[I.] Here indeed, if anywhere, Galileo exulted, in Dialogue 4 On the twin System of the World; for the first page of that dialogue—which in Italian is 409, but in Latin 309—thus begins: “After I myself had again and more often examined with myself the effects and accidents (partly seen by me myself, partly known from others) which are observed in the motions of the waters; and besides, having read and heard the remarkable vanities which many have adduced to render a reason of these accidents: not lightly did I feel myself drawn to admit these two conclusions, the necessary presuppositions being made.”

[Margin: Galileo’s 2 conclusions on the sea’s tide.]

But the conclusions which he at once subjoins are these: “If the terrestrial globe be immobile, then the flux and reflux of the sea cannot naturally happen. On the contrary, if to the same globe be conferred the motions already assigned, [it is] necessary that the sea be subject to flux and reflux, according to all those [things] which are observed in it.” Yet, a few [words] being interposed, he confesses that he does not so much arrogate to himself that he can render an adequate reason of all the effects which perhaps are detected in the seas placed outside the Mediterranean; but [says] that he nevertheless proposes a key which may open the door to a way never trodden by others, and he adds: “And although in other seas remote from us there can be found accidents unknown to our Mediterranean, nevertheless not on that account will that reason and cause which I shall produce cease to be true, provided it be confirmed by the accidents of our [own] sea, and fully satisfy them: for at last there must be one, true, and primary cause of effects of the same kind.” From which [words] now, right at the very threshold, the fault of his discourse and judgment appears: for if the accidents of the marine tide outside the Mediterranean are not of the same reckoning with the accidents seen in the Mediterranean, but very diverse, and in some place in a certain manner opposite—and indeed in seas much vaster than the Mediterranean is—how does he, with so confident a mind, affirm that the cause satisfying the Mediterranean tide will also satisfy all the tides of all seas? For he does just as if someone, the cause of a quartan fever being detected, [and] satisfying all its properties, should assert that the same is the cause of all fevers, although he had not foreknown their accidents. But let us hear from him—partly under the person of Salviati, partly under that of Sagredo—the history of the marine tide observed in the Mediterranean, that we may be able thoroughly to know the foundation of his opinion.

[Margin: The threefold period of the marine tide.]

[II.] He says, therefore, that three periods are observed in the fluxes and refluxes of the sea-water: the First, and chief and greatest, is the diurnal, by which alternately the waters are raised through about 6 hours, and through the other 6 hours are depressed; the Second, the monthly, which seems to be effected not indeed by the Moon, but [to be] varied by an alteration of the first, with a notable difference, according as the Moon shall have been new, or full, or bisected [half]; the Third, the annual, which seems to depend on the Sun, inasmuch as it [the Sun] renders the diurnal fluxes greater or less, and diverse in the Solstices from those

[…continues on p. 361 (PDF 396) with the catchword “ijs, qui”: “…from those which happen in the Equinoxes”—the rest of Galileo’s tidal observations and his motion-of-the-vessel explanation of the tides.]

(printed p. 361 — within Chapter XIV (the tides). Finishes Galileo’s tidal observations and reports the two causes he rejects (the Peripatetic struggle of waters and the Moon’s influence). Galileo’s own mechanism is then given with an engraved diagram: the compound of the Earth’s annual and diurnal motions unevenly accelerates and retards its surface, this inequality being “the chief and primary cause” of the tides; his five tidal “accidents” begin.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 361]

[from those] which happen in the Equinoxes.

[Margin: In the diurnal motion, a threefold variety.]

But now, in the diurnal tide, he affirms that three diversities are noticed: for in some place the waters swell and subside without any progressive motion; elsewhere, without rising and falling, they now advance toward the East, now run back toward the West; in some place, finally, there is varied both the rising or swelling and the progressive and regressive course—as happens at Venice, where the waters, by approaching, swell, and by receding, subside; and this they do at the extremity of the length of bays extended from West to East, and bounded by such shores as afford space for the water to diffuse itself when, raised, it swells. But if its course were intercepted by mountains or higher banks, there it would swell and subside without progressive motion. Further, the waters of the sea run and run back without swelling or change of height in the middle parts of the Mediterranean—as happens most evidently in the Pharos of Messina, or the Sicilian Strait, between Scylla and Charybdis, where the running waters, on account of the narrowness of the channel, are most swift; but in more open seas, and about the Balearic islands, Corsica, Sardinia, Elba, the African coast of Sicily, Malta, Crete, etc., the changes of height are very small, but the courses of the waters notable, especially where the sea is constricted between two islands, or between some island and the mainland.

[Margin: The causes of the marine tide rejected by Galileo.]

[III.] These [things] being first narrated, he refutes two causes of these effects, adduced by some. The First indeed, from some Peripatetic or other (whose name I know not) who, adhering to the text of Aristotle, had said that the deeper waters, by the weight of their mass, expel the less deep, which—thrust upward—strive to descend, from which continual struggle the flux and reflux arises; for [he held that] the waters alone which have a higher surface drive away the lower and humbler, but that the deeper [waters] cannot do this; then, when the higher have lain upon [pressed down] the lower, [these] briefly come to rest, and with them are reduced to equilibrium. The Second cause, which not a few refer to the Moon (predominant over humid bodies, and luring to itself and raising up a heap of waters, which—continually following the Moon—make a swelling in that part to which the Moon is vertical; but when the Moon shall have gone under the Horizon, that swelling returns after six hours, on account of the tractive virtue which the Moon shall have communicated to the opposite degree of the Zodiac); or certainly [those who hold] that the Moon, by its temperate heat, rarefies the waters, and therefore [that] they swell: this [opinion], I say, he therefore rejects, because the Moon daily goes round the whole Mediterranean, and yet the waters are not raised except in its more eastern extremities, and near Venice; nor does a moderate heat suffice to raise water by the force of rarefaction, as anyone can test in tepid and not-yet-boiling water; nor can the disparity of reasoning hence be rendered, why the Moon rarefies the waters at Venice, and does not rarefy [them] at Ancona, Naples, [or] Genoa. And so he counts these and similar causes among poetic fictions. And when Simplicio, in that dialogue, had said that he would rather reduce this effect to a miracle, as supernatural—since indeed Aristotle too, in the beginning of the Mechanical Questions, seems to ascribe the cause of certain things whose causes are hidden to a miracle, or to number [them] among the marvels—Salviati subjoins that, if a miracle is to be introduced for the marine tide, the motion of the earth is rather to be introduced, but [as] made by a miracle and supernaturally, to whose motion afterward the tide of the sea may follow naturally and by a simpler way; nor would there be need of several miracles.

[Margin: Other causes rejected.]

For neither (he says), the Earth being immobile, can a reason be rendered why the water at Venice, within 5 or 6 hours, swells ten palms and more—the weight not being changed, not the density, not the cold, not the saltness (lest anyone have recourse to rarefaction), but by a manifest ingress onto the shores—and yet [why] it is not sensibly raised at Ancona, nor at Durazzo, nor at Corfu. For if anyone should have recourse to the waters of the Ocean entering through the Strait of Gades [Gibraltar]—that is, a channel not more than 8 miles wide—if that water in six hours ought to reach the farthest shores of the Mediterranean, and to traverse two or three thousand miles, certainly in one hour it would pass through more than 400 miles—which is an incredible velocity; nor could the ships in that strait, or near [it], strive against them [the currents], which nevertheless they do. Since, therefore, this cannot be explained if the Earth, as a vessel containing the seas, rest immobile, it must be inquired whether through the motion of this vessel the causes of these changes can be explained. Which he does,

[Margin: The likeness of the tide taken from the water of a moved vessel.]

by considering what would happen to a vessel or ship full of water, if indeed the vessel or ship be moved with a placid progressive course toward one part, but yet with an unequal velocity: for the water, being fluid and not firmly cohering with the vessel, while the vessel is retarded, [the water] itself—retaining part of the conceived impetus—would run forward, and would be raised up at the leading extremity of the vessel; but, on the contrary, if the motion of the vessel were quickened, the water—retaining part of its slowness, and remaining somewhat behind, before the whole [water] could conceive the new impetus—would recede into the following part of the vessel, and there would be exalted [raised]; but in the middle of the vessel scarcely any swelling of the water would appear, but rather a more notable current than at the extreme margins. And indeed an effect of this kind one may discern in the tides of the Mediterranean; it is consonant, therefore, [that] the vessel itself, that is, the Earth, is moved by such motions, which now retard it, now quicken it; and [that] the Earth, further, on account of the mixture of the annual and diurnal motion, is moved now more slowly, now more swiftly, he teaches by the following diagram.

[Margin: The Earth’s motion, from the Diurnal and Annual, unequal.]

[IV.] From A, the center, let the great or annual orb BCDE be described, on whose periphery, any point being assumed—say B—let the globe of the Earth FGHK be described;

[Translator’s note — engraved diagram: the large circle is the great orb (annual orbit), with center A, lettered B at the top of its periphery (also outer-arc points O above, P at upper-left, Q at upper-right, C at lower-left, D at the bottom, E at lower-right; M and N flank A on a small inner arc). Riding on the orbit at B is the small Earth-globe FGHK: center B, with H at top, K at left, G at right, F at bottom (and L just below F). The globe both circles A annually (B → C, eastward) and spins daily about B (H → K → F → G).]

which is understood to be revolved with the motion of the center B toward the East C, [and] to be moved so that in one Solar year it traverses the whole periphery of the great orb. Besides, let the same globe be understood to be revolved daily about its own center B, likewise toward the East, from H, through K, into F, [and] G, until, 24 hours being completed, it has completed the diurnal revolution. For hence it comes about that any part of the circumference of this globe is moved, at different times, by contrary motions: for indeed, while the parts near H are moved toward the left part K, the parts constituted at F are moved toward G, the right region; and while the parts from G ascend into H, the parts from K descend into F. Therefore, this contrariety of motions being posited, while the motion of the diurnal vertigo is joined with the annual motion of the center B, [it is] necessary that there result a motion on the surface of the earth, now sufficiently accelerated, now as much retarded; for the parts near H will be moved most swiftly, when the annual and diurnal motion conspire into the same region, or tend—the one in C, the other in K—toward the left: “Wherefore, in such a case, the diurnal motion increases and accelerates the annual motion” (the words are Galileo’s own). On the contrary, in the part F the motion is retarded, because, although by the force of the annual motion it is borne toward the left, yet by the force of the diurnal motion it is borne toward the right: “Wherefore the diurnal motion subtracts from the annual motion.” But about the points G and K the annual motion is nearly simple and equal, since the diurnal adds nothing, or very little, to the annual motion, or subtracts [nothing or very little]—since indeed there [the part] is borne neither to the left nor to the right, neither upward nor downward. This inequality, therefore, of the Earth’s motions is the chief and primary cause of the marine tide, especially [the tide] made in longitude toward the East and West.

[Margin: 1st Accident.]

[V.] After these [things], Galileo considers five notable accidents of the marine tide. The First is, that the water, raised at the extremity of some vessel by the force of acceleration or retardation, does not stay in that exaltation, but not only reduces itself by flowing back to equilibrium, but also, from its own

[…continues on p. 362 (PDF 397) with the catchword “[à suo] pon[dere]”: “…from its own weight”—the rest of Galileo’s five tidal accidents, and Riccioli’s reply.]

(printed p. 362 — within Chapter XIV, continuing Galileo’s exposition: the five tidal “accidents” are completed and applied to explain six tidal effects (no tides in lakes, the six-hour periods, the Venice rise, the currents through narrows). Galileo’s cause of the monthly period follows (the Earth-Moon system moving faster at new moon than at full), and the annual variation begins with an engraved diagram.)

[Header: BOOK IX. SECTION IV. — 362]

[from its own] weight, with the conceived impetus it springs back into the opposite part, raising itself to the other side of the vessel—not otherwise than the ball of a plumb-line [pendulum], after [its] descent, ascends through the opposite arc.

[Margin: 2nd Accident.]

The Second is, that the aforesaid reciprocations of the water ascending hither and thither are more frequent in shorter vessels, rarer in longer—not otherwise than the vibrations of a plumb-line suspended from a shorter cord are more frequent than [those of one] suspended from a longer.

[Margin: 3rd Accident.]

The Third is, that among waters enclosed in channels of equal length, those which are deeper complete their reciprocations in shorter times, but those which are less deep, less frequently.

[Margin: 4th Accident.]

The Fourth is, that the waters enclosed in vessels or channels of the earth are alternately raised and depressed about the extremities of the vessel, without progressive motion—unless perhaps, by swelling, they overflow beyond the banks; but the parts placed in the middle run forward and backward without sensible swelling.

[Margin: 5th Accident.]

The Fifth is, that in small vessels the acceleration and retardation is participated in the same manner by the whole vessel and by any part of it; but in the immense channels of the sea, not so: for when one extremity, on account of the mixture of the diurnal and annual motion of the earth, is retarded, the other extremity is carried forward by a motion still most swift—as in the preceding figure, when the parts of the sea H are moved swiftly, the parts G nevertheless less swiftly, and the parts F most slowly; if the tract of sea be so long that it equal the quadrant HG, or the semicircle FGH.

[Margin: The cause of the marine tide’s effects.]

[VI.] These [things] being rightly considered, it is not difficult to render the reason of several effects which are conspicuous in the sea’s tide. First, indeed, in lakes, ponds, and small seas, sensible tides do not appear, on account of the frequency of the reciprocating vibrations, before they can complete their effect by the retardation and acceleration of the earth (which happen alternately from 12 to 12 hours); for first the waters, somewhat exalted at the ends by the narrowness of the vessel, slide back by their own weight to equilibrium within one, two, or three hours—and so a notable tide is impeded. Secondly, although the period of velocity may embrace 12 hours through the semicircle GHK, and the period of slowness 12 hours through the semicircle HFG, yet, from the diverse length and depth of the seas, it comes about that those alternations are made from 6 to 6 hours—or certainly these are more frequently observed in our seas, [though] not in all: since indeed in the Hellespont, the Aegean, and in the Euripus at Euboea, the periods are short enough, and very diverse among themselves. Thirdly, therefore, in seas and bays [that are] longer indeed, but not extended in longitude toward the East and West, but toward the poles—of which kind is nearly the Red Sea—almost no tide appears, because the motion of the earth is in longitude, not toward the poles of the world; and accordingly the impulse of the waters strikes the meridians, not the parallels to the Equator. Fourthly, from those [things] which we experience in a vessel full of water and agitated toward one part, it is easily established why, in the extremities of the Mediterranean, the water is raised notably—so that at Venice it ascends to 5 or 6 feet—but elsewhere the exaltation is very small, so much so that about Corsica and Sardinia, and in the estuaries of Rome and the Ligurian harbor, it does not exceed half a foot. Fifthly, therefore, the same quantity of water, although otherwise it run placidly, if nevertheless the whole [of it] must be transfused through a narrow channel out of a broader channel, [it is] necessary that it run with great impetus through the narrower—as happens in the Sicilian Strait, and the Magellanic, and in the sea enclosed between Africa and the island of St. Lawrence [Madagascar]. Sixthly, however, these changes can be varied not a little, both by the blasts of the winds and by the rivers bursting into the sea—especially as to the course of the waters, which are borne thither whither they are impelled by the rivers: so, in the Thracian Bosphorus, the water always runs from the Euxine into the Propontis, and in the Sicilian Strait it runs from the Ionian into the Tyrrhenian, [yet] more swiftly in the Sicilian, because it is extended along the longitude.

[VII.] Thus far Galileo concerning the cause of the diurnal period of the marine tide; after which, a few [things] being interposed concerning the perpetual breeze within the Tropics, concerning the easier navigation toward the West, and concerning the falsity of [there being] a motion of fire from the concave of the Moon [margin: The cause of the monthly variation of the marine tide], he passes to investigating the cause of the monthly variation, and affirms (Latin page 333) that, if the annual motion of the Earth were not altered, the monthly period of the marine tide would cease. The cause, further, of this monthly alteration he teaches to be, that in the annual orb not the earth alone is carried about, but the whole Lunar system LO, [and] the Moon, when at New [it] is at L, and is near the Sun A, or the center of the great orb, the great orb with respect to it is the arc MLN, etc., describable from A as center; but when it is at Full, at O, the great orb with respect to the Moon is POQ, etc., any arc of which is greater than any similar [arc], or [than an arc] of as many degrees of the lesser circle MLN, etc. But it is certain that, other things remaining equal, the same mobile, by the same force, is moved in a shorter time through similar arcs of a lesser circle than through [those] of a greater. For this we discern not only in the celestial motions, but also in the terrestrial: for hence it comes about that the vibrations of a shorter plumb-line, and one nearer the center, are completed in a shorter time than [those] of a longer plumb-line, on this ground, that they traverse the arcs of a lesser circle. Hence likewise [it comes about] that that iron rod [hastile] which the makers of horizontal clocks place parallel to the horizon and librating [swinging] at the sides, for regulating the times of the clock, renders the hours longer if the leaden weights, which are hung at the heads of the rod, be hung far from the center of the rod; but quickens them and renders [them] shorter, if the weights be placed nearer the center—on this ground, that here they must pass through [the arc] of a lesser, there of a greater, circle. Therefore likewise the Moon, at New, ought in the annual orb to pass through similar arcs in the lesser circle MLN, and accordingly in a shorter time; but at Full, [through] the arcs of the greater circle POQ, and in a longer time. That force, therefore, which moves not the earth FGHK alone, but the whole Lunar system OL, toward the East, ought—by reason of the Moon—to impart those monthly varieties to the terrestrial globe, and to render the annual motion non-uniform, and to refund [pour back] that variety into the tide of the sea, [which is] founded upon the annual motion of the earth together with the diurnal. But [as to] why the Astronomers have not observed these monthly variations in the annual motion of the Earth, or (as others will have it) of the Sun, [it is] no wonder, since many other subtleties [remain] hitherto unobserved by the Astronomers, or only roughly noticed.

[Margin: The cause of the annual variation in the Tide of the Sea.]

[VIII.] There remained the cause of the annual variation in the sea’s tide to be adduced, which Galileo begins to expound from Latin page 340 (Italian 451)—having premised, however, that it is more difficult to understand, and requires a great abstraction of mind. He says, therefore, that the inequality of additions and subtractions which the diurnal vertigo of the earth communicates to the annual motion depends on the inclination of the axis of the diurnal motion upon the plane of the great orb, or Ecliptic—on account of which inclination the Equator of the earth cuts the Ecliptic always at the same angle of inclination retained; but [that] the addition is as great as is the whole diameter of the Equator, the center of the Earth being [placed] in the solstitial points; but outside these [it is] less and less, according as the center of the Earth is less and less distant from the Equinoctial points, where those additions become least. But, that the matter may come out clearer, let there be designated, in the following figure, the great orb AIP, on whose circumference,

[Translator’s note — engraved diagram: the large oval is the great orb (annual orbit) seen obliquely, with its long diameter lettered A (a solstitial point, at the left, where the Earth’s globe is placed), running through center to P (the opposite solstitial point, at the right), with I an equinoctial point on the orbit. At A sits the Earth’s tilted globe CFBG (axis CAB inclined to the orbit-plane; the Equinoctial circle DGEF crossing it, its trace on the orbit-plane being the line DE). A second copy of the globe is drawn at the equinoctial position I (axis CIB, equator GEFD, trace DE, with the orbit-tangent HIL there perpendicular to DE, and the perpendiculars GS, FV onto HL). The diagram shows how the daily-rotation’s contribution to the orbital speed equals the full diameter DE at the solstice A, but shrinks to SV at the equinox I.]

[…continues on p. 363 (PDF 398) with the catchword “ipsius”: ”…[the half] DFE of the same Equinoctial [circle]“—the geometric demonstration of the annual variation, Galileo’s conclusion, and the start of Riccioli’s own “History of the Motions of the Sea.”]

(printed p. 363 — within Chapter XIV. Finishes Galileo’s geometric demonstration of the annual tidal variation and his conclusion ranking the tides among the strongest Copernican arguments, seconded by Gassendi but refuted by Chiaramonti, Cabeo, and Furner; Riccioli says judgment requires a fuller tide-history. A new sub-head opens, “A History of the Motions of the Sea,” beginning with the First Motion, from North to South.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 363]

[the half] DFE of the same Equinoctial [circle] remains inclined below the plane of the great orb, and the other half DGE raised above it. Let there now be made a diurnal revolution of that Equinoctial [circle] according to the consequence of the points DGEF, and let the motion of the center be from A toward I. But since, while the center of the terrestrial globe is in A, the axis CAB—erected to the diameter DE of the Equator—falls in the Solstitial Colure, whose common section with the great orb is AP, it follows

[Margin: The variation in the Solstices.]

that the line AP is perpendicular to the line DE (since the Colure is erected to the great orb); and accordingly the line DE touches the great orb in point A; so that, in this position, the motion of the center through the arc AM—which is by the force of the annual motion, of about one degree daily—behaves just as if it were made through the tangent DAE. And because the point D, carried by the diurnal vertigo through G into E, adds as much to the motion of the center (as if moved through the line DE) as is the whole diameter DE, and on the contrary subtracts as much while it is moved through the other lower semicircle EFD, it comes about that the additions and subtractions in this place are measured by the whole diameter DE.

[Margin: The variation in the Equinoxes.]

