A
DISCOURSE
TO THE MOST SERENE
Don Co&longs;imo II.
GREAT DUKE
TUSCANY,
CONCERNING
The
And
THE
WATER.
By GALILEUS GALILEI: Philo&longs;opher and
Mathematician, unto His mo&longs;t Serene Highne&longs;&longs;e.
Engli&longs;hed from the Second Edition of the ITALIAN,
compared with the Manu&longs;cript Copies, and reduced
into PROPOSITIONS:
By
Printed by WILLIAM LEYBOURN:
A DISCOVRSE
Pre&longs;ented to the Mo&longs;t Serene DON COSIMO II.
GREATDUKE of
CONCERNING
In, the WATER.
Con&longs;idering (Mo&longs;t Serene Prince) that the
publi&longs;hing this pre&longs;ent Treati&longs;e, of &longs;o
different an Argument from that which
many expect, and which according to the
intentions I propo&longs;ed in my ^{*} A&longs;tronomi
call
have put forth, might peradventure make
&longs;ome thinke, either that I had wholly
relinqui&longs;hed my farther imployment
about the new Cele&longs;tiall Ob&longs;ervations,
or that, at lea&longs;t, I handled them very
remi&longs;&longs;ely; I have judged fit to render an account, a&longs;well of my
deferring that, as of my writing, and publi&longs;hing this treati&longs;e.
derio.
As to the fir&longs;t, the la&longs;t di&longs;coveries of
of the mutations of Figure in
Moon, together with the Con&longs;equents depending thereupon, have
not &longs;o much occa&longs;ioned the demur, as the inve&longs;tigation of the times
of the Conver&longs;ions of each of the Four Medicean Planets about
piter,
to
ing its whole revolution in one naturall day, and 18 hours, and almo&longs;t
an halfe. The &longs;econd moves in its Orbe 14 13 min.
in an hour, and its compleat conver&longs;ion is con&longs;ummate in 3 dayes, 13
hours, and one third, or thereabouts. The third pa&longs;&longs;eth in an hour,
2 6 min.
dayes, 4 hours, or very neer. The fourth, and more remote than the
re&longs;t, goes in one houre, o
and fini&longs;heth it all in 16 dayes, and very neer 18 hours. But be
cau&longs;e the exce&longs;&longs;ive velocity of their returns or re&longs;titutions, requires a
mo&longs;t &longs;crupulous preci&longs;ene&longs;&longs;e to calculate their places, in times pa&longs;t
am therefore forced, with other Ob&longs;ervations, and more exact than
the former, and in times more remote from one another, to correct
the Tables of &longs;uch Motions, and limit them even to the &longs;horte&longs;t mo
ment: for &longs;uch exactne&longs;&longs;e my fir&longs;t Ob&longs;ervations &longs;uffice not; not only
in regard of the &longs;hort intervals of Time, but becau&longs;e I had not as then
found out a way to mea&longs;ure the di&longs;tances between the &longs;aid Planets
by any In&longs;trument: I Ob&longs;erved &longs;uch Intervals with &longs;imple relation
to the Diameter of the Body of
the eye, the which, though they admit not errors of above a Minute,
yet they &longs;uffice not for the determination of the exact greatne&longs;s of the
Spheres of tho&longs;e Stars. But now that I have hit upon a way of ta
king &longs;uch mea&longs;ures without failing, &longs;carce in a very few Seconds, I will
continue the ob&longs;ervation to the very occultation of
which &longs;hall &longs;erve to bring us to the perfect knowledge of the Moti
ons, and Magnitudes of the Orbes of the &longs;aid Planets, together
al&longs;o with &longs;ome other con&longs;equences thence ari&longs;ing. I adde to the&longs;e
things the ob&longs;ervation of &longs;ome ob&longs;cure Spots, which are di&longs;cover
ed in the Solar Body, which changing, po&longs;ition in that, propounds
to our con&longs;ideration a great argument either that the Sun revolves in
it &longs;elfe, or that perhaps other Starts, in like manner as
&longs;mall digre&longs;&longs;ions, le&longs;&longs;e than that of
they interpo&longs;e between the Sun and our eye, or el&longs;e hint the truth
of both this and that; the certainty of which things ought not to be
contemned, nor omitted.
Ob&longs;ervations of
the Solar Spots.
matters contiguous to the Body of the Sun, there continually produced
in great number, and afterwards di&longs;&longs;olved, &longs;ome in a &longs;horter, &longs;ome in a
longer time, and to be by the Conver&longs;ion or Revolution of the Sun in it
&longs;elfe, which in a Lunar Moneth, or thereabouts, fini&longs;heth its Period,
caried about in a Circle, an accident great of it &longs;elfe, and greater for
its Con&longs;equences.
ducing the Au
thor to write
this Treati&longs;e.
As to the other particular in the next place. ^{*} Many cau&longs;es have
moved me to write the pre&longs;ent Tract, the &longs;ubject whereof, is the
Di&longs;pute which I held &longs;ome dayes &longs;ince, with &longs;ome learned men of
this City, about which, as your Highne&longs;&longs;e knows, have followed
many Di&longs;cour&longs;es: The principall of which Cau&longs;es hath been the
Intimation of your Highne&longs;&longs;e, having commended to me Writing,
as a &longs;ingular means to make true known from fal&longs;e, reall from appa
rent Rea&longs;ons, farr better than by Di&longs;puting vocally, where the
one or the other, or very often both the Di&longs;putants, through too
or el&longs;e being tran&longs;ported by o&longs;tentation of not yeilding to one ano
ther, farr from the fir&longs;t Propo&longs;ition, with the novelty, of the
various Propo&longs;als, confound both them&longs;elves and their Auditors.
Moreover, it &longs;eemed to me convenient to informe your High
ne&longs;&longs;e of all the &longs;equell, concerning the Controver&longs;ie of which I
treat, as it hath been adverti&longs;ed often already by others: and becau&longs;e
the Doctrine which I follow, in the di&longs;cu&longs;&longs;ion of the point in hand,
is different from that of
I have con&longs;idered that again&longs;t the Authority of that mo&longs;t famous
Man, which among&longs;t many makes all &longs;u&longs;pected that comes not from
the Schooles of the Peripateticks, its farr better to give ones Rea&longs;ons
by the Pen than by word of mouth and therfore I re&longs;olved to write the
pre&longs;ent di&longs;cour&longs;e: in which yet I hope to demon&longs;trate that it was not
out of capritiou&longs;ne&longs;&longs;e, or for that I had not read or under&longs;tood
&longs;everall Rea&longs;ons per&longs;wade me to it, and the &longs;ame
tought me to fix my judgment on that which is grounded upon
Rea&longs;on, and not on the bare Authority of the Ma&longs;ter; and it is
mo&longs;t certaine according to the &longs;entence of
ting &longs;hould be free. Nor is the re&longs;olution of our Que&longs;tion in my
judgment without &longs;ome benefit to the Univer&longs;all, fora&longs;much 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.
Rea&longs;on to the
Authority ofan
Author.
this Argument.
I &longs;ay therfore, that being the la&longs;t Summer in company with certain
Learned men, it was &longs;aid in the argumentation; That Conden&longs;ation
was the propriety of Cold, and there was alledged for in&longs;tance, the
example of Ice: now I at that time &longs;aid, that, in my judgment,
the Ice &longs;hould be rather Water rarified than conden&longs;ed, and my
rea&longs;on was, becau&longs;e Conden&longs;ation begets diminution of Ma&longs;s, and
augmentation of gravity, and Rarifaction cau&longs;eth greater Lightne&longs;s,
and augmentarion of Ma&longs;&longs;e: and Water in freezing, encrea&longs;eth in
Ma&longs;&longs;e, and the Ice made thereby is lighter than the Water on which
it &longs;wimmeth.
the Propriety of
Cold, according
to the Peripate
ticks.
rarified, than
conden&longs;ed, and
why:
whole Gravity of Sollids the weight of &longs;uch another Ma&longs;&longs;e of the &longs;aid
Humido;
the more &longs;hall the
when by Compre&longs;&longs;ion it &longs;hall be conden&longs;ed and reduced to a le&longs;&longs;e Ma&longs;&longs;e.
tation of Bodies
Prop. 7.
not in the Nata
tion of Sollids.
It was an&longs;wered me, that that proceeded not from the greater Levity;
but from the Figure, large and flat, which not being able to pene
trate the Re&longs;i&longs;tance of the Water, is the cau&longs;e that it &longs;ubmergeth not.
I replied, that any piece of Ice, of what&longs;oever Figure, &longs;wims upon
the Water, a manife&longs;t &longs;igne, that its being never &longs;o flat and broad,
hath not any part in its floating: and added, that it was a manife&longs;t
proofe hereof to &longs;ee a piece of Ice of very broad Figure being thru&longs;t
to the botome of the Water, &longs;uddenly return to flote atoppe, which
had it been more grave, and had its &longs;wimming proceeded from its
Forme, unable to penetrate the Re&longs;i&longs;tance of the
would be altogether impo&longs;&longs;ible; I concluded therefore, that the Figure
was in &longs;ort a Cau&longs;e of the Natation or Submer&longs;ion of Bodies,
but the greater or le&longs;&longs;e Gravity in re&longs;pect of the Water: and there
fore all Bodyes heavier than it of what Figure &longs;oever they be, indiffe
rently go to the bottome, and the lighter, though of any figure, float
indifferently on the top: and I &longs;uppo&longs;e that tho&longs;e which hold other
wi&longs;e, were induced to that beliefe, by &longs;eeing how that diver&longs;ity
of Formes or Figures, greatly altereth the Velo&longs;ity, and Tardity
of Motion; &longs;o that Bodies of Figure broad and thin, de&longs;cend
far more lea&longs;urely into the Water, than tho&longs;e of a more compacted
Figure, though both made of the &longs;ame Matter: by which &longs;ome
might be induced to believe that the Dilatation of the Figure might
reduce it to &longs;uch amplene&longs;&longs;e that it &longs;hould not only retard but wholly
impede and take away the Motion, which I hold to be fal&longs;e. Upon
this Conclu&longs;ion, in many dayes di&longs;cour&longs;e, was &longs;poken much, and
many things, and divers Experiments produced, of which your
Highne&longs;&longs;e heard, and &longs;aw &longs;ome, and in this di&longs;cour&longs;e &longs;hall have
all that which hath been produced again&longs;t my A&longs;&longs;ertion, and what
hath been &longs;ugge&longs;ted to my thoughts on this matter, and for con
firmation of my Conclu&longs;ion: which if it &longs;hall &longs;uffice to remove that
(as I e&longs;teem hitherto fal&longs;e) Opinion, I &longs;hall thinke I have not
unprofitably &longs;pent my paynes and time. and although that come
not to pa&longs;&longs;e, yet ought I to promi&longs;e another benefit to my &longs;elfe,
namely, of attaining the knowledge of the truth, by hearing my
Fallacyes confuted, and true demon&longs;trations produced by tho&longs;e
of the contrary opinion.
And to proceed with the greate&longs;t plainne&longs;s and per&longs;picuity that
I can po&longs;&longs;ible, it is, I conceive, nece&longs;&longs;ary, fir&longs;t of all to declare
what is the true, intrin&longs;ecall, and totall Cau&longs;e, of the a&longs;cending of
&longs;ome Sollid Bodyes in the Water, and therein floating; or on the
contrary, of their &longs;inking. and &longs;o much the rather in a&longs;much as I
cannot &longs;atisfie my &longs;elfe in that which
this Subject.
Natation & &longs;ub
I &longs;ay then the Cau&longs;e why &longs;ome Sollid Bodyes de&longs;cend to the
Gravity of the Water; and on the contrary, the exce&longs;s of the
Waters Gravity above the Gravity of tho&longs;e, is the Cau&longs;e that others
do not de&longs;cend, rather that they ri&longs;e from the Bottom, and a&longs;cend
to the Surface. This was &longs;ubtilly demon&longs;trated by
his Book Of the NATATION of BODIES: Conferred afterwards
by a very grave Author, but, if I erre not invi&longs;ibly, as below for
defence of him, I &longs;hall endeavour to prove.
ids in the Wa
ter.
I, with a different Method, and by other meanes, will endeavour
to demon&longs;trate the &longs;ame, reducing the Cau&longs;es of &longs;uch Effects to
more intrin&longs;ecall and immediate Principles, in which al&longs;o are di&longs;co
vered the Cau&longs;es of &longs;ome admirable and almo&longs;t incredible Acci
dents, as that would be, that a very little quantity of Water, &longs;hould
be able, with its &longs;mall weight, to rai&longs;e and &longs;u&longs;tain a Solid Body, an
hundred or a thou&longs;and times heavier than it.
And becau&longs;e demon&longs;trative Order &longs;o requires, I &longs;hall define cer
tain Termes, and afterwards explain &longs;ome Propo&longs;itions, of which,
as of things true and obvious, I may make u&longs;e of to my pre&longs;ent pur
po&longs;e.
DEFINITION I.
of which equall Ma&longs;&longs;es weigh equally.
As if for example, two Balls, one of Wax, and the other of &longs;ome
Wood of equall Ma&longs;&longs;e, were al&longs;o equall in Weight, we &longs;ay, that
&longs;uch Wood, and the Wax are
DEFINITION II.
Sollids, weighing equally, though of Ma&longs;s they be
unequall.
As for example, a Ma&longs;s of Lead, and another of Wood, that
weigh each ten pounds, I call equall in Ab&longs;olute Gravity, though
the Ma&longs;s of the Wood be much greater then that of the Lead.
DEFINITION III.
which a Ma&longs;s, equall to a Ma&longs;s of the other, &longs;hall
weigh more.
And &longs;o I &longs;ay, that Lead is more grave
if you take of them two equall Ma&longs;&longs;es, that of the Lead weigheth
more.
DEFINITION IV.
that weigh more than this, without any re&longs;pect had to
the Ma&longs;&longs;es.
And thus a great piece of Wood is &longs;aid to weigh more than a
little lump of Lead, though the Lead be
the Wood. And the &longs;ame is to be under&longs;tood of the le&longs;s grave
&longs;pecie,
The&longs;e Termes defined, I take from the Mechanicks two Princi
ples: the fir&longs;t is, that
AXIOME. I.
are of equall Force and Moment in their operations.
Moment, among&longs;t Mechanicians, &longs;igrifieth that
Vertue, that Force, or that Efficacy, with which
the Mover moves, and the Moveable re&longs;i&longs;ts.
Velocity of the Motion, and on the diver&longs;e Inclinations of the Spaces
along which the Motion is made: For a de&longs;cending Weight makes a
greater
and in &longs;umme, what ever is the occa&longs;ion of &longs;uch Vertue, it ever retaines
the name of
Idiome, for, if I mistake not, I think we often &longs;ay; This is a weighty
bu&longs;ine&longs;&longs;e, but the other is of &longs;mall moment: and we con&longs;ider lighter mat
ters and let pa&longs;s tho&longs;e of Moment; a Metaphor, I &longs;uppo&longs;e, taken from
the Mechanicks.
As for example, two weights equall in ab&longs;olute Gravity, being
put into a Ballance of equall Arms, they &longs;tand in
ther one going down, nor the other up: becau&longs;e the equality of the
Di&longs;tances of both, from the Centre on which the Ballance is &longs;uppor
ted, and about which it moves, cau&longs;eth that tho&longs;e weights, the &longs;aid
Ballance moving, &longs;hall in the &longs;ame Time move equall Spaces, that is,
&longs;hall move with equall Velocity, &longs;o that there is no rea&longs;on for which
and therefore they make an
of &longs;emblable and equall Vertue.
The &longs;econd Principle is; That
AXIOME II.
the Velocity of the Motion.
So that Weights ab&longs;olutely equall, but conjoyned with Velocity
unequall, are of Force, Moment and Vertue unequall: and the
more potent, the more &longs;wift, according to the proportion of the Ve
locity 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 ab&longs;olutely equall being &longs;u&longs;pended, they do not
weigh down, and gravitate equally, but that which is at a greater
di&longs;tance from the Centre, about which the Beam moves, de&longs;cends,
rai&longs;ing the other, and the Motion of this which a&longs;cends is &longs;low, and
the other &longs;wift: and &longs;uch is the Force and Vertue, which from the
Velocity of the Mover, is conferred on the Moveable, which receives
it, that it can exqui&longs;itely compen&longs;ate, as much more Weight added to
the other &longs;lower Moveable: &longs;o 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 &longs;u&longs;pended at the greater di&longs;tance, may
&longs;u&longs;tain and poy&longs;e another ten times more grave ab&longs;olutely than it:
and that becau&longs;e the Stiliard moving, the le&longs;&longs;er Weight &longs;hall move
ten times fa&longs;ter than the bigger. It ought alwayes therefore to be
under&longs;tood, that Motions are according to the &longs;ame 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 &longs;ame Horizontall plain: and in &longs;umme,
alwayes both in like Inclinations. This proportion between the
Gravity and Velocity is found in all Mechanicall In&longs;truments: and
is con&longs;idered by
whereupon we al&longs;o may take it for a true A&longs;&longs;umption, That
AXIOME III.
and become of equall Moments, as oft as their Gravi
ties, with contrary proportion, an&longs;wer to the Velocity of
their Motions.
That is to &longs;ay, that by how much the one is le&longs;s grave than the other,
by &longs;o much is it in a con&longs;titution of moving more &longs;wiftly than that.
Having prefatically explicated the&longs;e things, we may begin to en
quire, what Bodyes tho&longs;e are which totally &longs;ubmerge in Water, and
go to the Bottom, and which tho&longs;e that by con&longs;traint float on the
top, &longs;o that being thru&longs;t by violence under Water, they return to
&longs;wim, with one part of their Ma&longs;s vi&longs;ible above the Surface of the
Water: and this we will do by con&longs;idering the re&longs;pective operati
on of the &longs;aid Solids, and of Water: Which operation followes
the Submer&longs;ion and &longs;inking; and this it is, That in the Submer&longs;ion
that the Solid maketh, being depre&longs;&longs;ed downwards by its proper
Gravity, it comes to drive away the water from the place where it
&longs;ucce&longs;&longs;ively &longs;ubenters, and the water repul&longs;ed ri&longs;eth and a&longs;cends
above its fir&longs;t levell, to which A&longs;cent on the other &longs;ide it, as being a
grave Body of its own nature, re&longs;i&longs;ts: And becau&longs;e the de&longs;cending
Solid more and more immerging, greater and greater quantity of
Water a&longs;cends, till the whole Sollid be &longs;ubmerged; its nece&longs;&longs;ary to
compare the Moments of the Re&longs;i&longs;tance of the water to A&longs;cen&longs;ion,
with the Moments of the pre&longs;&longs;ive Gravity of the Solid: And if the
Moments of the Re&longs;i&longs;tance of the water, &longs;hall equalize the Moments
of the Solid, before its totall Immer&longs;ion; in this ca&longs;e doubtle&longs;s there
&longs;hall be made an But if the Moment of the Solid, &longs;hall alwayes exceed the Moments
wherewith the repul&longs;ed water &longs;ucce&longs;&longs;ively makes Re&longs;i&longs;tance, that
Solid &longs;hall not only wholly &longs;ubmerge under water, but &longs;hall de&longs;cend
to the Bottom. But if, la&longs;tly, in the in&longs;tant of totall Submer&longs;ion,
the equality &longs;hall be made between the Moments of the prement
Solid, and the re&longs;i&longs;ting Water; then &longs;hall re&longs;t en&longs;ue, and the &longs;aid
Solid &longs;hall be able to re&longs;t indifferently, in what&longs;oever part of the
water. By this time is manife&longs;t the nece&longs;&longs;ity of comparing the
Gravity of the water, and of the Solid; and this compari&longs;on might
at fir&longs;t &longs;ight &longs;eem &longs;ufficient to conclude and determine which are the
Solids that float a-top, and which tho&longs;e that &longs;ink to the Bottom in the
water, a&longs;&longs;erting that tho&longs;e &longs;hall float which are le&longs;&longs;e grave
than the water, and tho&longs;e &longs;ubmerge, which are For it &longs;eems in appearance, that the Sollid in &longs;inking continually,
rai&longs;eth &longs;o much Water in Ma&longs;s, as an&longs;wers to the parts of its own
Bulk &longs;ubmerged: whereupon it is impo&longs;&longs;ible, that a Solid le&longs;s grave
weight greater than its own, and &longs;uch would a Ma&longs;s of water equall
to its own Ma&longs;s be. And likewi&longs;e it &longs;eems nece&longs;&longs;ary, that the graver
Solids do go to the Bottom, as being of a Force more than &longs;ufficient
for the rai&longs;ing a Ma&longs;&longs;e of water, equall to its own, though inferiour
in weight. Neverthele&longs;s the bu&longs;ine&longs;s &longs;ucceeds otherwi&longs;e: and
deficient, nor is it true, that the Solid in &longs;ubmerging, rai&longs;eth and
repul&longs;eth Ma&longs;&longs;es of Water, equall to the parts of it &longs;elf &longs;ubmerged;
but the Water repul&longs;ed, is alwayes le&longs;s than the parts of the Solid
&longs;ubmerged: and &longs;o much the more by how much the Ve&longs;&longs;ell in
which the Water is contained is narrower: in &longs;uch manner that it
hinders not, but that a Solid may &longs;ubmerge all under Water, with
out rai&longs;ing &longs;o much Water in Ma&longs;s, as would equall the tenth or
twentieth part of its own Bulk: like as on the contrary, a very
&longs;mall quantity of Water, may rai&longs;e a very great Solid Ma&longs;s, though
&longs;uch Solid &longs;hould weigh ab&longs;olutely a hundred times as much, or
more, than the &longs;aid Water, if &longs;o be that the Matter of that &longs;ame
Solid be And thus a great
Beam, as &longs;uppo&longs;e of a 1000 weight, may be rai&longs;ed and born afloat
by Water, which weighs not 50: and this happens when the Mo
ment of the Water is compen&longs;ated by the Velocity of its Motion.
mer&longs;ion of So
lids in the Wa
ter, is effected.
&longs;hall float on the
Water.
&longs;hall &longs;inke to the
botome.
&longs;hall re&longs;t in all
places of the Wa
ter.
the Water and
compared in all
Problems, of Na
tation of Bodies.
pul&longs;ed is ever le&longs;s
than the parts of
the Sollid &longs;ub
merged.
of water, may
float a very
great Solid Ma&longs;s.
But becau&longs;e &longs;uch things, propounded thus in ab&longs;tract, are &longs;ome
what difficult to be comprehended, it would be good to demon&longs;trate
them by particular examples; and for facility of demon&longs;tration, we
will &longs;uppo&longs;e the Ve&longs;&longs;els in which we are to put the Water, and place
the Solids, to be inviron'd and included with &longs;ides erected perpendi
cular to the Plane of the Horizon, and the Solid that is to be put
into &longs;uch ve&longs;&longs;ell to be either a &longs;treight Cylinder, or el&longs;e an upright
Pri&longs;me
of what hath been hinted, forming the en&longs;uing Theoreme.
The Ma&longs;s of the Water whicha&longs;cends in the &longs;ub
merging of a Solid, Pri&longs;me or Cylinder, or that
aba&longs;eth in taking it out, is le&longs;s than the Ma&longs;s of
the &longs;aid Solid, &longs;o depre&longs;&longs;ed or advanced: and
hath to it the &longs;ame proportion, that the Surface
of the Water circumfu&longs;ing the Solid, hath to the
&longs;ame circumfu&longs;ed Surface, together with the Ba&longs;e
of the Solid.
of the water rai
&longs;ed to the
&longs;ubmerged.
Levell E F G, before the Solid Pri&longs;me H I K be therein immerged;
but after that it is depre&longs;&longs;ed under Water, let the Water be rai&longs;ed as
high as the Levell L M, the Solid H I K &longs;hall then be all under Water,
and the Ma&longs;s of the elevated Water &longs;hall be L G, which is le&longs;s than the
H I K, being equall to the only part E I K,
which is contained under the fir&longs;t Levell
E F G. Which is manife&longs;t, becau&longs;e if
the Solid H I K be taken out, the Water
I G &longs;hall return into the place occupied by
the Ma&longs;s E I K, where it was continuate be
fore the &longs;ubmer&longs;ion of the Pri&longs;me. And
the Ma&longs;s L G being equall to the Ma&longs;s
E K: adde thereto the Ma&longs;s E N, and it
&longs;hall be the whole Ma&longs;s E M, compo&longs;ed of the parts of the Pri&longs;me E N,
and of the Water N F, equall to the whole Solid H I K: And, there
fore, the Ma&longs;s L G &longs;hall have the &longs;ame proportion to E M, as to the
Ma&longs;s H I K: But the Ma&longs;s L G hath the &longs;ame proportion to the Ma&longs;s
E M, as the Surface L M hath to the Surface M H: Therefore it is ma
nife&longs;t, that the Ma&longs;s of Water repul&longs;ed L G, is in proportion to the Ma&longs;s
of the Solid &longs;ubmerged 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 &longs;aid ambient water, and the Ba&longs;e of the Pri&longs;me H N. But if we
&longs;uppo&longs;e the fir&longs;t Levell of the Water the according to the Surface H M,
and the Pri&longs;me allready &longs;ubmerged H I K; and after to be taken out and
rai&longs;ed to E A O, and the Water to be faln from the fir&longs;t Levell H L M as
low as E F G; It is manife&longs;t, that the Pri&longs;me E A O being the &longs;ame with
H I K, its &longs;uperiour part H O, &longs;hall be equall to the inferiour E I K:
and remove the common part E N, and, con&longs;equently, the Ma&longs;s of the
Water L G is equall to the Ma&longs;s H O; and, therefore, le&longs;s than the
Solid, which is without the Water, namely, the whole Pri&longs;me E A O, to
which likewi&longs;e, the &longs;aid Ma&longs;s of Water abated L G, hath the &longs;ame propor
tion, that the Surface of the Waters circumfu&longs;ed L M hath to the &longs;ame
circumfu&longs;ed Surface, together with the Ba&longs;e of the Pri&longs;me A O: which
hath the &longs;ame demon&longs;tration with the former ca&longs;e above.
the immer&longs;ion of the Solid, or that ebbeth in elevating it, is not equall to
all the Ma&longs;s of the Solid, which is &longs;ubmerged or elevated, but to that
part only, which in the immer&longs;ion is under the fir&longs;t Levell of the Water,
and in the elevation remaines above the fir&longs;t Levell: Which is that
which was to be demon&longs;trated. We will now pur&longs;ue the things that
remain.
And fir&longs;t we will demon&longs;trate that,
THEOREME II.
a Pri&longs;me or Cylinder, inviron'd with Water, if we ele
vate that Solid perpendicularly, the Water circumfu
&longs;ed &longs;hall abate, and the Abatement of the Water,
&longs;hall have the &longs;ame proportion to the Elevation of the
Pri&longs;me, as one of the Ba&longs;es of the Pri&longs;me, hath to
the Surface of the Water Circumfu&longs;ed.
of the water aba
ted, to the Solid
rai&longs;ed.
Imagine in the Ve&longs;&longs;ell, as is afore&longs;aid, the
Pri&longs;me A C D B to be placed, and in the
re&longs;t of the Space the Water to be dif
fu&longs;ed as far as the Levell E A: and rai
&longs;ing the Solid, let it be transferred to
G M, and let the Water be aba&longs;ed from
E A to N O: I &longs;ay, that the de&longs;cent of
the Water, mea&longs;ured by the Line A O,
hath the &longs;ame proportion to the ri&longs;e of the
Pri&longs;me, mea&longs;ured by the Line G A, as the Ba&longs;e of the Solid G H
hath to the Surface of the Water N O. The which is manife&longs;t:
becau&longs;e the Ma&longs;s of the Solid G A B H, rai&longs;ed above the fir&longs;t Levell
E A B, is equall to the Ma&longs;s of Water that is aba&longs;ed E N O A.
