Scipione Chiaramonti's Book

From the questions this fellow asks, it seems to me that one may deduce that if only the sky, the stars, and their distances were permitted to keep the sizes and magnitudes which he has believed in up to this point (though he has surely never imagined for them any comprehensible magnitudes), then he would completely understand and be satisfied about the benefits which would proceed from them to the earth, which itself would no longer be such a trifling thing.

Nor would these stars any longer be so remote as to seem quite minute, but large enough to be able to act upon the earth. And the distance between them and Saturn would be in good proportion, and he would have Very probable reasons for everything, which I should very much like to have heard. But seeing how confused and contradictory he is in these few words leads me to believe that he is very thrifty with or else hard up for these probable reasons, and that what he calls reasons are more likely fallacies, even shadows of foolish fantasies.

Therefore I ask him whether these celestial bodies really act upon the earth, and whether it was for that purpose that they were made of such-and-such sizes and arranged at such-and-such distances, or whether they have nothing to do with terrestrial affairs? If they have nothing to do with the earth, then it is a great folly for us Terrestrials to want to be arbiters of their sizes and regulators of their local dispositions, we being quite ignorant of all their affairs and interests.

But if he says that they do act, and that it is to this end that they are directed, then this amounts to admitting what he denies in another place, and praising what he has just finished condemning when he said that celestial bodies located at such distances from the earth as to appear minuscule could not act upon it in any way.

In the starry sphere, which is already established at whatever distance it is, and which you have just decided is well proportioned for an influence upon terrestrial matters, a multitude of stars do appear quite small, and 100 times as many are entirely invisible to us–which is to appear smaller than small.

Therefore you must now (contradicting yourself) deny their action upon the earth, or else (still contradicting yourself) admit that their appearing small does not detract from their power to act. Or else (and this would be a frank and honest confession) you must grant and freely admit that your judgment about their sizes and distances was folly, not to say presumption or brashness.

Why does he say that the stars appear so small?

Is it because that is the way they look to us? Does he not know that this comes about from the instrument which we use in looking at them–that is, our eyes? Or for that matter that by changing instruments we may see them larger and larger, as much as we please? Who knows; perhaps to the earth, which beholds them without eyes, they may appear quite huge and as they really are?

But it is time for us to leave these trifles and get to more important matters. I have already demonstrated two things: first, at what distance the firmament may be placed so that the diameter of the earth’s orbit would make no greater variation in it than that which the terrestrial diameter makes with respect to the sun at its distance therefrom, and I then showed that in order to make a fixed star appear to us as of the size we see, it is not necessary to assume it to be larger than the sun. Now I should like to know whether Tycho or any of his disciples has ever tried to investigate in any way whether any phenomenon is perceived in the stellar sphere by which one might boldly affirm or deny the annual motion of the earth.

Really, to be quite frank, I do feel a great repugnance against having to concede the distance of the fixed stars to be so great that the alterations just explained would have to remain entirely imperceptible in them.

Do not completely despair, Simplicio; perhaps there is yet some way of tempering your difficulties. First of all, that the apparent size of the stars is not seen to alter visibly need not appear entirely improbable to you when you see that men’s estimates in such a matter may be so grossly in error, particularly when looking at brilliant objects.

Looking, for example, at a burning torch from a distance of two hundred paces, and then coming closer by three or four yards, do you believe that you yourself would perceive it as larger? For my part, I should certainly not discover this even if I approached by 20-30 paces.

Sometimes I have even happened to see such a light at a distance, and been unable to decide whether it was coming toward me or going away, when in fact it was approaching. Now what of this? If the same approach and retreat of Saturn (I mean double the distance from the sun to us) is almost entirely imperceptible, and if it is scarcely noticeable in Jupiter, what could it amount to in the fixed stars, which I believe you would not hesitate to place twice as far away as Saturn? In Mars, which while approaching us. . .

Let us say something which will perhaps satisfy you also on this point. Briefly, would you be content if those alterations really were perceived in the stars which seem to you so necessary if the annual motion belongs to the earth?

I wish you had said that if such a variation were perceived, nothing would remain that could cast doubt upon the earth’s mobility, since no counter could be found to such an event. But even though this may not make itself visible to us, the earth’s mobility Is not thereby excluded, nor its immobility necessarily proved.

It is possible, Copernicus declares, that the immense distance of the starry sphere makes such small phenomena unobservable. And as has already been remarked, it may be that up to the present they have not even been looked for, or, if looked for, not sought out in such a way as they need to be; that is, with all necessary precision and minute accuracy.

It is hard to achieve this precision, both on account of the imperfection of astronomical instruments, which are subject to much variation, and because of the shortcomings of those who handle them with less care than is required.

A cogent reason for putting little faith in such observations is the disagreement we find among astronomers in assigning the places, I shall say not merely of novas and of comets, but of the fixed stars themselves, and even of polar altitudes, about which they disagree most of the time by many minutes.

