A Discourse Presented to the Most Serene Don Cosimo II., Great Duke of Tuscany, Concerning the Natation of Bodies Vpon, and Submersion In, t · Galileo Galilei
COROLLARY III.
_One of the above named Solids, when more grave_ in specie _than the water, can never be sustained, by any whatever quantity of it._ For having seen how that the Moment wherewith such a Solid, as grave _in specie_ as the water, contrasts with the Moment of any Mass of water whatsoever, is able to retain it, even to its totall Submersion, without its ever ascending; it remaineth, manifest, that the water is far less able to raise it up, when it exceeds the same _in specie_: so, that though you infuse water till its totall Submersion, it shall still stay at the Bottome, and with such Gravity, and Resistance to Elevation, as is the excess of its Absolute Gravity, above the Absolute Gravity of a Mass equall to it, made of water, or of a Matter _in specie_ equally grave with the water: and, though you should moreover adde never so much water above the Levell of that which equalizeth the Altitude of the Solid, it shall not, for all that, encrease the Pression, or Gravitation, of the parts circumfused about the said Solid, by which greater pression, it might come to be repulsed; because, the Resistance is not made, but only by those parts of the water, which at the Motion of the said Solid do also move, and these are those only, which are comprehended by the two Superficies equidistant to the Horizon, and their parallels, that comprehend the Altitude of the Solid immerged in the water.
I conceive, I have by this time sufficiently declared and opened the way to the contemplation of the true, intrinsecall and proper Causes of diverse Motions, and of the Rest of many Solid Bodies in diverse _Mediums_, and particularly in the water, shewing how all in effect, depend on the mutuall excesses of the Gravity of the Moveables and of the _Mediums_: and, that which did highly import, removing the Objection, which peradventure would have begotten much doubting, and scruple in some, about the verity of my Conclusion, namely, how that notwithstanding, that the excess of the Gravity of the water, above the Gravity of the Solid, demitted into it, be the cause of its floating and rising from the Bottom to the Surface, yet a quantity of water, that weighs not ten pounds, can raise a Solid that weighs above 100 pounds: in that we have demonstrated, That it sufficeth, that such difference be found between the Specificall Gravities of the _Mediums_ and Moveables, let the particular and absolute Gravities be what they will: insomuch, that a Solid, provided that it be Specifically less grave than the water, although its absolute weight were 1000 pounds, yet may it be born up and elevated by ten pounds of water, and less: and on the contrary, another Solid, so that it be Specifically more grave than the water, though in absolute Gravity it were not above a pound, yet all the water in the Sea, cannot raise it from the Bottom, or float it.
This sufficeth me, for my present occasion, to have, by the above declared Examples, discovered and demonstrated, without extending such matters farther, and, as I might have done, into a long Treatise: yea, but that there was a necessity of resolving the above proposed doubt, I should have contented my self with that only, which is demonstrated by _Archimedes_, in his first _Book De Insidentibus humido_[14]: where in generall termes he infers and confirms the same Conclusions, namely, that Solids (_a_) less grave than water, swim or float upon it, the (_b_) more grave go to the Bottom, and the (_c_) equally grave rest indifferently in all places, yea, though they should be wholly under water. [14] _Of Natation_ (a) _Lib. 1, Prop. 4._ (b) _Id. Lib. 1. Prop. 3._ (c) _Id. Lib. 1. Prop. 3._ [Sidenote: The Authors defence of _Archimedes_ his Doctrine, against the oppositions of _Buonamico_.]
But, because that this Doctrine of Archimedes, perused, transcribed and examined by _Signor Francesco Buonamico_, in his _fifth Book of Motion, Chap. 29_, and afterwards by him confuted, might by the Authority of so renowned, and famous a Philosopher, be rendered dubious, and suspected of falsity; I have judged it necessary to defend it, if I am able so to do, and to clear _Archimedes_, from those censures, with which he appeareth to be charged. _Buonamico_ rejecteth the Doctrine of _Archimedes_, first[15], as not consentaneous with the Opinion of _Aristotle_, adding, that it was a strange thing to him, that the Water should exceed the Earth in Gravity[16], seeing on the contrary, that the Gravity of water, increaseth, by means of the participation of Earth. And he subjoyns presently after[17], that he was not satisfied with the Reasons of _Archimedes_, as not being able with that Doctrine, to assign the cause whence it comes, that a Boat and a Vessell, which otherwise, floats above the water, doth sink to the Bottom, if once it be filled with water; that by reason of the equality of Gravity, between the water within it, and the other water without, it should stay a top; but yet, nevertheless, we see it to go to the Bottom. [15] His first Objection against the Doctrine of _Archimedes_.