Therefore, E N O A and G A B H are two equall Pri&longs;mes; for of
equall Pri&longs;mes, the Ba&longs;es an&longs;wer contrarily to their heights: There
fore, as the Altitude A O is to the Altitude A G, &longs;o is the Superfi
cies or Ba&longs;e G H to the Surface of the Water N O. If therefore,
for example, a Pillar were erected in a wa&longs;te Pond full of Water,
or el&longs;e in a Well, capable of little more then the Ma&longs;s of the &longs;aid
Pillar, in elevating the &longs;aid Pillar, and taking it out of the Water,
according as it ri&longs;eth, the Water that invirons it will gradually abate,
and the aba&longs;ement of the Water at the in&longs;tant of lifting out the
Pillar, &longs;hall have the &longs;ame proportion, that the thickne&longs;s of the Pillar
hath to the exce&longs;s of the breadth of the &longs;aid Pond or Well, above
the thickne&longs;s of the &longs;aid Pillar: &longs;o that if the breadth of the Well
were an eighth part larger than the thickne&longs;s of the Pillar, and the
breadth of the Pond twenty five times as great as the &longs;aid thickne&longs;s,
in the Pillars a&longs;cending one foot, the water in the Well &longs;hall de&longs;cend
&longs;even foot, and that in the Pond only 1/25 of a foot.
le&longs;s grave
cie
&longs;tayeth not un
der water, in ve
ry &longs;mall depthst.
This Demon&longs;trated, it will not be difficult to &longs;hew the true
cau&longs;e, how it comes to pa&longs;s, that,
THEOREME III.
le&longs;s grave than Water, if it &longs;hould be totally &longs;ubmerged
in Water, &longs;tayes not underneath, but ri&longs;eth, though the
Water circumfu&longs;ed be very little, and in ab&longs;olute
Gravity, never &longs;o much inferiour to the Gravity of the
&longs;aid Pri&longs;me.
Let then the Pri&longs;me A E F B, be put into the Ve&longs;&longs;ell C D F B, the
&longs;ame being le&longs;s grave
Water infu&longs;ed ri&longs;e to the height of the Pri&longs;me: I &longs;ay, that the
Pri&longs;me left at liberty, it &longs;hall ri&longs;e, being born up
by the Water circumfu&longs;ed C D E A. For the
Water C E being &longs;pecifically more grave than
the Solid A F, the ab&longs;olute weight of the water
C E, &longs;hall have greater proportion to the ab&longs;o
lute weight of the Pri&longs;me A F, than the Ma&longs;s
C E hath to the Ma&longs;s A F (in regard the Ma&longs;s
hath the &longs;ame proportion to the Ma&longs;s, that the
weight ab&longs;olute hath to the weight ab&longs;olute,
in ca&longs;e the Ma&longs;&longs;es are of the &longs;ame Gravity
the Ma&longs;s C E is to the Ma&longs;s A F, as the Surface of the water A C, is
to the Superficies, or Ba&longs;e of the Pri&longs;me A B; which is the &longs;ame pro
portion as the a&longs;cent of the Pri&longs;me when it ri&longs;eth, hath to the de&longs;cent
of the water circumfu&longs;ed C E.
Therefore, the ab&longs;olute Gravity of the water C E, hath greater
proportion to the ab&longs;olute Gravity of the Pri&longs;me A F; than the
A&longs;cent of the Pri&longs;me A F, hath to the de&longs;cent of the &longs;aid
water C E. The Moment, therefore, compounded of the ab&longs;olute
Gravity of the water C E, and of the Velocity of its de&longs;cent, whil&longs;t
it forceably repul&longs;eth and rai&longs;eth the Solid A F, is greater than the
Moment compounded of the ab&longs;olute Gravity of the Pri&longs;me A F, and
of the Tardity of its a&longs;cent, with which Moment it contra&longs;ts and re
fi&longs;ts the repul&longs;e and violence done it by the Moment of the water:
Therefore, the Pri&longs;me &longs;hall be rai&longs;ed.
according to
which the Sub
mer&longs;ion & Na
tation of Solids
is made.
It followes, now, that we proceed forward to demon&longs;trate more
particularly, how much &longs;uch Solids &longs;hall be inferiour in Gravity to
the water elevated; namely, what part of them &longs;hall re&longs;t &longs;ubmerged,
and what &longs;hall be vi&longs;ible above the Surface of the water: but fir&longs;t
it is nece&longs;&longs;ary to demon&longs;trate the &longs;ub&longs;equent Lemma.
LEMMA I.
and of their Ma&longs;&longs;es.
Gravity of So
lids, are in a pro
portion com
pounded of their
Specifick Gravi
ties, and of their
Ma&longs;&longs;es.
Let A and B be two Solids. I &longs;ay, that the Ab&longs;olute Gravity
of A, hath to the Ab&longs;olute Gravity of B, a proportion com
pounded of the proportions of the &longs;pecificall Gravity of A, to
the Specificall Gravity of B, and of the Ma&longs;s
A to the Ma&longs;s B. Let the Line D have the
&longs;ame proportion to E, that the &longs;pecifick
Gravity of A, hath to the &longs;pecifick Gravity
of B; and let E be to F, as the Ma&longs;s A to the
Ma&longs;s B: It is manife&longs;t, that the proportion
of D to F, is compounded of the proportions
D and E; and E and F. It is requi&longs;ite,
therefore, to demon&longs;trate, that as D is to F, &longs;o the ab&longs;olute Gravity
of A, is to the ab&longs;olute Gravity of B. Take the Solid C, equall in
Ma&longs;s to the Solid A, and of the &longs;ame Gravity
B. Becau&longs;e, therefore, A and C are equall in Ma&longs;s, the ab&longs;olute
Gravity of A, &longs;hall have to the ab&longs;olute Gravity of C, the &longs;ame pro
portion, as the &longs;pecificall Gravity of A, hath to the &longs;pecificall Gravity
of C, or of B, which is the &longs;ame
cau&longs;e, C and B are of the &longs;ame Gravity
the ab&longs;olute weight of C, is to the ab&longs;olute weight of B, &longs;o the Ma&longs;s
C, or the Ma&longs;s A, is to the Ma&longs;s B; that is, as the Line E to the Line
F. As therefore, the ab&longs;olute Gravity of A, is to the ab&longs;olute
Gravity of C, &longs;o is the Line D to the Line E: and, as the ab&longs;olute
Gravity of C, is to the ab&longs;olute Gravity of B, &longs;o is the Line E to the
Line F: Therefore, by Equality of proportion, the ab&longs;olute Gra
vity of A, is to the ab&longs;olute Gravity of B, as the Line D to the
Line F: which was to be demon&longs;trated. I proceed now to demon
&longs;trate, how that,
THEOREME IV.
of water requi
&longs;ite to make a
Solid &longs;wim.
than the Water, being put into a Ve&longs;&longs;el, as above, of
what&longs;oever greatne&longs;&longs;e, and the Water, be afterwards
infu&longs;ed, the Solid &longs;hall re&longs;t in the bottom, unrai&longs;ed, till
the Water arrive to that part of the Altitude, of the
&longs;aid Pri&longs;me, to which its whole Altitude hath the
&longs;ame proportion, that the Specificall Gravity of the
Water, hath to the Specificall Gravity of the &longs;aid
Solid: but infu&longs;ing more Water, the Solid &longs;hall a&longs;cend.
Let the Ve&longs;&longs;ell be M L G N of any bigne&longs;s, and let there be pla
ced in it the Solid Pri&longs;me D F G E, le&longs;s grave
water; and look what proportion the
the water, hath to that of the Pri&longs;me, &longs;uch let the Altitude D F, have
to the Altitude F B. I &longs;ay, that infu&longs;ing water to the Altitude F B,
the Solid D G &longs;hall not float, but &longs;hall &longs;tand in
that every little quantity of water, that is infu&longs;ed, &longs;hall rai&longs;e it. Let
the water, therefore, be infu&longs;ed to the Levell A B C, and, becau&longs;e
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 Ma&longs;s
B G to the Ma&longs;s G D; as the proportion of the Ma&longs;s B G is to the
Ma&longs;s G D, as the proportion of the Ma&longs;s G D is to the Ma&longs;s A F, they
compo&longs;e the Proportion of the Ma&longs;s B G to the Ma&longs;s A F. Therefore,
the Ma&longs;s B G is to the Ma&longs;s A F, in a proportion compounded of the
proportions of the Specifick Gravity of the Solid G D, to the Speci
fick Gravity of the water, and of the Ma&longs;s G D
to the Ma&longs;s A F: But the &longs;ame proportions
of the Specifick Gravity of G D, to the Specifick
Gravity of the water, and of the Ma&longs;s G D to
the Ma&longs;s A F, do al&longs;o by the precedent
compound the proportion of the ab&longs;olute Gra
vity of the Solid D G, to the ab&longs;olute Gravity
of the Ma&longs;s of the water A F: Therefore,
as the Ma&longs;s B G is to the Ma&longs;s A F, &longs;o is the
Ab&longs;olute Gravity of the Solid D G, to the Ab
&longs;olute Gravity of the Ma&longs;s of the water A F. But as the Ma&longs;s B G
is to the Ma&longs;s A F; &longs;o is the Ba&longs;e of the Pri&longs;me D E, to the Surface
of the water AB; and &longs;o is the de&longs;cent of the water A B, to the
Elevation of the Pri&longs;me D G; Therefore, the de&longs;cent of the
the Pri&longs;me, is to the ab&longs;olute Gravity of the water: Therefore, the
Moment re&longs;ulting from the ab&longs;olute Gravity of the water A F, and
the Velocity of the Motion of declination, with which Moment it
forceth the Pri&longs;me D G, to ri&longs;e and a&longs;cend, is equall to the Moment
that re&longs;ults from the ab&longs;olute Gravity of the Pri&longs;me D G, and from
the Velocity of the Motion, wherewith being rai&longs;ed, it would a&longs;cend:
with which Moment it re&longs;i&longs;ts its being rai&longs;ed: becau&longs;e, therefore,
&longs;uch Moments are equall, there &longs;hall be an
water and the Solid. And, it is manife&longs;t, that putting a little more
water unto the other A F, it will increa&longs;e the Gravity and Moment,
whereupon the Pri&longs;me D G, &longs;hall be overcome, and elevated till that
the only part B F remaines &longs;ubmerged. Which is that that was to
be demon&longs;trated.
COROLLARY I.
in &longs;pecie
Ma&longs;s, as is the part of the Solid &longs;ubmerged, doth weigh ab&longs;olutely as
much as the whole Solid.
le&longs;s grave
cie
do &longs;ubmerge.
For, it being &longs;uppo&longs;ed, that the Specificall Gravity of the water,
is to the Specificall Gravity of the Pri&longs;me 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 ea&longs;ily demon&longs;trate, that as much water in Ma&longs;s
as is equall to the Solid B G, doth weigh ab&longs;olutely as much as the
whole Solid D G; For, by the
Gravity of a Ma&longs;s of water, equall to the Ma&longs;s B G, hath to the Ab
&longs;olute Gravity of the Pri&longs;me D G, a proportion compounded of the
proportions, of the Ma&longs;s B G to the Ma&longs;s G D, and of the Specifick
Gravit 7 of the water, to the Specifick Gravity of the Pri&longs;me: But
the Gravity
Pri&longs;me, is &longs;uppo&longs;ed to be as the Ma&longs;s G D to the Ma&longs;s G B. There
fore, the Ab&longs;olute Gravity of a Ma&longs;s of water, equall to the Ma&longs;s
B G, is to the Ab&longs;olute Gravity of the Solid D G, in a proportion
compounded of the proportions, of the Ma&longs;s B G to the Ma&longs;s G D,
and of the Ma&longs;s D G to the Ma&longs;s G B; which is a proportion of
equalitie. The Ab&longs;olute Gravity, therefore, of a Ma&longs;s of Water
equall to the part of the Ma&longs;s of the Pri&longs;me B G, is equall to the Ab
&longs;olute Gravity of the whole Solid D G.
COROLLARY II.
librate
the water.
into a Ve&longs;&longs;ell of any imaginable greatne&longs;s, and water being circumfu&longs;ed
about it to &longs;uch a height, that as much water in Ma&longs;s, as is the part of
the Solid &longs;ubmerged, doth/> weigh ab&longs;olutely as much as the whole Solid;
it &longs;hall by that water be ju&longs;tly &longs;u&longs;tained, be the circumfu&longs;ed Water in
quantity greater or le&longs;&longs;er.
For, if the Cylinder or Pri&longs;me M, le&longs;s grave than the water, gra.
ous Ve&longs;&longs;ell A B C D, and the water rai&longs;ed about it, to three
quarters of its height, namely, to its Levell A D: it &longs;hall be &longs;u&longs;tained
and exactly poy&longs;ed in
librium.
pen, if the Ve&longs;&longs;ell E N S F
were very &longs;mall, &longs;o, that be
tween the Ve&longs;&longs;ell and the So
lid M, there were but a very
narrow &longs;pace, and only capable of &longs;o much water, as the hundredth
part of the Ma&longs;s M, by which it &longs;hould be likewi&longs;e rai&longs;ed and erected,
as before it had been elevated to three fourths of the height of the
Solid: which to many at the fir&longs;t &longs;ight, may &longs;eem a notable Paradox,
and beget a conceit, that the Demon&longs;tration of the&longs;e effects, were
&longs;ophi&longs;ticall and fallacious: but, for tho&longs;e who &longs;o repute it, the Ex
periment is a means that may fully &longs;atisfie them. But he that &longs;hall
but comprehend of what Importance Velocity of Motion is, and how
it exactly compen&longs;ates the defect and want of Gravity, will cea&longs;e to
wonder, in con&longs;idering that at the elevation of the Solid M, the great
Ma&longs;s of water A B C D abateth very little, but the little Ma&longs;s of
water E N S F decrea&longs;eth very much, and in an in&longs;tant, as the Solid
M before did li&longs;e, howbeit for a very &longs;hort &longs;pace: Whereupon the
Moment, compounded of the &longs;mall Ab&longs;olute Gravity of the water
E N S F, and of its great Velocity in ebbing, equalizeth the Force and
and Moment, that re&longs;ults from the compo&longs;icion of the immen&longs;e Gra
vity of the water A B C D, with its great &longs;lowne&longs;&longs;e of ebbing;
&longs;ince that in the Elevation of the Sollid M, the aba&longs;ement of the le&longs;
&longs;er water E S, is performed ju&longs;t &longs;o much more &longs;wiftly than the great
Ma&longs;s of water A C, as this is more in Ma&longs;s than that which we thus
demon&longs;trate.
according to
which water ri
&longs;eth and falls in
different Ve&longs;&longs;els
at the Immer&longs;i
on and Elevati
on of
In the ri&longs;ing of the Solid M, its elevation hath the &longs;ame proportion
to the circumfu&longs;ed water E N S F, that the Surface of the &longs;aid water,
hath to the Superficies or Ba&longs;e of the &longs;aid Solid M; which Ba&longs;e hath
the &longs;ame proportion to the Surface of the water A D, that the aba&longs;e
the &longs;aid Solid M. Therefore, by Perturbation of proportion, in the
a&longs;cent of the &longs;aid Solid M, the aba&longs;ement of the water A B C D, to
the aba&longs;ement of the water E N S F, hath the &longs;ame proportion, that the
Surface of the water E F, hath to the Surface of the water A D;
that is, that the whole Ma&longs;s of the water E N S F, hath to the whole
Ma&longs;s A B C D, being equally high: It is manife&longs;t, therefore, that
in the expul&longs;ion and elevation of the Solid M, the water E N S F
&longs;hall exceed in Velocity of
on the other &longs;ide is exceeded by that in quantity: whereupon their
Moments in &longs;uch operations, are mutually equall.
con&longs;ider the pre&longs;ent Figure, (which if I be not deceived, may &longs;erve to
detect the errors of &longs;ome Practick Mechanitians, who upon a fal&longs;e founda
tion &longs;ome times attempt impo&longs;&longs;ible enterprizes,) in which, unto the large
Ve&longs;&longs;ell E I D F, the narrow Funnell or Pipe I C A B is continued, and &longs;up
po&longs;e water infu&longs;ed into them, unto the Levell L G H, which water &longs;hall
re&longs;t in this po&longs;ition, not without admiration in &longs;ome, who cannot conceive
Ma&longs;s of water G D, pre&longs;&longs;ing downwards, &longs;hould
not elevate and repul&longs;e the little quantity of the
other, contained in the Funnell or Pipe C L, by
which the de&longs;cent of it is re&longs;isted and hindered:
But &longs;uch wonder &longs;hall cea&longs;e, if we begin to &longs;uppo&longs;e
the water G D to be aba&longs;ed only to Q D, and
&longs;hall afterwards con&longs;ider, what the water C L
hath done, which to give place to the other, which
is de&longs;cended from the Levell G H, to the Levell
Q O, &longs;hall of nece&longs;&longs;ity have a&longs;cended in the &longs;ame
time, from the Levell Lunto A B. And the
a&longs;cent L B, &longs;hall be &longs;o much greater than the de
&longs;cent G Q, by how much the breadth of the Ve&longs;&longs;ell
G D, is greater than that of the Funnell I C;
which, in &longs;umme, 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, compen&longs;ates that of the Gravity of ano
ther, what wonder is it, if the &longs;wift a&longs;cent of the le&longs;&longs;er Water C L, &longs;hall
re&longs;i&longs;t the &longs;low de&longs;cent of the greater G D
The &longs;ame, therefore, happens in this operation, as in the Stilliard,
in which a weight of two pounds counterpoy&longs;eth an other of 200,
asoften as that &longs;hall move in the &longs;ame time, a &longs;pace 100 times great
er than this: which falleth out when one Arme of the Beam is an
Let the erroneous opinion o
tho&longs;e therefore cea&longs;e, who hold that a Ship is better, and ea&longs;ter born
up in a great abundance of water, then in a le&longs;&longs;er quantity, (
believed by23, Probl.
the contrary true, that its po&longs;&longs;ible, that a Ship may as well float in
ten Tun of water, as in an Ocean.
well in ten Tun
of water as in an
Ocean.
fiaclly graver
than the water,
cannot be born
up by any quan
tity of it.
But following our matter, I &longs;ay, that by what hath been hitherto
demon&longs;trated, we may under&longs;tand how, that
COROLLARY III.
can never be &longs;u&longs;tained, by any whatever quantity of it.
For having &longs;een how that the Moment wherewith &longs;uch a Solid
as grave
of water what&longs;oever, is able to retain it, even to its totall Submer&longs;ion:
without its ever a&longs;cending; it remaineth, manife&longs;t, that the water is
far le&longs;s able to rai&longs;e it up, when it exceeds the &longs;ame
that though you infu&longs;e water till its totall Submer&longs;ion, it &longs;hall &longs;till
&longs;tay at the Bottome, and with &longs;uch Gravity, and Re&longs;i&longs;tance to Eleva
tion, as is the exce&longs;s of its Ab&longs;olute Gravity, above the Ab&longs;olute Gra
vity of a Ma&longs;s equall to it, made of water, or of a Matter
equally grave with the water: and, though you &longs;hould moreover
adde never &longs;o much water above the Levell of that which equalizeth
the Altitude of the Solid, it &longs;hall not, for all that, encrea&longs;e the Pre&longs;&longs;ion
or Gravitation, of the parts circumfu&longs;ed about the &longs;aid Solid, by
which greater pre&longs;&longs;ion, it might come to be repul&longs;ed, becau&longs;e, the
Re&longs;i&longs;tance is not made, but only by tho&longs;e parts of the water, which
at the Motion of the &longs;aid Solid do al&longs;o move, and the&longs;e are tho&longs;e
only, which are comprehended by the two Superficies equidi&longs;tant to
the Horizon, and their parallels, that comprehend the Altitude of the
Solid immerged in the water.
I conceive, I have by this time &longs;ufficiently declared and opened
the way to the contemplation of the true, intrin&longs;ecall and proper
Cau&longs;es of diver&longs;e Motions, and of the Re&longs;t of many Solid Bodies in
diver&longs;e
effect, depend on the mutuall exce&longs;&longs;es of the Gravity of the Movea
bles and of the
moving the Objection, which peradventure would have begotter
much doubting, and &longs;cruple in &longs;ome, about the verity of my Con
clu&longs;ion, namely, how that notwith&longs;tanding, that the exce&longs;s of the
Gravity of the water, above the Gravity of the Solid, demitted into
it, be the cau&longs;e of its floating and ri&longs;ing from the Bottom to the Sur
face, yet a quantity of water, that weighs not ten pounds, can rai&longs;e
ted, That it &longs;ufficeth, that &longs;uch difference be found between the
Specificall Gravities of the
and ab&longs;olute Gravities be what they will: in&longs;omuch, that a Solid,
provided that it be Specifically le&longs;s grave than the water, although
its ab&longs;olute weight were 1000 pounds, yet may it be born up and
elevated by ten pounds of water, and le&longs;s: and on the contrary, a
nother Solid, &longs;o that it be Specifically more grave than the water,
though in ab&longs;olute Gravity it were not above a pound, yet all the
water in the Sea, cannot rai&longs;e it from the Bottom, or float it. This
&longs;ufficeth me, for my pre&longs;ent occa&longs;ion, to have, by the above declared
Examples, di&longs;covered and demon&longs;trated, without extending &longs;uch
matters farther, and, as I might have done, into a long Treati&longs;e:
yea, but that there was a nece&longs;&longs;ity of re&longs;olving the above propo&longs;ed
doubt, I &longs;hould have contented my &longs;elf with that only, which is
demon&longs;trated by
mido
Conclu&longs;ions, namely, that Solids (
float upon it, the (
qually grave re&longs;t indifferently in all places, yea, though they &longs;hould
be wholly under water.
Lib. 1.
Prop.
Lib. 1.
Prop.
But, becau&longs;e that this Doctrine of
bed and examined by
of Motion, Chap.
Authority of &longs;o renowned, and famous a Philo&longs;opher, be rendered
dubious, and &longs;u&longs;pected of fal&longs;ity; I have judged it nece&longs;&longs;ary to de
fend it, if I am able &longs;o to do, and to clear
cen&longs;ures, with which he appeareth to be charged.
jecteth the Doctrine of
the Opinion of
that the Water &longs;hould exceed the Earth in Gravity, &longs;eeing on the
contrary, that the Gravity of water, increa&longs;eth, by means of the parti
cipation of Earth. And he &longs;ubjoyns pre&longs;ently after, that he was
not &longs;atisfied with the Rea&longs;ons of
that Doctrine, to a&longs;&longs;ign the cau&longs;e whence it comes, that a Boat and
a Ve&longs;&longs;ell, which otherwi&longs;e, floats above the water, doth &longs;ink to the
Bottom, if once it be filled with water; that by rea&longs;on of the e
quality of Gravity, between the water within it, and the other water
without, it &longs;hould &longs;tay a top; but yet, neverthele&longs;s, we &longs;ee it to go to
the Bottom.
defence of
chimedes
ctrine, again&longs;t
the oppo&longs;itions
of
on again&longs;t the
Doctrine of
chimedes.
jection.
ction.
jection.
He farther addes, that
who &longs;aid, that light Bodies moved upwards, driven by the impul&longs;e
of the more grave Ambient: which if it were &longs;o, it &longs;hould &longs;eem of
nece&longs;&longs;ity to follow, that all naturall Bodies are by nature heavy,
if put in the Bottom of the water. And, howbeit,
a Pul&longs;ion in the Elements, by which the Earth is reduced into a Sphe
ricall Figure, yet neverthele&longs;s, in his judgement, it is not &longs;uch that it
can remove grave Bodies from their naturall places, but rather, that
it &longs;end them toward the Centre, to which (as he &longs;omewhat ob&longs;curely
continues to &longs;ay,) the water principally moves, if it in the interim
meet not with &longs;omething that re&longs;i&longs;ts it, and, by its Gravity, thru&longs;ts
it out of its place: in which ca&longs;e, if it cannot directly, yet at lea&longs;t
as well as it can, it tends to the Centre: but it happens, that light
Bodies by &longs;uch Impul&longs;ion, do all a&longs;cend upward: but this properly
they have by nature, as al&longs;o, that other of &longs;wimming. He concludes,
la&longs;tly, that he concurs with
in the Cau&longs;es, which he would referre to the facile and difficult Sepa
ration of the
that when the Moveable &longs;uperates the power of the
example, Lead doth the Continuity of water, it &longs;hall move thorow it,
el&longs;e not.
denved
Levity.
Natation & Sub
mer&longs;ion, accord
ing to the Peri
pateticks.
This is all that I have been able to collect, as produced again&longs;t
Principles and Suppo&longs;itions of
fal&longs;e, if the Doctrine be fal&longs;e, which depends upon them; but is
contented to alledge therein &longs;ome Inconveniences, and &longs;ome Repug
nances to the Doctrine and Opinion of
Objections, I &longs;ay, fir&longs;t, That the being of
ply different from the Doctrine of
to &longs;u&longs;pect it, there being no cau&longs;e, why the Authority of this &longs;hould
be preferred to the Authority of the other: but, becau&longs;e, where the
decrees of Nature are indifferently expo&longs;ed to the intellectuall eyes of
each, the Authority of the one and the other, lo&longs;eth all anthentical
ne&longs;s of Per&longs;wa&longs;ion, the ab&longs;olute power re&longs;iding in Rea&longs;on; therefore
I pa&longs;s to that which he alledgeth in the &longs;econd place, as an ab&longs;urd con
&longs;equent of the Doctrine of
be more grave than Earth. But I really find not, that ever
medes
Conclu&longs;ions: and if that were manife&longs;t unto me, I verily believe, I
&longs;hould renounce his Doctrine, as mo&longs;t erroneous. Perhapsthis Dedu
ction of
&longs;&longs;el, which &longs;wims as long as its voyd of water, but once full it &longs;inks to
the Bottom, and under&longs;tanding it of a Ve&longs;&longs;el of Earth, he infers again&longs;t
than water: this Ve&longs;&longs;ell &longs;wimmeth: therefore, this Ve&longs;&longs;ell is le&longs;&longs;e grave
than water. If this be the Illation. I ea&longs;ily an&longs;wer, granting that this
Ve&longs;&longs;ell is le&longs;&longs;e grave than water, and denying the other con&longs;equence,
The Ve&longs;&longs;el that &longs;wims
occupieth in the water, not only a place equall to the Ma&longs;s of the
Earth, of which it is formed; but equall to the Earth and to the Air
together, contained in its concavity. And, if &longs;uch a Ma&longs;s compoun
ded of Earth and Air, &longs;hall be le&longs;s grave than &longs;uch another quantity
of water, it &longs;hall &longs;wim, and &longs;hall accord with the Doctrine of
medes
with water, &longs;o that the Solid put in the water, be nothing but
Earth, nor occupieth other place, than that which is only po&longs;&longs;e&longs;t by
Earth, it &longs;hall then go to the Bottom, by rea&longs;on that the Earth is
heavier than the water: and this corre&longs;ponds well with the meaning
of
Experiment, In pre&longs;&longs;ing a Viall Gla&longs;s to the Bottom of the water,
when it is full of Air, it will meet with great re&longs;i&longs;tance, becau&longs;e it is
not the Gla&longs;s alone, that is pre&longs;&longs;ed under water, but together with
the Gla&longs;s a great Ma&longs;s of Air, and &longs;uch, that if you &longs;hould take as
much water, as the Ma&longs;s of the Gla&longs;s, 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 &longs;ubmerge without great violence:
but if we demit only the Gla&longs;s into the water, which &longs;hall be when
you &longs;hall fill the Gla&longs;s with water, then &longs;hall the Gla&longs;s de&longs;cend to
the Bottom; as &longs;uperiour in Gravity to the water.
