[I.] Since Galileo (Dialogue 3 On the System of the World, Ptolemaic and Copernican) endeavored, even from the sunspots themselves, to besmirch and destroy the annual motion of the Sun and to paint an annual motion upon the Earth—nay, numbered this among the three strongest arguments for the motion of the Earth (Dialogue 4, the penultimate page), saying: “Therefore, from the colloquies held during that four-day [conversation], we have remarkable testimonies for the Copernican system, from which these three [are] taken: the first, from the station and retrogradation of the Planets, and their approaches and elongations from the earth; the second, from the revolution of the Sun upon itself, and from those [things] which are observed in its Spots; the third, from the flux and reflux of the Sea; [these] seem to have a most evident force of concluding”—since, I say, he attributed so much to this argument, it behooves us, lest we seem to have failed in a duty once undertaken, to scrutinize this ford more diligently; and, this opportunity being offered, to explain the Motion of these Spots, in this place more easy of understanding for Readers already practiced, than it would perhaps have been [in] bk. 3, ch. 3.

[I.] First, therefore, Galileo—as he himself narrates in the history of the Solar Spots, written in three letters to Markus Welser—

[…continues on p. 352 (PDF 387) with the catchword “scriptis”: “…written [to Markus Welser]“—the beginning of the Epitome of the Galileo–Scheiner sunspot doctrine. (The Epitome here restarts its own internal numbering at “I.”)]

(printed p. 352 — within Chapter XII, the Epitome of the Galileo–Scheiner sunspot doctrine: Galileo’s letters to Welser establish that the spots are contiguous to the Sun, real, cloud-like, sharing a common rotation of about a month within a middle zone. The page then turns to Dialogue 3, where Galileo calls the sunspots a most clear witness for the Earth’s annual motion and recounts his discovery.)

[Header: BOOK IX. SECTION IV. — 352]

[Margin: Galileo’s opinions on the Solar Spots, from his own Epistles.] [Margin: From the 1st Epistle.]

written [to Markus Welser], who had forewarned him of these observations published a little before by our Apelles (after a table then lying hidden)—that is, by Christopher Scheiner, by the order of Fr. Theodor Busaeus the Provincial, who was unwilling that these novelties, not yet plainly explored, be published by our [men]—[Apelles] meanwhile suppressing his own name; in that history, I say, in Epistle 1, he [Galileo] approves the opinion of Apelles concerning the nearness of the Spots to the Sun, and their real existence, on account of the imperceptible parallax between them and the Sun. But because Apelles had said they are moved around the Sun from East to West—considering, namely, that motion which is conspicuous to us—Galileo concedes this indeed, if the whole conversion of them around the Sun be not considered; but if that be considered, [he holds] they are moved in that manner in which Venus and Mercury are moved around the Sun, namely from West to East: which is true if the motion be regarded in the upper, or in the inconspicuous, hemisphere of the Sun. He adds, moreover, that the evening spots, observed near the setting of the Sun, daily change their position, and descend from the upper parts of the Sun toward the lower; but the morning [spots] ascend from the lower parts of the Sun toward the upper. But their substance he denies to be very dense, but says it is similar to smokes or clouds; he denies likewise that they are fixed or wandering stars; he denies, finally, that they are moved in circles separated from the Sun—otherwise a swifter transit would be due to them than to Mercury under the Sun, and yet Mercury passes through the disk of the Sun in about six hours, but the Spots persist under it for several days.

[Margin: From the 2nd Epistle.]

[III.] But Epistle 2, to the same M. Welser, confirms certain [things] said [in] Epistle 1, and affirms these propositions concerning the Solar Spots. [That] they, besides the disordered and irregular motion by which several spots at once flow together into one, or flow apart from one into several, have another certain ordered and common and greatest motion, by which uniformly, in lines parallel among themselves, they are revolved about the globe of the Sun (to which they are contiguous), so that this vertigo of the Sun about its own center, and of the Spots about the globe of the Sun, completes its period or revolution in about one Lunar month, and that it is similar to the conversion of the Planets in their orbs, inasmuch as they are turned from West toward East: but their contiguity and vertigo with the Sun he confirms from this, that in their appearance or occultation about the margins of the Sun they are of small longitude (the same latitude being nevertheless kept), but in the middle of the solar disk they appear longer. Moreover, [that] the multitude of Spots does not appear in the whole disk of the Sun, but only in a certain middle Zone of its disk, which does not exceed 56 or 58 degrees of those of which the circumference of the greatest circle on the globe of the Sun is 360; so that, just as the maximum declination of the Planets from the Equator does not exceed toward North or South 23½ degrees in the Sun, but in the other Planets having latitude does not exceed Gr. 28 or 29, so neither does the maximum declination of the Solar Spots from the middle of the Sun’s disk exceed toward South or North 28 or 29 degrees of the Solar circumference. Hence he deduced [that] on the surface of the Solar globe there are two poles, about which the aforesaid vertigo takes place, and [that] the remaining points describe the peripheries of parallel circles, of which the greatest is that which is equally distant on both sides from those poles. But after he had demonstrated, by several arguments, in the same 2nd epistle, that these Spots are contiguous to the Sun, he teaches [that] many of them return a little longer than in 14 days, completing their course in one hemisphere of the Sun; and proves from his observations, and teaches, [that] if one of the spots traversed the disk of the Sun in 16 days, but another, most distant from the middle, namely by 30 degrees, traversed [it] in 14 days, or 13 [days] and 20½ hours, it would follow that the semidiameter of the Ethereal sphere—in which the aforesaid spots are revolved—would be double the semidiameter of the Solar body. He confirms, moreover, [that] the spots are in the very surface of the Solar globe, and are carried about by its vertigo, from the faculae brighter than the rest of the Sun which appear in it, and are moved by the same motion as the Spots; for neither is it credible that some body brighter than the Sun be found outside the Sun. He adds [that] the production and destruction of the Solar spots can be imitated by us, if we throw wax, pitch, or bitumen upon glowing iron—for thence a black spot is made in the iron, from which smoke is raised, flowing apart into various figures; and [that] many [spots], in the very middle of the Sun, are suddenly born and die away: [yet] that they are not within the substance of the Sun, as if its lakes or caverns. This is, summarily, the doctrine of Galileo concerning the Spots of the Sun, reduced from those three Epistles into an Epitome, many other [things] being studiously omitted which contribute nothing to our argument—[the spots] regarding neither Venus nor Mercury visible under the Sun, nor the spots of the Moon, nor the satellites of Jupiter, nor the reflection of the Solar light from the earth. Let us now see what the same [Galileo], under the person of Salviati, taught concerning the motion of these Spots in Dialogue 3 On the System of the World.

[Margin: Galileo’s doctrine on the motion of the Solar Spots, from Dialogue 3.]

[V.] In the Italian page 337 of that Dialogue—but [in] the Latin of the version, p. 255—he affirms [that] the Sun itself, by its own spots, is a most clear witness, and one worthy beyond all exception, for the annual motion of the Earth; and first [he affirms] that he was the inventor and observer—as of all other celestial novelties, so also of the Solar Spots—when he was professing Mathematics in the Paduan Gymnasium in the year 1610, and that concerning these he discoursed with certain [men] still living at Padua and at Venice; and first, from the sudden eruption and dissolution of these spots, he asserted the alterability of the heaven.

[Margin: A conjecture probable now, which in Dialogue 4, at the end, he calls a most evident testimony.]

He narrates, moreover, [that] he formerly judged these spots to be contiguous to the Sun, or adhering to its surface, and so to be revolved with its vertigo, as if monthly, so that this vertigo took place about the Axis of the Solar globe erected to the plane of the Ecliptic: since indeed the arcs described by the Spots over the Sun’s disk appeared to the observer’s eye as straight lines, and parallel to the plane of the Ecliptic. But if any deviation from that straightness appeared, he judged it to be not in the essential and primary motion of them, but from an accidental concurrence of small spots into one larger, or from a tumultuary disgregation [scattering] of one spot into several smaller spots. But the observations of the Spots being intermitted, and afterward resumed, he says he fell upon a very large, dense, and solitary spot, and observed its transit around noon for very many continuous days; and when he had noticed its path [iter] to be curvilinear, he straightway conceived in mind a vast hope, from this motion, of deciding about the motion of the Sun or of the Earth—which hope, turning to his Host Filippo Salviati, he expressed in these words: “Lo, Philip, a way to consequences of great moment seems to me to open hence. For indeed, if the Axis about which the Sun is revolved is not erected perpendicularly to the plane of the Ecliptic, but is inclined above it”—so as the recently-observed Spot indicated by its path—“we shall take, from the state of the Sun and of the Earth, that conjecture than which neither a firmer nor a more probable [one] was ever supplied to us by any other accident.”

At the request, therefore, of Salviati, he sets forth this conjecture in nearly these words: “If the earth,” he says, “is borne by an annual motion through the Ecliptic about the Sun, so that the Sun, remaining in the center of the Ecliptic, is rotated about it upon itself—not about the axis of the Ecliptic itself (which would be the axis of the annual motion of the Earth), but about an inclined axis—it is necessary that admirable changes be represented to us in the apparent motions of the Spots, even if the aforesaid Axis of the Sun be supposed to persist perpetually and immutably in the same inclination, and to be directed always toward the same point of the Universe. For if the terrestrial globe, by an annual motion, goes around the Sun, it will be necessary, First, that to us, who are carried around with [it], the transits of the Spots should sometime—but only twice per year—appear made through a straight line; but at all the remaining

[…continues on p. 353 (PDF 388) with the catchword “tem[poribus]”: ”…[at all the remaining] times through a curve”—the rest of Galileo’s four predicted appearances of the spot-paths, illustrated by an engraved three-figure diagram.]