Perhaps this Deduction of _Buonamico_, is founded upon that which he citeth of the Vessel, which swims as long as its voyd of water, but once full it sinks to the Bottom, and understanding it of a Vessel of Earth, he infers against _Archimedes_ thus: Thou sayst that the Solids which swim, are less grave than water: this Vessell swimmeth: therefore, this Vessell is lesse grave than water. If this be the Illation. I easily answer, granting that this Vessell is lesse grave than water, and denying the other consequence, namely, that Earth is less Grave than Water. The Vessel that swims occupieth in the water, not only a place equall to the Mass of the Earth, of which it is formed; but equall to the Earth and to the Air together, contained in its concavity. And, if such a Mass compounded of Earth and Air, shall be less grave than such another quantity of water, it shall swim, and shall accord with the Doctrine of _Archimedes_; but if, again, removing the Air, the Vessell shall be filled with water, so that the Solid put in the water, be nothing but Earth, nor occupieth other place, than that which is only possest by Earth, it shall then go to the Bottom, by reason that the Earth is heavier than the water: and this corresponds well with the meaning of _Archimedes_.
See the same effect illustrated, with such another Experiment, In pressing a Viall Glass to the Bottom of the water, when it is full of Air, it will meet with great resistance, because it is not the Glass alone, that is pressed under water, but together with the Glass a great Mass of Air, and such, that if you should take as much water, as the Mass of the Glass, and of the Air contained in it, you would have a weight much greater than that of the Viall, and of its Air: and, therefore, it will not submerge without great violence: but if we demit only the Glass into the water, which shall be when you shall fill the Glass with water, then shall the Glass descend to the Bottom; as superiour in Gravity to the water. [21] The Authors answer to the first Objection. [22] The Authors answer to the second Objection. Returning, therefore, to our first purpose; I say, that Earth is more grave than water, and that therefore, a Solid of Earth goeth to the bottom of it; but one may possibly make a composition of Earth and Air, which shall be less grave than a like Mass of Water; and this shall swim: and yet both this and the other experiment shall very well accord with the Doctrine of _Archimedes_. But because that in my judgment it hath nothing of difficulty in it, I will not positively affirme that _Signor Buonamico_, would by such a discourse object unto _Archimedes_ the absurdity of inferring by his doctrine, that Earth was less grave than Water, though I know not how to conceive what other accident he could have induced thence.
Perhaps such a Probleme (in my judgement false) was read by _Signor Buonamico_ in some other Author, by whom peradventure it was attributed as a singular propertie, of some particular Water, and so comes now to be used with a double errour in confutation of _Archimedes_, since he saith no such thing, nor by him that did say it was it meant of the common Element of Water. [Sidenote: The Authors answer to the third Objection.] The third difficulty in the doctrine of _Archimedes_ was, that he could not render a reason whence it arose, that a piece of Wood, and a Vessell of Wood, which otherwise floats, goeth to the bottom, if filled with Water. _Signor Buonamico_ hath supposed that a Vessell of Wood, and of Wood that by nature swims, as before is said, goes to the bottom, if it be filled with water; of which he in the following Chapter, which is the 30 of the fifth Book copiously discourseth: but I (speaking alwayes without diminution of his singular Learning) dare in defence of _Archimedes_ deny this experiment, being certain that a piece of Wood which by its nature sinks not in Water, shall not sinke though it be turned and converted into the forme of any Vessell whatsoever, and then filled with Water: and he that would readily see the Experiment in some other tractable Matter, and that is easily reduced into several Figures, may take pure Wax, and making it first into a Ball or other solid Figure, let him adde to it so much Lead as shall just carry it to the bottome, so that being a graine less it could not be able to sinke it, and making it afterwards into the forme of a Dish, and filling it with Water, he shall finde that without the said Lead it shall not sinke, and that with the Lead it shall descend with much slowness: & in short he shall satisfie himself, that the Water included makes no alteration.
