Chapter III: Part 3

But, if it hath already penetrated, and overcome the Continuity of the water, & is of its own nature more grave than the said water, why doth it not proceed in its sinking, but stop and suspend its self within that little dimple or cavitie, which with its ponderosity it hath made in the water? I answer; because that in submerging it self, so far as till its Superficies come to the Levell with that of the water, it loseth a part of its Gravity, and loseth the rest of it as it submergeth & descends beneath the Surface of the water, which maketh Ramperts and Banks round about it, and it sustaines this loss by means of its drawing after it, and carrying along with it, the Air that is above it, and by Contact adherent to it, which Air succeeds to fill the Cavity that is invironed by the Ramperts of water; so that that which in this case descends and is placed in the water, is not only the Board of Ebony or Plate of Iron, but a composition of Ebony and Air, from which resulteth a Solid no longer superiour in Gravity to the water, as was the simple Ebony, or the simple Gold. And, if we exactly consider, what, and how great the Solid is, that in this Experiment enters into the water, and contrasts with the Gravity of the same, it will be found to be all that which we find to be beneath the Surface of the water, the which is an aggregate and Compound of a Board of Ebony, and of almost the like quantity of Air, or a Mass compounded of a Plate of Lead, and ten or twelve times as much Air. But, Gentlemen, you that are my Antagonists in our Question, we require the Identity of Matter, and the alteration only of the Figure; therefore, you must remove that Air, which being conjoyned with the Board, makes it become another Body less grave than the Water, and put only the Ebony into the Water, and you shall certainly see the Board descend to the Bottom; and, if that do not happen, you have got the day. And to seperate the Air from the Ebony[44], there needs no more but only to bath the Superficies of the said Board with the same Water: for the Water being thus interposed between the Board and the Air, the other circumfused Water shall run together without any impediment, and shall receive into it the sole and bare Ebony, as it was to do.

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

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

To this, I answer, first; that treating of the operation of Figure in Bodies put into the Water, none can suppose them to be put into the Water without being wet; nor do I desire more to be done to the Board, then I will give you leave to do to the Ball. Moreover, it is untrue, that the Board sinks by vertue of the new Weight added to it by the Water, in the single and slight bathing of it: for I will put ten or twenty drops of Water upon the same Board, whilst it is sustained upon the water; which drops, because not conjoyned with the other Water circumfused, shall not so encrease the weight of it, as to make it sink: but if the Board being taken out, and all the water wiped off that was added thereto, I should bath all its Superficies with one only very small drop, and put it again upon the water, without doubt it shall sink, the other Water running to cover it, not being retained by the superiour Air; which Air by the interposition of the thin vail of water, that takes away its Contiguity unto the Ebony, shall without Renitence be seperated, nor doth it in the least oppose the succession of the other Water: but rather, to speak better, it shall descend freely; because it shall be all invironed and covered with water, as soon as its superiour Superficies, before vailed with water, doth arrive to the Levell of the universall Surface of the said water. To say, in the next place, that water can encrease the weight of things that are demitted into it, is most false; for water hath no Gravity in water[45], since it descends not: yea, if we would well consider what any immense Mass of water doth put upon a grave Body; that is placed in it, we shall find experimentally, that it, on the contrary, will rather in a great part deminish the weight of it[46], and that we may be able to lift an huge Stone from the Bottom of the water, which the water being removed, we are not able to stir. Nor let them tell me by way of reply, that although the superposed water augment not the Gravity of things that are in it, yet it increaseth the ponderosity of those that swim, and are part in the water and part in the Air, as is seen, for Example, in a Brass Ketle[47], which whilst it is empty of water, and replenished only with Air shall swim, but pouring of Water therein, it shall become so grave, that it shall sink to the Bottom, and that by reason of the new weight added thereto. To this I will return answer, as above, that the Gravity of the Water, contained in the Vessel is not that which sinks it to the Bottom, but the proper Gravity of the Brass, superiour to the Specificall Gravity of the Water: for if the Vessel were less grave than water, the Ocean would not suffice to submerge it[48]. And, give me leave to repeat it again, as the fundamentall and principall point in this Case, that the Air contained in this Vessel before the infusion of the Water, was that which kept it a-float[49], since that there was made of it, and of the Brass, a Composition less grave than an equall quantity of Water: and the place that the Vessel occupyeth in the Water whilst it floats, is not equall to the Brass alone, but to the Brass and to the Air together, which filleth that part of the Vessel that is below the Levell of the water: Moreover, when the Water is infused, the Air is removed, and there is a composition made of Brass and of water, more grave _in specie_ than the simple water, but not by vertue of the water infused, as having greater Specifick Gravity than the other water, but through the proper Gravity of the Brass, and through the alienation of the Air. Now, as he that should say that Brass, that by its nature goes to the Bottom, being formed into the Figure of a Ketle[50], acquireth from that Figure a vertue of lying in the Water without sinking, would say that which is false; because that Brass fashioned into any whatever Figure, goeth always to the Bottom, provided, that that which is put into the water be simple Brass; and it is not the Figure of the Vessel that makes the Brass to float, but it is because that that is not purely Brass which is put into the water, but an aggregate of Brass and of Air: so is it neither more nor less false, that a thin Plate of Brass or of Ebony, swims by vertue of its dilated & broad Figure: for the truth is, that it bares up without submerging, because that that which is put in the water, is not pure Brass or simple Ebony, but an aggregate of Brass and Air, or of Ebony and Air. And, this is not contrary unto my Conclusion, the which, (having many a time seen Vessels of Mettall, and thin pieces of diverse grave Matters float, by vertue of the Air conjoyned with them) did affirm, That Figure was not the Cause of the Natation or Submersion of such Solids as were placed in the water. Nay more, I cannot omit, but must tell my Antagonists, that this new conceit of denying that the Superficies of the Board should be bathed, may beget in a third person an opinion of a poverty of Arguments of defence on their part, since that such bathing was never insisted upon by them in the beginning of our Dispute, and was not questioned in the least, being that the Originall of the discourse arose upon the swiming of Flakes of Ice, wherein it would be simplicity to require that their Superficies might bedry: besides, that whether these pieces of Ice be wet or dry they alwayes swim, and as the Adversaries say, by reason of the Figure.

[45] Water hath no Gravity in Water.

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

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

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

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

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

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

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

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

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

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

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

[53] The force of Contact.

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

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

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

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

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

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

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

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

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

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

[61] How ships are moved in the water.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

PROBL. I.

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

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

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

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

THEOREME. VI.

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

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

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

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

THEOREME VII.

[Sidenote: The heaviest Bodies may swimme.]

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

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

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

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

THEOREME VIII.

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

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

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

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

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

THEOREME. IX.

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

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

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

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

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

LEMMA II.

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

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

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

THEOREME X.

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

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

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

COROLARY I.

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

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

COROLARY II.

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