(printed p. 353 — within Chapter XII, still expounding Galileo’s sunspot argument: the four predicted seasonal appearances of the spot-paths are illustrated by an engraved three-figure diagram (rectilinear, quadrant-curved, and general oblique cases). Sagredo reports the predictions confirmed, but Simplicio replies that the argument does not convert — the same phenomena could be saved with an immobile Earth and a mobile Sun — which Salviati concedes.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 353]

[at all the remaining] times through a curve. Secondly, the curvature of these arcs, through one half of the year, will appear to us inclined in the contrary manner than in the other half; that is, through six months the convexity of the arcs will be toward the upper part of the Solar disk, and through the other six months toward the lower. Thirdly, when the Spots begin to appear, and to rise to our eye, from the left part of the Sun’s disk, and cease, or be hidden, on the right part, the Eastern termini, or [the termini] of the first appearances, through six months will be lower than the termini of the occultations, and through the other six months they will be higher: namely, the Spots rising from higher points, and thence descending, in their progress will be hidden in lower points; and through only two days of the year will these termini be constituted in equilibrium: after which balancing, the inclination of the transit of the Spots will begin to become greater and greater, until after 3 months it comes out greatest; and thence, decreasing through another 3 months, it returns to equilibrium. Fourthly, on those very days on which the obliquity, or inclination, of the path of the Spots will be greatest, they will appear rectilinear; but on the days of the aforesaid equilibrium [they will appear] as curvilinear as possible.

[Margin: The variety of the motion of the Spots according to Galileo.]

[VI.] That we may illustrate this doctrine by schematisms [diagrams], as far as can be done on a plane (for globes would be more apt), with Galileo: let, in the following figures, O be the center of the Ecliptic, or of the great orb, and also of the Solar globe, whose whole hemisphere let us suppose to be seen by us earth-dwellers, on account of its huge distance. About this is described

[Translator’s note — engraved diagram (three figures): each figure is a circle representing the Sun’s disk, the great circle ABCD (A at top, C at bottom, B at left, D at right) bounding the visible hemisphere, with center O. Figure 1 (left): the solar axis EOI is tilted, and the spot-paths are drawn as straight, parallel lines across the disk—the principal one FOG through the center, with HL and KM parallel to it (dotted lines studded with dots for the spots); this is the rectilinear case. Figure 2 (center): the axis stands vertical (coinciding with AOC), poles E (top, near A) and I (bottom, near C), and the spot-path is the curved arc BGD (convex upward, through G above O) with the hidden return-arc BFD (through F below O). Figure 3 (right): the axis EOI is again obliquely tilted, poles E (upper) and I (lower, with point S near O), and the spot-path is the curve FNG / FNGS with unequal end-points. Letters keyed throughout the text below.]

the circle ABCD, representing the horizon of the Solar hemisphere, or the greatest circle terminating and dividing the conspicuous hemisphere of the Solar globe from the inconspicuous; and since our eye—not otherwise than the center both of the Earth and of the Sun—is in the plane of the Ecliptic, if we imagine the body of the Sun to be cut by the plane of the Ecliptic, that section will appear to our eye to be a straight line, which let us suppose to be BOD; to which the perpendicular AOC, drawn, will be the axis of the Ecliptic, about which the annual motion of the Earth takes place. Let us now think of the body of the Sun—about its own immobile center—revolved upon itself, not about the axis AOC perpendicular to the plane of the Ecliptic, but about the axis EOI somewhat inclined to the Ecliptic, which axis is fixed and immutable, or retaining perpetually the same inclination toward the same points of the Firmament and Universe; and let there be taken, in the Solar horizon, the point F, equally distant on both sides from the Poles E and I; from which, through O, let the diameter FOG be drawn, perpendicular to the axis EOI; for it will be the diameter of the greatest circle described about the Poles E, I.

[Margin: The 1st Case, the rectilinear path, explained by the 1st figure.]

Now if the Solar horizon ABCD, as it passes through the axis of the Ecliptic AOC, pass (with respect to us, who are moved together with the earth) through the poles E and I, the greatest circle whose diameter is FOG will be erected orthogonally to the circle, or Solar horizon, ABCD, to which a ray from our eye falls perpendicularly in O; and therefore the same ray will fall in the plane of the circle whose diameter is FOG, and its circumference will appear to us [as] a straight line, and such [will be] the motion of the spots through it as in the first figure is designated by the line FOG; but the paths of other spots will appear to describe other straight lines parallel to FOG itself, such as are HL and KM. And the same will happen after the Earth, after six months, has arrived there, so that it sees the other hemisphere of the Sun (which before was hidden from it)—provided that [hemisphere] be in such a position that the Solar horizon ABCD pass through the poles E and I. But since, on account of the annual motion of the Earth, the Solar horizon is continually changed, nor passes through the poles E and I except in the two aforesaid times or moments, it follows that not except at those two moments of the year does the path of the spots appear to us exactly rectilinear. Hence also it appears that, when the appearance and beginning of the motion proceeds from the part F toward G, to us observing at noon, the path of the spots ascends from the left

[Margin: The 2nd Case, the curved path, set forth by the 2nd figure.]

part, and the lower, toward the right and upper part of the Solar horizon. But if the Earth has now come into the part diametrically opposite, the transit will be from the left, but upper, part G, descending into the right lower [part] F; for you must, in this second case, imagine your eye placed not before, but behind, this first figure ABCD.

[VII.] Make now [suppose] that the Earth has departed from the aforesaid position, and has completed, after three months, a quadrant of the annual orb (look at the second figure), and that the plane of our Meridian pass through the axis of the Ecliptic AOC; for in the same plane will be the axis of the Solar revolution with its poles—one indeed conspicuous to us, which let be I, the other inconspicuous, E, or lying hidden in the surface of the Solar hemisphere hidden from us. For when the axis EI is inclined with its lower part toward us, the greatest circle described about it too will be raised upward to us, and will be such as is designated by BGDF; wherefore, if a spot rise in B, its path conspicuous to us will appear curved, and made through BGD, so that its convexity verges upward toward the northern limb of the Sun, and indeed with the greatest curvature, and in the hemisphere of the Sun conspicuous to us; but the remaining [part] of the spots’ path will be hidden, [made] through DFB, with the convexity turned downward. On the contrary, if the Earth, receding hence, complete a semicircle after six months, the conspicuous pole of the Solar axis will be E, and the path of a spot risen in B will be conspicuous through the arc BFD, swelling downward toward the southern limb of the Sun with its convexity; but the remaining path will be hidden to us, [made] through the arc DGB. Finally, to us observing at noon, the termini of the appearance B and of the occultation D will be in equilibrium, or equally distant from C or A. But what I have said of a spot risen in B holds of all others risen elsewhere—for they will describe arcs parallel to the arc BGD, or, after six months, BFD.

[Margin: The 3rd Figure and Case explained.]

But if the Earth be outside the aforesaid positions, so that neither the Solar horizon ABCD nor the Meridian AOC pass through the poles E, I of the Solar axis—as you see in the third figure—but the axis be EOI, the diameter of the greatest circle described about it will be FOG, and the periphery of the circle FNGS; wherefore, if the pole conspicuous to us be E, the conspicuous path of the spots will be the curve FNG, yet not with the greatest curvature, and its convex [part] will verge downward, nor will the termini of the appearance F and of the occultation G be in equilibrium, but F lower and G higher: but, on the contrary, the Earth being placed diametrically opposite to this position, and the pole I being conspicuous to it, the curvilinear path will be through the upper arc GSF, and the appearance in the upper point G, the occultation in the lower part F—but from left to right: for here too, in the second case of this third figure, you must imagine the eye of the observer to be behind, after the disk ABCD.

[VIII.] These are those admirable changes which Galileo divined, by his conjecture, as [things] to come, if indeed those three suppositions be admitted—namely, [that] the Sun carries the spots around with it by its own vertigo, and [that] its axis is inclined to the plane of the Ecliptic but with the same inclination perpetually remaining, and [that] the Earth is revolved by an annual motion around the Sun, [the Sun] remaining in the center of the World. But to Giovanni Francesco Sagredo, asking whether afterward such changes were really observed, Salviati (who sustains the person of Galileo in those dialogues) answers that the observations were continued at different times of the year, and that the events answered the prediction most exactly. Then Sagredo, turning to Simplicio, infers (Latin page 260, but Italian 344): “Lord Simplicio, if these [things] are true which Salviati has set forth (nor indeed is it lawful to doubt his assertions), for the Ptolemaics and Aristotelians there will be need of solid arguments, valid conjectures, and most firm experiments, that they may be able to counterbalance this objection of so great weight, and not incur the utter destruction of their opinion.”

