Discourse on Floating Bodies Part 1

Discourse on Floating Bodies.

by Galileo Galilei.

A DISCOVRSE

Presented to the Most Serene DON COSIMO II.

GREAT DUKE of _TUSCANY_:

CONCERNING

_The Natation of BODIES Upon, or Submersion_ _In, the WATER._

Considering (Most Serene Prince) that the publis.h.i.+ng this present Treatise, of so different an Argument from that which many expect, and which according to the intentions I proposed in my [A] Astronomicall _Adviso_, I should before this time have put forth, might peradventure make some thinke, either that I had wholly relinquished my farther imployment about the new Celestiall Observations, or that, at least, I handled them very remissely; I have judged fit to render an account, aswell of my deferring that, as of my writing, and publis.h.i.+ng this treatise.

[A] His Nuncio Siderio.

As to the first, the last discoveries of _Saturn_ to be tricorporeall, and of the mutations of Figure in _Venus_, like to those that are seen in the Moon, together with the Consequents depending thereupon, have not so much occasioned the demur, as the investigation of the times of the Conversions of each of the Four Medicean Planets about _Jupiter_, which I lighted upon in _April_ the year past, 1611, at my being in _Rome_; where, in the end, I a.s.sertained my selfe, that the first and neerest to _Jupiter_, moved about 8 _gr._ & 29 _m._ of its Sphere in an houre, makeing its whole revolution in one naturall day, and 18 hours, and almost an halfe. The second moves in its...o...b.. 14 _gr._ 13 _min._ or very neer, in an hour, and its compleat conversion is consummate in 3 dayes, 13 hours, and one third, or thereabouts. The third pa.s.seth in an hour, 2 _gr._ 6 _min._ little more or less of its Circle, and measures it all in 7 dayes, 4 hours, or very neer. The fourth, and more remote than the rest, goes in one houre, 0 _gr_ 54 _min._ and almost an halfe of its Sphere, and finisheth it all in 16 dayes, and very neer 18 hours. But because the excessive velocity of their returns or rest.i.tutions, requires a most scrupulous precisenesse to calculate their places, in times past and future, especially if the time be for many Moneths or Years; I am therefore forced, with other Observations, and more exact than the former, and in times more remote from one another, to correct the Tables of such Motions, and limit them even to the shortest moment: for such exactnesse my first Observations suffice not; not only in regard of the short intervals of Time, but because I had not as then found out a way to measure the distances between the said Planets by any Instrument: I Observed such Intervals with simple relation to the Diameter of the Body of _Jupiter_; taken, as we have said, by the eye, the which, though they admit not errors of above a Minute, yet they suffice not for the determination of the exact greatness of the Spheres of those Stars. But now that I have hit upon a way of taking such measures without failing, scarce in a very few Seconds, I will continue the observation to the very occultation of _JUPITER_, which shall serve to bring us to the perfect knowledge of the Motions, and Magnitudes of the Orbes of the said Planets, together also with some other consequences thence arising. I adde to these things the observation of some obscure Spots[1], which are discovered in the Solar Body, which changing, position in that, propounds to our consideration a great argument either that the Sun revolves in it selfe, or that perhaps other Starrs, in like manner as _Venus_ and _Mercury_, revolve about it, invisible in other times, by reason of their small digressions, lesse than that of _Mercury_, and only visible when they interpose between the Sun and our eye, or else hint the truth of both this and that; the certainty of which things ought not to be contemned, nor omitted.

[1] The Authors Observations of the Solar Spots

_Continuall observation hath at last a.s.sured me that these Spots are matters contiguous to the Body of the Sun, there continually produced in great number, and afterwards dissolved, some in a shorter, some in a longer time, and to be by the Conversion or Revolution of the Sun in it selfe, which in a Lunar Moneth, or thereabouts, finisheth its Period, caried about in a Circle, an accident great of it selfe, and greater for its Consequences._

As to the other particular in the next place [B] Many causes have moved me to write the present Tract, the subject whereof, is the Dispute which I held some dayes since, with some learned men of this City, about which, as your Highnesse knows, have followed many Discourses: The princ.i.p.all of which Causes hath been the Intimation of your Highnesse, having commended to me Writing, as a singular means to make true known from false, reall from apparent Reasons, farr better than by Disputing vocally, where the one or the other, or very often both the Disputants, through too greate heate, or exalting of the voyce, either are not understood, or else being transported by ostentation of not yeilding to one another, farr from the first Proposition, with the novelty, of the various Proposals, confound both themselves and their Auditors.

[B] The occasion inducing the Author to write this Treatise.

Moreover, it seemed to me convenient to informe your Highnesse of all the sequell, concerning the Controversie of which I treat, as it hath been advertised often already by others: and because the Doctrine which I follow, in the discussion of the point in hand, is different from that of _Aristotle_; and interferes with his Principles, I have considered that against the Authority of that most famous Man, which amongst many makes all suspected that comes not from the Schooles of the Peripateticks, its farr better to give ones Reasons by the Pen than by word of mouth, and therfore I resolved to write the present discourse: in which yet I hope to demonstrate that it was not out of capritiousnesse, or for that I had not read or understood _Aristotle_, that I sometimes swerve from his opinion, but because severall Reasons perswade me to it, and the same _Aristotle_ hath tought me to fix my judgment on that which is grounded upon Reason, and not on the bare Authority of the Master[2]; and it is most certaine according to the sentence of _Alcinoos_, that philosophating should be free. Nor is the resolution of our Question in my judgment without some benefit to the Universall[3], forasmuch as treating whether the figure of Solids operates, or not, in their going, or not going to the bottome in Water, in occurrences of building Bridges or other Fabricks on the Water, which happen commonly in affairs of grand import, it may be of great availe to know the truth.