[IX.] Let the center of the terrestrial orb now be transferred to I, one of the Equinoctial points, and let there be there the Equinoctial [circle] GEFD, and its common section with the great orb DE, and the axis CIB with the same inclination; but the tangent of the great orb in point I is no longer the line DE, but a certain other [line] which cuts this at right angles, namely the line HIL, along which the instituted motion of the center I is understood [to proceed], advancing through the circumference of the great orb. For, these [things] being posited, now the diameter DE no longer measures the additions and subtractions which the diurnal motion brings to the annual motion, since DE is not extended along the line HIL of the annual motion—nay, cuts it orthogonally; wherefore the termini D, E add nothing or subtract [nothing]; but the additions and subtractions are to be sought from that diameter which falls in the plane erected to the great orb, and which cuts it along the line HIL—which diameter indeed will be the line GF; and the additive motion (so to speak) will be that which is made from the point G through the semicircle GEF, but the subtractive, that which is made through the semicircle FDG. Further, since this diameter GF is not in the line HIL of the annual motion, but cuts it in point I—the terminus G remaining raised above, and F depressed below, the plane of the great orb—it does not determine the additions and subtractions according to its whole length; but their quantity is to be taken from the parts of the line HL which are intercepted between the perpendiculars raised upon it from the termini G, F—which [perpendiculars] are understood to be GS, FV—so that the measure of the additions is the line SV, less than GF or DE, which was the measure of the additions in the Solstices. And hence, at last, is that third variety of the annual period which appears in the tide of the sea, comparing the tides which happen in the Solstices and in the Equinoxes.

[Margin: Galileo’s conclusion.]

[X.] He concludes, therefore (Galileo, p. 342 of the Latin version), that the three fixed and perpetual causes of the marine tide are: the inequality of the diurnal motion communicated to the annual motion, but varied monthly by the annual motion (by which the whole Lunar system is transferred more swiftly in new moons, more slowly in full moons), and finally varied annually in the Solstices and Equinoxes by the inclination of the axis of the diurnal motion upon the plane of the great Orb; but [that] the remaining causes are accidental, and, without rule, partly unobserved, partly unobservable—namely, the blasts of the winds, the depths of the seas, and their diverse lengths, positions, and inclinations. But he wonders at Kepler—to whom those three motions of the Earth were known—[that] he nevertheless reduced the tide of the sea to the predominance of the Moon over the water, and other occult properties; and (p. 344 of the Latin, but Italian 456) [says] that one of the chief arguments for the motion of the Earth is this, drawn from the tide of the sea, saying: “Therefore, from the colloquies of this four-day [conversation], we have remarkable testimonies for the Copernican system, from which these three [are] taken: the first from the station, retrogradation, and approach and recession of the Planets; the second from the revolution of the Sun upon itself, and from those [things] which are observed in its spots; and the third from the flux and reflux of the sea—[these] seem sufficiently conclusive.” To whom so far subscribed Pierre Gassendi (Epistle 2 On the impressed motion from a translated mover, from p. 149 to 155), so that, by the example of the little boat full of water, he reduced Galileo’s reasons into an epitome; and after the argument from the Solar Spots—which he likewise thought demonstrative of the earth’s motion—he said: “So demonstrates Galileo, to whom this, besides, ought to be [granted]: that from the assigned motions of the earth he has so set forth the tide of the Sea that he seems at last to have found out its genuine cause.”

[Margin: Authors impugning Galileo.]

But the contrary felt [held] Chiaramonti, in his Italian defense of the Antitycho (part 4, chh. 24, 25, 26, 27, 28), where he refutes Galileo; P. Cabeo (on bk. 2 of the Meteors, text 6, from q. 7 to 10); and P. Georg Furner S.J. (book 9 of the Hydrography, from ch. 14 to 20)—which two Fathers far more fully and solidly refute Galileo’s invention. But neither their arguments, nor ours, against Galileo can be adequately understood, unless there be premised a history of the marine tide, and indeed a more accurate one than was done (bk. 2, ch. 15), where we were instructing the Beginner [Tyro], nor was there occasion to descend so profoundly into this controversy.

A History of the Motions of the Sea, collected from diverse Writers

[XI.] This history—besides those who have described to us the Indian navigations—touch upon, in the first place, not a few Authors named by us (bk. 2, ch. 15, in scholium 1), to whom are to be added: Bartolomeo Crescenzio (bk. 3 of the Mediterranean Nautics, from ch. 2 to 4); Bartolomeo Mastrius (disp. 4 On the heaven & Meteors, q. 4, from num. 148); Hieronymus Trimarchus (bk. 2 of the Meteors, disp. 1, from sect. 6 & 7); Federico Delfino (the little work On the tide of the sea); Albertus Magnus (On the properties of the elements, tr. 2, ch. 6); Francesco Resta (bk. 3 On watery Meteors, in the treatise On the Sea, from ch. 13 to 16); and Georg Furner (bk. 9 of the Hydrography); Lucas Aurigarius the Hollander (in the Marine Thesaurus); and Claude Duret. From these, very many concede three ordinary motions to the Sea: one in longitude, another in latitude, the third in altitude; for the extraordinary [ones], made by the winds, we do not here consider.

The First Motion of the Sea, from the North toward the South

[XII.] The motion of the sea from the North toward the South, long ago, with Aristotle (bk. 2 of the Meteors, ch. 1, text 6), recognized in the same place Alexander of Aphrodisias, St. Thomas, Vicomercato, Niphus, and most of the interpreters, as also Albertus Magnus (tract 3 of the Meteors, ch. 6). For the Maeotis marsh [Sea of Azov] flows into the Euxine Pontus [Black Sea] through the Cimmerian Bosphorus, and the Pontus into the Propontis, and the Propontis into the Aegean through the Thracian Bosphorus, and the Aegean into the Mediterranean.

[Margin: The 1st cause of this motion.]

Of which motion Aristotle brings a twofold cause: one, from the multitude and magnitude of the rivers bursting into the Maeotis and Euxine (of which kind are the Tanais [Don], the Danube, the Borysthenes [Dnieper]), but comparatively to the narrowness of the Maeotis and Euxine, and [their] small depth, which cannot contain so great a mass of waters within their channels, but are forced at once to discharge it into broader and deeper seas. For the Maeotis marsh, if we believe the Geographers, scarcely has six or seven ells [ulnas] of depth; for Aristotle adds that the Euxine is deeper than the Maeotis, and the Aegean sea than the Euxine, and the Sicilian [sea] than the Aegean; but the Sardonian and Tyrrhenian [are] the deepest of the whole Mediterranean. From the same abundance of waters bursting into the Euxine, Strabo reports (bk. 1 of the Geography) that the Pontus opened a way for itself by force into the Propontis—which from the beginning it did not have—and, by a continual percussion [battering], laid open an entrance for itself to the Herculean Strait [Gibraltar], into the Mediterranean. The other cause the Philosopher refers to the altitude of the earth, more elevated about the Arctic pole; whence he says it follows that from the Arctic pole a great force of waters runs down toward the South. But [as to] why the Caspian Sea, although great rivers discharge into it, and it be not very large, nevertheless does not run down openly into the Euxine or some other sea, the cause is [this]: because it does not communicate with it through any strait or channel; wherefore it is forced to transmit its waters through subterranean passages to the Euxine, and thence to the Mediterranean—as not a few of the Geographers think.

[Margin: The 1st confirmation of this motion.]

This motion, further, from the North toward the South, is confirmed, first, from the easier and swifter navigation which is from the North toward the South: since indeed—Fromondus being the asserter—[one] sails more swiftly and readily in the Atlantic from Denmark and Holland

[…continues on p. 364 (PDF 399) with the catchword “[Hollan]dia”: “…from Denmark and Holland”—the rest of the confirmations of the sea’s North→South motion.]

(printed p. 364 — within Chapter XIV, the “History of the Motions of the Sea.” Completes the First Motion (North to South) with its navigational confirmations and proposed causes (the Sun draining Torrid-Zone waters so polar waters run to the Equator). The Second Motion, from East to West, then opens, proven by the far easier westward navigation across the Atlantic and around the Cape.)

[Header: BOOK IX. SECTION IV. — 364]

[Hollan]dia into Spain, than from Spain into Holland or Denmark; Furner too, our [father] (bk. 9, ch. 22 of the Hydrography), affirms that ships which set sail from the Azores toward the Equator complete their voyage much more swiftly than those which, from Brazil or from Havana (southern places), attempt to return to the Azores; for these, that they may be less hindered (by an oblique navigation) by the currents [running] to the South, must skirt the shores of America between Florida and the island of Bahama and Virginia, and measure out a journey ten times longer than that which they had made from the Azores to Brazil.

[Margin: Vallesius’s error as to the cause of this motion.]

Which greater swiftness is, in its way, discerned also in the navigation from the Euxine to the Aegean, and from the Aegean into the rest of the Mediterranean, even when the winds rest—so that in vain did Francesco Vallesius (ch. 50 of the Sacred Philosophy) refer it to the North winds. Furner adds (bk. 9, ch. 31) that, in the Year 1630, a ship which had set sail from Dieppe, and in February had reached latitude 2 degrees near the Equinoctial, after it had run for 24 hours toward the Southwest [Libycum]—although it judged itself made more southern—was nevertheless, on account of the currents toward the Northeast [Graecus], still in the 2nd degree, where [it had been] before.

[Margin: 2nd Confirmation.]

It is confirmed, secondly, most evidently from the masses of ice which (by the testimony of Furner, in the place adduced above) are rolled down from the North toward the South—as those have experienced who have sailed across the Atlantic to North America, or thence into Norway: for [those] going toward Bergen of Norway, along the Vaegas, or [toward] Nieulandia, must always direct their course beyond Hunem [the Hoorn?], unless they wish to perish on account of the ice rushing from the North. And in the Year 1635 the French Fleet, sailing toward Canada, found certain huge bell-like [masses] of ice, and one of them so vast that they could scarcely draw themselves away from it over a space of 40 leagues; nor is it ever sailed to Canada but that floating islands of ice of this kind, rolling themselves from the North, are presently found. Since, therefore, glacial masses of this kind always rush toward the Equator from the Northern region, it is manifest that the sea thence perpetually runs toward the South.

[Margin: 3rd Confirmation.]

It is confirmed, thirdly, from those who have made the voyage to the Moluccas or the Philippine islands; for they have experienced an incredible velocity of the sea, now from the North toward the South for 12 hours, now from the South toward the North for another 12—as Furner narrates in the same place, and ch. 31. But also Fromondus notes, from the Enchiridion of Bartholin the Dane (bk. 4, ch. 8), that the Baltic Sea not only flows out from the North, but flows back toward the North—which he [Bartholin] attributes to the rivers flowing, on this side from the North, on that side from others toward the North, and [to their] impelling the Baltic by diverse motions. Many Geographers too—especially Mercator, Plancius, Magini, and Bertius—narrate that under the Arctic Pole there is an immense whirlpool [vorago], into which the sea is most rapidly borne through four Euripi; which, however—how it could be known—Pifferus wonders (on ch. 3 of the Sphere).

[Margin: The [daily] Flux of the Sea to be distinguished from this motion.]

To this motion, however, does not properly pertain that flux and reflux which is from the Gothic [Baltic] sea to the shores of Gaul, and in turn from the shores of Gaul toward the Gothic sea; for this is the daily tide of the sea, reciprocating to and fro—which is also discerned daily at Spitsbergen, at an elevation of 24 degrees [sic], from North to South, and in turn from South to North. Further, the cause of the course of the Sea from the North to the South in the Gothic and Atlantic [seas], or, toward the Moluccas and Philippines, now to the North, now to the South, is not to be referred either to rivers or to the height of mountains whence the waters glide down into the sea—since in that tract there are no such rivers flowing toward the South, nor is that part of the earth higher than the mountains of the Moon or of America; nay, the Dutch and Zeeland sea appears higher than many islands, and the Rhine and several other rivers flow from the Alps toward the North. But it seems rather to our Furner (bk. 9, ch. 22 of the Hydrography) [that it is] to be referred to the Sun, continually diminishing, by its heat and by the attraction of vapors, the waters which are within the Tropics; whence it comes about that, the waters failing at the surface, the waters run by their own weight, on this side from the North, on that from the South, toward the Equator, to equalize their level—especially if it is true (as the same Author there affirms) that, when the Sun is in Capricorn, the waters which are within the Tropics cross the Equator and rush toward the Tropic of Capricorn; and in turn, the Sun being placed in Cancer, the waters from the Tropic of Capricorn rush toward the Tropic of Cancer.

Of the same opinion is Francesco Resta (bk. 3 of the Meteorology, tract 1 On the Sea, ch. 16), affirming [that] it happens from the Sun’s action that the waters flow now toward one Tropic, now toward the other; nor does he think [it] to be contemned, what Aristotle had said on another occasion (sect. 23, probl. 20)—namely, that salt waters are more stable, on account of a certain viscosity similar to oil, but fresh [waters] flow more easily, and [that] the waters near the poles are established to be less salt, but could not flow toward the salt waters enclosed within the Tropics unless these, by their depression, yielded place—which [depression] would have to be equalized by the polar waters. Mastrius too (disp. 4 On the heaven and Meteors, q. 4, num. 148) thinks the sea-waters flow from the South and from the North toward the Equator, on this ground, that, by the excess of heat, much of the water contained in the Torrid Zone is converted into air, and, on the contrary, near the poles a great force of waters from the snows and mists rains down into the sea. But Bartolomeo Crescenzio (bk. 3 of the Mediterranean Nautics, ch. 2) so ascribes this motion to the Sun’s action, and admits [the waters] to flow from the poles to the Torrid [Zone], yet so as not to admit that the waters within the Torrid are rendered more depressed on account of consumed vapors; but [holds that], on account of the waters attracted by the Sun and converted first into vapors, then into air, the remaining waters of the seas, by the force of continuity, run to fill their place which was under the Torrid Zone. Finally, our Cabeo too (Meteors bk. 2, text 6, q. 2) approves the same cause—namely, hence a great consumption of water in the hotter places about the Equator, and a great abundance of rains and snows about the poles, and therefore [that], to preserve the equilibrium of the sea, the waters flow together from both poles toward the Equator; but he adds [that], just as in very cold weather, the more the surrounding air is colder, the more abundantly the water distills, as if by an alembic, so in the polar parts, where the surface of the earth is colder, the vapors ascending from the bowels of the earth to the hollows of the polar mountains more easily congeal into waters, and distill into more copious waters, and therefore thence greater rivers, or more copious springs of waters, burst forth.

[Margin: Whether more and greater rivers [rise] from the poles, or under the Equator.]

But Furner and Crescenzio teach the opposite: namely, that under the Equator more and greater rivers gush forth—of which kind are the Nile, the Manicongo, the Cuana, the Zaire, the Coanza, the Niger, and others in Africa; but in America, the Maranhão, the Aureliana, the Silver River [Río de la Plata], the river of St. Dominic, of St. John, and several other huge rivers, to which by no reckoning can [those] be compared which roll down from the Northern mountains into the sea. And they think the cause to be [this]: because under the Torrid [Zone] the soil, on account of the exhalations and vapors perpetually drawn out by the Sun, is filled with more and greater pores, to fill which more waters run from the subterranean reservoirs of waters. But to dispute of this is not of this place.

The Second Motion of the Sea, from the East toward the West

[XIII.] No less evident in the sea is this motion than the preceding: for it is established that far more swiftly—even with the wind ceasing, or with an equal tenor [of wind] impelling the sails—one sails from Palestine to Spain than from Spain to Palestine, and from England to Ireland than from Ireland to England. More swiftly too one sails from Spain to the West Indies, so that Mexico, or the islands nearer it, are reached in about one month, or at most two months; whereas thence, the reverse, one cannot sail back except in four, five, or even six months, and there is need—to flee the waters running toward the West—to obtain stronger winds blowing toward the East, and therefore an oblique course toward the North must be instituted. But also the Portuguese, when (the Cape of Good Hope being passed) they make for the East Indies, even if they use favorable winds, reach Goa or Malacca much more slowly than [those] sailing back thence toward the West; which many shipmasters testify, and our P. Antonio Magalhães the Portuguese confirmed, in the year 1633, when he was destined Procurator of the Goa Province for the General Congregation. For the sea so runs toward the Cape of Good Hope—especially between Ethiopia [Africa] and the island of St. Lawrence [Madagascar]—that there is far greater danger of shipwreck there than in the strait

[…continues on p. 365 (PDF 400) with the catchword “in fre[to]”: “…than in the strait of Sicily”—the rest of the eastward-current evidence, then the gyre-motion arising from the two, and the opening of the Tide proper (Flux and Reflux).]

(printed p. 365 — within Chapter XIV, the “History of the Motions of the Sea.” Finishes the Second Motion (East to West) with further navigational evidence and the proposed causes (solar attraction, Kepler’s magnetic Moon, occult celestial qualities) against Fromondus, who credits only the trade-winds; a compound gyre motion is described. The Third Motion — the Tide (flux and reflux) — then opens with its definition and three variations.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 365]

[in the strait] of Sicily, or in the sandy places of Flanders; and our Fathers, returning from the Chinese kingdom, or from East India, affirmed that not even with favorable winds could they sometimes resist [the course] toward the East, especially under the Equator. Hence, from this motion—[this] course of the waters into the West—are infamous for shipwrecks the Vale of Jehoshaphat at the Island of St. Lawrence [Madagascar], and, in the Mexican Gulf, the Island called the Dragon’s Mouth [Os Draconis], and [the waters] near Guadalupe and the harbor of Cartagena and St. Martha—so much so that ships, even with the wind helping, cannot stand against [it], and scarcely in one day [can make] one mile, or in 7½ days complete 40 miles, the sounding-lead being very often snatched toward the West, as Trimarchus testifies (bk. 2 of the Meteors, disp. 1, sect. 6, from the narration of the shipmasters of the Spanish Knights when he was at Madrid), and Willebrord Snell (in his Batavian Tiphys, bk. 2, prop. 8)—adding that, between Brazil and Angola, this motion of the sea is borne, from the 20th of April to the 20th of July, toward the North-West [Zephyroborea]; but from the 20th of October to the 20th of January, toward the South-West [Austrozephyrus]. There narrates too Adriaan Metius—and from him Furner (bk. 9 of the Hydrography, ch. 23)—of a certain ship’s captain sailing from Brazil to the island of St. Helena (which is to the east of Brazil) [who], when, with favorable winds, he had sailed several days in the same sixth parallel of the Equator and thought himself very near that island, found himself still near the coast of Brazil. Besides, those who sail from Gaul to Brazil make straight for Guinea, that thence, having got the sea-course toward the West, they may sail more happily; for this course is much more sensible within the Torrid [Zone] than far from it. But in the Pacific Sea this motion is most evident: for indeed [those] sailing from Acapulco make toward the South to the 10th degree of southern latitude, and, keeping their course in that parallel, in 85 days reach the islands of the Robbers [the Ladrones/Marianas], 3000 leagues being completed, without any use of their sails; and thence, ascending to the 13th degree of latitude, having departed from those islands, with the same felicity reach Manila, which is in Luzon, one of the Philippines. But from the nautical Ephemeris of Thomas Roe, an English nobleman who—sent by his King—was legate to the princes of India in the Year 1614, and especially from the diary of Walter Peyton, it is established that, when the English, on the 22nd of June, had reached the island Mohéli [in the Comoros], it was shown them by the inhabitants of that region that there had been a current which for 15 days flowed toward the East, and for another 15 days toward the West; which by their own experiment the English confirmed; and that island is between the Cape of Good Hope and the island of St. Lawrence, or Madagascar. But that also is marvelous which Lord de Hayes relates (in Furner) in his itinerary from Gaul to Constantinople: namely, that in the Danube the water runs down more swiftly morning and evening than about noon, and that this is manifest near Buda and Belgrade from the wheels of the mills.

[Margin: The cause of this motion.]

Whence Furner gathers the cause of the sea’s motion toward the West to be the Sun, perpetually attracting the vapors and exhalations (especially within the Torrid [Zone]), and this by its course toward the West; so that accordingly [it is] necessary that the waters run from the East, that by a continual course they may conserve the equilibrium of the sea. Be it that Kepler (in the introduction to the Commentaries on Mars) attributes it to the magnetic virtue of the Moon, drawing forth the waters while it [the Moon] is moved toward the West by the diurnal motion—which force he says to be so great that, unless in turn the earth drew the sea-waters to itself, all the sea-waters would be raised and would flow into the body of the Moon—which Furner thinks said gratis [groundlessly]. But others, with Vicomercato, attribute it to the diurnal motion of the heavens, snatching the air and sea toward the West; to whom does not gainsay Francesco Resta (in the named ch. 16), nor Mastrius (above). But the Author of the book On the elements [Tyennensis] attributes it partly to the heat of the Sun raising vapors, partly to an occult and as-if-magnetic virtue, by which, as it draws the clouds, so also it draws the sea-waters with it thither whither it [the Sun] itself is borne by the diurnal motion—from whom does not dissent Trimarchus, in the place already adduced. But Scaliger (exercitation 52), Contarini, the Coimbrans, and Aversa ascribe this to the occult qualities of the heaven, to whom Mastrius also tacitly assents. Further, Cabeo (Meteors bk. 2, text 6, q. 3), from the supposition that there is a motion of this kind, refers its cause partly to the perpetual or frequent East [subsolani] winds, especially within the Torrid [Zone], partly to the Sun drying up the waters, etc.

[Margin: By whom this motion is called into doubt.]