But Simplicio answers acutely and solidly [that], even if—the annual motion of the Earth being posited, and the remaining conditions of which [we spoke] above—the Phenomena of the Solar Spots be saved, yet this argument is not valid conversely; namely, [that] if such are the Phenomena of the Spots, [it does not follow that] the Earth is moved and the Solar axis is of fixed inclination, unless it be demonstrated that those Phenomena cannot otherwise be defended. For why could they not be saved, the annual motion of the Sun about the immobile Earth being posited? Then Salviati concedes indeed that this can be done, but [says] that many [things] must be admitted, and

[…continues on p. 354 (PDF 389) with the catchword “conti[nuo]”: ”…[many things and] continuous [improbabilities]“—Salviati’s qualification, and the start of Riccioli’s own reply to the sunspot argument.]

(printed p. 354 — within Chapter XII. Salviati’s simplicity claim for the Earth’s annual motion is endorsed by Gassendi, whom Riccioli convicts of a double error; the argument is cast in form and answered (the motions are equal in number under either hypothesis, and the Earth’s motion destroys more evident phenomena). The promised Epitome of Scheiner’s sunspot doctrine is then announced, beginning with the first Welser letter and Scheiner’s 1611 discovery.)

[Header: BOOK IX. SECTION IV. — 354]

[Margin: The annual motion of the Earth is gathered from the things said.]

continuous motions, by which the axis of the Sun perpetually changes its inclination to the axis of the Ecliptic, and on account of which that axis is bent from moment to moment toward other and other points of the Universe; and so that this axis has its own proper monthly revolution, distinct from the annual revolution—since indeed, every year, once, the whole variety of the motion of the spots is perfectly completed and recurs again—and [so] that that axis has a convertible inclination, so that sometimes it is in the plane of the Solar horizon (and therefore the path of the spots is rectilinear), but sometimes in the Meridian of the observer, yet outside the horizon of the Solar globe, and sometimes in other and other planes. But it is far more probable, says Salviati, that the axis of the Solar vertigo is unique and has a fixed inclination to the plane of the Ecliptic, nor [that] the Sun is moved by any other motion than by a simple revolution of about 27 or 28 days about its own immobile center, and [that] all the remaining changes of the spots happen through the single and simple annual motion of the Earth; than that, the Earth standing still, the Sun be implicated by manifold motions, and [those] of its own axis: Therefore it is also more probable that the Earth, rather than the Sun, is moved annually.

[Margin: Gassendi’s opinion on the annual motion of the Earth, but errors about the motion of the Spots.]

[IX.] Struck, therefore, by this argument among others, Pierre Gassendi (Epistle 2 On the Motion impressed by a moving mover, p. 148) did not hesitate to burst forth into these words:

“It is wonderful that the paths of the spots, while the Sun is in the Equinoctial points, describe as if straight lines on its disk; but in the others, and most of all in the Tropics, curved [lines]: nor can this be more conveniently saved than from the fact that—the Sun being always revolved upon those same poles of its Ecliptic, and carrying the spots down—the Earth so sets itself to it, now as if to the right or the left in the Equinoxes, now as if up or down in the Solstices, so that, on account of the explained containment of its axis, it sees the spots proceeding not in one way through the disk of the Sun, but with that recounted variety of straightness and curvature: so demonstrates Galileo.”

In which words a double error lurks: for, first, neither Galileo nor Scheiner, in their second [more mature] reflections, admit the vertigo of the Sun to take place upon the poles of the Ecliptic—otherwise the path of the Spots would always appear rectilinear to us; then, it is not true that their path is seen rectilinear in the Equinoxes, and most curvilinear in the Solstices, since, on the contrary, it rather appears rectilinear about the beginning of December and June (that is, nearer the Solstices), and most curvilinear about the beginning of March and September (namely, nearer the Equinoxes), as we shall presently narrate from the most certain observations of Scheiner. Now to the Argument gathered from this motion, reduced into form, we must respond.

[Margin: The argument reduced into form.]

[X.] It is more probable that the apparent motions of the Solar Spots are made by simpler and fewer motions, than by more, and more compounded. But if the Earth is moved annually around the Sun, rather than the Sun around the immobile Earth, the apparent motions of the Solar Spots are made by simpler and fewer motions, than if the Sun be supposed to be moved annually around the immobile Earth; Therefore it is more probable that the Earth, rather than the Sun, is moved annually. The MAJOR is clear from those most-received propositions, so often sung in this section—namely, that GOD and Nature do not endeavor through more [means] what can [be done] through fewer, and therefore that it is not even permitted to us to introduce a multiplicity of beings, much less of motions, without necessity, into the nature of things. The proof of the MINOR has been sufficiently indicated by comparing those [things] which were said at numbers 5, 6, & 7 with those which were said at the end of number 8; and they will be confirmed by the change of the Solar axis asserted by Scheiner and others, who expound these Phenomena by the hypothesis of a resting Earth.

[Margin: 1st and 2nd Response.]

I answer, 1 and 2, in the same manner in which I answered to the Major of Argument 1, which I proposed at chapter 9, number 5: namely, by conceding the Major, if the simplicity of these motions, at first sight, be greater and involve no greater absurdities, or save other phenomena more evident to sense than these; nor, inwardly inspected, involve more other motions with itself; but otherwise by denying the Major of the syllogism, and its proof. But in the same sense as I there denied [it], so I here deny the Minor: for if the Earth be supposed to be moved, and the Sun to remain in the center of the world, certain Phenomena more evident to sense are destroyed than is the motion of the Solar spots, and in the motion of the Earth there lie hidden very many other [motions], manifold in kind and number, most intricate, and in the understanding nothing more easily perceptible than the motion of the Solar axis having a convertible inclination—since the same convertibility of the inclination of the Earth’s axis to the Equator is involved with at least a double libration: one on account of the precession of the Equinoxes, the other on account of the obliquity of the Ecliptic, if we hear Copernicus.

[Margin: 3rd Response.]

I answer, 3, the Major being granted, by denying the Minor. For if the Earth be supposed to be moved annually, it must also be supposed to be moved by a diurnal revolution about its own axis; and, for the phenomena of the spots, there is required, besides, a vertigo of the Sun about its own axis, as if completable by a monthly revolution—which are three motions really distinct. But if the Earth be supposed to rest, a triple motion of the Sun too must be supposed: one of the Sun’s center, which is at once annual and diurnal, through a spiral line (whereby it therefore seems to be moved toward the East, because in the motion toward the West it is slower than the Fixed stars and the ideal motion of the prime Mobile); the second indeed, the annual [motion] of the Solar axis about its own fixed axis, from West to East; and the third, as if of a monthly vertigo, about another mobile axis, from East to West, as we shall make plain at number 22 & 23 from Scheiner. Equal, therefore, in each hypothesis is the multiplicity of real motions; but in the others there is a great disparity, on account of which [it] rather seems [it] should be pronounced for the rest of the Earth.

[Margin: 4th Response, Chiaramonti’s, rejected.]

Chiaramonti would answer, 4 (in the Defense of the Antitycho, part 4, ch. 18), that, without a motion of the Sun’s axis or an annual conversion of the Earth, the Phenomena of the Spots can be defended, if they be said to be moved in their own Epicycles; but this response supposes the Spots of the Sun not to inhere in the very body of the Sun—which is false—and, besides, multiplies the motions [to] as many as there are spots, which rather favors Galileo’s argument than destroys it.

[XI.] Now it is time that we respond to the solution of the argument for which (at bk. 3, ch. 3, at the end of number 8, and in the title of this chapter) I pledged my faith: [namely] the phenomena of the Solar Spots, especially [those] pertaining to motion, I would expound more clearly than I expounded there, and reduce into an Epitome for my Reader—who perhaps lacks books of this kind—[setting forth] what Scheiner first wrote about these in Apelles behind the Table, and what he afterward [wrote] in the Rosa Ursina, correcting himself, and (that I may not say [made] greater than the Sun) now made more illustrious, [as] he handed down to posterity. For, as it is not to be turned to dishonor to Galileo, so also to Scheiner [it is not dishonorable], if, in their first observations—on account of the novelty and perplexity of the phenomenon, and its sublime and arduous contemplation, which it otherwise demanded—they said some [things] less consonant with truth, since afterward, by correcting themselves, they deserved the praise of Astronomical sincerity; and Scheiner [deserved it] by so many and so exact observations, and theorems and problems about this argument, [which] he discoursed in the Rosa Ursina, so that he merited from Reinier, or René, Descartes, and from Johann Hevelius, that praise: namely, that nothing in this kind could have been done more accurately, or be hoped to be done in future.

[Margin: The praise of Fr. Nicolaus Zucchi for Scheiner.]

And Fr. Nicolaus Zucchi of our Society—who was an assiduous witness, instigator, and helper of Scheiner’s observations—in his new and noble Philosophy of Machines (part 5, section 12) began with this praise:

“It being first supposed here the Canons of the motion detected in the Sun in this our age—which, by the most constant labor of very many years, by deliberately [examining] the heaven more often day by day, the rules of a better Astronomy being employed, new [ones] wisely added, Fr. Christopher Scheiner of our Society established—the later [astronomers], not only the inspectors of books but also of the stars, so approved [them] that from them even those who before were his Censors corrected their own errors, supplied the omitted [things], in nothing daring to contradict; and most recently, through three years, the ordered courses of the Sun’s Spots were published [by] a man best deserving of Astronomy—whom I shall presently name in his Selenographia book.”