&longs;wer to the fir&longs;t
Objection.
&longs;wer to the &longs;e
cond Objection.
Returning, therefore, to our fir&longs;t purpo&longs;e; I &longs;ay, that Earth is
more grave than water, and that therefore, a Solid of Earth goeth to
the bottom of it; but one may po&longs;&longs;ibly make a compo&longs;ition of Earth
and Air, which &longs;hall be le&longs;s grave than a like Ma&longs;s of Water; and
this &longs;hall &longs;wim: and yet both this and the other experiment &longs;hall
very well accord with the Doctrine of
in my judgment it hath nothing of difficulty in it, I will not po&longs;itive
ly affirme that
unto
was le&longs;s grave than Water, though I know not how to conceive what
other accident he could have induced thence.
Perhaps &longs;uch a Probleme (in my judgement fal&longs;e) was read by
was attributed as a &longs;ingular propertie, of &longs;ome particular Water, and
&longs;o comes now to be u&longs;ed with a double errour in confutation of
chimedes,
meant of the common Element of Water.
The third difficulty in the doctrine of
could not render a rea&longs;on whence it aro&longs;e, that a piece of Wood,
and a Ve&longs;&longs;ell of Wood, which otherwi&longs;e floats, goeth to the bottom,
if filled with Water.
of Wood, and of Wood that by nature &longs;wims, as before is &longs;aid,
lowing Chapter, which is the 30 of the fifth Book copiou&longs;ly di&longs;cour&longs;
eth: but I (&longs;peaking alwayes without diminution of his &longs;ingular
Learning) dare in defence of
certain that a piece of Wood which by its nature &longs;inks not in Water,
&longs;hall not &longs;inke though it be turned and converted into the forme of a
ny Ve&longs;&longs;ell what&longs;oever, and then filled with Water: and he that would
readily &longs;ee the Experiment in &longs;ome other tractable Matter, and that is
ea&longs;ily reduced into &longs;everal Figures, may take pure Wax, and ma
king it fir&longs;t into a Ball or other &longs;olid Figure, let him adde to it &longs;o
much Lead as &longs;hall ju&longs;t carry it to the bottome, &longs;o that being a graine
le&longs;s it could not be able to &longs;inke it, and making it afterwards into
the forme of a Di&longs;h, and filling it with Water, he &longs;hall finde that with
out the &longs;aid Lead it &longs;hall not &longs;inke, and that with the Lead it &longs;hall de
&longs;cend with much &longs;lowne&longs;s: & in &longs;hort he &longs;hall &longs;atisfie him&longs;elf, that the
Water included makes no alteration. I &longs;ay not all this while, but that
its po&longs;&longs;ible of Wood to make Barkes, which being filled with water,
&longs;inke; but that proceeds not through its Gravity, encrea&longs;ed by the
Water, but rather from the Nailes and other Iron Workes, &longs;o that
it no longer hath a Body le&longs;s grave than Water, but one mixt of Iron
and Wood, more grave than a like Ma&longs;&longs;e of Water. Therefore let
not in nature: yea if the &longs;inking of the Woodden Ve&longs;&longs;ell when its full
of Water, may call in que&longs;tion the Doctrine of
he would not have you to follow, is on the contrary con&longs;onant and a
greeable to the Doctrine of the Peripateticks, &longs;ince it aptly a&longs;&longs;ignes a
rea&longs;on why &longs;uch a Ve&longs;&longs;ell mu&longs;t, when its full of Water, de&longs;cend to the
bottom; converting the Argument the other way, we may with
&longs;afety &longs;ay that the Doctrine of
eth with true experiments, and que&longs;tion the other, who&longs;e Deducti
ons are fa&longs;tened upon etroneou&longs;s Conclu&longs;ions. As for the other point
hinted in this &longs;ame In&longs;tance, where it &longs;eemes that
&longs;tands the &longs;ame not only of a piece of wood, &longs;haped in the forme of a
Ve&longs;&longs;ell, but al&longs;o of ma&longs;&longs;ie Wood, which filled,
would &longs;ay, &longs;oaked and &longs;teeped in Water, goes finally to the bottom
that happens in &longs;ome poro&longs;e Woods, which, while their Poro&longs;ity is re
pleni&longs;hed with Air, or other Matter le&longs;s grave than Water, are Ma&longs;
&longs;es &longs;pecificially le&longs;s grave than the &longs;aid Water, like as is that Viall of
Gla&longs;s while&longs;t it is full of Air: but when, &longs;uch light Matter depart
ing, there &longs;ucceedeth Water into the &longs;ame Poro&longs;ities and Cavities,
there re&longs;ults a compound of Water and Gla&longs;s more grave than a like
Ma&longs;s of Water: but the exce&longs;s of its Gravity con&longs;i&longs;ts in the Matter
of the Gla&longs;s, and not in the Water, which cannot be graver than it
&longs;elf: &longs;o that which remaines of the Wood, the Air of its Cavi
Poro&longs;ities with Water, and you &longs;hal have a Compo&longs;t of Water and
of Wood more grave than Water, but not by vertue of the Water re
ceived into and imbibed by the Poro&longs;ities, but of that Matter of the
Wood which remains when the Air is departed: and being &longs;uch it
&longs;hall, according to the Doctrine of
like as before, according to the &longs;ame Doctrine it did &longs;wim.
&longs;wer to the third
Objection.
As to that finally which pre&longs;ents it &longs;elf in the fourth place, namely,
that the
denying Po&longs;itive and Ab&longs;olute Levity, and truely e&longs;teeming all Bo
dies to be grave, &longs;aid, that that which moved upward was driven by
the circumambient Air, and therefore that al&longs;o the Doctrine of
victed and confuted: I an&longs;wer fir&longs;t, that
judgement hath impo&longs;ed upon
words more than ever he intended by them, or may from his Propo
&longs;itions be collected, in regard that
mitteth Po&longs;itive Levity, nor doth he &longs;o much as mention it: &longs;o that
much le&longs;s ought
might be the Cau&longs;e and Principle of the A&longs;cen&longs;ion of Fire, and other
Light Bodies: having but only demon&longs;trated, that Solid Bodies
more grave than Water de&longs;cend in it, according to the exce&longs;s of their
Gravity above the Gravity of that, he demon&longs;trates likewi&longs;e, how the
le&longs;s grave a&longs;cend in the &longs;ame Water, accordng to its exce&longs;s of Gra
ty, above the Gravity of them. So that the mo&longs;t that can be gather
ed from the Dem on&longs;tration of
of the Gravity of the Moveable above the Gravity of the Water, is
the Cau&longs;e that it de&longs;cends therein, &longs;o the exce&longs;s of the Gravity of
the water above that of the Moveable, is a &longs;ufficient Cau&longs;e why it de&longs;
cends not, but rather betakes it &longs;elf to &longs;wim: not enquiring whe
ther of moving upwards there is, or is not any other Cau&longs;e contrary
to Gravity: nor doth
&longs;hould &longs;ay: If the South Winde &longs;hall a&longs;&longs;ault the Barke with greater
ries it towards the South, the motion of it &longs;hall be towards the North:
but if the
motion &longs;hall be towards the South. The di&longs;cour&longs;e is excellent and
would be unworthily contradicted by &longs;uch as &longs;hould oppo&longs;e it, &longs;aying:
Thou mi&longs;-alledge&longs;t as Cau&longs;e of the motion of the Bark towards the
South, the
South Winde; mi&longs;-alledge&longs;t I &longs;ay, for it is the Force of the North
Winde oppo&longs;ite to the South, that is able to drive the Bark towards
the South. Such an Objection would be &longs;uperfluous, becau&longs;e he which
alledgeth for Cau&longs;e of the Motion the &longs;tream of the Water, denies not
affirmeth that the force of the Water prevailing over the South
Wind, the Bark &longs;hall move towards the South: and &longs;aith no more
than is true. And ju&longs;t thus when
of the Water prevailing over that by which the moveable de&longs;cends to
the Bottom, &longs;uch moveable &longs;hall be rai&longs;ed from the Bottom to the Sur
face alledgeth a very true Cau&longs;e of &longs;uch an Accident, nor doth he af
firm or deny that there is, or is not, a vertue contrary to Gravity, called
by &longs;ome Levity, that hath al&longs;o a power of moving &longs;ome Matters up
wards. Let therefore the Weapons of
gain&longs;t
all Bodies to be grave, &longs;ay that the Motion upwards is made, not
from an intrin&longs;ecal Principle of the Moveable, but only by the Im
pul&longs;e of the
him, &longs;ince he hath given him no Cau&longs;e of quarelling with him
But if this Apologie, produced in defence of
to &longs;ome in&longs;ufficient to free him from the Objections and Arguments
produced by
did al&longs;o fight again&longs;t
as the Cau&longs;e of the &longs;wimming of &longs;ome Bodies le&longs;s grave than it, I would
not que&longs;tion, but that I &longs;hould be able to maintaine the Doctrine of
and affirm no other Intrin&longs;ecal Principle of Motion to be in Elemen
tary Bodies &longs;ave only that towards the Centre of the Earth, nor no
other Cau&longs;e of moving upwards, &longs;peaking of that which hath the re
&longs;emblance of natural Motion, but only the repul&longs;e of the
and exceeding the Gravity of the Moveable: and as to the Rea&longs;ons
of
an&longs;wer them, and I would a&longs;&longs;ay to do it, if it were ab&longs;olutely nece&longs;&longs;a
ry to the pre&longs;ent Matter, or were it not too long a Digre&longs;&longs;ion for this
&longs;hort Treati&longs;e. I will only &longs;ay, that if there were in &longs;ome of our Elle
mentary Bodies an Intrin&longs;ecall Principle and Naturall Inclination
to &longs;hun the Centre of the Earth, and to move towards the Concave
of the Moon, &longs;uch Bodies, without doubt, would more &longs;wiftly a&longs;cend
through tho&longs;e
and the&longs;e are the more tenuous and &longs;ubtle; as is, for example, the
Air in compari&longs;on of the Water, we daily proving that we can with
farre more expeditious Velocity move a Hand or a Board to and a
gain in one than in the other: neverthele&longs;s, we never could finde any
Body, that did not a&longs;cend much more &longs;wiftly in the water than in the
Air. Yea of Bodies which we &longs;ee continually to a&longs;cend in the Water,
there is none that having arrived to the confines of the Air, do not whol
ly lo&longs;e their Motion; even the Air it &longs;elf, which ri&longs;ing with great Ce
lerity through the Water, being once come to its Region it lo&longs;eth all
an&longs;wer to the
fourth Object
ion.
Lib. 1. Prop. 7.
Lib. 1. Prop. 4.
Po&longs;itive Levi
ty.
defence of the
doctrine of
and the
who ab&longs;olutely
deny Levity:
Principle of the
Motion of de
&longs;cent in Naturall
Bodies, &longs;ave that
to the Centre.
the motion of
Impul&longs;e of the
ing the Move
able in Gravi
tie.
much &longs;wifter in
the Water, than
in the Air.
cending through
Water, lo&longs;e
their Motion,
comming to the
confines of the
Air.
And, howbeit, Experience &longs;hewes, that the Bodies, &longs;ucce&longs;&longs;ively
le&longs;s grave, do mo&longs;t expeditiou&longs;ly a&longs;cend in water, it cannot be doubt
ed, but that the Ignean Exhalations do a&longs;cend more &longs;wiftly
through the water, than doth the Air: which Air is &longs;een by Experi
ence to a&longs;cend more &longs;wiftly through the Water, than the Fiery Exha
lations through the Air: Therefore, we mu&longs;t of nece&longs;&longs;ity conclude,
that the &longs;aid Exhalations do much more expeditiou&longs;ly a&longs;cend through
the Water, than through the Air; and that, con&longs;equently, they are
moved by the Impul&longs;e of the Ambient
&longs;ick Principle that is in them, of avoiding the Centre of the Earth;
to which other grave Bodies tend.
Bodies al&longs;end
more &longs;wiftly
through Water.
ons ascend tho
row the Water
more &longs;wiftly
than doth the
Air; & the Air
a&longs;cends more
&longs;wiftly thorow
the Water, than
Air.
To that which for a finall conclu&longs;ion,
of going about to reduce the de&longs;cending or not de&longs;cending, to the
ea&longs;ie and unea&longs;ie Divi&longs;ion of the
of the Elements: I an&longs;wer, as to the fir&longs;t part, that that cannot in any
manner be admitted as a Cau&longs;e, being that in none of the Fluid
Re&longs;i&longs;tance again&longs;t Divi&longs;ion, but all by every the lea&longs;t Force, are di
vided and penetrated, as I will anon demon&longs;trate: &longs;o, that of &longs;uch
Re&longs;i&longs;tance of Divi&longs;ion there can be no Act, &longs;ince it &longs;elf is not in be
ing. As to the other part, I &longs;ay, that the predominancy of the Ele
ments in Moveables, is to be con&longs;idered, as far as to the exce&longs;&longs;e or
defect of Gravity, in relation to the
the Elements operate not, but only, &longs;o far as they are grave or light:
therefore, to &longs;ay that the Wood of the Firre &longs;inks not, becau&longs;e Air
predominateth in it, is no more than to &longs;ay, becau&longs;e it is le&longs;s grave
than the Water. Yea, even the immediate Cau&longs;e, is its being le&longs;s
grave than the Water: and it being under the predominancy of the
Air, is the Cau&longs;e of its le&longs;s Gravity: Therefore, he that alledgeth the
predominancy of the Element for a Cau&longs;e, brings the Cau&longs;e of the
Cau&longs;e, and not the neere&longs;t and immediate Cau&longs;e. Now, who knows
not that the true Cau&longs;e is the immediate, and not the mediate?
Moreover, he that alledgeth Gravity, brings a Cau&longs;e mo&longs;t per&longs;picuous
to Sence: The cau&longs;e we may very ea&longs;ily a&longs;&longs;ertain our &longs;elves;
whether Ebony, for example, and Firre, be more or le&longs;s grave than
water: but whether Earth or Air predominates in them, who &longs;hall
make that manife&longs;t? Certainly, no Experiment can better do it
than to ob&longs;erve whether they &longs;wim or &longs;ink. So, that he who knows,
not whether &longs;uch a Solid &longs;wims, unle&longs;s when he knows that Air pre
dominates in it, knows not whether it &longs;wim, unle&longs;s he &longs;ees it &longs;wim,
for then he knows that it &longs;wims, when he knows that it is Air that
predominates, but knows not that Air hath the predominance, unle&longs;s
he &longs;ees it &longs;wim: therefore, he knows not if it &longs;wims, till &longs;uch time
as he hath &longs;een it &longs;wim.
confutation of
the Peripateticks
Cau&longs;es of Nata
tion & Submer&longs;i
on.
fluids void of
Re&longs;i&longs;tance a
gain&longs;t Divi&longs;ion.
nancy of Ele
ments in Move
ables to be con
&longs;idered only in
relation to their
excefs or defect
of Gravity in
reference to the
ate Cau&longs;e of Na
tation is that the
Moveable is le&longs;s
grave than the
Water.
ticks alledge for
the rea&longs;on of
Natation the
Cau&longs;e of the
Cau&longs;e.
Cau&longs;e mo&longs;t per
&longs;picuous to
&longs;ence:
Let us not then de&longs;pi&longs;e tho&longs;e Hints, though very dark, which
Rea&longs;on, after &longs;ome contemplation, offereth to our Intelligence, and
lets be content to be taught by
&longs;ubmerge in water, when it &longs;hall be &longs;pecifically more grave than it
and that if it &longs;hall be le&longs;s grave, it &longs;hall of nece&longs;&longs;ity &longs;wim, and
that it will re&longs;t indifferently in any place under water, if its Gravity
be perfectly like to that of the water.
tation Prop. 7.
Lib. 1.
Prop. 4.
Lib. 1:
Prop. 3.
The&longs;e things explained and proved, I come to con&longs;ider that which
offers it &longs;elf, touching what the Diver&longs;ity of figure given unto the
&longs;aid Moveable hath to do with the&longs;e Motions and Re&longs;ts; and pro
ceed to affirme, that,
THEOREME V.
Swimming.
Figure no Cau&longs;e
of its ab&longs;olute
Natation or Sub
mer&longs;ion.
So that if a Solid being formed, for example, into a Spherical
Figure, doth &longs;ink or &longs;wim in the water, I &longs;ay, that being formed
into any other Figure, the &longs;ame figure in the &longs;ame water, &longs;hall
&longs;ink or &longs;wim: nor can &longs;uch its Motion by the Expan&longs;ion or by o
ther mutation of Figure, be impeded or taken away.
on of
tards the Veloci
ty of the a&longs;cent
or de&longs;cent of the
Moveable in the
water; but doth
not deprive it of
all Motion.
The Expan&longs;ion of the Figure may indeed retard its Velocity, a&longs;
well of a&longs;cent as de&longs;cent, and more and more according as the &longs;aid Fi
gure is reduced to a greater breadth and thinne&longs;s: but that it may bere
duced to &longs;uch a form as that that &longs;ame matter be wholly hindred from
moving in the &longs;ame water, that I hold to be impo&longs;&longs;ible. In this I have
met with great contradictors, who producing &longs;ome Experiments, and
in perticular a thin Board of Ebony, and a Ball of the &longs;ame Wood
and &longs;hewing how the Ball in Water de&longs;cended to the bottom, and
the Board being put lightly upon the Water &longs;ubmerged not, but re&longs;t
ed; have held, and with the Authority of
&longs;elves in their Opinions, that the Cau&longs;e of that Re&longs;t was the breadth
of the Figure, u able by its &longs;mall weight to pierce and penetrate the
Re&longs;i&longs;tance of the Waters Cra&longs;&longs;itude, which Re&longs;i&longs;tance is readily o
vercome by the other Sphericall Figure.
This is the Principal point in the pre&longs;ent Que&longs;tion, in which I per
&longs;wade my &longs;elf to be on the right &longs;ide.
Therefore, beginning to inve&longs;tigate with the examination of ex
qui&longs;ite Experiments that really the Figure doth not a jot alter the de&longs;
cent or A&longs;cent of the &longs;ame Solids, and having already demon&longs;tra
ted that the greater or le&longs;s Gravity of the Solid in relation to the Gra
vity of the
gure worketh, its nece&longs;&longs;ary to make the Experiment with Matter
wherein variety of Gravities hath no place. For making u&longs;e of Mat
ters which may be different in their Specifical Gravities, and meeting
with varieties of effects of A&longs;cending and De&longs;cending, we &longs;hall al
wayes be left un&longs;atisfied whether that diver&longs;ity derive it &longs;elf really
from the &longs;ole Figure, or el&longs;e from the divers Gravity al&longs;o. We may
remedy this by takeing one only Matter, that is tractable and ea&longs;ily
reduceable into every &longs;ort of Figure. Moreover, it wil 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 in
different either to A&longs;cend or De&longs;cend; &longs;o that we may pre&longs;ently ob
&longs;erve any the lea&longs;t difference that derives it &longs;elf from the diver&longs;ity of
Figure.
Now to do this, Wax is mo&longs;t apt, which, be&longs;ides its incapacity of
receiveing any &longs;en&longs;ible alteration from its imbibing of Water, is duct
ile or pliant, and the &longs;ame piece is ea&longs;ily reduceable into all Figures:
and being
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.
ment in Wax,
that proveth Fi
gute to have no
Operation in
Natation & Sub
mer&longs;ion.
This Matter prepared, and, for example, a Ball being made there
of as bigge as an Orange or biger, and that made &longs;o grave as to
&longs;ink to the bottom, but &longs;o lightly, that takeing thence one only Grain
of Lead, it returnes to the top, and being added, it &longs;ubmergeth to
the bottom, let the &longs;ame Wax afterwards be made into a very broad
and thin Flake or Cake; and then, returning to make the &longs;ame Ex
periment, you &longs;hall &longs;ee that it being put to the bottom, it &longs;hall, with the
Grain of Lead re&longs;t below, and that Grain deducted, it &longs;hall a&longs;cend to
the very Surface, and added again it &longs;hall dive to the bottom. And
this &longs;ame effect &longs;hall happen alwaies in all &longs;ort of Figures, as wel re
gular as irregular: nor &longs;hall you ever finde any that will &longs;wim with
out the removall of the Grain of Lead, or &longs;inke to the bottom unle&longs;s
it be added: and, in &longs;hort, about the going or not going to the Bot
tom, you &longs;hall di&longs;cover no diver&longs;ity, although, indeed, you &longs;hall about
the quick and &longs;low de&longs;cent: for the more expatiated and di&longs;tended
Figures move more &longs;lowly a&longs;wel in the diveing to the bottom as in
the ri&longs;ing to the top; and the other more contracted and compact Fi
gures, more &longs;peedily. Now I know not what may be expected from
the diver&longs;ity of Figures, if the mo&longs;t contrary to one another operate
not &longs;o much as doth a very &longs;mall Grain of Lead, added or removed.
Me thinkes I hear &longs;ome of the Adver&longs;aries to rai&longs;e a doubt upon
my produced Experiment. And fir&longs;t, that they offer to my con&longs;idera
tion, that the Figure, as a Figure &longs;imply, and disjunct from the Matter
workes not any effect, but requires to be conjoyned with the Matter
wherewith it may be able ro execute the de&longs;ired operation. Like
as we &longs;ee it verified by Experience, that the Acute and &longs;harp Angle is
more apt to cut, than the Obtu&longs;e; 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 &longs;harp
edge, cuts Bread or Wood with much ea&longs;e, which it will not do, if
the edge be blunt and thick: but he that will in&longs;tead of Steel, take
Wax, and mould it into a Knife, undoubtedly &longs;hall never know the
effects of &longs;harp and blunt edges: becau&longs;e neither of them will cut,
the Wax being unable by rea&longs;on of its flexibility, to overcome the
hardne&longs;s of the Wood and Bread. And, therefore, applying the
like di&longs;cour&longs;e to our purpo&longs;e, they &longs;ay, that the difference of Figure
will &longs;hew different effects, touching Natation and Submer&longs;ion, but
not conjoyned with any kind of Matter, but only with tho&longs;e Matters
which, by their Gravity, are apt to re&longs;i&longs;t the Velocity of the water,
whence he that would elect for the Matter, Cork or other light wood
unable, through its Levity, to &longs;uperate the Cra&longs;&longs;itude of the water,
and of that Matter &longs;hould forme Solids of divers Figures, woulld in
vain &longs;eek to find out what operation Figure hath in Natation or Sub
mer&longs;ion; becau&longs;e all would &longs;wim, and that not through any property
of this or that Figure, but through the debility of the Matter, want
ing &longs;o much Gravity, as is requi&longs;ite to &longs;uperate and overcome the
Den&longs;ity and Cra&longs;&longs;itude of the water.
gain&longs;t the Expe
riment in Wax.
Its needfull, therefore, if wee would &longs;ee the effect wrought by the
Diver&longs;ity of Figure, fir&longs;t to make choice of a Matter of its nature
apt to penetrate the Cra&longs;&longs;itude of the water. And, for this effect,
they have made choice of &longs;uch a Matter, as fit, that being readily re
duced into Sphericall Figure, goes to the Bottom; and it is Ebony
of which they afterwards making a &longs;mall Board or Splinter, as thin as
a Lath, have illu&longs;trated how that this, put upon the Surface of the
water, re&longs;ts there without de&longs;cending to the Bottom: and making, on
the other&longs;ide, of the &longs;ame wood a Ball, no le&longs;s than a hazell Nut,
they &longs;hew, that this &longs;wims not, but de&longs;cendes. From which Experi
ment, they think they may frankly conclude, that the Breadth ofthe
Figure in the flat Lath or Board, is the cau&longs;e of its not de&longs;cendingto
the Bottom, fora&longs;much as a Ball of the &longs;ame Matter, not different
from the Board in any thing but in Figure, &longs;ubmergeth in the &longs;ame
water to the Bottom. The di&longs;cour&longs;e and the Experiment hath really
&longs;o much of probability and likely hood of truth in it, that it would be
no wonder, if many per&longs;waded by a certain cur&longs;ory ob&longs;ervation,
&longs;hould yield credit to it; neverthele&longs;s, I think I am able to di&longs;cover,
how that it is not free from falacy.
ment in Ebany,
brought to di&longs;
prove the Expe
timent in Wax.
Beginning, therefore, to examine one by one, all the particulars that
operate not in naturall things, but neither are they ever &longs;eperated
from the Corporeall &longs;ub&longs;tance: nor have I ever alledged them &longs;tript
of &longs;en&longs;ible Matter, like as al&longs;o I freely admit, that in our endeavour
ing to examine the Diver&longs;ity of Accidents, dependant upon the va
riety of Figures, it is nece&longs;&longs;ary to apply them to Matters, which ob
&longs;truct not the various operations of tho&longs;e various Figures: and I ad
mit and grant, that I &longs;hould do very ill, if I would experiment the in
fluence of Acutene&longs;&longs;e of edge with a Knife of Wax, applying it to cut
an Oak, becau&longs;e there is no Acutene&longs;s in Wax able to cut that
very hard wood. But yet &longs;uch an Experiment of this Knife, would
not be be&longs;ides the purpo&longs;e, to cut curded Milk, or other very yielding
Matter: yea, in &longs;uch like Matters, the Wax is more commodious
than Steel; for finding the diver&longs;ity depending upon Angles, more or
le&longs;s Acute, for that Milk is indifferently cut with a Rai&longs;or, and with
a Knife, that hath a blunt edge. It needs, therefore, that regard be
had, not only to the hardne&longs;s, &longs;olidity or Gravity of Bodies, which
under divers figures, are to divide and penetrate &longs;ome Matters, but it
forceth al&longs;o, that regard be had, on the other &longs;ide, to the Re&longs;i&longs;tance
of the Matters, to be divided and penetrated. But &longs;ince I have in
making the Experiment concerning our Conte&longs;t, cho&longs;en a Matter
which penetrates the Re&longs;i&longs;tance of the water; and in all figures de&longs;
cendes to the Bottome, the Adver&longs;aries can charge me with no defect;
yea, I have propounded &longs;o much a more excellent Method than they,
in as much as I have removed all other Cau&longs;es, of de&longs;cending or
not de&longs;cending to the Bottom, and retained the only &longs;ole and pure
variety of Figures, demon&longs;trating that the &longs;ame Figures all de&longs;cende
with the only alteration of a Grain in weight: which Grain being
removed, they return to float and &longs;wim; it is not true, therefore,
(re&longs;uming the Example by them introduced) that I have gon about
to experiment the efficacy of Acutene&longs;s, in cutting with Matters un
able to cut, but with Matters proportioned to our occa&longs;ion; &longs;ince
they are &longs;ubjected to no other variety, then that alone which depends
on the Figure more or le&longs;s a cute.
&longs;eperable from
Corporeall Sub
&longs;tance.
the Objection a
gain&longs;t the Expe
riment of the
Wax.
