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  [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
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  spelling including multiple spellings of the same word, all spelling
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  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.

Having prefatically explicated these things, we may begin to enquire,
what Bodyes those are which totally submerge in Water, and go to the
Bottom, and which those that by constraint float on the top, so that
being thrust by violence under Water, they return to swim, with one
part of their Mass visible above the Surface of the Water: and this we
will do by considering the respective operation of the said Solids,
and of Water: Which operation followes the Submersion and sinking; and
this it is[6], That in the Submersion that the Solid maketh, being
depressed downwards by its proper Gravity, it comes to drive away the
water from the place where it successively subenters, and the water
repulsed riseth and ascends above its first levell, to which Ascent on
the other side it, as being a grave Body of its own nature, resists:
And because the descending Solid more and more immerging, greater and
greater quantity of Water ascends, till the whole Sollid be submerged;
its necessary to compare the Moments of the Resistance of the water to
Ascension, with the Moments of the pressive Gravity of the Solid: And
if the Moments of the Resistance of the water, shall equalize the
Moments of the Solid, before its totall Immersion[7]; in this case
doubtless there shall be made an _Equilibrium_, nor shall the Body
sink any farther. But if the Moment of the Solid, shall alwayes exceed
the Moments wherewith the repulsed water successively makes
Resistance[8], that Solid shall not only wholly submerge under water, but
shall descend to the Bottom. But if, lastly, in the instant of totall
Submersion, the equality shall be made between the Moments of the
prement Solid, and the resisting Water[9]; then shall rest, ensue, and
the said Solid shall be able to rest indifferently, in whatsoever part
of the water. By this time is manifest the necessity of comparing the
Gravity of the water, and of the Solid[10]; and this comparison might at
first sight seem sufficient to conclude and determine which are the
Solids that float a-top, and which those that sink to the Bottom in
the water, asserting that those shall float which are lesse grave _in
specie_ than the water, and those submerge, which are _in specie_ more
grave. For it seems in appearance, that the Sollid in sinking
continually, raiseth so much Water in Mass, as answers to the parts of
its own Bulk submerged: whereupon it is impossible, that a Solid less
grave _in specie_, than water, should wholly sink, as being unable to
raise a weight greater than its own, and such would a Mass of water
equall to its own Mass be. And likewise it seems necessary, that the
graver Solids do go to the Bottom, as being of a Force more than
sufficient for the raising a Masse of water, equall to its own, though
inferiour in weight. Nevertheless the business succeeds otherwise: and
though the Conclusions are true, yet are the Causes thus assigned
deficient, nor is it true, that the Solid in submerging, raiseth and
repulseth Masses of Water, equall to the parts of it self submerged;
but the Water repulsed, is alwayes less than the parts of the Solid
submerged[11]: and so much the more by how much the Vessell in which the
Water is contained is narrower: in such manner that it hinders not,
but that a Solid may submerge all under Water, without raising so much
Water in Mass, as would equall the tenth or twentieth part of its own
Bulk: like as on the contrary, a very small quantity of Water, may
raise a very great Solid Mass[12], though such Solid should weigh
absolutely a hundred times as much, or more, than the said Water, if
so be that the Matter of that same Solid be _in specie_ less grave
than the Water. And thus a great Beam, as suppose of a 1000 weight,
may be raised and born afloat by Water, which weighs not 50: and this
happens when the Moment of the Water is compensated by the Velocity of
its Motion.

    [6] How the submersion of Solids in the Water, is effected.

    [7] What Solids shall float on the Water.

    [8] What Solids shall sinke to the botome.

    [9] What Solids shall rest in all places of the Water.

    [10] The Gravitie of the Water and Solid must be compared in all
    Problems, of Natation of Bodies.

    [11] The water repelled is ever less than the parts of the Sollid
    submerged.

    [12] _A_ small quantity of water, may float a very great Solid
    Mass.

But because such things, propounded thus in abstract, are somewhat
difficult to be comprehended, it would be good to demonstrate them by
particular examples; and for facility of demonstration, we will
suppose the Vessels in which we are to put the Water, and place the
Solids, to be inviron'd and included with sides erected perpendicular
to the Plane of the Horizon, and the Solid that is to be put into such
vessell to be either a streight Cylinder, or else an upright Prisme.

_The which proposed and declared, I proceed to demonstrate the truth
of what hath been hinted, forming the ensuing Theoreme._




_THEOREME I._

    [Sidenote: The Proportion of the water raised to the Solid
    submerged.]

  The Mass of the Water which ascends in the submerging of a Solid,
    Prisme or Cylinder, or that abaseth in taking it out, is less
    than the Mass of the said Solid, so depressed or advanced: and
    hath to it the same proportion, that the Surface of the Water
    circumfusing the Solid, hath to the same circumfused Surface,
    together with the Base of the Solid.


_Let the Vessell be A B C D, and in it the Water raised up to the
Levell E F G, before the Solid Prisme H I K be therein immerged; but
after that it is depressed under Water, let the Water be raised as
high as the Levell L M, the Solid H I K shall then be all under Water,
and the Mass of the elevated Water shall be L G, which is less than
the Masse of the Solid depressed, namely of H I K, being equall to the
only part E I K, which is contained under the first Levell E F G.
Which is manifest, because if the Solid H I K be taken out, the Water
I G shall return into the place occupied by the Mass E I K, where it
was continuate before the submersion of the Prisme. And the Mass L G
being equall to the Mass E K: adde thereto the Mass E N, and it shall
be the whole Mass E M, composed of the parts of the Prisme E N, and of
the Water N F, equall to the whole Solid H I K: And, therefore, the
Mass L G shall have the same proportion to E M, as to the Mass H I K:
But the Mass L G hath the same proportion to the Mass E M, as the
Surface L M hath to the Surface M H: Therefore it is manifest, that
the Mass of Water repulsed L G, is in proportion to the Mass of the
Solid submerged H I K; as the Surface L M, namely, that of the Water
ambient about the Sollid, to the whole Surface H M, compounded of the
said ambient water, and the Base of the Prisme H N. But if we suppose
the first Levell of the Water the according to the Surface H M, and
the Prisme allready submerged H I K; and after to be taken out and
raised to E A O, and the Water to be faln from the first Levell H L M
as low as E F G; It is manifest, that the Prisme E A O being the same
with H I K, its superiour part H O, shall be equall to the inferiour E
I K: and remove the common part E N, and, consequently, the Mass of
the Water L G is equall to the Mass H O; and, therefore, less than the
Solid, which is without the Water, namely, the whole Prisme E A O, to
which likewise, the said Mass of Water abated L G, hath the same
proportion, that the Surface of the Waters circumfused L M hath to the
same circumfused Surface, together with the Base of the Prisme A O:
which hath the same demonstration with the former case above._

[Illustration]

_And from hence is inferred, that the Mass of the Water, that riseth
in the immersion of the Solid, or that ebbeth in elevating it, is not
equall to all the Mass of the Solid, which is submerged or elevated,
but to that part only, which in the immersion is under the first
Levell of the Water, and in the elevation remaines above the first
Levell: Which is that which was to be demonstrated. We will now pursue
the things that remain._

And first we will demonstrate that,




THEOREME II.

    [Sidenote: The proportion of the water abated, to the Solid
    raised.]

  _When in one of the above said Vessels, of what ever breadth,
    whether wide or narrow, there is placed such a Prisme or
    Cylinder, inviron'd with Water, if we elevate that Solid
    perpendicularly, the Water circumfused shall abate, and the
    Abatement of the Water, shall have the same proportion to the
    Elevation of the Prisme, as one of the Bases of the Prisme, hath
    to the Surface of the Water Circumfused._


[Illustration]

Imagine in the Vessell, as is aforesaid, the Prisme A C D B to be
placed, and in the rest of the Space the Water to be diffused as far
as the Levell E A: and raising the Solid, let it be transferred to G
M, and let the Water be abased from E A to N O: I say, that the
descent of the Water, measured by the Line A O, hath the same
proportion to the rise of the Prisme, measured by the Line G A, as the
Base of the Solid G H hath to the Surface of the Water N O. The which
is manifest: because the Mass of the Solid G A B H, raised above the
first Levell E A B, is equall to the Mass of Water that is abased E N
O A. Therefore, E N O A and G A B H are two equall Prismes; for of
equall Prismes, the Bases answer contrarily to their heights:
Therefore, as the Altitude A O is to the Altitude A G, so is the
Superficies or Base G H to the Surface of the Water N O. If therefore,
for example, a Pillar were erected in a waste Pond full of Water, or
else in a Well, capable of little more then the Mass of the said
Pillar, in elevating the said Pillar, and taking it out of the Water,
according as it riseth, the Water that invirons it will gradually
abate, and the abasement of the Water at the instant of lifting out
the Pillar, shall have the same proportion, that the thickness of the
Pillar hath to the excess of the breadth of the said Pond or Well,
above the thickness of the said Pillar: so that if the breadth of the
Well were an eighth part larger than the thickness of the Pillar, and
the breadth of the Pond twenty five times as great as the said
thickness, in the Pillars ascending one foot, the water in the Well
shall descend seven foot, and that in the Pond only 1/25 of a foot.

    [Sidenote: Why a Solid less grave _in specie_ than water, stayeth
    not under water, in very small depths:]

This Demonstrated, it will not be difficult to show the true cause,
how it comes to pass, that,




THEOREME III.

  _A Prisme or regular Cylinder, of a substance specifically less
    grave than Water, if it should be totally submerged in Water,
    stayes not underneath, but riseth, though the Water circumfused
    be very little, and in absolute Gravity, never so much inferiour
    to the Gravity of the said Prisme._


Let then the Prisme A E F B, be put into the Vessell C D F B, the same
being less grave _in specie_ than the Water: and let the Water infused
rise to the height of the Prisme: I say, that the Prisme left at
liberty, it shall rise, being born up by the Water circumfused C D E
A. For the Water C E being specifically more grave than the Solid A F,
the absolute weight of the water C E, shall have greater proportion to
the absolute weight of the Prisme A F, than the Mass C E hath to the
Mass A F (in regard the Mass hath the same proportion to the Mass,
that the weight absolute hath to the weight absolute, in case the
Masses are of the same Gravity _in specie_.) But the Mass C E is to
the Mass A F, as the Surface of the water A C, is to the Superficies,
or Base of the Prisme A B; which is the same proportion as the ascent
of the Prisme when it riseth, hath to the descent of the Water
circumfused C E.

[Illustration]

Therefore, the absolute Gravity of the water C E, hath greater
proportion to the absolute Gravity of the Prisme A F; than the Ascent
of the Prisme A F, hath to the descent of the said water C E. The
Moment, therefore, compounded of the absolute Gravity of the water C
E, and of the Velocity of its descent, whilst it forceably repulseth
and raiseth the Solid A F, is greater than the Moment compounded of
the absolute Gravity of the Prisme A F, and of the Tardity of its
ascent, with which Moment it contrasts and resists the repulse and
violence done it by the Moment of the water: Therefore, the Prisme
shall be raised.

    [Sidenote: The Proportion according to which the Submersion &
    Natation of Solids is made.]

It followes, now, that we proceed forward to demonstrate more
particularly, how much such Solids shall be inferiour in Gravity to
the water elevated; namely, what part of them shall rest submerged,
and what shall be visible above the Surface of the water: but first it
is necessary to demonstrate the subsequent Lemma.




LEMMA I.

    [Sidenote: The absolute Gravity of Solids, are in a proportion
    compounded of their Specifick Gravities, and of their Masses.]

  _The absolute Gravities of Solids, have a proportion compounded of
    the proportions of their specificall Gravities, and of their
    Masses._


[Illustration]

Let A and B be two Solids. I say, that the Absolute Gravity of A,
hath to the Absolute Gravity of B, a proportion compounded of the
proportions of the specificall Gravity of A, to the Specificall
Gravity of B, and of the Mass A to the Mass B. Let the Line D have the
same proportion to E, that the specifick Gravity of A, hath to the
specifick Gravity of B; and let E be to F, as the Mass A to the Mass
B: It is manifest, that the proportion of D to F, is compounded of the
proportions D and E; and E and F. It is requisite, therefore, to
demonstrate, that as D is to F, so the absolute Gravity of A, is to
the absolute Gravity of B. Take the Solid C, equall in Mass to the
Solid A, and of the same Gravity _in specie_ with the Solid B.
Because, therefore, A and C are equall in Mass, the absolute Gravity
of A, shall have to the absolute Gravity of C, the same proportion, as
the specificall Gravity of A, hath to the specificall Gravity of C, or
of B, which is the same _in specie_; that is, as D is to E. And,
because, C and B are of the same Gravity _in specie_, it shall be,
that as the absolute weight of C, is to the absolute weight of B, so
the Mass C, or the Mass A, is to the Mass B; that is, as the Line E to
the Line F. As therefore, the absolute Gravity of A, is to the
absolute Gravity of C, so is the Line D to the Line E: and, as the
absolute Gravity of C, is to the absolute Gravity of B, so is the Line
E to the Line F: Therefore, by Equality of proportion, the absolute
Gravity of A, is to the absolute Gravity of B, as the Line D to the
Line F: which was to be demonstrated. I proceed now to demonstrate,
how that,




THEOREME IV.

    [Sidenote: The proportion of water requisite to make a Solid
    swim:]

  _If a Solid, Cylinder, or Prisme, lesse grave specifically than the
    Water, being put into a Vessel, as above, of whatsoever
    greatnesse, and the Water, be afterwards infused, the Solid shall
    rest in the bottom, unraised, till the Water arrive to that part
    of the Altitude, of the said Prisme, to which its whole Altitude
    hath the same proportion, that the Specificall Gravity of the
    Water, hath to the Specificall Gravity of the said Solid: but
    infusing more Water, the Solid shall ascend._


[Illustration]

Let the Vessell be M L G N of any bigness, and let there be placed in
it the Solid Prisme D F G E, less grave _in specie_ than the water;
and look what proportion the Specificall Gravity of the water, hath to
that of the Prisme, such let the Altitude D F, have to the Altitude F
B. I say, that infusing water to the Altitude F B, the Solid D G shall
not float, but shall stand in _Equilibrium_, so, that that every
little quantity of water, that is infused, shall raise it. Let the
water, therefore, be infused to the Levell A B C; and; because the
Specifick Gravity of the Solid D G, is to the Specifick Gravity of the
water, as the altitude B F is to the altitude F D; that is, as the
Mass B G to the Mass G D; as the proportion of the Mass B G is to the
Mass G D, as the proportion of the Mass G D is to the Mass A F, they
compose the Proportion of the Mass B G to the Mass A F. Therefore, the
Mass B G is to the Mass A F, in a proportion compounded of the
proportions of the Specifick Gravity of the Solid G D, to the
Specifick Gravity of the water, and of the Mass G D to the Mass A F:
But the same proportions of the Specifick Gravity of G D, to the
Specifick Gravity of the water, and of the Mass G D to the Mass A F,
do also by the precedent _Lemma_, compound the proportion of the
absolute Gravity of the Solid D G, to the absolute Gravity of the Mass
of the water A F: Therefore, as the Mass B G is to the Mass A F, so is
the Absolute Gravity of the Solid D G, to the Absolute Gravity of the
Mass of the water A F. But as the Mass B G is to the Mass A F; so is
the Base of the Prisme D E, to the Surface of the water A B; and so is
the descent of the water A B, to the Elevation of the Prisme D G;
Therefore, the descent of the water is to the elevation of the Prisme,
as the absolute Gravity of the Prisme, is to the absolute Gravity of
the water: Therefore, the Moment resulting from the absolute Gravity
of the water A F, and the Velocity of the Motion of declination, with
which Moment it forceth the Prisme D G, to rise and ascend, is equall
to the Moment that results from the absolute Gravity of the Prisme D
G, and from the Velocity of the Motion, wherewith being raised, it
would ascend: with which Moment it resists its being raised: because,
therefore, such Moments are equall, there shall be an _Equilibrium_
between the water and the Solid. And, it is manifest, that putting a
little more water unto the other A F, it will increase the Gravity and
Moment, whereupon the Prisme D G, shall be overcome, and elevated till
that the only part B F remaines submerged. Which is that that was to
be demonstrated.