The Doctrine of Christopher Scheiner on the Solar Spots, from Apelles behind the Hidden Table, or the Letters written to Markus Welser

[Margin: From the 1st Epistle.]

[XII.] In the first Epistle—given in the Year 1611, on the 12th day of November—he narrates that about eight months before (namely, in March of the Year 1611) he directed an optical tube, which magnified an object nearly eight-hundred-fold in surface, at the Sun, that he might explore the optical magnitude of its diameter relative to the Moon;

[…continues on p. 355 (PDF 390) with the catchword “[So]lem”: “…at the Sun, that he might explore the optical magnitude of its diameter relative to the Moon”—the rest of the Epitome of Scheiner’s Welser-letters, then his doctrine from the Rosa Ursina .]

(printed p. 355 — within Chapter XII, continuing the Epitome of Scheiner’s Welser letters: the spots are no artifacts of eye, glass, or air, though Scheiner first wrongly judged them stars near the Sun; later letters describe their appearance, births, and deaths, and the pinhole-camera proof of their reality. The second sub-head, Scheiner’s doctrine from the Rosa Ursina, then opens with Riccioli’s defense of Scheiner against Galileo’s charge of plagiarism.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 355]

[at the Sun], that he might explore the optical magnitude of its diameter relative to the Moon; and on that occasion he saw certain blackish spots in the Sun, but was then not solicitous about them; but afterward, in the month of October, having returned to this observation, at first he doubted whether those spots were from some hidden defect in the air, or the eye, or the glasses of the Telescope. But when, with different eyes employed in testimony, and the glasses and tubes being changed—eight [being] employed—the same spots appeared in the same order, position, and number, he concluded that they were not from a defect of the eyes or the glasses; but neither from the air—both because they were moved by the motion of the prime mobile with the Sun the whole day (and nothing in the air is so constantly moved by such a motion under so small a portion of the heaven as the Sun is); and because they admitted no parallax the whole day, as they ought [to have], if they had been near us in the air, but appeared the whole day on the disk of the Sun; and because, by their own motion, they were turned from the eastern limb of the Sun to the western, with the Sun, for several days, until they vanished from the eyes; and, finally, because their phenomena seemed unvaried through mists and clouds. But since he then thought it unworthy to admit in the Sun—a most lucid body—some spots blacker than the Lunar ones, and [since] the same ones did not return yet to view, but always other and new [ones], he judged them not to be revolved by the Sun, nor to be in the Sun, but [to be] as stars going either below or around the Sun by their own peculiar motions, and eclipsing it to us. He confesses, nevertheless, that not all the observations which Welser granted [him to publish] were then most exact, and [that] certain [spots], inspected without a tube, seemed simple [single], which through the tube appear aggregated out of many.

[Margin: From the 2nd & 3rd Epistle.]

[XIII.] In the 2nd Epistle—given in the Year 1611, on the 19th day of December—he reports that he was intent on the conjunction of Venus with the Sun, which by Magini’s Ephemerides ought to begin on the 11th day of December, at the 11th hour of the night, and to last at least 40 [hours]; but [it was] not seen under the Sun, whence he took the argument that it [Venus], in the superior conjunction, is borne above the Sun. But in the 3rd Epistle—written on the 26th of December—he contends [that] the Spots are not in the very body of the Sun: because, since they do not all appear under the Sun for fifteen days, from their first appearance to occultation, if they were turned with it they ought to return after another fifteen days, or a little after; but by the experiment of two months none were seen to return. But, on the other hand—from the defect of all parallax from the Sun, and from this, that in their appearance and occultation about the limbs of the Sun they grow slender, and from several seen in the middle of the Sun they seem to coalesce into one at the margins, and because in the middle of the Sun’s disk they are swift, at the limbs slow—he gathers them to be near the Sun, and to be moved about the Sun by their own motions, and to be certain Heliacal stars, very dense, opaque, and deep, inasmuch as [they intercept] the light of the Sun; and to be erratic [wandering] stars rather than fixed; and [that], as around Saturn and Jupiter there are satellites, so around the Sun, etc.

[Margin: From the 4th Epistle.]

[XIV.] In the 4th Epistle—written to the same [Welser] in the Year 1612, on the 16th day of January, from 30 observations begun on the 10th day of December of the Year 1611 to the 12th day of January of the Year 1612—he affirms [that] the spots, in entering and leaving the Sun, are seen small, slower, and blacker, and at the same time united; but in the middle of the Solar disk large, swifter, less black, and more separated from each other: but [that] certain ones, and very large, unexpectedly arise not in the limb, but nearly in the middle of the Sun’s disk, or there suddenly fail [disappear], before they reach the margin of the Sun; but [that] certain ones divide from one into two—and that in nearly the middle of the Sun—or two coalesce into one, and so, divided or conjoined, persist up to [their] exit. He adds [that] their path appears parallel to the Ecliptic, but suspends [his] opinion; yet he thinks it certain that those which traverse the middle Sun delay more under the Sun than those far from the middle, whence he takes a new argument [that] they are not affixed to the Sun (which is revolvable about its own center): for one spot, seen under the Sun, [delayed] at least 16 days; another, more distant from the middle of the Sun, delayed under the Sun at most 14 days; but another, 13.

[Margin: From the 5th Epistle.]

[XV.] At length, in Epistle 5—given to Welser in the Year 1612, on the 25th day of July—he first confirms [that] these spots are not a mockery or a mere spectrum, appearing by a defect of the eye, glass, or air; since to whatever eye, in whatever position under the open air, without glasses, the same [spots] are seen in the same order, position, and number, if a ray of the Sun, through a bare hole not exceeding the magnitude of a pea, be received in a dark chamber on a paper equidistant from the Sun’s disk. And, besides, because the same [spots] were seen and observed in diverse places—namely, at Rome by the Fathers Christopher Grienberger and Paul Guldin, distinguished Mathematicians of the Society of Jesus, [and] by Galileo and others—from which, and from his own observations, he concludes (with a certain Venetian, who concealed his name under “Protogenes”) that these spots are real bodies, not in the Sun, but near the Sun; not spherical, but of irregular and variable figure, and therefore not stars:

[Margin: Judicial Astrology [harmed] by the Solar Spots.]

yet their interposition, unknown to the old Astrology, greatly harms [it], since, for varying the sublunary effects, so many bodies, persisting so long beneath the Sun, can do more than Mercury alone conjoined to the Sun, and not wont to delay under it except for a few hours.

The Doctrine of Christopher Scheiner on the Spots of the Sun, from the Rosa Ursina, reduced into an Epitome

[XVI.] Book 1. Since Galileo—in the Discourse on the Comet of the Year 1618 (p. 3), and in the Assayer [Trutinator] (p. 2 & 209), and in the dialogues On the System of the World (page 337 Italian)—vaunts himself as the first inventor of the Solar Spots and of all the novelties of the heaven, and makes Apelles (namely, Scheiner) guilty of theft, as if, after seeing Galileo’s writings about the spots, he began to observe them, and boasted himself the first observer of them: Scheiner purges himself from this imposture. For indeed [he says] that he, with no previous rumor or indication, began to observe them in the Year 1611, in March, while he explored the magnitude of the Sun by the Telescope, and afterward, in October, resumed the observations, and warned about these Fr. Adam Tanner and Fr. Jacob Gretser—who indicated this to M. Welser, the Maecenas of all literary men; and [that] Welser, by many letters, extorted at last from him the novelty of this phenomenon, and solicited that it be published in print: which [was done] by the three earlier letters, given in the year 1611, but under the feigned name of Apelles, because Fr. Theodor Busaeus the Provincial was unwilling that these novelties, not yet sufficiently explored, be published under the certain name of Scheiner. But Welser communicated Scheiner’s letters at once to Galileo in the Year 1612, on the 6th day of January; but Galileo, answering him in the same year, on the 4th day of May, affirms that he had observed the Sun’s Spots before the eighteenth month [i.e. eighteen months earlier]: and yet he produces no observation of the Year 1611 with a diagram, but only of the Year 1612, from the 5th day of April; whereas he ought to have produced diagrams of the spots observed in the Year 1611, and the beginning of the Year 1612, as Scheiner produced—whereby he might at least make it probable that he was not later than Scheiner in observing those [things].

[Margin: Scheiner vindicated from the imposture of the theft of Galileo’s observations.]

