solid. And if they shal yet persist in their doubt, that such a Solid sinks not through inability to divide the water, I will return them this reply, that if they put it under water, and then let it go, they shall see it divide the water, and presently ascend with no less celerity, than that with which it divided the Air in descending: so that to say that this Solid ascends in the Air, but that coming to the water, it ceaseth its Motion, and therefore the water is more difficult to be divided, concludes nothing: for I, on the contrary, will propose them a piece of Wood, or of Wax, which riseth from the bottom of the water, and easily divides its Resistance, which afterwards being arrived at the Air, stayeth there, and hardly toucheth it; whence I may aswell say, that the water is more easier divided than the Air.

[92] _Archimed. De Insident. humi_ lib. 2. prop. 1.

I will not on this occasion forbear to give warning of another fallacy of these persons, who attribute the reason of sinking or swimming to the greater or lesse Resistance of the Crassitude of the water against Division, making use of the example of an Egg, which in sweet water goeth to the bottom, but in salt water swims; and alledging for the cause thereof, the faint Resistance of fresh water against Division, and the strong Resistance of salt water. But if I mistake not, from the same Experiment, we may aswell deduce the quite contrary; namely, that the fresh water is more dense, and the salt more tenuous and subtle, since an Egg from the bottom of salt water speedily ascends to the top, and divides its Resistance, which it cannot do in the fresh, in whose bottom it stays, being unable to rise upwards. Into such like perplexities, do false Principles Lead men: but he that rightly Philosophating, shall acknowledge the excesses of the Gravities of the Moveables and of the Mediums, to be the Causes of those effects, will say, that the Egg sinks to the bottom in fresh water, for that it is more grave than it, and swimeth in the salt, for that its less grave than it: and shall without any absurdity, very solidly establish his Conclusions.

Therefore the reason totally ceaseth, that _Aristotle_ subjoyns in the Text saying[93]; The things, therefore, which have great breadth remain above, because they comprehend much, and that which is greater, is not easily divided. Such discoursing ceaseth, I say, because its not true, that there is in water or in Air any Resistance of Division; besides that the Plate of Lead when it stays, hath already divided and penetrated the Crassitude of the water, and profounded it self ten or twelve times more than its own thickness: besides that such Resistance of Division, were it supposed to be in the water, could not rationally be affirmed to be more in its superiour parts than in the middle, and lower: but if there were any difference, the inferiour should be the more dense, so that the Plate would be no less unable to penetrate the lower, than the superiour parts of the water; nevertheless we see that no sooner do we wet the superiour Superficies of the Board or thin Piece of Wood, but it precipitatly, and without any retension, descends to the bottom.

[93] Text 45.

I believe not after all this, that any (thinking perhaps thereby to defend _Aristotle_) will say, that it being true, that the much water resists more than the little, the said Board being put lower descendeth, because there remaineth a less Mass of water to be divided by it: because if after the having seen the same Board swim in four Inches of water, and also after that in the same to sink, he shall try the same Experiment upon a profundity of ten or twenty fathom water, he shall see the very self same effect. And here I will take occasion to remember, for the removall of an Error that is too common; That that Ship or other whatsoever Body, that on the depth of an hundred or a thousand fathom, swims with submerging only six fathom of its own height, [_or in the Sea dialect, that draws six fathom water_] shall swim in the same manner in water, that hath but six fathom and half an Inch of depth[94]. Nor do I on the other side, think that it can be said, that the superiour parts of the water are the more dense, although a most grave Authour hath esteemed the superiour water in the Sea to be so, grounding his opinion upon its being more salt, than that at the bottom: but I doubt the Experiment, whether hitherto in taking the water from the bottom, the Observatour did not light upon some spring of fresh water there spouting up: but we plainly see on the contrary, the fresh Waters of Rivers to dilate themselves for some miles beyond their place of meeting with the salt water of the Sea, without descending in it, or mixing with it, unless by the intervention of some commotion or turbulency of the Windes.

[94] A Ship that in 100 Fathome water draweth 6 Fathome, shall
float in 6 Fathome and 1/2 an Inch of depth.