COROLLARY I.

    [Sidenote: _H_ow far Solids less grave _in specie_ than water, do
    submerge.]

  _By what hath been demonstrated, it is manifest, that Solids less
    grave_ in specie _than the water, submerge only so far, that as
    much water in Mass, as is the part of the Solid submerged, doth
    weigh absolutely as much as the whole Solid._

For, it being supposed, that the Specificall Gravity of the water, is
to the Specificall Gravity of the Prisme D G, as the Altitude D F, is
to the Altitude F B; that is, as the Solid D G is to the Solid B G; we
might easily demonstrate, that as much water in Mass as is equall to
the Solid B G, doth weigh absolutely as much as the whole Solid D G;
For, by the _Lemma_ foregoing, the Absolute Gravity of a Mass of
water, equall to the Mass B G, hath to the Absolute Gravity of the
Prisme D G, a proportion compounded of the proportions, of the Mass B
G to the Mass G D, and of the Specifick Gravit{y} of the water, to the
Specifick Gravity of the Prisme: But the Gravity _in specie_ of the
water, to the Gravity _in specie_ of the Prisme, is supposed to be as
the Mass G D to the Mass G B. Therefore, the Absolute Gravity of a
Mass of water, equall to the Mass B G, is to the Absolute Gravity of
the Solid D G, in a proportion compounded of the proportions, of the
Mass B G to the Mass G D, and of the Mass D G to the Mass G B; which
is a proportion of equalitie. The Absolute Gravity, therefore, of a
Mass of Water equall to the part of the Mass of the Prisme B G, is
equall to the Absolute Gravity of the whole Solid D G.


COROLLARY II.

    [Sidenote: _A_ Rule to equilibrate Solids in the water.]

  _It followes, moreover, that a Solid less grave than the water,
    being put into a Vessell of any imaginable greatness, and water
    being circumfused about it to such a height, that as much water
    in Mass, as is the part of the Solid submerged, do weigh
    absolutely as much as the whole Solid; it shall by that water be
    justly sustained, be the circumfused Water in quantity greater or
    lesser._

[Illustration]

For, if the Cylinder or Prisme M, less grave than the water, _v. gra._
in Subsequiteriall proportion, shall be put into the capacious Vessell
A B C D, and the water raised about it, to three quarters of its
height, namely, to its Levell A D: it shall be sustained and exactly
poysed in _Equilibrium_. The same will happen; if the Vessell E N S F
were very small, so, that between the Vessell and the Solid M, there
were but a very narrow space, and only capable of so much water, as
the hundredth part of the Mass M, by which it should be likewise
raised and erected, as before it had been elevated to three fourths of
the height of the Solid: which to many at the first sight, may seem a
notable Paradox, and beget a conceit, that the Demonstration of these
effects, were sophisticall and fallacious: but, for those who so
repute it, the Experiment is a means that may fully satisfie them. But
he that shall but comprehend of what Importance Velocity of Motion is,
and how it exactly compensates the defect and want of Gravity, will
cease to wonder, in considering that at the elevation of the Solid M,
the great Mass of water A B C D abateth very little, but the little
Mass of water E N S F decreaseth very much, and in an instant, as the
Solid M before did rise, howbeit for a very short space: Whereupon the
Moment, compounded of the small Absolute Gravity of the water E N S F,
and of its great Velocity in ebbing, equalizeth the Force and and
Moment, that results from the composition of the immense Gravity of
the water A B C D, with its great slownesse of ebbing; since that in
the Elevation of the Sollid M, the abasement of the lesser water E S,
is performed just so much more swiftly than the great Mass of water A
C, as this is more in Mass than that which we thus demonstrate.

    [Sidenote: _T_he proportion according to which water riseth and
    falls in different Vessels at the Immersion and Elevation of
    Solids.]

In the rising of the Solid M, its elevation hath the same proportion
to the circumfused water E N S F, that the Surface of the said water,
hath to the Superficies or Base of the said Solid M; which Base hath
the same proportion to the Surface of the water A D, that the
abasement or ebbing of the water A C, hath to the rise or elevation of
the said Solid M. Therefore, by Perturbation of proportion, in the
ascent of the said Solid M, the abasement of the water A B C D, to the
abasement of the water E N S F, hath the same proportion, that the
Surface of the water E F, hath to the Surface of the water A D; that
is, that the whole Mass of the water E N S F, hath to the whole Mass A
B C D, being equally high: It is manifest, therefore, that in the
expulsion and elevation of the Solid M, the water E N S F shall exceed
in Velocity of _M_otion the water A B C D, asmuch as it on the other
side is exceeded by that in quantity: whereupon their Moments in such
operations, are mutually equall.

[Illustration]

  _And, for ampler confirmation, and clearer explication of this, let
  us consider the present Figure, (which if I be not deceived, may
  serve to detect the errors of some Practick Mechanitians who upon a
  false foundation some times attempt impossible enterprizes,) in
  which, unto the large Vessell E I D F, the narrow Funnell or Pipe I
  C A B is continued, and suppose water infused into them, unto the
  Levell L G H, which water shall rest in this position, not without
  admiration in some, who cannot conceive how it can be, that the
  heavie charge of the great Mass of water G D, pressing downwards,
  should not elevate and repulse the little quantity of the other,
  contained in the Funnell or Pipe C L, by which the descent of it is
  resisted and hindered: But such wonder shall cease, if we begin to
  suppose the water G D to be abased only to Q D, and shall
  afterwards consider, what the water C L hath done, which to give
  place to the other, which is descended from the Levell G H, to the
  Levell Q O, shall of necessity have ascended in the same time, from
  the Levell L unto A B. And the ascent L B, shall be so much greater
  than the descent G Q, by how much the breadth of the Vessell G D,
  is greater than that of the Funnell I C; which, in summe, is as
  much as the water G D, is more than the water L C: but in regard
  that the Moment of the Velocity of the Motion, in one Moveable,
  compensates that of the Gravity of another what wonder is it, if
  the swift ascent of the lesser Water C L, shall resist the slow
  descent of the greater G D?_

The same, therefore, happens in this operation, as in rhe Stilliard,
in which a weight of two pounds counterpoyseth an other of 200,
asoften as that shall move in the same time, a space 100 times greater
than this: which falleth out when one Arme of the Beam is an hundred
times as long as the other. Let the erroneous opinion of those
therefore cease, who hold that a Ship is better, and easier born up in
a great abundance of water, then in a lesser quantity[13], (_this was
believed by_ Aristotle _in his Problems, Sect. 23, Probl. 2._) it being
on the contrary true, that its possible, that a Ship may as well float
in ten Tun of water, as in an Ocean.

    [13] A ship flotes as well in ten Tun of Water as in an Ocean.

    [Sidenote: A Solid specifiaclly graver than the water, cannot be
    born up by any quantity of it.]

But following our matter, I say, that by what hath been hitherto
demonstrated, we may understand how, that


COROLLARY III.

  _One of the above named Solids, when more grave_ in specie _than the
    water, can never be sustained, by any whatever quantity of it._

For having seen how that the Moment wherewith such a Solid, as grave
_in specie_ as the water, contrasts with the Moment of any Mass of
water whatsoever, is able to retain it, even to its totall Submersion,
without its ever ascending; it remaineth, manifest, that the water is
far less able to raise it up, when it exceeds the same _in specie_:
so, that though you infuse water till its totall Submersion, it shall
still stay at the Bottome, and with such Gravity, and Resistance to
Elevation, as is the excess of its Absolute Gravity, above the
Absolute Gravity of a Mass equall to it, made of water, or of a Matter
_in specie_ equally grave with the water: and, though you should
moreover adde never so much water above the Levell of that which
equalizeth the Altitude of the Solid, it shall not, for all that,
encrease the Pression, or Gravitation, of the parts circumfused about
the said Solid, by which greater pression, it might come to be
repulsed; because, the Resistance is not made, but only by those parts
of the water, which at the Motion of the said Solid do also move, and
these are those only, which are comprehended by the two Superficies
equidistant to the Horizon, and their parallels, that comprehend the
Altitude of the Solid immerged in the water.

I conceive, I have by this time sufficiently declared and opened the
way to the contemplation of the true, intrinsecall and proper Causes
of diverse Motions, and of the Rest of many Solid Bodies in diverse
_Mediums_, and particularly in the water, shewing how all in effect,
depend on the mutuall excesses of the Gravity of the Moveables and of
the _Mediums_: and, that which did highly import, removing the
Objection, which peradventure would have begotten much doubting, and
scruple in some, about the verity of my Conclusion, namely, how that
notwithstanding, that the excess of the Gravity of the water, above
the Gravity of the Solid, demitted into it, be the cause of its
floating and rising from the Bottom to the Surface, yet a quantity of
water, that weighs not ten pounds, can raise a Solid that weighs above
100 pounds: in that we have demonstrated, That it sufficeth, that such
difference be found between the Specificall Gravities of the _Mediums_
and Moveables, let the particular and absolute Gravities be what they
will: insomuch, that a Solid, provided that it be Specifically less
grave than the water, although its absolute weight were 1000 pounds,
yet may it be born up and elevated by ten pounds of water, and less:
and on the contrary, another Solid, so that it be Specifically more
grave than the water, though in absolute Gravity it were not above a
pound, yet all the water in the Sea, cannot raise it from the Bottom,
or float it. This sufficeth me, for my present occasion, to have, by
the above declared Examples, discovered and demonstrated, without
extending such matters farther, and, as I might have done, into a long
Treatise: yea, but that there was a necessity of resolving the above
proposed doubt, I should have contented my self with that only, which
is demonstrated by _Archimedes_, in his first _Book De Insidentibus
humido_[14]: where in generall termes he infers and confirms the same
Conclusions, namely, that Solids (_a_) less grave than water, swim or
float upon it, the (_b_) more grave go to the Bottom, and the (_c_)
equally grave rest indifferently in all places, yea, though they
should be wholly under water.

    [14] _Of Natation_ (a) _Lib. 1, Prop. 4._ (b) _Id. Lib. 1. Prop.
    3._ (c) _Id. Lib. 1. Prop. 3._

    [Sidenote: The Authors defence of _Archimedes_ his Doctrine,
    against the oppositions of _Buonamico_.]

But, because that this Doctrine of Archimedes, perused, transcribed
and examined by _Signor Francesco Buonamico_, in his _fifth Book of
Motion, Chap. 29_, and afterwards by him confuted, might by the
Authority of so renowned, and famous a Philosopher, be rendered
dubious, and suspected of falsity; I have judged it necessary to
defend it, if I am able so to do, and to clear _Archimedes_, from
those censures, with which he appeareth to be charged. _Buonamico_
rejecteth the Doctrine of _Archimedes_, first[15], as not consentaneous
with the Opinion of _Aristotle_, adding, that it was a strange thing
to him, that the Water should exceed the Earth in Gravity[16], seeing on
the contrary, that the Gravity of water, increaseth, by means of the
participation of Earth. And he subjoyns presently after[17], that he was
not satisfied with the Reasons of _Archimedes_, as not being able with
that Doctrine, to assign the cause whence it comes, that a Boat and a
Vessell, which otherwise, floats above the water, doth sink to the
Bottom, if once it be filled with water; that by reason of the
equality of Gravity, between the water within it, and the other water
without, it should stay a top; but yet, nevertheless, we see it to go
to the Bottom.

    [15] His first Objection against the Doctrine of _Archimedes_.

    [16] His Second Objection.

    [17] His third Objection.

He farther addes[18], that _Aristotle_ had clearly confuted the Ancients,
who said, that light Bodies moved upwards[19], driven by the impulse of
the more grave Ambient: which if it were so, it should seem of
necessity to follow, that all naturall Bodies are by nature heavy, and
none light: For that the same would befall the Fire and Air, if put in
the Bottom of the water. And, howbeit, _Aristotle_ grants a Pulsion in
the Elements, by which the Earth is reduced into a Sphericall Figure,
yet nevertheless, in his judgement; it is not such that it can remove
grave Bodies from their naturall places, but rather, that it send them
toward the Centre, to which (as he somewhat obscurely continues to
say,) the water principally moves, if it in the interim meet not with
something that resists it, and, by its Gravity, thrusts it out of its
place: in which case, if it cannot directly, yet at least as well as
it can, it tends to the Centre: but it happens, that light Bodies by
such Impulsion, do all ascend upward: but this properly they have by
nature, as also, that other of swimming. He concludes, lastly[20], that he
concurs with _Archimedes_ in his Conclusions; but not in the Causes,
which he would referre to the facile and difficult Separation of the
_Medium_, and to the predominance of the Elements, so that when the
Moveable superates the power of the _Medium_; as for example, Lead
doth the Continuity of water, it shall move thorow it, else not.

    [18] His fourth Objection.

    [19] The _A_ncients denyed _A_bsolute Levity.

    [20] The causes of Natation & Submersion, according to the
    Peripateticks.

This is all that I have been able to collect, as produced against
_Archimedes_ by _Signor Buonamico_: who hath not well observed the
Principles and Suppositions of _Archimedes_; which yet must be false,
if the Doctrine be false, which depends upon them; but is contented to
alledge therein some Inconveniences, and some Repugnances to the
Doctrine and Opinion of _Aristotle_. In answer to which Objections, I
say, first[21], That the being of _Archimedes_ Doctrine, simply different
from the Doctrine of _Aristotle_, ought not to move any to suspect it,
there being no cause, why the Authority of this should be preferred to
the Authority of the other: but, because, where the decrees of Nature
are indifferently exposed to the intellectuall eyes of each, the
Authority of the one and the other, loseth all a{u}thenticalness of
Perswasion, the absolute power residing in Reason; therefore I pass to
that which he alledgeth in the second place[22], as an absurd consequent
of the Doctrine of _Archimedes_, namely, That water should be more
grave than Earth. But I really find not, that ever _Archimedes_ said
such a thing, or that it can be rationally deduced from his
Conclusions: and if that were manifest unto me, I verily believe, I
should renounce his Doctrine, as most erroneous. Perhaps this
Deduction of _Buonamico_, is founded upon that which he citeth of the
Vessel, which swims as long as its voyd of water, but once full it
sinks to the Bottom, and understanding it of a Vessel of Earth, he
infers against _Archimedes_ thus: Thou sayst that the Solids which
swim, are less grave than water: this Vessell swimmeth: therefore,
this Vessell is lesse grave than water. If this be the Illation. I
easily answer, granting that this Vessell is lesse grave than water,
and denying the other consequence, namely, that Earth is less Grave
than Water. The Vessel that swims occupieth in the water, not only a
place equall to the Mass of the Earth, of which it is formed; but
equall to the Earth and to the Air together, contained in its
concavity. And, if such a Mass compounded of Earth and Air, shall be
less grave than such another quantity of water, it shall swim, and
shall accord with the Doctrine of _Archimedes_; but if, again,
removing the Air, the Vessell shall be filled with water, so that the
Solid put in the water, be nothing but Earth, nor occupieth other
place, than that which is only possest by Earth, it shall then go to
the Bottom, by reason that the Earth is heavier than the water: and
this corresponds well with the meaning of _Archimedes_. See the same
effect illustrated, with such another Experiment, In pressing a Viall
Glass to the Bottom of the water, when it is full of Air, it will meet
with great resistance, because it is not the Glass alone, that is
pressed under water, but together with the Glass a great Mass of Air,
and such, that if you should take as much water, as the Mass of the
Glass, and of the Air contained in it, you would have a weight much
greater than that of the Viall, and of its Air: and, therefore, it
will not submerge without great violence: but if we demit only the
Glass into the water, which shall be when you shall fill the Glass
with water, then shall the Glass descend to the Bottom; as superiour
in Gravity to the water.