How then could Scheiner steal his observations—anterior in time, and performed before April of the Year 1612—from the observations of Galileo, which neither then nor afterward were published? But Galileo, in that epistle, excuses himself, that he did not publish his observations earlier, on account of the suspension of [his] mind and the fear of erring; but Scheiner, meanwhile, had absolutely published many of his propositions, and indeed contrary to the sayings of Galileo: for Scheiner had then already said the apparent motions of the Spots to be unequal, and their delays under the Sun diverse, and certain ones to be blacker than the spots of the Moon, and things similar to these—the opposite of which Galileo affirms in the Epistles to Welser. Therefore, if Galileo wrote nothing about the Sun’s spots before he saw Scheiner’s Apelles behind the Table—communicated by the Venetian from Welser—nay, [if] he determined nothing certain about them, but Scheiner, meanwhile, had published in print many [things], and contrary to these which Galileo afterward decreed, how could he steal his observations from Galileo’s writings? Then, it is false that Scheiner vaunted himself in his letters as the first observer; for neither did he there deny that others had observed them, nor did he usurp to himself the invidious nomenclature of first inventor, but only narrated what had unexpectedly come to him without any previous rumor or indication—which could be true, even if a thousand years before someone else had observed the same, but with Scheiner not knowing: be it that really it was so, as the facts themselves (which speak more than words), and the chronological comparison of other observations with the Scheinerian, testify. To which I add the Rosa Ursina—in which, among other [things], the curvilinear motion of the Spots (except at two times of the year) is demonstrated—[which] began to be printed in the Year 1626, and was published in the Year 1630. But Galileo’s dialogues were published in the

[…continues on p. 356 (PDF 391) with the catchword “[An]no”: “…in the Year [1632]“—the rest of the chronological vindication of Scheiner, and the Epitome of the Rosa Ursina sunspot doctrine.]

(printed p. 356 — within Chapter XII, the Epitome of Scheiner’s Rosa Ursina: summaries of Book 2 (the Helioscope and observing methods) and Book 3 (some 1425 observations, 1618–1627, with the spot-paths oblique to the Ecliptic and seasonally reversing curvature), then the opening propositions of Book 4 Part 1 (the faculae prove the spots on the Sun’s own surface; the paths are uniform, rectilinear twice yearly and curved between).)

[Header: BOOK IX. SECTION IV. — 356]

[An]no 1632. Since, therefore, in their third [dialogue], Galileo himself corrects [himself], and admits the curvilinear motion of the spots—which he had always otherwise thought rectilinear—some could suspect that this was done by him from having seen the Rosa Ursina, or from having heard the [things] which at Rome P. Scheiner had communicated to many outsiders, whom he admitted in good faith as witnesses and observers of his observations: especially since Galileo says, in that dialogue, that twice only in the year the path of the Spots is rectilinear, and that for six months it ought to be curved upward, for the other [six] curved downward, and affirms that the event answered this his own vaticination [prophecy]; nor yet does he dare to say in which months of the year these changes occur—which assuredly he ought to have said, and would have said, if he could have decided these from his own observations. It is therefore no light indication that he inserted this emendation of his into the Dialogues, not so much from his own observations as from the sight or hearing of others’—which, however, I would not dare absolutely to affirm. Moreover, Scheiner, in this book, puts the diagrams of observations formerly held at Ingolstadt.

[Margin: From book 2.]

[XVII.] Book 2 teaches the use of the Helioscope (which [is made] with colored glasses) and of the Telioscope (which [is made] with glasses or lenses not colored); and demonstrates from optical foundations the choice, approbation, and combining of lenses; as also the admission of the species [image] through a bare hole, and the transmission through the Telioscope; the difficulties in observing the Spots and Faculae, and the cautions to be employed; likewise the practice of drawing the vertical line (or perpendicular) and the Ecliptic, [and] the times suitable for observing—although at the end of book 3 he exhibits a new machine, by which the Solar spots are most easily observed.

[Margin: From book 3.]

Book 3. He exhibits and explains the observations themselves of the Spots, both his own and others’.

[Margin: The motion of the Spots somehow oblique to the Ecliptic, and into which regions.]

And he forewarns (page 161) that the paths of the Spots proceed obliquely to the Ecliptic, from the North-East into the South-West, from the vernal equilibrium [equinox]—which falls at the end of February and the beginning of March—up to the autumnal equilibrium, which falls at the end of August and the beginning of September; but in the first three months (March, April, May) the path-arcs are concave toward the South-East, convex toward the North-West; but in the other three later [months], after the rectilinear station celebrated at the end of May and the beginning of June (namely, June, July, August), the concavities of the paths are turned toward the West-North, and the convexities toward the South-East. But all contrary [things] happen from the autumnal equilibrium (which falls at the end of August and the beginning of September) up to the vernal [equilibrium], which [falls] at the end of February and the beginning of March: for in its first three months (September, October, November) the paths of the spots are concave toward the North-East, convex toward the South-West. But after the winter station was celebrated, rectilinear, at the end of November, the bendings of the spots in December, January, [and] February are concave toward the South-West, convex toward the North-East. But now in this book are contained the observations held from the Year 1618 to 1627, which are comprehended in 71 images; and the number of observations exhibited in them ascends, as I have reckoned, to the number of 1425—the greatest part of which was held by him at Rome, [and] a few, some [of them], by others of our Society at Ingolstadt, Freiburg, [and] Douai. He terminates this book, finally, with a new Telescopic and Heliotropic instrument [made] by P. Grienberger, by which—without the angle of the Ecliptic and the vertical, without the leading-in of a perpendicular, without the altitude of the Sun—the course of the spots, the position of the Ecliptic, and the rest necessary to this business is most expeditiously taken; demonstrations being added that prove the instrument, devised by Grienberger himself: and a Table of Right Ascensions and Declinations constructed by the same, for one quadrant of the Ecliptic, for every five minutes of degrees.

[Margin: From book 4, part 1.]

[XVIII.] In Part 1 of book 4, from the observations of book 3, Scheiner demonstrates the following propositions. Cap. 1. All the spots, says he, which pertain to the Sun, as long as they appear, never appear outside the Sun, but rise with it, and—the diurnal motion being performed—set with it, from whatever part of the [Earth’s] orb they be viewed. And Cap. 2. All the spots always seem to be moved from the Eastern region of the Sun into the Western [region] of the same. And Cap. 3, 4, 5, 6. No part of the heaven of the Moon, of Mercury, or of Venus can, by its interposition, cause any Spot on the Sun. And Cap. 7. No spot or facula appears outside the conspicuous disk of the Sun; the Light of the Solar Faculae is stronger than the rest of the light of the Sun, and [than] the diurnal light scattered through the aether; the Faculae of the Sun are parts of the Sun, which—since they are moved by the same motion as the Spots—argue that the Spots are in the very Sun, and so that the Sun rotates about its own center; otherwise, if the faculae were outside the Sun, placed in the margins, they would sparkle outside the Sun: Hence are barred the proper Epicycles and Eccentrics of the Spots and Faculae, and it is gathered—even from this alone—that they are not stars distinct from the Sun. And Cap. 8. No spot has been seen, hitherto, either to stand still on the Sun, or to go back, or to plunge headlong, after so many years of observations (that is, from the Year 1611 to 1627); whence it is confirmed that they are carried about by the Sun, and not by their own Eccentrics or Epicycles. And Cap. 9. The paths of all the Spots appearing at the same time (other things being equal) appear of the same kind and position—that is, of all [either] rectilinear, or of all curvilinear, and swelling with their convexity into the same region; whence it is gathered that there is a certain motion universal to all, [arising] from a certain common subject moving them. And Cap. 10. All the paths of the Spots described yearly by the same parallels are, to sense, similar to themselves, and for the most part equal in time; that is, if (for example) in the Year 1627, on the 22nd day of August, such motions are described by a spot in such a parallel of the Sun, then also in the Year 1628, on the 22nd day of August, if any spot be in such a parallel, it will describe a motion similar to the aforesaid—that is, curvilinear upward, if [the other was] curvilinear upward—and so of the past and future years. And Cap. 11. All Spots in parallels equally distant from the greatest parallel of the Solar globe, and distant from each other by a six-month interval, have similar motions, but contrary in position and tendency; from which uniformity it is confirmed that they are moved by the motion of one universal subject. And Cap. 12.

[Margin: When the path [is] rectilinear.]

The paths of all the Spots and Faculae become, twice in the year, rectilinear to sense—namely, once about the end of November and the beginning of December, and again about the end of May and the beginning of June—and yet their paths are oblique to the Ecliptic; and the time of the rectilinear delays under the Sun is of about two weeks, or nearly 14 days. But the tendency of the sub-brumal [near-winter] rectilinear [paths] is from the rising South into the setting North; but of the sub-aestival [near-summer ones], from the rising North to the setting South. And Cap. 13. [He shows] that the Sphere in which the Spots are thought to be rotated about the Sun is not greater than the Sun, and is concentric with it; and Cap. 14. but neither eccentric [heterocentric]; and Cap. 15. but neither greater than the Sun and of mixed eccentricity. And Cap. 16. All the paths of the Spots become, from rectilinear, curvilinear, so that

[Margin: When the path of the Spots [is] curvilinear.]

from about the beginning of December they become, through three months (December, January, February), daily more curvilinear, the arc swelling upward toward the Northern part of the Sun, and at the beginning of March they become most curved; but thence the curvature decreases more and more in March, April, May, until at the end of May they come out, to sense, rectilinear; hence again they pass off into curvilinear, so that from the beginning of June their curvature continually increases—but downward, toward the South—through three months (June, July, August), at the end of which this curvature is greatest; but thence, from the beginning of September, the curvature decreases through three other months (September, October, November), until at the end of November the paths come out rectilinear. And Cap. 17. From the said motions he gathers [that] the motion of the Spots is, to sense, regular and ordered, and uniformly deformed, and about a mobile axis of the Sun—since the spots are swiftest in the middle, slower (with proportion) about the limbs, and [move] from East to West always, and have appeared so constantly with a reciprocal passing from rectilinear into curvilinear paths. The motion, too, of this axis and of the poles, from West to East, so that in one half-year one pole is in the part of the Sun conspicuous to us, the other in the inconspicuous [part], and, conversely, in the other half-year the [pole] which was conspicuous is hidden, has become known from the six-month contrariety of the course: And from the ascent and descent of the Axis and Poles, every change [vicissitude] appearing in the motion of the Spots comes about. And Cap. 18.

