Part 1
Produced by Tim Madden and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive)
[Transcriber's Notes
All apparent printer's errors retained. Variation in punctuation are as in the original, but missing full stops at end of paragraphs have been supplied. There are inconsistencies in the use of italics, spacing of words and use of full stop after 'AXIOME', abbreviations etc. All are retained to match text. There is a great variation in spelling including multiple spellings of the same word, all spelling has been retained to match text. There are several instances of obviously missing letters or inverted n & u. These have been changed or obvious letters replaced, with the changes surrounded by {}.
All instances are detailed at the end of the text. It should also be noted that in the original text there is a missing line at the end of page 24 in original text.
There are a number of instances in the original text where 'that' is immediately followed by a second 'that' in the sentence. These could be potential printer's errors or, since several of them make sense, part of the author's style. They have been left in the text as they appear in the original text.
The original text has many sidenotes, some are true sidenotes, introductions to paragraphs etc, some acting as footnotes with some marked in original text with *. These have been dealt with in three ways with the footnotes placed after their relevant paragraph and sidenotes place before their relevant paragraph.
1) Footnotes marked with capital letter. These were sidenotes in original text marked with * in the original text and thus acting like footnotes.
2) Footnotes marked with number. These were sidenotes in original text that were unmarked but acting like normal footnotes. The anchor in the text was placed at the most suitable relevant place in comparison with the placement of the sidenote text in the margin, but still should be considered only an approximate placement.
3) Sidenotes placed at start of the relevant paragraph. Some sidenotes were considered not to be relevant as footnotes, introductions to paragraphs etc, and were left as sidenotes before their relevant paragraph.]
* * * * *
A DISCOURSE _PRESENTED_ TO THE MOST SERENE Don Cosimo II. GREAT DUKE _OF_ TUSCANY,
CONCERNING
The _NATATION_ of BODIES Vpon, And _SUBMERSION_ In, THE WATER.
By GALILEUS GALILEI: Philosopher and Mathematician unto His most Serene Highnesse.
Englished from the Second Edition of the ITALIAN, compared with the Manuscript Copies, and reduced into PROPOSITIONS:
By _THOMAS SALUSBURY_, Esq;
_LONDON_:
Printed by WILLIAM LEYBOURN:
_M DC LXIII._
* * * * *
[Decoration]
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 publishing 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 publishing 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 assertained 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 Orbe 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 passeth 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 restitutions, 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 assured 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 principall 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 Mass, and augmentation of gravity, and Rarifaction causeth greater Lightness, and augmentarion of Masse: and Water in freezing, encreaseth in Masse, 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 Masse of the said Medium; as_ Archimedes _proves in his_ [C] First Booke De Insidentibus Humido; _when ever the Masse 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 Masse._
[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 retard 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 Assertion, 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 passe, 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 quantity 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 Masses weigh equally._
As if for example, two Balls, one of Wax, and the other of some Wood of equall Masse, 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 Mass they be unequall._
As for example, a Mass of Lead, and another of Wood, that weigh each ten pounds, I call equall in Absolute Gravity, though the Mass 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 Mass, equall to a Mass 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 Masses, that of the Lead weigheth more.
DEFINITION IV.
_But I call that Body more grave absolutely than this, if that weigh more than this, without any respect had to the Masses._
And thus a great piece of Wood is said to weigh more than a little lump of Lead, though the Lead be _in specie_ more heavy than the Wood. And the same is to be understood of the less grave _in specie_, and the less grave absolutely.
These Termes defined, I take from the Mechanicks two Principles: the first is, that
AXIOME. I.
_Weights absolutely equall, moved with equall Velocity, are of equall Force and Moment in their operations._
_DEFINITION V._
Moment, amongst Mechanicians, signifieth that Vertue, that Force, or that Efficacy, with which the Mover moves, and the Moveable resists.
_Which Vertue dependes not only on the simple Gravity, but on the Velocity of the Motion, and on the diverse Inclinations of the Spaces along which the Motion is made: For a descending Weight makes a greater Impetus in a Space much declining, than in one less declining; and in summe, what ever is the occasion of such Vertue, it ever retaines the name of Moment; nor in my Judgement, is this sence new in our Idiome, for, if I mistake not, I think we often say; This is a weighty businesse, but the other is of small moment: and we consider lighter matters and let pass those of Moment; a Metaphor, I suppose, taken from the Mechanicks._
As for example, two weights equall in absolute Gravity, being put into a Ballance of equall Arms, they stand in _Equilibrium_, neither one going down, nor the other up: because the equality of the Distances of both, from the Centre on which the Ballance is supported, and about which it moves, causeth that those weights, the said Ballance moving, shall in the same Time move equall Spaces, that is, shall move with equall Velocity, so that there is no reason for which this Weight should descend more than that, or that more than this; and therefore they make an _Equilibrium_, and their Moments continue of semblable and equall Vertue.
The second Principle is; That
AXIOME II.
_The Moment and Force of the Gravity, is encreased by the Velocity of the Motion._
So that Weights absolutely equall, but conjoyned with Velocity unequall, are of Force, Moment and Vertue unequall: and the more potent, the more swift, according to the proportion of the Velocity of the one, to the Velocity of the other. Of this we have a very pertinent example in the Balance or Stiliard of unequall Arms, at which Weights absolutely equall being suspended, they do not weigh down, and gravitate equally, but that which is at a greater distance from the Centre, about which the Beam moves, descends, raising the other, and the Motion of this which ascends is slow, and the other swift: and such is the Force and Vertue, which from the Velocity of the Mover, is conferred on the Moveable, which receives it, that it can exquisitely compensate, as much more Weight added to the other slower Moveable: so that if of the Arms of the Balance, one were ten times as long as the other, whereupon in the Beames moving about the Centre, the end of that would go ten times as far as the end of this, a Weight suspended at the greater distance, may sustain and poyse another ten times more grave absolutely than it: and that because the Stiliard moving, the lesser Weight shall move ten times faster than the bigger. It ought alwayes therefore to be understood, that Motions are according to the same Inclinations, namely, that if one of the Moveables move perpendicularly to the Horizon, then the other makes its Motion by the like Perpendicular; and if the Motion of one were to be made Horizontally; that then the other is made along the same Horizontall plain: and in summe, alwayes both in like Inclinations. This proportion between the Gravity and Velocity is found in all Mechanicall Instruments: and is considered by _Aristotle_, as a Principle in his _Mechanicall Questions_; whereupon we also may take it for a true Assumption, That
AXIOME III.
_Weights absolutely unequall, do alternately counterpoyse and become of equall Moments, as oft as their Gravities, with contrary proportion, answer to the Velocity of their Motions._
That is to say, that by how much the one is less grave than the other, by so much is it in a constitution of moving more swiftly than that.