I said “from a supposition,” because he himself doubts of this motion, and rather thinks it false; but Fromondus (bk. 5, ch. 1, art. 6) denies it, and says that that ease of navigation toward the West wholly proceeds from the East [subsolani] winds blowing continually, chiefly within the Tropics—which winds Joseph Acosta acknowledged and testified (bk. 3, ch. 4 & 8), and the Dutch nautical diary of the Year 1595, from which it is had that the ship sailed from Lima in the Year 1580, and in the months of February and March completed, under the same parallel, 1700 leagues toward the West, the wind in the Pacific Sea being perpetually favorable; and [that] Álvaro de Mendaña, sailing from Peru, by the same benefit reached in a short time the islands of Solomon. Hence, therefore, it is (says Fromondus, and Cabeo nearly subscribes) that the Spaniards make straight for the Canaries, that there they may fill their sails with the winds blowing from the East, and by a very short voyage reach the island of St. Dominic [Hispaniola]; but on the return they are forced to go out of the Torrid [Zone] up to the 37th, or even 40th, degree of elevation, that they may enjoy the West winds [Favonii], by which somehow they return into Spain by a long and oblique course—be it that, from the 40th degree on, the winds are now inconstant, by the testimony of Acosta (bk. 3, ch. 7).

[Margin: Confirmation of this motion.]

But since even in a parity of winds—nay, with favorable winds blowing toward the East—navigation toward the East is most difficult, as we narrated above; to which add, from Scaliger (exercitation 52), who learned [it] from the shipmasters, that one reaches the island Madagascar under the eighth southern parallel, [and] Moabar of India in 20 days, whence one does not return except in three months, with whatever equal force of winds—since, I say, these [things] are so, and very many shipmasters, or [those] most skilled in navigation, after Columbus acknowledge, besides the winds, also and chiefly this course of the waters, it is not to be said that they are deceived in a matter of so great moment.

A Motion of the Sea arising from the two aforesaid

[XIV.] Therefore, from the motion of the Sea from the Pole (especially the Arctic) toward the Equator, and from the motion of the same toward the West, there follows a certain other motion in a gyre [circle], by which it [the sea] seems to return toward the East through certain straits and along shores: for while it strikes against opposite shores, it is forced to flow back. So Contarini (bk. 2 On the Elements), and Scaliger (exercitation 52), and others noted: the Mediterranean, by striking against the shores of Africa and Spain—since through the narrows of the Gaditan [Gibraltar] strait it cannot wholly flow out as fast as would be fair—returns by a winding course toward the shores of Africa up to the coasts of Asia Minor, and by this bend flows along the coast of Dalmatia toward Venice, and from Venice along the shores of Italy is carried up to the Sicilian strait. But in the Sicilian strait it is most well-known that one part of the waters is borne upward at the same time, and the other downward, most swiftly. The reciprocal up-and-down motion, however, is noticed in most Euripi or Straits—and in the Sicilian strait indeed, twice in single days, it is moved in a gyre to opposite parts; but this pertains to the tide [aestus], of which below. Scaliger adds that in the Scythian Ocean the waters run toward the East, and in the Atlantic toward the Land of Labrador. But marvelous is what Furner says (bk. 9, ch. 6): that in six hours the Mediterranean flows out through the Gaditan strait, but the Ocean enters [as] victor for 18 hours. But if anyone desires other notable examples of waters running into diverse regions of the world, let him consult Furner (bk. 9 of the Hydrography, ch. 31).

On the Third Motion of the Sea, which is called the Tide, or Flux and Reflux in general, where [there are] certain Marvels

[XV.] Although the motion of the Sea—especially that which we indicated at number 14—can be called Flux and Reflux, yet, the word being used more strictly by Sailors and the more skilled Hydrographers, by the name “Flux and Reflux of the sea” is understood that motion which is not merely boreal [northern], but is made with a certain alteration, on account of which the Sea swells and subsides as if by boiling up and boiling down [defervescendo]; whence it is also called the Sea’s Tide [Aestus]; and those bays and harbors in which is manifest the access of the swelling Sea and the recess of the subsiding [Sea] are called Estuaries. But some think the “Tide” [Aestus] [is so] named (whence also “summer,” aestas) from burnt air, or from the abundance of heat. But now the Phoenicians of old, and afterward the rest of the Sailors, observed three variations of this tide: one which happens twice daily; the second, which

[…continues on p. 366 (PDF 401) with the catchword “quae”: “…the second, which [happens monthly]…”—the rest of the three variations of the Tide, and Riccioli’s account of the flux and reflux.]

(printed p. 366 — within Chapter XIV, the account of the Tide. Finishes the common preliminaries (the tide occurs in the deep, certain springs and wells tide with the sea, the tide’s connexion with the Moon). Then “An Accurate History of the Sea’s Tide” opens with the European tides — the mostly tideless Mediterranean, the great Euripi and Straits, and the huge tides of Britain and the Channel.)

[Header: BOOK IX. SECTION IV. — 366]

[from the bottom] drives the sea-beasts upward to the surface of the sea, as affirm Albertus Magnus (On the properties of the Elements, tr. 2, ch. 6), Vallesius (ch. 52 of the Sacred Philosophy), and Francesco Resta (tr. 1 On the Sea, ch. 13); nor does Pliny deny it absolutely, but speaks comparatively—[for Pliny says, bk. 2, ch. 97:] “But about the shores rather than in the deep are these motions detected.” And not only the sea, but certain springs swell like seas.

[Margin: The tide of the sea even in the deep. — Wells and Springs tiding together with the Sea.]

Such was the spring, enclosed in the manner of a well, at Gades [Cadiz], near the temple of Hercules, which swelled and subsided with the Ocean, but at other times did this at different times, as Pliny reports (bk. 2, ch. 97). But also Ortelius narrates that in Connaught of Ireland a spring is found on the top of a mountain, which, according to the prescript of the neighboring sea, swells and subsides twice daily. Pliny adds (above) that on the bank of the Baetis [Guadalquivir] there was a town whose wells subsided when the tide grew, and grew when the tide decreased, but at the middle times were unmoved; and that the same was the nature of one well, which was at Seville. Finally, Albertus Magnus (On the properties of the elements, tr. 2, ch. 5) reports that the fresh waters of certain cities of Arabia along the sea—as in the city Azim and Albastrach—are wont to tide with the sea.

[Margin: Whether men die when the tide recedes.]

But that is marvelous, if true, which Pliny narrates (bk. 2, ch. 98), saying from Aristotle: “To these Aristotle adds that no animal expires except when the tide recedes. This was much observed in the Gallic Ocean, and found only in man.” Which Bodin thinks false. But Levinus Lemnius (bk. 4 On the miracles of nature, ch. 1), although he dares not disapprove Pliny, yet adds that he has detected some [men] to have died at the access of the Ocean, and, in the maritime tract of Belgium, [men] to be in danger—strong men [coming into peril] with the tide acceding, feeble [ones] with it receding. But Furner affirms (bk. 9, ch. 1) that mixed bodies never abound more in humors than when the Sea tides and swells; nor are they ever more dried up than when the sea subsides and decreases—wherefore, since the Moon predominates over humors, it is a sign that the sea’s tide has a great connexion with the Moon. To this it is agreed: that, if any shore feels the tide, [the tide] there becomes greatest where are the mouths of great rivers, and that those coasts which are stretched out into the sea experience it sooner than those which have receded within the lands; on the contrary, the rivers themselves, lakes, [and] ponds—just as neither the seas which are similar to ponds, like the Caspian—do not suffer a tide of themselves, except through the mouths by which they communicate with the sea.

[Margin: Pliny’s universal opinion concerning the Tide.]

Lastly, that [saying] of Pliny is to be recalled, from bk. 2, ch. 97: “But all tides in the Ocean cover and inundate greater spaces than in the rest of the sea, etc.”—neither lakes nor rivers are similarly moved.

An Accurate History of the Sea’s Tide

[Margin: The Mediterranean Tides.]

[XVI.] The Tides of Europe are thus. In the Mediterranean the greatest part of the shores lacks a sensible tide—certainly, as in the Caspian none [exists] (although this rather pertains to Asia), so neither [does] the Euxine Sea, of which is that [saying] of Pliny (bk. 2, ch. 97): “The Pontus always flows out into the Propontis, [but] the sea never flows back inward into the Pontus.” In which place he adds, thirdly, that one reaches Utica from Italy on the third day, the tide running strong. For the African shores at Utica, Tunis, Hippo, and certain other coasts feel some tide, but [a] greater [one] the island of Malta. In the Adriatic gulf, about Ravenna and Aquileia, formerly [the tide] was so great (by the testimony of Procopius, bk. 1 On the Gothic War) that it occupied many thousands of paces, and the sailors in the morning would await the tide, by which they might the sooner bring in their wares; but in the evening [the tide] was wont to subside and flow back: now it occupies about two miles of the Venetian shore, and, boiling up from the bottom (as Contarini noted), rises 3, 5, or 6 feet. Therefore the city [Venice] is wont, from time to time, to fortify itself with bars and banks, lest it be overwhelmed by the tide. But about Corsica, Sardinia, and in the estuaries of Rome, and about Elba, Malta, [and] Crete, [the tide] scarcely [rises] half a foot. On the coast of the Province [Provence] at Marseille, a whole foot rises; in the rest of the Tyrrhenian no tide is felt, whether on the western coasts of Italy, or on the eastern shores of Gaul and Spain; but neither is any [tide] ascribed to the shores of Greece.

[Margin: The Euripi.]

A greater tide, or flux and reflux of the waves, is discerned in the Euripi and Straits: for Pliny testifies (bk. 2, ch. 97) that the Tauromenitan [Taormina] Euripus flows and reflows several times a day; and Patricius, in his Pancosmia, says that in Liburnia, at the town of Assuerus, there is a most narrow Euripus of 10 paces, where the sea tides more than twenty times a day.

[Margin: The Chalcidic Euripus.]

But nothing more memorable than the Chalcidic Euripus, between Boeotia and the island of Euboea, where—not at uncertain times or turns (as it pleased Livy, Decade 3, bk. 8), but seven times by day and seven times by night—the sea flows and reflows, as Cicero affirms (bk. 1 On the Nature of the Gods), Strabo (bk. 1), Pomponius Mela (bk. 2, ch. 4), and Pliny (bk. 2, ch. 97); which Euripus indeed St. Basil elegantly describes (homily 6 of the Hexaemeron); but it is borne with so great an impetus sometimes that it seems to rush from the highest mountains. But Gillius, who explored those places (as Francesco Resta narrates, tr. 1 On the Sea), affirms, from the relation of the inhabitants, that that Euripus now tides only four times, not seven, [but] sometimes does not keep these turns. The cause Scaliger (exercitation 52) refunds into the waters intercepted by underlying rocks, which are poured back alternately.

[Margin: Whether Aristotle threw himself into the Euripus.]

But some report—from Sts. Justin and Nazianzen, and from Procopius, Caelius, [and] Vicomercato (in the description of Euboea, and others), [and] Magini—that Aristotle, from despair of grasping the cause of this Euripus, threw himself headlong into it, saying, “Since I do not grasp thee, O Euripus, do thou grasp Aristotle”—but nothing of the kind about Aristotle [does] Laertius [report] in his life.

[Margin: The Tide of the Sicilian Strait.]

But before we go out from the Mediterranean, the tide of the Sicilian Strait, or of Messina, must be observed—where, although the water rises a little above one palm at Scylla and Charybdis, nevertheless it flows and reflows up and down most rapidly, so much so that Aristotle numbered it among the marvels of the world. Bartolomeo Crescenzio narrates (bk. 3 of the Mediterranean Nautics) that, when he entered this strait near Scylla and Charybdis in the Year 1594, on the 3rd of August, the waters drove the stern; but when he had reached the middle of the Channel, another current of water rushed in from Rhegio [Reggio], which, meeting the former, produced a tide of as-if-boiling water, with a swelling and whirlpools—not otherwise than a cauldron full of water is wont to seethe when fire is put under it—which swelling of the tide lasted through a quarter of an hour, until the water rolling forth from Rhegio overcame the other, which had come from Scylla, or the tower of the Pharos of Messina. He adds, further, that certain Messinese knights affirmed to him that every six hours that meeting of the waters and the tide happens, which they attributed to waters enclosed in caverns and poured back thence; but Crescenzio attributes it to the Moon, of which it was then the 17th day, and it was the 15th hour Italian [reckoning]. Also in the Year 1595, when the same Crescenzio wished to go out from the mouth of the strait with galleys, from that conflict of the waters he experienced no small fear: for the water running from Rhegio toward the Pharos so impelled the ships that one after another passed most swiftly; but when they were made nearer the shore, another water, meeting from the opposite [side], repelled them—certainly on account of the motion of the waters in a gyre. Things similar to these I have often heard from Fathers of our Society, who, for the sake of preaching or steering, have sailed into Sicily.

[Margin: Whether any tide in the Baltic. — The Tide of Norway, Denmark, England, Holland, [and] Flanders.]

Outside the Mediterranean, the European shores of the Scythian and Baltic Sea have no sensible tide, by the testimony of Bartholin the Dane; yet Cardano (On the Variety of things, bk. 1, ch. 4) reports that beyond Sweden there is a promontory Nasus [the Nose], so named from the likeness of a nose, under which there is a whirlpool which every six hours boils with so rapid a tide that, by flowing back, it sucks back the ships—which also Olaus Magnus affirms. The rest of the Norwegian shores (especially the western), as also the English, Irish, Danish, Dutch, [and] Flemish, suffer huge tides, so much so that in Britain the shore is laid bare for 9 miles, and the Thames feels the tide up to London, up to 50 or 60 miles, the water raising itself about 20 cubits. Nay, Pliny (bk. 2, ch. 97) says: “Pytheas of Marseille is the author that the tide swells above Britain by eighty cubits”; to whom nearly consents Georg Braun, in his Bristol [Civitates], confessing this swelling to ascend to 66 feet; and Furner (bk. 9, ch. 20), who says it was observed by himself that the tide at the Bay of Manche [the Channel] is sometimes raised 70 feet. But also that is worthy of note, which Beda reports (in Surius, tome 2) in the life of St. Cuthbert (ch. 17): namely, that in the Lindisfarne region, the tide of the British Ocean acceding twice daily, [the place] becomes an island; and, the shores being twice laid bare, that which had been an island appears joined to the mainland,

[…continues on p. 367 (PDF 402) with the catchword “appa[rere]”: “…appears [joined to the mainland]“—the rest of the European tides, then the African, Asiatic, and American tides, and the start of the diurnal-period section.]

(printed p. 367 — within Chapter XIV, the geographic tide-catalog. Finishes the European tides, then surveys the African, Asiatic (including the marvelous Cambay tide), and American tides, with a notable digression arguing that Moses did not exploit the ebb-tide at the Red Sea crossing. A sub-head then opens, “On the Diurnal Period and Time of the Tide.”)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 367]

[the island] appears [joined to the mainland].

[Margin: A marvelous spring of Ireland.]

I have already said above, from Ortelius, that in Connaught of Ireland there is a mountain on whose top a spring swells twice daily, and twice subsides. They report that on the shores of Iceland also terrible tides happen daily.

[Margin: The Belgian and Gallic Tide.]

In Belgium and at Calais the tide, at new and full Moon, rises to 15, or even 18 and 20, feet; the Gallic shores facing the West experience also a very great tide. But in them two [things] are most worthy of note. The First is that the mouth of the Garonne is filled in seven hours and drained in five, as Scaliger noted (exercitation 52)—although Lord de Candale (in Furner, bk. 9 of the Hydrography, ch. 1) observed [it] to be filled in 6¾ equinoctial hours, but to be drained and subside in 6. The Other is what Francesco Resta narrates (tr. 2 On the sea, ch. 15), and Furner (bk. 9, ch. 21), and I seem to myself to have heard from the Fathers of our Society—namely, that at the Mount of St. Michael and at St. Malo the tide rises to 70 feet, and sometimes 90, and recedes through three leagues; and that on the shore of Normandy there comes to be daily an Island, to which, the sea flowing back through the sand, one returns [on foot], it now being made not an Island, but Mainland.

[Margin: The Portuguese and Spanish tide.]

It is known that all the Portuguese rivers suffer a tide in their mouths, but especially the Tagus, which on that account flows back toward its source for 4 miles; but the Baetis [Guadalquivir] back-flows up to 50 miles. On which occasion I repeat that [saying] of Pliny (bk. 2, ch. 97):

[Margin: Marvelous wells.]

“On the bank of the Baetis there is a town, whose wells are diminished when the tide grows, [and] grow when [it] decreases, [but] are unmoved at the middle times. The same nature [is] in a town of Seville, in one well, [though] common to the rest”—who, in the same chapter, a little before had said: “At Gades [Cadiz], which is the nearest spring to the temple of Hercules, enclosed in the manner of a well, at times swells together with the Ocean and diminishes, but at other times [does] each [of these] at contrary times.” But, the [Straits of] Gades being surpassed, let us migrate to the African coasts.

[Margin: The African tides.]

The shores of AFRICA which are washed by the Mediterranean already, as we said, experience their tide. But those [washed] by the Atlantic Ocean [have] none sensible, until one reaches the Tropic of Cancer; for within the Tropics the sea tides, especially beyond the Equator, near the Black [Niger] river; and at the 1st degree indeed a flux begins, similar to the Portuguese, and is stretched up to the island of St. Thomas, situated under the Equator—where, however, it is not greater than the Venetian tide, as Trimarchus heard from the shipmasters and reported (bk. 2 Meteors, disp. 1, sect. 7), and the same has Ramusio (tome 1 of the Navigations, p. 126). But now at Guinea the Sea seethes with so great an impetus from the tide that ships can scarcely stand fast with three anchors, lest they be dashed [together]. But the mouths of the Black [Niger] river, as Fromondus narrates (in the Meteors), swell in 4 hours, [and] subside in 8; or, to use the words of Scaliger (exercitation 52): “At Ginega of Ethiopia it accedes by fours, recedes by eights; and those mouths lie open 20 miles”—where Ramusio too (tome 1 of the navigations, p. 118) confirms the flux of 4 hours and the reflux of 8.

[Margin: The Tide of the Red Sea.]

Finally, in the Erythrean, or Red, Sea (whatever Galileo may impugn, [arguing] that the causes adduced by him are thereby damaged) so great is the daily tide that the haters of the sacred letters have dared, says Scaliger (exercitation 52), rashly to lie that Moses crossed on dry [ground], having got the occasion from the reflowing sea—which, however, could not happen, says the same, on this ground: that up to Suez (which town lies in the innermost recess) the sea so covers that shore that it never uncovers the bottom of the sea by which the Hebrews crossed.

[Margin: Moses by no means used the occasion of this tide.]

Besides, as Trimarchus notes (bk. 2 Meteors, disp. 1, sect. 7), from the place to which the sea reaches in [its] recess, up to the place through which Moses, with the Hebrew people, crossed on dry foot, there intervene thirty and more miles; nor could the Egyptians have lain hidden on this side—who, if they had so suddenly feared a new tide, would not have committed themselves to it so intrepidly. Now, since we too have crossed with Moses through the Red Sea into Asia, let us cull the more notable [things] of the Asiatic tides.

[Margin: The Asiatic tides. — The East Indian tide.]

The tides of ASIA toward the North are unknown, [but] toward the South and East are manifest—which indeed [show] how anxious they held Alexander the Great and his shipmasters at the mouths of the Indus, narrates more fully Quintus Curtius (bk. 9), and Nearchus (in Ramusio, tome 1 of the navigations): for the sea receded with so great an impetus that it left three ships destitute on the dry shore, which afterward the returning tide restored to their course. But that [is] pleasant, which Pliny relates (bk. 13, ch. 25): “Those who sailed among the Indians,” he says, “[as] Alexander’s soldiers, handed down that the foliage of the marine trees was green in the water, [but], taken out, at once dried up by the Sun into salt,” etc.; and, after a few [words]: “In the same tract the tide covers the woods of the islands, although [they are] taller than the tallest plane-trees and poplars; the leaves of these [are like] those of the laurel, the flower like the violet in odor and color; the berry like olives, and itself of pleasant odor, [the leaves] springing forth in autumn, the leaves never falling. The smaller of these the sea wholly covers; the tops of the greatest stand out, to which ships are moored, and, when the tide recedes, [they are moored] to the roots.” But of a Gulf distant from the Indus river 60 miles, Linschoten narrates (in the 2nd part of the East Indies, ch. 9) that there is the most rapacious reciprocation of the sea of all that have anywhere been seen, so much so that it was a terror, nay a stupor, to Alexander the Great. Further, at Calicut—as the Fathers of our Society narrate, especially Nicolaus Godignus (bk. 1 On the affairs of Abyssinia, ch. 11), and Trimarchus attests (in the section already praised)—the increments of the sea become greater at Full Moons, whereas at the mouths of the Indus they become [greater] at New Moons. Ramusio adds (tome 1 of the navigations, p. 131) that there the sea so reflows in six hours that it leaves ships on the dry. At the coast of the Ganges the tide is worthy of so great a river’s mouth; but greater at the shore of Cambay [Khambhat], where—as both the Fathers of our Society report, and most Writers on this argument—

[Margin: The marvelous tide of Cambay.]

the Sea, in 2 hours, pouring itself onto the shore, occupies about 30 leagues, but elsewhere 15 miles (as Trimarchus has, and Ramusio, tome 1, p. 330), and indeed with so great rapidity that, unless men, warned by cymbals, flee with a hastened course, they are overwhelmed by the tide; but when it reflows, likewise in two hours, very many ships stick destitute on the dry. The inhabitants of that place, however, have in some place very ample wells, in which the ships settle until the tide boils away, lest they be snatched by it to the sea with danger; but for this there is need of skilled shipmasters, that the vessels may be able, when the sea reflows, to remain in the said wells, as Eduardo Barbosa narrates (in Ramusio, in the place reviewed). Of the shore of Persia, Scaliger has thus (exercitation 52): “On account of the shore, Diuobandel of the Rumi sometimes becomes an island, [and] is sometimes part of the mainland. That word signifies the Holy Port of the Turks. But neither is that returning, nor [that] occupation, by a release, in all the places of the shores.” But in the Chinese kingdom the river Yanna (which name signifies “the son of the Sea”) suffers a tide daily up to Nanking, or up to the lake nearest to Nanking [Nanquino]—although at Peking it is not felt except at new and full Moon. So has our Nicolaus Trigautius (bk. 3 On the Christian expedition among the Chinese, ch. 9). At the Moluccas and Philippines the sea does not rise above 3 feet, says Furner (bk. 9, ch. 21).