[Margin: When the greatest curvature, and the equilibrium.]

The paths of all the Spots [are] rectilinear about the beginning of June, and about the beginning of September most curvilinear toward the South; but about the beginning of December rectilinear, and about the beginning of March most curved toward the North; but when they are most curved, then also they are in Equilibrium, so that the termini of the rising and of the occultation—if the Sun be with its center equally distant from

[…continues on p. 357 (PDF 392) with the catchword “ab”: ”…[equally distant] from the horizon”—the rest of the Rosa Ursina propositions (the optical/refraction irregularity, then the physical generation and decay of the Spots).]

(printed p. 357 — within Chapter XII, continuing the Epitome of Scheiner’s Rosa Ursina Book 4: the apparent irregularity of the compound spot-motion arises from refraction in the telescope lenses, so the true regularity confirms the spots are on the Sun. The page then treats the physical growth and decay of spots and faculae — their life-cycle proving real generation and corruption of solar matter.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 357]

[equally distant] from the horizon—appear equally elevated, that is, in the 90th degree of the Ecliptic. And Cap. 19. All the courses of the Spots, if the annual [course] be regarded separately, and the monthly separately, are regular—that is, both that which is made by the Solar poles describing little circles by an annual revolution, and that which is completed in the space of about a month; but if they be compounded together, from them some irregularity is conflated, yet, in a single course, imperceptible: which here he shows concerning the rectilinear motion, and Cap. 20. concerning the curvilinear; but from Cap. 21 to 33 he shows that that irregularity is from the refraction of the Solar rays, transmitted through the glass lenses, received into an image of the Sun—from which it happens that about the margins of the Sun greater arcs are seen to be traversed by the Spots in less time, and about the middle of the Sun lesser [arcs] in more time; and therefore that from this irregularity no parallax of the Spots, or distance from the Sun, can be gathered. And Cap. 34. He gathers the true regularity of the motion of the Spots from corrected experiences, and [argues] that, if they be in the Sun, it ought to be regular; and that they are in the Sun he confirms by the arguments indicated above, and by others to be indicated. Thus far concerning [their] motion.

[Margin: The growth and diminution of the Spots.]

[XIX.] But now, in the same first part of book 4, Cap. 35, he treats of the growth and diminution of the Spots and Faculae—not only Optical, or apparent, but also Physical and real—and says [that] the spots are on the physical surface of the Sun, just as there are hills on the surface of the Earth (which is not Geometrically spherical); and [that] none of them is moved about its own center. Besides, although all the spots (other things being equal) optically seem smaller near the margins of the Sun, and larger toward the middle of the Solar disk, yet, by a physical growth, [they are] sometimes larger about the margins, and, by a physical diminution, [smaller] about the middle—appearing so when the compensation is made. And Cap. 36. He shows [that] the Solar Spots, round, rotated about the Sun, present to sight, from [their] aspect, the same disposition on the hemisphere of the Sun which they would exhibit if they were similarly rotated about their own center, conjoined with the center of the Sun. Cap. 37. He asserts [that] a physical growth and decrease has befallen all the spots hitherto observed, but [one] varied and successive; and [that] the whole time of the growth of the same spot is nearly equal to the time of [its] decrease, though the parts of this time do not have an equal or uniform quantity of magnitude, nor are the times of the growth of one spot equal to the times of the growth of another spot; but [that] the diameter of the spots is physically increased sometimes two-, three-fold and more; and [that] the growths of some [happen] not rarely from the aggregation of several, just as [their] decreases [happen] from disaggregation. Cap. 38. He reviews the various modes by which the physical augmentation can take place, and chooses,

[Margin: The obscurity and opacity, [and] color, of the Spots.]

as the most probable, that one which is made not by alteration alone, or by rarefaction, but by generation from the Solar matter. Cap. 39. He treats of the variable obscurity and brightness of the Spots. And Cap. 40. of the nucleus of the Spots—that is, of the blacker part in the middle. Cap. 41. [That] the Spots cannot be shadows projected onto the Sun. Cap. 42. Nor can they be a mere apparent opacity, but Cap. 43. [that] there is in them a true opacity, and Cap. 44. a true color, and Cap. 45. [that] it is probably blackness, Cap. 46. and [that] it is physically intensified in the nuclei; concerning which Cap. 47. he dispatches many little questions, as Cap. 48. many concerning the light and brightness of the spots. But thereafter Cap. 49. he treats of the figures of the Spots, [which are] irregular and slender and subsequently variable; And Cap. 50. [that] the physical Solar surface is alterable in several ways by so great a variety of Spots, Faculae, [and] Umbrae. And Cap. 51. he teaches, by many arguments, [that] the Spots and Faculae are physically generated and perish on the surface of the Sun;

[Margin: The Physical and Astronomical rising and setting of the Spots and Faculae.]

for the understanding of which know that the Astronomical Rising of the Spots is so called when, on account of the vertigo of the Sun, they begin to appear on its eastern margin (which, to us Northerners turned toward the South, is the left); but the Astronomical Setting is so called when, on account of the same vertigo, they begin to be hidden on the western margin of the Sun (and, to us, the right), and to traverse the upper hemisphere of the Sun, hidden from us. But the Physical Rising is so called when they really come into being anew, and therefore appear indiscriminately on any part of the Solar disk, provided it be conspicuous to us; and the Physical Setting, or destruction, is when they are extinguished and really cease to be. These [things] being laid down: The greatest part of the Spots, says Scheiner, is born immediately on the face of the Sun, far from the rising margin, grows, and proceeds to the western limb, until it sets astronomically; a great part of them, likewise, rises astronomically, but before the astronomical setting physically fails entirely; many also there are which obtain neither an astronomical rising nor setting, but between the one and the other begin and cease to be on the face of the Sun: yet certain ones there are which last from the astronomical rising up to the astronomical setting—whether they be of those which had physically risen in the hemisphere of the Sun hidden from us, or [of those] which, by their duration, are equal to the whole conversion of the Sun of about 27 days. But rarely does a large spot appear which is not born physically and does not fail without an astronomical rising and setting; and spots of this kind grow with the company of many [others], which, however, after about two or three days, are diminished, the retinue of the spots withdrawing itself.

[Margin: The rising and setting of the Faculae.]

But of the Faculae, many perish, after an astronomical rising, before [their] setting; many, without an astronomical rising, flash forth anew on the face of the Sun and set astronomically; some, but more rarely, are kindled and extinguished in the middle of the Sun, without an astronomical rising or setting. Besides, neither do they all return after a vertigo of 27 days, nor have any hitherto endured so [long] that, in one whole year—not to say in several—they have returned with repeated vertigoes; therefore very many have perished before the year’s end. To this, the secondary Spots and Faculae, which are outside the middle Zone of the Sun, are in perpetual change of themselves, and with these the surface of the Sun is full. Finally, there have been some months in which no large spot appeared on the Sun: Are these not physically evident arguments of a real rising and destruction? Again, Cap. 52. he confirms the same generation and corruption, in that a greater number of Spots is kindled into faculae; for this can be done neither by rarefaction alone, nor by their dissipation from the Sun made through rarefaction—as if that part of the Sun now shines through which before was suffering an eclipse by the spots; for in this way they would not appear on the margin of the Sun, if we suppose it (as the Peripatetics posit) both perfectly round and of uniform density and opacity. In which place he confutes, at length, certain [men] saying [that] the Sun has a certain crust, thin and transparent in one place, opaque in another, in which [the spot] is enclosed, or [men] defending these Phenomena more violently in some other way through translucency. Hence Cap. 53. he teaches [that] the Solar Spots cannot be made from a mere concurrence of opaque parts, if hard orbs be supposed to be rotated perpetually about the Sun; but [that] they are generated and corrupted, as much as the Faculae [are]; again Cap. 54. he establishes [this] from the manner of [their] beginning and ceasing.

[Margin: The various modes of the destruction and rising of the Spots.]

For some Spots, in the middle of the Sun’s disk, decrease in bulk, and are attenuated into a shadow [umbra], so that they are scarcely distinguished from the rest of the surface of the Sun, except by the agitation of the instrument: which shadow sometimes comes out into a facula, sometimes vanishes without a facula; but sometimes is split into minute spots, like black points, which points, advancing together in order through several days, pass off into faculae. And not rarely they leave behind them a tract and a faculent or shadowy trail, or are dilated into one continuous shadow, or, the others vanishing, grow strong again, and increase into new spots, which again pass off into shadows or torches [faces], by a reciprocal, as it were, struggle. Often some Spots seem to be overwhelmed on every side by brighter matter, until they become torches; and the faculae are sometimes pure, sometimes fenced about with nebulous traces. But all the Spots at last end either in Faculae, or in shadows, or in the ordinary surface of the Sun. But in their rising, many, from the thinnest shadows, as if from spiders’ webs, made denser, blacken and grow; many, from the smallest and discrete [shadows], boil up and, dilated, make one continuous Spot; many, from Faculae joined with a shadow, degenerate into spots—yet always the beginnings are smaller in intensity and extension, and the growths are completed sometimes after a few hours, sometimes only after whole days. Again, the Faculae are more unstable than the Spots, more difficult to observe, and for the most part larger than the Spots from which they have arisen. Yet not by a continuous chain, as it were, of reciprocal rising and destruction is a facula made from a Spot, and from this facula a second spot, and from the second spot a second facula, and so to infinity; but this succession is frequently interrupted, nor does it last except as the condition of the underlying matter permits. Who, all these [things] being weighed, would not concede their physical rising and destruction? For what greater indication of such a rising and corruption have we in the sublunary region too?