But let us proceed a little farther, and ob&longs;erve, how that indeed
the Con&longs;ideration, which, they &longs;ay, ought to be had about the Election
of the Matter, to the end, that it may be proportionate for the ma
king of our experiment, is needle&longs;ly introduced, declaring by the ex
ample of Cutting, that like as Acutene&longs;s is in&longs;ufficient to cut, unle&longs;s
when it is in a Matter hard and apt to &longs;uperate the Re&longs;i&longs;tance of the
wood or other Matter, which we intend to cut; &longs;o the aptitude of
de&longs;cending or notde&longs;cending in water, ought and can only be known
in tho&longs;e Matters, that are able to overcome the Renitence, and &longs;upe
rate the Cra&longs;&longs;itude of the water. Unto which, I &longs;ay, that to make
di&longs;tinction and election, more of this than of that Matter, on which to
as the &longs;olidity or obduratene&longs;s of the &longs;aid Bodies &longs;hall be greater
or le&longs;s, is very nece&longs;&longs;ary: but withall I &longs;ubjoyn, that &longs;uch di&longs;tinct
ion, election and caution would be &longs;uperfluous and unprofitable, if
the Body to be cut or penetrated, &longs;hould have no Re&longs;i&longs;tance, or
&longs;hould not at all with&longs;tand the Cutting or Penitration: and if the
Knife were to be u&longs;ed in cutting a Mi&longs;t or Smoak, one of Paper
would be equally &longs;erviceable with one of
by rea&longs;on the water hath not any Re&longs;i&longs;tance again&longs;t the Penitration
of any Solid Body, all choice of Matter is &longs;uperfluous and needle&longs;s,
and the Election which I &longs;aid above to have been well made of a
Matter reciprocall in Gravity to water, was not becau&longs;e it was ne
ce&longs;&longs;ary, for the overcoming of the cra&longs;&longs;iitude of the water, but its
Gravity, with which only it re&longs;i&longs;ts the &longs;inking of Solid Bodies: and
for what concerneth the Re&longs;i&longs;tance of the cra&longs;&longs;itude, if we narrowly
con&longs;ider it, we &longs;hall find that all Solid Bodies, as well tho&longs;e that
&longs;ink, as tho&longs;e that &longs;wim, are indifferently accomodated and apt to
bring us to the knowledge of the truth in que&longs;tion. Nor will I
be frighted out of the belief of the&longs;e Conclu&longs;ions, by the Experi
ments which may be produced again&longs;t me, of many &longs;everall Woods,
Corks, Galls, and, moreover, of &longs;ubtle &longs;lates and plates of all &longs;orts
of Stone and Mettall, apt by means of their Naturall Gravity, to
move towards the Centre of the Earth, the which, neverthele&longs;s, be
ing impotent, either through the Figure (as the Adver&longs;aries thinke)
or through Levity, to break and penetrate the Continuity of the
parts of the water, and to di&longs;tract its union, do continue to &longs;wimm
without &longs;ubmerging in the lea&longs;t: nor on the other &longs;ide, &longs;hall the
Authority of
meth the contrary to this, which Experience &longs;hews me.
&longs;uch Levity, nor
of &longs;uch Figure,
but that it doth
penetrate the
Cra&longs;&longs;itude of
the Water.
I return, therefore, to a&longs;&longs;ert, that there is not any Solid of &longs;uch
Levity, nor of &longs;uch Figure, that being put upon the water, doth not
divide and penetrate its Cra&longs;&longs;itude: yea if any with a more per
&longs;picatious eye, &longs;hall return to ob&longs;erve more exactly the thin Boards
of Wood, he &longs;hall &longs;ee them to be with part of their thickne&longs;s under
water, and not only with their inferiour Superficies, to ki&longs;&longs;e the
Superiour of the water, as they of nece&longs;&longs;ity mu&longs;t have believed, who
have &longs;aid, that &longs;uch Boards &longs;ubmerge not, as not being able to di
vide the Tenacity of the parts of the water: and, moreover, he
&longs;hall &longs;ee, that &longs;ubtle &longs;hivers of Ebony, Stone or Metall, when they
float, have not only broak the Continuity of the water, but are with
all their thickne&longs;s, under the Surface of it; and more and more,
according as the Matters are more grave: &longs;o that a thin Plate of
Lead, &longs;hall be lower than the Surface of the circumfu&longs;ed water, by
at lea&longs;t twelve times the thickne&longs;s of the Plate, and Gold &longs;hall dive
of the Plate, as I &longs;hall anon declare.
Figures, laid up
on the water, do
penetrate its
Cra&longs;&longs;itude, and
in what propor
tion.
But let us proceed to evince, that the water yields and &longs;ufters it
&longs;elf to be penetrated by every the lighte&longs;t Body; and therewithall
demon&longs;trate, how, even by Matters that &longs;ubmerge not, we may
come to know that Figure operates nothing about the going or
not going to the Bottom, &longs;eeing that the water &longs;uffers it &longs;elf to be
penetrated equally by every Figure.
Make a Cone, or a Piramis of Cypre&longs;s, of Firre, or of other
Wood of like Gravity, or of pure Wax, and let its height be &longs;ome
what great, namely a handfull, or more, and put it into the water
with the Ba&longs;e downwards: fir&longs;t, you &longs;hall &longs;ee that it will penetrate
the water, nor &longs;hall it be at all impeded by the largene&longs;s of the Ba&longs;e,
nor yet &longs;hall it &longs;ink all under water, but the part towards the point
&longs;hall lye above it: by which &longs;hall be manife&longs;t, fir&longs;t, that that Solid
forbeares not to &longs;ink out of an inabillity to divide the Continuity
of the water, having already divided it with its broad part, that in
the opinion of the Adver&longs;aries is the le&longs;s apt to make the divi&longs;ion.
The Piramid being thus fixed, note what part of it &longs;hall be &longs;ub
merged, and revert it afterwards with the point downwards, and
you &longs;hall &longs;ee that it &longs;hall not dive into the water more than before,
but if you ob&longs;erve how far it &longs;hall &longs;ink, every per&longs;on expert in
Geometry, may mea&longs;ure, that tho&longs;e parts that remain out of the
water, both in the one and in the other Experiment are equall to
an hair: whence he may manife&longs;tly conclude, that the acute Figure
which &longs;eemed mo&longs;t apt to part and penetrate the water, doth not
part or penetrate it more than the large and &longs;pacious.
ment of a Cone,
demitted with
its Ba&longs;e, and af
ter with its
Point down
wards.
And he that would have a more ea&longs;ie Experiment, let him take
two Cylinders of the &longs;ame Matter, one long and &longs;mall, and the o
ther &longs;hert, but very broad, and let him put them in the water, not
di&longs;tended, but erect and endways: he &longs;hall &longs;ee, if he diligently
mea&longs;ure the parts of the one and of the other, that in each of them
the part &longs;ubmerged, retains exactly the &longs;ame proportion to that
out of the water, and that no greater part is &longs;ubmerged of that
long and &longs;mall one, than of the other more &longs;pacious and broad:
howbeit, this re&longs;ts upon a very large, and that upon a very little
Superficies of water: therefore the diver&longs;ity of Figure, occa&longs;ioneth
neither facility, nor difficulty, in parting and penetrating the Con
tinuity of the water; and, con&longs;equently, cannot be the Cau&longs;e of the
Natation or Submer&longs;ion. He may likewi&longs;e di&longs;cover the non
operating of variety of Figures, in ari&longs;ing from the Bottom of the
water, towards the Surface, by taking Wax, and tempering it with
a competent quantity of the filings of Lead, &longs;o that it may become
a con&longs;iderable matter graver than the water: then let him make
fa&longs;ten to it as much Cork, or other light matter, as ju&longs;t &longs;erveth to
rai&longs;e it, and draw it towards the Surface: for afterwards changing
the &longs;ame Wax into a thin Cake, or into any other Figure, that
&longs;ame Cork &longs;hall rai&longs;e it in the &longs;ame manner to a hair.
This &longs;ilenceth not my Antagoni&longs;ts, but they &longs;ay, that all the
di&longs;cour&longs;e hitherto made by me little importeth to them, and that it
&longs;erves their turn, that they have demon&longs;trated in one only parti
cular, and in what matter, and under what Figure plea&longs;eth them,
namely, in a Board and in a Ball of Ebony, that this put in the
water, de&longs;cends to the Bottom, and that &longs;tays atop to &longs;wim:
and the Matter being the &longs;ame, and the two Bodies differing in no
thing but in Figure, they affirm, that they have with all per&longs;picuity
demon&longs;trated and &longs;en&longs;ibly manife&longs;ted what they undertook; and
la&longs;tly, that they have obtained their intent. Neverthele&longs;s, I believe,
and thinke, I can demon&longs;trate, that that &longs;ame Experiment proveth
nothing again&longs;t my Conclu&longs;ion.
And fir&longs;t, it is fal&longs;e, that the Ball de&longs;cends, and the Board not:
for the Board &longs;hall al&longs;o de&longs;cend, if you do to both the Figures, as
the words of our Que&longs;tion requireth; that is, if you put them both
into the water.
ments of Nata
tion, the Solid
is to be put into,
not upon the
water.
of Natation &longs;ta
ted.
That the Antagoni&longs;ts having an opinion, that
the Figure would alter the Solid Bodies, in relation to the de&longs;cending
or not de&longs;cending, a&longs;cending or not a&longs;cending in the &longs;ame
v. gr.
being of a Sphericall Figure, &longs;hall de&longs;cend to the Bottom, being reduced
into &longs;ome other Figure, &longs;hall not de&longs;cend: I holding the contrary, do
affirm, that a Corporeall Solid Body, which reduced into a Sphericall Fi
gure, or any other, &longs;hall go to the Bottom, &longs;hall do the like under what&longs;oever
other Figure, &c.
But to be in the water, implies to be placed in the water, and by
vironed by the Superficies of the Ambient Body, therefore, then
&longs;hall the two Figures be in the water, when the Superficies of the
water, &longs;hall imbrace and inviron them: but when the Adver&longs;aries
&longs;hew the Board of Ebony not de&longs;cending to the Bottom, they put it
not into the water, but upon the water, where being by a certain im
pediment (as by and by we will &longs;hew) retained, it is invironed, part
by water, and part by air, which thing is contrary to our agreement,
that was, that the Bodies &longs;hould be in the water, and not part in
water, and part in air.
according to
about the things which go to the Bottom, as tho&longs;e which ari&longs;e from the
Bottom to &longs;wimme, and who &longs;ees not that things placed in the Bottom,
mu&longs;t have water about them.
It is now to be noted, that the Board of Ebany and the Ball, put
more &longs;lowly; and &longs;lower and &longs;lower, according as it &longs;hall be more
broad and thin, and of this Tardity the breadth of the Figure is the
true Cau&longs;e: But the&longs;e broad Boards that &longs;lowly de&longs;cend, are the
&longs;ame, that being put lightly upon the water, do &longs;wimm: Therefore,
if that were true which the Adver&longs;aries affirm, the &longs;ame numerical
Figure, would in the &longs;ame numericall water, cau&longs;e one while Re&longs;t, and
another while Tardity of Motion, which is impo&longs;&longs;ible: for every per
ticular Figure which de&longs;cends to the Bottom, hath of nece&longs;&longs;ity its own
determinate Tardity and &longs;lowne&longs;s, proper and naturall unto it, accor
ding to which it moveth, &longs;o that every other Tardity, greater or le&longs;&longs;er
is improper to its nature: if, therefore, a Board, as &longs;uppo&longs;e of a foot
&longs;quare, de&longs;cendeth naturally with &longs;ix degrees of Tardity, it is impo&longs;&longs;i
ble, that it &longs;hould de&longs;cend with ten or twenty, unle&longs;s &longs;ome new impe
diment do arre&longs;t it. Much le&longs;s can it, by rea&longs;on of the &longs;ame Figure
re&longs;t, and wholly cea&longs;e to move; but it is nece&longs;&longs;ary, that when ever it
re&longs;teth, there do &longs;ome greater impediment intervene than the breadth
of the Figure. Therefore, it mu&longs;t be &longs;omewhat el&longs;e, and not the Fi
gure, that &longs;tayeth the Board of Ebany above water, of which Eigure
the only Effect is the retardment of the Motion, according to which
it de&longs;cendeth more &longs;lowly than the Ball. Let it be confe&longs;&longs;ed, there
fore, rationally di&longs;cour&longs;ing, that the true and &longs;ole Cau&longs;e of the Ebanys
going to the Bottom, is the exce&longs;s of its Gravity above the Gravity of
the water: and the Cau&longs;e of the greater or le&longs;s Tardity, the breadth
of this Figure, or the contractedne&longs;s of that: but of its Re&longs;t, it can
by no means be allowed, that the quallity of the Figure, is the Cau&longs;e
thereof: a&longs;well, becau&longs;e, making the Tardity greater, according as
the Figure more dilateth, there cannot be &longs;o immen&longs;e a Dilatation, to
which there may not be found a corre&longs;pondent immence Tardity.
without redu&longs;ing it to Nullity of Motion; as, becau&longs;e the Figures
produced by the Antagoni&longs;ts for effecters of Re&longs;t, are the &longs;elf &longs;ame
that do al&longs;o go to the Bottom.
on of the Expe
riment in the
Ebany.
Figure hath its
own peculiat
Tardity.
Re&longs;i&longs;tance of
the Medium a
gain&longs;t Divi&longs;ion,
have nothing to
do with the Ef
fect of Natation
or Submer&longs;ion,
by an Experi
ment in Wall
nut tree,
I will not omit another rea&longs;on, founded al&longs;o upon Experience, and
if I deceive not my &longs;elf, manife&longs;tly concluding, how that the Intro
ducton of the breadth or amplitude of Figure, and the Re&longs;i&longs;tance of
the water again&longs;t penetration, have nothing to do in the Effect of de
&longs;cending, or a&longs;cending, or re&longs;ting in the water. ^{*}Take a piece of wood
or other Matter, of which a Ball a&longs;cends from the Bottom of the water
&longs;o that it is manife&longs;t, that the Ball of Ebony more readily divideth the
water in de&longs;cending, than the other in a&longs;cending; 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 Antagoni&longs;ts, which &longs;wims; and if
it be true, that this floats above water, by rea&longs;on of the Figure, unable
through its breadth, to pierce the Cra&longs;&longs;itude of the &longs;ame, the other of
Wallnut-tree, without all que&longs;tion, being thru&longs;t unto the Bottom, will
&longs;tay there, as le&longs;s apt, through the &longs;ame impediment of Figure, to di
vide the &longs;aid Re&longs;i&longs;tance of the water. But if we &longs;hall find, and by
experience &longs;ee, that not only the thin Board, but every other Figure
of the &longs;ame Wallnut-tree will return to float, as undoubtedly we &longs;hall,
then I mu&longs;t de&longs;ier my oppo&longs;ers to forbear to attribute the floating of
the Ebony, unto the Figure of the Board, in regard that the Re&longs;i&longs;tance
of the water is the &longs;ame, as well to the a&longs;cent, as to the de&longs;cent, and the
force of the Wallnut-trees a&longs;cen&longs;ion, is le&longs;&longs;e than the Ebonys force in
going to the Bottom.
Nay, I will &longs;ay more, that if we &longs;hall con&longs;ider Gold in compari&longs;on
of water, we &longs;hall find, that it exceeds it in Gravity almo&longs;t twenty times,
&longs;o 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 &longs;ome Woods, which are not above a fiftieth part le&longs;s
grave than water, whereupon their A&longs;cen&longs;ion therein is very &longs;low, and
a thou&longs;and times weaker than the
notwith&longs;tanding, a plate of Gold &longs;wims without de&longs;cending 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, &longs;hall re&longs;t there
without a&longs;cending. Now if the Figure can ob&longs;truct the Penetration,
and impede the de&longs;cent of Gold, that hath &longs;o great an
can it choo&longs;e but &longs;uffice to re&longs;i&longs;t the &longs;ame Penetration of the other mat
ter in a&longs;cending, when as it hath &longs;carce a thou&longs;andth part of the
that the Gold hath in de&longs;cending? Its therefore, nece&longs;&longs;ary, that that
which &longs;u&longs;pends the thin Plate of Gold, or Board of Ebony, upon the
water, be &longs;ome thing that is wanting to the other Cakes and Boards of
Matters le&longs;s grave than the water; &longs;ince that being put to the Bottom,
and left at liberty, they ri&longs;e up to the Surface, without any ob&longs;truction:
But they want not for flatne&longs;s and breadth of Figure: Therefore, the
&longs;paciou&longs;ne&longs;&longs;e of the Figure, is not that which makes the Gold and Ebony
to &longs;wim.
ment in Gold, to
prove the non
operating of Fi
gure in Natation
and Submer&longs;ion.
And, becau&longs;e, that the exce&longs;s of their Gravity above the Gravity of
the water, is que&longs;tionle&longs;s the Cau&longs;e of the &longs;inking of the flat piece of
Ebony, and the thin Plate of Gold, when they go to the Bottom, there
fore, of nece&longs;&longs;ity, when they float, the Cau&longs;e of their &longs;taying above
water, proceeds from Levity, which in that ca&longs;e, by &longs;ome Accident,
Board, rendering it no longer as it was before, whil&longs;t it did fink more
ponderous than the water, but le&longs;s.
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, &longs;o that it
&longs;tay there without &longs;inking, and diligently ob&longs;erve its effect. And
fir&longs;t, &longs;ee how fal&longs;e the a&longs;&longs;ertion of
that it &longs;tayeth above water, through its unability to pierce and pene
trate the Re&longs;i&longs;tance of the waters Cra&longs;&longs;itude: for it will manife&longs;tly
appear, not only that the &longs;aid Plates have penetrated the water, but
al&longs;o that they are a con&longs;iderable matter lower than the Surface of the
&longs;ame, the which continueth eminent, and maketh as it were a Rampert
on all &longs;ides, round about the &longs;aid Plates, the profundity of which they
&longs;tay &longs;wimming: and, according as the &longs;aid Plates &longs;hall be more grave
than the water, two, four, ten or twenty times, it is nece&longs;&longs;ary, that
their Superficies do &longs;tay below the univer&longs;all Surface of the water, &longs;o
much more, than the thickne&longs;s of tho&longs;e Plates, as we &longs;hal more di&longs;tinctly
&longs;hew anon. In the mean &longs;pace, for the more ea&longs;ie under&longs;tanding of what
I &longs;ay, ob&longs;erve with me a little the pre&longs;ent
Scheme: in which let us &longs;uppo&longs;e the Surface
of the water to be di&longs;tended, according to the
Lines F L D B, upon which if one &longs;hall put a
board of matter &longs;pecifically more grave than
water, but &longs;o lightly that it &longs;ubmetge not, it
&longs;hall not re&longs;t any thing above, but &longs;hall enter with its whole thickne&longs;s
into the water: and, moreover, &longs;hall &longs;ink al&longs;o, as we &longs;ee by the Board
A I, O I, who&longs;e breadth is wholly &longs;unk into the water, the little Ram
perts of water L A and D O incompa&longs;&longs;ing it, who&longs;e Superficies is no
tably higher than the Superficies of the Board. See now whether it be
true, that the &longs;aid Board goes not to the Bottom, as being of Figure
unapt to penetrate the Cra&longs;&longs;itude of the water.
But, if it hath already penetrated, and overcome the Continuity of
the water, & is of its own nature more grave than the &longs;aid water, why
doth it not proceed in its &longs;inking, but &longs;top and &longs;u&longs;pend its &longs;elf within
that little dimple or cavitie, which with its pondero&longs;ity it hath made in
the water? I an&longs;wer; becau&longs;e that in &longs;ubmerging it &longs;elf, &longs;o far as till its
Superficies come to the Levell with that of the water, it lo&longs;eth a part
of its Gravity, and lo&longs;eth the re&longs;t of it as it &longs;ubmergeth & de&longs;cends be
neath the Surface of the water, which maketh Ramperts and Banks
round about it, and it &longs;u&longs;taines this lo&longs;s by means of its drawing after it,
and carrying along with it, the Air that is above it, and by Contact ad
herent to it, which Air &longs;ucceeds to fill the Cavity that is invironed by
the Ramperts of water: &longs;o that that which in this ca&longs;e de&longs;cends and is
placed in the water, is not only the Board of Ebony or Plate of Iron,
no longer &longs;uperiour in Gravity to the water, as was the &longs;imple Ebony,
or the &longs;imple Gold. And, if we exactly con&longs;ider, what, and how
great the Solid is, that in this Experiment enters into the water, and
contra&longs;ts with the Gravity of the &longs;ame, 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 almo&longs;t
the like quantity of Air, or a Ma&longs;s compounded of a Plate of Lead,
and ten or twelve times as much Air. But, Genrlemen, you that
are my Antagoni&longs;ts in our Que&longs;tion, we require the Identity of
Matter, and the alteration only of the Figure; therefore, you mu&longs;t
remove that Air, which being conjoyned with the Board, makes it
become another Body le&longs;s grave than the Water, and put only the
Ebony into the Water, and you &longs;hall certainly &longs;ee the Board de&longs;cend
to the Bottom; and, if that do not happen, you have got the day.
And to &longs;eperate the Air from the Ebony, there needs no more but
only to bath the Superficies of the &longs;aid Board with the &longs;ame Water:
for the Water being thus interpo&longs;ed between the Board and the Air,
the other circumfu&longs;ed Water &longs;hall run together without any impedi
ment, and &longs;hall receive into it the &longs;ole and bare Ebony, as it was to do.
having penitra
ted the Water,
do not proceed
to a totail Sub
mer&longs;ion.
rate the Air from
Solids in demit
ting them into
the water.
But, me thinks I hear &longs;ome of the Adver&longs;aries cunningly oppo&longs;ing
this, and telling me, that they will not yield, by any means, that
their Board be wetted, becau&longs;e 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 a
greement, which was, that the Matter be the &longs;ame.
To this, I an&longs;wer, fir&longs;t; that treating of the operation of Figure
in Bodies put into the Water, none can &longs;uppo&longs;e them to be put into
the Water without being wet; nor do I de&longs;ire 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 &longs;inks by vertue of the new Weight added
to it by the Water, in the &longs;ingle and &longs;light bathing of it: for I will
put ten or twenty drops of Water upon the &longs;ame Board, whil&longs;t it is
&longs;u&longs;tained upon the water, which drops, becau&longs;e not conjoyned with
the other Water circumfu&longs;ed, &longs;hall not &longs;o encrea&longs;e the weight of it, as
to make it &longs;ink: but if the Board being taken out, and all the water
wiped off that was added thereto, I &longs;hould bath all its Superficies
with one only very &longs;mall drop, and put it again upon the water, with
out doubt it &longs;hall &longs;ink, the other Water running to cover it, not be
ing retained by the &longs;uperiour Air; which Air by the interpo&longs;ition of
the thin vail of water, that takes away its Contiguity unto the Ebony,
&longs;hall without Renitence be &longs;eperated, nor doth it in the lea&longs;t oppo&longs;e
the &longs;ucce&longs;&longs;ion of the other Water: but rather, to &longs;peak better, it
&longs;hall de&longs;cend freely; becau&longs;e it &longs;hall be all invironed and covered
water, doth arrive to the Levell of the univer&longs;all Surface of the &longs;aid
water. To &longs;ay, in the next place, that water can encrea&longs;e the weight
of things that are demitted into it, is mo&longs;t fal&longs;e, for water hath no
Gravity in water, &longs;ince it de&longs;cends not: yea, if we would well con&longs;i
der what any immen&longs;e Ma&longs;s of water doth put upon a grave Body;
that is placed in it, we &longs;hall find experimentally, that it, on the con
trary, will rather in a great part demini&longs;h the weight of it, 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 &longs;tir. Nor let
them tell me by way of reply, that although the &longs;uperpo&longs;ed water
augment not the Gravity of things that are in it, yet it increa&longs;eth the
pondero&longs;ity of tho&longs;e that &longs;wim, and are part in the water and part
in the Air, as is &longs;een, for Example, in a Bra&longs;s Ketle, which whil&longs;t it
is empty of water, and repleni&longs;hed only with Air &longs;hall &longs;wim, but
pouring of Water therein, it &longs;hall become &longs;o grave, that it &longs;hall &longs;ink
to the Bottom, and that by rea&longs;on of the new weight added thereto.
To this I will return an&longs;wer, as above, that the Gravity of the
Water, contained in the Ve&longs;&longs;el is not that which &longs;inks it to the Bot
tom, but the proper Gravity of the Bra&longs;s, &longs;uperiour to the Specificall
Gravity of the Water: for if the Ve&longs;&longs;el were le&longs;s grave than
water, the Ocean would not &longs;uffice to &longs;ubmerge it. And, give me
leave to repeat it again, as the fundamentall and principall point in
this Ca&longs;e, that the Air contained in this Ve&longs;&longs;el before the infu&longs;ion of
the Water, was that which kept it a-float, &longs;ince that there was made
of it, and of the Bra&longs;s, a Compo&longs;ition le&longs;s grave than an equall quanti
ty of Water: and the place that the Ve&longs;&longs;el occupyeth in the
Water whil&longs;t it floats, is not equall to the Bra&longs;s alone, but to the
Bra&longs;s and to the Air together, which filleth that part of the Ve&longs;&longs;el
that is below the Levell of the water: Moreover, when the Water
is infu&longs;ed, the Air is removed, and there is a compo&longs;ition made of
Bra&longs;s and of water, more grave
not by vertue of the water infu&longs;ed, as having greater Specifick
Gravity than the other water, but through the proper Gravity of
the Bra&longs;s, and through the alienation of the Air. Now, as he that
&longs;hould &longs;ay that Bra&longs;s, that by its nature goes to the Bottom, being
formed into the Figure of a Ketle, acquireth from that Figure a
vertue of lying in the Water without &longs;inking, would &longs;ay that which
is fal&longs;e; becau&longs;e that Bra&longs;s fa&longs;hioned into any whatever Figure,
goeth always to the Bottom, provided, that that which is put into the
water be &longs;imple Bra&longs;s; and it is not the Figure of the Ve&longs;&longs;el that
makes the Bra&longs;s to float, but it is becau&longs;e that that is not purely
Bra&longs;s which is put into the water, but an aggregate of Bra&longs;s and of
Air: &longs;o is it neither more nor le&longs;s fal&longs;e, that a thin Plate of Bra&longs;s
truth is, that it bares up without &longs;ubmerging, becau&longs;e that that which
is put in the water, is not pure Bra&longs;s or &longs;imple Ebony, but an ag
gregate of Bra&longs;s and Air, or of Ebony and Air. And, this is not
contrary unto my Conclu&longs;ion, the which, (having many a time &longs;een
Ve&longs;&longs;els of Mettall, and thin pieces of diver&longs;e grave Matters float, by
vertue of the Air conjoyned with them) did affirm, That Figure
was not the Cau&longs;e of the Natation or Submer&longs;ion of &longs;uch Solids as
were placed in the water. Nay more, I cannot omit, but mu&longs;t tell
my Antagoni&longs;ts, that this new conceit of denying that the Superfi
cies of the Board &longs;hould be bathed, may beget in a third per&longs;on an
opinion of a poverty of Arguments of defence on their part, &longs;ince
that &longs;uch bathing was never in&longs;i&longs;ted upon by them in the beginning
of our Di&longs;pute, and was not que&longs;tioned in the lea&longs;t, being that the
Originall of the di&longs;cour&longs;e aro&longs;e upon the &longs;wiming of Flakes of Ice,
wherein it would be &longs;implicity to require that their Superficies might
bedry: be&longs;ides, that whether the&longs;e pieces of Ice be wet or dry they
alwayes &longs;wim, and as the Adver&longs;aries &longs;ay, by rea&longs;on of the Figure.
no Gravity in
Water.
mini&longs;heth the
Gravity of So
lids immerged
therein.
ment of a Bra&longs;s
Ketle &longs;wiming
when empty, &
&longs;inking when
full, alledged to
prove that water
gravitates in
water, an&longs;wered.
ficeth not to
&longs;ink a Ve&longs;&longs;el &longs;pe
cifically le&longs;s
grave than wa
ter.
of the Natation
of empty Ve&longs;&longs;els
of Matters gra
ver
the water.
nor the breadth
of Figure, is the
Cau&longs;e of Nata
tion.