[2] _Aristotle_ prefers Reason to the Authority ofan Author.

[3] The benefit of this Argument.

I say therfore, that being the last Summer in company with certain Learned men, it was said in the argumentation; That Condensation was the propriety of Cold[4], and there was alledged for instance, the example of Ice: now I at that time said, that, in my judgment, the Ice should be rather Water rarified than condensed[5], and my reason was, because Condensation begets diminution of Ma.s.s, and augmentation of gravity, and Rarifaction causeth greater Lightness, and augmentarion of Ma.s.se: and Water in freezing, encreaseth in Ma.s.se, and the Ice made thereby is lighter than the Water on which it swimmeth.

[4] Condensation the Propriety of Cold, according to the Peripateticks.

[5] Ice rather water rarified, than condensed, and why:

_What I say, is manifest, because, the medium subtracting from the whole Gravity of Sollids the weight of such another Ma.s.se of the said Medium; as_ Archimedes _proves in his_ [C] First Booke De Insidentibus Humido; _when ever the Ma.s.se of the said Solid encreaseth by Distraction, the more shall the_ Medium _detract from its entire Gravity; and lesse, when by Compression it shall be condensed and reduced to a lesse Ma.s.se._

[C] In lib: 1. of Natation of Bodies Prop. 7.

[Sidenote: Figure operates not in the Natation of Sollids.]

It was answered me, tha{t} that proceeded not from the greater Levity, but from the Figure, large and flat, which not being able to penetrate the Resistance of the Water, is the cause that it submergeth not. I replied, that any piece of Ice, of whatsoever Figure, swims upon the Water, a manifest signe, that its being never so flat and broad, hath not any part in its floating: and added, that it was a manifest proofe hereof to see a piece of Ice of very broad Figure being thrust to the botome of the Water, suddenly return to flote atoppe, which had it been more grave, and had its swimming proceeded from its Forme, unable to penetrate the Resistance of the _Medium_, that would be altogether impossible; I concluded therefore, that the Figure was in sort a Cause of the Natation or Submersion of Bodies, but the greater or lesse Gravity in respect of the Water: and therefore all Bodyes heavier than it of what Figure soever they be, indifferently go to the bottome, and the lighter, though of any figure, float indifferently on the top: and I suppose that those which hold otherwise, were induced to that beliefe, by seeing how that diversity of Formes or Figures, greatly altereth the Velosity, and Tardity of Motion; so that Bodies of Figure broad and thin, descend far more leasurely into the Water, than those of a more compacted Figure, though both made of the same Matter: by which some might be induced to believe that the Dilatation of the Figure might reduce it to such amplenesse that it should not only r.e.t.a.r.d but wholly impede and take away the Motion, which I hold to be false. Upon this Conclusion, in many dayes discourse, was spoken much, and many things, and divers Experiments produced, of which your Highnesse heard, and saw some, and in this discourse shall have all that which hath been produced against my a.s.sertion, and what hath been suggested to my thoughts on this matter, and for confirmation of my Conclusion: which if it shall suffice to remove that (as I esteem hitherto false) Opinion, I shall thinke I have not unprofitably spent my paynes and time. and although that come not to pa.s.se, yet ought I to promise another benefit to my selfe, namely, of attaining the knowledge of the truth, by hearing my Fallacyes confuted, and true demonstrations produced by those of the contrary opinion.

And to proceed with the greatest plainness and perspicuity that I can possible, it is, I conceive, necessary, first of all to declare what is the true, intrinsecall, and totall Cause, of the ascending of some Sollid Bodyes in the Water, and therein floating; or on the contrary, of their sinking and so much the rather in asmuch as I cannot satisfie myselfe in that which _Aristotle_ hath left written on this Subject.

[Sidenote: The cause of the Natation & submersion of Solids in the Water.]

I say then the Cause why some Sollid Bodyes descend to the Bottom of Water, is the excesse of their Gravity, above the Gravity of the Water; and on the contrary, the excess of the Waters Gravity above the Gravity of those, is the Cause that others do not descend, rather that they rise from the Bottom, and ascend to the Surface. This was subtilly demonstrated by _Archimedes_ in his Book Of the NATATION of BODIES: Conferred afterwards by a very grave Author, but, if I erre not invisibly, as below for defence of him, I shall endeavour to prove.

I, with a different Method, and by other meanes, will endeavour to demonstrate the same, reducing the Causes of such Effects to more intrinsecall and immediate Principles, in which also are discovered the Causes of some admirable and almost incredible Accidents, as that would be, that a very little quant.i.ty of Water, should be able, with its small weight, to raise and sustain a Solid Body, an hundred or a thousand times heavier than it.

And because demonstrative Order so requires, I shall define certain Termes, and afterwards explain some Propositions, of which, as of things true and obvious, I may make use of to my present purpose.

DEFINITION I.

_I then call equally Grave_ in specie, _those Matters of which equall Ma.s.ses weigh equally._

As if for example, two b.a.l.l.s, one of Wax, and the other of some Wood of equall Ma.s.se, were also equall in Weight, we say, that such Wood, and the Wax are _in specie_ equally grave.

DEFINITION II.

_But equally grave in Absolute Gravity, we call two Sollids, weighing equally, though of Ma.s.s they be unequall._

As for example, a Ma.s.s of Lead, and another of Wood, that weigh each ten pounds, I call equall in Absolute Gravity, though the Ma.s.s of the Wood be much greater then that of the Lead.

_And, consequently, less Grave_ in specie.

DEFINITION III.

_I call a Matter more Grave_ in specie _than another, of which a Ma.s.s, equall to a Ma.s.s of the other, shall weigh more._

And so I say, that Lead is more grave _in specie_ than Tinn, because if you take of them two equall Ma.s.ses, that of the Lead weigheth more.

DEFINITION IV.