Galileo Galilei
Intorno alle cose che stanno in su l'acqua o che in quella si muovono

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The third difficulty in the doctrine of Archimedes was that he could not understand why a piece of wood or a vessel of wood, which otherwise floats, goes to the bottom if filled with water. Signor Buonamico supposed that a vessel of wood, and of wood that by nature floats, goes to the bottom if it is filled with water; of which he has much to say in the following Chapter, which is the 30th of his fifth Book: but I (speaking always without diminution of his singular learning) dare to deny this experiment in defense of Archimedes, being certain that piece of Wood which by its nature does not sink in Water, shall not sink if it be turned and converted into the form of any vessel whatsoever, and then filled with Water: and he that would readily see the Experiment in some other tractable substance that is easily made into different shapes may take pure Wax, and making it first into a ball or other solid figure, let him add to it as much lead as shall just carry it to the bottom, so that being a grain less it would not sink, and making it afterwards into the form of a dish, and filling it with Water, he shall find that without the said lead it shall not sink, and that with the lead, it shall descend with much slowness; and in short he shall satisfy himself that the Water included makes no alteration. I do not mean to say that one cannot make boats of wood which sink, being filled with water; but that it is not through being made heavier by the water, but rather from the nails and other iron parts, so that it is no longer a body less heavy than water, but one of mixed iron and wood, heavier than the same volume of water. Therefore let Signor Buonamico leave off asking for the reason of an effect that does not exist in nature. In fact, if the sinking of a wooden vessel full of water calls into question the doctrine of Archimedes, which he would not have you follow, and is consistent with the doctrine of the Peripatetics, since they have an apt reason why such a vessel must, when it is full of water, descend to the bottom, then, turning the argument around, we may with safety say that the doctrine of Archimedes is true, since it aptly agrees with true experiments, and question the other, which leads to erroneous conclusions. As for the other point hinted in this same instance, where it seems that Buonamico understands the same not only of a piece of wood shaped in the form of a vessel, but also of a block of wood, which filled, if you like, or as I believe he would say, soaked and steeped in water, finally goes to the bottom, that happens in some porous woods which, while their porosity is filled with air, or other matter less heavy than water, are volumes less heavy than the said water, like that vial of glass while it is full of air. But when the air departs and is replaced by water in those porosities and cavities, there results a compound of water and glass heavier than the same volume of water; but the excess of its weight consists in the glass, not in the water, which cannot be heavier than itself; so that which remains of the wood when the air departs from its cavities, if it is heavier in specific weight than water, then just fill its porosities with water, and you shall have a compound of water and wood heavier than water, but not because of the water which comes into the porosities, but because of the matter of the wood which remains when the air departs; and being heavier, it must go to the bottom according to the doctrine of Archimedes, just as before, according to the same doctrine, it floated.

As to his fourth objection, namely that Aristotle has already proved wrong those Ancients who denied positive and absolute Levity, and considering all bodies heavy, said that what moved upward was driven up by the surrounding air, that therefore the doctrine of Archimedes, as an adherent of such an opinion, was also proved wrong, I answer first, that Signor Buonamico has, in my judgment, imposed upon Archimedes, and he has deduced more from his words than he ever intended by them, or may be deduced from his propositions, seeing that Archimedes neither denies nor admits positive Levity, nor does he so much as mention it. So much the less ought Buonamico to infer that he denied Levity might be the cause and principle of the ascension of Fire, and other light bodies, having only demonstrated that solid bodies heavier than water descend in it, according to the excess of their weight above the weight of water, demonstrating likewise how the less heavy ascend in the same water, according to the excess of the specific weight of water above their specific weight. Thus the most that can be gathered from the demonstration of Archimedes is that, just as the excess of weight of the moveable above the weight of water is the cause that it sinks, so the excess of the weight of the water above the weight of the moveable is a sufficient cause why it does not sink, but rather floats; not inquiring whether there may not also be any other cause of its moving upwards, contrary to gravity. Nor does Archimedes argue any less properly than one who should say: If the south wind drives the boat north with greater impetus than the stream of the river which carries it south, then its motion shall be towards the north. But if the impetus of the river is greater than the wind, it shall be towards the south. The argument is excellent and would be unworthily contradicted by some one who might oppose it saying: You erroneously say it is the river which takes the boat south, its impetus being greater than that of the wind, for it is the force of the North Wind, opposite to the South, that is able to drive the boat towards the south. Such an objection would be superfluous because the one who alleges the river as the cause of motion does not deny the North Wind could do the same, but only says that since the force of the river is greater than that of the south wind, the boat shall move towards the south, and he says no more than is true. And this is just what Archimedes says, that the weight of the water being greater than the weight with which the moveable sinks, this moveable will be lifted from the bottom to the surface, and he gives a very true cause why this should happen, nor does he affirm or deny that there is or is not a virtue contrary to gravity, called Levity by some, that also has the power of moving some substances upwards.