[XX.] These [things]

[…continues on p. 358 (PDF 393) with the catchword “His”: “These [things] being so / laid down”—¶XX, the close of the Rosa Ursina epitome and Riccioli’s turn to the solution of the sunspot argument.]

(printed p. 358 — within Chapter XII, still the Epitome of the Rosa Ursina: the total absence of parallax (the same spots seen simultaneously from Europe and the Indies) proves the spots lie at the Sun, Riccioli concluding it safest that they ride the rotating Sun. Book 4 Part 2 then begins the Theory — the spots’ twofold regular motion, rectilinear twice a year — and a large engraved diagram of the general system opens.)

[Header: BOOK IX. SECTION IV. — 358]

[Margin: The place of the Spots and Faculae.]

[XX.] These [things] being established, now (Cap. 55) he shows that the place of the Spots and Faculae is truly in the Sun itself, or very near [it], from the defect of all parallax: since indeed they were observed, by diverse observers in diverse places of the earth, at the same time, and found in the same part of the Sun, as appears from the Schematisms [diagrams]; but if any were observed at a different time, they were nevertheless found, by the later observers, advanced toward the western part of the Solar disk, by as much as the proportion of the intervening time required relative to the vertigo of about 27 days. For hence, at least, it is concluded that they do not so far stand off from the Sun as to admit a parallax sensible to us. And Scheiner affirms that there were transmitted to him and to P. Paul Guldin, from the West Indies, by P. Caspar Ruess (formerly instructed by him at Ingolstadt), and from the East [Indies] by others, many observations; which, compared with his own and others’ held in Europe, no parallax at all was detected, but the same spots [were] seen on both sides in the same place of the Sun—which P. Charles Malapert also noted, comparing his own observations with the Coimbra observations held by P. Wilhelm Wely from the year 1620 to 1623, and with [those] received from Kalisz in Poland.

[Margin: A Spot is shown to be in the Sun itself.]

But, the Tychonic distances being supposed, Scheiner shows [that] the spots, from the defect of all sensible parallax, are nearer to the Sun than the Sun itself, [when] apogee, is to itself, [when] constituted at its mean distance; and he concludes the chapter by asserting [that], when the Sun lacks every spot, this happens in the whole orb of the earth; and when a new spot arises, this happens everywhere at the same time and [the same] place of the Sun; and when some spot occupies the center of the Solar disk or the Ecliptic, this happens everywhere on earth at the same time; nor was a deviation of any spot from the Sun’s disk ever noted. But (Cap. 56) he teaches [that] the Spots are in the very body of the Sun, from the inequality of the apparent refraction introduced into the motion of the Spots through the observing lenses; and (Cap. 57) from the Faculae, which were shown above to be in the Sun—therefore the Spots too, which are moved by a like motion and order [are in the Sun]; And (Cap. 58) from the usual slenderness of the Spots about the horizon or limb of the Sun; And (Cap. 59) from the intervals of two spots, or the daily advance of one; And (Cap. 60) from the proportional intervals of times and motions by which the Spots are moved when they advance with a rectilinear course through parallel lines on the Sun’s disk; And (Cap. 61) from the as-if-Elliptical path of the spots, then when the course is curvilinear; And (Cap. 62) from the properties of the curvilinear paths, which recur at six-month intervals; And (Cap. 63) from the intervals of one curvilinear course; And (Cap. 64) from the polar circlet which the axis of the vertigo of the spots describes; And (Cap. 65) from the periodic return of many spots which, before 28 days, are not corrupted

[Margin: Examples of returning Spots.]

—but their return the place, time, motion, and the same parallel persuade: such was [the spot] which, in the Year 1625, [lasted] from the 22nd day of March at the 8⅓ morning hour to the 4th day of April at the 1⅑ evening hour, in the southern parallel of the Sun; and another, of the same year, from the 11th day of May to the 18th of June, in the northern parallel; and a third, which in the same year arose on the 8th day of June, but [was] completed on the 19th, and lasted up to the 15th of July, from north to south; and from a fourth spot, which in the same year was born on the 12th day of July, but, [being] adult on the 24th, set astronomically, and—the hidden hemisphere of the Sun being traversed—arose astronomically on the 6th day of August at the 7½ morning hour, and set Astronomically on the 19th day at the 4¾ afternoon hour; and so of the rest. And (Cap. 66) from the secondary Spots about the poles and circlets of this motion, going with a [motion] proportional to the other motion. I myself would add [that] it is possible [that] the spots are in the very physical surface of the Sun, and are revolved by the motion of the Solar vertigo; but, this possible case being brought into act in reality, we would have no other, or no greater, indications and arguments than those we now have; therefore those arguments are most sufficient for concluding [that] this [matter] rather is so, than that they [the spots] are moved by many motions, and their own proper ones.

[Margin: From part 2 of book 4.]

[XXI.] In the 2nd part of book 4 he explains the Theory of the Solar Phenomenon—especially [that] which pertains to the motion of the spots—and (Cap. 1, reduced to a summary) teaches these [things]. The regular apparent motion of the spots about the center of the Sun is twofold: one annual, the other nearly monthly; which, since they are twice in the year—six-month intervals being interposed, namely at the beginning of June and of December—rectilinear, it is necessary that its axis lie in the apparent circle, or horizon, of the Sun; and because for six months it is curvilinear toward the south, and [for] six toward the north,

[Margin: A preparation for the Theory of this Phenomenon.]

General System and Theory of the Motion of the Solar Spots

[Translator’s note — engraved diagram: the large circle is the Sun’s visible disk, with the four cardinal points lettered A at the left (marked “Oriens” = East), B at the right (“Occidens” = West), C at the top (“Boreas” = North), and D at the bottom (“Auster” = South); the center is E (the eye, = center of the Solar globe). The horizontal diameter A–E–B is the line of the Solar Ecliptic (the equilibrium line); the vertical C–D is the Sun’s fixed axis, parallel to the celestial Ecliptic’s axis. A small Arctic circlet GZ sits at the top about pole C, and a small Antarctic circlet FYP at the bottom about pole D, each of radius ≈ 7°. A fan of straight lines converges through E: the parallel chords R–L, K–S (northern spot-paths) above the diameter, and T–N, M–Q (southern spot-paths) below it, represent the rectilinear-appearing courses of the spots at different seasons; the small lettered points (t, s, r, q and o at the top; e, d, c, b, a, f, g, Y, h, i at the bottom) mark the monthly positions of the moving axis-poles around the two circlets.]

[XXII.] In the preceding figure, from the center of the Solar globe E is described the solar horizon BCAD, which determines the Sun’s hemisphere conspicuous to us from the [hemisphere] hidden,

[…continues on p. 359 (PDF 394) with the catchword “[oc]culto”: “…hidden (although the hemisphere is not seen by us, on account of its huge distance, but [appears] a flat disk)“—the full explanation of the diagram and Scheiner’s theory of the spot-paths month by month.]

(printed p. 359 — within Chapter XII, continuing the Rosa Ursina Epitome: the diagram of the Sun’s fixed axis and two polar circlets is explained, the mobile poles marching monthly around them to produce the seasonal spot-paths. The Corollary holds all this more safely explained by the Sun’s annual axis-motion than by the Earth’s; the spots’ “Royal Way” zone and two size-tables follow.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 359]

[oc]culto (although the hemisphere is not seen by us, on account of its huge distance, but [appears] a flat disk); and let the Sun be feigned, for convenience’ sake, to be in the Meridian, or in the Ninetieth [degree], etc.; and let there be, in the Solar horizon, four cardinal points: A, the eastern; B, the western; C, the Northern; and D, the southern. Let the line of the Solar Ecliptic be AEB, whose fixed axis—parallel to the axis of the celestial Ecliptic—is CD, whose northern pole on the Sun’s perimeter is C, and southern D; for, on account of the Sun’s greatest distance, we can assume ADBC for the perimeter of the greatest circle on the Sun, and the line CD for its axis, even though, strictly, we do not see the greatest circle of the Sun. Let there now be described, from pole C, the circlet GZor; and from pole D, the circlet FYPc, whose semidiameter CZ, or DY, subtends 7 degrees of the Solar perimeter, of which the whole perimeter ACBD is 360. But let the circlet GQ be called Arctic or Boreal, and the circlet PF, Antarctic or Austral: which circlets, indeed, are to be thought of [as lying] not in the same plane of the Solar horizon (as this page exhibits), but erected orthogonally to it; and they are to be divided into twelve equal segments, for the twelve, as it were, Signs, and the twelve months of the year; and these circlets the poles of that axis describe by an annual motion—the axis about which the monthly motion of the spots takes place, which we shall call the mobile axis.