Some peradventure, by way of defence, may &longs;ay, that wetting the
Board of Ebony, and that in the &longs;uperiour Superficies, it would,
though of it &longs;elf unable to pierce and penetrate the water, be born
downwards, if not by the weight of the additionall water, at lea&longs;t
by that de&longs;ire and propen&longs;ion that the &longs;uperiour parts of the water
have to re-unite and rejoyn them&longs;elves: by the Motion of which
parts, the &longs;aid Board cometh in a certain manner, to be depre&longs;&longs;ed
downwards.
Solid de&longs;cends
not out of any
affectation of u
nion in the upper
parts of the wa
ter.
This weak Refuge will be removed, if we do but con&longs;ider, that
the repugnancy of the inferiour parts of the water, is as great against
Di&longs;-union, as the Inclination of its &longs;uperiour parts is to union: nor can
the uper unite them&longs;elves without depre&longs;&longs;ing the board, nor can it
de&longs;cend without di&longs;uniting the parts of the nether Water: &longs;o that
it doth follow, by nece&longs;&longs;ary con&longs;equence, that for tho&longs;e re&longs;pects, it &longs;hall
not de&longs;cend. Moreover, the &longs;ame that may be &longs;aid of the upper
parts of the water, may with equall rea&longs;on be &longs;aid of the nethe,
namely, that de&longs;iring to unite, they &longs;hall force the &longs;aid Board
upwards.
Happily, &longs;ome of the&longs;e Gentlemen that di&longs;&longs;ent from me, will won
der, that I affirm, that the contiguous &longs;uperiour Air is able to &longs;u&longs;tain
that Plate of
would in a certain &longs;ence allow the Air, a kind of Magnetick vertue
of &longs;u&longs;taining the grave To &longs;a
tis&longs;ie all I may, to all doubts, I have been con&longs;idering how by &longs;ome
other &longs;en&longs;ible Experiment I might demon&longs;trate, how truly that little
contiguous and &longs;uperiour Air &longs;u&longs;taines tho&longs;e Solids, which being by
&longs;ubmerge not, unle&longs;s they be fir&longs;t thorowly bathed; and have found,
that one of the&longs;e Bodies having de&longs;cended to the Bottom, by conveigh
ing to it (without touching it in the lea&longs;t) a little Air, which conjoyneth
with the top of the &longs;ame; it becometh &longs;ufficient, not only, as before to
&longs;u&longs;tain it, but al&longs;o to rai&longs;e it, and to carry it back to the top, where it
&longs;tays and abideth in the &longs;ame manner, till &longs;uch time, as the a&longs;&longs;i&longs;tance
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, &longs;o grave, that it lea&longs;urely
de&longs;cends to the Bottom, making with all its Superficies very &longs;mooth and
pollite: and this being put gently into the water, almo&longs;t wholly &longs;ub
mergeth, there remaining vi&longs;&longs;ible only a little of the very top, the which
solong as it is conjoyned with the Air, &longs;hall retain the Ball a-top, but
the Contiguity of the Air taken away by wetting it, it &longs;hall de&longs;cend to
the Bottom and there remain. Now to make it by vertue of the Air, that
before &longs;u&longs;tained it to return again to the top, and &longs;tay there, thru&longs;t into
the water a Gla&longs;s rever&longs;ed with the mouth downwards, the which &longs;hall
carry with it the Air it contains, and move this towards the Ball, aba&longs;ing
it till &longs;uch time that you &longs;ee, by the tran&longs;parency of the Gla&longs;s, that the
contained Air do arrive to the &longs;ummity of the
draw the Gla&longs;s upwards, and you &longs;hall &longs;ee the
stay on the top of the water, if you carefully part the Gla&longs;s and the water
without overmuch commoving and di&longs;turbing it. There is, therefore, a
certain affinity between the Air and other
ed, &longs;o, that they &longs;eperate not without a kind of violence. The &longs;ame
likewi&longs;e is &longs;een in the water; for if we &longs;hall wholly &longs;ubmerge &longs;ome
in it, &longs;o that it be thorowly bathed, in the drawing of it afterwards gent
ly out again, we &longs;hall &longs;ee the water follow it, and ri&longs;e notably above its
Surface, before it &longs;eperates from it. Solid
and alike in Superficies, &longs;o, that they make an exact Contact without
the interpo&longs;ition of the lea&longs;t Air, that may part them in the &longs;eperation
and yield untill that the ambient
do hold very firmly conjoyned, and are not to be &longs;eperated without great
force but, becau&longs;e, the Air, Water, and other Liquids, very expedi
tiou&longs;ly &longs;hape them&longs;elves to contact with any Solid
Superficies do exqui&longs;itely adopt them&longs;elves to that of the Solids, without
any thing remaining between them, therefore, the effect of this Con
junction and Adherence is more manife&longs;tly and frequently ob&longs;erved in
them, than in hard and inflexible
ly conjoyn with exactne&longs;s of Contact. This is therefore that Magne
tick vertue, which with firm Connection conjoyneth all Bodies, that do
touch without the interpo&longs;ition of flexible fluids; and, who knows, but
that that a Contact, when it is very exact, may be a &longs;ufficient Cau&longs;e of
the Union and Continuity of the parts of a naturall
the
it bears up tho&longs;e
Solids in the wa
ter, that are con
tiguous with it.
the Airs Conti
guity in the Na
tation of Solids.
Contact.
on of Conjunct
ion betwixt So
lids and the Air
contiguous to
them.
ation of Con
junction be
twixt Solids &
the water.
affectation and
Conjunction be
twixt Solids
them&longs;eives.
be the Cau&longs;e of
the Continuity
of Naturall Bo
dies.
Now, pur&longs;uing my purpo&longs;e, I &longs;ay; that it needs not, that we have
recour&longs;e to the Tenacity, that the parts of the water have among&longs;t them
&longs;elves, by which they re&longs;i&longs;t and oppo&longs;e Divi&longs;ion, Di&longs;traction, and Seper
ration, becau&longs;e there is no &longs;uch Coherence and Re&longs;i&longs;tance of Divi&longs;ion
for if there were, it would be no le&longs;s in the internall parts than in tho&longs;e
nearer the &longs;uperiour or externall Surface, &longs;o that the &longs;ame Board, find
ing alwayes the &longs;ame Re&longs;i&longs;tance and Renitence, would no le&longs;s &longs;top in
the middle of the water than about the Surface, which is fal&longs;e. More
over, what Re&longs;i&longs;tance can we place in the Continuity of the water
if we &longs;ee that it is impo&longs;&longs;ible to &longs;ind any Body of what&longs;oever Matter
Figure or Magnitude, which being put into the water, &longs;hall be ob&longs;tructed
and impeded by the Tenacity of the parts of the water to one another
&longs;o, but that it is moved upwards or downwards, according as the Cau&longs;e
of their Motion tran&longs;ports it? And, what greater proof of it can we de
&longs;ier, than that which we daily &longs;ee in Muddy waters, which being put into
Ve&longs;&longs;els to be drunk, and being, after &longs;ome hours &longs;etling, &longs;till, as we &longs;ay
thick in the end, after four or &longs;ix dayes they are wholly &longs;etled, and be
come pure and clear? Nor can their Re&longs;i&longs;tance of Penetration &longs;tay tho&longs;e
impalpable and in&longs;en&longs;ible Atomes of Sand, which by rea&longs;on of their
exceeding &longs;mall force, &longs;pend &longs;ix dayes in de&longs;cending the &longs;pace of half
a yard.
of
ter, proveth that
that Element
hath no aver&longs;i
on to Divi&longs;ion.
de&longs;cending &longs;o little a way, is a &longs;ufficient Argument of the Waters Re&longs;i&longs;tance
of Divi&longs;ion; becau&longs;e that is no re&longs;i&longs;ting of Divi&longs;ion, but a retarding of
and that in the &longs;ame in&longs;tant, it permits it &longs;elf to be divided: nor doth the
Retardation of Motion at all favour the Adver&longs;aries cau&longs;e, for that they are
to in&longs;tance in a thing that wholly prohibiteth Motion, and procureth Re&longs;t;
it is nece&longs;&longs;ary, therefore, to find out Bodies that &longs;tay in the water, if one would
&longs;hew its repugnancy to Divi&longs;ion, and not &longs;uch as move in it, howbeit
&longs;lowly.
oppo&longs;e divi&longs;ion,
and at the &longs;ame
time permit it
&longs;elf to be divi
ded.
What then is this Cra&longs;&longs;itude of the water, with which it re&longs;i&longs;teth Di
vi&longs;ion? What, I be&longs;eech you, &longs;hould it be, if we (as we have &longs;aid above)
with all diligence attempting the reduction of a Matter into &longs;o like a
Gravity with the water, that forming it into a dilated Plate it re&longs;ts &longs;u&longs;
pended as we have &longs;aid, between the two waters, it be impo&longs;&longs;ible to
effect it, though we bring them to &longs;uch an Equiponderance, that as
much Lead as the fourth part of a Grain of Mu&longs;terd-&longs;eed, added to the
&longs;ame expanded Plate, that in Air [e. out of the water
or fix pounds, &longs;inketh it to the Bottom, and being &longs;ub&longs;tracted, it a&longs;cends
to the Surface of the water? I cannot &longs;ee, (if what I &longs;ay be true, as it is
mo&longs;t certain) what minute vertue and force we can po&longs;&longs;ibly find or ima
gine, to which the Re&longs;i&longs;tance of the water again&longs;t Divi&longs;ion and Penetra
that it is nothing: becan&longs;e, if it were of any &longs;en&longs;ible power, &longs;ome
large Plate might be found or compounded of a Matter alike in Gra
vity to the water, which not only would &longs;tay between the two wa
ters; but, moreover, &longs;hould not be able to de&longs;cend or a&longs;cend with
out notable force. We may likewi&longs;e collect the &longs;ame from an o
ther Experiment, &longs;hewing that the Water gives way al&longs;o in the &longs;ame
manner to tran&longs;ver&longs;all Divi&longs;ion; for if in a &longs;etled and &longs;tanding water
we &longs;hould place any great Ma&longs;s that goeth not to the bottom, draw
ing it with a &longs;ingle (Womans) Hair, we might carry it from place to
place without any oppo&longs;ition, and this whatever Figure it hath,
though that it po&longs;&longs;e&longs;s a great &longs;pace of water, as for in&longs;tance, a great
Beam would do moved &longs;ide-ways. Perhaps &longs;ome might oppo&longs;e me
and &longs;ay, that if the Re&longs;i&longs;tance of water again&longs;t Divi&longs;ion, as I affirm,
were nothing; Ships &longs;hould not need &longs;uch a force of Oars and Sayles
for the moving of them from place to place in a tranquile Sea, or
&longs;tanding Lake. To him that &longs;hould make &longs;uch an objection, I would
reply, that the water contra&longs;teth not again&longs;t, nor &longs;imply re&longs;i&longs;teth
Divi&longs;ion, but a &longs;udden Divi&longs;ion, and with &longs;o much greater Reni
tence, by how much greater the Velocity is: and the Cau&longs;e of this
Re&longs;i&longs;tance depends not on Cra&longs;&longs;itude, or any other thing that ab&longs;o
lutely oppo&longs;eth Divi&longs;ion, but becau&longs;e that the parts of the water
divided, in giving way to that Solid that is moved in it, are them
&longs;elves al&longs;o nece&longs;&longs;itated locally to move, &longs;ome to the one &longs;ide, and &longs;ome
to the other, and &longs;ome downwards: and this mu&longs;t no le&longs;s be done
by the waves before the Ship, or other Body &longs;wimming through the
water, than by the po&longs;teriour and &longs;ub&longs;equent; becau&longs;e, the Ship
proceeding forwards, to make it &longs;elf a way to receive its Bulk, it is
requi&longs;ite, that with the Prow it repul&longs;e the adjacent parts of the
water, as well on one hand as on the other, and that it move them
as much tran&longs;ver&longs;ly, as is the half of the breadth of the Hull: and
the like removall mu&longs;t tho&longs;e waves make, that &longs;ucceeding the Poump
do run from the remoter parts of the Ship towards tho&longs;e of the
middle, &longs;ucce&longs;&longs;ively to repleni&longs;h the places, which the Ship in ad
vancing forwards, goeth, leaving vacant. Now, becau&longs;e, all Moti
tions are made in Time, and the longer in greater time: and it being
moreover true, that tho&longs;e Bodies that in a certain time are moved
by a certain power &longs;uch a certain &longs;pace, &longs;hall not be moved the &longs;ame
&longs;pace, and in a &longs;horter Time, unle&longs;s by a greater Power: therefore,
the broader Ships move &longs;lower than the narrower, being put on by
an equall Force: and the &longs;ame Ve&longs;&longs;el requires &longs;o much greater
force of Wind, or Oars, the fa&longs;ter it is to move.
draw a great
Ma&longs;s thorow the
Water; which
proveth, that it
hath no Re&longs;i&longs;t
ance again&longs;t
tran&longs;ver&longs;all Di
vi&longs;ion.
moved in the
water.
a certain &longs;pace in
a certain Time,
by a certain
power, cannot be
moved the
&longs;ame &longs;pace, and
in a &longs;horter time,
but by a greater
power.
be moved by any petit force; only it is true, that a le&longs;&longs;er force more
&longs;lowly moves it: but if the waters Re&longs;i&longs;tance of Divi&longs;ion, were in any
manner &longs;en&longs;ible, it would follow, that the &longs;aid Ma&longs;s, &longs;hould, notwith
&longs;tanding the percu&longs;&longs;ion of &longs;ome &longs;en&longs;ible force, continue immoveable, which isYea, I will &longs;ay farther, that &longs;hould we retire our &longs;elves into the
more internall contemplation of the Nature of water and other Fluids,
perhaps we &longs;hould di&longs;cover the Con&longs;titution of their parts to be &longs;uch, that
they not only do not oppo&longs;e Divi&longs;ion, but that they have not any thing in
them to be divided: &longs;o that the Re&longs;i&longs;tance that is ob&longs;erved in moving
a great Throng of People, wherein we find impediment, and not by any
difficulty in the Divi&longs;ion, for that none of tho&longs;e per&longs;ons are divided
whereof the Croud is compo&longs;ed, but only in moving of tho&longs;e per&longs;ons &longs;ide
ways which were before divided and disjoyned: and thus we find
Re&longs;i&longs;tance in thru&longs;ting a Stick into an heap of Sand, not becau&longs;e any part
of the Sand is to be cut in pieces, but only to be moved and rai&longs;ed. two
who&longs;e parts were continuall, and here Divi&longs;ion &longs;eemeth nece&longs;&longs;ary; the
here there is no nece&longs;&longs;ity of dividing but of moving only. Now, I am
not well re&longs;olved, whether water and other Fluids may be e&longs;teemed to
be of parts continuall or contiguous only; yet I find my &longs;elf indeed incli
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 &longs;ee >
between the Conjunction of the parts of an hard or Solid Body, and the
and Fluid: for if, for example, I take a Ma&longs;s of Silver or other Solid
and hard Mettall, I &longs;hall in dividing it into two parts, find not only the
greater, dependent on that vertue, whatever it be, which holds the parts
united: and &longs;o if we would divide again tho&longs;e two parts into other two
and &longs;ucce&longs;&longs;ively into others and others, we &longs;hould &longs;till find a like Re&longs;i&longs;t
ance, but ever le&longs;s by how much &longs;maller the parts to be divided &longs;hall be;
but if, la&longs;tly, employing mo&longs;t &longs;ubtile and acute In&longs;truments, &longs;uch as are
the mo&longs;t tenuous parts of the Fire, we &longs;hall re&longs;olve it (perhaps) into its
la&longs;t and lea&longs;t Particles, there &longs;hall not be left in them any longer either
Re&longs;i&longs;tance of Divi&longs;ion, or &longs;o much as a capacity of being farther divi
ded, e&longs;pecially by In&longs;truments more gro&longs;&longs;e than the acuities of Fire: and
what Knife or Ra&longs;or put into well melted Silver can we finde, that will
divide a thing which &longs;urpa&longs;&longs;eth the &longs;eparating power of Fire? Certainly
none: becau&longs;e either the whole &longs;hall be reduced to the mo&longs;t minute and
ultimate Divi&longs;ions, or if there remain parts capable &longs;till of other Suddi
Fire; but a Stick or Rod of Iron, moved in the melted Met all, is not
&longs;uch a one. Of a like Con&longs;titution and Con&longs;i&longs;tence, I account the parts
rea&longs;on of their Temtity; or if not ab&longs;olutely indivi&longs;ible, yet at lea&longs;t
not to be divided by a Board, or other Solid Body, palpable unto the
band, the Sector being alwayes required to be more &longs;harp than the Solid
to be cut. Solid Bodies, therefore, do only move, and not divide the
treame&longs;t minuity, and therefore capable of being moved, either many of
them at once, or few, or very few, they &longs;oon give place to every &longs;mall Cor
pu&longs;cle, that de&longs;cends in the &longs;ame: for that, it being little and light, de
&longs;cending in the Air, and arriving to the Surface of the Water, it meets
with Particles of Water more &longs;mall, and of le&longs;s Re&longs;i&longs;tance again&longs;t
Motion and Extru&longs;ion, than is its own prement and extru&longs;ive force,
whereupon it &longs;ubmergeth, and moveth &longs;uch a portion of them, as is pro
portionate to its Power. There is not, therefore, any Re&longs;i&longs;tance in
Water again&longs;t Divi&longs;ion, nay, there is not in it any divi&longs;ible parts. I
adde, moreover, that in ca&longs;e yet there &longs;bould be any &longs;mall Re&longs;i&longs;tance
move a very great natant Machine, or in e&longs;&longs;aying by the addition of one
&longs;mall Grain of Lead to &longs;ink, or by removall of it to rai&longs;e a very broad
Plate of Matter, equall in Gravity with Water, (which likewi&longs;e will
not happen, in ca&longs;e we proceed with dexterity) we may ob&longs;erve that that
Re&longs;i&longs;tance is a very different thing from that which the Adver&longs;aries pro
duce for the Cau&longs;e of the Natation of the Plate of Lead or Board of Ebo
ny, for that one may make a Board of Ebony, which being put upon the
Water &longs;wimmeth, and cannot be &longs;ubmerged, no not by the addition of an
bundred Grains of Lead put upon the &longs;ame, and afterwards being ba
thed, not only &longs;inks, though the &longs;aid Lead be taken away, but though
moreover a quantity of Cork, or of &longs;ome other light Body fa&longs;tened to it,
&longs;ufficeth not to hinder it from &longs;inking unto the bottome: &longs;o that you
&longs;ee, that although it were granted that there is a certain &longs;mall Re&longs;i&longs;t
ance of Divi&longs;ion found in the &longs;ubstance of the Water, yet this hath no
thing to do with that Cau&longs;e which &longs;upports the Board above the Water,
with a Re&longs;i&longs;tance an hundred times greater than that which men can
find in the parts of the Water: nor let them tell me, that only the Sur-
that &longs;uch Re&longs;i&longs;tance is found greate&longs;t in the beginning of the Submer&longs;ion,
as it al&longs;o &longs;eems that in the beginning, Motion meets with greater oppo&longs;iti
on, than in the continuance of it; becau&longs;e, fir&longs;t, I will permit, that the
dle, and inferiour parts, or that tho&longs;e above be wholly removed, and
tho&longs;e in the middle only made u&longs;e off, and yet you &longs;hall &longs;ee the effect for
Beam through the Water, is likewi&longs;e to divide the upperparts, and is
al&longs;o 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 a while be &longs;u&longs;pended and
&longs;etled, 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
&longs;o &longs;oon as it is dimitted upon the Water, hath not only begun to move
and divide it, but is for a good &longs;pace dimerged into it.
Liquids, &longs;o farte
from re&longs;i&longs;ting
Divi&longs;ion, that
they contain not
any thing that
may be divided.
ance a Solid
findeth in mo
ving through
the water, like
to that we meet
with in pa&longs;&longs;ing
through a
throng of peo
ple;
ing a Stick into
an heap of Sand.
Penetration, one
in Bodies conti
nuall, the other
in Bodies only
contiguous.
not of continu
all, but only
of contiguous
parts.
faction he hath
given, as to this
point, in Lib. de
Motu. Dial.
ence betwixt the
Conjunction of
the parts of a Bo
dy when Solid,
and when fluid.
of parts that ad
mit of no fat
ther divi&longs;ion.
ted into the wa
ter, do onely
move, and not
divide it.
any Re&longs;i&longs;tance
of Divi&longs;ion in
water, it mu&longs;t
needs be &longs;mall,
in that it is over
come by an
Hair, a Grain of
Lead, or a &longs;light
bathing of the
Solid.
of the Water, do
no more re&longs;i&longs;t
Divi&longs;ion, than
the middle or
lowe&longs;t parts.
&longs;i&longs;tance of divi
&longs;ion, not greater
in the begin
ning of the Sub
mer&longs;ion.
Let us receive it, therefore, for a true and undoubted Conclu&longs;i
on, That the Water hath not any Renitence again&longs;t &longs;imple Divi&longs;i
on, and that it is not po&longs;&longs;ible 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 &longs;hall be exceeded by
the Water in Gravity (although &longs;uch exce&longs;&longs;e and difference be in
&longs;en&longs;ible) &longs;hall be prohibited, and taken away, by the Cra&longs;&longs;itude of
the &longs;aid Water. When, therefore, we &longs;ee the Board of Ebony, or
of other Matter, more grave than the Water, to &longs;tay in the Con
fines of the Water and Air, without &longs;ubmerging, we mu&longs;t have re
cour&longs;e to &longs;ome other Originall, for the inve&longs;ting the Cau&longs;e of that
Effect, than to the breadth of the Figure, unable to overcome the
Renitence with which the Water oppo&longs;eth Divi&longs;ion, &longs;ince there is
no Re&longs;i&longs;tance; and from that which is not in being, we can expect
no Action. It remains mo&longs;t true, therefore, as we have &longs;aid before, that
this &longs;o &longs;ucceds, for that that which in &longs;uch manner put upon the wa
ter, not the &longs;ame Body with that which is put
this which is put
for that it is more grave than the Water, &longs;inketh, and that which is
put
Air, that both together are &longs;pecifically le&longs;s grave than the Water,
and therefore they do not de&longs;cend.
I will farther confirm this which I &longs;ay. Gentlemen, my Antago
ni&longs;ts, we are agreed, that the exce&longs;s or defect of the Gravity of the
Solid, unto the Gravity of the Water, is the true and proper Cau&longs;e
of Natation or Submer&longs;ion.
to be had in ex
perimenting the
operation of Fi
gure in Natati
on.
Now, if you will &longs;hew that be&longs;ides the former Cau&longs;e, there is ano
ther which is &longs;o powerfull, that it can hinder and remove the Sub
mer&longs;ion of tho&longs;e very Solids, that by their Gravity &longs;ink, and if you
will &longs;ay, that this is the breadth or amplene&longs;s of Figure, you are ob
lieged, when ever you would &longs;hew &longs;uch an Experiment, fir&longs;t to make
the circum&longs;tances certain, that that Solid which you put into the
Water, be not le&longs;s grave
any one might with rea&longs;on &longs;ay, that not the Figure, but the Levity
was the cau&longs;e of that Natation. But I &longs;ay, that when you &longs;hall di
more grave
Ebony, there is in the Water a Ma&longs;s of Air, united with the Ebony,
and &longs;uch, and &longs;o light, that of both there re&longs;ults a Compo&longs;ition le&longs;s
grave than the Water: See, therefore, that you remove the Air, and
put the Ebony alone into the Water, for &longs;o you &longs;hall immerge a So
lid more grave then the Water, and if this &longs;hall not go to the Bottom,
you have well Philo&longs;ophized, and I ill.
Now, &longs;ince we have found the true Cau&longs;e of the Natation of tho&longs;e
Bodies, which otherwi&longs;e as being graver than the Water, would de
&longs;cend to the bottom, I think, that for the perfect and di&longs;tinct know
ledge of this bu&longs;ine&longs;s, it would be good to proceed in a way of di&longs;
covering demon&longs;tratively tho&longs;e particular Accidents that do attend
the&longs;e effects, and,
PROBL. I.
Water, that &longs;o they may be able by vertue of the
Contigucus Air to &longs;tay afloat.
proportion Fi
gures ought to
have to the wa
ters Gravity,
that by help of
the contiguous
Air, they may
&longs;wim.
Let, therefore, for better illu&longs;tration, D F N E be a Ve&longs;&longs;ell,
wherein the water is contained, and &longs;uppo&longs;e a Plate or Board,
who&longs;e thickne&longs;s is comprehended between the Lines I C and
O S, and let it be of Matter exceeding the water in Gravity, &longs;o that
being put upon the water, it dimergeth and aba&longs;eth below the Levell
of the &longs;aid water, leaving the little Banks A I and B C, which are at
the greate&longs;t height they can be, &longs;o that if the Plate I S &longs;hould but
de&longs;cend any little &longs;pace farther, the little Banks or Ramparts would
no longer con&longs;i&longs;t, but expul&longs;ing the Air A I C B, they would dif
fu&longs;e them&longs;elves over the Superficies I C, and
would &longs;ubmerge the Plate. The height AIBC
is therefore the greate&longs;t profundity that the
little Now I &longs;ay,
that from this, and from the proportion in Gra
vity, that the Matter of the Plate hath to the
water, we may ea&longs;ily &longs;inde of what thickne&longs;s, at mo&longs;t, we may make
the &longs;aid Plates, to the end, they may be able to bear up above water:
for if the Matter of the Plate or
heavy again as the water, a
of a thickne&longs;s equall to the greate&longs;t height of the
thick as A I is high: which we will thus demon&longs;trate. Lot the So
lid I S be donble in Gravity to the water, and let it be a regular
our and inferiour, alike and equall, and at Right Angles with the o
ther laterall Superficies, and let its thickne&longs;s I O be equall to the
greate&longs;t Altitude of the Banks of water: I &longs;ay, that if it be put upon
the water, it will not &longs;ubmerge: for the Altitude
A I being equall to the Altitude I O, the Ma&longs;s
of the Air A B C I &longs;hall be equall to the Ma&longs;s of
the Solid C I O S: and the whole Ma&longs;s A O S B
double to the Ma&longs;s I S; And &longs;ince the Ma&longs;s
of the Air A C, neither encrea&longs;eth nor dimi
ni&longs;heth the Gravity of the Ma&longs;s I S, and the Solid I S was &longs;uppo&longs;ed
double in Gravity to the water; Therefore as much water as the
Ma&longs;s &longs;ubmerged A O S B, compounded of the Air A I C B, and of
the Solid I O S C, weighs ju&longs;t as much as the &longs;ame &longs;ubmerged Ma&longs;s
A O S B: but when &longs;uch a Ma&longs;s of water, as is the &longs;ubmerged part of
the Solid, weighs as much as the &longs;aid Solid, it de&longs;cends not farther,
but re&longs;teth, as by
mon&longs;trated: Therefore, I S &longs;hall de&longs;cend no farther, but &longs;hall re&longs;t.