    [21] The Authors answer to the first Objection.

    [22] The Authors answer to the second Objection.

Returning, therefore, to our first purpose; I say, that Earth is more
grave than water, and that therefore, a Solid of Earth goeth to the
bottom of it; but one may possibly make a composition of Earth and
Air, which shall be less grave than a like Mass of Water; and this
shall swim: and yet both this and the other experiment shall very well
accord with the Doctrine of _Archimedes_. But because that in my
judgment it hath nothing of difficulty in it, I will not positively
affirme that _Signor Buonamico_, would by such a discourse object unto
_Archimedes_ the absurdity of inferring by his doctrine, that Earth
was less grave than Water, though I know not how to conceive what
other accident he could have induced thence.

Perhaps such a Probleme (in my judgement false) was read by _Signor
Buonamico_ in some other Author, by whom peradventure it was
attributed as a singular propertie, of some particular Water, and so
comes now to be used with a double errour in confutation of
_Archimedes_, since he saith no such thing, nor by him that did say it
was it meant of the common Element of Water.

    [Sidenote: The Authors answer to the third Objection.]

The third difficulty in the doctrine of _Archimedes_ was, that he
could not render a reason whence it arose, that a piece of Wood, and a
Vessell of Wood, which otherwise floats, goeth to the bottom, if
filled with Water. _Signor Buonamico_ hath supposed that a Vessell of
Wood, and of Wood that by nature swims, as before is said, goes to the
bottom, if it be filled with water; of which he in the following
Chapter, which is the 30 of the fifth Book copiously discourseth: but
I (speaking alwayes without diminution of his singular Learning) dare
in defence of _Archimedes_ deny this experiment, being certain that a
piece of Wood which by its nature sinks not in Water, shall not sinke
though it be turned and converted into the forme of any Vessell
whatsoever, and then filled with Water: and he that would readily see
the Experiment in some other tractable Matter, and that is easily
reduced into several Figures, may take pure Wax, and making it first
into a Ball or other solid Figure, let him adde to it so much Lead as
shall just carry it to the bottome, so that being a graine less it
could not be able to sinke it, and making it afterwards into the forme
of a Dish, and filling it with Water, he shall finde that without the
said Lead it shall not sinke, and that with the Lead it shall descend
with much slowness: & in short he shall satisfie himself, that the
Water included makes no alteration. I say not all this while, but that
its possible of Wood to make Barkes, which being filled with water,
sinke; but that proceeds not through its Gravity, encreased by the
Water, but rather from the Nailes and other Iron Workes, so that it no
longer hath a Body less grave than Water, but one mixt of Iron and
Wood, more grave than a like Masse of Water. Therefore let _Signor
Buonamico_ desist from desiring a reason of an effect, that is not in
nature: yea if the sinking of the Woodden Vessell when its full of
Water, may call in question the Doctrine of _Archimedes_, which he
would not have you to follow, is on the contrary consonant and
agreeable to the Doctrine of the Peripateticks, since it aptly
assignes a reason why such a Vessell must, when its full of Water,
descend to the bottom; converting the Argument the other way, we may
with safety say that the Doctrine of _Archimedes_ is true, since it
aptly agreeth with true experiments, and question the other, whose
Deductions are fastened upon erroneouss Conclusions. As for the other
point hinted in this same Instance, where it seemes that _Benonamico_
understands the same not only of a piece of wood, shaped in the forme
of a Vessell, but also of massie Wood, which filled, _scilicet_, as I
believe, he would say, soaked and steeped in Water, goes finally to
the bottom that happens in some porose Woods, which, while their
Porosity is replenished with Air, or other Matter less grave than
Water, are Masses specificially less grave than the said Water, like
as is that Viall of Glass whilest it is full of Air: but when, such
light Matter departing, there succeedeth Water into the same
Porosities and Cavities, there results a compound of Water and Glass
more grave than a like Mass of Water: but the excess of its Gravity
consists in the Matter of the Glass, and not in the Water, which
cannot be graver than it self: so that which remaines of the Wood, the
Air of its Cavities departing, if it shall be more grave _in specie_
than Water, fil but its Porosities with Water, and you shall have a
Compost of Water and of Wood more grave than Water, but not by vertue
of the Water received into and imbibed by the Porosities, but of that
Matter of the Wood which remains when the Air is departed: and being
such it shall, according to the Doctrine of _Archimedes_, goe to the
bottom, like as before, according to the same Doctrine it did swim.

    [Sidenote: The Authors answer to the fourth Objection.]

As to that finally which presents itself in the fourth place,
namely, that the _Ancients_ have been heretofore confuted by
_Aristotle_, who denying Positive and Absolute Levity, and truely
esteeming all Bodies to be grave, said, that that which moved upward
was driven by the circumambient Air, and therefore that also the
Doctrine of _Archimedes_, as an adherent to such an Opinion was
convicted and confuted: I answer first, that _Signor Buonamico_ in my
judgement hath imposed upon _Archimedes_, and deduced from his words
more than ever he intended by them, or may from his Propositions be
collected, in regard that _Archimedes_ neither denies, nor admitteth
Positive Levity, nor doth he so much as mention it: so that much less
ought _Buonamico_ to inferre, that he hath denyed that it might be the
Cause and Principle of the Ascension of Fire, and other Light Bodies[23]:
having but only demonstrated, that Solid Bodies more grave than Water
descend in it, according to the excess of their Gravity above the
Gravity of that, he demonstrates likewise, how the less grave ascend
in the same Water[24], accordng to its excess of Gravity, above the
Gravity of them. So that the most that can be gathered from the
Demonstration of _Archimedes_ is, that like as the excess of the
Gravity of the Moveable above the Gravity of the Water, is the Cause
that it descends therein, so the excess of the Gravity of the water
above that of the Moveable, is a sufficient Cause why it descends not,
but rather betakes it self to swim: not enquiring whether of moving
upwards there is, or is not any other Cause contrary to Gravity: nor
doth _Archimedes_ discourse less properly than if one should say: If
the South Winde shall assault the Barke with greater _Impetus_ than is
the violence with which the Streame of the River carries it towards
the South, the motion of it shall be towards the North: but if the
_Impetus_ of the Water shall overcome that of the Winde, its motion
shall be towards the South. The discourse is excellent and would be
unworthily contradicted by such as should oppose it, saying: Thou
mis-alledgest as Cause of the motion of the Bark towards the South,
the _Impetus_ of the Stream of the Water above that of the South
Winde; mis-alledgest I say, for it is the Force of the North Winde
opposite to the South, that is able to drive the Bark towards the
South. Such an Objection would be superfluous, because he which
alledgeth for Cause of the Motion the Stream of the Water, denies not
but that the Winde opposite to the South may do the same, but only
affirmeth that the force of the Water prevailing over the South Wind,
the Bark shall move towards the South: and saith no more than is true.
And just thus when _Archimedes_ saith, that the Gravity of the Water
prevailing over that by which the moveable descends to the Bottom,
such moveable shall be raised from the Bottom to the Surface alledgeth
a very true Cause of such an Accident, nor doth he affirm or deny that
there is, or is not, a vertue contrary to Gravity, called by some
Levity, that hath also a power of moving some Matters upwards. Let
therefore the Weapons of _Signor Buonamico_ be directed against
_Plato_[25], and other _Ancients_, who totally denying _Levity_, and
taking all Bodies to be grave, say that the Motion upwards is made,
not from an intrinsecal Principle of the Moveable, but only by the
Impulse of the _Medium_; and let _Archimedes_ and his Doctrine escape
him, since he hath given him no Cause of quarelling with him. But if
this Apologie, produced in defence of _Archimedes_, should seem to
some insufficient to free him from the Objections and Arguments,
produced by _Aristotle_ against _Plato_, and the other _Ancients_, as if
they did also fight against _Archimedes_, alledging the Impulse of the
Water as the Cause of the swimming of some Bodies less grave than it[26],
I would not question, but that I should be able to maintaine the
Doctrine of _Plato_ and those others to be most true, who absolutely
deny Levity, and affirm no other Intrinsecal Principle of Motion to be
in Elementary Bodies save only that towards the Centre of the Earth[27],
nor no other Cause of moving upwards, speaking of that which hath the
resemblance of natural Motion, but only the repulse of the _Medium_,
fluid, and exceeding the Gravity of the Moveable[28]: and as to the
Reasons of _Aristotle_ on the contrary, I believe that I could be able
fully to answer them, and I would assay to do it, if it were
absolutely necessary to the present Matter, or were it not too long a
Digression for this short Treatise. I will only say, that if there
were in some of our Ellementary Bodies an Intrinsecall Principle and
Naturall Inclination to shun the Centre of the Earth, and to move
towards the Concave of the Moon, such Bodies, without doubt, would
more swiftly ascend through those _Mediums_ that least oppose the
Velocity of the Moveable, and these are the more tenuous and subtle;
as is, for example, the Air in comparison of the Water, we daily
proving that we can with farre more expeditious Velocity move a Hand
or a Board to and again in one than in the other[29]: nevertheless, we
never could finde any Body, that did not ascend much more swiftly in
the water than in the Air. Yea of Bodies which we see continually to
ascend in the Water, there is none that having arrived to the confines
of the Air, do not wholly lose their Motion[30]; even the Air it self,
which rising with great Celerity through the Water, being once come to
its Region it loseth all

    [23] Of Natation, Lib. 1. Prop. 7.

    [24] Of Natation, Lib. 1. Prop. 4.

    [25] _Plato_ denyeth Positive Levity.

    [26] The Authors defence of the doctrine of _Plato_ and the
    _Ancients_, who absolutely deny Levity:

    [27] According to _Plato_ there is no Principle of the Motion, of
    descent in Naturall Bodies, save that to the Centre.

    [28] No cause of the motion of Ascent, save the Impulse of the
    _Medium_, exceeding the Moveable in Gravitie.

    [29] Bodies ascend much swifter in the Water, than in the Air.

    [30] All Bodies ascending through Water, lose their Motion,
    comming to the confines of the Air.

    [Sidenote: The lighter Bodies ascend more swiftly through Water.]

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.]

But to be in the water, implies to be placed in the water, and by
_Aristotles_ own Definition of place, to be placed, importeth to be
invironed by the Superficies of the Ambient Body, therefore, then
shall the two Figures be in the water, when the Superficies of the
water, shall imbrace and inviron them: but when the Adversaries shew
the Board of Ebony not descending to the Bottom, they put it not into
the water, but upon the water, where being by a certain impediment (as
by and by we will shew) retained, it is invironed, part by water, and
part by air, which thing is contrary to our agreement, that was, that
the Bodies should be in the water, and not part in water, and part in
air.

  _The which is again made manifest, by the questions being put as
  well about the things which go to the Bottom, as those which arise
  from the Bottom to swimme, and who sees not that things placed in
  the Bottom, must have water about them._

    [Sidenote: The confutation of the Experiment in the Ebany.]

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.

    [D] The Figure & Resistance of the Medium against Division, have
    nothing to do with the Effect of Natation or Submersion, by an
    Experiment in Wallnut tree.

    [Sidenote: An Experiment in Gold, to prove the non-operating of
    Figure in Natation and Submersion.]

Nay, I will say more, that if we shall consider Gold in comparison of
water, we shall find, that it exceeds it in Gravity almost twenty
times, so that the Force and Impetus, wherewith a Ball of Gold goes to
the Bottom, is very great. On the contrary, there want not matters, as
Virgins Wax, and some Woods, which are not above a fiftieth part less
grave than water, whereupon their Ascension therein is very slow, and
a thousand times weaker than the _Impetus_ of the Golds descent: yet
notwithstanding, a plate of Gold swims without descending to the
Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin
Board of Wood, which put in the Bottom of the Water, shall rest there
without ascending. Now if the Figure can obstruct the Penetration, and
impede the descent of Gold, that hath so great an _Impetus_, how can
it choose but suffice to resist the same Penetration of the other
matter in ascending, when as it hath scarce a thousandth part of the
_Impetus_ that the Gold hath in descending? Its therefore, necessary,
that that which suspends the thin Plate of Gold, or Board of Ebony,
upon the water, be some thing that is wanting to the other Cakes and
Boards of Matters less grave than the water; since that being put to
the Bottom, and left at liberty, they rise up to the Surface, without
any obstruction: But they want not for flatness and breadth of Figure:
Therefore, the spaciousnesse of the Figure, is not that which makes
the Gold and Ebony to swim.

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.

[Illustration]

    [Sidenote: Why solids having penitrated the Water, do not proceed
    to a totall Submersion.]

But, if it hath already penetrated, and overcome the Continuity of
the water, & is of its own nature more grave than the said water, why
doth it not proceed in its sinking, but stop and suspend its self
within that little dimple or cavitie, which with its ponderosity it
hath made in the water? I answer; because that in submerging it self,
so far as till its Superficies come to the Levell with that of the
water, it loseth a part of its Gravity, and loseth the rest of it as
it submergeth & descends beneath the Surface of the water, which
maketh Ramperts and Banks round about it, and it sustaines this loss
by means of its drawing after it, and carrying along with it, the Air
that is above it, and by Contact adherent to it, which Air succeeds to
fill the Cavity that is invironed by the Ramperts of water; so that
that which in this case descends and is placed in the water, is not
only the Board of Ebony or Plate of Iron, but a composition of Ebony
and Air, from which resulteth a Solid no longer superiour in Gravity
to the water, as was the simple Ebony, or the simple Gold. 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.

    [44] How to seperate the Air from Solids in demitting them into
    the water.

But, me thinks I hear some of the Adversaries cunningly opposing this,
and telling me, that they will not yield, by any means, that their
Board be wetted, because the weight added thereto by the Water, by
making it heavier than it was before, draws it to the Bottom, and that
the addition of new weight is contrary to our agreement, which was,
that the Matter be the same.

To this, I answer, first; that treating of the operation of Figure
in Bodies put into the Water, none can suppose them to be put into the
Water without being wet; nor do I desire more to be done to the Board,
then I will give you leave to do to the Ball. 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. Now, as he that should say that Brass, that by
its nature goes to the Bottom, being formed into the Figure of a
Ketle[50], acquireth from that Figure a vertue of lying in the Water
without sinking, would say that which is false; because that Brass
fashioned into any whatever Figure, goeth always to the Bottom,
provided, that that which is put into the water be simple Brass; and
it is not the Figure of the Vessel that makes the Brass to float, but
it is because that that is not purely Brass which is put into the
water, but an aggregate of Brass and of Air: so is it neither more nor
less false, that a thin Plate of Brass or of Ebony, swims by vertue of
its dilated & broad Figure: for the truth is, that it bares up without
submerging, because that that which is put in the water, is not pure
Brass or simple Ebony, but an aggregate of Brass and Air, or of Ebony
and Air. And, this is not contrary unto my Conclusion, the which,
(having many a time seen Vessels of Mettall, and thin pieces of
diverse grave Matters float, by vertue of the Air conjoyned with them)
did affirm, That Figure was not the Cause of the Natation or
Submersion of such Solids as were placed in the water. Nay more, I
cannot omit, but must tell my Antagonists, that this new conceit of
denying that the Superficies of the Board should be bathed, may beget
in a third person an opinion of a poverty of Arguments of defence on
their part, since that such bathing was never insisted upon by them in
the beginning of our Dispute, and was not questioned in the least,
being that the Originall of the discourse arose upon the swiming of
Flakes of Ice, wherein it would be simplicity to require that their
Superficies might bedry: besides, that whether these pieces of Ice be
wet or dry they alwayes swim, and as the Adversaries say, by reason of
the Figure.