But returning to _Aristotle_, I say, that the breadth of Figure hath nothing to do in this business more or less, because the said Plate of Lead, or other Matter, cut into long Slices, swim neither more nor less[95]; and the same shall the Slices do, being cut anew into little pieces, because its not the breadth but the thickness that operates in this business. I say farther, that in case it were really true, that the Renitence to Division were the proper Cause of swimming[96], the Figures more narrow and short, would much better swim than the more spacious and broad, so that augmenting the breadth of the Figure, the facility of supernatation will be deminished, and decreasing, that this will encrease.

[95] Thickness not breadth of Figure to be respected in Natation.

[96] Were Renitence the cause of Natation, breadth of Figure would
hinder the swiming of Bodies.

And for declaration of what I say, consider that when a thin Plate of Lead descends, dividing the water, the Division and discontinuation is made between the parts of the water, invironing the perimeter or Circumference of the said Plate, and according to the bigness greater or lesser of that circuit, it hath to divide a greater or lesser quantity of water, so that if the circuit, suppose of a Board, be ten Feet in sinking it flatways, it is to make the seperation and division, and to so speak, an incission upon ten Feet of water; and likewise a lesser Board that is four Feet in Perimeter, must make an incession of four Feet. This granted, he that hath any knowledge in Geometry, will comprehend, not only that a Board sawed in many long thin pieces, will much better float than when it was entire, but that all Figures, the more short and narrow they be, shall so much the better swim. Let the Board A B C D be, for Example, eight Palmes long, and five broad, its circuit shall be twenty six Palmes; and so many must the incession be, which it shall make in the water to descend therein: but if we do saw ir, as suppose into eight little pieces, according to the Lines E F, G H, {&}c. making seven Segments, we must adde to the twenty six Palmes of the circuit of the whole Board, seventy others; whereupon the eight little pieces so cut and seperated, have to cut ninty six Palmes of water. And, if moreover, we cut each of the said pieces into five parts, reducing them into Squares, to the circuit of ninty six Palmes, with four cuts of eight Palmes apiece; we shall adde also sixty four Palmes, whereupon the said Squares to descend in the water, must divide one hundred and sixty Palmes of water, but the Resistance is much greater than that of twenty six; therefore to the lesser Superficies, we shall reduce them, so much the more easily will they float: and the same will happen in all other Figures, whose Superficies are simular amongst themselves, but different in bigness: because the said Superficies, being either deminished or encreased, always diminish or encrease their Perimeters in subduple proportion; to wit, the Resistance that they find in penetrating the water; therefore the little pieces gradually swim, with more and more facility as their breadth is lessened.

_This is manifest; for keeping still the same height of the Solid,
with the same proportion as the Base encreaseth or deminisheth,
doth the said Solid also encrease or diminish; whereupon the Solid
more diminishing than the Circuit, the Cause of Submersion more
diminisheth than the Cause of Natation: And on the contrary, the
Solid more encreasing than the Circuit, the Cause of Submersion
encreaseth more, that of Natation less._

And this may all be deduced out of the Doctrine of _Aristotle_ against his own Doctrine.

Lastly, to that which we read in the latter part of the Text[97], that is to say, that we must compare the Gravity of the Moveable with the Resistance of the Medium against Division, because if the force of the Gravity exceed the Resistance of the _Medium_, the Moveable will descend, if not it will float. I need not make any other answer, but that which hath been already delivered; namely, that its not the Resistance of absolute Division, (which neither is in Water nor Air) but the Gravity of the _Medium_ that must be compared with the Gravity of the Moveables; and if that of the _Medium_ be greater, the Moveable shall not descend, nor so much as make a totall Submersion, but a partiall only; because in the place which it would occupy in the water, there must not remain a Body that weighs less than a like quantity of water: but if the Moveable be more grave, it shall descend to the bottom, and possess a place where it is more conformable for it to remain, than another Body that is less grave. And this is the only true proper and absolute Cause of Natation and Submersion, so that nothing else hath part therein: and the Board of the Adversaries swimmeth, when it is conjoyned with as much Air, as, together with it, doth form a Body less grave than so much water as would fill the place that the said Compound occupyes in the water; but when they shall demit the simple Ebony into the water, according to the Tenour of our Question, it shall alwayes go to the bottom, though it were as thin as a Paper.

