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Galileo Galilei Quarta pagina |
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The same, therefore, happens in this operation as in the steelyard, in which a weight of two pounds balances another of 200, if that shall move in the same time a space 100 times greater than this: which happens when one arm of the beam is 100 times as long as the other. Let them give up their erroneous opinion, then, who believe that a ship is better, and easier floated, in a great abundance of water than in a lesser quantity (this was believed by Aristotle in his Problems, Sect. 23, Prob. 2) it being true on the contrary that a ship may as well float in ten ton of water as in an Ocean. But, following our subject, I say that by what has been demonstrated so far, we may understand how it is that if one of the above named solids is heavier in specific weight than water, then it can never be raised, by any quantity of water whatsoever. For having seen how the moment of a solid equally heavy in specific weight with water compares with the moment of any amount of water, we see that this water can retain the solid up to its complete immersion without raising it; and it is clear that the water is even less able to lift it up if it is heavier in specific weight; so that if we pour in water up to its complete immersion, it will still rest at the bottom, and with so much weight and resistance to being lifted as is the excess of its absolute weight over the absolute weight of a volume equal to it made of water or of a material equal in specific weight to water. And though you should add an enormous quantity of water above the level of that which equals the height of the solid, it would not, for all that, increase the pressure or weight of the parts surrounding the said solid in such a way that it would be expelled; for the comparison is only made for those parts of the water which move when the solid moves, and these are just those which are between the two surfaces, equidistant and parallel to each other and to the horizon, which bound the solid immersed in the water.
It seems to me I have by this time sufficiently declared and opened the way to the contemplation of the true, intrinsical and proper causes of diverse motions and of rest in many solid bodies in diverse mediums, and particularly in water, showing how all, in effect, depend on the mutual excesses of the gravity of the moveables and of the mediums. And that very important point, removing the objection which perhaps would have given rise to doubt and scruple in some about the truth of my conclusion, namely how that notwithstanding that the excess of the weight of the water above the weight of the solid is 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 suffices that there be a difference between the specific weights of the medium and the moveable, whatever may be the absolute weights. And in fact a solid, provided that it be less in specific weight than water, although its absolute weight were 1000 pounds, yet it may be born up and elevated by ten pounds of water, and less: and on the contrary, another solid, provided that it be heavier in specific weight than water, even if were in absolute weight no more than one pound, yet all the water in the Sea cannot raise it from the bottom or float it. This suffices, for my present occasion, to have declared the above examples, without extending matters further, as I might have done, into a long Treatise. And indeed, if there had not been that necessity of resolving the above doubt, I would have contented myself with what is demonstrated by Archimedes in his first Book on Bodies in Water: where in general terms he infers and confirms the same conclusions, namely that solids (a) less in specific weight than water float upon it, and (b) heavier in specific weight go to the bottom, and (c) equal in specific weight rest indifferently in all places, though they should be wholly under water.
But because this doctrine of Archimedes, perused, transcribed, and examined by Signor Francesco Buonamico in his fifth Book of Motion, Chap. 29, and afterwards confuted by him, 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 to do so, and to clear Archimedes from those censures with which he appears to be charged. Buonamico rejects the doctrine of Archimedes, first, as not agreeing with the opinion of Aristotle, adding that it was a strange thing to him, that water should exceed earth in gravity, seeing on the contrary that the gravity of water increases by the addition of earth. And he adds presently that he was not satisfied with the reasons of Archimedes, as he could not by means of that doctrine assign a cause that a boat or a vessel, which otherwise floats on the water, sinks to the bottom if once filled with water; that by reason of the equality of gravity of the water within it and the other water without, it should stay on top, but yet, nevertheless we see it go to the bottom. He further adds that Aristotle had clearly confuted the Ancients who said that light Bodies moved upwards driven by the impulse of the heavier Ambient: which if it were so, it should seem to follow necessarily that all natural Bodies are by nature heavy, and none light: for the same would happen to Fire and Air if put at the bottom of the water. And however that may be, Aristotle grants an Impulse to the Elements, by which the Earth is reduced into a spherical figure, yet nevertheless, in his judgment it is not such that it sends all the elements toward the center, to which (as he somewhat obscurely continues to say) the water principally moves, if in the interim it does not meet with something that resists it, and by its Gravity, thrusts it out of its place: in which case, if it cannot directly, yet at least as well as it can, it tends to the center: but it happens that light bodies, by such