The Essential Galileo (18 page)

1.
Cf. Galilei 1890–1909, 3: 53–96; translated by Edward Stafford Carlos (1880) from Galileo Galilei,
Sidereus nuncius
(Venice, 1610); revised by Finoc-chiaro for this volume. For the historical background, see the Introduction, especially §0.3 and §0.4.

2.
Sextus Propertius (c. 50 B.C.–c. 16 B.C.),
Elegies
, iii, 2, 17–22.

3.
The original Latin text speaks of
diameters
. In correcting it to
radii
, I follow Stafford Carlos (1880, 8), but modernize his archaic
semi-diameters
. Favaro (1890–1909, 3: 59.18) also makes the correction. For more information, see Van Helden 1989, 35 n. 19; Pantin 1992, 56–57 n. 5; Battistini 1993, 187 n. 59.

4.
Here and in the rest of
The Sidereal Messenger
I have changed Stafford Carlos' translation of
perspicillum
as
telescope
because the latter word was not coined until 1611. For more information, see Rosen 1947; Van Helden 1989, 112; Pantin 1992, 50 n. 5; Battistini 1993, 190 n. 72.

5.
Here I retain Stafford Carlos' (1880, 9) translation of the original Latin
excogitati
. This rendition was also adopted by Drake (1983, 18). Other correct translations are
contrived
(Van Helden 1989, 36) and
conceived
, or
conçue
in French (Pantin 1992, 7). The more important point is to note that Galileo is
not
claiming to have been the
first
to
invent
the instrument, and his account in the next paragraph makes this disclaimer explicit.

CHAPTER 2

From
Discourse on Bodies in Water
(1612)
¹

[§2.1 Shape vs. Density in Floating and Sinking]
²

[87] Let us not then despise those hints, though very feeble, which after some contemplation reason offers to our intelligence. Let us agree to be taught by Archimedes that any solid body will sink to the bottom in water when its specific gravity is greater than that of water; that it will of necessity float if its specific gravity is less; and that it will rest indifferently in any place under water if its specific gravity is perfectly equal to that of water.

These things explained and proved, I come to consider what the diversity of shape of a given body has to do with its motion and rest. Again, I affirm the following.

The diversity of shapes given to this or that solid cannot in any way be the cause of its absolute sinking or floating.
³
Thus, for example, if a solid shaped into a spherical figure sinks or floats in water, I say that when shaped into any other figure the same solid shall sink or float in the same water; nor can its motion be prevented or taken away by the width or any other feature of the shape.

[88] The width of the shape may indeed retard its velocity of ascent or descent, and more and more according as the said shape is reduced to a greater width and thinness; but I hold it to be impossible that it may be reduced to such a form that the same material be wholly hindered from moving in the same water. In this I have met with great opponents who produce some experiments, especially the following: they take a thin board of ebony and a ball of the same wood, and show that the ball in water descends to the bottom, and that if the board is placed lightly upon the water then it is not submerged but floats. They hold, and with the authority of Aristotle they confirm their opinion, that the cause of that floating is the width of the shape, unable by its small weight to pierce and penetrate the resistance of the coarseness of the water, which resistance is readily overcome by the other, spherical shape.

This is the principal point in the present controversy, in which I shall strive to make clear that I am on the right side.

Let us begin by trying to investigate, with the help of exquisite experiments, that the shape does not really alter one bit the descent or ascent of the same solid. We have already demonstrated that the greater or lesser gravity of the solid in relation to the gravity of the medium is the cause of descent or ascent. Whenever we want to test what effect the diversity of shape produces, it is necessary to make the experiment with materials whose gravities do not vary; for if we make use of materials that are different in their specific gravities and we meet with various effects of ascending and descending, we shall always be left uncertain whether in reality that diversity derives solely from the shape or else from the gravity as well. We may remedy this by using only one material that is malleable and easily reducible into every sort of shape. Moreover, it will be an excellent expedient to take a kind of material very similar to water in specific gravity; for such a material, as far as it pertains to the gravity, is indifferent to ascending or descending, and so we easily observe the least difference that derives from the diversity of shape.

Now, to do this, wax is most apt. Besides its incapacity to receiving any sensible alteration from its imbibing water, wax is pliant and [89] the same piece is easily reducible into all shapes. And since its specific gravity is less than that of water by a very inconsiderable amount, by mixing it with some lead filings it is reduced to a gravity exactly equal to that of water.

