The Essential Galileo

by Galilei, Galileo, Finocchiaro, Maurice A.

  SAGR. I see it very well. However, just as from this simplicity you infer a high probability for the truth of this system, others, on the other hand, might perhaps draw contrary conclusions; because such an arrangement is the very ancient one of the Pythagoreans and agrees so well with the observations, one might wonder (not without reason) how it could have had so few followers in the course of thousands of years, how it could have been rejected by Aristotle himself, and how even after Copernicus it could continue to suffer the same fate.

  SALV. Sagredo, if you had ever happened to hear (as I have very many times) what kinds of stupidities suffice to make the common people stubbornly unwilling [355] to listen to (let alone accept) these novelties, I think you would wonder much less about the fact that there have been so few followers of this view. However, in my opinion, we should pay little attention to such brains; to confirm the earth’s immobility and to remain unmoved in this belief, they regard as a very conclusive proof the fact that they cannot eat in Constantinople in the morning and have supper in Japan in the evening; and they are certain that the earth, being very heavy, cannot go up above the sun only to come back crashing down. We need not take into account these people, whose number is infinite, nor keep track of their stupidities; we need not try to gain the support of men whose definition contains only the genus but lacks the difference, in order to have them as companions in very subtle and delicate discussions. Moreover, what gain would you think you could ever make with all the demonstrations in the world when dealing with brains so dull that they are incapable of recognizing their extreme follies?

  My wonderment, Sagredo, is much different from yours. You are surprised that there are so few followers of the Pythagorean opinion, whereas I am amazed at how there could ever have been anyone who accepted and followed it; nor can I ever sufficiently admire the eminence of mind of those who have accepted and regarded it as true, and who with the liveliness of their intellect have done violence to their own senses, so much so that they have been able to prefer what their theorizing told them over what their sensory experiences showed them very clearly to the contrary. We have already seen that the reasons against the earth’s diurnal rotation, which have been examined, appear to be very good; the fact that they have been regarded as most conclusive by the Ptolemaics, Aristotelians, and all their followers is a very good argument for their effectiveness. However, the observations that clearly contradict its annual motion appear to be even more powerful, so much so that (I repeat it) there is no end to my admiration of how in Aristarchus and Copernicus their reason could have done so much violence to their senses as to become, in opposition to the latter, mistress of their belief.

  SAGR. Are we, then, also going to hear other powerful objections against this annual motion?

  SALV. We are. These are so clearly based on our sense experience that, if a higher and better sense than the common and natural ones had not joined with [356] reason, I suspect that I too would have been much more recalcitrant against the Copernican system than I have been since a lamp clearer than usual has shed light on my path.

  SAGR. Now then, Salviati, let us join the fray, for any word uttered for any other purpose seems to me to be wasted.

  SALV. I am ready to serve you.54 I have already explained to you the structure of the Copernican system. [357] Against its truth the first extremely fierce assault comes from Mars itself: if it were true that its distance from the earth varies such that the farthest minus the closest distance [358] equals twice the distance from the earth to the sun, it would be necessary that when it is closest to us its disk should appear more than sixty times larger than when it is farthest; [359] however, this variation of apparent size is not perceived; instead, at opposition to the sun, when it is close to the earth, it appears barely four or five times larger than near [360] conjunction, when it is hidden behind the sun’s rays. Another and greater difficulty is due to Venus: if (as Copernicus claims) it should turn around the sun and be sometimes beyond the sun and sometimes in between, and if it should recede from us [361] and approach us by a difference equal to the diameter of the circle it describes, then when it is positioned between us and the sun and is closest to us its disk would appear almost forty times larger [362] than when it positioned beyond the sun and is near its other conjunction; however, the difference is almost imperceptible. To this we should add another difficulty: it seems reasonable that the body of Venus is inherently dark and shines only because of the sun’s illumination, like the moon; if this is so, then when positioned between us and the sun it should appear sickle shaped, as the moon does when it is likewise near the sun; but this phenomenon is not observed in Venus. Thus, Copernicus declared that either it is inherently luminous, or its substance is such as to be capable of absorbing sunlight and transmitting it through its interior, so that it appears to be always shining; this is how Copernicus excused Venus for not changing its apparent shape;55 as regards the small variation in its apparent size, he said nothing. About Mars he said much less than was necessary; I believe the reason is that he was unable to account to his own satisfaction for a phenomenon so incompatible with his position; and yet, persuaded by many other confirmations, he stuck to it and regarded it as true. Furthermore, there is a feature that alters the order in such a way as to render it unlikely and false: all planets together with the earth move around the sun, which is at the center of their revolutions; only the moon perturbs this order, by performing its proper motion around the earth; and then it, the earth, and the whole elemental sphere all together move around the sun in one year.

  These are the difficulties that make me marvel at Aristarchus and Copernicus; they must have known about those difficulties but were unable to solve them; and yet, because of other wonderful confirmations, they trusted what reason told them so much that they confidently asserted that the [363] structure of the universe can have no other configuration but the one constructed by them. There are then other very serious and very beautiful difficulties which are not easily solved by mediocre intellects, but which were understood and explained by Copernicus; we will discuss them below, after answering other objections which seem to undermine this position. Now, coming to the clarifications and solutions of the three very serious objections advanced above, I say that the first two not only do not contradict the Copernican system, but favor it considerably and absolutely; for both Mars and Venus do vary in apparent size in accordance with the required proportions, and Venus does appear sickle shaped when between us and the sun and, in general, changes in apparent shape exactly like the moon.

  SAGR. But how could this be hidden from Copernicus and revealed to you?

  SALV. These things can be understood only with the sense of vision, which nature has not granted us in such a perfect state as to be able to discern such differences; indeed the very instrument for seeing contains impediments within itself. However, in our time God saw fit to allow the human mind to make a marvelous invention, which renders our vision more perfect by increasing its power by four, six, ten, twenty, thirty, and forty times; as a result, countless objects that were invisible to us because of their distance or extremely small size are now rendered highly visible by means of the telescope.

  SAGR. 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?

  SALV. 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.

  SAGR. 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.

  SIMP. 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.

  SALV. 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

  SIMP. 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.

  SALV. 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.

  SAGR. 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.

  SALV. 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.

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

  SALV. 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.

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

  SALV. 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 elongations57 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.