    [45] Water hath no Gravity in Water.

    [46] Water deminisheth the Gravity of Solids immerged therein.

    [47] The Experiment of a brass Ketle swiming when empty, & sinking
    when full, alledged to prove that water gravitates in water,
    answered.

    [48] An Ocean sufficeth not to sink a Vessel specifically less
    grave than water.

    [49] Air, the Cause of the Natation of empty Vessels of Matters
    graver _in specie_ than the water.

    [50] Neither Figure, nor the breadth of Figure, is the Cause of
    Natation.

Some peradventure, by way of defence, may say, that wetting the Board
of Ebony, and that in the superiour Superficies, it would, though of
it self unable to pierce and penetrate the water, be born downwards,
if not by the weight of the additionall water, at least by that desire
and propension that the superiour parts of the water have to re-unite
and rejoyn themselves: by the Motion of which parts, the said Board
cometh in a certain manner, to be depressed downwards.

    [Sidenote: The Bathed Solid descends not out of any affectation
    of union in the upper parts of the water.]

This weak Refuge will be removed, if we do but consider, that the
repugnancy of the inferiour parts of the water, is as great against
Dis-union, as the Inclination of its superiour parts is to union: nor
can the uper unite themselves without depressing the board, nor can it
descend without disuniting the parts of the nether Water: so that it
doth follow, by necessary consequence, that for those respects, it
shall not descend. Moreover, the same that may be said of the upper
parts of the water, may with equall reason be said of the nether,
namely, that desiring to unite, they shall force the said Board
upwards.

Happily, some of these Gentlemen that dissent from me, will wonder,
that I affirm, that the contiguous superiour Air is able to sustain
that Plate of Brass or of Silver, that stayeth above water; as if I
would in a certain sence allow the Air[51], a kind of Magnetick vertue of
sustaining the grave Bodies, with which it is contiguous. To satisfie
all I may, to all doubts, I have been considering how by some other
sensible Experiment I might demonstrate, how truly that little
contiguous and superiour Air sustaines those Solids, which being by
nature apt to descend to the Bottom, being placed lightly on the water
submerge not, unless they be first thorowly bathed; and have found,
that one of these Bodies having descended to the Bottom, by
conveighing to it (without touching it in the least) a little Air,
which conjoyneth with the top of the same, it becometh sufficient, not
only, as before to sustain it, but also to raise it, and to carry it
back to the top, where it stays and abideth in the same manner, till
such time, as the assistance of the conjoyned Air is taken away. And
to this effect, I have taken a Ball of Wax, and made it with a little
Lead, so grave, that it leasurely descends to the Bottom, making with
all its Superficies very smooth and pollite: and this being put gently
into the water, almost wholly submergeth, there remaining vissible
only a little of the very top[52], the which so long as it is conjoyned
with the Air, shall retain the Ball a-top, but the Contiguity of the
Air taken away by wetting it, it shall descend to the Bottom and there
remain. Now to make it by vertue of the Air, that before sustained it
to return again to the top, and stay there, thrust into the water a
Glass reversed with the mouth downwards, the which shall carry with it
the Air it contains, and move this towards the Ball, abasing it till
such time that you see, by the transparency of the Glass, that the
contained Air do arrive to the summity of the _B_all[53]: then gently
withdraw the Glass upwards, and you shall see the _B_all to rise, and
afterwards stay on the top of the water[54], if you carefully part the
Glass and the water without overmuch commoving and disturbing it.
There is, therefore, a certain affinity between the Air and other
Bodies, which holds them unied, so, that they seperate not without a
kind of violence. The same likewise is seen in the water[55]; for if we
shall wholly submerge some Body in it, so that it be thorowly bathed,
in the drawing of it afterwards gently out again, we shall see the
water follow it, and rise notably above its Surface, before it
seperates from it. Solid Bodies, also[56], if they be equall and alike in
Superficies, so, that they make an exact Contact without the
interposition of the least Air, that may part them in the seperation
and yield untill that the ambient _Medium_ succeeds to replenish the
place, do hold very firmly conjoyned, and are not to be seperated
without great force but, because, the Air, Water, and other Liquids,
very expeditiously shape themselves to contact with any Solid
_B_odies, so that their Superficies do exquisitely adopt themselves to
that of the Solids, without any thing remaining between them,
therefore, the effect of this Conjunction and Adherence is more
manifestly and frequently observed in them, than in hard and
inflexible Bodies, whose Superficies do very rarely conjoyn with
exactness of Contact[57]. This is therefore that Magnetick vertue, which
with firm Connection conjoyneth all Bodies, that do touch without the
interposition of flexible fluids; and, who knows, but that that a
Contact, when it is very exact, may be a sufficient Cause of the Union
and Continuity of the parts of a naturall _B_ody?

    [51] _A_ Magnetisme in the _A_ir, by which it bears up those
    Solids in the water, that are contiguous with it.

    [52] The Effect of the Airs Contiguity in the Natation of Solids.

    [53] The force of Contact.

    [54] _A_n Affectation of Conjunction betwixt Solids and the Air
    contiguous to them.

    [55] The like affectation of Conjunction betwixt Solids & the
    water.

    [56] Also the like affectation and Conjunction betwixt Solids
    themselves.

    [57] Contact may be the Cause of the Continuity of Naturall
    Bodies.

Now, pursuing my purpose, I say; that it needs not, that we have
recourse to the Tenacity, that the parts of the water have amongst
themselves, by which they resist and oppose Division, Distraction, and
Seperation, because there is no such Coherence and Resistance of
Division for if there were, it would be no less in the internall parts
than in those nearer the superiour or externall Surface, so that the
same Board, finding alwayes the same Resistance and Renitence, would
no less stop in the middle of the water than about the Surface, which
is false. Moreover, what Resistance can we place in the Continuity of
the water, if we see that it is impossible to find any Body of
whatsoever Matter, Figure or Magnitude, which being put into the
water, shall be obstructed and impeded by the Tenacity of the parts of
the water to one another, so, but that it is moved upwards or
downwards, according as the Cause of their Motion transports it? And,
what greater proof of it can we desier, than that which we daily see
in Muddy waters, which being put into Vessels to be drunk, and being,
after some hours setling[58], still, as we say, thick in the end, after
four or six dayes they are wholly setled, and become pure and clear?
Nor can their Resistance of Penetration stay those impalpable and
insensible Atomes of Sand, which by reason of their exceeding small
force, spend six dayes in descending the space of half a yard.

    [58] The settlement of _M_uddy Water, proveth that that Element
    hath no aversion to Division.

  _Nor let them say, that the seeing of such small Bodies, consume
  six dayes in descending so little a way, is a sufficient Argument
  of the Waters Resistance of Division; because that is no resisting
  of Division, but a retarding of Motion; and it would be simplicity
  to say, that a thing opposeth Division[59], and that in the same
  instant, it permits it self to be divided: nor doth the Retardation
  of Motion at all favour the Adversaries cause, for that they are to
  instance in a thing that wholly prohibiteth Motion, and procureth
  Rest; it is necessary, therefore, to find out Bodies that stay in
  the water, if one would shew its repugnancy to Division, and not
  such as move in it, howbeit but slowly._

    [59] Water cannot oppose division, and at the same time permit it
    self to be divided.

What then is this Crassitude of the water, with which it resisteth
Division? What, I beseech you, should it be, if we (as we have said
above) with all diligence attempting the reduction of a Matter into so
like a Gravity with the water, that forming it into a dilated Plate it
rests suspended as we have said, between the two waters, it be
impossible to effect it, though we bring them to such an
Equiponderance, that as much Lead as the fourth part of a Grain of
Musterd-seed, added to the same expanded Plate, that in Air [_i. e.
out of the water_] shall weigh four or six pounds, sinketh it to the
Bottom, and being substracted, it ascends to the Surface of the water?
I cannot see, (if what I say be true, as it is most certain) what
minute vertue and force we can possibly find or imagine, to which the
Resistance of the water against Division and Penetration is not
inferiour; whereupon, we must of necessity conclude that it is
nothing: because, if it were of any sensible power, some large Plate
might be found or compounded of a Matter alike in Gravity to the
water, which not only would stay between the two waters; but,
moreover, should not be able to descend or ascend without notable
force. We may likewise collect the same from an other Experiment[60],
shewing that the Water gives way also in the same manner to
transversall Division; for if in a setled and standing water we should
place any great Mass that goeth not to the bottom, drawing it with a
single Womans Hair, we might carry it from place to place without any
opposition, and this whatever Figure it hath, though that it possess a
great space of water, as for instance, a great Beam would do moved
side-ways. Perhaps some might oppose me and say, that if the
Resistance of water against Division, as I affirm, were nothing; Ships
should not need such a force of Oars and Sayles for the moving of them
from place to place in a tranquile Sea, or standing Lake. To him that
should make such an objection, I would reply[61], that the water
contrasteth not against, nor simply resisteth Division, but a sudden
Division, and with so much greater Renitence, by how much greater the
Velocity is: and the Cause of this Resistance depends not on
Crassitude, or any other thing that absolutely opposeth Division, but
because that the parts of the water divided, in giving way to that
Solid that is moved in it, are themselves also necessitated locally to
move, some to the one side, and some to the other, and some downwards:
and this must no less be done by the waves before the Ship, or other
Body swimming through the water, than by the posteriour and
subsequent; because, the Ship proceeding forwards, to make it self a
way to receive its Bulk, it is requisite, that with the Prow it
repulse the adjacent parts of the water, as well on one hand as on the
other, and that it move them as much transversly, as is the half of
the breadth of the Hull: and the like removall must those waves make,
that succeeding the Poump do run from the remoter parts of the Ship
towards those of the middle, successively to replenish the places,
which the Ship in advancing forwards, goeth, leaving vacant. Now,
because, all Motitions are made in Time[62], and the longer in greater
time: and it being moreover true, that those Bodies that in a certain
time are moved by a certain power such a certain space, shall not be
moved the same space, and in a shorter Time, unless by a greater
Power: therefore, the broader Ships move slower than the narrower,
being put on by an equall Force: and the same Vessel requires so much
greater force of Wind, or Oars, the faster it is to move.

    [60] An hair will draw a great Mass thorow the Water; which
    proveth, that it hath no Resistance against transversall
    Division.

    [61] How ships are moved in the water.

    [62] Bodies moved a certain space in a certain Time, by a
    certain power, cannot be moved the same space and in a shorter
    time, but by a greater power.

  _But yet for all this, any great Mass swimming in a standing Lake,
  may be moved by any petit force; only it is true, that a lesser
  force more slowly moves it: but if the waters Resistance of
  Division, were in any manner sensible, it would follow, that the
  said Mass, should, notwithstanding the percussion of some sensible
  force, continue immoveable, which is not so[63]. Yea, I will say
  farther, that should we retire our selves into the more internall
  contemplation of the Nature of water and other Fluids, perhaps we
  should discover the Constitution of their parts to be such, that
  they not only do not oppose Division, but that they have not any
  thing in them to be divided: so that the Resistance that is
  observed in moving through the water[64], is like to that which we meet
  with in passing through a great Throng of People, wherein we find
  impediment, and not by any difficulty in the Division, for that
  none of those persons are divided whereof the Croud is composed,
  but only in moving of those persons side-ways which were before
  divided and disjoyned: and thus we find Resistance in thrusting a
  Stick into an heap of Sand, not because any part of the Sand is to
  be cut in pieces, but only to be moved and raised[65]. Two manners of
  Penetration, therefore, offer themselves to us, one in Bodies,
  whose parts were continuall, and here Division seemeth necessary,
  the other in the aggregates of parts not continuall, but contiguous
  only[66], and here there is no necessity of dividing but of moving
  only. Now, I am not well resolved, whether water and other Fluids
  may be esteemed to be of parts continuall or contiguous only[67]; yet I
  find my self indeed inclined to think that they are rather
  contiguous (if there be in Nature no other manner of aggregating,
  than by the union, or by the touching of the extreams:) and I am
  induced thereto by the great difference that I see between the
  Conjunction of the parts of an hard or Solid Body[68], and the
  Conjunction of the same parts when the same Body shall be made
  Liquid and Fluid: for if, for example, I take a Mass of Silver or
  other Solid and hard Mettall, I shall in dividing it into two
  parts, find not only the resistance that is found in the moving of
  it only[69], but an other incomparably greater, dependent on that
  vertue, whatever it be, which holds the parts united: and so if we
  would divide again those two parts into other two, and successively
  into others and others, we should still find a like Resistance, but
  ever less by how much smaller the parts to be divided shall be; but
  if, lastly, employing most subtile and acute Instruments, such as
  are the most tenuous parts of the Fire, we shall resolve it
  (perhaps) into its last and least Particles, there shall not be
  left in them any longer either Resistance of Division, or so much
  as a capacity of being farther divided, especially by Instruments
  more grosse than the acuities of Fire: and what Knife or Rasor put
  into well melted Silver can we finde, that will divide a thing
  which surpasseth the separating power of Fire? Certainly none:
  because either the whole shall be reduced to the most minute and
  ultimate Divisions, or if there remain parts capable still of other
  Subdidivisions, they cannot receive them, but only from acuter
  Divisors than Fire; but a Stick or Rod of Iron, moved in the melted
  Metall, is not such a one. Of a like Constitution and Consistence,
  I account the parts of Water[70], and other Liquids to be, namely,
  incapable of Division by reason of their Ienuity; or if not
  absolutely indivisible, yet at least not to be divided by a Board,
  or other Solid Body, palpable unto the hand, the Sector being
  alwayes required to be more sharp than the Solid to be cut. Solid
  Bodies, therefore, do only move, and not divide the Water[71], when put
  into it; whose parts being before divided to the extreamest
  minuity, and therefore capable of being moved, either many of them
  at once, or few, or very few, they soon give place to every small
  Corpuscle, that descends in the same: for that, it being little and
  light, descending in the Air, and arriving to the Surface of the
  Water, it meets with Particles of Water more small, and of less
  Resistance against Motion and Extrusion, than is its own prement
  and extrusive force; whereupon it submergeth, and moveth such a
  portion of them, as is proportionate to its Power. There is not,
  therefore, any Resistance in Water against Division, nay, there is
  not in it any divisible parts. I adde; moreover, that in case yet
  there should be any small Resistance found (which is absolutely
  false)[72] haply in attempting with an Hair to move a very great natant
  Machine, or in essaying by the addition of one small Grain of Lead
  to sink, or by removall of it to raise a very broad Plate of
  Matter, equall in Gravity with Water, (which likewise will not
  happen, in case we proceed with dexterity) we may observe that that
  Resistance is a very different thing from that which the
  Adversaries produce for the Cause of the Natation of the Plate of
  Lead or Board of Ebony, for that one may make a Board of Ebony,
  which being put upon the Water swimmeth, and cannot be submerged,
  no not by the addition of an hundred Grains of Lead put upon the
  same, and afterwards being bathed, not only sinks, though the said
  Lead be taken away, but though moreover a quantity of Cork, or of
  some other light Body fastened to it, sufficeth not to hinder it
  from sinking unto the bottome: so that you see, that although it
  were granted that there is a certain small Resistance of Division
  found in the substance of the Water, yet this hath nothing to do
  with that Cause which supports the Board above the Water, with a
  Resistance an hundred times greater than that which men can find in
  the parts of the Water: nor let them tell me, that only the Surface
  of the Water hath such Resistance[73], and not the internall parts, or
  that such Resistance is found greatest in the beginning of the
  Submersion, as it also seems that in the beginning, Motion meets
  with greater opposition, than in the continuance of it; because,
  first, I will permit, that the Water be stirred, and that the
  superiour parts be mingled with the middle[74], and inferiour parts, or
  that those above be wholly removed, and those in the middle only
  made use off, and yet you shall see the effect for all that, to be
  still the same: Moreover, that Hair which draws a Beam through the
  Water, is likewise to divide the upperparts, and is also to begin
  the Motion, and yet it begins it, and yet it divides it: and
  finally, let the Board of Ebony be put in the midway, betwixt the
  bottome and the top of the Water, and let it there for awhile be
  suspended and setled, and afterwards let it be left at liberty, and
  it will instantly begin its Motion, and will continue it unto the
  bottome. Nay, more, the Board so soon as it is dimitted upon the
  Water, hath not only begun to move and divide it, but is for a good
  space dimerged into it._

    [63] The parts of Liquids, so farre from resisting Division, that
    they contain not any thing that may be divided.