I say not all this while, but that its possible of Wood to make Barkes, which being filled with water, sinke; but that proceeds not through its Gravity, encreased by the Water, but rather from the Nailes and other Iron Workes, so that it no longer hath a Body less grave than Water, but one mixt of Iron and Wood, more grave than a like Masse of Water. Therefore let _Signor Buonamico_ desist from desiring a reason of an effect, that is not in nature: yea if the sinking of the Woodden Vessell when its full of Water, may call in question the Doctrine of _Archimedes_, which he would not have you to follow, is on the contrary consonant and agreeable to the Doctrine of the Peripateticks, since it aptly assignes a reason why such a Vessell must, when its full of Water, descend to the bottom; converting the Argument the other way, we may with safety say that the Doctrine of _Archimedes_ is true, since it aptly agreeth with true experiments, and question the other, whose Deductions are fastened upon erroneouss Conclusions.
As for the other point hinted in this same Instance, where it seemes that _Benonamico_ understands the same not only of a piece of wood, shaped in the forme of a Vessell, but also of massie Wood, which filled, _scilicet_, as I believe, he would say, soaked and steeped in Water, goes finally to the bottom that happens in some porose Woods, which, while their Porosity is replenished with Air, or other Matter less grave than Water, are Masses specificially less grave than the said Water, like as is that Viall of Glass whilest it is full of Air: but when, such light Matter departing, there succeedeth Water into the same Porosities and Cavities, there results a compound of Water and Glass more grave than a like Mass of Water: but the excess of its Gravity consists in the Matter of the Glass, and not in the Water, which cannot be graver than it self: so that which remaines of the Wood, the Air of its Cavities departing, if it shall be more grave _in specie_ than Water, fil but its Porosities with Water, and you shall have a Compost of Water and of Wood more grave than Water, but not by vertue of the Water received into and imbibed by the Porosities, but of that Matter of the Wood which remains when the Air is departed: and being such it shall, according to the Doctrine of _Archimedes_, goe to the bottom, like as before, according to the same Doctrine it did swim.
So that the most that can be gathered from the Demonstration of _Archimedes_ is, that like as the excess of the Gravity of the Moveable above the Gravity of the Water, is the Cause that it descends therein, so the excess of the Gravity of the water above that of the Moveable, is a sufficient Cause why it descends not, but rather betakes it self to swim: not enquiring whether of moving upwards there is, or is not any other Cause contrary to Gravity: nor doth _Archimedes_ discourse less properly than if one should say: If the South Winde shall assault the Barke with greater _Impetus_ than is the violence with which the Streame of the River carries it towards the South, the motion of it shall be towards the North: but if the _Impetus_ of the Water shall overcome that of the Winde, its motion shall be towards the South. The discourse is excellent and would be unworthily contradicted by such as should oppose it, saying: Thou mis-alledgest as Cause of the motion of the Bark towards the South, the _Impetus_ of the Stream of the Water above that of the South Winde; mis-alledgest I say, for it is the Force of the North Winde opposite to the South, that is able to drive the Bark towards the South.
Such an Objection would be superfluous, because he which alledgeth for Cause of the Motion the Stream of the Water, denies not but that the Winde opposite to the South may do the same, but only affirmeth that the force of the Water prevailing over the South Wind, the Bark shall move towards the South: and saith no more than is true. And just thus when _Archimedes_ saith, that the Gravity of the Water prevailing over that by which the moveable descends to the Bottom, such moveable shall be raised from the Bottom to the Surface alledgeth a very true Cause of such an Accident, nor doth he affirm or deny that there is, or is not, a vertue contrary to Gravity, called by some Levity, that hath also a power of moving some Matters upwards. Let therefore the Weapons of _Signor Buonamico_ be directed against _Plato_[25], and other _Ancients_, who totally denying _Levity_, and taking all Bodies to be grave, say that the Motion upwards is made, not from an intrinsecal Principle of the Moveable, but only by the Impulse of the _Medium_; and let _Archimedes_ and his Doctrine escape him, since he hath given him no Cause of quarelling with him.