At the beginning, therefore, of December, let the southern pole of the mobile axis be in contact F, and the northern in G; and so let the mobile axis be FEG: let then pole F be moved, on the surface of the Sun conspicuous to us, but toward the East, so that, December being completed, at the beginning of January it be in a, and pole G have arrived, by a contrary motion, in l, but on the surface of the Sun hidden from us; and let the mobile axis be aEl: but at the beginning of February, let the southern pole be in b, and the northern in m; and let the mobile axis then be bEm: and at last, a quadrant Fc being completed, let the southern pole, at the beginning of March, be in c, and the northern in Z; and let the mobile axis be cEZ: and so let these poles proceed, that at the beginning of April the southern be in d, and the northern in n; and at the beginning of May, the southern in e, the northern in o; and at the beginning of June let the southern be in the contact P of the Solar horizon (setting to us heliacally, or hiding itself behind the back of the Sun), but the northern, in contact O, rise to us, about to walk through, for six months, the semicircle conspicuous to us OrG; just as the southern will walk through the hidden semicircle PYF. And so, at the beginning of July, the southern pole will be in f, the northern in p; but at the beginning of August the southern will be in g, the northern in q; and at the beginning of September the southern will be in Y, the northern in r; but at the beginning of October the southern will be in h, the northern in s; and at the beginning of November the southern will be in i, the northern in t; finally, the annual revolution being completed, at the beginning of December the southern pole will be again in contact F, rising to us optically, and the [northern] in contact G, setting to us optically. [Translator’s note: the 1651 print here repeats “austrinus” (southern) for the G‑pole, where “borealis” (northern) is meant—cf. the paragraph’s own setup, in which G is the northern pole.]

[Margin: The position of December.]

[XXIII.] When the southern pole is in contact F, and the [northern] in G, the paths of the Spots are, to sense, rectilinear, but not parallel to the Solar Ecliptic AEB; nay, the greatest parallel described by the path of the spots is TES (which, however, to avoid confusion, I did not express in the figure), whose greatest southern declination from the Solar Ecliptic—namely, the arc TA—and the northern, BS, is equal to the arc GC, that is, of 7 degrees; and the motion of the spots is from the eastern point T toward S, or certainly in [lines] parallel to that line TES.

[Margin: The position of June.]

But when the southern pole is in contact P, and the northern in O, the motion of the spots from East to West is rectilinear to sense, but the greatest parallel described by them is KEN, declining to the north by the arc AK, and to the south by the arc BN, of 7 degrees.

[Margin: The position of March.]

When the southern pole is in the middle of the conspicuous semicircle, or in c, and the northern in Z, the curvature of the paths of the Spots is greatest, the convexity swelling toward the north; but the diameter of the greatest parallel described by the spots in [their] monthly motion coincides with the line AEB of the Solar Ecliptic, and declines nothing from it; and this station is called the vernal Equilibrium: for there, the Sun being (as we posited) in the Meridian or in the Ninetieth degree of the Ecliptic, the termini A and B of the greatest parallel appear equally elevated above our horizon.

[Margin: The position of September.]

When the southern pole shall be in the middle Y of the hidden semicircle, and the northern in the middle r of the conspicuous [one], the curvature of the paths is greatest, but with the convexity swelling toward the south; and then too the diameter of the greatest parallel coincides with AEB, without any declination, and it becomes the autumnal Equilibrium, the termini A, B being equally elevated, etc.

In the remaining seasons of the year the convexity of the paths is as follows: that, through the greatest part of December, January, and nearly all of February, it swells toward the arc ARC of the Solar perimeter, intercepted between the eastern and northern points; but through the greatest part of March, April, and nearly all of May, they swell toward CLB, intercepted between the northern and western cardinal points of the Sun; but through nearly all of June, all of July, and nearly all of August, they swell toward AMD, the arc intercepted between the rising and southern cardinal points; finally, through nearly all of September, all of October, and nearly all of November, they swell toward BQD, the arc intercepted between the western and southern cardinal points of the Solar perimeter.

[Margin: A Corollary for the rest of the Earth.]

Thus you see [that], by a single annual motion of the Solar axis into the consequents of the Signs (if you regard its conspicuous pole), and by an as-if-monthly motion of the spots into the antecedents (or from East to West, if you regard their path conspicuous to us), made about that mobile axis, the phenomena of the motions of the Spots are saved; and [that] this annual motion of the Solar axis is more safely, and without absurdity, posited, than the annual [motion] of the Earth.

[Margin: The Royal Zone of the Spots.]

[XXIV.] The Torrid Zone of the Sun (so to call it), or Royal Way, within which the greatest part of the Faculae and Spots and ordinary [spots] proceeds, is contained by the arc MAR (rising) and QBL (setting), whose termini are parallel to the Solar Ecliptic, but within it the paths and bendings become wonderfully inclined and alternating; the whole breadth of this Zone does not exceed 60 degrees, of which 30 are to be understood in the arc AM (or BQ), the remaining 30 in the arc AR (or BL), although in the small figure we have not expressed that quantity. Wherefore, since the Zones (so to call them, “cold,” on account of the scarcity of faculae) are of 7 degrees—as is CG and DP—there remain, for the remaining temperate Zones (in which rare and not very conspicuous Spots or Faculae occur, namely the arcs RG and OL, or MP and FQ), 53 degrees each [in total].

[Margin: From book 4, part 2.]

[XXV.] These [things] being done, Scheiner treats (Cap. 3) of the quantity of the Sun’s circle conspicuous to us, and its difference from the Sun’s greatest circle; And (Cap. 4 and 5) of the apparent diameter of the Sun, and the mode of observing it; And (Cap. 6) of the magnitude of the Sun and of the Spots, both visual and true, the Tychonic distance of the Sun being supposed, and the quantity of the terrestrial diameter, which he supposes as one may see in the subjoined table:

According to Tycho and Scheiner:

[Margin: The Magnitude of the Spots.]

These [things] being supposed, he sets down the various classes of spots, with [their] quantity, beginning from the smallest (which are like a point) and proceeding up to the greatest, which I have reduced into the synopsis of the following table:

Of Spot E he gives the example [of one observed] in the Year 1625, in April, and says it was equal to Europe; and of Spot F, [one observed] in the Year 1626, on the 26th of May, [which he says was] greater than Africa; and of Spot G, [one observed] in the Year 1625,

[…continues on p. 360 (PDF 395) with the catchword “1625”: “…in the Year 1625”—the rest of Scheiner’s spot-size examples, and the continuation of the Rosa Ursina Theory.]

(printed p. 360 — closes Chapter XII with the spot-size examples and a refutation of Chiaramonti’s placing the spots below the Moon. Chapter XIII then dissolves four quick arguments for the Earth’s motion “from things moving East” (the trade-wind, mine-fibers, a turning iron lamina, the need for agitation), deferring the tides. Chapter XIV, the great tide chapter, opens with Galileo’s two tidal conclusions from Dialogue 4 and his three tidal periods, with Riccioli’s critique that Galileo over-claims a single cause.)

[Header: BOOK IX. SECTION IV. — 360]

[in the Year] 1625, on the 15th of March, [which he says was] equal to Asia; and finally, of Spot H, he gives the example [of one observed] in the Year 1625, on the 19th of April, [which he] says was nearly equal to the disk, or half-circumference, of the Earth; but because to us the Sun is higher [farther] than to Tycho, by about sevenfold, and its diameter to the diameter of the earth [is] not as 5½ to 1, but as nearly 34 to 1 (as we said, bk. 3, ch. 11), therefore the aforesaid spots come out nearly sevenfold larger than Scheiner put [them]. The remaining [things] which he treats toward the end of the book pertain to the qualities and substance of the Sun and of the heavens, of which enough has been said elsewhere.

[XXVI.] When I had written these [things], I fell upon Chiaramonti’s book 9 On the Universe, in whose ch. 1 he reports the opinions of several [men] on the Sun’s spots; especially of Jean Tarde, who thinks them stars, and calls [them] the Bourbon stars [sidera Borbonia]. But in ch. 5 he contends [that] they are far below the Moon, on this ground: that if they were contiguous to the Sun, and one of them were so great as to equal the terrestrial globe, its shadow nevertheless would not be longer than two semidiameters of the earth; but if it ought to overshadow for us a particle of the Sun, it would be necessary that the apex of its shadow reach the earth, and it would be [a length] of nearly 1105 terrestrial semidiameters—as great as is the minimum distance of the Sun posited by Copernicus.

[Margin: Chiaramonti’s hallucination concerning the shadows of the Solar Spots.]

But the good old man is deceived: for neither, in order that an opaque body cover for us a part of the luminous body, is it necessary that its shadow reach our eye—as is clear from the central but annular Solar Eclipses, concerning which we [treated] (bk. 5, ch. 8, num. 4, and ch. 9, problem 7)—but it suffices if it intercept for us some rays of the luminous body: the privation of which, in the air and in our eye, cannot be called a shadow simply, but at most a shadow in a certain respect [secundum quid].