And if the Solid I S &longs;hall be Se&longs;quialter in Gravity to the water, it
&longs;hall float, as long as its thickne&longs;s be not above twice as much as the
greate&longs;t Altitude of the Ramparts of water, that is, of A I. For I S
being Se&longs;quialter in Gravity to the water, and the Altitude O I
being double to I A, the Solid &longs;ubmerged A O S B, &longs;hall be al&longs;o
Se&longs;quialter in Ma&longs;s to the Solid I S. And becau&longs;e the Air A C,
neither increa&longs;eth nor dimini&longs;heth the pondero&longs;ity of the Solid I S:
Therefore, as much water in quantity as the &longs;ubmerged Ma&longs;s AOSB,
weighs as much as the &longs;aid Ma&longs;s &longs;ubmerged: And, therefore, that
Ma&longs;s &longs;hall re&longs;t. And briefly in generall.
Lib. 1. Prop. 3.
THEOREME. VI.
portion to the Gravity of the Water, that the Alti
tude of the Rampart, hath to the thickne&longs;s of the
Solid, that Solid &longs;hall not &longs;ink, but being never &longs;o lit
tle thicker it &longs;hall.
on of the great
e&longs;t thickne&longs;s of
Solids, beyond
which encrea
&longs;ed they &longs;ink.
Let the Solid I S be &longs;uperior in Gravity to the water, and of &longs;uch
thickne&longs;s, that the Altitude of the Rampart A I, be in proporti
on to the thickne&longs;s of the Solid I O, as the exce&longs;s of the Gravi
ty of the &longs;aid Solid I S, above the Gravity of a Ma&longs;s of water equall
to the Ma&longs;s I S, is to the Gravity of the Ma&longs;s of water equall to the
I &longs;ay, that the Solid I S &longs;hall not
&longs;inke, but being never &longs;o little thicker it &longs;hall
go to the bottom: For being that as A I is
to I O, &longs;o is the Exce&longs;s of the Gravity of the
Solid I S, above the Gravity of a Ma&longs;s of water
equall to the Ma&longs;s I S, to the Gravity of the
&longs;aid Ma&longs;s of water: Therefore, compounding, as A O is to O I, &longs;o
&longs;hall the Gravity of the Solid I S, be to the Gravity of a Ma&longs;s of water
equall to the Ma&longs;s I S: And, converting, as I O is to O A, &longs;o &longs;hall the
Gravity of a Ma&longs;s of water equall to the Ma&longs;s I S, be to the Gravity
of the Solid I S: But as I O is to O A, &longs;o is a Ma&longs;s of water I S, to a
Ma&longs;s of water equall to the Ma&longs;s A B S O: and &longs;o is the Gravity of
a Ma&longs;s of water I S, to the Gravity of a Ma&longs;s of water A S: Therefore
as the Gravity of a Ma&longs;s of water, equall to the Ma&longs;s I S, is to the
Gravity of the Solid I S, &longs;o is the &longs;ame Gravity of a Ma&longs;s of water
I S, to the Gravity of a Ma&longs;s of Water A S: Therefore the Gra
vity of the Solid I S, is equall to the Gravity of a Ma&longs;s of water e
quall to the Ma&longs;s A S: But the Gravity of the Solid I S, is the &longs;ame
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 compri&longs;ed in the
place of the &longs;aid Compound A O S B: And, therefore, it &longs;hall make
an
farther. But if its thickne&longs;s I O &longs;hould be increa&longs;ed, it would be ne
ce&longs;&longs;ary al&longs;o to encrea&longs;e the Altitude of the Rampart A I, to main
tain the due proportion: But by what hath been &longs;uppo&longs;ed, the Alti
tude of the Rampart A I, is the greate&longs;t that the Nature of the
Water and Air do admit, without the waters repul&longs;ing the Air ad
herent to the Superficies of the Solid I C, and po&longs;&longs;e&longs;&longs;ing the &longs;pace
A I C B: Therefore, a Solid of greater thickne&longs;s than I O, and of the
&longs;ame Matter with the Solid I S, &longs;hall not re&longs;t without &longs;ubmerging,
but &longs;hall de&longs;cend to the bottome: which was to be demon&longs;trated.
In con&longs;equence of this that hath been demon&longs;trated, &longs;undry and va
rious Conclu&longs;ions may be gathered, by which the truth of my prin
cipall Propo&longs;ition comes to be more and more confirmed, and the
imperfection of all former Argumentations touching the pre&longs;ent
Que&longs;tion cometh to be di&longs;covered.
THEOREME VII.
Bodies may
&longs;wimme.
heavie&longs;t of all Bodies, known by us, may float upon
the Water.
Becau&longs;e its Gravity being con&longs;idered to be almo&longs;t twenty times
greater than that of the water, and, moreover, the greate&longs;t Alti
tude that the Rampart of water can be extended to, without break
ing the Contiguity of the Air, adherent to the Surface of the Solid,
that is put upon the water being predetermined, if we &longs;hould make
a Plate of Gold &longs;o thin, that it exceeds not the nineteenth part ofthe
Altitude of the &longs;aid Rampart, this put lightly upon the water &longs;hall
re&longs;t, without going to the bottom: and if Ebony &longs;hall chance to be
in &longs;e&longs;qui&longs;eptimall proportion more grave than the water, the greate&longs;t
thickne&longs;s that can be allowed to a Board of Ebony, &longs;o that it may be
able to &longs;tay above water without &longs;inking, would be &longs;eaven times
more than the height of the Rampart Tinn, gr.
grave than water, &longs;hall &longs;wimm as oft as the thickne&longs;s of its Plate,
exceeds not the 7th part of the Altitude of the Rampart.
cites this as a
Propo&longs;ition, there
fore I make it of
that number.
And here I will not omit to note, as a &longs;econd Corrollary dependent
upon the things demon&longs;trated, that,
THEOREME VIII.
Submer&longs;ion, col
lected from the
thickne&longs;s, exclu
ding the length
and breadth of
Plates.
Natation of tho&longs;e grave Bodies, which otherwi&longs;e
do &longs;ubmerge, but al&longs;o the determining what be tho&longs;e
Boards of Ebony, or Plates of Iron or Gold that will
&longs;wimme, depends not on it, rather that &longs;ame determina
tion is to be collected from the only thickne&longs;s of tho&longs;e
Figures of Ebony or Gold, wholly excluding the con
&longs;ideration of length and breadth, as having no way
any &longs;hare in this Effect.
It hath already been manife&longs;ted, that the only cau&longs;e of the Nata
tion of the &longs;aid Plates, is the reduction of them to be le&longs;s grave
than the water, by means of the connexion of that Air, which de
&longs;cendeth together with them, and po&longs;&longs;e&longs;&longs;eth place in the water;
which place &longs;o occupyed, if before the circumfu&longs;ed water diffu&longs;eth
it &longs;elf to fill it, it be capable of as much water, as &longs;hall weigh equall
with the Plate, the Plate &longs;hall remain &longs;u&longs;pended, and &longs;inke no
farther.
Now let us &longs;ee on which of the&longs;e three dimen&longs;ions of the Solid
depends the terminating, what and how much the Ma&longs;s of that ought
to be, that &longs;o the a&longs;&longs;i&longs;tance of the Air contiguous unto it, may &longs;uffice
to render it &longs;pecifically le&longs;s grave than the water, whereupon it may
re&longs;t without Submer&longs;ion. It &longs;hall undoubtedly be found, that the
length and breadth have not any thing to do in the &longs;aid determina
tion, but only the height, or if you will the thickne&longs;s: for, if we take
a Plate or Board, as for Example, of Ebony, who&longs;e Altitude hath
unto the greate&longs;t po&longs;&longs;ible Altitude of the Rampart, the proportion
above declared, for which cau&longs;e it &longs;wims indeed, but yet not if we
never &longs;o little increa&longs;e its thickne&longs;s; I &longs;ay, that retaining its thick
ne&longs;s, and encrea&longs;ing its Superficies to twice, four times, or ten times
its bigne&longs;s, or dmini&longs;ning it by dividing it into four, or &longs;ix, or
twenty, or a hundred parts, it &longs;hall &longs;till in the &longs;ame manner continue
to float: but encrea&longs;ing its thickne&longs;s only a Hairs breadth, it will
alwaies &longs;ubmerge, although we &longs;hould multiply the Superficies a
hundred and a hundred times. Now fora&longs;much as that this is a
Cau&longs;e, which being added, we adde al&longs;o the Effect, and being remo
ved, it is removed; and by augmenting or le&longs;&longs;ening the length or
breadth in any manner, the effect of going, or not going to the bot
tom, is not added or removed: I conclude, that the greatne&longs;s and
&longs;malne&longs;s of the Superficies hath no influence upon the Natation or
Submer&longs;ion. And that the proportion of the Altitude of the Ram
parts of Water, to the Altitude of the Solid, being con&longs;tituted in
the manner afore&longs;aid, the greatne&longs;s or &longs;malne&longs;s of the Superficies,
makes not any variation, is manife&longs;t from that which hath been above
demon&longs;trated, and from this, that,
Whence Cylinders or Prifmes, namely, the Board, be they great or
little, &longs;o that they be all of equall thickne&longs;s, have the &longs;ame proportion
to their Conterminall Air, which hath for Ba&longs;e the &longs;aid Superficies of
the Board, and for height the Ramparts of water; &longs;o that alwayes
of that Air, and of the Board, Solids are compounded, that in Gravity
equall a Ma&longs;s of water equall to the Ma&longs;s of the Solids, compounded
of Air, and of the Board: whereupon all the &longs;aid Solids do in the
&longs;ame manner continue afloat. We will conclude in the third place,
that,
Cylinders ha
ving the &longs;ame
Ba&longs;e, are to one
another as their
heights.
THEOREME. IX.
of all Matters,
float by hep of
the Rampart re
pleni&longs;hed with
Air, and &longs;ome
but only touch
the water.
grave than the Water, do by Benefit of the &longs;aid Ram
part, not only float, but &longs;ome Figures, though of the
grave&longs;t Matter, do &longs;tay wholly above Water, wetting
only the inferiour Surface that toucheth the Water.
And the&longs;e &longs;hall be all Figures, which from the inferiour Ba&longs;e up
wards, grow le&longs;&longs;er and le&longs;&longs;er; the which we &longs;hall exemplifie for
this time in Piramides or Cones, of which Figures the pa&longs;&longs;ions sre
common. We will demon&longs;trate therefore, that,
which being put with its Ba&longs;e upon the Water, re&longs;ts not only without
&longs;ubmerging, but without wetting it more then its Ba&longs;e.
For the explication of which it is requi&longs;ite, that we fir&longs;t demon&longs;trate
the &longs;ub&longs;equent Lemma, namely, that,
LEMMA II.
Gravities.
Ma&longs;&longs;es are in
contrary pro
portion to their
Specifick Gra
vities, are equall
in ab&longs;olute Gra
vity.
Let A C and B be two Solids, and let the Ma&longs;s A C be to the
Ma&longs;s B, as the Specificall Gravity of the Solid B, is to the Speci
ficall Gravity of the Solid A C: I &longs;ay, the Solids A C and B are
equall in ab&longs;olute weight, that is, equally grave. For
if the Ma&longs;s A C be equall to the Ma&longs;s B, then, by the
A&longs;&longs;umption, the Specificall Gravity of B, &longs;hall be e
quall to the Specificall Gravity of A C, and being e
quall in Ma&longs;s, and of the &longs;ame Specificall Gravity they
&longs;hall ab&longs;olutely weigh one as much as another. But
if their Ma&longs;&longs;es &longs;hall be unequall, let the Ma&longs;s A C be greater, and in it
take the part C, equall to the Ma&longs;s B. And, becau&longs;e the Ma&longs;&longs;es B
and C are equall; the Ab&longs;olute weight of B, &longs;hall have the &longs;ame pro
portion to the Ab&longs;olute weight of C, that the Specificall Gravity of
B, hath to the Specificall Gravity of C; or of C A, which is the
&longs;ame
B, hath to the Specificall Gravity of C A, the like proportion, by the
A&longs;&longs;umption, hath the Ma&longs;s C A, to the Ma&longs;s B; that is, to the Ma&longs;s C:
as the Ma&longs;s A C to the Ma&longs;s
&longs;o is the ab&longs;olute weight of A C, to the ab&longs;olute weight of C: There
fore the ab&longs;olute weight of B, hath the &longs;ame proportion to the ab&longs;o
lute weight of C, that the ab&longs;olute weight of A C, hath to the ab
&longs;olute weight of C: Therefore, the two Solids A C and B are equall
in ab&longs;olute Gravity: which was to be demon&longs;trated. Having de
mon&longs;trated this, I &longs;ay,
THEOREME X.
the Water &longs;hall not &longs;ubmerge, nor wet any more than
its Ba&longs;e.
Cones and Pira
mides of any
demittedinto the
water, re&longs;t only
their Ba&longs;es.
Let the greate&longs;t po&longs;&longs;ible Altitude of the Rampart be the Line D B,
and the Diameter of the Ba&longs;e of the Cone to be made of any Mat
ter a&longs;&longs;igned 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, &longs;o let the Altitude of the
Rampart D B, be to the third part of the Piramide
or Cone A B C, de&longs;cribed upon the Ba&longs;e, who&longs;e
Diameter is B C: I &longs;ay, that the &longs;aid Cone A B C,
and any other Cone, lower then the &longs;ame, &longs;hall re&longs;t
upon the Surface of the water B C without &longs;inking.
Draw D F parallel to B C, and &longs;uppo&longs;e the Pri&longs;me
or Cylinder E C, which &longs;hall be tripple to the Cone
A B C. And, becau&longs;e the Cylinder D C hath the &longs;ame 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,
&longs;o is the Specificall Gravity of the Cone A B C, to the Specificall Gra
vity of the water: Therefore, as the Ma&longs;s of the Solid D C, is to the
Ma&longs;s of the Cone A
to the Specificall Gravity of the water: Therefore, by the precedent
Lemma, the Cone A B C weighs in ab&longs;olute Gravity as much as a
Ma&longs;s of Water equall to the Ma&longs;s D C: But the water which by the
impo&longs;ition of the Cone A B C, is driven out of its place, is as much
as would preci&longs;ely lie in the place D C, and is equall in weight to the
Cone that di&longs;placeth it: Therefore, there &longs;hall be an
and the Cone &longs;hall re&longs;t without farther &longs;ubmerging. And its ma
nife&longs;t,
COROLARY I.
of the &longs;ame Ba&longs;e,
tho&longs;e of lea&longs;t Al
titude &longs;hall &longs;ink
the lea&longs;t.
al&longs;o le&longs;s grave, and &longs;hall &longs;o much the more re&longs;t without Submer&longs;ion.
COROLARY II.
water, with the Apix or Point downwards, re&longs;t without Submer&longs;ion.
Cones and Pira
mides of any
Matter, which
demitted with
the Point down
wards do float a
top.
Becau&longs;e if we rea&longs;&longs;ume what hath been above demon&longs;trated, of
Pri&longs;ms and Cylinders, and that on Ba&longs;es equall to tho&longs;e of the
&longs;aid Cylinders, we make Cones of the &longs;ame Matter, and thrree
times as high as the Cylinders, they &longs;hall re&longs;t afloat, for that in Ma&longs;s
and Gravity they &longs;hall be equall to tho&longs;e Cylinders, and by having
their Ba&longs;es equall to tho&longs;e of the Cylinders, they &longs;hall leave equall
Ma&longs;&longs;es of Air included within the Ramparts. This, which for Exam
ple &longs;ake hath been demon&longs;trated, in Pri&longs;ms, Cylinders, Cones and
Piramids, might be proved in all other Solid Figures, but it would
require a whole Volume (&longs;uch is the multitude and variety of their
Symptoms and Accidents) to comprehend the particuler demon&longs;tration
of them all, and of their &longs;everall Segments: but I will to avoid prolixity
in the pre&longs;ent Di&longs;cour&longs;e, content my &longs;elf, that by what I have declared
every one of ordinary Capacity may comprehend, that there is not
any Matter &longs;o grave, no not Gold it &longs;elf, of which one may not form
all &longs;orts of Figures, which by vertue of the &longs;uperiour Air adherent to
them, and not by the Waters Re&longs;i&longs;tance of Penetration, do remain
afloat, &longs;o that they &longs;ink not. Nay, farther, I will &longs;hew, for removing
that Error, that,
THEOREME XI.
Cone, demitted
with the Point
downwards &longs;hal
&longs;wim, with its
Ba&longs;e downward
&longs;hall &longs;ink.
downward &longs;hall &longs;wimme, and the &longs;ame put with the
Ba&longs;e downwards &longs;hall &longs;inke, and it &longs;hall be impo&longs;&longs;ible
to make it float.
Now the quite contrary would happen, if the difficulty of Pene
trating the water, were that which had hindred the de&longs;cent, for
that the &longs;aid Cone is far apter to pierce and penetrate with its &longs;harp
Point, than with its broad and &longs;pacious Ba&longs;e.
And, to demon&longs;trate this, let the Cone be
as the water, and let its height be tripple to the height of the Rampart
tom: for the Aeriall Cylinder contained betwixt
the Ramparts
Cone
compounded of the Air
becau&longs;e the Cone
vity to the water, therefore as much water as the whole Ma&longs;&longs;e
as the Cone
and the Cone Now, I &longs;ay farther,
that the &longs;ame Cone placed with the Ba&longs;e downwards, &longs;hall &longs;ink to
the bottom, without any po&longs;&longs;ibility of returning again, by any means
to &longs;wimme.
Let, therefore, the Cone be
water, and let its height be tripple the height
of the Rampart of water L B: It is already
manife&longs;t, that it &longs;hall not &longs;tay wholly out of
the water, becau&longs;e the Cylinder being com
prehended betwixt the Ramparts
equall to the Cone
the Cone, beig double in Gravity to the
water, it is evident that the weight of the &longs;aid
Cone &longs;hall be double to the weight of the Ma&longs;s of water equall to the
Cylinder
&longs;hall de&longs;cend.
COROLARY I.
the &longs;aid Cone
&longs;wim, if one im
merge a part
thereof.
Which you may &longs;ee, comparing with the water as well the part
that &longs;hall immerge as the other above water. Let us therefore
of the Cone A B D, &longs;ubmergeth part N T O S, and advance the
Point N S F above water. The Altitude of the Cone F N S, &longs;hall
either be more than half the whole Altitude of the Cone F T O, or
it &longs;hall not be more: if it &longs;hall be more than half, the Cone F N S
&longs;hall be more than half of the Cylinder E N S C: for the Altitude
of the Cone F N S, &longs;hall be more than Se&longs;quialter of the Altitude
of the Cylinder E N S C: And, becau&longs;e the Matter of the Cone is
&longs;uppo&longs;ed to be double in Specificall Gravity to the water, the water
which would be contained within the Rampart E N S C, would be
le&longs;s grave ab&longs;olutely than the Cone F N S; &longs;o that the whole Cone
F N S cannot be &longs;u&longs;tained by the Rampart: But the part immerged
N T O S, by being double in Specificall Gravity to the water, &longs;hall
re&longs;pect of the part &longs;ubmerged, as the part above water &longs;hall de
&longs;cend to the bottom. But if the Altitude of the Point F N S, &longs;hall
be half the Altitude of the whole Cone F T O, the &longs;ame Altitude of
the &longs;aid
therefore, E N S C &longs;hall be double to the Cone F N S; and as much
water in Ma&longs;s as the
part of the
N T O S, is double in Gravity to the water, a Ma&longs;s of water equall
to that compounded of the
&longs;hall weigh le&longs;s than the
a Ma&longs;s of water equall to the Solid N T O S: Therefore, the
&longs;ha l al&longs;o de&longs;cend. Again, becau&longs;e the Solid N T O S, is &longs;eptuple
to the
tion of the Solid N T O S, &longs;hall be to the
to two: Therefore, the whole Solid compounded of the
E N S C, and of the Solid N T O S, is much le&longs;s than double the
Solid N T O S: Therefore, the &longs;ingle Solid N T O S, is much graver
than a Ma&longs;s of water equall to the Ma&longs;s, compounded of the
linder E N S C, and of N T O S.
COROLARY II.
Cones towards
the Cu&longs;pis remo
ved, it &longs;hall &longs;till
&longs;ink.
way the part of the Cone F N S, the &longs;ole remainder N T O S would
go to the bottom.
COROLARY III.
N T O S &longs;till encrea&longs;ing, and the Ma&longs;s of Air contained in the Rampart
dimini&longs;hing, which ever grows le&longs;s, the more the Cone &longs;ubmergeth.
Cone is immer
ged, the more
impo&longs;&longs;ible is its
floating.
That Cone, therefore, that with its Ba&longs;e upwards, and its
downward mu&longs;t of nece&longs;&longs;ity &longs;inke. They have argued farre
from the truth, therefore, who have a&longs;cribed the cau&longs;e of Natation
to waters re&longs;i&longs;tance of Divi&longs;ion, as to a pa&longs;&longs;ive principle, and to the
breadth of the Figure, with which the divi&longs;ion is to be made, as the
Efficient.
I come in the fourth place, to collect and conclude the rea&longs;on of
that which I have propo&longs;ed to the Adver&longs;aries, namely,
THE OREME XII.
to the Bottome; But by the help of the Air con
tained in the Rampart, re&longs;t without &longs;ubmerging.
Figure & great
ne&longs;&longs;e, that natu
rally &longs;ink, may
by help of the
Air in the Ram
part &longs;wimme.
The truth of this Propo&longs;ition is &longs;ufficiently manife&longs;t in all tho&longs;e
Solid Figures, that determine in their uppermo&longs;t part in a plane
Superficies: for making &longs;uch Figures of &longs;ome Matter &longs;pecifi
cally as grave as the water, putting them into the water, &longs;o that the
whole Ma&longs;s be covered, it is manife&longs;t, that they &longs;hall re&longs;t in all
places, provided, that &longs;uch a Matter equall in weight to the water,
may be exactly adju&longs;ted: and they &longs;hall by con&longs;equence, re&longs;t or
lie even with the Levell of the water, without making any Rampart.
If, therefore, in re&longs;pect of the Matter, &longs;uch Figures are apt to re&longs;t
without &longs;ubmerging, though deprived of the help of the Rampart,
it is manife&longs;t, that they may admit &longs;o much encrea&longs;e of Gravity,
(without encrea&longs;ing their Ma&longs;&longs;es) 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 &longs;u&longs;tained, they
&longs;hall re&longs;t afloat, but being bathed, they &longs;hall de&longs;cend, 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 de&longs;cent: but in tho&longs;e
Figures that go le&longs;&longs;ening upwards towards the top, &longs;ome Per&longs;ons
may, and that not without much &longs;eeming Rea&longs;on, doubt whether
the &longs;ame may be done, and e&longs;pecially by tho&longs;e which terminate in a
very acute Point, &longs;uch as are your Cones and &longs;mall Piramids. Touch
ing the&longs;e, therefore, as more dubious than the re&longs;t, I will endeavour
to demon&longs;trate, that they al&longs;o lie under the &longs;ame Accident of going,
or not going to the Bottom, be they of any whatever bigne&longs;s. Let
therefore the Cone be A B D, made of a matter
&longs;pecifically as grave as the water; it is manife&longs;t
that being put all under water, it &longs;hall re&longs;t in
all places (alwayes provided, that it &longs;hall weigh
exactly as much as the water, which is almo&longs;t
impo&longs;&longs;ible to effect) and that any &longs;mall weight
being added to it, it &longs;hall &longs;ink to the bottom:
but if it &longs;hall de&longs;cend downwards gently, I &longs;ay,
that it &longs;hall make the Rampart E S T O, and
that there &longs;hall &longs;tay out of the water the point A S T, tripple in
height to the Rampart E S: which is manife&longs;t, for the Matter of the
becomes indifferent to move downwards or upwards; and the Cone
the concave of the Rampart
Gravity: and, therefore, there &longs;hall be a perfect
con&longs;equently, a Re&longs;t. Now here ari&longs;eth a doubt, whether the
Cone
wholly under water, it goes to the bottom, but yet not in &longs;uch &longs;ort,
as to take from the Rampart the vertue of &longs;u&longs;taining it that it &longs;ink not,
and, the rea&longs;on of the doubt is this: that although at &longs;uch time as
the Cone
height to the Altitude of the Rampart
part is above water; [for although in the De&longs;cent of the Cone the
Point
Rampart
greater proportion than the Rampart, in that
it dimini&longs;heth according to all the three Di
men&longs;ions, but the Rampart according to two
only, the Altitude &longs;till remaining the &longs;ame;
or, if you will, becau&longs;e the Cone
mini&longs;hing, according to the proportion of the
cubes of the Lines that do &longs;ucce&longs;&longs;ively become
the Diameters of the Ba&longs;es of emergent Cones,
and the Ramparts dimini&longs;h according to the proportion of the
Squares of the &longs;ame Lines; whereupon the proportions of the Points
are alwayes Se&longs;quialter of the proportions of the Cylinders, con
tained within the Rampart; &longs;o that if, for Example, the height of
the emergent Point were double, or equall to the height of the
Rampart, in the&longs;e ca&longs;es, the Cylinder contained within the Ram
part, would be much greater than the &longs;aid Point, becau&longs;e it would be
either &longs;e&longs;quialter or tripple, by rea&longs;on of which it would perhaps
&longs;erve over and above to fu&longs;tain the whole Cone, &longs;ince the part &longs;ub
merged would no longer weigh any thing;] yet, neverthele&longs;s, when
any Gravity is added to the whole Ma&longs;s of the Cone, &longs;o that al&longs;o the
part &longs;ubmerged is not without &longs;ome exce&longs;&longs;e of Gravity above the
Gravity of the water, it is not manife&longs;t, whether the Cylinder con
tained within the Rampart, in the de&longs;cent that the Cone &longs;hall make,
can be reduced to &longs;uch a proportion unto the emergent Point, and to
&longs;uch an exce&longs;&longs;e of Ma&longs;s above the Ma&longs;s of it, as to compen&longs;ate the
exce&longs;&longs;e of the Cones Specificall Gravity above the Gravity of the wa
ter: and the Scruple ari&longs;eth, becau&longs;e that howbeit in the de&longs;cent
made by the Cone, the emergent Point
there is al&longs;o a diminution of the exce&longs;s of the Cones Gravity above
doth al&longs;o contract it &longs;elf, and the Cylinder contained in it doth de
mini&longs;h. Neverthele&longs;s it &longs;hall be demon&longs;trated, how that the Cone
Matter exactly equall in Gravity to the Water, if there may
be affixed to it &longs;ome Weight, by means of which it may de&longs;cend to
the bottom, when &longs;ubmerged under water, it may al&longs;o by vertue of
the Rampart &longs;tay above without &longs;inking.
Let, therefore, the Cone
and alike in &longs;pecificall Gravity to the water. It is manife&longs;t, that
being put lightly into the water, it &longs;hall re&longs;t without de&longs;cending;
and it &longs;hall advance above water, the Point
Rampart
more depre&longs;&longs;ed, &longs;o that it advance above wa
ter, only the Point
the Point
to the Cone
is to the cube of the Line
der
the Square of
But the Cone
the Cylinder
water which might be contained in the Rampart
double in Ma&longs;s and in Weight to the Cone
would be able to &longs;u&longs;tain the double of the Weight of the Cone
Therefore, if to the whole Cone
Weight as the Gravity of the Cone
part of the weight of the Cone
the Rampart
the Cone
weight of the Cone
water. But if the Altitude of the Cone
of the Altitude of the Cone
Cone
the Cylinder
twelve; and, therefore, the Cylinder
as twelve to eight; and the exce&longs;s of the Cylinder
the Cone
fore if to the Cone
twenty &longs;evenths of the weight of the Cone
more then its &longs;eventh part, it al&longs;o &longs;hall continue to &longs;wimme, and
Rampart. This that hath been demon&longs;trated in Cones, exactly holds
in Piramides, although the one or the other &longs;hould be very &longs;harp in
their Point or Cu&longs;pis: From whence we conclude, that the &longs;ame
Accident &longs;hall &longs;o much the more ea&longs;ily happen in all other Figures,
by how much the le&longs;s &longs;harp the Tops &longs;hall be, in which they deter
mine, being a&longs;&longs;i&longs;ted by more &longs;pacious Ramparts.
e&longs;t effected in
Figures broad
toward the top.