[97] Lib. 4. c. 6. Text 45.

[Decoration]

FINIS.

[Decoration]

* * * * *

[Detailed Transcriber's Notes

The text has been made to match the original text as much as
possible including variation in spelling, punctuation, italics etc.
The following, details apparent printer's errors as well as changes
or additions to aid readability of text.

Page 1, missing full stop after abbreviation gr. '0 gr 54 min.'.

Page 3, sidenote, missing space between words 'the Authority ofan
Author.'.

Page 3, printer's error, augmentarion for augmentation 'and
augmentarion of Masse'.

Page 4, missing letter t 'tha{t} that proceeded not'.

Page 4, printer's error or inconsistent punctuation, 'my paynes and
time. and although'.

Page 6, inconsistent punctuation, full stop after axiome where as
there are none after those following 'AXIOME. I.'.

Page 9, missing full stop added to end of paragraph 'or else an
upright Prisme.'.

Page 11, printer's error, missing letter C in illustration, 'the
Prisme A C D B to be placed'.

Page 15, printer's error or archaic lettering, final y looking like
a 7 in original text'and of the Specifick Gravit{y}'.

Page 16, printer's error, letter N for T in text to refer to
illustration, 'if the Vessell E N S F'.

Page 16, printer's error, duplicate word in text 'equalizeth the
Force and and Moment,'.

Page 17, printer's error, rhe for the 'as in rhe Stilliard,'.

Page 17, missing space between words 'asoften as that'.

Page 18, sidenote, printer's error, specifiaclly for specifically
'A Solid specifiaclly graver'.

Page 20, potential printer's error, properly for property, 'but
this properly they have'.

Page 20, printer's error, n for u 'loseth all a{u}thenticalness'.

Page 22, printer's error or variation in spelling, Benonamico for
Buonamico 'it seemes that Benonamico'.

Page 23, printer's error, missing i 'accordng to its excess'.

Page 24, missing line at the end of page in original text 'its
Region it loseth all'.

Page 26, missing letter n 'u{n}able by its small weight'.

Page 29, missing letter e 'that I have gon{e} about'.

Page 32, unclear symbol in original text 'other Figure, {&}c.'.

Page 37, potential printer's error, comma in unusual position
'whatever Figure, goeth always'.

Page 38, missing space between words 'Superficies might bedry:'.

Page 39, missing letter t, unied for united 'which holds them unied'.

Page 41, printer's error, Motitions for Motions 'all Motitions are
made'.

Page 42, sidenote, possible missing letter e, 'Se{e} what satisfaction'.

Page 43, printer's error, Subdidivisions for Subdivisions, 'other
Subdidivisions,'.

Page 49, missing letter i, dminishing for diminishing 'or dminishing
it by dividing'.

Page 50, sidenote, printer's error, missing letter l, hep for help
'float by hep of'.

Page 53, printer's error, missing letter n, beig for being 'beig
double in Gravity'.

Page 54, printer's error, missing letter l, 'sha{l}l also descend.'.

Page 55, printer's error, missing letter r, 'to fo{r}m Solid Bodies'.

Page 56, printer's error, missing letter A, 'Cone S {A} T'.

Page 57, printer's error, missing letter t, 'of which i{t} may
descend'.

Page 58, sidenote, printer's error, inverted n, 'Natatio{n} easiest
effected'.

Page 59, missing letter u, 'witho{u}t all Question,'.

Page 59, printer's error, inverted n, 'with an other Experime{n}t'.

Page 59, potential printer's error, sidenote ends with comma, 'Or
rather Contiguity,'.

Page 61, missing letter a, 'that in this c{a}se the water,'.

Page 74, printer's error, ir for it, 'but if we do saw ir,'.

Page 75, unclear symbol in original text '{&}c. making seven
Segments'.
]

End of Project Gutenberg's Discourse on Floating Bodies, by Galileo Galilei