[Margin: The American tides.]

AMERICA’s Tides, finally, are thus. The Northern shores of North America are without tides, but the Southern have it manifest, and at Veragua [it is] strong; but in some place (by the testimony of Oviedo, ch. 9, and Pedro of Seville, part 5, ch. 1) it runs out to eight thousand paces, and on the Mexican shore (excepting, however, the Gulf, which is exempt) so swift in [its] recess that it seems at once to vanish from the eyes. At the islands Martinique and the Caribbees the sea scarcely rises one foot. Near Cuba and Hispaniola none [is] sensible except at Full and New Moons, especially in March and September—for then the waters are higher and more agitated. The river of the Amazons, or Maranhão, is said to feel the tide and saltness of the sea up to a hundred leagues. On the Peruvian and Paria shores the tide is no moderate [one], and near Panama it occupies two leagues. But nowhere [is the] tide more admirable than in the Magellanic [Strait], in which two tides—one from the Atlantic, the other from the Pacific Sea—meeting each other, raise the waters into a heap with a manifest swelling, as the Fathers Joseph Acosta (bk. 3 of the history of the new world, ch. 13 & 14) and Alfonso Ovalle of our Society (in the Chilean History) testify; of which tide indeed Bartolomeo Crescenzio drew a diagram (bk. 3 of the Mediterranean Nautics, ch. 2), affirming this strait to be 100 leagues long and very tortuous. Hence, sailing to the Archipelago of St. Lazarus, a tide is found which daily, in 12 hours, is borne toward the South with so great an impetus that it burst a rope of 27 inches’ thickness—so narrates Furner (bk. 9 of the Hydrography, ch. 16).

On the Diurnal Period and Time of the Tide

[Margin: 1st Observation concerning the time of the diurnal tide.]

[XVII.] First, from the common opinion and observation of the skilled—from the ancient Phoenicians down to our times—it is established, speaking regularly,

[…continues on p. 368 (PDF 403) with the catchword “[loquen]do”: “…speaking [regularly]“—the rest of the diurnal period and time of the Tide.]

(printed p. 368 — within Chapter XIV, the account of the Tide. ¶XVII sets out four observations on the diurnal tide-period: two floods and ebbs in each lunar day of 24h 48m tracking the Moon’s meridian passage, the daily 48-minute lag, local variation by harbor and coast, and de Candale’s hour-circle rule. A new sub-head then begins ¶XVIII, on the monthly periods and varieties of the tides.)

[Header: BOOK IX. SECTION IV. — 368]

[speaking regularly], in those places in which there is a tide: where first the Moon shall have been elevated above the horizon by about one Sign [30°], the increment of the sea begins, and it so flows that it is raised above the banks, and—unless their height obstruct—spreads beyond the accustomed limits toward the mainland; but in the mouths of rivers it drives back their waters toward the source; and that swelling continually grows, until the Moon reaches the Meridian of that place, or certainly (as Simon Stevin thinks) the Ninetieth degree of the Ecliptic computed from the horizon; for then the highest increment happens, which is wont to be called the Living Water [Aqua viva], or the Living [part] of the waters: but when the Moon, the Meridian being left, has begun to descend toward the Horizon, the waters of the Sea begin to subside and to flow back, until the Moon is distant from the Horizon by about one Sign; for then the highest decrement happens, after which the waters stand somewhat, until, the Moon being placed one Sign below the Horizon, they begin again to grow, up to its arrival at the Nadir of the Meridian (that is, the part of the Meridian existing in the hidden hemisphere below the horizon), or certainly to the Ninetieth degree of the Ecliptic numbered below the Horizon—at which time again the Living Waters and the highest increments of the sea are: soon, when the Moon has begun to ascend toward the rising Horizon, the waters of the sea begin to subside; and when the Moon, before its Cosmic [heliacal] rising, is distant from the horizon by one Sign, they sink deeply, and in that state stand up to the [moment] when the Moon is exalted one Sign above the horizon. And so, in the period of one Lunar day—which consists of 24 Solar hours and ⅘ [of an hour], or 48 horary minutes—twice daily in the aforesaid places the flux and tide happens, and twice the reflux and subsiding of the tide; and in most places the sea grows for six hours, and for six [hours] decreases. Be it that in some [places] this rule is not kept: for, as already said, the mouths of the Garonne are filled in seven hours, [and] subside in five, if we believe Scaliger; or [the sea] grows there for 6¾ hours, and decreases for 6, if we stand with Lord de Candale and Furner. About the Hipponensian [Hippo] shore of Africa, the Malinae and Ledones—that is, the flux and reflux—are thus, by the testimony of St. Augustine (bk. 1 On the miracles of Sacred Scripture, ch. 7): “But the great Malina boils for five hours, and for seven hours uncovers the backs of the shores.” But at the mouths of the Black [Niger] river, by fours [every four hours] the increments, by eights [every eight] the decrements, happen; and at the shores of Cambay the tide happens most rapidly in two hours, and twice the reflux; but in the Chalcidic Euripus formerly seven times in a day, now four times, the tide happens. Finally, in some place it suffers no certain rule, which is thought [to happen] in the place of a prodigy, as between Staten and Bergen at the shores of Norway. With which limitation are to be understood the words of Pliny (bk. 2, ch. 97), which it pleases [me] to subjoin.

[Margin: Pliny’s notable passage on the sea’s tide.]

“Many [things] have been said concerning the nature of the waters; but [that] the Tide of the sea should accede and reciprocate [is] most marvelous—in many ways indeed, but the cause [is] in the Sun and Moon. Twice between two risings of the Moon they flow in, and twice they flow back, [in] always twenty-four hours; and first, swelling with it [the Moon] as it raises itself with the world, soon—the Moon declining from the meridian summit of the heaven toward the West—subsiding; and again, from the [Moon’s] setting beneath the lowest [part] of the heaven, and toward the parts contrary to the meridian, acceding [and] inundating; thence, until it rises again, swallowing themselves back.” The remaining words of his pertain to the second observation.

[Margin: 2nd Observation.]

Secondly, it has been observed that the beginning of the tide does not happen at the same hour (although in the same place), but daily later by 48 horary minutes, on this ground: that the Moon rises daily later by as many minutes—and this on account of its own proper motion, by which it daily advances toward the East by about 12 degrees, for which there are required, of the diurnal motion toward the West, 48 minutes [of time]. Wherefore, since at Antwerp, at new and full Moon, the highest tide happens at the 6th hour after midnight, on the following day it does not happen except at the hour 6 and 48’; and on the third day after the new moon and full moon, it does not happen except at the hour 7 [and] 36’; and so thereafter, on the single days which are between the Syzygies of the Moon, they postpone the tides by 48 minutes. But although the tides of the sea so depend on the Moon, yet their turns return after hours not temporal [unequal] but Equinoctial [equal]. All which [things] Pliny himself acknowledged and taught (bk. 2, ch. 97), saying:

[Margin: Pliny’s remaining words.]

“Nor ever at the same time at which it reflowed the day before—as though panting with the star [the Moon] drawing the seas with it by a greedy draught, and constantly rising elsewhere than the day before: yet at equal intervals reciprocal, and always [by] sixes of hours—not of any [particular] day or night or place, but Equinoctial; and therefore unequal in the space of the common hours, since more of them fall into those days or nights (the measure of those [hours] varying), and only at the equinox everywhere equal. A huge argument, and full of the light and turn of the day, [that] those are dull who deny that the stars pass underneath and again rise the same, and [that] the face of [the world] is similar to the lands; nay rather, that the universal nature [is] thence in the same works of rising and setting, etc.” And so the diurnal period of the tides has for its measure the Lunar day of 24 hours and 48’.

[Margin: 3rd Observation.]

Thirdly, it has been observed, as Furner has (bk. 9 of the Hydrography, ch. 1 & 7), that although some places be under the same meridian, or very nearly, yet they do not suffer the tide at the same hour. Which happens partly on account of the situation of the harbors—for harbors which are stretched out further into the sea feel the tide sooner, and are sooner freed from it, than those which have receded inward, especially obliquely winding; partly on account of rocks or shoals and mounds of sand and similar obstacles; partly, finally, on account of the nature of the soil and the air, which in neighboring places is sometimes very diverse, so much so that in one place there is the highest serenity, in another a most turbulent air. From the first of the three aforesaid causes, the waters tiding from the South toward the North fill Bessunda, the port of Spitsbergen, at the 3rd hour [European reckoning], and yet in a port a little higher the water is not at its highest except at the 9th hour, although the one be not distant from the other more than 20 German miles. So in the coast of Frisia, on the day of new and full Moon, the living water, or highest tide, happens at the 9th hour before noon, and yet at Enkhuizen it happens at noon itself, and at Amsterdam at the 3rd hour after noon, although nonetheless these places be very near—for Amsterdam is within the bay of the sea more than Enkhuizen. So, if the coasts of Britain, Normandy, and Picardy be considered, it will easily appear why, by one hour, the tide happens sooner on the British coast, inasmuch as [it is] stretched out more toward the West than in Normandy. But from the second cause it happens that in some place the sea grows not step by step, but, after obstacles are overcome, suddenly takes its whole increment, and the waves of the tiding Ocean roll most swiftly, like certain casks, one after another into the harbors and shores, so as to outstrip the swiftness of any horse—as is seen at the Mount of St. Michael near Avranches, and on the bank of the Seine, and at the mouth of the Garonne.

[Margin: Pedro de Medina’s error.]

From the said [things] it is established that that rule of Pedro de Medina is false, which Crescenzio refutes (bk. 3 of the Mediterranean Nautics, ch. 3): namely, that the Sea is filled when the Moon is at the Northeast [Graecum], or between North and East [Subsolanum], or at the Southwest [Libycum], or between South and West [Zephyrum]; but on the contrary decreases when the Moon is between North and West, or when between Southeast and South. For this, although in some place and sometimes can happen, yet not always nor everywhere.

[Margin: 4th Observation.]

Rather true is what Lord de Candale observed, and from him Furner reports (bk. 9, ch. 1): the tide of the sea happens daily, in the same place, at the same time at which the Moon cuts the same horary circle, or [the circle] drawn through the poles of the world.

On the Monthly Periods and Varieties of the Tides

[XVIII.] Besides the increments which the Sea daily receives, the Moon approaching to the Meridian above or below the horizon, it receives also greater [ones] when [it is] at Full Moons than at New Moons, and at New Moons [more] than [when the Moon is] far from them, and least at the quadratures, or a little after the quadratures; but elsewhere more at New Moons than at Full Moons. This is so true that even on those shores in which, through all the rest of the month, no sensible tide appears, nevertheless some swelling appears at new or full Moon, as happens in the Mexican Gulf, and near Cuba and Hispaniola, as also on some Mediterranean coasts, and in that branch of the river Yanson [Yangtze] which is up to the city of Peking. In some place, therefore, greater increments happen at New Moons, as at Calicut; on the contrary, elsewhere greater at Full Moons, as at the mouths of the Indus. In some place also the highest increments do not happen on the very day of the new moon or full moon, but two days, or three days, after—as at Dieppe, and elsewhere, where the tides are greater on the 17th day of the Moon than on the 15th; just as the consistency, or mediocrity, of the waters [is] not at the very quadratures, but about two days after; whence that proverb among the Venetians: “From the eighth to the ninth the water does not move; from the twenty-first to the twenty-

[…continues on p. 369 (PDF 404) with the catchword “[ven]tidue”: “…to the twenty-two[nd]“—the rest of the monthly tide-variations, then the annual periods of the Tide.]

(printed p. 369 — within Chapter XIV, ¶XVIII continues the monthly tide-variations, marshalling St. Augustine’s account of the alternating Ledo and Malina tides over the lunar month together with numerous other authorities. A sub-head then begins ¶XIX, on the annual periods of the tides, which peak at the equinoxes.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 369]

[from the twenty-first to the twenty-]two[nd], the water does not move”: which, rendered into Latin, is thus: “From the eighth to the ninth day the water moves not; from the twenty-first to the twenty-second, it neither grows nor decreases.” And then, as Crescenzio says (bk. 3 of the Mediterranean Nautics, ch. 2), the sea-waters are called “waters of gall” [aquae fellis], when at the time of New Moon ☌ and Full Moon ☍ they are called “living waters” [aquae vivae]: where he adds, from his own experiments, that the greatest increments of the waters are at the New Moon, from which thereafter they become lesser up to the eighth day of the Moon, when they are lowest, and so persevere up to the 11th day, within which days the least tides happen; from the 11th to the 17th they grow, so that on the 17th day they are in the highest exaltation, and thence decrease up to the 22nd, and so persist up to the 25th, within which likewise the least fluxes happen. But how the monthly variety of the tides behaves about the Hipponensian [Hippo] shore of Africa and the neighboring coasts, or even at the shores of the Ocean, we shall learn better from St. Augustine himself (bk. 1 On the miracles of Sacred Scripture, ch. 7), whose words are:

[Margin: St. Augustine’s opinion on the sea’s tide.]

“Concerning the daily inundations and recessions of the Ocean, a question is always reborn; for this daily inundation, twice in the day, from time to time, through twenty-four hours is always completed; and by alternating weeks the change of the Ledo and Malina accompanies [it]. But the Ledo has six hours of inundation, and as many of recess. But the great Malina boils for five hours, and uncovers the backs of the shores for seven hours: which nevertheless shows its concord with the Moon, in that, before the Moon is born [new], for three days, it always begins at seven hours, and after the beginnings of the nascent Moon it is wont to have other three days and seven hours. Likewise, before the full moon, it begins by three days and twelve hours, and after as much course of its time consumes its term. But the six [Malinae] of each season—namely of spring and summer, of autumn and winter—according to the Lunar computation, that is, all together twenty-four, the common Year has, excepting indeed the Embolisms [intercalary lunations], which retain twenty-six Malinae.”

And so, from his opinion, the common Year of twelve Lunations has 24 great tides—twelve at New Moons, and as many at Full Moons—which begin to be increased above the ordinary [tides] three days before the new moon, and at the 7th hour, and grow up to the 3rd day of the Moon and the 7th hour; but the Malinae, or great tides, of the Full Moons begin to grow three days and 12 hours before the Full Moon, and are increased up to the 3rd day after the full moon and the 12th hour.

[Margin: Scaliger’s and Trimarchus’s opinion.]

To these it pleases [me] to subjoin the words of Scaliger (exercitation 52): “Namely, in the quadratures there is malacia [calm], commonly called calma; in the full moons the seas are more swollen, so that they seem to suspend themselves by the desire of the star.” But now, if we believe Joseph Scaliger (bk. 2 On the emendation of times, p. 162), the first Frankish-Saxons who inhabited the Gallic shores discerned the beginnings and ends of the Lunar months no otherwise than from the tides made at the New Moon—so just and fixed were they; to whom subscribes Furner (bk. 9, ch. 21), adding that on the Gallic coast the tide of the New Moon lasts for two or three days, and thence decreases up to the 8th day, when the water is lowest, and so lasts to the 11th day; thence grows to the 14th day, and so lasts up to the 17th; hence diminishes to the 22nd, and so lasts up to the 25th; thence grows up to the New Moon. A little otherwise concerning the Sea’s tide [does] Trimarchus [treat] (bk. 2 Meteors, disp. 1, sect. 7), where he says that on the 8th and 21st [days] of the Moon the Tide is none, or very small, and therefore that the sailors then say that the water is fatigued and languid; but at the New Moon and Full Moon [the tide is] greatest, and therefore [the first] is called by the sailors the “head of the water,” the second the “living water”; but he confesses that these [things] are commonly observed in the Adriatic gulf. But Chiaramonti (bk. 13 On the Universe, ch. 22) says that at the port of Cesenatico the sailors call the water “of gall” and “dead,” which happens at the quadratures of the Moon.

[Margin: Resta’s opinion.]

Francesco Resta (tract 1 On the Sea, in his Meteorology, ch. 15) says: “At the Interlunium and the Full Moon the tides are violent, in the quadratures slack; somewhat fuller at the full moon than at the new moon.” But what I said above concerning the Chinese sea at the mouths of the Yanson [Yangtze] seems to be true of some other [sea] also; for Albertus Magnus says (tr. 2 On the properties of the elements, ch. 6):

[Margin: Albertus Magnus’s observation on the tide of single months.]

“It is found that the sea, from the beginning of the Moon up to the full moon, accedes; and from the full moon up to the perfect waning of the Moon, recedes, making in one month only one access and one recess.”

[Margin: Pliny’s authority.]

Nor is the opinion of Pliny obscure in this matter (bk. 2, ch. 97), saying: “For the lunar difference is manifold; and first, by sevens of days indeed [there are] moderate tides from the new [moon] to the half moon, fuller from it [overflowing], and at the full [moon] they boil most; thence they grow mild, equal to the seventh from the first; and again on the other side they are increased by the half moon, equal at the conjunction of the Sun. Plainly the same [are] more mild [when] northern, and receding farther from the lands, than when, gone off into the south, [the Moon] exerts its force by a nearer effort.” In the New Moon, therefore, he reckons great tides happen, in the Full Moon greater; and from the new moon and from the full moon, through the first seven days of the Moon, [the tides] are diminished up to the first and second quadrature, and after each take increments. But he adds: “Yet not at those very joints of the times which I have said, but a few days after; just as neither at the full [moon] nor newest [moon], but afterward.”

[Margin: Borrus’s singular opinion on the tide at the New Moon.]

Since these [things] are so, nonetheless Hieronymus Borrus of Arezzo, in his dialogue On the flux and reflux of the Sea (p. 132), says that at the New Moons the tide is as if insensible, and therefore that it is then said by the Venetians that “the Sea is in Oil” [Mare esse in Oleo], because it stands still just as if it were oil; and yet he concedes that then the waters of the sea are so raised that they cannot be sailed without danger—but he says this comes not from the tide properly so called, but from the storms and winds and changes similar to these, which happen at the new moons, adding that on those same days all the humors are greatly altered, and give signs of notable change. To which can be referred what Galen handed down (bk. 3 On the Critical days), referring their changes especially to the Moon—whom, however, Giovanni Pico tries to confute at length (bk. 3 Against the Astrologers, ch. 16). But to me it does not seem likely that so many other shipmasters and Writers asserted the magnitude of the tides at New Moons unless they had noted them at a calm sea too; and indeed, how unskillfully would the Venetians call the sea “oil,” if it were raised and agitated by the most turbulent tempests and storms! They mean, therefore (unless I am mistaken), that the sea is then in the highest tide, but so that it calmly preserves that swelling for some time; or that it perhaps does not become greatest on the very day of the New Moon, but some days after. Yet the same Borrus (p. 175) narrates, from observation, that on the first 15 days of the Moon the fluxes are greater and more lasting than the refluxes; but on the remaining 15 days those [fluxes] are less than these [refluxes]. Thus far concerning the Monthly changes of the marine Tide.

On the Annual Periods and Varieties of the Tides, and others reduced to the annual

[XIX.] Let us begin from Pliny (bk. 2, ch. 97), that we may confer some light from his words. He, therefore, speaking of the differences of the tides which are from the Moon, when he had indicated the monthly [ones], subjoined:

[Margin: The Period of the years and the tides, from Pliny; and concerning the equinoctial [tides].]

“By eights of years also, to the beginning of the motion and the hundredth [revolution] of the Moon, the increments are recalled by the very motions and revolutions, the Sun’s annual causes augmenting all these—[the seas] swelling most at the two equinoxes, and at the autumnal more than the vernal; but empty [low] at the [winter] solstice, and more at the [summer] solstice.” And before him Tacitus (bk. 1 of the Annals) had said: “By the star [constellation] of the equinox the ocean swells most.” But why do not these turns rather return at 19 years, since then the Moon and Sun revert most nearly to the same turns, or certainly at other Lunar periods? Of which we [treat] more (bk. 4, ch. 19). But now we do not inquire the cause, being devoted only to the history of the Tides.

[Margin: St. Augustine’s authority on the equinoctial tides.]