THEOREME XIII.
or &longs;wim, upon
bathing or not
bathing of their
tops.
go, and not go, to the Bottom, according as their Sumi
ties or Tops &longs;hall be bathed or not bathed.
And this Accident being common to all &longs;orts of Figures, without
exception of &longs;o much as one. Figure hath, therefore, no part
in the production of this Effect, of &longs;ometimes &longs;inking, and &longs;ome
times again not &longs;inking, but only the being &longs;ometimes conjoyned
to, and &longs;ometimes &longs;eperated from, the &longs;upereminent Air: which
cau&longs;e, in fine, who &longs;o &longs;hall rightly, and, as we &longs;ay, with both his
Eyes, con&longs;ider this bu&longs;ine&longs;s, will find that it is reduced to, yea, that
it really is the &longs;ame with, the true, Naturall and primary cau&longs;e of
Natation or Submer&longs;ion; to wit, the exce&longs;s or deficiency of the
Gravity of the water, in relation to the Gravity of that Solid Mag
nitude, 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
&longs;elf alone goes to the bottom, if upon it you fa&longs;ten 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 le&longs;s, &longs;o the Board of Ebony, of its own nature more grave than
water; and, therefore, de&longs;cending to the bottom, when it is demit
ted by it &longs;elf alone into the water, if it &longs;hall be put upon the water,
conjoyned with an Expanded vail of Air, that together with the
Ebony doth de&longs;cend, and that it be &longs;uch, as that it doth make with
it a compound le&longs;s grave than &longs;o much water in Ma&longs;s, as equalleth
the Ma&longs;s already &longs;ubmerged and depre&longs;&longs;ed beneath the Levell of the
waters Surface, it &longs;hall not de&longs;cend any farther, but &longs;hall re&longs;t, for
no other than the univer&longs;all and mo&longs;t common cau&longs;e, which is that
Solid Magnitudes, le&longs;s grave
bottom.
So that if one &longs;hould take a Plate of Lead, as for Example, a finger
thick, and an handfull broad every way, and &longs;hould attempt to make
it &longs;wimme, with putting it lightly on the water, he would lo&longs;e his
Labour, becau&longs;e that if it &longs;hould be depre&longs;&longs;ed an Hairs breadth be
and &longs;ink; but if whil&longs;t it is going downwards, one &longs;hould make
certain Banks or Ramparts about it, that &longs;hould hinder the do fu&longs;ion
of the water upon the &longs;aid Plate, the which Banks &longs;hould ri&longs;e &longs;o
high, as that they might be able to contain as much water, as &longs;hould
weigh equally with the &longs;aid Plate, it would, without all Que&longs;tion,
de&longs;cend no lower, but would re&longs;t, as being &longs;u&longs;tained by vertue of
the Air contained within the afore&longs;aid Ramparts: and, in &longs;hort,
there would be a Ve&longs;&longs;ell by this means formed with the bottom of
Lead. But if the thinne&longs;s of the Lead &longs;hall be &longs;uch, that a very
&longs;mall height of Rampart would &longs;uffice to contain &longs;o much Air, as might
keep it afloat, it &longs;hall al&longs;o re&longs;t without the Artificiall Banks or Ram
parts, but yet not without the Air, becau&longs;e the Air by it &longs;elf makes
Banks &longs;ufficient for a &longs;mall height, to re&longs;i&longs;t the Superfu&longs;ion of the
water: &longs;o that that which in this ca&longs;e &longs;wimmes, is as it were a
Ve&longs;&longs;ell filled with Air, by vertue of which it continueth afloat.
I will, in the la&longs;t place, with an other Experimeut, attempt to
remove all difficulties, if &longs;o be there &longs;hould yet be any doubt le&longs;t in
any one, touching the opperation of this ^{*}Continuity of the Air, with
the thin Plate which &longs;wims, and afterwards put an end to this part of
my di&longs;cour&longs;e.
tiguity,
I &longs;uppo&longs;e my &longs;elf to be que&longs;tioning with &longs;ome of my Oponents.
Whether Figure have any influence upon the encrea&longs;e or diminu
tion of the Re&longs;i&longs;tance in any Weight again&longs;t its being rai&longs;ed in the
Air, and I &longs;uppo&longs;e, that I am to maintain the Affirmative, a&longs;&longs;ert
ing that a Ma&longs;s of Lead, reduced to the Figure of a Ball, &longs;hall be
rai&longs;ed with le&longs;s force, then if the &longs;ame had been made into a thinne
and broad Plate, becau&longs;e that it in this &longs;pacious Figure, hath a great
quantity of Air to penetrate, and in that other, more compacted and
contracted very little: and to demon&longs;trate the truth of &longs;uch my O
pinion, I will hang in a &longs;mall thred fir&longs;t 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 &longs;o much Weight, till that at la&longs;t it brings up the Ball of Lead
out of the water: to do which, &longs;uppo&longs;e a Gravity of thirty Ounces
&longs;ufficeth; I afcerwards reduce the &longs;aid Lead into a flat and thinne
Plate, the which I likewi&longs;e put into the water, &longs;u&longs;pended by three
threds, which hold it parallel to the Surface of the water, and put
ting in the &longs;ame manner, Weights to the other end, till &longs;uch time as
the Place comes to be rai&longs;ed and drawn out of the water: I finde
that thirty &longs;ix ounces will not &longs;uffice to &longs;eperate it from the water,
and rai&longs;e it thorow the Air: and arguing from this Experiment, I af
firm, that I have fully demon&longs;trated the truth of my Propo&longs;ition.
He re my Oponents de&longs;ires me to look down, &longs;hewing me a thing
Plate out of the water, it draws after it another Plate
call it)
Surface of the Plate of Lead, is rai&longs;ed above the Levell of the other
water, more than the thickne&longs;s of the back of a Knife: Then he
goeth to repeat the Experiment with the Ball, and makes me &longs;ee,
that it is but a very &longs;mall quantity of water, which cleaves to its
compacted and contracted Figure: and then he &longs;ubjoynes, that its
no wonder, if in &longs;eperating the thinne and broad Plate from the
water, we meet with much greater Re&longs;i&longs;tance, than in &longs;eperating the
Ball, &longs;ince together with the Plate, we are to rai&longs;e a great quantity of
water, which occurreth not in the Ball: He telleth me moreover,
how that our Que&longs;tion is, whether the Re&longs;i&longs;tance of Elevation be
greater in a dilated Plate of Lead, than in a Ball, and not whether
more re&longs;i&longs;teth a Plate of Lead with a great quantity of water, or a
Ball with a very little water: He &longs;heweth me in the clo&longs;e, that the
putting the Plate and the Ball fir&longs;t into the water, to make proofe
thereby of their Re&longs;i&longs;tance in the Air, is be&longs;ides our ca&longs;e, which
treats of Elivating in the Air, and of things placed in the Air, and
not of the Re&longs;i&longs;tance that is made in the Confines of the Air and
water, and by things which are part in Air and part in water: and
la&longs;tly, 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 rai&longs;ed with
the very &longs;ame Force that rai&longs;eth the Ball. Seeing, and under&longs;tand
ing the&longs;e things, I know not what to do, unle&longs;s to grant my &longs;elf con
vinced, and to thank &longs;uch a Friend, for having made me to &longs;ee that
which I never till then ob&longs;erved: and, being adverti&longs;ed by this &longs;ame
Accident, to tell my Adver&longs;aries, that our Que&longs;tion 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 &longs;peak of &longs;inking, and
not &longs;inking 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 le&longs;s do we treat of the greater
or le&longs;&longs;er Force requi&longs;ite in &longs;eperating this or that Body from the Air;
not omitting to tell them, in the la&longs;t place, that the Air doth re&longs;i&longs;t,
and gravitate downwards in the water, ju&longs;t &longs;o much as the water (if
I may &longs;o &longs;peak) gravitates and re&longs;i&longs;ts upwards in the Air, and that the
&longs;ame force is required to &longs;inke a Bladder under water, that is full of
Air, as to rai&longs;e it in the Air, being full of water, removing the con
&longs;ideration of the weight of that Filme or Skinne, and confidering the
water and the Air only. And it is likewi&longs;e true, that the &longs;ame Force
is required to &longs;ink a Cup or &longs;uch like Ve&longs;&longs;ell under water, whil&longs;t it is
full of Air, as to rai&longs;e it above the Superficies of the water, keeping
con&longs;trained in the &longs;ame manner to follow the Cup which contains it,
and to ri&longs;e above the other water into the Region of the Air, as the
Air is forced to follow the &longs;ame Ve&longs;&longs;ell under the Surface of the wa
ter, till that in this ca&longs;e the water, &longs;urmounting the brimme of the
Cup, breaks in, driving thence the Air, and in that ca&longs;e, the &longs;aid
brimme coming out of the water, and arriving to the Confines of the
Air, the water falls down, and the Air &longs;ub-enters to fill the cavity of
the Cup: upon which en&longs;ues, that he no le&longs;s tran&longs;gre&longs;&longs;es the Arti
cles of the
Air, to &longs;ee if it de &longs;eend to the bottom in water, then he that makes
proof of the Re&longs;i&longs;tance again&longs;t Elevation in Air with a Plate of Lead,
joyned with a like quantity of water.
ment of the op
peration of Fi
gures, in en
crea&longs;ing or le&longs;
&longs;ening of the
Airs Re&longs;i&longs;tance
of Divi&longs;ion.
I have &longs;aid all that I could at pre&longs;ent think of, to maintain the
A&longs;&longs;ertion I have undertook. It remains, that I examine that which
wherein I &longs;hall note two things: the one that it being true as hath
been demon&longs;trated, that Figure hath nothing to do about the moving
or not moving it &longs;elf upwards or downwards, it &longs;eemes that
at his fir&longs;t falling upon this Sp. culation, was of the &longs;ame opinion, as
in my opinion may be collected from the examination of his words.
Tis true, indeed, that in e&longs;&longs;aying afterwards to render a rea&longs;on of
&longs;uch effect, as not having in my conceit hit upon the right, (which
in the &longs;econd place I will examine) it &longs;eems that he is brought to
admit the largene&longs;&longs;e of Figure, to be intere&longs;&longs;ed in this operation.
As to the fir&longs;t particuler, hear the preci&longs;e words of
nion touching
the Operation
of Figure ex
amined.
Lib. 4. Cap.
66.
pa&longs;s, it is not difficult to &longs;ee.
not Figure the
cau&longs;e of Motion
ab&longs;olutely, but
of &longs;wi&longs;t or &longs;low
motion,
Here fir&longs;t I note, that the terms being four, which fall under the
pre&longs;ent con&longs;ideration, namely, Motion, Re&longs;t, Slowly and Swiftly:
And
cluding them from being the Cau&longs;e of ab&longs;olute and &longs;imple Motion,
it &longs;eems nece&longs;&longs;ary, that he exclude them on the other &longs;ide, from being
the Cau&longs;e of Re&longs;t, &longs;o that his meaning is this. Figures are not the
Cau&longs;es of moving or not moving ab&longs;olutely, but of moving quickly
or &longs;lowly: and, here, if any &longs;hould &longs;ay the mind of
exclude Figures from being Cau&longs;es of Motion, but yet not from
being Cau&longs;es of Re&longs;t, &longs;o that the &longs;ence would be to remove from
Figures, there being the Cau&longs;es of moving &longs;imply, but yet not there
being Cau&longs;es of Re&longs;t, I would demand, whether we ought with
manner, the cau&longs;es of Re&longs;t in tho&longs;e Bodies, which otherwi&longs;e would
move, or el&longs;e &longs;ome particular Figures only, as for Example, broad
becau&longs;e every Body hath &longs;ome Figure, which is fal&longs;e: but if &longs;ome
particular Figures only may be in &longs;ome manner a Cau&longs;e of Re&longs;t, as,
for Example, the broad, then the others would be in &longs;ome manner
the Cau&longs;es of Motion: for if from &longs;eeing &longs;ome Bodies of a contracted
Figure move, which after dilated into Plates re&longs;t, may be inferred,
that the Amplitude of Figure hath a part in the Cau&longs;e of that Re&longs;t;
&longs;o from &longs;eeing &longs;uch like Figures re&longs;t, which afterwards contracted
move, it may with the &longs;ame rea&longs;on be affirmed, that the united and
contracted Figure, hath a part in cau&longs;ing Motion, as the remover of
that which impeded it: The which again is directly oppo&longs;ite to what
Be&longs;ides, if
ing Cau&longs;es of not moving in &longs;ome Bodies, which moulded into ano
ther 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, re&longs;t upon the
water, &longs;ince the Cau&longs;e was apparent, namely, the Amplitude of
Figure. Let us conclude, therefore, that the meaning of
in this place is to affirm, that Figures are not the Cau&longs;es of ab&longs;olutely
moving or not moving, but only of moving &longs;wiftly or &longs;lowly: which
we ought the rather to believe, in regard it is indeed a me&longs;t true con
ceipt and opinion. Now the mird of
pearing by con&longs;equence, rather contrary at the fir&longs;t &longs;ight, then fa
vourable to the a&longs;&longs;ertion of the Oponents, it is nece&longs;&longs;ary, that their
Interpretation be not exactly the &longs;ame with that, but &longs;uch, as being
in part under&longs;tood by &longs;ome of them, and in part by others, was &longs;et
down: and it may ea&longs;ily be indeed &longs;o, being an Interpretation
con&longs;onent to the &longs;ence of the more famous Interpretors, which is,
that the Adverbe
be joyned to the Verbe to
the purport of
Cau&longs;es ab&longs;olutely of moving or not moving, but yet are Cau&longs;es
cundum quid, viz
Auxiliary and Concomitant Cau&longs;es: and this Propo&longs;ition is received
and a&longs;&longs;erted as true by
thus writes.
things float, and others &longs;ink, among which the Figures of Bodies hath
the fir&longs;t place,
Text. 42.
Concerning this Propo&longs;ition, I meet with many doubts and diffi
culties, for which me thinks the words of
&longs;uch a con&longs;truction and &longs;ence, and the difficulties are the&longs;e.
Fir&longs;t in the order and di&longs;po&longs;ure of the words of
ticle
pre&longs;umption in my favour, &longs;eeing that the writing and the Text
&longs;aith, Figures are not the Cau&longs;e of moving &longs;imply upwards or
downwards, but of quicker or &longs;lower Motion: and, &longs;aith not,
Figures are not &longs;imply the Cau&longs;es of moving upwards or down
wards, and when the words of a Text receive, tran&longs;po&longs;ed, a &longs;ence
different from that which they found, taken in the order wherein
the Author di&longs;po&longs;eth them, it is not convenient to inverte them.
And who will affirm that
would di&longs;po&longs;e the words in &longs;uch &longs;ort, that they &longs;hould import a
different, nay, a contrary &longs;ence? contrary, I &longs;ay, becau&longs;e under
&longs;tood as they are written; they &longs;ay, that Figures are not the
Cau&longs;es of Motion, but inverted, they &longs;ay, that Figures are the
Cau&longs;es of Motion, &c.
Moreover, if the intent of
are not &longs;imply the Cau&longs;es of moving upwards or downwards, but
only Cau&longs;es
words,
&longs;ubjoining this would have been not only &longs;uperfluous but fal&longs;e, for
that the whole tenour of the Propo&longs;ition would import thus much.
Figures are not the ab&longs;olute Cau&longs;es of moving upwards or down
wards, but are the ab&longs;olute Cau&longs;e of the &longs;wift or &longs;low Motion;
which is not true: becau&longs;e the primary Cau&longs;es of greater or le&longs;&longs;er
Velocity, are by
buted to the greater or le&longs;&longs;er Gravity of Moveables, compared a
mong them&longs;elves, and to the greater or le&longs;&longs;er Re&longs;i&longs;tance of the
are in&longs;erted by
are in that place nominated: and Figure comes afterwards to be
con&longs;idered,
of the Gravity, the which divides either with the Figure, or with
the
Gravity or Levity, would opperate nothing.
Iadde, that if
&longs;ome &longs;ort the Cau&longs;e of moving or not moving, the inqui&longs;ition
which he makes immediately in a doubtfull manner, whence it
comes, that a Plate of Lead flotes, would have been impertinent;
for if but ju&longs;t before he had &longs;aid, that Figure was in a certain &longs;ort
the Cau&longs;e of moving or not moving, he needed not to call in
Que&longs;tion, by what Cau&longs;e the Plate of Lead &longs;wims, and then a&longs;cri
bing the Cau&longs;e to its Figure; and framing a di&longs;cour&longs;e in this manner.
Figure is a Cau&longs;e
doubted, for what Cau&longs;e a thin Plate of Lead goes not to the bottom;
it &longs;hall be an&longs;wered, that that proceeds from its Figure: a di&longs;cour&longs;e
where is the occa&longs;ion of doubting? And who &longs;ees not, that if
had held, that Figure was in &longs;ome &longs;ort a Cau&longs;e of Natation, he
would without the lea&longs;t He&longs;itation have writ; That Figure is in a
certain &longs;ort the Cau&longs;e of Natation, and therefore the Plate of Lead
in re&longs;pect of its large and expatiated Figure &longs;wims; but if we take
the propo&longs;ition of
deed it is true, the en&longs;uing words come in very oppo&longs;itely, as well in
the introduction of &longs;wift and &longs;low, as in the que&longs;tion, which very
pertinently offers it &longs;elf, and would &longs;ay thus much.
Figures are not the Cau&longs;e of moving or not moving &longs;imply up
wards or downwards, but of moving more quickly or &longs;lowly: But if
it be &longs;o, the Cau&longs;e is doubtfull, whence it proceeds, that a Plate of
Lead or of Iron broad and thin doth &longs;wim, &c. And the occa&longs;ion of
the doubt is obvious, becau&longs;e it &longs;eems at the fir&longs;t glance, that the
Figure is the Cau&longs;e of this Natation, &longs;ince the &longs;ame Lead, or a le&longs;s
quantity, but in another Figure, goes to the bottom, and we have
already affirmed, that the Figure hath no &longs;hare in this effect.
La&longs;tly, if the intent of
that Figures, although not ab&longs;olutely, are at lea&longs;t in &longs;ome mea&longs;ure
the Cau&longs;e of moving or not moving: I would have it con&longs;idered,
that he names no le&longs;s the Motion upwards, than the other down
wards: and becau&longs;e 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 Adver&longs;aries &longs;ay) of their Figure, re&longs;t afloat; it is &longs;it that
they &longs;hould produce &longs;ome other Experiment of tho&longs;e Matters, which
by their Nature &longs;wims, but retained by their Figure re&longs;t at the
bottom. But &longs;ince this is impo&longs;&longs;ible to be done, we conclude, that
of &longs;imply moving or not moving.
But though he hath exqui&longs;itely Philo&longs;ophiz'd, in inve&longs;tigating
the &longs;olution of the doubts he propo&longs;eth, yet will I not undertake
to maintain, rather various difficulties, that pre&longs;ent them&longs;elves
unto me, give me occa&longs;ion of &longs;u&longs;pecting that he hath not entirely
di&longs;plaid unto us, the true Cau&longs;e of the pre&longs;ent Conclu&longs;ion: which
difficulties I will propound one by one, ready to change opinion,
when ever I am &longs;hewed, that the Truth is different from what I &longs;ay;
to the confe&longs;&longs;ion whereof I am much more inclinable than to contra
diction.
in affirming a
Needle dimitted
long wayes to
&longs;ink.
that broad Plates of Iron or Lead, float or &longs;wim; he addeth (as
it were &longs;trengthening the occa&longs;ion of doubting) fora&longs;much as other
things, le&longs;s, and le&longs;s grave, be they round or long, as for in&longs;tance a
Now I here doubt, or rather am certain,
that a Needle put lightly upon the water, re&longs;ts afloat, no le&longs;s than the
thin Plates of Iron or Lead. I cannot believe, albeit it hath been
told me, that &longs;ome to defend
Needle demitted not longwayes but endwayes, and with the Point
downwards; neverthele&longs;s, not to leave them &longs;o much as this, though
very weak refuge, and which in my judgement
would refu&longs;e, I &longs;ay it ought to be under&longs;tood, that the Needle mu&longs;t
be demitted, according to the Dimen&longs;ion named by
is the length: becau&longs;e, if any other Dimen&longs;ion than that which is
named, might or ought to be taken, I would &longs;ay, that even the Plates
of Iron and Lead, &longs;ink to the bottom, if they be put into the water
edgewayes and not flatwayes. But becau&longs;e
Figures go not to the bottom, it is to be under&longs;tood, being demitted
broadwayes: and, therefore, when he &longs;aith, long Figures as a
Needle, albeit light, re&longs;t not afloat, it ought to be under&longs;tood of
them when demitted longwayes.
mitted with the Point downwards, is to father upon him a great imper
tinency; for in this place he &longs;aith, that little Particles of Lead or Iron,
if they be round or long as a Needle, do &longs;ink to the bottome; &longs;o that by
his Opinion, a Particle or &longs;mall Grain of Iron cannot &longs;wim: and if he
thus believed, what a great folly would it be to &longs;ubjoyn, that neither
would a Needle demitted endwayes &longs;wim? And what other is &longs;uch a
Needle, but many &longs;uch like Graines accumulated one upon another? It
was too unworthy of &longs;uch a man to &longs;ay, that one &longs;ingle Grain of Iron could
not &longs;wim, and that neither can it &longs;wim, though you put a hundred more
upon it.
La&longs;tly, either
wayes upon the water, would &longs;wim, or he believed that it would
not &longs;wim: If he believed it would not &longs;wim, he might well &longs;peak
as indeed he did; but if he believed and knew that it would &longs;loat,
why, together with the dubious Problem of the Natation of broad
Figure, though of ponderous Matter, hath he not al&longs;o introduced
the Que&longs;tion; whence it proceeds, that even long and &longs;lender Fi
gures, howbeit of Iron or Lead do &longs;wim? And the rather, for that
the occa&longs;ion of doubting &longs;eems greater in long and narrow Figures,
than in broad and thin, as from
is manife&longs;ted.
No le&longs;&longs;er an inconvenience would they fa&longs;ten upon
in his defence &longs;hould &longs;ay, that he means a Needle pretty thick, and
not a &longs;mall one; for take it for granted to be intended of a &longs;mall one
and I will again charge him with having avoided a more wonderfull
and intricate Probleme, and introduced the more facile and le&longs;s
wonderfull.
We &longs;ay freely therefore; that
broad Figure did &longs;wim, but the long and &longs;lender, &longs;uch as a Needle,
not. The which neverthele&longs;s is fal&longs;e, as it is al&longs;o fal&longs;e in round
Bodies: becau&longs;e, as from what hath been predemon&longs;trated, may be ga
thered, little Balls of Lead and Iron, do in like manner &longs;wim.
He propo&longs;eth likewi&longs;e another Conclu&longs;ion, which likewi&longs;e &longs;eems
different from the truth, and it is, That &longs;ome things, by rea&longs;on of
their littlene&longs;s fly in the Air, as the &longs;mall du&longs;t of the Earth, and the
thin leaves of beaten Gold: but in my Opinion, Experience &longs;hews
us, that that happens not only in the Air, but al&longs;o in the water, in
which do de&longs;cend, even tho&longs;e Particles or Atomes of Earth, that
di&longs;tur be it, who&longs;e minuity is &longs;uch, that they are not de&longs;ervable, &longs;ave
only when they are many hundreds together. Therefore, the du&longs;t
of the Earth, and beaten Gold, do not any way &longs;u&longs;tain them&longs;elves
in the Air, but de&longs;cend downwards, and only fly to and again in
the &longs;ame, when &longs;trong Windes rai&longs;e them, or other agitations of the
Air commove them: and this al&longs;o happens in the commotion of the
water, which rai&longs;eth its Sand from the bottom, and makes it muddy.
But
which he makes no mention, nor names other than the lightne&longs;s of
&longs;uch Minutiæ or Atomes, and the Re&longs;i&longs;tance of the Cra&longs;&longs;itudes of the
Water and Air, by which we &longs;ee, that he &longs;peakes of a calme, and
not di&longs;turbed and agitated Air: but in that ca&longs;e, neither Gold nor
Earth, be they never &longs;o &longs;mall, are &longs;u&longs;tained, but &longs;peedily de&longs;cend.
fir meth &longs;ome
Bodies volatile
for their Minu
ity, Text. 42.
ced the Cau&longs;e of
Natation in
certain &longs;iery A
tomes.
He pa&longs;&longs;eth next to confute
would have it, that &longs;ome Fiery Atomes, which continually a&longs;cend
through the water, do &longs;pring upwards, and &longs;u&longs;tain tho&longs;e grave Bodies,
which are very broad, and that the narrow de&longs;cend to the bottom,
for that but a &longs;mall quantity of tho&longs;e Atomes, encounter and re&longs;i&longs;t
them.
De Cœlo
lib.
4. cap.
6.
text. 43.
I &longs;ay,
much more occurre in the Air, as the &longs;ame
gain&longs;t him&longs;elf, but after he had moved the objection, he &longs;lightly re
&longs;olves it, with &longs;aying, that tho&longs;e Corpu&longs;cles which a&longs;cend in the Air,
make not their Here I will not &longs;ay, that the
rea&longs;on alledged by
in my judgement, that it is not wholly confuted by
&longs;aith, that were it true, that the calid a&longs;cending Atomes, &longs;hould
&longs;u&longs;tain Bodies grave, but very broad, it would much more be done
in the Air, than in Water, for that haply in the Opinion of
through the Air, than through the water. And if this be &longs;o, as I veri
ly believe it is, the Objection of
give occa&longs;ion of &longs;u&longs;pecting, that he may po&longs;&longs;ibly be deceived in more
than one particular: Fir&longs;t, becau&longs;e tho&longs;e calid Atomes, (whether
they be Fiery Corpu&longs;cles, or whether they be Exhalations, or in
&longs;hort, whatever other matter they be, that a&longs;cends upwards through
the Air) cannot be believed to mount fa&longs;ter through Air, than
through water: but rather on the contrary, they peradventure move
more impetuou&longs;ly through the water, than through the Air, as hath
been in part demon&longs;trated above. And here I cannot finde the rea
&longs;on, why
Moveable, is more &longs;wift in Air, than in water, hath not adverti&longs;ed
us, that from the contrary Motion, the contrary &longs;hould nece&longs;&longs;arily
follow; to wit, that it is more &longs;wift in the water, than in the Air: for
&longs;ince that the Moveable which de&longs;cendeth, moves &longs;wifter through
the Air, than through the water, if we &longs;hould &longs;uppo&longs;e its Gravity
gradually to dimini&longs;h, it would fir&longs;t become &longs;uch, that de&longs;cending
&longs;wiftly through the Air, it would de&longs;cend but &longs;lowly through the
water: and then again, it might be &longs;uch, that de&longs;cending in the
Air, it &longs;hould a&longs;cend in the water: and being made yet le&longs;s grave,
it &longs;hall a&longs;cend &longs;wiftly through the water, and yet de&longs;cend likewi&longs;e
through the Air: and in &longs;hort, before it can begin to a&longs;cend, though
but &longs;lowly through the Air, it &longs;hall a&longs;cend &longs;wiftly through the water:
how then is it true, that a&longs;cending Moveables move &longs;wifter through
the Air, than through the water?
futed by
&longs;totle,
futation of
mocritus
by the Author.
