The Essential Galileo (42 page)

S
AGR.
    But Venus and Mars are not objects that are invisible because of their distance or small size; indeed we perceive them with our simple natural vision. So why do we not distinguish the variations in their size and shape?

S
ALV.
    Here the major impediment stems from our eyes themselves, as I just mentioned. Objects that are shining and distant are not represented by our eyes as simple and sharp; instead, they are presented to us adorned with adventitious and extraneous rays, so long and thick that their bare little body appears to us enlarged ten, twenty, one hundred, and one thousand times more than it would be presented to us without the radiant head of hair which is not part of it.

S
AGR.
    I now remember reading something on this subject, perhaps in the
Sunspot Letters
or in
The Assayer
published by our common friend. You ought to explain more clearly how this matter stands, both to refresh my memory [364] and for the understanding of Simplicio, who may not have seen these writings; I think this information is essential in order to comprehend what we are dealing with.

S
IMP.
    Frankly, everything that Salviati is now advancing is new to me, for, to tell you the truth, I have not had the curiosity to read those books. Nor have I so far placed much trust in the newly introduced spyglass; on the contrary, following in the footsteps of my fellow Peripatetic philosophers, I have regarded as fallacies and deceptions of the lenses what others have admired as stupendous achievements. However, if I have been in error so far, I should like to be freed from it; enticed by the other novelties I heard from you, I will more carefully listen to the rest.

S
ALV.
    The confidence these men have in their own cleverness is as unjustified as the little regard they have for the judgment of others; it is very revealing that they should consider themselves to be better qualified to judge this instrument, without having ever experimented with it, than those who have made thousands of experiments with it and continue to make them every day. However, please let us forget about such stubborn persons, who cannot even be criticized without doing them more honor than they deserve.

Returning to our purpose, I say that shining objects appear to our eyes surrounded by additional rays, either because their light is refracted by the fluids covering the pupils, or because it is reflected by the edges of the eyelids (thus scattering the reflected rays onto the same pupils), or for some other reason; hence, these objects appear much larger than if their bodies were represented without such irradiation. This enlargement becomes proportionately greater and greater as such brilliant objects are smaller and smaller; for example, if we assume that the increase due to the shining hair is four inches, and that this addition is made around a circle with a diameter of four inches, then its apparent size is increased nine times, but …
⁵⁶

S
IMP.
    I suspect you meant to say “three times”; for by adding four inches on one side and four on the other to a circle with a diameter of four inches, you are tripling its dimensions, not increasing them nine times.

S
ALV.
    A little geometry is needed, Simplicio. It is true that the diameter [365] increases threefold, but the surface (which is what we are talking about) increases ninefold; for, Simplicio, the surfaces of circles are to each other as the squares of their diameters, and so a circle with a diameter of four inches is to another of twelve as the square of four is to the square of twelve, namely, as 16 is to 144; hence, the latter will be nine times larger, not three. So, please be careful, Simplicio.

Now, let us go forward. If we were to add the same head of hair four inches wide to a circle with a diameter of only two inches, the diameter of the whole wreath would be ten inches, and its whole surface compared to the area of the naked little body would be as one hundred to four (for these are the squares of ten and two); therefore, the enlargement would be twenty-five times. Finally, the four inches of hair added to a small circle with a diameter of one inch would enlarge it eighty-one times. Thus, the enlargements constantly take place in greater and greater proportions as the real objects being enlarged are smaller and smaller.

S
AGR.
    The difficulty that troubled Simplicio did not really trouble me; but there are some things which I want to understand better. In particular, I should like to know on what basis you claim that this enlargement is always equal for all visible objects.

S
ALV.
    I already explained myself in part when I said that only brilliant objects are enlarged, not dark ones; now I shall add the rest. Brilliant objects that shine with a brighter light produce a greater and stronger reflection on our pupils, and so they appear to be enlarged much more than those which are less bright. In order not to dwell on this particular any longer, let us see what our true mentor teaches us. Tonight, when it is very dark, let us look at the planet Jupiter; we will see it appear very bright and very large. Let us look at it through a tube, or through a small hole made with a fine needle in a piece of paper, or even through the small slit we can create by closing our hand and leaving some space between our palm and fingers; we will then see the disk of the same Jupiter stripped of its rays and so small that we will easily judge it smaller than one-sixtieth the size it appears when its great torch is observed with the naked eye. [366] Let us then look at the Dog Star, which is very beautiful and larger than any other fixed star, and which appears to the naked eye not much smaller than Jupiter; when we remove its head of hair in the manner indicated, its disk will be seen to be so small that it will be judged one-twentieth that of Jupiter; indeed, whoever lacks perfect vision will have great difficulty perceiving it; from this we may reasonably conclude that, insofar as the light of this star is much brighter than that of Jupiter, it produces a greater irradiation than Jupiter does. Furthermore, the irradiations of the sun and moon are almost nothing, due to the fact that their size by itself takes up so much space in our eye as to leave no room for the adventitious rays; thus, their disks are seen shaved and clear cut. We can ascertain the same truth by means of another experiment, which I have made several times; I am referring to ascertaining that bodies shining with a brighter light are surrounded by rays much more than those whose light is dimmer. I have observed Jupiter and Venus together several times when they were twenty-five or thirty degrees away from the sun and the sky was very dark; when I observed them with the naked eye, Venus appeared at least eight and perhaps even ten times larger than Jupiter; but when they were observed with a telescope, the disk of Jupiter was seen to be at least four times larger than that of Venus, and the brightness of Venus' shine was incomparably greater than the extremely dim light of Jupiter; this derived only from the fact that Jupiter was extremely far from the sun and from us, and Venus was close to us and the sun.