Let us hear, therefore, St. Augustine (bk. 1 On the Miracles of Sacred Scripture, ch. 7), saying of the Malinae, or tides: “Of each [season], the two middle Malinae of the aforesaid times—namely, the equinoctial [ones]—consume more [time], when either the day or night of any [particular] course, [being] stronger than usual, is wont to become higher in inundation; but, intervals being interposed, again as much [time] is always intermitted by the Ledo.” Nay, if we hear Trimarchus (bk. 2 meteor., disp. 1, sect. 7), the sailors, speaking at least of the Adriatic tides, think them greater in winter than in summer, and by day than by night. Francesco Resta adds (in his Meteorology, tract 1 On the sea, ch. 15), from Albertus Magnus and others, that the tide is varied from the nearness of the Moon to the sea (which we have learned from Pliny too, bk. 2, ch. 97, saying that, the Moon having gone off to the south, the tides become greater on account of the nearer force of the star), and from the nearness of the Moon to the Zenith of those who are near the sea—or, the nearer it is to their vertex; then, from the various disposition toward the Sun, and from the longer days the diurnal tides are stronger, and on the contrary the nocturnal [stronger] when the nights are longer than the days—yet so that, from the vernal Equinox to the summer Solstice, and from the summer Solstice to the autumnal Equinox, the fluxes are greater than in the rest of the year, but stronger in

[…continues on p. 370 (PDF 405) with the catchword “augmen[ta]”: “…stronger in [their] increments”—the rest of the annual variations of the Tide.]

(printed p. 370 — within Chapter XIV. ¶XIX closes the annual tide-variations, ending with de Candale’s rule that the greatest tides come at the new and full Moons of September and March, the lowest at the solstices. A sub-head then begins ¶XX, on the nautical rules for finding the hour of the “Living Water” from the Moon’s daily 48-minute lag, and the First Table of tide-hours for the Spanish, Gascon, Channel, and English coasts begins, continuing on p. 371.)

[Header: BOOK IX. SECTION IV. — 370]

[stronger in their] increment than in the decrement of days. Besides, [Delphino] affirms that the tides are greater when the Moon is in Pisces and at the end of Aquarius, and when the Pleiades aid the Moon; but Delphino, in his treatise on this matter, says that Venus and Jupiter, [when] near the Sun and Moon, help to set the waters in motion. And Hieronymus Borrus, in his dialogue on the tide of the sea (p. 175), says it has been observed that the fluxes are the greater and more lasting, [in proportion] as the Sun and Moon linger for more hours above the horizon; but [in proportion] as the Luminaries are for more hours below the horizon, the fluxes are lesser and briefer than the refluxes. But I fear lest some of these [things] be reported as still uncertain, and from the presumption of conjecture rather than from a history worthy of credit. That, however, deserves all credit which, from the observation of Lord de Candale, Furner reports (bk. 9 of the Hydrography, ch. 21): namely, that at the mouths of the Garonne and on the Medoc coast the tides are never greater than at the New Moons and Full Moons which happen in September and then in March; and that the waters are lowest at the winter Solstices, and then at the summer [Solstices].

On the Nautical Rules for discerning the Hour of the Living Water, or highest tide, on any given day of the Moon, in a given Port of Europe

[XX.] The highest increment of the tide, where it happens daily in [various] places, so far depends on the Moon, and follows by certain steps its ascent to the meridian above, or its descent to the meridian below the horizon, that already, from this, over many years the shipmasters have framed for themselves most sure rules, by which it can be known at what hour in this or that port the highest tide will be—beginning from the day of new and full Moon, and daily expecting the highest tide later by 48 minutes than the day before: of which thing we shall exhibit a specimen, partly from Bartolomeo Crescenzio (bk. 3 of the Mediterranean Nautics, ch. 3), partly from our [Father] Furner (bk. 9 of the Hydrography, chs. 2, 3, & 4). But Crescenzio confesses that he drew rules of this kind from a certain distinguished Cantabrian shipmaster, whom Nicolaus Sagrus of Ragusa (or Epidaurus) brings on in his dialogues on the tide of the sea. From him, therefore, we shall reduce into a briefer table the hours at which, on the day of New and Full Moon, the highest tide happens in the places written below; for, this being known, the hour of the highest tide on the following days (numbered also from the New Moon or Full Moon) will easily be known, by adding daily four-fifths of one hour, or 48 minutes. For example:

since in the strait of Gades [Gibraltar], on the day of new and full Moon, the living water or highest tide happens at hour 1½ after midnight, and again at hour 1½ after noon; if you wish to know the hour of the living water for the second day of the Moon, or the 16th (which is the second after the full moon), to hour 1½, or hour 1 and 30 minutes, add 48 minutes, and you will have hour 2 and 18 minutes after midnight, and likewise after noon: so, on the third day of the Moon and the 17th day, the living water will there be at hour 3 and 6 minutes, both after noon and after midnight, as appears by adding 48 minutes to hours 2 [and] 18 minutes; and so on thereafter for the rest. We shall, moreover, append the vernacular names (as he too sets them down), since the Latin [names] often fail, or do not exactly answer [to them]; and since on maps the vernacular [names] are usually written for the most part—and therefore, lest anyone think them Latin, we shall mark them with a distinct typeface.

First Table of the Hours of the Living Water, or highest Tide, at New and Full Moon, the hours numbered both from noon and from midnight, from the Cantabrian Shipmaster & Crescenzio

[Margin: The hour given is that of the highest tide (“living water”) on the day of New ☌ or Full ☍ Moon, counted alike from midnight and from noon; for each following day add 48 minutes.]

[…continues on p. 371 (PDF 406) with the catchword “[di]ctum”: “…called Langosneus [Land’s End]“—the rest of the First Table (the English and Irish establishments), then Furner’s Second Table of tide-hours.]

(printed p. 371 — within Chapter XIV, continuing ¶XX. The First Table of tide-hours finishes with the English and Irish establishments. Riccioli then introduces a Second Table, recast from Fr. Georg Furner’s Hydrography: a tide-clock grid giving the hour of the living water for any day of the Moon, keyed by letters to each port’s establishment; the table continues on p. 372.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 371]

… [Cape of Cornwall] called Langosneus [Land’s End], which is the chief cape of England, in the water-run — completing the entry begun on p. 370. The First Table runs out as follows:

Thus far from Crescenzio and that distinguished Cantabrian shipmaster.

There now follows another Table, from Fr. Georg Furner of our Society (bk. 9 of the Hydrography, ch. 2)—which we shall reduce into another, somewhat clearer form (unless I am mistaken), with capital letters added at the head of the table, that by them we may indicate, in the other part of the table, which places regard such a position [of the Moon] and time of high water. The use of the table we shall teach at numbers XXI and XXII.

Second Table of the Hours of the Living Water, or highest Tide, on any given day of the Moon, in the Ports written below, from Fr. Georg Furner of the Society of Jesus

[Margin: The hour of the living water is read against the day of the Moon (counted from New ☌ at left, or from Full ☍ at the paired count) and against the column-letter A–H proper to the port. Each column is 45 minutes later than the one before it; each lunar day is 48 minutes (⅘ hour) later than the one before. The letters mark the bearing of the Moon (from the meridian) at which high water occurs—the “establishment” of the port.]

Bearing of the Moon at high water (here O. = West):

• A — S. & N. (South / North)
• B — S. ¼ S.O. / N. ¼ N.E. (South, a quarter toward Southwest / North, a quarter toward Northeast)
• C — S. S.O. / N. N.E. (South-Southwest / North-Northeast)
• D — S.O. ¼ S. / N.E. ¼ N. (Southwest, a quarter toward South / Northeast, a quarter toward North)
• E — S.O. / N.E. (Southwest / Northeast)
• F — S.O. ¼ O. / N.E. ¼ E. (Southwest, a quarter toward West / Northeast, a quarter toward East)
• G — O. S.O. / E. N.E. (West-Southwest / East-Northeast)
• H — O. ¼ S.O. / E. ¼ N.E. (West, a quarter toward Southwest / East, a quarter toward Northeast)

Pars I — Day of the Moon (☌ = from New Moon, ☍ = from Full Moon); the cells give the hour : minute of the living water.

[…continues on p. 372 (PDF 407) with the remainder of Furner’s Second Table (Pars II — the further compass-bearing columns) and the rules for its use (¶XXI–XXII).]

(printed p. 372 — within Chapter XIV, continuing ¶XX–XXII. A key-list matches the letters A–R at the head of Furner’s table to actual ports of the Channel and the English and Irish coasts. ¶XXI explains the use of the table, and ¶XXII states the Problem — given the day of the Moon, to find the hour of the living water in a given port — with a worked Garonne-mouth example begun here.)

[Header: BOOK IX. SECTION IV. — 372]

Places corresponding to the letters set at the head of the table

[Margin: On the day of ☌ and ☍ of the Sun [= New and Full Moon] the living water is after noon and after midnight; the hours (Hor.) and minutes (M.) follow. The letters are those at the head of Furner’s Second Table; each is 45 minutes later than the one before.]

The Use of the Preceding Table

[XXI.] At the head of the preceding Table there are three Zones [bands]. In the first of these, the capital letters, in the order of the Alphabet, signify the places belonging to that column, to be indicated after the tables by the like letters [the foregoing key-list]. In the second are the quarters of the Winds according to the more recent shipmasters, by which they are wont to signify not only the situation of places, but also the hour of the tide on the day of new and full Moon: assigning to each whole Rhumb three hours, to a half-Rhumb one hour and a half, and to a quarter-part of a Rhumb three quarters of an hour. [The text here prints “octo” (eight) where the arithmetic requires “toto” (whole): a whole Rhumb = 3 h, a half = 1½ h, a quarter = ¾ h.] When, therefore, they wish to express that at Amsterdam, or Rotterdam, the full and living water happens, on the day of new and full Moon, at hour 3 after noon and at hour 3 after midnight (as you see in Column E), they say that Amsterdam and Rotterdam are situated toward Sud-Ouest [SW] & toward Nord-Est [NE]; which is indicated by the initial letters S O & N E set in the second Zone of the head. But if you desire to know the winds and quarters indicated by these letters, consult our table 2 & 3, set forth in bk. 2, ch. 17. But where there is this fraction ¼, it signifies one quarter of the next rhumb. If, however, anyone does not wish to use this manner of signifying, he can omit it, since it is least necessary to the Reader. Lastly, in the third Zone of the head are the letters H. M., signifying the Hours & the Minutes, or sixtieth parts of an hour.

Besides, in the 1st & 2nd parts of the table there are ten columns, of which the first contains the first 15 days of the Lunation, numbered from ☌, or from the day of the New Moon; the second the remaining 15 days, numbered from ☍, or from the Full Moon; the rest contain the hours at which the highest tides, or living waters, happen in the places indicated by the capital letters of the 1st or 2nd [zone of the] head, and corresponding to the age of the Moon, or the days numbered from the New Moon or Full Moon. These being set down, we shall teach how to solve, with Furner, the chief Problem of Hydrography by the aid of the aforesaid table, or even of Crescenzio’s Table.

Problem. Given the Day of the Moon, to know the Hour of the Living Water, or highest Tide, in a given Port or shore

[Margin: Example of the Problem.]

[XXII.] Seek in the Catalogue of places the place about which you are in doubt, and see to which of the initial letters it belongs; then seek that initial letter in the upper head of the first or second part of Furner’s Table; for in its column, over against the given day of the Moon (which is marked in the first or second column), you will find the hour—both after midnight and after noon—at which the highest tide happens in that place. EXAMPLE: It is desired to know at what hour the highest tide happens at the Garonne mouth on the day of new and full Moon, or even on the 4th day. If

[…continues on p. 373 (PDF 408) with the catchword “Si”: “If [you run through the Catalogue of places, you will find the Garonne mouth belongs to the letter E]“—the rest of the worked example, then the survey of opinions on the cause of the Tide.]

(printed p. 373 — within Chapter XIV. The worked Garonne example of ¶XXII finishes, with a rule for adapting Crescenzio’s table to any lunar day. A new sub-head then opens the survey of opinions on the cause of the tide (¶XXIII), citing the tide as “the Sepulchre of human curiosity” and its unexplained puzzles; ¶XXIV states the First Opinion (Timaeus, revived by Chiaramonti) that the rivers cause the tide, and ¶XXV begins its refutation.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 373]

If you run through the Catalogue of places, you will find that the Garonne mouth belongs to the letter E; which letter is found above the seventh Column at the head of the first part of the table. Descending, therefore, by that column, you will see, over against the day ☌.0 (that is, the day of New Moon) and over against the day 15.☍ (that is, the day of Full Moon), Hour 3.0; but over against the 4th day after the New Moon, Hour 6.12′. Conclude, therefore, that at the Garonne mouth the highest tide happens, both on the day of new and of full Moon, at hour 3 after midnight, and again at hour 3 after noon; but on the 4th day of the Moon (to which the 19th day also answers), it happens at hour 6 and 12 minutes, or one-fifth part of an hour, after midnight, and again at hour 6.12 after noon.

[Margin: The method of examining the numbers of the Table.]

But if you use Crescenzio’s Table—in which are noted only the hours of the highest tide for the day of New Moon and Full Moon—if you are anxious about the other days, multiply 48′ by the number of days, or the age of the ☽ [Moon], and divide the sum by 60; and add the Quotient of the division, with its fractions (if there be any), to the Hours of the highest tide of the new or full Moon, and from the sum cast off 12 hours if it exceed them; for the remainder will give the hour of the highest tide for the given day of the Moon. As in the example just adduced, the 4th day of the Moon is given, and the Hour of the highest tide at the Garonne mouth on the day of New Moon is hour 3; 48′ being therefore multiplied by 4, there result 192 minutes, which, divided by 60, make a quotient of hours 3.12′; which quotient, added to the 3 Hours, makes Hours 6.12′, as above: and this is the method of examining the numbers of Furner’s Table, if perchance some error has crept in through the fault of the Typographers—as we have detected (more than once) to have crept into Furner’s table, and have emended.

Opinions on the Cause of the Sea’s Tide are surveyed

[XXIII.] Acutely indeed did our [Father] Caussin, in his doctrine on the Resurrection (in commending the divine works of the first week), say that the Flux and Reflux of the sea is the Sepulchre of human curiosity. For no schools as yet, says Simon Maiolus (Colloquy 10 of the Dog-day [Conversations]), have sufficiently unraveled this question. Nor without merit does Julius Caesar Scaliger (exercitation 52) begin this treatment with those words: “Perhaps silence conduced more to the opinion of a good repute than boldness. For what I am wont everywhere to cry—that we know nothing—suits especially this inquiry, which treats of the sea’s motion”; and below: “Now some god must be summoned by us from the machine [Θεός … ἀπὸ μηχανῆς]. For who would not say that, in this matter, Philosophy herself stammers?” But much more difficult does the reflux of the Sea seem to explain than the flux: wherefore St. Augustine—when he had said (partly in bk. 7 On the City of God, ch. 22, partly in bk. 1 On the Marvels of Sacred Scripture, ch. 7) that two Goddesses were consecrated by the Romans to this matter, namely Venilia or Malina for the access of the sea (which the Italians call Marea), and for the recess Salacia or Ledo, or Lidona—said: “But the reasonable inundation of this perseverance, by which it recedes, is hidden from our minds, [and] prepares no smaller advancement for the knowledge of man, who knows it not”; and a little after: “We are permitted to consider the inundating swellings of the Sea, but of the receding one we are deprived of the understanding.” To these add the verses of Lucan adduced in bk. 2, ch. 15, at the end of Scholium 5.

[Margin: The heads of the difficulty, and an Epitome of the marvels in the sea’s tide.]

And truly so various are the accidents of this motion, and so admirable, that they always seem about to surpass every effort of the human mind, whoever shall have wished to investigate their sufficient cause and reason, and to explain it once investigated. For what mortal could expound why a great part of the Sea lacks a tide, while a great part likewise is subject to it? Why it shows so great a dependence on the Moon, and yet, that [Moon] being silent at the new moon or hidden below the horizon, the same tides—or greater—return? Why in many places the access is completed in six hours and the recess in as many, and yet somewhere [there is] an increment of about seven [hours] and a decrement of five, as nearly at the Garonne mouth; elsewhere the waters flow in by fours and reflow by eights, as at the Niger mouths and the shores of Guinea; elsewhere, as at the coast of Cambay, they burst in within two hours most rapidly and within two hours flee back and are swallowed up? Why, again, in other places fifteen whole days are required—namely from the new moon to the full moon—that the fullness of waters, continually growing, may take its highest increase, and as many days that they may subside, namely from the full moon to the following new moon (which happens in the Chinese sea at the mouth of the Pachin river, and in some seas around Cuba & Hispaniola)? Why at the Indus mouths the tides are greater at full moon than at new, [but] on the contrary near Calicut greater at new moons than at full; and universally greater at New and Full Moons than at the Quadratures? Further, why, in neighboring ports or mouths and nearly on the same Meridian, the highest tide is made some hours earlier for one than for the other? Besides, why somewhere the Ocean swells so superbly that it is raised, by tiding, to 80 cubits, as in Britain, while elsewhere—as at Marseille, Ancona, Rimini—it scarcely ascends to a foot or a foot and a half? Finally, who could narrate why the wells which are at Cadiz & at Seville—some should grow with the sea’s tide and subside with its recess, others the reverse, others at different times behave in both ways? All which admirable accidents of the marine tide it has pleased [me] to gather into one epilogue, lest, in reviewing the individual recent opinions to show their insufficiency, it be needful so often to repeat them.

[Margin: 1st Opinion, of Timaeus & Chiaramonti.]

[XXIV.] The First opinion, of Timaeus in Plato and Plutarch (bk. 3 On the opinions of the Philosophers, ch. 17), attributes the cause to the rivers: “Timaeus,” says Plutarch, “lays the cause upon the rivers bursting through the mountains of the Celts into the Atlantic; for by thrusting [it] with their force, they rouse the sea’s tide, and on the contrary, [that force] being relaxed, they drive the sea back again, and make the refluent tide.” This very opinion of Timaeus, Scipio Chiaramonti has very recently revived (bk. 13 On the Universe, ch. 22), but embracing all rivers, not only those of the Celts; and he adds that, by the dashing of the waves against the shores, the water is attenuated into exhalations and vapors. Since, therefore, from the waters of the rivers continually entering there is so great an increment that, for their evaporation, that motion does not suffice which is made either in the reflux or in the time intermediate between the sensible flux and reflux, it is necessary that the seas swell from this source and cause the tide; but from this very swelling they collide among themselves with a greater motion, and thence the evaporation is increased, until the water, attenuated into exhalations, which was superabounding, decreases and seems to flow back. For since [Chiaramonti] had before seemed to himself to have shown that the Sea’s tide arises from the increment of the waters, and yet not from rarefaction, he argued that it could not arise from any other source than from the water of the rivers entering—since water naturally grows in no other way than either by rarefaction, or by the addition of water to water from the new generation of waters, or from their inflowing and concourse into one place. And (ch. 26) he affirms that therefore, at the shores of the Ligurian and the rest of the Tyrrhenian sea, no sensible tide arises, because few and small rivers enter into it; but why at the Moon’s quadratures the tide is made smaller than on the days nearest the New Moon and Full Moon (and is therefore then called the “waters of gall”), supposing then, from Ptolemy, the Moon’s greater nearness to the lands, he gives the cause in these words: “The motion of the sea-water, while it laps and slips back from the shore, is on account of evaporation, as I said before: in the waters of gall the access is greater than in the [ordinary] flux, [yet] less than in the reflux; and while it slips back, the relapse is greater than in the flux, less than in the reflux: the collision toward evaporation is therefore less than in the flux, but greater than in the reflux; for this reason, that the Moon is nearer the earth: it aids the water toward evaporation more than when it is farther off, and therefore a smaller collision of the waves suffices to dissolve just as much water into vapors.”

[Margin: Refutation of the 1st Opinion.]

[XXV.] But against the opinion of both there are very evident and many arguments. For the tide would have to happen on the opposite banks, toward which the rivers thrust the water; and so, from the Celtic or Gallic rivers, a tide would be stirred up at the islands and continents lying opposite toward the West of Gaul; and where the waters of two great rivers meet head-on—say, of the Niger river [flowing] from Africa toward America, and of the Amazon river flowing from America—there, that is, in the mid-sea, a greater tide and heap of waters would be made than at the shores. Besides, since very great rivers enter the Caspian Sea, there would have to be on its shores, or in the middle, a most powerful tide. Moreover, the tide would have to be continually increased, just as the rivers continually run down into the sea, and indeed more in spring than in autumn, on account of the abundance of melting snows. All which [things] are false. Furthermore, the very mouths of the rivers rather

[…continues on p. 374 (PDF 409) with the catchword “æstum”: ”…[the very mouths of the rivers rather show] the tide [coming up against the river’s current]“—the rest of the refutation of the river-cause opinion.]

(printed p. 374 — within Chapter XIV. ¶XXV closes the refutation of the river-cause opinion, Riccioli calculating that all the world’s rivers in six hours would raise the sea by at most a barley-grain’s thickness. The doxography continues with the 2nd through 5th opinions (Plato’s abyss, Sfondrati’s currents, the shape of shores, and Adelandus’s “arms” of the sea), each proposed and refuted.)

[Header: BOOK IX. SECTION IV. — 374]

[the very mouths of the rivers rather] suffer the tide from the sea, and are repelled by it toward their sources; and when the sea floods, the rivers flow back, but when it ebbs, they flow [forward]—as Francesco Resta acutely noted against Timaeus (bk. 3 of the Meteorology, tract 1, ch. 16), adding that there are many seas which receive great rivers and yet do not tide, or do not tide in proportion to the rivers’ magnitude. Vicomercato, moreover, was wont to object to Timaeus the paucity of the water which the rivers bring into the sea, [too] inept to augment its so vast and ample surface by a sensible increment.