That which hath made
&longs;wifter in Air, than in water, was fir&longs;t, the having referred the
Cau&longs;es of &longs;low and quick, as well in the Motion of A&longs;cent, as of
De&longs;cent, only to the diver&longs;ity of the Figures of the Moveable, and to
the more or le&longs;s Re&longs;i&longs;tance of the greater or le&longs;&longs;er Cra&longs;&longs;itude, or Ra
rity of the
of the Gravities of the Moveables, and of the
notwith&longs;tanding, is the mo&longs;t principal point in this affair: for if the
augmentation and diminution of the Tardity or Velocity, &longs;hould
have only re&longs;pect to the Den&longs;ity or Rarity of the
that de&longs;cends in Air, would de&longs;cend in water: becau&longs;e whatever
difference is found between the Cra&longs;&longs;itude of the water, and that of
the Air, may well be found between the Velocity of the &longs;ame Move
able in the Air, and &longs;ome other Velocity: and this &longs;hould be its
proper Velocity in the water, which is ab&longs;olutely fal&longs;e. The other
occa&longs;ion is, that he did believe, that like as there is a po&longs;itive and in
trin&longs;ecall Quality, whereby Elementary Bodies have a propen&longs;ion
of moving towards the Centre of the Earth, &longs;o there is another like
flying the Centre, and moving upwards: by Vertue of which in
trin&longs;e call Principle, called by him Levity, the Moveables which have
that &longs;ame Motion more ea&longs;ily penetrate the more &longs;ubtle
than the more den&longs;e: but &longs;uch a Propo&longs;ition appears likewi&longs;e un
certain, as I have above hinted in part, and as with Rea&longs;ons and
Experiments, I could demon&longs;trate, did not the pre&longs;ent Argument im
portune me, or could I di&longs;patch it in few words.
The Objection therefore of
he &longs;aith, that if the Fiery a&longs;cending Atomes &longs;hould &longs;u&longs;tain Bodies
grave, but of a di&longs;tended Figure, it would be more ob&longs;ervable in
the Air than in the water, becau&longs;e &longs;uch Corpu&longs;cles move &longs;wifter in
that, than in this, is not good; yea the contrary would evene, for
that they a&longs;cend more &longs;lowly through the Air: and, be&longs;ides their
moving &longs;lowly, they a&longs;cend, not united together, as in the water,
but di&longs;continue, and, as we &longs;ay, &longs;catter: And, therefore, as
pu&longs;h or
have the &longs;aid grave Bodies to be more ea&longs;ily &longs;u&longs;tained by the &longs;aid
Fiery a&longs;cending Atomes in the Air than in the Water: not ob&longs;erv
ing, that the &longs;aid Bodies are much more grave in that, than in this,
and that &longs;uch 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 ea&longs;ily
&longs;u&longs;tained in the Air, than in the Water?
Let us conclude, therefore, that
better Philo&longs;ophated than
nife&longs;t Experiment that overthrows his Rea&longs;on, and this it is, That
if it were true, that calid a&longs;cending Atomes &longs;hould 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 &longs;uperiour in Gravity to the
water, the which being reduced into a Ball, or other contracted
Figure, &longs;hould go to the bottom, as encountring but few Fiery A
tomes; and which being di&longs;tended afterwards into a dilated and
thin Plate, &longs;hould come to be thru&longs;t upwards by the impul&longs;ion of a
great Multitude of tho&longs;e Corpu&longs;cles, and at la&longs;t carried to the very
Surface of the water: which wee &longs;ee not to happen; Experience
&longs;hewing us, that a Body gra.
hardly, and with very great lea&longs;ure goeth to the bottom, will re&longs;t
there, and will al&longs;o de&longs;cend thither, being reduced into what&longs;oever
other di&longs;tended Figure. We mu&longs;t needs &longs;ay then, either that in the
water, there are no &longs;uch a&longs;cending Fiery Atoms, or if that &longs;uch there
be, that they are not able to rai&longs;e and lift up any Plate of a Matter,
I e&longs;teem the &longs;econd to be true, under&longs;tanding it of water, con&longs;tituted
in its naturall Coldne&longs;s. But if we take a Ve&longs;&longs;el of Gla&longs;s, or Bra&longs;s,
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 &longs;o little, that it goes &longs;lowly to the bottom; I &longs;ay, that putting
&longs;ome burning Coals under the &longs;aid Ve&longs;&longs;el, as &longs;oon as the new Fiery
Atomes &longs;hall have penetrated the &longs;ub&longs;tance of the Ve&longs;&longs;el, they &longs;hall
without doubt, a&longs;cend through that of the water, and thru&longs;ting a
gain&longs;t the fore&longs;aid Solid, they &longs;hall drive it to the Superficies, and
there detain it, as long as the incur&longs;ions of the &longs;aid Corpu&longs;cles &longs;hall
la&longs;t, which cea&longs;ing after the removall of the Fire, the Solid being a
bandoned by its &longs;upporters, &longs;hall return to the bottom.
futed by the
Authour.
But
treat of rai&longs;ing and &longs;u&longs;taining of Plates of Matters, but very little
heavier than the water, or extreamly thin: but in Matters very
grave, and of &longs;ome thickne&longs;s, as Plates of Lead or other Mettal, that
&longs;ame Effect wholly cea&longs;eth: In Te&longs;timony of which, let's ob&longs;erve
that &longs;uch Plates, being rai&longs;ed by the Fiery Atomes, a&longs;cend through
all the depth of the water, and &longs;top at the Confines of the Air, &longs;till
&longs;taying under water: but the Plates of the Opponents &longs;tay not, but
only when they have their upper Superficies dry, nor is there any
means to be u&longs;ed, that when they are within the water, they may
not &longs;ink to the bottom. The cau&longs;e, therefore, of the Supernatation
of the things of which
natation of the things of which we &longs;peak is another. But, returning
to
than
the Objection which he maketh again&longs;t him, and oppo&longs;ed him with
&longs;aying, that if the calid a&longs;cendent Corpu&longs;cles were tho&longs;e that rai&longs;ed
the thin Plate, much more then would &longs;uch a Solid be rai&longs;ed and
born upwards through the Air, it &longs;heweth that the de&longs;ire in
to detect
Philo&longs;ophizing: which de&longs;ire of his he hath di&longs;covered in other oc
ca&longs;ions, and that we may not digre&longs;s too far from this place, in the
Text precedent to this Chapter which we have in hand; where he
attempts to confute the &longs;ame
ing him&longs;elf with names only, had e&longs;&longs;ayed more particularly to de
clare what things Gravity and Levity were; that is, the Cau&longs;es of
de&longs;cending and a&longs;cending, (and had introduced Repletion and Va
cuity) a&longs;cribing this to Fire, by which it moves upwards, and that to
the Earth, by which it de&longs;cends; afterwards attributing to the
Air more of Fire, and to the water more of Earth. But
de&longs;iring a po&longs;itive Cau&longs;e, even of a&longs;cending Motion, and not as
would be in reference to Repletion, argueth again&longs;t
&longs;aith: If it be true, as you &longs;uppo&longs;e, then there &longs;hall be a great Ma&longs;s
of water, which &longs;hall have more of Fire, than a &longs;mall Ma&longs;s of Air,
and a great Ma&longs;s of Air, which &longs;hall have more of Earth than a lit
tle Ma&longs;s of water, whereby it would en&longs;ue, that a great Ma&longs;s of Air,
&longs;hould come more &longs;wiftly downwards, than a little quantity of
water: But that is never in any ca&longs;e &longs;oever: Therefore
di&longs;cour&longs;eth erroneou&longs;ly.
his de&longs;ire of
finding
critus
ror, to exceed
that of di&longs;co
veting Truth.
ibid.
But in my opinion, the Doctrine of
gation overthrown, but if I erre not, the manner of
either concludes not, or if it do conclude any thing, it may with e
quall force be re&longs;tored again&longs;t him&longs;elf.
tains more Earth, than a &longs;mall quantity of water, but yet will deny,
that &longs;uch a Ma&longs;s of Air, &longs;hall go fa&longs;ter downwards than a little water,
and that for many rea&longs;ons. Fir&longs;t, becau&longs;e if the greater quantity
of Earth, contained in the great Ma&longs;s of Air, ought to cau&longs;e a greater
Velocity than a le&longs;s quantity of Earth, contained in a little quantity
of water, it would be nece&longs;&longs;ary, fir&longs;t, that it were true, that a
greater Ma&longs;s of pure Earth, &longs;hould move more &longs;wiftly than a le&longs;s:
But this is fal&longs;e, though
becau&longs;e not the greater ab&longs;olute, but the greater &longs;pecificall Gravity,
is the cau&longs;e of greater Velocity: nor doth a Ball of Wood, weigh
ing ten pounds, de&longs;cend more &longs;wiftly than one weighing ten Ounces,
and that is of the &longs;ame Matter: but indeed a Bullet of Lead of four
Ounces, de&longs;cendeth more &longs;wiftly than a Ball of Wood of twenty
Pounds: becau&longs;e the Lead is more grave Therefore, its not nece&longs;&longs;ary, that a great Ma&longs;s of Air, by rea&longs;on of
the much Earth contained in it, do de&longs;cend more &longs;wiftly than a little
Ma&longs;s of water, but on the contrary, any what&longs;oever Ma&longs;s of water,
&longs;hall move more &longs;wiftly than any other of Air, by rea&longs;on the partici
pation of the terrene parts
Air. Let us note, in the &longs;econd place, how that in multiplying the
Ma&longs;s of the Air, we not only multiply that which is therein of terrene,
but its Fire al&longs;o: whence the Cau&longs;e of a&longs;cending, no le&longs;s encrea&longs;eth,
by vertue of the Fire, than that of de&longs;cending on the account of its
multiplied Earth. It was requi&longs;ite in increa&longs;ing the greatne&longs;s of the
Air, to multiply that which it hath of terrene only, leaving its Fire
in its fir&longs;t &longs;tate, for then the terrene parts of the augmented Air,
overcoming the terrene parts of the &longs;mall quantity of water, it might
with more probability have been pretended, that the great quanti
ty of Air, ought to de&longs;cend with a greater
quantity of water.
Specificall, not
the greater ab
&longs;olute Gravity,
is the Cau&longs;e of
Velocity.
water &longs;hal move
more &longs;wiftly,
than any of Air,
and why.
Therefore, the Fallacy lyes more in the Di&longs;cour&longs;e of
in that of
one &longs;imply grave, and the other &longs;imply 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 &longs;hall
be a great Ma&longs;s of Air, who&longs;e Gravity &longs;hall exceed the Gravity of a
little quantity of water; and therefore &longs;uch a Ma&longs;s of Air &longs;hall de
&longs;cend more &longs;wiftly than that little water: But that is never &longs;een to
occurr: Therefore its not true, that the mean Elements do partici
pate of the one, and the other quality. This argument is fallacious,
no le&longs;s than the other again&longs;t
La&longs;tly,
were true, it would follow, that a great Ma&longs;s of Air &longs;hould move
more &longs;wiftly than a &longs;mall Ma&longs;s of water, and afterwards &longs;ubjoyned,
that that is never &longs;een in any Ca&longs;e: methinks others may become de
&longs;irous to know of him in what place this &longs;hould evene, which he de
duceth again&longs;t
it never falls out &longs;o. To &longs;uppo&longs;e to &longs;ee it in the Element of water,
or in that of the Air is vain, becau&longs;e neither doth water through
water, nor Air through Air move, nor would they ever by any
whatever participation others a&longs;&longs;ign 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 mo&longs;t improper place and
periment:
is none, and were there, nothing would move in it: there remaine
the Region of Fire, but being &longs;o far di&longs;tant from us, what Experi
ment can a&longs;&longs;ure us, or hath a&longs;&longs;ertained
&longs;hould as of a thing mo&longs;t obvious to &longs;ence, affirm what he produ
ceth in confutation of
is moved no &longs;wifter than a little one of water? But I will dwell no
longer upon this matter, whereon I have &longs;poke &longs;ufficiently: but
leaving
goes about to render the true rea&longs;on, how it comes to pa&longs;s, that the
thin Plates of Iron or Lead do &longs;wim on the water; and, moreover,
that Gold it &longs;elf being beaten into thin Leaves, not only &longs;wims in
water, but flyeth too and again in the Air. He &longs;uppo&longs;eth that of
Continualls, &longs;ome are ea&longs;ily divi&longs;ible, others not: and that of the
ea&longs;ily divi&longs;ible, &longs;ome are more &longs;o, and &longs;ome le&longs;s: and the&longs;e he
affirms we &longs;hould e&longs;teem the Cau&longs;es. He addes that that is ea&longs;ily
divi&longs;ible, which is well terminated, and the more the more divi&longs;ible,
and that the Air is more &longs;o, than the water, and the water than the
Earth. And, la&longs;tly, he &longs;uppo&longs;eth that in each kind, the le&longs;&longs;e quan
tity is ea&longs;lyer divided and broken than the greater.
4. c.
6. t. 44.
Here I note, that the Conclu&longs;ions of
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 ea&longs;ily divi&longs;ible than Lead, and Lead than Silver, in
a&longs;much as Wax receives all the terms more ea&longs;iler than Lead, and
Lead than Silver. Its true, moreover, that a little quantity of Sil
ver is ea&longs;lier divided than a great Ma&longs;s: and all the&longs;e Propo&longs;itions
are true, becau&longs;e true it is, that in Silver, Lead and Wax, there
is &longs;imply a Re&longs;i&longs;tance again&longs;t Divi&longs;ion, and where there is the ab&longs;o
lute, there is al&longs;o the re&longs;pective. But if as well in water as in Air,
there be no Renitence again&longs;t &longs;imple Divi&longs;ion, how can we &longs;ay, that
the water is ea&longs;lier divided than the Air? We know not how to ex
tricate our &longs;elves from the Equivocation: whereupon I return to
an&longs;wer, that Re&longs;i&longs;tance of ab&longs;olute Divi&longs;ion is one thing, and Re
&longs;i&longs;tance of Divi&longs;ion made with &longs;uch and &longs;uch Velocity is another.
But to produce Re&longs;t, and to abate the Motion, the Re&longs;i&longs;tance of
ab&longs;olute Divi&longs;ion is nece&longs;&longs;ary; and the Re&longs;i&longs;tance of &longs;peedy Di
vi&longs;ion, cau&longs;eth not Re&longs;t, but &longs;lowne&longs;s of Motion. But that as well
in the Air, as in water, there is no Re&longs;i&longs;tance of &longs;imple Divi&longs;ion, is
manife&longs;t, for that there is not found any Solid Body which divides
not the Air, and al&longs;o the water: and that beaten Gold, or &longs;mall
du&longs;t, are not able to &longs;uperate the Re&longs;i&longs;tance of the Air, is contrary
to that which Experience &longs;hews us, for we &longs;ee Gold and Du&longs;t to go
waving to and again in the Air, and at la&longs;t to de&longs;cend down
wards, and to do the &longs;ame in the water, if it be put therein, and &longs;e
parated from the Air. And, becau&longs;e, as I &longs;ay, neither the water,
nor the Air do re&longs;i&longs;t &longs;imple Divi&longs;ion, it cannot be &longs;aid, that the water
re&longs;i&longs;ts more than the Air. Nor let any object unto me, the Exam
ple of mo&longs;t light Bodies, as a Feather, or a little of the pith of El
der, or water-reed that divides the Air and not the water, and from
this infer, that the Ait is ea&longs;lier divi&longs;ible than the water; for I &longs;ay
unto them, that if they do well ob&longs;erve, they &longs;hall &longs;ee the &longs;ame
Body likewi&longs;e divide the Continuity of the water, and &longs;ubmerge in
part, and in &longs;uch a part, as that &longs;o much water in Ma&longs;s would weigh
as much as the whole Solid. And if they &longs;hal yet per&longs;i&longs;t in their doubt,
that &longs;uch a Solid &longs;inks 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 &longs;hall &longs;ee it divide the water, and pre&longs;ently a&longs;cend with no le&longs;s
celerity, than that with which it divided the Air in de&longs;cending: &longs;o that
to &longs;ay that this Solid a&longs;cends in the Air, but that coming to the water,
it cea&longs;eth its Motion, and therefore the water is more difficult to be
divided, concludes nothing: for I, on the contrary, will propo&longs;e them
a piece of Wood, or of Wax, which ri&longs;eth from the bottom of the
water, and ea&longs;ily divides its Re&longs;i&longs;tance, which afterwards being arri
aswell &longs;ay, that the water is more ea&longs;ier divided than the Air
De
In&longs;ident, humi2. prop.
1.
I will not on this occa&longs;ion forbear to give warning of another fal
lacy of the&longs;e per&longs;ons, who attribute the rea&longs;on of &longs;inking or &longs;wimming
to the greater or le&longs;&longs;e Re&longs;i&longs;tance of the Cra&longs;&longs;itude of the water again&longs;t
Divi&longs;ion, making u&longs;e of the example of an Egg, which in &longs;weet water
goeth to the bottom, but in &longs;alt water &longs;wims; and alledging for the
cau&longs;e thereof, the faint Re&longs;i&longs;tance of fre&longs;h water again&longs;t Divi&longs;ion, and
the &longs;trong Re&longs;i&longs;tance of &longs;alt water But if I mi&longs;take not, from the &longs;ame
Experiment, we may aswell deduce the quite contrary; namely, that
the fre&longs;h water is more den&longs;e, and the &longs;alt more tenuous and &longs;ubtle,
&longs;ince an Egg from the bottom of &longs;alt water &longs;peedily a&longs;cends to the
top, and divides its Re&longs;i&longs;tance, which it cannot do in the fre&longs;h, in who&longs;e
bottom it &longs;tays, being unable to ri&longs;e upwards. Into &longs;uch like perplex
ities, do fal&longs;e Principles Lead men: but he that rightly Philo&longs;ophating,
&longs;hall acknowledge the exce&longs;&longs;es of the Gravities of the Moveables and
of the Mediums, to be the Cau&longs;es of tho&longs;e effects, will &longs;ay, that the
Egg &longs;inks to the bottom in fre&longs;h water, for that it is more grave than
it, and &longs;wimeth in the &longs;alt, for that its le&longs;s grave than it: and &longs;hall
without any ab&longs;urdity, very &longs;olidly e&longs;tabli&longs;h his Conclu&longs;ions.
Therefore the rea&longs;on totally cea&longs;eth, that
Text &longs;aying; The things, therefore, which have great breadth remain
above, becau&longs;e they comprehend much, and that which is greater,
is not ea&longs;ily divided. Such di&longs;cour&longs;ing cea&longs;eth, I &longs;ay, becau&longs;e its not
true, that there is in water or in Air any Re&longs;i&longs;tance of Divi&longs;ion; be
&longs;ides that the Plate of Lead when it &longs;tays, hath already divided and
penetrated the Cra&longs;&longs;itude of the water, and profounded it &longs;elf ten or
twelve times more than its own thickne&longs;s: be&longs;ides that &longs;uch Re&longs;i&longs;tance
of Divi&longs;ion, were it &longs;uppo&longs;ed to be in the water, could not rationally
be affirmed to be more in its &longs;uperiour parts than in the middle, and
lower: but if there were any difference, the inferiour &longs;hould be the
more den&longs;e, &longs;o that the Plate would be no le&longs;s unable to penetrate
the lower, than the &longs;uperiour parts of the water; neverthele&longs;s we &longs;ee
that no &longs;ooner do we wet the &longs;uperious Superficies of the Board or
thin Piece of Wood, but it precipitatly, and without any reten&longs;ion,
de&longs;cends to the bottom.
I believe not after all this, that any (thinking perhaps thereby to
defend
&longs;i&longs;ts more than the little, the &longs;aid Board being put lower de&longs;cendeth,
becau&longs;e there remaineth a le&longs;s Ma&longs;s of water to be divided by it: be
cau&longs;e if after the having &longs;een the &longs;ame Board &longs;wim in four Inches of
water, and al&longs;o after that in the &longs;ame to &longs;ink, he &longs;hall try the &longs;ame
Experiment upon a profundity of ten or twenty fathom water, he
&longs;hall &longs;ee the very &longs;elf &longs;ame effect. And here I will take occa&longs;ion to
that Ship or other what&longs;oever Body, that on the depth of an hundred
or a thou&longs;and fathom, &longs;wims with &longs;ubmerging only &longs;ix fathom of its
own height, [
&longs;wim in the &longs;ame manner in water, that hath but &longs;ix fathom and half
an Inch of depth. Nor do I on the other &longs;ide, think that it can be
&longs;aid, that the &longs;uperiour parts of the water are the more den&longs;e, al
though a mo&longs;t grave Authour hath e&longs;teemed the &longs;uperiour water in
the Sea to be &longs;o, grounding his opinion upon its being more &longs;alt, than
that at the bottom: but I doubt the Experiment, whether hitherto
in taking the water from the bottom, the Ob&longs;ervatour did not light
upon &longs;ome &longs;pring of fre&longs;h water there &longs;pouting up: but we plainly
&longs;ee on the contrary, the fre&longs;h Waters of Rivers to dilate them&longs;elves
for &longs;ome miles beyond their place of meeting with the &longs;alt water of
the Sea, without de&longs;cending in it, or mixing with it, unle&longs;s by the
intervention of &longs;ome commotion or turbulency of the Windes.
in 100 Fathome
water draweth
6 Fathome, &longs;hall
float in 6 Fa
thome and 1/2 an
Inch of depth.
But returning to
nothing to do in this bu&longs;ine&longs;s more or le&longs;s, becau&longs;e the &longs;aid Plate of
Lead, or other Matter, cut into long Slices, &longs;wim neither more nor
le&longs;s; and the &longs;ame &longs;hall the Slices do, being cut anew into little
pieces, becau&longs;e its not the breadth but the thickne&longs;s that operates in
this bu&longs;ine&longs;s. I &longs;ay farther, that in ca&longs;e it were really true, that the
Renitence to Divi&longs;ion were the proper Cau&longs;e of &longs;wimming, the Fi
gures more narrow and &longs;hort, would much better &longs;wim than the more
&longs;pacious and broad, &longs;o that augmenting the breadth of the Figure,
the facility of &longs;upernatation will be demini&longs;hed, and decrea&longs;ing, that
this will encrea&longs;e.
breadth of Fi
gure to be re
&longs;pected in Na
tation.
tence the cau&longs;e
of Natation,
breadth of Fi
gure would
hinder the
&longs;wiming of Bo
dies.
And for declaration of what I &longs;ay, con&longs;ider that when a thin Plate
of Lead de&longs;cends, dividing the water, the Divi&longs;ion and di&longs;continu
ation is made between the parts of the water, invironing the perime
ter or Circumference of the &longs;aid Plate, and according to the big
ne&longs;s greater or le&longs;&longs;er of that circuit, it hath to divide a greater or
le&longs;&longs;er quantity of water, &longs;o that if the circuit, &longs;uppo&longs;e of a Board,
be ten Feet in &longs;inking it flatways, it is to make the &longs;eperation and
divi&longs;ion, and to &longs;o &longs;peak, an inci&longs;&longs;ion upon ten Feet of water; and
likewi&longs;e a le&longs;&longs;er Board that is four Feet in Perimeter, mu&longs;t make an
ince&longs;&longs;ion of four Feet. This granted, he that hath any knowledge
in Geometry, will comprehend, not only that a Board &longs;awed in many
long thin pieces, will much better float than when it was entire, but
that all Figures, the more &longs;hort and narrow they be, &longs;hall &longs;o much the
better &longs;wim. Let the Board ABCD be, for Example, eight
Palmes long, and five broad, its circuit &longs;hall be twenty &longs;ix Palmes;
and &longs;o many mu&longs;t the ince&longs;&longs;ion be, which it &longs;hall make in the water to
de&longs;cend therein: but if we do &longs;aw ir, as &longs;uppo&longs;e into eight little
we mu&longs;t adde to the twenty &longs;ix Palmes of the circuit of the whole
Board, &longs;eventy others; whereupon the eight little pieces &longs;o cut and
&longs;eperated, have to cut ninty &longs;ix Palmes of water. And, if moreover,
we cur each of the &longs;aid pieces into five parts, re
ducing them into Squares, to the circuit of ninty
&longs;ix Palmes, with four cuts of eight Palmes apiece;
we &longs;hall adde al&longs;o &longs;ixty four Palmes, whereupon
the &longs;aid Squares to de&longs;cend in the water, mu&longs;t
divide one hundred and &longs;ixty Palmes of water,
but the Re&longs;i&longs;tance is much greater than that of
twenty &longs;ix; therefore to the le&longs;&longs;er Superficies,
we &longs;hall reduce them, &longs;o much the more ea&longs;ily
will they float: and the &longs;ame will happen in all
other Figures, who&longs;e Superficies are &longs;imular among&longs;t them&longs;elves, but
different in bigne&longs;s: becau&longs;e the &longs;aid Superficies, being either demini
&longs;hed or encrea&longs;ed, always dimini&longs;h or encrea&longs;e their Perimeters in
&longs;ubduple proportion; to wit, the Re&longs;i&longs;tance that they find in pene
trating the water; therefore the little pieces gradually &longs;wim, with more
and more facility as their breadth is le&longs;&longs;ened.
the &longs;ame proportion as the Ba&longs;e encrea&longs;eth or demini&longs;heth, doth the &longs;aid
Solid al&longs;o encrea&longs;e or dimini&longs;h; whereupon the Solid more dimini&longs;hing
than the Circuit, the Cau&longs;e of Submer&longs;ion more dimini&longs;heth than the Cau&longs;e
of Natation: And on the contrary, the Solid more encrea&longs;ing than the
Circuit, the Cau&longs;e of Submer&longs;ion encrea&longs;eth more, that of Natation
le&longs;s.
And this may all be dedueed out of the Doctrine of
gain&longs;t his own Doctrine.
La&longs;tly, to that which we read in the latter part of the Text, that
is to &longs;ay, that we mu&longs;t compare the Gravity of the Moveable with
the Re&longs;i&longs;tance of the Medium again&longs;t Divi&longs;ion, becau&longs;e if the force of
the Gravity exceed the Re&longs;i&longs;tance of the
de&longs;cend, if not it will float. I need not make any other an&longs;wer,
but that which hath been already delivered; namely, that its not
the Re&longs;i&longs;tance of ab&longs;olute Divi&longs;ion, (which neither is in Water nor
Air) but the Gravity of the
Gravity of the Moveables; and if that of the
Moveable &longs;hall not de&longs;cend, nor &longs;o much as make a totall Submer&longs;ion,
but a partiall only: becau&longs;e in the place which it would occupy in
the water, there mu&longs;t not remain a Body that weighs le&longs;s than a like
quantity of water: but if the Moveable be more grave, it &longs;hall de&longs;
cend to the bottom, and po&longs;&longs;e&longs;s a place where it is more conformable
And this
is the only true proper and ab&longs;olute Cau&longs;e of Natation and Sub
mer&longs;ion, &longs;o that nothing el&longs;e hath part therein: and the Board of the
Adver&longs;aries &longs;wimmeth, when it is conjoyned with as much Air,
as, together with it, doth form a Body le&longs;s grave than &longs;o much water
as would fill the place that the &longs;aid Compound occupyes in the
water; but when they &longs;hall demit the &longs;imple Ebony into
the water, according to the Tenour of our Que
&longs;tion, it &longs;hall alwayes go to the bottom,
though it were as thin as a
Paper.
6.
Text 45.