Impulse ascend upward: but this property they have by nature, as also that other property of floating. . He concludes finally, that he concurs with Archimedes in his conclusions, but not in the causes, which he would refer to the relative difficulty of separation of the Medium, and to the predominance of the Elements, so that when the Moveable overcomes the power of the Medium, as for example, Lead does in water, it shall move through it, and otherwise not. This is all that I have been able to collect that is produced against Archimedes by Signor Buonamico, who has not observed very well the principles and suppositions of Archimedes; which yet must be false if the Doctrine which depends on them be false. But he is content to allege some inconveniences in it, and some repugnances to the doctrine and opinion of Aristotle. In answer to which objections, I say, first, that the doctrine of Archimedes being simply different from that of Aristotle ought not to move anyone to suspect it, there being no cause why the Authority of this should be preferred to the Authority of the other. But where the decrees of Nature are indifferently exposed to the intellectual eyes of everyone, the Authority of the one and the other loses all right to persuade, the absolute power residing in Reason. Therefore I pass to that which he alleges in the second place, as an absurd consequence of the Doctrine of Archimedes, namely that water should be heavier than earth. But I really cannot find that Archimedes ever said such a thing, or that it can be rationally deduced from his conclusions: and if that were proved to me, I verily believe I should renounce his Doctrine as most erroneous. Perhaps this deduction of Buonamico is founded upon that which he cites of the vessel which floats as long as it is empty of water, but once full it sinks to the bottom. And understanding it as an earthen vessel, he infers against Archimedes thus: you say that solids which float are less heavy in specific weight than water; this vessel floats, therefore this vessel is less heavy in specific weight than water. If this is his meaning, I easily answer, and grant that this vessel is less heavy in specific weight than water, but denying the other consequence, namely that earth is less heavy in specific weight than water. The vessel that floats occupies in the water not just a place equal to the volume of the earth of which it is formed, but equal to the earth and to the air together, contained in its concavity. And if such a volume compounded of earth and air should be less heavy than an equal volume of water, it shall float, and it shall agree with the Doctrine of Archimedes. But if, again, removing the air, the vessel shall be filled with water, so that the solid put in the water be nothing but earth, nor occupy any other place than that which is occupied by earth, it shall then go to the bottom, by reason that earth is heavier than water. And this corresponds well with the meaning of Archimedes. See the same effect illustrated with such another experiment: in pushing down a vial glass to the bottom of the water when it is full of air, you will meet with great resistance, because it is not the glass alone that is pushed under water, but a great volume of air together with the glass, such that if you should take as much water as the volume of the glass and of the air contained in it, you would have a weight much greater than that of the vial, and of its air. And therefore it will not submerge without great violence. But if we put only the glass into the water, which shall be when you fill the glass with water, then the glass shall descend to the bottom, as greater in specific weight than water. Returning, therefore, to our first purpose, I say that earth is heavier than water and that therfore a solid of earth goes to the bottom; but one may make a composition of earth and air which shall be less heavy than the same volume of water, and this shall float: and yet both this and the other experiment agree very well with the doctrine of Archimedes. And since there is, in my judgment, no difficulty here, I will not positively affirm that Signor Buonamico would by such an argument attribute the absurdity to Archimedes that his doctrine makes earth less heavy than water, although I do not know what else his meaning could be.
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Forse tal problema... |
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And for ampler confirmation and clearer explication of this, let us consider the present figure, (which, if I am not mistaken, may serve to reveal the error of some who practice mechanics, and who sometimes attempt impossible enterprises on false foundations) in which the large vessel EIDF is connected to a very narrow pipe ICAB. Suppose water is infused to the level LGH; it will rest in this postion, not without the wonder of some, who will not immediately understand how it can be that the heavy load of the great volume of water GD, pressing down, does not lift and push out the small quantity of the other water contained in the pipe CL. But such wonder will cease if we begin to imagine the water GD to be lowered just as far as QO, and we consider what will have happened to the water CL. This, in order to make place for the other water which has descended from the level GH to the level QO, must of necessity in the same time have gone up from the level L to AB, and the ascent LB will be so much greater than the descent GQ, as the breadth of the vessel GD is greater than the that of the pipe LC, which, in sum, is as much as the amount of water GD is greater than the amount LC. But since the moment of the velocity of motion in one moveable compensates that of the weight in the other, what wonder will there be if the very rapid ascent of the little water CL should resist the very slow descent of the greater GD?