[Margin: The quantity of sea-water by Chiaramonti’s calculation.]

Chiaramonti, on the contrary (bk. 13 On the Universe, chs. 17 & 19), strives to demonstrate that the water brought in by the rivers has a sensible proportion to the sea’s water. And in ch. 17, indeed, he supposes (for abundance) that the Earth is everywhere covered with waters, and its depth everywhere is one Italian mile; and that the semidiameter of the Earth alone is 3034 Italian miles, but with the water 3035, so that the diameter is 6070—which he makes to the circumference as 7 to 22, and therefore this circumference 19077 miles. From which, by the rules of Archimedes, he gathers the solidity of the terrestrial sphere together with the waters to be 117,142,218,733 cubic miles. Likewise, the diameter of the Earth alone being assumed 6068, he gathers the circumference 19070, and the solidity 117,033,475,546 cubic miles. Wherefore, these cubes being subtracted from the former, there remain for the water alone 108,743,187 cubic miles—so that the Earth alone contains water 1076 times over. But since only half of the Earth is covered with waters, and this very [covering] is not everywhere deep by one mile, but at most by half a mile, therefore the sea’s water actually amounts to only a fourth part of the preceding sum, namely 27,185,797 cubic miles. But in ch. 19, to investigate the quantity of water which the rivers bring into the Sea, he uses the river Arno, by which (he says) one sails toward Pisa from Florence up to Callone, 40 miles distant, in 8 hours, when the river is moderately swift, [running] of itself, without oars and sails; and therefore that water in 8 hours completes 40 miles, that is, 13333 perches (for he gives 333⅓ perches to one mile), and therefore traverses a single perch in length in two seconds of an hour at most. Let now the Maragnon [Amazon] be of such velocity, whose breadth at the mouth is 70 leagues, that is (says Chiaramonti) 105 miles, or 35000 perches; and let the depth likewise be everywhere of one perch at the mouth; therefore the Maragnon in two seconds of an hour will roll out 35000 cubic perches, and in the whole year 3,030,480. Why [should] I [adduce] so many other rivers of the whole world?

[Margin: The quantity of the Sea by our calculation. — The tribute of the rivers brought into the Sea.]

But in the aforesaid calculation, the consideration of the water which is brought in by the rivers in a whole year is superfluous, since the sea’s tide happens in many places daily and twice in six hours: it would have been necessary, therefore, to consider the water which is brought in over 12 hours, or at most in one day; then, that it might be established what proportion it had with the water of the whole sea, to gather a more probable total from all the rivers of the world, at least as described in geographical maps and histories, and to compare it with the sea’s water. Which we have done elsewhere, in a whole little work communicated to prudent men, which perhaps we shall publish in volume 2 of the Almagest, book 4 (which will be the Geographical [one]); and we showed, with the greatest probability, that all the known rivers taken together do not pour into the sea in 6 hours more than 150 cubic miles—which, distributed into paces, or cubic feet, would make indeed 150,000,000,000 paces, but 18,750,000,000,000 feet. Now from what was said (bk. 2, ch. 14), the surface of the terraqueous globe is 336,434,176 square Italian miles; therefore half of it, as we said there, falls to the surface of the Seas taken together, namely 168,217,088 square miles, which make 168,217,088,000,000 square paces, that is 4,205,427,200,000,000 square feet. By which, the whole tribute of the rivers (which is 18,750,000,000,000 cubic feet) being divided [into them], there comes a Quotient of 224, fractions neglected. Wherefore, if the rivers’ water were to be distributed to the individual feet of the sea’s surface, with an equal height added everywhere, there would fall to each [foot] a water-height as great as is the 224th part of a foot’s height—that is, as great as is scarcely the thickness of a barley-grain: so far is it [from being possible] that they [the rivers] should be able to produce the marine tide; and much less, if a great part of the water which the sea receives from the rivers it transmits through subterranean channels to another neighboring sea, and this by other chasms—as Furner learnedly discusses concerning the Caspian and the Mediterranean (bk. 9 of the Hydrography, ch. 6).

[Margin: 2nd Opinion, of Plato. — Refutation of the 2nd opinion.]

[XXVI.] The Second opinion was Plato’s own, who referred the cause of the sea’s tide to waters bursting forth alternately from Tartarus, or the abyss, and being re-absorbed: of which Plutarch [speaks] thus (bk. 3 On the opinions [of the Philosophers], ch. 17): “Plato refers the cause to a certain heaving-up; for the waters are lifted by the gaping of a certain cavern, and flow out widely, and then flow back to the same place, whereby the surging seas are tossed.” But from this scarcely any of the accidents which we reviewed at number XXIII can have its cause rendered—especially those which are connected with the Moon’s turns. Granted, we do not deny that there are deep whirlpools of waters in the bowels of the earth, and that their gulfs contribute something to the variety of the tides; and to this Philippus (in Resta, from the reading of the Seventy interpreters) refers the words of Job, ch. 38: “Hast thou entered into the springs of the sea?”

[Margin: 3rd Opinion, of Pandolfo Sfondrati.]

[XXVII.] The Third opinion was Pandolfo Sfondrati’s, in his treatise on this matter, who attributed this to the motions of the Sea from East to West, and from North to South—on the ground that so much water cannot be transmitted at once through the narrows of the Strait of Gibraltar, of Magellan, and the like; and he says that these very motions of the sea happen so that [the sea] may run to supply what the Sun has consumed into vapors, and to preserve the sea in its equilibrium.

[Margin: Refutation of the 3rd opinion.]

But the sea’s tide is far different from those two motions, and has far more admirable and diverse accidents, whose reason cannot be rendered by those motions alone. And indeed, since the Pacific does not run toward the East before the tide, it cannot be the cause of the tide in the Strait of Magellan coming from the Pacific sea; nor can the sea’s course toward the North be the cause of those huge tides which happen at the shores of Britain—since rather the sea runs (and indeed not in alternating sixes of hours, but perpetually) from the North toward the Equator.

[Margin: 4th Opinion, ascribed to Pico & Buccaferreo. — Refutation of the 4th opinion.]

[XXVIII.] The Fourth opinion is attributed to Giovanni Pico and Buccaferreo, as referring this effect to the diversity of the shores resisting and repelling the waters toward the diverse declivity of the channels in which the sea is contained; just as in a shaken vessel the water flows hither and thither unevenly to the sides, according to the vessel’s bottom and its diverse margins. But of Giovanni Pico’s opinion presently [more]: meanwhile, whatever it be, it is convicted as insufficient by the connexion of the marine tide with the Moon, and by the accidents enumerated at number 23. Add that it would be necessary, while the tide happens at one shore, for the reflux to happen at the opposite shore—which, however, is proved by no history.

[Margin: 5th Opinion, of Adelandus. — from Pico.]

[XXIX.] The Fifth opinion was that of Adelandus, speaking from the opinion of the Saracens; concerning whom Giovanni Pico writes thus (bk. 3 Against the Astrologers, ch. 15): “When the arms of the sea (namely those which the interposed mass of land separates) hasten with a roused impulse to meet and flow together, it happens—both by the interposed mountains and by the situation of the land itself—that, while they fail of that course, they are carried back; and thence, whither both the paternal and the natural motion impels, they are recalled by the situation of the place itself”; and a little after, Pico says: “This opinion of his is not greatly abhorrent from the likeness of truth: since by a natural propensity the parts of each element are borne toward their own integrity. What wonder, then, if [the waters], shut off from [their] place by the lands lying between, while the present [waters] of the Ocean strive to run together, strike the shores in acceding, and by the opposing repulse equally retrocede; which cause being removed (as happens in the southern sea), we see these tides not appear.” Therefore, besides the diverse situation of the shores, there is supposed by these [authors] a natural propensity of the water to a mutual concourse, and as it were an embrace through the arms of the sea, that the parts may be preserved together with their whole.

[Margin: Refutation of the 5th opinion.]

But against this opinion—besides the connexion of the marine tide with the Moon, and the effects reviewed at number 23—there are the arguments of Francesco Resta (bk. 3 Meteor., tr. 1, ch. 14) and of Cabeo (bk. 2 Meteor., text 6, q. 6). For if the water seeks conjunction with other water, and on that account the tide happens, it ought to happen also in lakes, ponds, and the Caspian Sea; then, since (the Caspian excepted) the rest of the seas are now continuous, what need was there of a greater conjunction? And in what part of the sea, finally, ought this union to happen? Besides, there are no further seas on this side of those shores, to which nevertheless the sea, by acceding, makes a tide; for either the tide stops at the banks, if they be low, or, overflowing above them, covers the shores—so that the sea seems rather to seek conjunction with the land than with the water: for what sea is there on this side of the Venetian, Gallic, British, [or] Indian shore? None, certainly; and yet to these the sea floods up with so great a tide,

[…continues on p. 375 (PDF 410) with the catchword “mare”: “…the sea [seems therefore rather to flee the waters which are in the mid-ocean]“—the rest of the refutation of the 5th opinion, then opinions 6 through 13.]

(printed p. 375 — within Chapter XIV, the survey of tidal opinions continues, each proposed and refuted: the 6th through 13th, including the world-animal’s breathing, the diurnal heaven’s sweep, vapors and winds, subterranean fire, an Angel of the waters, the Luminaries (the most widely held view), the Moon’s occult influence, and the Moon’s heating and rarefying of the water — the last refuted since the water’s weight is unchanged and no heat is felt.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 375]

[None, certainly; and yet to these the sea floods up with so great a tide as] the sea: it seems, therefore, rather to flee the waters which are in the mid-ocean, and to be separated from them by a kind of sedition, than to be joined—unless perhaps it repents of that sedition, and by reflowing rolls back thither, whence it had departed. But if you say that near the shores there is friendly and sympathetic water, to which it wishes to be joined, then let it stick with that, once it has joined itself to it, and not by reflowing be disjoined from it. But enough [are] the many [arguments] against this fiction.

[Margin: 6th Opinion, of the Stoics & Apollonius of Tyana. — Refutation of the 6th opinion.]

[XXX.] The Sixth opinion was the Stoics’ (in Solinus, ch. 36), who thought the world to be an animal, and, through the chasms of the earth near the sea-bottom (as through bodily nostrils), by reciprocal inspiration and expiration, now to re-absorb the waters, now to blow them out, and so to rouse the tide as if by panting. So also Apollonius of Tyana attributes the same to spirits panting beneath the sea; to which that animate faculty—which Kepler attributes to the whole globe compacted of earth and water—is not a little favorable. Against this fiction Cabeo rises up at length (2 Meteor., text 6, q. 6); but it suffices to have enumerated the accidents of the marine tide, especially connected with the Moon, as we did at number 23; for it immediately appears that, by this panting—however great the soul—those effects cannot be produced. Rather, someone might attribute this to the inspiration and expiration of the Moon, of which opinion St. Basil makes mention (homily 6 of the Hexaemeron), saying: “The sea, as if by the exhalations of the Moon, is drawn backward, and again by its inhalations is compelled to its proper measure.”

[Margin: 7th Opinion, of Alpetragius & certain Arabs. — Refutation of the 7th opinion.]

[XXXI.] The Seventh opinion attributes the sea’s tide to the diurnal motion [of the heavens] sweeping all things with it. So certain Arabs (in Albertus Magnus, On the properties of the elements, tract 2, ch. 6), and among them Alpetragius (if we believe Giovanni Pico, bk. 3, ch. 15, against the Astrologers). But if this opinion were true, the flux and reflux would not happen except according to longitude, and [would be] greatest under the Equator; nor would the vicissitudes of the lunar motions produce so great a variety of tides—besides that it is false that the sea is swept by the diurnal whirling of the heaven, especially given the fluidity of the heavens, for which it was sufficiently disputed in section 1 of this book, ch. 7.

[Margin: 8th Opinion, which Giovanni Pico adduces. — Refutation of the 8th opinion.]

[XXXII.] The Eighth opinion, which Giovanni Pico adduces in the second place (bk. 3 Against the Astrologers, ch. 15), refers the cause to vapors and winds excited from denser water, whence a tumult and vehement motion, and thence a heat requiring a larger place, whence the tide; which, when it has cooled, the seas are laid flat and subside. But since Pico is there wholly bent on excluding the Moon, and yet so great a relation of the tides to the Moon is proved by history, it would have been necessary to show how, without the Moon, the vicissitudes of the tides are nevertheless attempered to the Moon’s motions. To this it is added that even a tranquil sea, agitated by no winds, is nevertheless subject to the tide; nay, when a vehement storm comes on, the tide properly so called is diminished, as Trimarchus affirms (bk. 2 Meteor., disp. 1, sect. 7).

[Margin: 9th Opinion, of Thomas Lydianus. — Refutation of the 9th opinion.]

[XXXIII.] The Ninth opinion attributes the sea’s tide to a boiling-up, but [arising] from subterranean heat and fires—with which I, when younger, had sprinkled a great part of this cause. So Thomas Lydianus (in Fromondus) says that beneath the sea-bottom a fire lurks, which kindles the abundant bitumen existing there, whence, as the fire exhales, the sea swells. And although Francesco Resta (bk. 3 Meteorology, tr. 1, ch. 14) thinks it not unlikely that the tide is a certain boiling of the sea, like boiling water, made by spirits and vapors rising from the sea-bottom—for if a spirit enclosed in the earth excites Earthquakes and moves the earth, how much more easily can it move the waters and raise them—yet afterward he recoiled from this opinion; for that necessity always remains in force, of rendering the reason why the tides happen with those vicissitudes preserved which we reviewed at number 23, and why they receive laws from the Moon in so many effects. Cabeo adds (2 Meteor., text 6, q. 6) that motions made by fire are lawless and tumultuary, as appears in earthquakes, in Vesuvius, in Etna; but the Tides are periodic, and return at fixed times. Finally, against this opinion are the arguments against rarefaction, to be adduced at number 37.

[Margin: 10th Opinion, of Lessius. — Refutation of the 10th opinion.]

[XXXIV.] The Tenth opinion recurs to the Intelligences, which, as they are the movers of the heavens, so [are movers] also of the Seas. This opinion is attributed to Leonardus Lessius by Fromondus, who asserts that the Intelligence presiding over the waters is called, in the Apocalypse, the Angel of the waters. On which occasion Francesco Resta, in the place lately adduced, says that it can also be attributed to these evil spirits, since of Behemoth (that is, an evil demon) it is said in Job 41: “He will make the deep sea boil like a pot, and set it as when ointments boil.” But for three reasons this opinion is not received: first, because it recurs to the [deus-ex-]machine without necessity, or out of weariness of inquiring into the proper cause in nature; second, because the sea’s tide in many places is irregular, and so does not seem to need an Intelligence; third, because the marine tide is altogether Lunatic—that is, attempered to the Moon’s turns—wherefore recourse seems rather to be had to the Moon than to an Intelligence; to which, at length, most of the Authors recur (the Sun, however, not excluded), as we shall soon see.

[Margin: 11th Opinion, of Pliny & Pytheas. — Caesar’s opinion.]

[XXXV.] The Eleventh opinion, therefore, throws the sea’s tide upon the Luminaries, but chiefly upon the Moon. Which Pliny indeed (bk. 2, ch. 97) asserted indeterminately, saying: “That the sea’s tide accedes and reciprocates is most marvelous—in many ways indeed; but the cause [is] in the Sun and Moon”; nor does he explain the manner. But in Plutarch (bk. 3 On the opinions, ch. 17), Pytheas of Marseille [says] that the access of the sea happens by the Moon’s increment, but the recess by its decrement. Which opinion has by far the most Authors for it; but the whole difficulty consists in the manner by which the Luminaries effect the varieties of the tides which we adduced at number 23—especially the Moon, even when it either lurks below the horizon, or is new and does not reflect the Sun’s rays to earth and sea, or is within the Torrid [zone] and does not strike with perpendicular rays the waters of the temperate or frigid Zones. Meanwhile, of the common opinion is that [saying] of Caesar (bk. 4 of the Commentaries): “On the same night it happened that the Moon was full, which is wont to produce the greatest maritime tides in the Ocean.”

[Margin: 12th Opinion, of Contareno & Faber. — Refutation of the 12th opinion.]

[XXXVI.] The Twelfth opinion, therefore, recurs to the occult influences of the Luminaries, as Contareno and Faber, and certain Astrologers whom Pico touches (bk. 3 Against the Astrologers, ch. 15)—from the [objection] that the Moon cannot so move the waters when it is beneath the lowest [part] of the earth; for then the Moon’s light, which is the vehicle of influences, cannot reach them. But this opinion does not solve the question, and is just as if it said that the cause of the tide is unknown and hidden from us. But Cardinal Contareno adds that, by this occult power of the Moon, the sea’s waters are rarefied, and, when they have been highly rarefied, produce the tide; but it does not appear how, placed beneath the lowest part of the earth, it can rarefy them—besides other [things] which we shall soon oppose to this rarefaction.

[Margin: 13th Opinion. — Of Contareno, Aversa, Crescenzio, Borrus, [and] de Rheita. — Refutation of the 13th opinion.]

[XXXVII.] The Thirteenth opinion, very akin to the Ninth, judges that the Luminaries, and chiefly the Moon, produce the tide by heating and rarefying the waters, and attenuating [them] into vapors, but not consuming them. So Contareno (bk. 2 On the elements), Raphael Aversa (vol. 2 Philos., q. 42, sect. 7), Crescenzio (bk. 3 of the Nautics), and Hieronymus Borrus (in his tract on this matter, p. 125), and most recently Antonio Maria de Rheita (in his Sidereo-mystic Eye [Radius], bk. 4, ch. 3). For they say that the Moon, by ascending, gradually rarefies the waters, until—it coming to the Meridian—being highly rarefied they swell; but, it descending from the Meridian and striking the waters with more oblique rays, [the Moon] diminishes the rarefaction, and they, being condensed more and more, flow back and return to their pristine state, or are resolved into vapors. But Galileo (dialogue 4 On the System of the World), and Chiaramonti (bk. 13 On the Universe, ch. 22), and Francesco Resta (tr. 1 On the sea, ch. 14) prove that the sea’s waters are not rarefied by the Moon’s heat in the tide; because, if the water were rarer, it would also be lighter in the same bulk, and some heat would be felt in it, and some smoke would appear, as in boiling water; but if just as much of the same sea-water—drawn before the tide and in the tide—be weighed, it is found of the same weight, and no indication of rarefaction or heat is detected in it by density or smoke. Nor do ships sink more in the tide than at other times, which would nevertheless necessarily happen if the water were rarefied and made lighter. Galileo adds that, if the tide were made thus, a vehement heat would be necessary (which cannot come from the Moon), and so much that, by reason of the burning, it would render the sea-water intolerable to a finger immersed in it. Against which opinion Cabeo (2 Meteor., text 6, q. 6) brings [the example of] must [new wine], which, by vehemently swelling, boils without intolerable heat; and conversely [of] water long since heated, which yet boils no more, because its subtler parts, rarefied in the first boiling, [were resolved] into

[…continues on p. 376 (PDF 411) with the catchword “bullas”: “…into bubbles”—the rest of the refutation of the 13th opinion, and the further opinions on the cause of the Tide.]

(printed p. 376 — within Chapter XIV. The refutation of the 13th opinion (the Moon heats and rarefies the waters) closes. ¶XXXVIII proposes and refutes the 14th opinion (the Moon’s dominion over humors), and ¶XXXIX the 15th (vapors and blasts beneath the sea excited by the Sun and Moon, with Furner’s analogy of the tide as the sea’s fever). ¶XL then opens the 16th opinion, the Moon’s “magnetic power.”)

[Header: BOOK IX. SECTION IV. — 376]

[the subtler parts, rarefied in the first boiling, were resolved into] bubbles which have vanished, and these into air. But granted that rarefaction be not repugnant on this head [cause], it yet remains to render the reason why the Moon, placed beneath the earth, can rarefy the waters more in [its] access to the lowest Meridian than when it is above the horizon and recedes from the meridian; and why it can [do] more upon remoter waters—such as are around Ireland, England, Holland, Belgium, where the tides are strongest—than upon nearer ones, such as are from Cadiz up to the Tropic of Cancer, where there is no sensible tide; why, again, [it can do] more at the New Moon than at the Quadratures, in which it both pours a greater light upon the waters and comes out nearer to them; and so of the other diversities adduced at number 23. To the first difficulty, however, Borrus and others respond, with Albumasar (bk. 2 of the Introduction), that the rays of the Moon, when below the horizon, are reflected back to the earth and water of our hemisphere by the heaven set opposite; but these suppose the heaven to be hard and apt to reflect light—and then that light would be much more languid, and the flux would thence be made nearly threefold smaller.

[Margin: 14th Opinion, of Scotus, John of St. Thomas, Resta, Mastrius, and nearly [of] Pliny.]

[XXXVIII.] The Fourteenth opinion recurs to that power of the Moon by which it predominates over the humors; for just as the humors of plants, of shellfish, and of the other living things are moved [by the Moon], and especially abound at the full moon, so the sea’s waters seem able to be moved and to swell by the Moon—and to grow not only through rarefaction, but also through a new augmentation. So Scotus (on bk. 2, dist. 14, q. 3); John of St. Thomas (in Mastrius, disp. 4 On the heaven and Meteors, q. 4, no. 154); nor does it displease Mastrius himself; and to this Resta acquiesces (tr. 1 On the Sea, ch. 14); and Pliny favors [it] (bk. 2, ch. 99), saying, after expounding the sea’s tide in chs. 97 and 98: “Whereby a true conjecture arises, that not in vain is the star of the Moon thought to be a spirit. This is what saturates the lands, and by approaching fills bodies, by departing empties them: therefore with its increment the shellfish grow, and especially those creatures feel the spirit which have no blood, etc.”; and (ch. 101): “The Moon, a feminine and soft star, dissolves the humor and draws [it], [but] does not take [it] away.” As, therefore, shellfish abound in humor—not because they are fed more abundantly at the full moon (as Vallesius would have it, ch. 71 of the Sacred Philosophy), but on account of the milder nights and the heat dissolving the concreted humors (as Aristotle teaches, bk. 1 On the parts of animals, ch. 5)—so the tides happen when the gross humors are dissolved.