Therefore let the weapons of Signor Buonamico be directed against Plato, and other Ancients, who, totally denying Levity, and taking all bodies to be heavy, say that motion upwards is made, not from an intrinsic principle of the moveable, but only by the impulse of the medium; and let Archimedes and his doctrine escape him, since he has given him no cause of quarreling with him. But if this apology in defense of Archimedes should seem insufficient to some to free him from the objections and arguments produced by Aristotle against Plato, and the other Ancients, as if they also fought against Archimedes, alleging the impulse of the water as the cause of the floating of some bodies less heavy than it, I do not doubt that I could maintain the doctrine of Plato and those others to be most true, who absolutely deny Levity, and affirm no other intrinsical principle of motion to be in elementary bodies save that towards the center of the earth, nor no other cause of moving upwards (speaking of that which resembles natural motion) but only the impulse of the fluid medium of greater specific weight than the moveable: and as to the reasons of Aristotle to the contrary, I believe that I could fully answer them, and I would attempt 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 elementary bodies an Intrinsic Principle and Natural Inclination to shun the center of the earth, and to move towards the concave of the moon, such bodies, without doubt, would ascend more swiftly through those mediums that oppose their velocity the least, and these are the more tenuous and subtle mediums, as is air in comparison with water, as we see every day that we can more easily move a hand or a board to and fro in one than in the other: nevertheless we could never find any Body that did not ascend much more swiftly in water than in air. Indeed, of Bodies which we see continually ascending in water, there is none that, having arrived to the confines of the air, do not wholly lose their motion; even the Air itself, which rises with great swiftness through the water, having come to its own region, loses all motion. And although experience shows that successively lighter Bodies ascend swiftly through water, it cannot be doubted that Fiery Exhalations ascend more swiftly through water than air does: which air is seen by experience to ascend more swiftly through water than Fiery Exhalations through air. Therefore, we must of necessity conclude that the said Exhalations ascend more swiftly through water than through air. And consequently they are moved by the impulse of the ambient medium, and not by an intrinsic Principle that is in them of avoiding the center of the earth, to which other heavy bodies tend.

To that last point of Signor Buonamico, referring sinking or not sinking to the ease of division of the medium, and to the predominance of the elements, I answer, as to the first part, that this cannot be in any manner admitted as a Cause, since in none of the fluid mediums, as Air, Water, and other Liquids, is there any resistance against division, but they are all divided and penetrated by every force, however small, as I will demonstrate below. Thus there can be no effect of this Resistance to Division, since it does not exist. As to the other part, I say that the predominance of the elements in moveables is to be considered only as it affects the excess or deficiency of the specific weight in relation to that of the medium: since for this purpose the elements operate only insofar as they are heavy or light. Therefore to say that the wood of the fir tree does not sink because Air predominates in it is no more than to say that it is less heavy than water. Indeed, the immediate Cause is its being less heavy than water: and air predominating in it is the Cause of its being less heavy. Therefore whoever says the predominance of the element is a Cause, brings the Cause of a Cause, and not the nearest and immediate Cause. Now who does not know that the true Cause is the immediate Cause, and not the mediate? Also, whoever calls heaviness the Cause brings a Cause which is most accessible to sense. This cause we may very easily ascertain ourselves, whether Ebony, for example, and Fir, are more or less heavy than water: but whether Earth or Air predominates in them, who can know that? Certainly no experiment can do it better than to observe whether they sink or float. So that he who does not know whether such a solid floats unless he knows that Air predominates in it, does not know whether it will float until he sees it float, for then he knows that it floats and that Air predominates in it. But he does not know that Air predominates unless he sees it float. Therefore he does not know if it will float until such time as he sees it float.