But if this Apologie, produced in defence of _Archimedes_, should seem to some insufficient to free him from the Objections and Arguments, produced by _Aristotle_ against _Plato_, and the other _Ancients_, as if they did also fight against _Archimedes_, alledging the Impulse of the Water as the Cause of the swimming of some Bodies less grave than it[26], I would not question, but that I should be able to maintaine the Doctrine of _Plato_ and those others to be most true, who absolutely deny Levity, and affirm no other Intrinsecal Principle of Motion to be in Elementary Bodies save only that towards the Centre of the Earth[27], nor no other Cause of moving upwards, speaking of that which hath the resemblance of natural Motion, but only the repulse of the _Medium_, fluid, and exceeding the Gravity of the Moveable[28]: and as to the Reasons of _Aristotle_ on the contrary, I believe that I could be able fully to answer them, and I would assay to do it, if it were absolutely necessary to the present Matter, or were it not too long a Digression for this short Treatise.
I will only say, that if there were in some of our Ellementary Bodies an Intrinsecall Principle and Naturall Inclination to shun the Centre of the Earth, and to move towards the Concave of the Moon, such Bodies, without doubt, would more swiftly ascend through those _Mediums_ that least oppose the Velocity of the Moveable, and these are the more tenuous and subtle; as is, for example, the Air in comparison of the Water, we daily proving that we can with farre more expeditious Velocity move a Hand or a Board to and again in one than in the other[29]: nevertheless, we never could finde any Body, that did not ascend much more swiftly in the water than in the Air. Yea of Bodies which we see continually to ascend in the Water, there is none that having arrived to the confines of the Air, do not wholly lose their Motion[30]; even the Air it self, which rising with great Celerity through the Water, being once come to its Region it loseth all [23] Of Natation, Lib. 1. Prop. 7. [24] Of Natation, Lib. 1. Prop. 4. [25] _Plato_ denyeth Positive Levity. [26] The Authors defence of the doctrine of _Plato_ and the _Ancients_, who absolutely deny Levity: [27] According to _Plato_ there is no Principle of the Motion, of descent in Naturall Bodies, save that to the Centre.
To that which for a finall conclusion, _Signor Buonamico_ produceth of going about to reduce the descending or not descending, to the easie and uneasie Division of the _Medium_, and to the predominancy of the Elements: I answer, as to the first part, that that cannot in any manner be admitted as a Cause, being that in none of the Fluid _Mediums_, as the Air, the Water, and other Liquids, there is any Resistance against Division[32], but all by every the least Force, are divided and penetrated, as I will anon demonstrate: so, that of such Resistance of Division there can be no Act, since it self is not in being. As to the other part, I say, that the predominancy of the Elements in Moveables[33], is to be considered, as far as to the excesse or defect of Gravity, in relation to the _Medium_: for in that Action, the Elements operate not, but only, so far as they are grave or light: therefore, to say that the Wood of the Firre sinks not, because Air predominateth in it, is no more than to say, because it is less grave than the Water.
Yea, even the immediate Cause, is its being less grave than the Water[34]: and it being under the predominancy of the Air, is the Cause of its less Gravity: Therefore, he that alledgeth the predominancy of the Element for a Cause, brings the Cause of the Cause, and not the neerest and immediate Cause. Now, who knows not that the true Cause is the immediate, and not the mediate[35]? Moreover, he that alledgeth Gravity, brings a Cause most perspicuous to Sence[36]: The cause we may very easily assertain our selves; whether Ebony, for example, and Firre, be more or less grave than water: but whether Earth or Air predominates in them, who shall make that manifest? Certainly, no Experiment can better do it than to observe whether they swim or sink. So, that he who knows, not whether such a Solid swims, unless when he knows that Air predominates in it, knows not whether it swim, unless he sees it swim, for then he knows that it swims, when he knows that it is Air that predominates, but knows not that Air hath the predominance, unless he sees it swim: therefore, he knows not if it swims, till such time as he hath seen it swim. [32] Water & other fluids void of Resistance against Division. [33] _T_he predominancy of Elements in Moveables to be considered only in relation to their excess or defect of Gravity in reference to the _Medium_.
Text from Project Gutenberg, public domain in the United States.