Let us prepare this material. For example, let us make a ball of wax as big as an orange, or bigger, and let us make it so heavy as to sink to the bottom, but so slightly that by taking out only one grain of lead it returns to the top and by adding one back it sinks to the bottom.

Let the same wax afterwards be made into a very broad and thin flake or slab. Then, returning to make the same experiment, you shall see that when placed at the bottom with the grain of lead it shall rest there; that with the grain removed it shall ascend to the surface; and that when the lead is added again it shall dive to the bottom. This same effect shall happen always for all sorts of shapes, regular as well as irregular; nor shall you ever find any that will float without the removal of the grain of lead, or sink to the bottom unless it be added. In short, about the going or not going to the bottom, you shall discover no difference, although indeed you shall about its quickness or slowness; for the wider and more extended shapes move more slowly in diving to the bottom as well as in rising to the top, and the more contracted and compact shapes more speedily. Now I do not know what may be expected from the diversity of shapes, if the most different ones do not produce as much as does a very small grain of lead, when added or removed.

I think I hear some of my adversaries raise a doubt about the experiment I produced. First, they offer to my consideration that the shape, simply as shape and separate from matter, does not have any effect but requires to be conjoined with matter; and furthermore, not with every material, but only with that wherewith it may be able to execute the desired operation. For we see it verified by experience that the acute and sharp angle is more apt to cut than the obtuse, yet always provided that both the one and the other be joined with a material apt to cut, such as, for example, with steel. Therefore, a knife with a fine and sharp edge cuts bread or wood with much ease, which it will not do if the edge be blunt and thick; but he that will instead of steel take wax and mould it into a knife undoubtedly shall never know the effects of sharp and blunt edges, because neither of them [90] will cut, the wax being unable by reason of its flexibility to overcome the hardness of the wood and bread. Now, applying similar reasoning to our purpose, they say that the difference of shape will not show different effects regarding flotation and submersion when conjoined with any kind of matter, but only with those materials that by their gravity are apt to overcome the resistance of the viscosity of the water; thus, he that would choose cork or other light wood (unable through its lightness to overcome the resistance of the coarseness of the water) and from that material should form solids of various shapes, would in vain seek to find out what effect shape has in flotation and submersion; for all would float, and that not through any property of this or that shape, but through the weakness of the material, lacking sufficient gravity as is requisite to overcome and conquer the density and coarseness of the water. It is necessary, therefore, if we would see the effect produced by the diversity of shape, first to choose a material apt by its nature to penetrate the coarseness of the water. For this purpose, they have chosen a material that, being readily reduced into spherical shape, goes to the bottom; and it is ebony, of which they afterwards make a small board or splinter, as thin as a leaf, and show that, when placed upon the surface of the water, it rests there without descending to the bottom; on the other hand, having made a ball of the same wood no smaller than a hazelnut, they show that this does not float but descends. From this experiment they think they may frankly conclude that the width of the shape in the flat board is the cause of its not descending to the bottom, inasmuch as a ball of the same material, no different from the board in anything but in shape, sinks to the bottom in the same water. The reasoning and the experiment have really so much probability and likelihood that it would be no wonder if many should be persuaded by a certain initial appearance and yield credit to them; nevertheless, I think I can show that they are not free from fallacy.

Let us begin, therefore, to examine one by one all the particulars that have been produced. I say that shapes, as simple shapes, not only do not operate in natural things, but neither are they ever separated from corporeal substance. Nor have I ever alleged them to be stripped of sensible matter. Likewise, I also freely admit that in our endeavoring [91] to examine the diversity of effects dependent upon the variety of shapes, it is necessary to apply them to materials that do not obstruct the various operations of those various shapes. And I admit and grant that I should be wrong if I would experiment about the influence of acuteness of edge with a knife of wax, applying it to cut an oak, because there is no acuteness in wax able to cut that very hard wood. But yet such an experiment with this knife would not be besides the purpose to cut curdled milk, or other very yielding matter; indeed, with such materials, wax is more appropriate than steel for finding the diversity depending upon more or less acute angles because that milk is indifferently cut with a razor and with a knife that has a blunt edge. It is necessary, therefore, that regard be had not only to the hardness, solidity, or gravity of the bodies which under diverse shapes are to divide and penetrate some materials, but also to the resistance of the materials to be divided and penetrated. But in making the experiment concerning our controversy, I have chosen a material that penetrates the resistance of the water and in all shapes descends to the bottom, and so my adversaries can charge me with no defect; indeed, I have proposed a more excellent method than they have, inasmuch as I have removed all other causes of descending or not descending to the bottom and retained the sole and pure variety of shapes, demonstrating that the same shapes all descend with the addition of only one grain in weight and return to the surface and float with its removal. It is not true, therefore (returning to the example introduced by them), that I have gone about experimenting on the efficacy of acuteness in cutting with materials unable to cut; rather, I have done so with materials proportioned to our occasion, since they are subjected to no other variation than that alone which depends on the shape being more or less acute.