Let us then not despise those hints, obscure though they are, which Reason, after some contemplation, offers to our intelligence, and let us be content to be taught by Archimedes, that any Body shall sink in water when it shall be heavier in specific weight than water, and that if it shall be less heavy, it shall necessarily float, and that it will rest indifferently in any place in the water if its specific weight be exactly the same as water.

These things explained and proved, I come to consider what effect the shape of the moveable may have on these motions and rests. And I proceed to affirm that:

The diversity of shapes given to this or that Solid cannot in any way be a Cause of its absolute sinking or floating; so that if a Solid being formed, for example, into a sphere, sinks or floats in water, I say that being formed into any other shape, that same shape will sink or float in the same water. Nor can such motion be changed or taken away by any change of the shape.

Broadening of the shape may indeed retard its velocity, whether of ascent or descent, and more and more according as the shape is made broader and thinner: but that it may be so broadened as to be completely hindered from moving in the same water I hold to be impossible. In this I have met with some naysayers, who producing some experiments, and in particular a thin board of ebony and a ball of the same wood, and showing how the ball sank to the bottom in water, and the board being put lightly on the water did not sink, but rested, have held, and, with the authority of Aristotle, confirmed themselves in their opinions, that the Cause of that Rest was the breadth of the shape, unable by its small weight to pierce and penetrate the resistance of the water's materiality, which resistance is readily overcome by the other spherical shape.

This is the Principal point in the present Question, in which I persuade myself I am on the right side.

As we begin to investigate, therefore, with sensitive experiments, how it is that shape really does not in the least influence whether a solid ascends or descends, and having already demonstrated that the cause of ascent or descent is the specific weight of the solid in relation to the specific weight of the medium, and wanting to test what the effect of the shape is, it is necessary to use substances of fixed, constant specific weight. For if we use materials with different specific weights, then, meeting with various effects in ascending and descending, we shall always be left unsatisfied whether these various effects derive from the various shapes, or from the various specific weights also. We may remedy this by taking only one substance, which is tractable and easily molded into any shape. Moreover, it will be an excellent expedient to take a substance with the same specific weight as water. For such a substance, as far as its specific weight is concerned, is indifferent either to ascend or descend, so that we may immediately notice the least difference that derives from its shape.

Now to do this, wax is most apt, for besides having no propensity to change its properties by absorption of water, it is ductile, or pliant, and the same piece is easily molded into any shape. And being in specific weight only slightly less heavy than water, one can bring it to a specific weight exactly equal to water by mixing into it some filings of lead.

Having prepared such a substance, for example in a ball as big as an orange or bigger, and having made it so heavy as to sink to the bottom, but so light that it would return to the top if even one grain of lead were removed, and so that it would sink to the bottom if that one grain were returned to it, let this same wax be made into a very broad and thin flake or cake. Then, returning to the same experiment, you shall see that if it is put on the bottom, with the grain of lead, it will rest there, and if that grain is removed, it will ascend right to the surface, and if you add the grain it will again dive to the bottom. And the same effect will always happen with any shape, regular or irregular; nor shall you ever find any shape that will float without removal of the grain of lead, or sink unless it be added. And in short, in going to the bottom or not going, you will find no difference, although you will find considerable difference in quickness or slowness of the descent; for the more expanded and distended shapes move more slowly, both in diving to the bottom and in rising to the top; and the more contracted and compact shapes more speedily. Now I do not know what effect may be expected from change of shape if the most extreme difference in shape has less effect than the smallest grain of lead, added or removed.