    [64] The Resistance a Solid findeth in moving through the water,
    like to that we meet with in passing through a throng of people:

    [65] Or in thrusting a Stick into an heap of Sand.

    [66] Two kinds of Penetration, one in Bodies continuall, the other
    in Bodies only contiguous.

    [67] Water consists not of continuall, but only of contiguous
    parts.

    [68] _Se{e} what satisfaction he hath given, as to this point, in
    Lib. de Motu. Dial. 2._

    [69] Great difference betwixt the Conjunction of the parts of a
    Body when Solid, and when fluid.

    [70] Water consists of parts that admit of no farther division.

    [71] Solids dimitted into the water, do onely move, and not divide
    it.

    [72] If there were any Resistance of Division in water, it must
    needs be small, in that it is overcome by an Hair, a Grain of
    Lead, or a slight bathing of the Solid.

    [73] The uper parts of the Water, do no more resist Division than
    the middle or lower parts.

    [74] Waters Resistance of division, not greater in the beginning
    of the Submersion.

Let us receive it, therefore, for a true and undoubted Conclusion,
That the Water hath not any Renitence against simple Division, and
that it is not possible to find any Solid Body, be it of what Figure
it will, which being put into the Water, its Motion upwards or
downwards, according as it exceedeth, or shall be exceeded by the
Water in Gravity (although such excesse and difference be insensible)
shall be prohibited, and taken away, by the Crassitude of the said
Water. When, therefore, we see the Board of Ebony, or of other Matter,
more grave than the Water, to stay in the Confines of the Water and
Air, without submerging, we must have recourse to some other
Originall, for the investing the Cause of that Effect, than to the
breadth of the Figure, unable to overcome the Renitence with which the
Water opposeth Division, since there is no Resistance; and from that
which is not in being, we can expect no Action. It remains most true,
therefore, as we have said before, that this so succeds, for that that
which in such manner put upon the water, not the same Body with that
which is put _into_ the Water: because this which is put _into_ the
Water, is the pure Board of Ebony, which for that it is more grave
than the Water, sinketh, and that which is put _upon_ the Water, is a
Composition of Ebony, and of so much Air, that both together are
specifically less grave than the Water, and therefore they do not
descend.

I will farther confirm this which I say. Gentlemen, my Antagonists, we
are agreed, that the excess or defect of the Gravity of the Solid,
unto the Gravity of the Water, is the true and proper Cause of
Natation or Submersion.

    [Sidenote: Great Caution to be had in experimenting the operation
    of Figure in Natation.]

Now, if you will shew that besides the former Cause, there is another
which is so powerfull, that it can hinder and remove the Submersion of
those very Solids, that by their Gravity sink, and if you will say,
that this is the breadth or ampleness of Figure, you are oblieged,
when ever you would shew such an Experiment, first to make the
circumstances certain, that that Solid which you put into the Water,
be not less grave _in specie_ than it, for if you should not do so,
any one might with reason say, that not the Figure, but the Levity was
the cause of that Natation. But I say, that when you shall dimit a
Board of Ebony into the Water, you do not put therein a Solid more
grave _in specie_ than the Water, but one lighter, for besides the
Ebony, there is in the Water a Mass of Air, united with the Ebony, and
such, and so light, that of both there results a Composition less
grave than the Water: See, therefore, that you remove the Air, and put
the Ebony alone into the Water, for so you shall immerge a Solid more
grave then the Water, and if this shall not go to the Bottom, you have
well Philosophized and I ill.

Now, since we have found the true Cause of the Natation of those
Bodies, which otherwise, as being graver than the Water, would descend
to the bottom, I think, that for the perfect and distinct knowledge of
this business, it would be good to proceed in a way of discovering
demonstratively those particular Accidents that do attend these
effects, and,




PROBL. I.

    [Sidenote: To finde the proportion Figures ought to have to the
    waters Gravity, that by help of the contiguous Air, they may
    swim.]

  _To finde what proportion severall Figures of different Matters
    ought to have, unto the Gravity of the Water, that so they may be
    able by vertue of the Contiguous Air to stay afloat._


[Illustration]

Let, therefore, for better illustration, D F N E be a Vessell,
wherein the water is contained, and suppose a Plate or Board, whose
thickness is comprehended between the Lines I C and O S, and let it be
of Matter exceeding the water in Gravity, so that being put upon the
water, it dimergeth and abaseth below the Levell of the said water,
leaving the little Banks A I and B C, which are at the greatest height
they can be, so that if the Plate I S should but descend any little
space farther, the little Banks or Ramparts would no longer consist,
but expulsing the Air A I C B, they would diffuse themselves over the
Superficies I C, and would submerge the Plate. The height A I B C is
therefore the greatest profundity that the little Banks of water admit
of. Now I say, that from this, and from the proportion in Gravity,
that the Matter of the Plate hath to the water, we may easily finde of
what thickness, at most, we may make the said Plates, to the end, they
may be able to bear up above water: for if the Matter of the Plate or
Board I S were, for Example, as heavy again as the water, a Board of
that Matter shall be, at the most of a thickness equall to the
greatest height of the Banks, that is, as thick as A I is high: which
we will thus demonstrate. Let the Solid I S be double in Gravity to
the water, and let it be a regular Prisme, or Cylinder, to wit, that
hath its two flat Superficies, superiour and inferiour, alike and
equall, and at Right Angles with the other laterall Superficies, and
let its thickness I O be equall to the greatest Altitude of the Banks
of water: I say, that if it be put upon the water, it will not
submerge: for the Altitude A I being equall to the Altitude I O, the
Mass of the Air A B C I shall be equall to the Mass of the Solid C I O
S: and the whole Mass A O S B double to the Mass I S; And since the
Mass of the Air A C, neither encreaseth nor diminisheth the Gravity of
the Mass I S, and the Solid I S was supposed double in Gravity to the
water; Therefore as much water as the Mass submerged A O S B,
compounded of the Air A I C B, and of the Solid I O S C, weighs just
as much as the same submerged Mass A O S B: but when such a Mass of
water, as is the submerged part of the Solid, weighs as much as the
said Solid, it descends not farther, but resteth, as by (_a_)
_Archimedes_[75], and above by us, hath been demonstrated: Therefore, I S
shall descend no farther, but shall rest. And if the Solid I S shall
be Sesquialter in Gravity to the water, it shall float, as long as its
thickness be not above twice as much as the greatest Altitude of the
Ramparts of water, that is, of A I. For I S being Sesquialter in
Gravity to the water, and the Altitude O I, being double to I A, the
Solid submerged A O S B, shall be also Sesquialter in Mass to the
Solid I S. And because the Air A C, neither increaseth nor diminisheth
the ponderosity of the Solid I S: Therefore, as much water in quantity
as the submerged Mass A O S B, weighs as much as the said Mass
submerged: And, therefore, that Mass shall rest. And briefly in
generall.

    [75] Of Natation Lib. 1. Prop. 3.

[Illustration]




THEOREME. VI.

    [Sidenote: The proportion of the greatest thickness of Solids,
    beyond which encreased they sink.]

  _When ever the excess of the Gravity of the Solid above the Gravity
    of the Water, shall have the same proportion to the Gravity of
    the Water, that the Altitude of the Rampart, hath to the
    thickness of the Solid, that Solid shall not sink, but being
    never so little thicker it shall._


[Illustration]

Let the Solid I S be superior in Gravity to the water, and of such
thickness, that the Altitude of the Rampart A I, be in proportion to
the thickness of the Solid I O, as the excess of the Gravity of the
said Solid I S, above the Gravity of a Mass of water equall to the
Mass I S, is to the Gravity of the Mass of water equall to the Mass I
S. I say, that the Solid I S shall not sinke, but being never so
little thicker it shall go to the bottom: For being that as A I is to
I O, so is the Excess of the Gravity of the Solid I S, above the
Gravity of a Mass of water equall to the Mass I S, to the Gravity of
the said Mass of water: Therefore, compounding, as A O is to O I, so
shall the Gravity of the Solid I S, be to the Gravity of a Mass of
water equall to the Mass I S: And, converting, as I O is to O A, so
shall the Gravity of a Mass of water equall to the Mass I S, be to the
Gravity of the Solid I S: But as I O is to O A, so is a Mass of water
I S, to a Mass of water equall to the Mass A B S O: and so is the
Gravity of a Mass of water I S, to the Gravity of a Mass of water A S:
Therefore as the Gravity of a Mass of water, equall to the Mass I S,
is to the Gravity of the Solid I S, so is the same Gravity of a Mass
of water I S, to the Gravity of a Mass of Water A S: Therefore the
Gravity of the Solid I S, is equall to the Gravity of a Mass of water
equall to the Mass A S: But the Gravity of the Solid I S, is the same
with the Gravity of the Solid A S, compounded of the Solid I S, and of
the Air A B C I. Therefore the whole compounded Solid A O S B, weighs
as much as the water that would be comprised in the place of the said
Compound A O S B: And, therefore, it shall make an _Equilibrium_ and
rest, and that same Solid I O S C shall sinke no farther. But if its
thickness I O should be increased, it would be necessary also to
encrease the Altitude of the Rampart A I, to maintain the due
proportion: But by what hath been supposed, the Altitude of the
Rampart A I, is the greatest that the Nature of the Water and Air do
admit, without the waters repulsing the Air adherent to the
Superficies of the Solid I C, and possessing the space A I C B:
Therefore, a Solid of greater thickness than I O, and of the same
Matter with the Solid I S, shall not rest without submerging, but
shall descend to the bottome: which was to be demonstrated. In
consequence of this that hath been demonstrated, sundry and various
Conclusions may be gathered, by which the truth of my principall
Proposition comes to be more and more confirmed, and the imperfection
of all former Argumentations touching the present Question cometh to
be discovered.

_And first we gather from the things demonstrated, that,_




THEOREME VII.

    [Sidenote: The heaviest Bodies may swimme.]

  _All Matters, how heavy soever, even to Gold it self, the heaviest
    of all Bodies, known by us, may float upon the Water._


Because its Gravity being considered to be almost twenty times greater
than that of the water, and, moreover, the greatest Altitude that the
Rampart of water can be extended to, without breaking the Contiguity
of the Air, adherent to the Surface of the Solid, that is put upon the
water being predetermined, if we should make a Plate of Gold so thin,
that it exceeds not the nineteenth part of the Altitude of the said
Rampart, this put lightly upon the water shall rest, without going to
the bottom: and if Ebony shall chance to be in sesquiseptimall
proportion more grave than the water, the greatest thickness that can
be allowed to a Board of Ebony, so that it may be able to stay above
water without sinking, would be seaven times more than the height of
the Rampart Tinn, _v. gr._ eight times more grave than water, shall
swimm as oft as the thickness of its Plate, exceeds not the 7th part
of the Altitude of the Rampart.

    [Sidenote: _He elsewhere cites this as a Proposition, therefore I
    make it of that number._]

And here I will not omit to note, as a second Corrollary dependent
upon the things demonstrated, that,




THEOREME VIII.

    [Sidenote: Natation and Submersion, collected from the thickness,
    excluding the length and breadth of Plates.]

  _The Expansion of Figure not only is not the Cause of the Natation
    of those grave Bodies, which otherwise do submerge, but also the
    determining what be those Boards of Ebony, or Plates of Iron or
    Gold that will swimme, depends not on it, rather that same
    determination is to be collected from the only thickness of those
    Figures of Ebony or Gold, wholly excluding the consideration of
    length and breadth, as having no wayes any share in this Effect._


It hath already been manifested, that the only cause of the Natation
of the said Plates, is the reduction of them to be less grave than the
water, by means of the connexion of that Air, which descendeth
together with them, and possesseth place in the water; which place so
occupyed, if before the circumfused water diffuseth it self to fill
it, it be capable of as much water, as shall weigh equall with the
Plate, the Plate shall remain suspended, and sinke no farther.

Now let us see on which of these three dimensions of the Solid
depends the terminating, what and how much the Mass of that ought to
be, that so the assistance of the Air contiguous unto it, may suffice
to render it specifically less grave than the water, whereupon it may
rest without Submersion. It shall undoubtedly be found, that the
length and breadth have not any thing to do in the said determination,
but only the height, or if you will the thickness: for, if we take a
Plate or Board, as for Example, of Ebony, whose Altitude hath unto the
greatest possible Altitude of the Rampart, the proportion above
declared, for which cause it swims indeed, but yet not if we never so
little increase its thickness; I say, that retaining its thickness,
and encreasing its Superficies to twice, four times, or ten times its
bigness, or dminishing it by dividing it into four, or six, or twenty,
or a hundred parts, it shall still in the same manner continue to
float: but encreasing its thickness only a Hairs breadth, it will
alwaies submerge, although we should multiply the Superficies a
hundred and a hundred times. Now forasmuch as that this is a Cause,
which being added, we adde also the Effect, and being removed, it is
removed; and by augmenting or lessening the length or breadth in any
manner, the effect of going, or not going to the bottom, is not added
or removed: I conclude, that the greatness and smalness of the
Superficies hath no influence upon the Natation or Submersion. And
that the proportion of the Altitude of the Ramparts of Water, to the
Altitude of the Solid, being constituted in the manner aforesaid, the
greatness or smalness of the Superficies, makes not any variation, is
manifest from that which hath been above demonstrated, and from this,
that, _The Prisms and Cylinders which have the same Base, are in
proportion to one another as their heights._ Whence Cylinders or
Prismes[76], namely, the Board, be they great or little, so that they be
all of equall thickness, have the same proportion to their
Conterminall Air, which hath for Base the said Superficies of the
Board, and for height the Ramparts of water; so that alwayes of that
Air, and of the Board, Solids, are compounded, that in Gravity equall
a Mass of water equall to the Mass of the Solids, compounded of Air,
and of the Board: whereupon all the said Solids do in the same manner
continue afloat. We will conclude in the third place, that,

    [76] Prismes and Cylinders having the same Base, are to one
    another as their heights.




THEOREME. IX.

    [Sidenote: All Figures of all Matters, float by hep of the
    Rampart replenished with Air, and some but only touch the water.]

  _All sorts of Figures of whatsoever Matter, albeit more grave than
    the Water, do by Benefit of the said Rampart, not only float, but
    some Figures, though of the gravest Matter, do stay wholly above
    Water, wetting only the inferiour Surface that toucheth the
    Water._


And these shall be all Figures, which from the inferiour Base upwards,
grow lesser and lesser; the which we shall exemplifie for this time in
Piramides or Cones, of which Figures the passions are common. We will
demonstrate therefore, that,

  _It is possible to form a Piramide, of any whatsoever Matter
  preposed, which being put with its Base upon the Water, rests not
  only without submerging, but without wetting it more then its
  Base._

For the explication of which it is requisite, that we first
demonstrate the subsequent Lemma, namely, that,




LEMMA II.