[Margin: The 14th opinion is refuted.]

But against this manner militate those [arguments] which we adduced at the end of number 37 against opinion 13; and besides, all marine, fluvial, and lacustrine waters ought, at least at the full moon, to suffer a tide—if indeed the Moon, by predominating over all humid bodies, can produce a swelling of humid things.

[Margin: 15th Opinion, of Aristotle, Heraclitus, [Apollonius of] Tyana, [and] Vallesius.]

[XXXIX.] The Fifteenth opinion refers the cause of the tide to vapors and blasts beneath the waters, and around the sea-waters, excited by the Sun and Moon according to their varied disposition. Aristotle and Heraclitus (says Plutarch, bk. 3 On the opinions, ch. 17) judge these to happen from the Sun; for it whirls round with itself, by its rotation, very many blasts, which, rushing on and thrusting the Atlantic, [cause] it to swell and to make the tide; and these at length being lulled, the tide, gathering itself, goes back gradually—and this is the reciprocation. Perhaps Apollonius of Tyana meant the same when he said that it happens from spirits bursting out of the sea and moved around it; and Vallesius (ch. 52 of the Sacred Philosophy), who refers the proximate cause of the tide to the blasts enclosed within the earth’s caverns, but the remote [cause] to the Moon and Sun generating and moving those blasts.

[Margin: Trimarchus’s opinion. — Bacon’s opinion.]

Trimarchus too (bk. 2 Meteor., disp. 1, sect. 7, nos. 86 and 87) refers this motion to exhalations beneath the sea, such as [are] beneath the earth at the time of earthquakes; which, when they have been rarefied by the heat of the Sun and Moon, seek an exit and burst out with great force—the sailors attesting that, when the tide comes on, ships (even in calm weather) tremble so as in an earthquake. But these exhalations bursting into blasts, he thinks were infused into the Sea by God from the beginning of the world, yet are preserved by the action of the stars; and, being pressed by the mass of the sea, are thrust back into the caverns, whence the reflux happens. Nay, before him, Roger Bacon, in his Epistle to Clement V, Supreme Pontiff, said that by the Light of the Moon vapors are excited beneath the waters, engulfing the waters with blister-like swellings, which it cannot consume; and that fewer [vapors] are excited by the weaker rays, when it irradiates the seas obliquely, but more by the stronger and straighter [rays], when it strikes them in the Meridian; and that the same rays, while the Moon is beneath the lowest [part] of the earth, are reflected from the highest heaven, or from the eighth or ninth sphere, as being dense and terminating the sight. But [Bacon] adds that the tide becomes more sluggish as the Moon approaches the meridian, because the vapors are dissolved by the stronger rays—and therefore he is reprehended by Giovanni Pico (bk. 3 Against the Astrologers, ch. 15), because he speaks against the experience of a greater tide at the Meridian.

[Margin: Cabeo’s opinion.]

But our [Father] Cabeo (2 Meteor., text 6, q. 9), when he had taught that this motion happens not from rarefaction or a real augmentation of the water, nor from a merely local motion impressed by the Moon (because [then] the tide would happen everywhere and always toward the West), adds that in the Moon, besides heat and light, there are other active qualities, manifest to us in [their] effects, although unnamed—among which are catarrhs and fluxions, most troublesome in lunatics at the time of the lunar syzygies, even if they live shut up in their chambers; that similarly, therefore, the tide happens not from the attenuation of the water itself, but from the attenuation of spirits, or a boiling-up, rising from the sea-bottom—not as if they boil from heat, but because they are moved by the Moon’s peculiar force (just as in must a swelling happens without boiling, and just as catarrhs are moved by the Moon); but that the spirits which are in the sea-bottom are analogous to the spirits of saltpetre and sulphur, and therefore that the tide happens only in those waters in which there are such spirits; nor does the cloud or earth interposed between the Moon and our sea hinder—just as the walls of houses do not hinder the Moon from moving, by its peculiar power, the spirits or humors in our bodies, and stirring up fluxions or catarrhs.

[Margin: Furner’s opinion. — The Sea’s tide is its fever.]

Lastly, our [Father] Furner likewise (bk. 9 of the Hydrography, ch. 8) professes that the sea’s tide is a certain secret, and the greatest mystery to be beheld in the sea; but that its likely cause, from the Moon, is the commotion of the vapors and exhalations enclosed in the sea-water. For as the causes of fevers can be referred to two heads—namely, to the disposition of the humors of the human body, and to the active power of an external agent; and [as] the mass of humors, like a kind of ferment, is cooked by the force of the external agent, is inflated, putrefies, and, being filtered through the blood, is inflamed (so that from the diversity of inflammable humors there is a diverse species of fevers, and from the same, and also from the diverse acting-power of the exterior agent, the motions and periods of fevers are retarded or incited)—so the material cause of the marine tide are the warm vapors and exhalations which are in the soil and earth lying beneath the sea, and probably of the same nature with the rest of the earth, from which metals are dug. For it is established, in digging them out, that where the diggers have proceeded beyond 80 or 100 paces, although before they always experienced cold, they soon find so great a heat that they cannot tolerate it beyond three hours without danger, and it is necessary to withdraw thence—which especially those narrated who explored the mines of Hungary, whose depth is greater than 300 cubits. But although such warm and viscous exhalations and vapors are from the Sun, yet the Moon has the power of moving them by its influences; and these, inflated more (partly by [its] light, partly by the Moon’s other influences), raise the seas and cause the tide, according to the disposition both of the aforesaid vapors and exhalations, and of the ports, shores, and coasts. And hence also is that which Pliny said (bk. 2, ch. 98): “All seas are purged at the full moon, and some also at a fixed time. About Messina and Mylae, dung-like refuse is cast out onto the shore, whence the fable that the oxen of the Sun were stabled there”; which Strabo before had noted (bk. 1 of the Geography), saying: “When the sea belches forth, the shores give a hoarse voice”—whence the access has a certain force, so that it repels foreign [things]. And this indeed they call a certain purgation of the sea, by which both corpses and fragments of shipwrecks are cast out to land. Finally, [Furner] says that if anyone attentively considers the history of the marine tide, he will find in it all the symptoms of fevers, and the sole difference [is] in two points: the first is that the Moon is applied to the sea, in moving [it], more regularly than any external agent [is applied] to the human body in stirring up fevers; the other is that the human body, on account of the greater compactness of its parts, cannot swell from fevers and vary its pristine shape. If Pliny had heard this, he would much more gladly have pronounced what he said (bk. 2, ch. 97): “but about the shores, rather than in the deep, are these motions detected, since in the body too the extremities feel the pulse of the veins—that is, the spirits—more.”

[Margin: 16th Opinion, of the Conimbricenses, Zanardus, [and] Scaliger.]

[XL.] The Sixteenth opinion prefers to recognize in the Moon a certain magnetic power, by which, through local

[…continues on p. 377 (PDF 412) with the catchword “[loca]lem”: “…through local [motion it draws the waters to itself]“—the rest of the magnetic opinion (Gilbert and Kepler), and the further opinions on the cause of the Tide.]

(printed p. 377 — within Chapter XIV. ¶XL finishes the 16th (magnetic) opinion, quoting and refuting Kepler’s theses on the mutual attraction of Earth and Moon. ¶XLI states the 17th opinion — Galileo’s Earth-motion theory, to be refuted below — and ¶XLII gives Riccioli’s own eclectic 18th opinion (the Moon stirring sea-bottom vapors, with many concurring causes), admitting he cannot explain the tide at the Moon’s lower meridian. A sub-head then begins ¶XLIII, the refutation of Galileo’s cause of the diurnal tide.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 377]

[the Moon, by a magnetic power, through local] motion draws the waters to itself and allures [them], until, by their own weight, on account of the excessive heap, they fall back again and subside. Of which opinion seem to be the Conimbricenses (2 Meteor., tr. 8), Zanardus (q. 30), and Scaliger (exercitation 52). Who, when he had said of the sea’s tide, from many Authors, “Since it was observed to follow the Moon’s course, they judged the Moon [to be] its author,” and had at once objected, “But the Moon does not touch the waters,” immediately resolves [it], saying: “This made trouble for some of the Peripatetics—to whom the Magnet too ought to have made [trouble]: if motion in iron happens from the stone [lodestone] without contact, why will not the Sea follow the body of the most noble star?” And toward the end of that exercitation: “I would dare to affirm that there is not then a new generation of waters” (namely, when the tide happens); “with what design I should profess Rarefaction, I truly know not. Yet that they are suspended at that time, like iron by a Magnet, every single month, everywhere except that one shore, has been found by perpetual observations.” He speaks especially of the Full Moons—in which, however, at the shores of the Indus the increments of the sea are smaller than at the New Moons.

[Margin: Gilbert. — Kepler.]

The same thing William Gilbert tacitly insinuates (bk. 6 On the Magnet, ch. 6), when he attributes both to the Moon and to the earth a magnetic power for attracting and leading round kindred bodies. But most lucidly of all, Kepler, in the Introduction to the Commentaries on Mars, whose opinion we shall expound only in his own very words, distributed into various propositions, which are of this kind:

[Margin: Kepler’s theses on the Sea’s Tide.]

1. “If the Moon and the Earth were not retained, each in its orbit, by an animal force or some other equipollent [force], the Earth would ascend to the Moon by a fifty-fourth part of the interval; the Moon would descend to the Earth by about fifty-three parts of the interval, and there they would be joined—supposing, however, that the substance of each is of one and the same density.”

2. “If the Earth ceased to attract its waters to itself, the sea-waters would all be raised, and would flow into the body of the Moon.”

3. “The orb of the tractive power which is in the Moon reaches even to the lands, and allures the waters under the Torrid Zone, inasmuch as [it goes] into its own meeting, wherever it falls upon the vertex of a place—insensibly in enclosed seas, sensibly there where there are the widest channels of the Ocean, [where] the waters [have] a spacious freedom of reciprocation. Which being done, the shores of the Zones and of the lateral Climates are laid bare, and, if anywhere even under the torrid [zone] the nearer [parts] of the Ocean make rather-withdrawn bays [are laid bare]. And so, the waters rising in the wider channel of the Ocean, it can happen that in its narrower bays (provided they be not too narrowly enclosed) the waters, even with the Moon present, seem to flee from it—inasmuch as, the supply of waters being drawn off, they subside outside.”

4. “But the Moon swiftly flying over the vertex, since the waters cannot follow so swiftly, the flux of the Ocean indeed happens, under the Torrid [zone], toward the West, until it impinges on the opposite shores and is curved by them; but the assembly of the waters—or the army which is on its march toward the Torrid [zone]—is dissolved by the Moon’s departure, being deserted, namely, by the tract [force] which had roused it; and, having taken impetus, as in water-vessels, it returns and leaps up to its own shores and covers them; and this impetus, through the Moon’s absence, begets another impetus, until the Moon, returning, takes up the reins of this impetus, and moderates [it], and carries [it] round together with its own motion. Thus the shores equally open are all filled at the same hours; the more withdrawn ones [are filled] later, some in diverse manner on account of the diverse approaches of the Ocean.”

Yet the same [Kepler], in the Epitome of Copernican Astronomy (bk. 1, p. 128), adds, as a helping cause of the tide, the natural inertia of the waters resisting toward the West (since the earth withdraws itself toward the East), and [says] that hence is the flux of the waters which renders navigation easier toward the West—which, however, is not felt at the shores of America toward the East, on account of the vast length of the Ocean not impinging on any obstacle.

[Margin: Refutation of the 16th opinion.]

But how many [things are] here asserted, how many dissembled, against the credit of history! For how false it is that the tide happens primarily and per se from East to West, since many tides happen from North to South, and vice versa. Besides, if the Moon by a magnetic force and a merely local motion allured the waters, surely those which are nearer to it—or all [of them] most of all when it became nearest to them. But it happens otherwise: for greater tides happen at the English, Dutch, [and] Belgian shores, whose waters are farther from the Moon than in many parts of the Torrid Zone; and with the Moon, in the quadratures, descending toward the lands, the smallest tides happen. Again, if in the more withdrawn seas smaller tides happen than in the more open ones, why is there not a greater tide in the Tyrrhenian than in the Adriatic—especially in places set under the same meridian? Finally, there are many other accidents commemorated by us at number 23, whose cause does not appear in this magnetic power.

[Margin: 17th Opinion. — Of Seleucus. — And of Galileo.]

[XLI.] The Seventeenth opinion ascribes this motion of the Sea to the diurnal and annual motion of the Earth together. Which formerly some Seleucus or other devised, of whom Plutarch [speaks] thus expressly (bk. 3 On the opinions of the Philosophers, ch. 17): “Seleucus the Mathematician, himself also moving the Earth, says that the whirling of the Moon meets [the Earth’s] circular and [diurnal] motion; by which impetus, a blast gathering itself between these two bodies and rushing into the Atlantic, the sea is, by a probable reason, disturbed.” But his opinion—though his name [is] silent through oblivion—Galileo carps at (dialogue 4 On the System of the World, Latin p. 343), because the Moon’s motion is not contrary to the Earth’s motion, since it is toward the same quarter. And therefore [Galileo] himself explained the sea’s tide in another way, through the unequal motion of the Earth, as we have already narrated from number 1 to 10—which we shall soon most evidently show to be false, from number 43.

[Margin: 18th Opinion, our own.]

[XLII.] The Eighteenth, Our own opinion, collected and selected from many of the premised [opinions], is that the sea’s tide likewise happens from the Moon, stirring up the humors, vapors, and exhalations in the sea-bottom, and moving them (without rarefaction) at the sensible surface of the sea, according to their diversity—as opinions 14 and 15 hold; yet so that to its variety there concur not only the Sun and the rest of the positions of the stars, but also the incursion of Rivers nearer to the tiding places (as opinion 1 holds); and the double current of the sea, of which [we treated] from number 11 to 15 (as opinion 3 holds); and the gulfs of waters vomiting forth from subterranean whirlpools and again re-absorbing the waters (as opinion 2 holds); and the diverse situations of channels and shores (as opinion 4 holds); and sometimes the winds (as opinion 8 holds); and subterranean fires (as opinion 9 holds). Although these [be] fused into one, yet the effects which we enumerated at number 23 will always be worthy of admiration—and especially that which is discerned in the diurnal period of the returning tide, when the Moon, below the horizon, accedes to the lowest [point] of the meridian. For that the Moon transmits its power through the whole terrestrial globe, and that this is by no means blunted or remitted—or [that it travels] to the opposite part of the highest heaven, whence it is reflected back to us, having twice traversed an immense space (since indeed we recognize the other heavens as by no means solid)—is not yet persuaded to me. But neither through the monthly libration of the Moon, and the diverse emersions or occultations of its spots toward [its] margins, can we explain this diurnal vicissitude. Nor hitherto have I found a man who satisfies me in this part; nor am I ashamed to be ignorant of it—[I] who do not doubt that I am ignorant of many other [things] easier to know.

[Margin: The final cause of the Marine Tide.]

But the final cause of these motions Francesco Resta touched briefly and expeditiously, from Bodin (bk. 3 of the Meteorology, tract 1, ch. 15): for the sea’s Tide serves both for washing away and checking its own filth, and for fisheries, and for the more opportune landings of ships for importing and exporting wares; and for the salt-pans, or natural workshops for making salt; and for stirring up many living things. I add, also, [that it serves] for supplying abundant matter for the praises of GOD the Creator, and for acknowledging the imbecility of our own intellect. Now to Galileo, who imposed on us the necessity of so prolix a treatment, lest we should seem to wish to demolish, with a light arm, an argument which he himself esteemed of so great weight for the Earth’s motion.

Refutation of the Cause of the Diurnal Tide adduced by Galileo

[XLIII.] The doctrine of Galileo, delivered from number 4 to 7, must be repeated in this place, together with the diagram there set forth. For he said that the cause of the diurnal flux and reflux, returning twice in [each] twelve hours, is the unequal diurnal motion of the Earth HKFG about its center B, toward the Eastern quarter from H to K; for this motion is faster in the upper semicircle GHK, because it seconds the motion of the center B (carried by the force of the annual motion toward the same quarter, from B to C); but in the lower semicircle KFG the Earth’s motion is slower, as striving against the annual motion of the center B; and therefore there happens alternate-

[…continues on p. 378 (PDF 413) with the catchword “[alterna]tim”: “…alternately [an acceleration and a retardation of the parts of the Earth’s surface]“—the rest of the recapitulation and refutation of Galileo’s diurnal-tide cause.]

(printed p. 378 — within Chapter XIV, ¶XLIII: Riccioli’s point-by-point refutation of Galileo’s diurnal-tide cause, with the mechanism’s engraved diagram re-printed. Arguments 1–5 are given: the Earth’s motional inequality is real but imperceptible; Galileo contradicts himself and Copernicus on the carried-along air; a tide needs a sudden, not gradual, velocity-change; the tide demonstrably tracks the Moon; and an Earth-driven tide would be universal along every East–West shore.)

[Header: BOOK IX. SECTION IV. — 378]

[and therefore there happens alternate]ly a tide and a reflux, and the rest, which we there described.

[Translator’s note — engraved diagram (a re-print of the figure at p. 361): the great annual orb, with center A (the Sun) at its lower middle and the cardinal points O (top), P, C, D, Q around it; the Earth-globe is the middle circle HKFG (H top, K left, G right, F bottom) with center B and a small inner circle; the Earth’s own path carries B around, with O marking the top and L the bottom of that path, and the small arcs M–N flanking A below. It illustrates Galileo’s compound motion: the Earth’s surface-point at H (where the diurnal and annual motions conspire) moves fastest, at F (where they oppose) slowest.]

But against this cause there are very many arguments, partly our own, partly others’. And first, indeed, Galileo’s argument is either null or invalid; for that inequality [of the Earth’s motion] is not real, says Chiaramonti, but optical, and merely apparent to an eye feigned to be at A; for to it the parts GHK will seem faster under the Firmament, because the center B of the circle GHKF—as [the center] of an Epicycle—is advanced toward the same quarter; but the parts KFG will seem retrograde a little below the points K and G, on account of [their] motion contrary to the motion of the center B. By which reasoning Galileo himself tried to show that the Retrogradation of the Planets is not real but apparent. Add that to us—who are not at A, but on the surface GHKF, on which we behold the sea’s motion—the Earth’s motion is not only not unequal (since Galileo confesses it to be in itself equal), but cannot even appear unequal: both because we are turned in the same manner with the Earth, and because we cannot observe by any sense even any motion of it, much less the inequality. But if we were at the center B, the Earth’s motion would appear to us equal.

[Margin: Galileo’s argument in form.]

But Galileo’s argument, reduced to form, was of this kind: “In every vessel full of water, and moved now more slowly, now more swiftly, the water now flows to one margin, now flows to the other margin. But the Earth is a vessel of this kind, therefore etc.” To which argument Chiaramonti concedes the Major concerning real velocity and slowness, [but] denies it concerning the merely apparent; but the Minor, by which the Earth is supposed to be moved more slowly and more swiftly, he denies as to real velocity and slowness, [and] concedes as to [velocity] apparent to an eye feigned at A. Cabeo touched something similar, rather obscurely (2 Meteor., text 6, at the end of question 8). But each is deceived: for not only to an eye at A, but [to one] placed anywhere, the point of the Earth H, in mundane space, on account of the mixed motion (from the diurnal about center B, and the annual of center B about center A), would have completed a much greater journey than if it had been moved by the diurnal motion alone about center B—so much so that, according to what was said with Kepler (ch. 6, no. 2), such a point [H] at the Equator completes, by the diurnal motion indeed, in one hour 240 German miles, but by the force of the annual motion 740, that is, with the motions compounded, 980 miles; whereas, on the contrary, the point F would complete in one hour 500 miles.

[Margin: 2nd Argument against Galileo.]

Secondly, Galileo contradicts himself and Copernicus, while he attributes to the water a motion diverse, and sometimes contrary, to the motion of the earth, and yet derives its origin from the earth’s own diurnal and annual revolution, and not from elsewhere. Which contradiction I too formerly noted, and saw observed by Chiaramonti (in the Defense of the Anti-Tycho, part 4, ch. 25), and by our [Father] Furner (bk. 9 Hydrography, ch. 15). For Copernicus, objecting to himself (bk. 1 of the Revolutions, ch. 7) why heavy things thrown perpendicularly upward fall back into the same point of the earth, although meanwhile [the earth is] withdrawn with so great swiftness; and [why] the clouds themselves, and whatever else hangs in the air, do not seem always to be carried Westward, if we are rolled with the earth toward the East—responded (ch. 8) with those words: “What then should we say of the clouds, and of the rest hanging in the air in any way whatever, or subsiding, and again tending into the heights? Except that not only the earth, with the watery element conjoined to it, is so moved, but also no small part of the air, and whatever things have a kinship with the earth in the same manner—whether because the neighboring air, mixed with earthy or watery matter, follows the same nature as the earth, or because the motion of the air is acquired, [a motion] which it shares from the earth by contiguity, by a perpetual revolution and without resistance.” Which doctrine Galileo receives (dialogue 2 On the System of the World). Therefore, if not only watery bodies, but also clouds and things like them, which are near the earth and yet cohere less with it, are moved with the same velocity and kind of motion as the earth toward the East, the water likewise—the whole of any sea whatever—ought to be moved equally with the earth’s globe toward the same quarter, if this common motion be attended to; nor will it be able to be moved elsewhither, or unequally, except by some peculiar motion from without, such as from the winds. Therefore, while Galileo attributes to the Sea a motion of flux and reflux diverse from the diurnal conversion of the Earth—on the ground that the water is fluid and does not wholly obey that motion which, nevertheless, the air (neighbor to the earth, and far more fluid) does obey—he is repugnant both to Copernicus and to himself.