I think I hear some of my adversaries raise a doubt about my experiment. And first, they offer to my consideration that pure shape, apart from substance, has no effect, but must be conjoined with substance, and not with just any substance, but with such a substance as enables shape to have its effect. As, for example, we see it verified by experience that an acute and sharp angle is better for cutting than an obtuse angle, yet always provided that it be joined with a substance apt to cut, say steel. Therefore a knife with a fine and sharp edge cuts bread or wood with ease, which it will not do if the edge is blunt and thick. But anyone who takes wax instead of steel, and molds it into a knife, will undoubtedly never know the effects of sharp and blunt edges, because neither of them will cut, the wax being unable, by reason of its softness, to overcome the hardness of the wood and the bread. And, therefore, applying the same argument to our experiment, they say that difference of shape will show different effects in sinking and floating, but not with just any substance, but only with those substances which, by their weight, are able to overcome the viscosity of the water. So that if someone would select cork, or another light wood, which is unable by its levity to penetrate the materiality of the water, and would make various shapes of it, he would seek in vain to find the effect of shape on floating or sinking, because they all would float, and not because of any property of this or that shape, but because of the weakness of the substance, lacking the weight to overcome and penetrate the denseness and materiality of the water. It is necessary, therefore, if we want to see the effect of the shape, first to choose a substance which is apt by its nature to penetrate the materiality of the water. And for this effect they have chosen an appropriate substance, namely ebony, which in spherical shape goes readily to the bottom. And having afterwards made a small board or chip, as thin as a lath, they illustrated how this, being put on the surface, rests there without sinking. And on the other hand a ball of this same wood the size of a hazel nut does not float but sinks. From this experiment they think they may frankly conclude that the breadth of the shape in the flat lath or chip is the cause of its not sinking to the bottom, since a ball of the same substance, not different from the chip in anything but shape, sinks in the same water to the bottom. The argument and the experiment have, really, so much plausibility and likelihood of truth that it would be no wonder if many should give credit to it, persuaded by superficial observation. Nevertheless, I think I can show that it is not free from fallacy.

Beginning, therefore, to examine, one by one, all the particulars that have been produced, I say that pure shape, separate from substance, not only has no effect in natural processes, but it is not even to be found, and I have never alleged that shape can be separated from substance. And I also freely admit that in our experiments to determine the effect of shape it is necessary to use substances which do not obscure the effects of shape. And I admit and grant that I should do very badly if I experimented on the influence of sharp edges using a knife of wax, trying to cut oak, because there exists no sharpness which would enable wax to cut that very hard wood. Yet such an experiment with this knife would not be beside the purpose to cut curdled milk, or other very yielding matter. Indeed, for these substances, wax is a better choice than steel to test whether cutting depends on the angle's being more or less acute, for curdled milk is cut equally well with a razor or with a dull knife. It is necessary, therefore, to consider not only the hardness, solidity, or weight of the bodies, which with their various shapes are to divide and penetrate other substances, but one must also consider, on the other side, the resistance of the substances that are to be divided and penetrated. But since I have chosen for this experiment in our contest a substance which penetrates the resistance of water, and which in every shape descends to the bottom, my adversaries cannot charge me with any defect; indeed, I have given a better experiment than theirs, inasmuch as I have removed all other causes of descending or not descending to the bottom, and retained only the shape, demonstrating that all shapes descend with only the alteration of a grain in weight: which grain being removed, they return to float. It is not true, therefore, considering again their objection, that I have gone about experimenting on the effect of sharpness in cutting with a substance unable to cut, but rather with a substance most appropriate to the question, since it is changed in no way other than shape.

But let us proceed a little further and observe that this question of selecting the substance, which they say must be appropriate to the experiment, was introduced needlessly, when they declared, using the example of cutting, that just as sharpness is insufficient to cut unless when it is in a substance hard enough to overcome the resistance of wood or other matter which we intend to cut, just so the aptitude of substances to descend or not descend in water can only be known for those substances that are able to overcome the resistance and penetrate the materiality of the water. To this I say that to make distinctions, and to select this substance rather than that to make shapes for cutting or penetrating this or that Body, according as the solidity or hardness of the said Body is greater or less, is very necessary. But I would add that such distinctions, selections and caution would be superfluous and unnecesary if the Body to be cut or penetrated should have no resistance at all to withstand cutting or penetration. And if the knife were to be used in cutting a Mist or Smoke, one of paper would be just as good as one of Damascus steel. And since water has no resistance to the penetration of any solid body, all choice of substance is superfluous and needless, and the selection I approved above, of a substance having the same specific weight as water, was not because it was necessary to overcome the materiality of water, but rather to overcome its weight, which is the only way it resists the sinking of solid bodies. And as far as the resistance of the materiality is concerned, if we consider it carefully, we shall find that all solid bodies, whether they float or sink, are equally appropriate and apt to bring us to the knowledge of the truth in question. Nor will I be frightened out of the truth of these conclusions by the experiments which may be produced against me, of many several woods, corks, galls, and also thin slates and plates of all sorts of stone and metal, which by their natural gravity should move towards the center of the earth, but which nevertheless either because of their shape (as the adversaries think) or through levity, being unable to break and penetrate the continuity of the parts of the water and to divide its oneness, continue to float without sinking in the least: nor on the other side shall the authority of Aristotle move me, who in more than one place declares the contrary to what experience shows me.