As a matter of fact, how would you expect anyone to be sure, with a quadrant or sextant that customarily has an arm three or four yards long, that he is not out by two or three minutes in the setting of the perpendicular or the alignment of the alidade? (note: An instrument for angular measurements.) For on such a circumference this will be no more than the thickness of a millet seed. Besides which, it is almost impossible for the instrument to be constructed absolutely accurate and then maintained so. Ptolemy distrusted an armillary instrument constructed by Archimedes himself for determining the entry of the sun into the equinox.

I grant you all this, but neither the one fact nor the other suffices to make us certain in affairs of such importance. I want to have us use instruments far larger than those of Tycho’s; quite precise ones, and made at minimum cost, whose sides will be four, six, twenty, thirty, or fifty miles, so that a degree is a mile wide, a minute is fifty yards, and a second is little less than a yard. In a word, we may have them as large as we please, without their costing us a thing.

Being at a villa of mine near Florence, I plainly observed the arrival of the sun at the summer solstice and its subsequent departure. For one evening at its setting it hid itself behind a cliff in the Pietrapana Mountains, about sixty miles away, leaving only a small shred of itself revealed to the north, the breadth of which was not the hundredth part of its diameter. But the following evening, at the same position of setting, it left a like part of itself showing which was noticeably thinner. This is a conclusive proof that it had commenced to move away from the tropic; yet the sun’s return between the first and second observations surely did not amount to one second of arc along the horizon. Making the observation later with a fine telescope which would multiply the disc of the sun more than a thousandfold turned out to be pleasant and easy.

Now my idea is for us to make our observations of the fixed stars with similar instruments, utilizing some star in which the changes would be conspicuous. These are, as I have already explained, the ones which are farthest from the ecliptic.

Among them Vega, a very large star close to the pole of the ecliptic, would be the most convenient when operating in the manner I am about to describe to you, so far as the more northern countries are concerned, though I am going to make use of another star. I have already been looking by myself for a place well adapted for such observations. The place Is an open plain, above which there rises to the north a very prominent mountain, at the summit of which is built a little chapel facing west and east, so that the ridgepole of its roof may cut at right angles the meridian over some house situated in the plain.

I wish to affix a beam parallel to that ridgepole and about a yard above it. This done, I shall seek in the plain that place from which one of the stars of the Big Dipper is hidden by this beam which I have placed, just when the star crosses the meridian. Or else, if the beam is not large enough to hide the star, I shall find the place from which the disc of the star is seen to be cut in half by the beam–an effect which can be discerned perfectly by means of a fine telescope.

It will be very convenient if there happens to be some house at the place from which this event can be perceived, but if not, then I shall drive a stick firmly into the ground and affix a mark to indicate where the eye is to be placed whenever the observation is to be repeated. I shall make the first of these observations at the summer solstice, in order to continue them from month to month, or whenever I please, until the other solstice.

By means of such observations, the star’s rising or lowering can be perceived no matter how small it may be. And if in the course of these operations any such variation shall happen to become known, how great an achievement will be made in astronomy’ For by this means, besides ascertaining the annual motion, we shall be able to gain a knowledge of the size and distance of that same star.

It seems the other way around to me, for it is improbable that if anyone had tried this he would not have mentioned the result, whichever opinion it turned out to favor. But no one is known to have availed himself of this method, for the above or for any other purpose; and without a fine telescope it could not very well be put into effect.

I must not and cannot refuse anything which Sagredo pleads for. The delay that I requested was only to give me time to rearrange in my mind the premises which are useful for a clear and comprehensive explanation of the manner in which these events take place in the Copernican as well as in the Ptolemaic system.

More easily and simply in the former than in the latter, so that it may be clearly seen that the former hypothesis is as easy for nature to put into effect as it is hard for the intellect to comprehend.

Nevertheless I hope, by utilizing explanations other than those resorted to by Copernicus, to make even the learning of it very much less obscure. In order to do this, I shall set forth some assumptions as known and self-evident, as follows:

1. I assume that:

• the earth is a spherical body which rotates about its own axis and poles
• every point on its surface traces out the circumference of a circle, greater or lesser according as the designated point is more or less distant from the poles. Of these circles, that one is greatest which is traced out by a point equidistant from the poles.

All these circles are parallel to one another, and we shall refer to them as parallels.

2. The earth being spherical in shape and its material being opaque, half its surface is continually lighted and the rest is dark.

The boundary which separates the lighted part from the dark being a great circle, we shall call this the boundary circle of light.

3. When the boundary circle of light passes through the earth’s poles It will cut all the parallels into equal sections, it being a great circle; but, not passing through the poles, it will cut them all into unequal parts except the central circle; this, being also a great circle, will be cut into equal parts in any case.

4. Since the earth turns about its own poles, the length of day and night is determined by the arcs of the parallels cut by the boundary circle of light.

The arc which remains in the illuminated hemisphere determines the length of the day, and the remainder that of the night.

These things being set forth, we may wish to draw a diagram for a clearer understanding of what comes next. (Fig. 6) First let us indicate the circumference of a circle, to represent for us the orbit of the earth, described in the plane of the ecliptic.

This we may divide by two diameters into four equal parts; Capricorn, Cancer, Libra, and Aries, which shall here represent at the same time the four cardinal points; that is, the two solstices and the two equinoxes. And in the center of this circle, let us denote the sun, O, fixed and immovable