But let us proceed a little farther. Let us note how needlessly indeed they introduce the consideration that the material chosen ought to be proportionate for the making of our experiment; using the example of cutting, they declare that just as acuteness is insufficient to cut unless it exists in a material that is hard and apt to overcome the resistance of the wood or other material which we intend to cut, so the aptitude of descending or not descending in water can and should be recognized only in those [92] materials that are able to overcome the resistance and conquer the coarseness of the water. On this I say that it is indeed necessary to make a distinction and selection of this or that material on which to impress the shapes for cutting and penetrating this or that body based on whether the solidity or hardness of the said bodies shall be greater or less; but then I add that such distinction, selection, and caution would be superfluous and unprofitable if the body to be cut or penetrated should have no resistance or should not oppose at all the cutting or penetration; and if the knife were to be used in cutting mist or smoke, one of paper would be equally serviceable with one of Damascus steel. And so, because water does not have any resistance against penetration by any solid body, all choice of material is superfluous and needless; and the selection, which I said above to have been well made, of a material similar in gravity to water was made not because it was necessary for overcoming the coarseness of the water, but for overcoming its gravity with which only it resists the sinking of solid bodies; and for what concerns the resistance of the coarseness, if we carefully consider it, we shall find that all solid bodies (those that sink as well as those that float) are indifferently accommodated and apt to bring us to the knowledge of the truth in question. Nor will I be frightened off from believing these conclusions by the experiments that may be produced against me: that although many pieces of wood, cork, clay, and even thin plates of all sorts of stone and metal are ready by means of their natural gravity to move towards the center of the earth, nevertheless they are impotent (either because of their shape, as my adversaries think, or because of their lightness) to break and penetrate the continuity of the parts of the water and to disturb its union, and they continue to float without submerging in the least. Nor, on the other hand, shall I be moved by the authority of Aristotle, who in more than one place affirms the contrary of what experience shows me.

I return, therefore, to assert that there is no solid of such lightness, or of such shape, that being put upon the water does not divide and penetrate its coarseness. Indeed, if anyone with a more perspicacious eye shall return to observe more exactly the thin boards of wood, he shall see part of their thickness to be under water; their lower surface is not the only part that kisses the upper surface of the water, as those of necessity must have believed who have said that such [93] boards are not submerged, not being able to divide the tenacity of the parts of the water. Moreover, he shall see that when the very thin slivers of ebony, stone, or metal float, they not only have broken the continuity of the water, but also are under its surface with all their thickness, and more and more according as the materials are heavier; thus, a thin plate of lead shall be lower than the surface of the surrounding water by at least twelve times the thickness of the plate, and gold shall dive below the level of the water almost twenty times the thickness of the plate, as I shall show anon.

But let us proceed to evince that the water yields and allows itself to be penetrated by the lightest solid; and thereby demonstrate how, even from materials that are not submerged, we may come to know that shape accomplishes nothing about the going or not going to the bottom, given that the water allows itself to be penetrated equally by every shape.

Make a cone or pyramid of cypress, fir, or other wood of similar weight, or of pure wax, and let its height be very great, namely a palm or more; and put it into the water with the base downwards. First, you shall see that it will penetrate the water and will not be at all impeded by the width of the base; nor yet shall it sink all under water, but the part near the vertex shall lie above it. From this it is manifest that such a solid does not refrain from sinking out of an inability to divide the continuity of the water, having already divided it with its broad part, which in the opinion of my adversaries is less apt to make the division. The pyramid being thus positioned, note what part of it is submerged. Then, turn it with the vertex downwards. You shall see that it shall not penetrate the water more than before. Instead, if you observe how far it shall sink, every person expert in geometry may measure that those parts that remain out of the water are equal to a hair in the one as well as in the other experiment. Thus, one may manifestly conclude that the acute shape, which seemed most apt to part and penetrate the water, does not part or penetrate it any more than the large and spacious.