    [Sidenote: Solids whose Masses are in contrary proportion to
    their Specifick Gravities are equall in absolute Gravity.]

  _Solids whose Masses answer in proportion contrarily to their
    Specificall Gravities, are equall in Absolute Gravities._


[Illustration]

Let A C and B be two Solids, and let the Mass A C be to the Mass B,
as the Specificall Gravity of the Solid B, is to the Specificall
Gravity of the Solid A C: I say, the Solids A C and B are equall in
absolute weight, that is, equally grave. For if the Mass A C be equall
to the Mass B, then, by the Assumption, the Specificall Gravity of B,
shall be equall to the Specificall Gravity of A C, and being equall in
Mass, and of the same Specificall Gravity they shall absolutely weigh
one as much as another. But if their Masses shall be unequall, let the
Mass A C be greater, and in it take the part C, equall to the Mass B.
And, because the Masses B and C are equall; the Absolute weight of B,
shall have the same proportion to the Absolute weight of C, that the
Specificall Gravity of B, hath to the Specificall Gravity of C; or of
C A, which is the same _in specie_: But look what proportion the
Specificall Gravity of B, hath to the Specificall Gravity of C A, the
like proportion, by the Assumption, hath the Mass C A, to the Mass B,
that is, to the Mass C: Therefore, the absolute weight of B, to the
absolute weight of C, is as the Mass A C to the Mass C: But as the
Mass A C, is to the Mass C, so is the absolute weight of A C, to the
absolute weight of C: Therefore the absolute weight of B, hath the
same proportion to the absolute weight of C, that the absolute weight
of A C, hath to the absolute weight of C: Therefore, the two Solids A
C and B are equall in absolute Gravity: which was to be demonstrated.
Having demonstrated this, I say,




THEOREME X.

    [Sidenote: There may be Cones and Piramides of any Matter, which
    demitted into the water, rest only their Bases.]

  _That it is possible of any assigned Matter, to form a Piramide or
    Cone upon any Base, which being put upon the Water shall not
    submerge, nor wet any more than its Base._


[Illustration]

Let the greatest possible Altitude of the Rampart be the Line D B,
and the Diameter of the Base of the Cone to be made of any Matter
assigned B C, at right angles to D B: And as the Specificall Gravity
of the Matter of the Piramide or Cone to be made, is to the
Specificall Gravity of the water, so let the Altitude of the Rampart D
B, be to the third part of the Piramide or Cone A B C, described upon
the Base, whose Diameter is B C: I say, that the said Cone A B C, and
any other Cone, lower then the same, shall rest upon the Surface of
the water B C without sinking. Draw D F parallel to B C, and suppose
the Prisme or Cylinder E C, which shall be tripple to the Cone A B C.
And, because the Cylinder D C hath the same proportion to the Cylinder
C E, that the Altitude D B, hath to the Altitude B E: But the Cylinder
C E, is to the Cone A B C, as the Altitude E B is to the third part of
the Altitude of the Cone: Therefore, by Equality of proportion, the
Cylinder D C is to the Cone A B C, as D B is to the third part of the
Altitude B E: But as D B is to the third part of B E, so is the
Specificall Gravity of the Cone A B C, to the Specificall Gravity of
the water: Therefore, as the Mass of the Solid D C, is to the Mass of
the Cone A _B_ C, so is the Specificall Gravity of the said Cone, to
the Specificall Gravity of the water: Therefore, by the precedent
Lemma, the Cone A B C weighs in absolute Gravity, as much as a Mass of
Water equall to the Mass D C: But the water which by the imposition of
the Cone A B C, is driven out of its place, is as much as would
precisely lie in the place D C, and is equall in weight to the Cone
that displaceth it: Therefore, there shall be an _Equilibrium_, and
the Cone shall rest without farther submerging. And its manifest,


COROLARY I.

    [Sidenote: Amongst Cones of the same Base, those of least
    Altitude shall sink the least.]

  _That making upon the same Basis, a Cone of a less Altitude, it
    shall be also less grave, and shall so much the more rest without
    Submersion._


COROLARY II.

    [Sidenote: There may be Cones and Piramides of any Matter, which
    demitted with the Point downwards do float atop.]

  _It is manifest, also, that one may make Cones and Piramids of any
    Matter whatsoever, more grave than the water, which being put
    into the water, with the Apix or Point downwards, rest without
    Submersion._

Because if we reassume what hath been above demonstrated, of Prisms
and Cylinders, and that on Bases equall to those of the said
Cylinders, we make Cones of the same Matter, and three times as high
as the Cylinders, they shall rest afloat, for that in Mass and Gravity
they shall be equall to those Cylinders, and by having their Bases
equall to those of the Cylinders, they shall leave equall Masses of
Air included within the Ramparts. This, which for Example sake hath
been demonstrated, in Prisms, Cylinders, Cones and Piramids, might be
proved in all other Solid Figures, but it would require a whole Volume
(such is the multitude and variety of their Symptoms and Accidents) to
comprehend the particuler demonstration of them all, and of their
severall Segments: but I will to avoid prolixity in the present
Discourse, content my self, that by what I have declared every one of
ordinary Capacity may comprehend, that there is not any Matter so
grave, no not Gold it self, of which one may not form all sorts of
Figures, which by vertue of the superiour Air adherent to them, and
not by the Waters Resistance of Penetration, do remain afloat, so that
they sink not. Nay, farther, I will shew, for removing that Error,
that,




THEOREME XI.

    [Sidenote: A Piramide or Cone, demitted with the Point downwards
    shal swim, with its Base downward shall sink.]

  _A Piramide or Cone put into the Water, with the Point downward
    shall swimme, and the same put with the Base downwards shall
    sinke, and it shall be impossible to make it float._


Now the quite contrary would happen, if the difficulty of Penetrating
the water, were that which had hindred the descent, for that the said
Cone is far apter to pierce and penetrate with its sharp Point, than
with its broad and spacious Base.

And, to demonstrate this, let the Cone be _A B C_, twice as grave as
the water, and let its height be tripple to the height of the Rampart
_D A E C_: I say, first, that being put lightly into the water with
the Point downwards, it shall not descend to the bottom: for the
Aeriall Cylinder contained betwixt the Ramparts _D A C E_, is equall
in Mass to the Cone _A B C_; so that the whole Mass of the Solid
compounded of the Air _D A C E_, and of the Cone _A B C_, shall be
double to the Cone _A C B_: And, because the Cone _A B C_ is supposed
to be of Matter double in Gravity to the water, therefore as much
water as the whole Masse _D A B C E_, placed beneath the Levell of the
water, weighs as much as the Cone _A B C_: and, therefore, there shall
be an _Equilibrium_, and the Cone _A B C_ shall descend no lower. Now,
I say farther, that the same Cone placed with the Base downwards,
shall sink to the bottom, without any possibility of returning again,
by any means to swimme.

[Illustration]

Let, therefore, the Cone be _A B D_, double in Gravity to the water,
and let its height be tripple the height of the Rampart of water L B:
It is already manifest, that it shall not stay wholly out of the
water, because the Cylinder being comprehended betwixt the Ramparts _L
B D P_, equall to the Cone _A B D_, and the Matter of the Cone, beig
double in Gravity to the water, it is evident that the weight of the
said Cone shall be double to the weight of the Mass of water equall to
the Cylinder _L B D P_: Therefore it shall not rest in this state, but
shall descend.

[Illustration]


COROLARY I.

    [Sidenote: Much less shall the said Cone swim, if one immerge a
    part thereof.]

  _I say farther; that much lesse shall the said Cone stay afloat, if
    one immerge a part thereof._

Which you may see, comparing with the water as well the part that
shall immerge as the other above water. Let us therefore of the Cone A
B D, submergeth part N T O S, and advance the Point N S F above water.
The Altitude of the Cone F N S, shall either be more than half the
whole Altitude of the Cone F T O, or it shall not be more: if it shall
be more than half, the Cone F N S shall be more than half of the
Cylinder E N S C: for the Altitude of the Cone F N S, shall be more
than Sesquialter of the Altitude of the Cylinder E N S C: And, because
the Matter of the Cone is supposed to be double in Specificall Gravity
to the water, the water which would be contained within the Rampart E
N S C, would be less grave absolutely than the Cone F N S; so that the
whole Cone F N S cannot be sustained by the Rampart: But the part
immerged N T O S, by being double in Specificall Gravity to the water,
shall tend to the bottom: Therefore, the whole _C_one F T O, as well
in respect of the part submerged, as the part above water shall
descend to the bottom. But if the Altitude of the Point F N S, shall
be half the Altitude of the whole Cone F T O, the same Altitude of the
said Cone F N S shall be Sesquialter to the Altitude E N: and,
therefore, E N S C shall be double to the Cone F N S; and as much
water in Mass as the _C_ylinder E N S C, would weigh as much as the
part of the _C_one F N S. But, because the other immerged part N T O
S, is double in Gravity to the water, a Mass of water equall to that
compounded of the _C_ylinder E N S C, and of the Solid N T O S, shall
weigh less than the _C_one F T O, by as much as the weight of a Mass
of water equall to the Solid N T O S: Therefore, the _C_one sha{l}l
also descend. Again, because the Solid N T O S, is septuple to the
Cone F N S, to which the _C_ylinder E S is double, the proportion of
the Solid N T O S, shall be to the _C_ylinder E N S C, as seaven to
two: Therefore, the whole Solid compounded of the _C_ylinder E N S C,
and of the Solid N T O S, is much less than double the Solid N T O S:
Therefore, the single Solid N T O S, is much graver than a Mass of
water equall to the Mass, compounded of the _C_ylinder E N S C, and of
N T O S.


COROLARY II.

    [Sidenote: Part of the Cones towards the Cuspis removed, it shall
    still sink.]

  _From whence it followeth, that though one should remove and take
    away the part of the Cone F N S, the sole remainder N T O S would
    go to the bottom._


COROLARY III.

    [Sidenote: The more the Cone is immerged, the more impossible is
    its floating.]

  _And if we should more depress the Cone F T O, it would be so much
    the more impossible that it should sustain it self afloat, the
    part submerged N T O S still encreasing, and the Mass of Air
    contained in the Rampart diminishing, which ever grows less, the
    more the Cone submergeth._

That Cone, therefore, that with its Base upwards, and its _Cuspis_
downwards doth swimme, being dimitted with its Base downward must of
necessity sinke. They have argued farre from the truth, therefore, who
have ascribed the cause of Natation to waters resistance of Division,
as to a passive principle, and to the breadth of the Figure, with
which the division is to be made, as the Efficient.

I come in the fourth place, to collect and conclude the reason of
that which I have proposed to the Adversaries, namely,




THEOREME XII.

    [Sidenote: Solids of any Figure & greatnesse, that naturally
    sink, may by help of the Air in the Rampart swimme.]

  _That it is possible to fo{r}m Solid Bodies, of what Figure and
    greatness soever, that of their own Nature goe to the Bottome;
    But by the help of the Air contained in the Rampart, rest without
    submerging._


[Illustration]

The truth of this Proposition is sufficiently manifest in all those
Solid Figures, that determine in their uppermost part in a plane
Superficies: for making such Figures of some Matter specifically as
grave as the water, putting them into the water, so that the whole
Mass be covered, it is manifest, that they shall rest in all places,
provided, that such a Matter equall in weight to the water, may be
exactly adjusted: and they shall by consequence, rest or lie even with
the Levell of the water, without making any Rampart. If, therefore, in
respect of the Matter, such Figures are apt to rest without
submerging, though deprived of the help of the Rampart, it is
manifest, that they may admit so much encrease of Gravity, (without
encreasing their Masses) as is the weight of as much water as would be
contained within the Rampart, that is made about their upper plane
Surface: by the help of which being sustained, they shall rest afloat,
but being bathed, they shall descend, having been made graver than the
water. In Figures, therefore, that determine above in a plane, we may
cleerly comprehend, that the Rampart added or removed, may prohibit or
permit the descent: but in those Figures that go lessening upwards
towards the top, some Persons may, and that not without much seeming
Reason, doubt whether the same may be done, and especially by those
which terminate in a very acute Point, such as are your Cones and
small Piramids. Touching these, therefore, as more dubious than the
rest, I will endeavour to demonstrate, that they also lie under the
same Accident of going, or not going to the Bottom, be they of any
whatever bigness. Let therefore the Cone be A B D, made of a matter
specifically as grave as the water; it is manifest that being put all
under water, it shall rest in all places (alwayes provided, that it
shall weigh exactly as much as the water, which is almost impossible
to effect) and that any small weight being added to it, it shall sink
to the bottom: but if it shall descend downwards gently, I say, that
it shall make the Rampart E S T O, and that there shall stay out of
the water the point A S T, tripple in height to the Rampart E S: which
is manifest, for the Matter of the Cone weighing equally with the
water, the part submerged _S B D T_, becomes indifferent to move
downwards or upwards; and the Cone _A S T_, being equall in Mass to
the water that would be contained in the concave of the Rampart _E S T
O_, shall be also equall unto it in Gravity: and, therefore, there
shall be a perfect _Equilibrium_, and, consequently, a Rest. Now here
ariseth a doubt, whether the Cone _A B D_ may be made heavier, in such
sort, that when it is put wholly under water, it goes to the bottom,
but yet not in such sort, as to take from the Rampart the vertue of
sustaining it that it sink not, and, the reason of the doubt is this:
that although at such time as the Cone _A B D_ is specifically as
grave as the water, the Rampart _E S T O_ sustaines it, not only when
the point _A S T_ is tripple in height to the Altitude of the Rampart
_E S_, but also when a lesser part is above water; [for although in
the Descent of the Cone the Point _A S T_ by little and little
diminisheth, and so likewise the Rampart _E S T O_, yet the Point
diminisheth in greater proportion than the Rampart, in that it
diminisheth according to all the three Dimensions, but the Rampart
according to two only, the Altitude still remaining the same; or, if
you will, because the Cone _S {A} T_ goes diminishing, according to
the proportion of the cubes of the Lines that do successively become
the Diameters of the Bases of emergent Cones, and the Ramparts
diminish according to the proportion of the Squares of the same Lines;
whereupon the proportions of the Points are alwayes Sesquialter of the
proportions of the Cylinders, contained within the Rampart; so that
if, for Example, the height of the emergent Point were double, or
equall to the height of the Rampart, in these cases, the Cylinder
contained within the Rampart, would be much greater than the said
Point, because it would be either sesquialter or tripple, by reason of
which it would perhaps serve over and above to sustain the whole Cone,
since the part submerged would no longer weigh any thing;] yet,
nevertheless, when any Gravity is added to the whole Mass of the Cone,
so that also the part submerged is not without some excesse of Gravity
above the Gravity of the water, it is not manifest, whether the
Cylinder contained within the Rampart, in the descent that the Cone
shall make, can be reduced to such a proportion unto the emergent
Point, and to such an excesse of Mass above the Mass of it, as to
compensate the excesse of the Cones Specificall Gravity above the
Gravity of the water: and the Scruple ariseth, because that howbeit in
the descent made by the Cone, the emergent Point _A S T_ diminisheth,
whereby there is also a diminution of the excess of the Cones Gravity
above the Gravity of the water, yet the case stands so, that the
Rampart doth also contract it self, and the Cylinder contained in it
doth deminish. Nevertheless it shall be demonstrated, how that the
Cone _A B D_ being of any supposed bignesse, and made at the first of
a Matter exactly equall in Gravity to the Water, if there may be
affixed to it some Weight, by means of which i{t} may descend to the
bottom, when submerged under water, it may also by vertue of the
Rampart stay above without sinking.

