[92] On 19 February at forty minutes, only two stars were in view, west of Jupiter, rather large, and arranged in the same straight line with Jupiter, in the direction of the ecliptic:
The nearer star was seven minutes from Jupiter and six minutes from the star further to the west.
On 20 February the sky was cloudy.
On 21 February at one hour and thirty minutes, three stars, rather small, were in view, placed thus:
The star to the east was two minutes from Jupiter, which was three minutes from the next on the west; and this one was seven minutes from the star further on the west. They were exactly in the same straight line parallel to the ecliptic.
On 25 February at one hour and thirty minutes (for on the three previous nights the sky was overcast), three stars appeared:
Two were on the east, four minutes apart, the same as the distance of the nearer star from Jupiter; on the west there was one star at a distance of two minutes from Jupiter. They were exactly in the same straight line in the direction of the ecliptic.
On 26 February at thirty minutes, only a pair of stars was present:
One was on the east, ten minutes from Jupiter; the other was on the west, at a distance of six minutes. The eastern star was slightly smaller than the western. But at the fifth hour, three stars were visible:
On 27 February at one hour and four minutes, the stars appeared in the following configuration:
Besides the two already mentioned, a third star was in view, on the west, near Jupiter, very small; it had previously been hidden behind Jupiter, and it was now one minute from the planet. The star on the east was seen to be further off than before, being at a distance of eleven minutes from Jupiter. On this night, for the first time, I decided to observe the progression of Jupiter and its adjacent planets along the zodiac, by reference to some fixed star; for there was a fixed star in view, [93] eastwards of Jupiter, at a distance of eleven minutes from the eastern planet, and a little to the south, in the following manner:
The star furthest to the east was ten minutes from Jupiter; the next was near Jupiter, being at a distance of thirty seconds from the planet; the next star was on the western side, at a distance of two minutes and thirty seconds from Jupiter; and the star further to the west was one minute from this. The two stars near to Jupiter appeared small, especially the one on the east; the outer stars were very bright, particularly the one on the west. They made a straight line in the direction of the ecliptic exactly. The progression of these planets towards the east was plainly seen by reference to the aforesaid fixed star, for Jupiter and its attendant planets were nearer to it, as may be seen in the figure. At the fifth hour, the star on the east near to Jupiter was one minute from the planet.
On 28 February at the first hour, only two stars were visible, one on the east at a distance of nine minutes from Jupiter, and another on the west at a distance of two minutes. They were both rather bright, and in the same straight line with Jupiter. Moreover, a straight line drawn from the fixed star perpendicular to this straight line fell upon the planet on the east, as in this figure:
But at the fifth hour a third star was seen at a distance of two minutes from Jupiter on the east, in the position shown in the figure:
On 1 March at forty minutes, four stars, all on the east, were seen. The one nearest to Jupiter was two minutes from it; the next was one minute from this; the third was twenty seconds from the second, and was brighter than the others; [94] and the one still further to the east was four minutes from the third, and was smaller than the others. They formed a line that was almost straight; only the third from Jupiter was slightly above the line. The fixed star formed an equilateral triangle with Jupiter and the most easterly planet, as in the following figure:
On 2 March at forty minutes, three planets were in attendance, two on the east and one on the west, in the configuration shown in this diagram:
The one furthest to the east was seven minutes from Jupiter and thirty seconds from the next; the one on the west was separated from Jupiter by an interval of two minutes. The outer ones were brighter and larger than the middle one, which appeared very small. The one furthest to the east seemed to be raised a little towards the north, out of the straight line drawn through the others and Jupiter. The fixed star already mentioned was at a distance of eight minutes from the western planet, along the perpendicular drawn from the same planet to the straight line passing through all the planets, as shown in the figure given.
I have wanted to report these comparisons of the position of Jupiter and its adjacent planets to a fixed star so that anyone may be able to understand from them that the movements of these planets both in longitude and in latitude agree exactly with the motions derived from tables.
These are my observations of the four Medicean Planets, recently discovered for the first time by me. Although I am not yet able to deduce by calculation from these observations the orbits of these bodies, I may be allowed to make some statements based upon them, well worthy of attention. In the first place, since they are sometimes behind and sometimes before Jupiter at like distances and deviate from this planet towards the east and towards the west only within very narrow limits of divergence, and since they accompany this planet when its motion is retrograde as well as when it is direct, no one can doubt that they perform their revolutions around this planet while at the same time they all together accomplish orbits of twelve years’ duration around the center of the world. Moreover, they revolve in unequal circles, which is evidently the conclusion [95] from the fact that I never saw two planets in conjunction when their distance from Jupiter was great, whereas near Jupiter two, three, and sometimes all four have been found closely packed together. Furthermore, it may be deduced that the revolutions of the planets that describe smaller circles around Jupiter are more rapid, for the satellites nearer to Jupiter are often seen in the east when the day before they have appeared in the west, and vice versa; also the satellite moving in the greatest orbit seems to me, after carefully weighing the timing of its returning to positions previously noticed, to have a periodic time of half a month.
Additionally, we have a notable and splendid argument to remove the scruple of those who can tolerate the revolution of the planets around the sun in the Copernican system, but are so disturbed by the motion of one moon around the earth (while both accomplish an orbit of a year’s length around the sun) that they think this constitution of the universe must be rejected as impossible. For now we have not just one planet revolving around another while both traverse a vast orbit around the sun, but four planets which our sense of sight presents to us circling around Jupiter (like the moon around the earth) while the whole system travels over a mighty orbit around the sun in the period of twelve years.
Lastly, I must not pass over the consideration of the reason why it happens that the Medicean Stars, in performing very small revolutions around Jupiter, seem sometimes more than twice as large as at other times. We can by no means look for an explanation in the mists of the earth’s atmosphere, for they appear increased or diminished while the discs of Jupiter and the neighboring fixed stars are seen quite unaltered. It seems altogether untenable that they approach and recede from the earth at the points of their revolutions nearest to and furthest from the earth to such an extent as to account for such great changes, for a strict circular motion can by no means produce those phenomena; and an elliptical motion (which in this case would be almost rectilinear) seems to be both unthinkable and by no means in harmony with the observed phenomena. But I gladly offer the explanation that has occurred to me upon this subject, and I submit it to the judgment and criticism of all true philosophers. It is known that when atmospheric mists intervene, the sun and moon appear larger, but the fixed stars and planets smaller; hence the former luminaries, when near the horizon, are larger than at other times, but stars appear smaller and are frequently scarcely visible; and they are still more diminished if those mists are bathed in light; so stars appear very small by day and
in the twilight, but the moon does not appear so, as I have previously remarked. Moreover, it is certain that not only the earth, but also the moon, has its own vaporous sphere enveloping it, [96] for the reasons which I have previously mentioned, and especially for those that shall be stated more fully in my System; and we may accordingly decide that the same is true with regard to the rest of the planets; so it seems to be by no means an untenable opinion to place also around Jupiter an atmosphere denser than the rest of the aether, around which, like the moon around the sphere of the elements, the Medicean Planets revolve; then by the interposition of this atmosphere, they appear smaller when they are at apogee; but when in perigee, through the absence or attenuation of that atmosphere, they appear larger. Lack of time prevents me from going further into these matters; my readers may expect further remarks upon these subjects in a short time.
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 o
vercome 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.
The Essential Galileo Page 11