Having explained these things, it will not be hard to understand how it can happen that, when Mars is in opposition to the sun and hence more than seven times closer to the earth than when it is near conjunction, it appears to us four or five times larger in the former configuration than in the latter, although we should see it more than fifty times larger. The cause of this is simply the irradiation; for if we strip it of the adventitious rays, we will find it enlarged exactly by the required proportion. To strip it of its head of hair, the only excellent means is the telescope, which enlarges its disk by nine hundred or a thousand times; thus, we see it bare and clear cut like that of the moon, and different in size in the two positions exactly in accordance with the required proportion.

Then, as regards Venus, it should appear almost forty times larger at its evening conjunction below the sun than at its other morning conjunction; and yet it is seen as not even doubled. [367] Here, besides the irradiation effect, what is happening is that it is sickle shaped and its horns not only are very thin but also are receiving the sunlight obliquely; hence, this light is very dim in intensity and little in amount, and consequently its irradiation is less than when the planet's hemisphere appears entirely illuminated. On the other hand, the telescope clearly shows us its horns as clear cut and distinct as those of the moon; and they are seen as part of a very large circle, which is almost forty times larger than its same disk when it is beyond the sun at the end of its appearance as a morning star.

S
AGR.
    Oh, Nicolaus Copernicus, how pleased you would have been to see this part of your system confirmed by such clear observations!

S
ALV.
    Indeed; but how much less would have been his reputation among the experts for preeminence of intellect! For, as I said before, he constantly continued to claim what was in accordance with arguments even though it was contrary to sensory experiences; and I cannot stop marveling at the fact that he should have persisted in saying that Venus turns around the sun and is sometimes more than six times farther from us than at other times, although it always appears equal to itself, even when it should appear forty times larger.

S
AGR.
    In regard to Jupiter, Saturn, and Mercury, I think we should also see differences in their apparent size corresponding exactly to their different distances.

S
ALV.
    In the case of the two superior planets, I have exactly observed these differences almost every year for the past twenty-two years.

In the case of Mercury, no observation of any consequence is possible because it becomes visible only at its maximum elongations
⁵⁷
from the sun (where its distances from the earth are insignificantly different), and hence these differences are imperceptible. It is similar with its changes of shape, which must occur absolutely as in Venus; that is, when we see Mercury, it should appear in the shape of a semicircle, as Venus also does at its maximum elongation; but Mercury's disk is so small and its light so bright (due to its being so close to the sun) that the power of the telescope is not enough to shave its hair and make it appear completely shorn.

There remains what seemed to be a great difficulty with the earth's motion; that is, unlike all the other planets that revolve around the sun, [368] it alone does so (in one year) accompanied by the moon together with the whole elemental sphere, while the same moon moves every month around the earth. Here we must, once again, proclaim and exalt the admirable perspicacity of Copernicus and at the same time pity his misfortune; for he does not live in our time when, to remove the apparent absurdity of the shared motion of the earth and moon, we can see that Jupiter (being almost another earth) goes around the sun in twelve years accompanied not by one moon but by four moons, together with all that may be contained within the orbs of the four Medicean Stars.

S
AGR.
    For what reason do you call the four planets surrounding Jupiter moons?

S
ALV.
    They would appear such to someone who looked at them while standing on Jupiter. For they are inherently dark and receive light from the sun, which is evident from their being eclipsed when they enter inside the cone of Jupiter's shadow; moreover, because the only part of them that is illuminated is the hemisphere facing the sun, they appear always entirely lit to us who are outside their orbits and closer to the sun; but to someone on Jupiter they would appear entirely lit when they were in the parts of their orbits away from the sun, whereas when in the inner parts (namely, between Jupiter and the sun), from Jupiter they would be seen as sickle shaped; in short, to Jupiter's inhabitants they would show the same changes of shape which the moon shows to us terrestrials.

Now you see how wonderfully in tune with the Copernican system are these first three strings that at first seemed so out of tune. Furthermore, from this Simplicio will be able to see the degree of probability with which one may conclude that the sun rather than the earth is the center of the revolutions of the planets. Finally, the earth is placed between heavenly bodies that undoubtedly move around the sun, namely, above Mercury and Venus and below Saturn, Jupiter, and Mars; therefore, likewise will it not be highly probable and perhaps necessary to grant that it too goes around the sun?

[§8.7 Day IV: The Cause of the Tides and the
Inescapability of Error]
⁵⁸

[445] S
IMP.
    Salviati, these phenomena
⁵⁹
did not just start to happen; they are very old and have been observed by infinitely many persons.

Many have striven to explain them by means of some reason or other.

Just a few miles from here, a great Peripatetic has advanced a new cause fished out of a certain text of Aristotle not duly noticed by his interpreters; from this text he gathers that the true cause of these motions derives from nothing but the different depths of the seas; for where the depth is greater, the water is greater in quantity and hence heavier, and so it displaces the more shallow water; once raised, this water wants to go down; the ebb and flow derives from this constant struggle. Then there are many who refer this to the moon, saying that it has special dominion over the water. Lately a certain clergyman
⁶⁰
has published a small treatise in which he says that, as the moon moves through the sky, it attracts and raises toward itself a bulge of water which constantly follows it, so that there is always a high tide in the part which lies under the [446] moon; but since the high tide returns when it is under the horizon,
⁶¹
he claims that to explain this effect one must say that the moon not only keeps this faculty naturally within itself, but also has the power of giving it to the opposite point of the zodiac. As I believe you know, others also say that the moon with its moderate heat has the power of rarefying the water, which rises as it expands.
⁶²
We have also had someone who …
⁶³