[Illustration]

[Illustration]

Let, therefore, the Cone _A B D_ be of any supposed greatnesse, and
alike in specificall Gravity to the water. It is manifest, that being
put lightly into the water, it shall rest without descending; and it
shall advance above water, the Point _A S T_, tripple in height to the
height of the Rampart _E S_: Now, suppose the Cone _A B D_ more
depressed, so that it advance above water, only the Point _A I R_,
higher by half than the Point _A S T_, with the Rampart about it _C I
R N_. And, because, the Cone _A B D_ is to the Cone _A I R_, as the
cube of the Line _S T_ is to the cube of the Line _I R_, but the
Cylinder _E S T O_, is to the Cylinder _C I R N_, as the Square of _S
T_ to the Square of _I R_, the Cone _A S T_ shall be Octuple to the
Cone _A I R_, and the Cylinder _E S T O_, quadruple to the Cylinder _C
I R N_: But the Cone _A S T_, is equall to the Cylinder _E S T O_:
Therefore, the Cylinder _C I R N_, shall be double to the Cone _A I
R_: and the water which might be contained in the Rampart _C I R N_,
would be double in Mass and in Weight to the Cone _A I R_, and,
therefore, would be able to sustain the double of the Weight of the
Cone _A I R_: Therefore, if to the whole Cone _A B D_, there be added
as much Weight as the Gravity of the Cone _A I R_, that is to say, the
eighth part of the weight of the Cone _A S T_, it also shall be
sustained by the Rampart _C I R N_, but without that it shall go to
the bottome: the Cone _A B D_, being, by the addition of the eighth
part of the weight of the Cone _A S T_, made specifically more grave
than the water. But if the Altitude of the Cone _A I R_, were two
thirds of the Altitude of the Cone _A S T_, the Cone _A S T_ would be
to the Cone _A I R_, as twenty seven to eight; and the Cylinder _E S T
O_, to the Cylinder _C I R N_, as nine to four, that is, as twenty
seven to twelve; and, therefore, the Cylinder _C I R N_, to the Cone
_A I R_, as twelve to eight; and the excess of the Cylinder _C I R N_,
above the Cone _A I R_, to the Cone _A S T_, as four to twenty seven:
therefore if to the Cone _A B D_ be added so much weight as is the
four twenty sevenths of the weight of the Cone _A S T_, which is a
little more then its seventh part, it also shall continue to swimme,
and the height of the emergent Point shall be double to the height of
the Rampart. This that hath been demonstrated in Cones, exactly holds
in Piramides, although the one or the other should be very sharp in
their Point or Cuspis[77]: From whence we conclude, that the same Accident
shall so much the more easily happen in all other Figures, by how much
the less sharp the Tops shall be, in which they determine, being
assisted by more spacious Ramparts.

    [77] Natatio{n} easiest effected in Figures broad toward the top.




THEOREME XIII.

    [Sidenote: All Figures sink or swim, upon bathing or not bathing
    of their tops.]

  _All Figures, therefore, of whatever greatnesse, may go, and not
    go, to the Bottom, according as their Sumities or Tops shall be
    bathed or not bathed._


And this Accident being common to all sorts of Figures, without
exception of so much as one. Figure hath, therefore, no part in the
production of this Effect, of sometimes sinking, and sometimes again
not sinking, but only the being sometimes conjoyned to, and sometimes
seperated from, the supereminent Air: which cause, in fine, who so
shall rightly, and, as we say, with both his Eyes, consider this
business, will find that it is reduced to, yea, that it really is the
same with, the true, Naturall and primary cause of Natation or
Submersion; to wit, the excess or deficiency of the Gravity of the
water, in relation to the Gravity of that Solid Magnitude, that is
demitted into the water. For like as a Plate of Lead, as thick as the
back of a Knife, which being put into the water by it self alone goes
to the bottom, if upon it you fasten a piece of Cork four fingers
thick, doth continue afloat, for that now the Solid that is demitted
in the water, is not, as before, more grave than the water, but less,
so the Board of Ebony, of its own nature more grave than water; and,
therefore, descending to the bottom, when it is demitted by it self
alone into the water, if it shall be put upon the water, conjoyned
with an Expanded vail of Air, that together with the Ebony doth
descend, and that it be such, as that it doth make with it a compound
less grave than so much water in Mass, as equalleth the Mass already
submerged and depressed beneath the Levell of the waters Surface, it
shall not descend any farther, but shall rest, for no other than the
universall and most common cause, which is that Solid Magnitudes, less
grave _in specie_ than the water, go not to the bottom.

So that if one should take a Plate of Lead, as for Example, a finger
thick, and an handfull broad every way, and should attempt to make it
swimme, with putting it lightly on the water, he would lose his
Labour, because that if it should be depressed an Hairs breadth beyond
the possible Altitude of the Ramparts of water, it would dive and
sink; but if whilst it is going downwards, one should make certain
Banks or Ramparts about it, that should hinder the defusion of the
water upon the said Plate, the which Banks should rise so high, as
that they might be able to contain as much water, as should weigh
equally with the said Plate, it would, witho{u}t all Question, descend
no lower, but would rest, as being sustained by vertue of the Air
contained within the aforesaid Ramparts: and, in short, there would be
a Vessell by this means formed with the bottom of Lead. But if the
thinness of the Lead shall be such, that a very small height of
Rampart would suffice to contain so much Air, as might keep it afloat,
it shall also rest without the Artificiall Banks or Ramparts, but yet
not without the Air, because the Air by it self makes Banks sufficient
for a small height, to resist the Superfusion of the water: so that
that which in this case swimmes, is as it were a Vessell filled with
Air, by vertue of which it continueth afloat.

I will, in the last place, with an other Experime{n}t, attempt to
remove all difficulties, if so be there should yet be any doubt left
in any one, touching the opperation of this [E]Continuity of the Air,
with the thin Plate which swims, and afterwards put an end to this
part of my discourse.

    [E] Or rather Contiguity,

I suppose my self to be questioning with some of my Oponents.

Whether Figure have any influence upon the encrease or diminution of
the Resistance in any Weight against its being raised in the Air[78]; and
I suppose, that I am to maintain the Affirmative, asserting that a
Mass of Lead, reduced to the Figure of a Ball, shall be raised with
less force, then if the same had been made into a thinne and broad
Plate, because that it in this spacious Figure, hath a great quantity
of Air to penetrate, and in that other, more compacted and contracted
very little: and to demonstrate the truth of such my Opinion, I will
hang in a small thred first the Ball or Bullet, and put that into the
water, tying the thred that upholds it to one end of the Ballance that
I hold in the Air, and to the other end I by degrees adde so much
Weight, till that at last it brings up the Ball of Lead out of the
water: to do which, suppose a Gravity of thirty Ounces sufficeth; I
afterwards reduce the said Lead into a flat and thinne Plate, the
which I likewise put into the water, suspended by three threds, which
hold it parallel to the Surface of the water, and putting in the same
manner, Weights to the other end, till such time as the Plate comes to
be raised and drawn out of the water: I finde that thirty six ounces
will not suffice to seperate it from the water, and raise it thorow
the Air: and arguing from this Experiment, I affirm, that I have fully
demonstrated the truth of my Proposition. Here my Oponents desires me
to look down, shewing me a thing which I had not before observed, to
wit, that in the Ascent of the Plate out of the water, it draws after
it another Plate (_if I may so call it_) of water, which before it
divides and parts from the inferiour Surface of the Plate of Lead, is
raised above the Levell of the other water, more than the thickness of
the back of a Knife: Then he goeth to repeat the Experiment with the
Ball, and makes me see, that it is but a very small quantity of water,
which cleaves to its compacted and contracted Figure: and then he
subjoynes, that its no wonder, if in seperating the thinne and broad
Plate from the water, we meet with much greater Resistance, than in
seperating the Ball, since together with the Plate, we are to raise a
great quantity of water, which occurreth not in the Ball: He telleth
me moreover, how that our Question is, whether the Resistance of
Elevation be greater in a dilated Plate of Lead, than in a Ball, and
not whether more resisteth a Plate of Lead with a great quantity of
water, or a Ball with a very little water: He sheweth me in the close,
that the putting the Plate and the Ball first into the water, to make
proofe thereby of their Resistance in the Air, is besides our case,
which treats of Elivating in the Air, and of things placed in the Air,
and not of the Resistance that is made in the Confines of the Air and
water, and by things which are part in Air and part in water: and
lastly, they make me feel with my hand, that when the thinne Plate is
in the Air, and free from the weight of the water, it is raised with
the very same Force that raiseth the Ball. Seeing, and understanding
these things, I know not what to do, unless to grant my self
convinced, and to thank such a Friend, for having made me to see that
which I never till then observed: and, being advertised by this same
Accident, to tell my Adversaries, that our Question is, whether a
Board and a Ball of Ebony, equally go to the bottom in water, and not
a Ball of Ebony and a Board of Ebony, joyned with another flat Body of
Air: and, farthermore, that we speak of sinking, and not sinking to
the bottom, in water, and not of that which happeneth in the Confines
of the water and Air to Bodies that be part in the Air, and part in
the water; nor much less do we treat of the greater or lesser Force
requisite in seperating this or that Body from the Air; not omitting
to tell them, in the last place, that the Air doth resist, and
gravitate downwards in the water, just so much as the water (if I may
so speak) gravitates and resists upwards in the Air, and that the same
Force is required to sinke a Bladder under water, that is full of Air,
as to raise it in the Air, being full of water, removing the
consideration of the weight of that Filme or Skinne, and considering
the water and the Air only. And it is likewise true, that the same
Force is required to sink a Cup or such like Vessell under water,
whilst it is full of Air, as to raise it above the Superficies of the
water, keeping it with the mouth downwards; whilst it is full of
water, which is constrained in the same manner to follow the Cup which
contains it, and to rise above the other water into the Region of the
Air, as the Air is forced to follow the same Vessell under the Surface
of the water, till that in this c{a}se the water, surmounting the
brimme of the Cup, breaks in, driving thence the Air, and in that
case, the said brimme coming out of the water, and arriving to the
Confines of the Air, the water falls down, and the Air sub-enters to
fill the cavity of the Cup: upon which ensues, that he no less
transgresses the Articles of the _Convention_, who produceth a Plate
conjoyned with much Air, to see if it descend to the bottom in water,
then he that makes proof of the Resistance against Elevation in Air
with a Plate of Lead, joyned with a like quantity of water.

    [78] An Experiment of the operation of Figures, in encreasing or
    lessening of the Airs Resistance of Division.

    [Sidenote: _Aristotles_ opinion touching the Operation of Figure
    examined.]

I have said all that I could at present think of, to maintain the
Assertion I have undertook. It remains, that I examine that which
_Aristotle_ hath writ of this matter towards the end of his Book De
Cælo[79]; wherein I shall note two things: the one that it being true as
hath been demonstrated, that Figure hath nothing to do about the
moving or not moving it self upwards or downwards, its seemes that
_Aristotle_ at his first falling upon this Speculation, was of the
same opinion, as in my opinion may be collected from the examination
of his words. 'Tis true, indeed, that in essaying afterwards to render
a reason of such effect, as not having in my conceit hit upon the
right, (which in the second place I will examine) it seems that he is
brought to admit the largenesse of Figure, to be interessed in this
operation. As to the first particuler, hear the precise words of
_Aristotle_.

    [79] _Aristot. de Cælo_ Lib. 4. Cap 6.

_Figures are not the Causes of moving simply upwards or downwards, but
of moving more slowly or swiftly[80][81], and by what means this comes to
pass, it is not difficult to see._

    [80] _Aristotle_ makes not Figure the cause of Motion absolutely,
    but of swift or slow motion,

    [81] Lib. 4. Cap. 6: Text. 42.

Here first I note, that the terms being four, which fall under the
present consideration, namely, Motion, Rest, Slowly and Swiftly: And
_Aristotle_ naming figures as Causes of Tardity and Velocity,
excluding them from being the Cause of absolute and simple Motion, it
seems necessary, that he exclude them on the other side, from being
the Cause of Rest, so that his meaning is this. Figures are not the
Causes of moving or not moving absolutely, but of moving quickly or
slowly: and, here, if any should say the mind of _Aristotle_ is to
exclude Figures from being Causes of Motion, but yet not from being
Causes of Rest, so that the sence would be to remove from Figures,
there being the Causes of moving simply, but yet not there being
Causes of Rest, I would demand, whether we ought with _Aristotle_ to
understand, that all Figures universally, are, in some manner, the
causes of Rest in those Bodies, which otherwise would move, or else
some particular Figures only, as for Example, broad and thinne
Figures: If all indifferently, then every Body shall rest: because
every Body hath some Figure, which is false; but if some particular
Figures only may be in some manner a Cause of Rest, as, for Example,
the broad, then the others would be in some manner the Causes of
Motion: for if from seeing some Bodies of a contracted Figure move,
which after dilated into Plates rest, may be inferred, that the
Amplitude of Figure hath a part in the Cause of that Rest; so from
seeing such like Figures rest, which afterwards contracted move, it
may with the same reason be affirmed, that the united and contracted
Figure, hath a part in causing Motion, as the remover of that which
impeded it: The which again is directly opposite to what _Aristotle_
saith, namely, that Figures are not the Causes of Motion. Besides, if
_Aristotle_ had admitted and not excluded Figures from being Causes of
not moving in some Bodies, which moulded into another Figure would
move, he would have impertinently propounded in a dubitative manner,
in the words immediately following, whence it is, that the large and
thinne Plates of Lead or Iron, rest upon the water, since the Cause
was apparent, namely, the Amplitude of Figure. Let us conclude,
therefore, that the meaning of _Aristotle_ in this place is to affirm,
that Figures are not the Causes of absolutely moving or not moving,
but only of moving swiftly or slowly: which we ought the rather to
believe, in regard it is indeed a most true conceipt and opinion. Now
the mind of _Aristotle_ being such, and appearing by consequence,
rather contrary at the first sight, then favourable to the assertion
of the Oponents, it is necessary, that their Interpretation be not
exactly the same with that, but such, as being in part understood by
some of them, and in part by others, was set down: and it may easily
be indeed so, being an Interpretation consonent to the sence of the
more famous Interpretors, which is, that the Adverbe _Simply_ or
_Absolutely_, put in the Text, ought not to be joyned to the Verbe to
_Move_, but with the Noun _Causes_: so that the purport of
_Aristotles_ words, is to affirm, That Figures are not the Causes
absolutely of moving or not moving, but yet are Causes _Secundum
quid_, _viz._ in some sort; by which means, they are called Auxiliary
and Concomitant Causes: and this Proposition is received and asserted
as true by _Signor Buonamico Lib. 5. Cap. 28._ where he thus writes.
_There are other Causes concomitant, by which some things float, and
others sink, among which the Figures of Bodies hath the first place_,
&c.

Concerning this Proposition, I meet with many doubts and difficulties,
for which me thinks the words of _Aristotle_ are not capable of such a
construction and sence, and the difficulties are these.

First in the order and disposure of the words of _Aristotle_, the
particle _Simpliciter_, or if you will _absoluté_, is conjoyned with
the Verb _to move_, and seperated from the Noun _Causes_, the which is
a great presumption in my favour, seeing that the writing and the Text
saith, Figures are not the Cause of moving simply upwards or
downwards, but of quicker or slower Motion: and, saith not, Figures
are not simply the Causes of moving upwards or downwards, and when the
words of a Text receive, transposed, a sence different from that which
they sound, taken in the order wherein the Author disposeth them, it
is not convenient to inverte them. And who will affirm that
_Aristotle_ desiring to write a Proposition, would dispose the words
in such sort, that they should import a different, nay, a contrary
sence? contrary, I say, because understood as they are written; they
say, that Figures are not the Causes of Motion, but inverted, they
say, that Figures are the Causes of Motion, &c.