[Margin: 3rd Argument.]

Thirdly, if the Earth’s diurnal motion together with the annual could produce the Sea’s flux and reflux, it ought to produce it on account of the sudden change of motion, and the abrupt transit from velocity to slowness, or from slowness to velocity—as appears in a vessel full of water; for unless it is shaken by a sudden change, the water does not sensibly fluctuate, nor is it raised now to one, now to the other margin. But even if the Earth be admitted to move unequally, yet the change from velocity to slowness does not happen all in one impulse, nor at once, but little by little and imperceptibly around the points K and G—exactly as in the Planets moved through an Epicycle. Which argument I found afterward in Cabeo (2 Meteor., text 6, q. 8). Nay, this very inequality is insensible, especially far from the points F and H, as we shall show in ch. 19 from numbers 9 and 11.

[Margin: 4th Argument.]

Fourthly, from the History of the diurnal sea-tide given from number 17, and from the Nautical Rules for discerning the hour of the highest tide, or living water, given from numbers 20, 21, and 22, it is evident that the sea’s tide has the greatest connexion with the Moon’s diurnal and monthly motion; and that, in the same places where it happens, it is daily postponed by about 48 minutes—namely, by as many minutes as the Moon daily rises later, on account of its proper motion; and that the highest tide happens when the Moon accedes to the Meridian, above or below the Horizon, even outside [the moment of] noon or midnight. Which rules the shipmasters collected from long observation and most certain experiments—since indeed ignorance of these would be very pernicious to them. But if the sea’s tide depended on the motion of the earth, and took its vicissitudes and laws from it, the aforesaid rules would be vain and most fallacious; for no cause can be taken from the motion of the earth, on account of which, the Moon acceding to the Meridian, the highest tide of the whole day or night should happen, or why it should be daily retarded by 48 horary minutes. And therefore Galileo, in that dialogue 4, as if in jest—not to say in contempt—belittles the opinion of those who ascribe the sea’s tide to the Moon, and either shows himself unskilled in nautical matters, or craftily dissembles their rules. But he could not deceive the skilled, nor will he ever be able to persuade the shipmasters to take the rules of the tides from this feigned, uncertain, and insensible motion of the earth, and to desert those which they have acquired from the Moon’s motion, with so great a consensus of the craftsmen and so great a success of navigation.

[Margin: 5th Argument.]

Fifthly, if the sea’s flux and reflux happened from the diurnal whirling of the Earth toward the East—but unequally, in that manner which Galileo feigns—it ought to be universal to any sea extended according to the length of the earth from West to East, and to be felt alternately on every eastern and western shore; and so the shore of Africa, which is from the western mouth of the Strait of Gibraltar up to the Tropic of Cancer, and

[…continues on p. 379 (PDF 414) with the catchword “est”: “…and is immune from the tide [ought to experience a tide]“—the rest of the fifth argument, and the further arguments against Galileo’s tidal cause.]

(printed p. 379 — within Chapter XIV, ¶XLIII: the arguments against Galileo’s diurnal-tide cause continue, numbers 5 through 12 — chiefly that shores on the same meridian tide differently, that North–South-facing seas (which Galileo’s theory would leave tideless) tide strongly, that the tide is a swelling from the bottom rather than a mere flow, and that its variations track the Moon rather than the hours of the day, with absurd nautical consequences drawn from the supposed whirl.)

[Header: ON THE SYSTEM OF THE MOVED EARTH — 379]

[the shore of Africa, from the Strait of Gibraltar to the Tropic of Cancer, which] is immune from the tide, ought to experience a tide when the waters returned from the eastern shore of America; or the western shore of Spain would feel the tide when the waters return from the shore of Syria—at least in those 8 hours in which it was observed by the people of Cadiz that the waters of the Mediterranean flow out through that strait into the Ocean. Which I say because Galileo says that no tide happens on the Eastern shore of Spain, on the ground that the waters of the Ocean, having entered through the Strait of Gibraltar, resist the waters of the Mediterranean carried toward Spain—which is not true of the whole day, but at most of 15 or 16 hours.

[Margin: 6th Argument.]

Sixthly, if the sea’s tide were from the Earth’s diurnal revolution (as Galileo wishes), then in those shores which face toward the Eastern or Western quarter and are at the same time under nearly the same Meridian, the tide would be in the same manner, and at the same hour, and in the same measure, without sensible difference. But this is repugnant to daily experience, and to the history of the tide already given: for if anyone considers the tides which happen on the shores of England, Belgium, Gaul, Lusitania, and Guinea, he will detect a very notable difference, both in the time and in the measure of the tides. Besides, it would be necessary that, at the time when the sea is high on one Eastern shore, it should be low on the western shore opposite to it—which is likewise against the history of the marine tide; and much less could the waters of two seas, meeting each other in the same tract of sea, cause the tide—but at the same time both would run toward the East, or both toward the West. But it happens otherwise in the Strait of Magellan, in which the waters, rushing on this side from the Atlantic Ocean, on that side from the Pacific sea, and meeting each other, produce in the middle of that strait a notable tide, and afterward, subsiding, flow back—the ones into the Atlantic, the others into the Pacific.

[Margin: 7th Argument.]

Seventhly, if the sole cause of the marine tide were the inequality of the Earth’s motion toward the East, surely no sensible or great tide could happen in shores and ports situated toward the North or South; and therefore Galileo, either through unskillfulness or through craft, denied that a tide happens in the Red Sea. But that this is false, the History of the marine tide teaches by very many and manifest experiments. For not only in the Red Sea does a tide happen, but at the southern shores of America beyond the Mexican gulf, and likewise on the southern coast of the East Indies, from Calicut to Cambay—where it is so rapid and vehement that in 15 [minutes] at the least it occupies [several] miles of shore in two hours, and in as many hours, by reflowing, lays the same bare, and drives the waters of the Indus river upward toward [its] source, and then, by reflowing, leaves the ships on the dry. And if the English, Dutch, and others be questioned, who every year sail to Spitsbergen to acquire whales by fishing, up to the 80th degree of polar altitude, they will attest that the waves of the tiding Ocean are rolled and rush from South toward North—and indeed more vehemently than anywhere it happens from East to West, or from West to East. As in the Archipelago of St. Lazarus the tide is borne daily toward the South with such force that it bursts ropes of 27 inches’ thickness, as Furner narrates (bk. 9 Hydrography, ch. 16), who uses this very argument against Galileo, as also Cabeo (2 Meteor., text 6, q. 8).

[Margin: 8th Argument.]

Eighthly, the continuous motion of the Earth toward the East—and so rapid that in 24 hours it would revolve the whole globe of the earth with the enclosed waters—would impede not only the tides strictly so called, which happen by the sea’s motion toward the Poles or the Equator, but also the other fluxes of the sea running toward the North or toward the South; for it would at length overcome their motion and involve [it] together with itself. But it is established that the sea’s waters run from the North or from the South toward the Equator, as appears from the history given at number 12. Besides, [the Earth’s motion] would impede either the tide, or the flux and reflux of the Chalcidic Euripus, and of the currents between Africa and the island of St. Lawrence [Madagascar], and the courses of the ice rushing from the North, of which [we treated] at the same number 12.

[Margin: 9th Argument.]

Ninthly, since in the preceding figure the Earth’s motion is supposed by Galileo to be slower in the lower semicircle KFG (because it is illuminated by the Sun), and faster in the nocturnal semicircle GHK—if the tide happened on account of the Earth’s motion, it would be necessary that for about 12 hours daily the sea should everywhere flow, and for as many [hours] reflow, and that of the two effects of this motion one should be felt in places tending from K, through F, to G, the other in places [tending] from G, [through] H, to K, with perpetual succession: to which motion, however, observation is repugnant.

[Margin: 10th Argument.]

Tenthly, if the Sea’s tide, properly and strictly so called, be rightly considered, it is not a mere local motion, but a certain swelling-up from the sea-bottom itself toward [the surface]—granted that the waters thus swelling then run toward the lower parts of the sea or shores. But if it were from the motion of the earth, it would be a mere flowing-toward and flowing-back by the local motion of the waters going and returning hither and thither.

[Margin: 11th Argument.]

Eleventhly, if the Earth’s motion toward the East, by its inequality, were the sole cause of the marine tide, the variation arising from the transit from velocity to slowness would always be observed everywhere at sunrise; and [the variation] arising from slowness to velocity at sunset; and the variation arising from the highest slowness would be observed at noon, but [the variation] arising from the highest velocity at midnight. For in the figure set forth by Galileo, the transit from the swift earth-motion to the slow happens at the point K of the terrestrial Equator (and similarly in its parallels), where the Sun A begins to be seen; and the transit from the slower motion to the swifter happens around the point G, where the Sun ceases to be seen and seems to set; but the highest slowness happens at the point F, to which the Sun A makes noon, and the highest velocity at the point H, where it is midnight. But no experiment supports this observation; nay, almost the whole history of the marine tide is repugnant [to it], whose varieties—as to the beginning and end of the tide, or as to its highest or lowest measure—depend not on the four cardinal points of the day, but on the Lunar elevation above the horizon, and its descent, and on its access to the highest or lowest [point] of the Meridian.

[Margin: 12th Argument against Galileo.]

Twelfthly, if from the diurnal whirling of the Earth in 24 hours the sea’s flux and reflux arose—since in each hour 15 degrees of the terrestrial Equator and of each parallel are revolved toward the East, so that this motion be proportioned to the impulse of the earth driving the waters—it would be necessary that the waters running from West to East, from the shore of the western region at sunrise, should reach the opposite shore in about as much time as the degrees of longitude intercepted between the western and eastern shore require: namely, after one hour [later] if they were distant 15 degrees, and after two if 30 degrees, and so of the rest. And so, from the shore of Spain the waves ought sometimes to reach the shore of Syria in 3⅔ hours (because it is distant in longitude about 55 degrees); and from the shore of North America (the Land of Florida) to the western shore of Spain—just as from the shore of New France to the western shore of Gaul—the waves would sometimes consume just as much time (because they are distant among themselves about 55 degrees in longitude). Sometimes, I say—namely when, on account of the inequality of the diurnal motion asserted by Galileo, [the waters] would impinge on the shores of the western land, and thence return toward the East to the shores opposite in the same parallel. But from the eastern shore of England to the western shore of Denmark or Norway (which are distant 6 or 7 degrees of longitude from each other) the waves would flow within 24 or 28 horary minutes. But hence would follow three inconveniences, or three effects repugnant to nautical experiments.

[Margin: The highest velocity of ships.]

First: ships sailing eastward in such parallels would experience, of themselves (when the winds did not obstruct), an incredible velocity—and as great as they have never experienced; for in the parallel of latitude 30 degrees, through which one nearly sails from Spain to Syria, each degree contains 61¼ Italian miles (of which, according to what was said bk. 2, ch. 7, one degree at the Equator contains 72½). Therefore, if in each hour the sea-water carrying a ship completed 15 degrees, surely that ship would traverse in one hour 918 Italian miles; but in the latitude of 45 degrees it would complete in one hour 756 miles—whereas it scarcely, even in a whole day, by the swiftest course, completes in the Mediterranean 500 miles, but in the Ocean 200, as I said (bk. 2, ch. 16, no. 8). Secondly: ships meanwhile meeting, by a contrary course, the waves reflowing from West to East, would experience an incredible and insuperable resistance—whereas it is certain that those sailing westward are perpetually aided by the sea’s course toward the West, as we showed at number 13. Thirdly: it would follow that, in that tract of sea which is between England and Denmark or Norway, the waves would flow within 24 or 28 horary minutes, and reflow as often to the opposite shores; and so 24 tides would happen daily, and as many refluxes—which has hitherto been detected not only [not] there, but not even in any Euripus whatever.

[…continues on p. 380 (PDF 415) with the catchword “Deci-”: “Thirteenthly [Decimotertiò]…”—the remaining arguments against Galileo’s tidal cause.]

(printed p. 380 — the close of Chapter XIV. The 13th argument against Galileo notes that enclosed North–South bays like the Red Sea and Adriatic tide strongly, contrary to his theory. ¶XLIV then refutes Galileo’s cause of the monthly and annual tide-variations with four arguments, and ¶XLV casts Galileo’s reasoning as a syllogism, which Riccioli answers by denying the Minor and retorting the syllogism.)

[Header: BOOK IX. SECTION IV. — 380]

[Margin: 13th Argument.]

Thirteenthly, from Galileo’s opinion—admitted, indeed, with little consistency as to the earth’s motion, but nevertheless by hypothesis—it would follow that, in seas or bays narrower according to [their] length and enclosed within neighboring shores (especially those facing North and South), no sensible tide happens; of which kind are not only the Red Sea (of which it was said above), but also the sea between England, Norway, Denmark, and Belgium, and our Adriatic Sea (which is narrower than the Tyrrhenian), or the Venetian Gulf, and the Persian Gulf, and the Bay of Bengal, and the Chinese Gulf: and yet in them notable tides happen—so much so that between England and Belgium it rises on that side 50 and 70 feet, on this side 15 and 20, as our [Father] Furner has often observed and narrated (bk. 9 Hydr., ch. 20). But re-read the history of the marine tide, where there is discourse of the tides of the Bays and Straits.

The Cause of the Monthly and Annual variety of the marine Tide, feigned by Galileo, is refuted

[XLIV.] If you recall to memory what I said at number 7: Galileo wishes the diurnal motion of the Earth and of the Lunar heaven, taken together, to be slower at the New Moons (because the Moon must then describe, in the same time, a greater arc of the annual orb), but faster at the Full Moons (because [it describes] a smaller arc). But from what was said at numbers 8 and 9, the diurnal motion at the Solstices adds more to the annual motion than at the Equinoxes, by Galileo’s hypothesis; and so he tries to defend the monthly and annual varieties which are in the sea’s tide—which, however, he did not expound determinately, I believe lest a sincere exposition of them should obstruct his own hypothesis. But against Galileo’s hypothesis are the following arguments, in great part taken from Cabeo (2 Meteor., text 6, q. 9 and 10) and Furner (bk. 9 Hydrography, ch. 19).

[Margin: 1st Argument against Galileo.]

First, if at the New Moons the diurnal motion of the earth turns out faster than at the Full Moons, and this difference is so great as to produce a sensible difference in the marine tide, this difference would long since have been observed in the diurnal motion of the Sun (for which Galileo and all the Copernicans substitute the motion of the earth)—and the more easily, the more often this happens within the year, that is, at least twelve times at the new moons and twelve times at the full moons. But neither Copernicus, nor Tycho, nor any other Astronomer observed this difference—[they] who nevertheless observed other, subtler differences of the celestial motions, and [ones] growing only with time.

[Margin: 2nd Argument.]

Secondly, for the Moon to be faster at the New Moon and slower at the Full Moon, it would not be necessary that the Earth itself then move faster or slower, but the Earth’s accustomed motion would suffice, together with the diverse distance of the Moon from the center of the annual orb—to which, made nearer, it would be faster at the conjunction ☌, but, made remoter, it would appear slower at the opposition ☍.

[Margin: 3rd, principal Argument.]

Thirdly, and principally, from Galileo’s hypothesis it would follow that greater tides happen at the New Moons (the Earth being then incited in [its] diurnal motion, and consequently the waters fluctuating more), and more also at the Quadratures than at the Full Moons, and indeed on the very days of the New Moon. But we have already shown (number 18, from the history of the marine tide) that the contrary happens; for in most places the tide is greater, or not less, at the Full Moons than at the New Moons; but nowhere [is it] greater at the Quadratures than at the Full Moons: and in many places the highest increments of the tides do not happen on the very day of the New Moon or Full Moon, but one or another—or even a third—day after, as we said in the same place.

[Margin: 4th Argument.]

Fourthly, if—because the Earth’s diurnal motion is swiftest at the Solstices (as Cabeo gathers, rather timidly, from Galileo’s doctrine adduced at numbers 8 and 9, since the diurnal motion most conspires with the annual and adds as much as the whole diameter of the earth requires)—it follows that the tide is greater at the Solstices than at the Equinoxes, and greatest of all at the Solstitial New Moons (as the same Cabeo gathers): but this is against experiment and the history given at number 19. If, however (as Furner thence gathers), the tide is smaller at the Solstices than at the Equinoxes, it would follow that the tide made at the Solstitial full moon daily grows toward the quadrature, the more one recedes from the Solstitial day; and, on the contrary, that the tides made at the Equinoctial quadratures are greater than the tides made at the Solstitial new or full moons. But by experiment it is established that each is false, and that the tides made at the Solstices (whether the Moon be new or full) are far greater than those which happen at the quadratures, as was said at number 18.

To one rightly considering this whole Hypothesis of Galileo, therefore, it will be manifest that it, for the most part, not only does not explain the cause of the marine tide, but even destroys the effect itself, and utterly overturns almost the whole history of it handed down by the most skilled shipmasters. Now, therefore, that we may sail out of this tide, let us dissolve Galileo’s Argument reduced to form.

[Margin: Galileo’s argument in syllogistic form. — Proof of the Major.]

[XLV.] “That Hypothesis is to be repudiated by which the cause of the Sea’s Tide cannot be rendered, and on the contrary that [is] to be embraced by which it can. But by the Hypothesis of an immobile Earth the cause of the Sea’s Tide cannot be rendered; and by the Hypothesis of the Earth moved with a diurnal and annual motion it can. Therefore the Hypothesis of an immobile Earth is to be repudiated; but the Hypothesis of the Earth moved with a diurnal and annual motion is to be embraced.” The MAJOR does not seem to be called into controversy; for even if the other [things] were unequal, and by the hypothesis of an Earth at rest the cause of some motions—at least the elementary—were rendered equally well or better, yet so great is the variety of the marine tide, and so celebrated and of such moment is the question concerning the Sea’s tide, that if by some hypothesis it could at length be settled, and a sufficient and highly probable cause of all (or the chief) effects and accidents which appear in that motion could be adduced, there would be no cause why that hypothesis should not be preferred to that [other] which can exhibit no sufficient cause of them.

[Margin: Proof of the Minor.]

The prior part of the MINOR, which is negative, is proved from the things said here and there by Galileo, indicated from number 3 to 10; and from the refutations and difficulties against all the opinions concerning the cause of the sea’s tide which suppose the Earth immobile, or which do not number its motion among the causes—[opinions] which we ourselves adduced from number 23 to 42. But the posterior part is evident from Galileo’s doctrine, explicated from number 2 to 10.

[Margin: 1st Response.]

I respond, first, the Major being granted, by denying the Minor as to each part. As to the prior [part] indeed, because, without the motion of the Earth, the cause is rendered by opinion 18, brought forward at number 42—not, indeed, evident as to all the effects of the marine tide, but evident as to some, and as to others probable; but where the explanation fails, it fails in that [point] in which, by the hypothesis of a moving earth, no explanation at all was rendered by Galileo—namely, why, the Moon being placed below the Horizon, the tide happens just the same as when the Moon is above the horizon; since Galileo acknowledges no necessary connexion between the diurnal tide and the Moon’s motion and position, nor adduces for this peculiar effect a peculiar cause from the earth’s motion (as neither for many other effects). Wherefore, although by the hypothesis of an Earth at rest the cause of the sea’s tides is not rendered absolute and wholly satisfying to our intellect, yet, compared to the explanations which Galileo tried to beg from the hypothesis of a moving Earth, it is rendered much more probable, and congruent with very many effects, and repugnant to none.

But the second part of the Minor is denied, on account of the twelve arguments made at number 43 and the four at number 44 against Galileo—from which it clearly is established that Galileo, in very many [points], is repugnant to the most manifest experiments and observations concerning the sea’s tide, made from the time of the Phoenicians down to our times; and (as our Furner rightly said, bk. 9, ch. 16, of his most erudite Hydrography) has inquired into the cause of a thing which does not at all exist in the nature of things—that is, the cause of a certain chimerical tide, feigned by himself, and not such as it really is, and such as has long since been observed by those skilled in maritime matters.

[Margin: 2nd Response.]

It is responded, secondly, by retorting very many of the arguments set forth at numbers 43 and 44 against Galileo, by saying:

“If the Earth were moved, and by its motion were the efficient cause of the sea’s tide, in that manner which Galileo explains, the sea’s tide would not be such as it really is; therefore either the Earth is not moved, or by its motion it is not the cause of the sea’s tide in that manner which Galileo explains.”

[…continues on p. 381 (PDF 416) with the catchword “CA-”: Caput XV — “Baliani’s System set forth,” presenting his hypothetical tidal mechanism by way of his letters.]