I return therefore to assert that there is no solid of such levity, nor of such shape, that being put upon the water it does not divide and penetrate its materiality. Indeed, if anyone with a more perceptive eye comes to observe more exactly the thin boards of wood, he will see that some of their thickness is under the water, and not just that the lower surface kisses the upper surface of the water, as they must necessarily have believed who said that these boards do not sink because they cannot divide the tenacity of the parts of the water. And moreover he shall see that thin slivers of ebony, stone, or metal, when they float, do not just break the continuity of the water, but are underneath the surface of it with their entire thickness, and the more so as the substance is heavier. Thus a thin plate of lead will be lower than the surface of the surrounding water by at least twelve times the thickness of the plate, and gold will be lower than the level of the water by almost twenty times the thickness of the plate, as I shall set out below. But let us proceed to demonstrate that the water yields, and allows itself to be penetrated, by even the lightest body; and thereby to prove that we may learn that shape plays no role in floating and sinking, even by means of substances which do not sink, seeing that water allows itself to be penetrated by all shapes alike.

Make a cone or pyramid of cypress, fir, or other wood of similar specific weight, or of pure wax, and let its height be rather large, say the size of your hand or more, and put it into the water with the base downwards. First, you will see that it will penetrate the water, not at all impeded by the largeness of the base, nor will it sink completely under water, but the part towards the point will remain above it. From this it is clear, first, that the solid does not refuse to sink because it is unable to divide the continuity of the water, having already divided it with its broad part, that in the opinion of my adversaries is less able to make this division. The pyramid being thus fixed, note what part of it is submerged, and then turn it over with the point downwards, and you shall see that it sinks no more than before, and if you observe how far it sinks, every person expert in geometry may measure that those parts which remain out of water, both in the one and in the other experiment, are equal to a hair. And from this he may clearly conclude that the sharp pointed shape, which seemed more able to part and penetrate the water, does not part or penetrate it more than a large, broad shape. And if someone wants an easier experiment, let him take two cylinders of the same substance, one long and thin, and the other short and broad, and let him put them into the water, not lengthwise, but straight up and down. He will see, if he diligently measures the parts of the one and of the other, that in each of them the submerged part has exactly the same proportion to the part out of the water, and that no greater part is submerged of the long, thin one than of the other, which is broader, although this one rests on a very large surface of water, and the other on a very small surface. Therefore the difference in the shape causes neither greater nor lesser ability to part and peneterate the continuity of the water, and consequently cannot be the cause of sinking or floating. He may likewise discover that various shapes have no effect on the rising of bodies from the bottom to the surface of the water by an experiment with wax. He should mix lead filings into it so that it is considerably heavier than water, and then let him make it into a ball and thrust it to the bottom of the water, and fasten to it as much cork, or other light matter, as will just suffice to raise it and draw it towards the surface. For afterwards, changing the same wax into a thin cake or any other shape, that same cork will raise it in the same manner to a hair.

This does not silence my antagonists, who say that all my arguments to this point are irrelevant to them, and that it is enough for them that they have demonstrated in one particular case, using a substance and shape that they choose, namely a chip and a ball of ebony, that one put in the water sinks and the other stays on the top and floats. And since the substance is the same, and the two bodies differ only in shape, they affirm that they have clearly demonstrated and manifestly proved what they undertook, and lastly that they have achieved their purpose. Nevertheless, I believe and think I can demonstrate that that same experiment proves nothing against my conclusion.

And first, it is false that the ball sinks and the chip does not, for the chip will also sink if you do to both shapes what is required by the words of our Question: that is if you put them both into the water.

Le parole furon tali...