Moreover, if the intent of _Aristotle_ had been to say, that Figures
are not simply the Causes of moving upwards or downwards, but only
Causes _Secundum quid_, he would not have adjoyned those words, _but
they are Causes of the more swift or slow Motion_; yea, the subjoining
this would have been not only superfluous but false, for that the
whole tenour of the Proposition would import thus much. Figures are
not the absolute Causes of moving upwards or downwards, but are the
absolute Cause of the swift or slow Motion; which is not true: because
the primary Causes of greater or lesser Velocity, are by _Aristotle_
in the 4th of his _Physicks_, _Text. 71._ attributed to the greater or
lesser Gravity of Moveables, compared among themselves, and to the
greater or lesser Resistance of the _Medium's_, depending on their
greater or less Crassitude: and these are inserted by _Aristotle_ as
the primary Causes; and these two only are in that place nominated:
and Figure comes afterwards to be considered, _Text. 74._ rather as an
Instrumentall Cause of the force of the Gravity, the which divides
either with the Figure, or with the _Impetus_; and, indeed, Figure by
it self without the force of Gravity or Levity, would opperate
nothing.

I adde, that if _Aristotle_ had an opinion that Figure had been in
some sort the Cause of moving or not moving, the inquisition which he
makes immediately in a doubtfull manner, whence it comes, that a Plate
of Lead flotes, would have been impertinent; for if but just before he
had said, that Figure was in a certain sort the Cause of moving or not
moving, he needed not to call in Question, by what Cause the Plate of
Lead swims, and then ascribing the Cause to its Figure; and framing a
discourse in this manner. Figure is a Cause _Secundum quid_ of not
sinking: but, now, if it be doubted, for what Cause a thin Plate of
Lead goes not to the bottom; it shall be answered, that that proceeds
from its Figure: a discourse which would be indecent in a Child, much
more in _Aristotle_; For where is the occasion of doubting? And who
sees not, that if _Aristotle_ had held, that Figure was in some sort a
Cause of Natation, he would without the least Hesitation have writ;
That Figure is in a certain sort the Cause of Natation, and therefore
the Plate of Lead in respect of its large and expatiated Figure swims;
but if we take the proposition of _Aristotle_ as I say, and as it is
written, and as indeed it is true, the ensuing words come in very
oppositely, as well in the introduction of swift and slow, as in the
question, which very pertinently offers it self, and would say thus
much.

Figures are not the Cause of moving or not moving simply upwards or
downwards, but of moving more quickly or slowly: But if it be so, the
Cause is doubtfull, whence it proceeds, that a Plate of Lead or of
Iron broad and thin doth swim, &c. And the occasion of the doubt is
obvious, because it seems at the first glance, that the Figure is the
Cause of this Natation, since the same Lead, or a less quantity, but
in another Figure, goes to the bottom, and we have already affirmed,
that the Figure hath no share in this effect.

Lastly, if the intent of _Aristotle_ in this place had been to say,
that Figures, although not absolutely, are at least in some measure
the Cause of moving or not moving: I would have it considered, that he
names no less the Motion upwards, than the other downwards: and
because in exemplifying it afterwards, he produceth no other
Experiments than of a Plate of Lead, and Board of Ebony, Matters that
of their own Nature go to the bottom, but by vertue (as our
Adversaries say) of their Figure, rest afloat; it is fit that they
should produce some other Experiment of those Matters, which by their
Nature swims, but retained by their Figure rest at the bottom. But
since this is impossible to be done, we conclude, that _Aristotle_ in
this place, hath not attributed any action to the Figure of simply
moving or not moving.

But though he hath exquisitely Philosophiz'd, in investigating the
solution of the doubts he proposeth, yet will I not undertake to
maintain, rather various difficulties, that present themselves unto
me, give me occasion of suspecting that he hath not entirely displaid
unto us, the true Cause of the present Conclusion: which difficulties
I will propound one by one, ready to change opinion, whenever I am
shewed, that the Truth is different from what I say; to the confession
whereof I am much more inclinable than to contradiction.

    [Sidenote: _Aristotle_ erred in affirming a Needle dimitted long
    wayes to sink.]

_Aristotle_ having propounded the Question, whence it proceeds, that
broad Plates of Iron or Lead, float or swim; he addeth (as it were
strengthening the occasion of doubting) forasmuch as other things,
less, and less grave, be they round or long, as for instance a Needle
go to the bottom. Now I here doubt, or rather am certain that a Needle
put lightly upon the water, rests afloat, no less than the thin Plates
of Iron or Lead. I cannot believe, albeit it hath been told me, that
some to defend _Aristotle_ should say, that he intends a Needle
demitted not longwayes but endwayes, and with the Point downwards;
nevertheless, not to leave them so much as this, though very weak
refuge, and which in my judgement _Aristotle_ himself would refuse, I
say it ought to be understood, that the Needle must be demitted,
according to the Dimension named by _Aristotle_, which is the length:
because, if any other Dimension than that which is named, might or
ought to be taken, I would say, that even the Plates of Iron and Lead,
sink to the bottom, if they be put into the water edgewayes and not
flatwayes. But because _Aristotle_ saith, broad Figures go not to the
bottom, it is to be understood, being demitted broadwayes: and,
therefore, when he saith, long Figures as a Needle, albeit light, rest
not afloat, it ought to be understood of them when demitted longwayes.

  _Moreover, to say that_ Aristotle _is to be understood of the
  Needle demitted with the Point downwards, is to father upon him a
  great impertinency; for in this place he saith, that little
  Particles of Lead or Iron, if they be round or long as a Needle, do
  sink to the bottome; so that by his Opinion, a Particle or small
  Grain of Iron cannot swim: and if he thus believed, what a great
  folly would it be to subjoyn, that neither would a Needle demitted
  endwayes swim? And what other is such a Needle, but many such like
  Graines accumulated one upon another? It was too unworthy of such a
  man to say, that one single Grain of Iron could not swim, and that
  neither can it swim, though you put a hundred more upon it._

Lastly, either _Aristotle_ believed, that a Needle demitted longwayes
upon the water, would swim, or he believed that it would not swim: If
he believed it would not swim, he might well speak as indeed he did;
but if he believed and knew that it would float, why, together with
the dubious Problem of the Natation of broad Figures, though of
ponderous Matter, hath he not also introduced the Question; whence it
proceeds, that even long and slender Figures, howbeit of Iron or Lead
do swim? And the rather, for that the occasion of doubting seems
greater in long and narrow Figures, than in broad and thin, as from
_Aristotles_ not having doubted of it, is manifested.

No lesser an inconvenience would they fasten upon _Aristotle_, who in
his defence should say, that he means a Needle pretty thick, and not a
small one; for take it for granted to be intended of a small one; and
it shall suffice to reply, that he believed that it would swim; and I
will again charge him with having avoided a more wonderfull and
intricate Probleme, and introduced the more facile and less
wonderfull.

We say freely therefore, that _Aristotle_ did hold, that only the
broad Figure did swim, but the long and slender, such as a Needle,
not. The which nevertheless is false, as it is also false in round
Bodies: because, as from what hath been predemonstrated, may be
gathered, little Balls of Lead and Iron, do in like manner swim.

    [Sidenote: _Aristotle_ affirmeth some Bodies volatile for their
    Minuity, Text. 42.]

He proposeth likewise another Conclusion, which likewise seems
different from the truth, and it is, That some things, by reason of
their littleness fly in the Air, as the small dust of the Earth, and
the thin leaves of beaten Gold: but in my Opinion, Experience shews
us, that that happens not only in the Air, but also in the water, in
which do descend, even those Particles or Atomes of Earth, that
disturbe it, whose minuity is such, that they are not deservable, save
only when they are many hundreds together. Therefore, the dust of the
Earth, and beaten Gold, do not any way sustain themselves in the Air,
but descend downwards, and only fly to and again in the same, when
strong Windes raise them, or other agitations of the Air commove them:
and this also happens in the commotion of the water, which raiseth its
Sand from the bottom, and makes it muddy. But _Aristotle_ cannot mean
this impediment of the commotion, of which he makes no mention, nor
names other than the lightness of such Minutiæ or Atomes, and the
Resistance of the Crassitudes of the Water and Air, by which we see,
that he speakes of a calme, and not disturbed and agitated Air: but in
that case, neither Gold nor Earth, be they never so small, are
sustained, but speedily descend.

    [Sidenote: _Democritus_ placed the Cause of Natation in certain
    fiery Atomes.]

He passeth next to confute _Democritus_[82], which, by his Testimony would
have it, that some Fiery Atomes, which continually ascend through the
water, do spring upwards, and sustain those grave Bodies, which are
very broad, and that the narrow descend to the bottom, for that but a
small quantity of those Atomes, encounter and resist them.

    [82] _Aristot. De Cælo_ lib. 4. cap. 6. text. 43.

I say, _Aristotle_ confutes this position[83], saying, that that should
much more occurre in the Air, as the same _Democritus_ instances
against himself, but after he had moved the objection, he slightly
resolves it, with saying, that those Corpuscles which ascend in the
Air, make not their _Impetus_ conjunctly. Here I will not say, that
the reason alledged by _Democritus_ is true[84], but I will only say, it
seems in my judgement, that it is not wholly confuted by _Aristotle_,
whilst he saith, that were it true, that the calid ascending Atomes,
should sustain Bodies grave, but very broad, it would much more be
done in the Air, than in Water, for that haply in the Opinion of
_Aristotle_, the said calid Atomes ascend with much greater Force and
Velocity through the Air, than through the water. And if this be so,
as I verily believe it is, the Objection of _Aristotle_ in my
judgement seems to give occasion of suspecting, that he may possibly
be deceived in more than one particular: First, because those calid
Atomes, (whether they be Fiery Corpuscles, or whether they be
Exhalations, or in short, whatever other matter they be, that ascends
upwards through the Air) cannot be believed to mount faster through
Air, than through water: but rather on the contrary, they peradventure
move more impetuously through the water, than through the Air, as hath
been in part demonstrated above. And here I cannot finde the reason,
why _Aristotle_ seeing, that the descending Motion of the same
Moveable, is more swift in Air, than in water, hath not advertised us,
that from the contrary Motion, the contrary should necessarily follow;
to wit, that it is more swift in the water, than in the Air: for since
that the Moveable which descendeth, moves swifter through the Air,
than through the water, if we should suppose its Gravity gradually to
diminish, it would first become such, that descending swiftly through
the Air, it would descend but slowly through the water: and then
again, it might be such, that descending in the Air, it should ascend
in the water: and being made yet less grave, it shall ascend swiftly
through the water, and yet descend likewise through the Air: and in
short, before it can begin to ascend, though but slowly through the
Air, it shall ascend swiftly through the water: how then is it true,
that ascending Moveables move swifter through the Air, than through
the water?

    [83] _Democritus_ confuted by _Aristotle_, text 43.

    [84] _Aristotles_ confutation of _Democritus_ refuted by the
    Author.

That which hath made _Aristotle_ believe, the Motion of Ascent to be
swifter in Air, than in water, was first, the having referred the
Causes of slow and quick, as well in the Motion of Ascent, as of
Descent, only to the diversity of the Figures of the Moveable, and to
the more or less Resistance of the greater or lesser Crassitude, or
Rarity of the _Medium_; not regarding the comparison of the Excesses
of the Gravities of the Moveables, and of the _Mediums_: the which
notwithstanding, is the most principal point in this affair: for if
the augmentation and diminution of the Tardity or Velocity, should
have only respect to the Density or Rarity of the _Medium_, every Body
that descends in Air, would descend in water: because whatever
difference is found between the Crassitude of the water, and that of
the Air, may well be found between the Velocity of the same Moveable
in the Air, and some other Velocity: and this should be its proper
Velocity in the water, which is absolutely false. The other occasion
is, that he did believe, that like as there is a positive and
intrinsecall Quality, whereby Elementary Bodies have a propension of
moving towards the Centre of the Earth, so there is another likewise
intrinsecall[85], whereby some of those Bodies have an _Impetus_ of flying
the Centre, and moving upwards: by Vertue of which intrinsecall
Principle, called by him Levity, the Moveables which have that same
Motion more easily penetrate the more subtle _Medium_, than the more
dense: but such a Proposition appears likewise uncertain, as I have
above hinted in part, and as with Reasons and Experiments, I could
demonstrate, did not the present Argument importune me, or could I
dispatch it in few words.

    [85] Lib. 4. Cap. 5.

The Objection therefore of _Aristotle_ against _Democritus_, whilst he
saith, that if the Fiery ascending Atomes should sustain Bodies grave,
but of a distended Figure, it would be more observable in the Air than
in the water, because such Corpuscles move swifter in that, than in
this, is not good; yea the contrary would evene, for that they ascend
more slowly through the Air: and, besides their moving slowly, they
ascend, not united together, as in the water, but discontinue, and, as
we say, scatter: And, therefore, as _Democritus_ well replyes,
resolving the instance they make not their push or _Impetus_
conjunctly.

_Aristotle_, in the second place, deceives himself, whilst he will
have the said grave Bodies to be more easily sustained by the said
Fiery ascending Atomes in the Air than in the Water: not observing,
that the said Bodies are much more grave in that, than in this, and
that such a Body weighs ten pounds in the Air, which will not in the
water weigh 1/2 an ounce; how can it then be more easily sustained in
the Air, than in the Water?

    [Sidenote: _Democritus_ confuted by the Authour.]

Let us conclude, therefore, that _Democritus_ hath in this particular
better Philosophated than _Aristotle_. But yet will not I affirm, that
_Democritus_ hath reason'd rightly, but I rather say, that there is a
manifest Experiment that overthrows his Reason, and this it is, That
if it were true, that calid ascending Atomes should uphold a Body,
that if they did not hinder, would go to the bottom, it would follow,
that we may find a Matter very little superiour in Gravity to the
water, the which being reduced into a Ball, or other contracted
Figure, should go to the bottom, as encountring but few Fiery Atomes;
and which being distended afterwards into a dilated and thin Plate,
should come to be thrust upwards by the impulsion of a great Multitude
of those Corpuscles, and at last carried to the very Surface of the
water: which wee see not to happen; Experience shewing us, that a Body
_v. gra._ of a Sphericall Figure, which very hardly, and with very
great leasure goeth to the bottom, will rest there, and will also
descend thither, being reduced into whatsoever other distended Figure.
We must needs say then, either that in the water, there are no such
ascending Fiery Atoms, or if that such there be, that they are not
able to raise and lift up any Plate of a Matter, that without them
would go to the bottom: Of which two Positions, I esteem the second to
be true, understanding it of water, constituted in its naturall
Coldness. But if we take a Vessel of Glass, or Brass, or any other
hard matter, full of cold water, within which is put a Solid of a flat
or concave Figure, but that in Gravity exceeds the water so little,
that it goes slowly to the bottom; I say, that putting some burning
Coals under the said Vessel, as soon as the new Fiery Atomes shall
have penetrated the substance of the Vessel, they shall without doubt,
ascend through that of the water, and thrusting against the foresaid
Solid, they shall drive it to the Superficies, and there detain it, as
long as the incursions of the said Corpuscles shall last, which
ceasing after the removall of the Fire, the Solid being abandoned by
its supporters, shall return to the bottom.

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 Cælo_ 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.

[Illustration]

  _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