Now from this swelling of the ocean in those parts of the earth, proceed the flowings and ebbings in the Atlantic, Spanish, British, and German seas; which though they have their set times, yet upon several shores they happen at several hours of the day. And they receive some augmentation from the north, by reason that the shores of China and Tartary, hindering the general course of the waters, make them swell there, and discharge themselves in part through the strait of Anian into the Northern Ocean, and so into the German Sea.
As for the spring tides which happen at the time of the new and full moons, they are caused by that simple motion, which at the beginning I supposed to be always in the moon. For as, when I showed the cause of the eccentricity of the earth, I derived the elevation of the waters from the simple motion of the sun; so the same may here be derived from the simple motion of the moon. For though from the generation of clouds, there appear in the sun a more manifest power of elevating the waters than in the moon; yet the power of increasing moisture in vegetables and living creatures appears more manifestly in the moon than in the sun; which may perhaps proceed from this, that the sun raiseth up greater, and the moon lesser drops of water. Nevertheless, it is more likely, and more agreeable to common observation, that rain is raised not only by the sun, but also by the moon; for almost all men expect change of weather at the time of the conjunctions of the sun and moon with one another and with the earth, more than in the time of their quarters.
In the last place, the cause why the spring tides are greater at the time of the equinoxes hath been already sufficiently declared in this article, where I have demonstrated, that the two motions of the earth, namely, its simple motion in the little circle l b k c, and its diurnal motion in l d k e, cause necessarily a greater elevation of waters when the sun is about the equinoxes, than when he is in other places. I have therefore given possible causes of the phenomenon of the flowing and ebbing of the ocean.
Cause of the precession of the equinoxes.
11. As for the explication of the yearly precession of the equinoctial points, we must remember that, as I have already shown, the annual motion of the earth is not in the circumference of a circle, but of an ellipsis, or a line not considerably different from that of an ellipsis. In the first place, therefore, this elliptical line is to be described.
Let the ecliptic ♎ ♑ ♈ ♋ (in [fig. 5]) be divided into four equal parts by the two strait lines a b and ♑ ♋, cutting one another at right angles in the centre c. And taking the arch b d of two degrees and sixteen minutes, let the strait line d e be drawn parallel to a b, and cutting ♑ ♋ in f; which being done, the eccentricity of the earth will be c f. Seeing therefore the annual motion of the earth is in the circumference of an ellipsis, of which ♑ ♋ is the greater axis, a b cannot be the lesser axis; for a b and ♑ ♋ are equal. Wherefore the earth passing through a and b, will either pass above ♑, as through g, or passing through ♑, will fall between c and a; it is no matter which. Let it pass therefore through g; and let g l be taken equal to the strait line ♑ ♋; and dividing g l equally in i, g i will be equal to ♑ f, and i l equal to f ♋; and consequently the point i will cut the eccentricity c f into two equal parts; and taking i h equal to i f, h i will be the whole eccentricity. If now a strait line, namely, the line ♎ i ♈, be drawn through i parallel to the strait lines a b and e d, the way of the sun in summer, namely, the arch ♎ g ♈, will be greater than his way in winter, by 8¼ degrees. Wherefore the true equinoxes will be in the strait line ♎ i ♈; and therefore the ellipsis of the earth's annual motion will not pass through a, g, b, and l; but through ♎, g, ♈ and l. Wherefore the annual motion of the earth is in the ellipsis ♎ g ♈ l; and cannot be, the eccentricity being salved, in any other line. And this perhaps is the reason, why Kepler, against the opinion of all the astronomers of former time, thought fit to bisect the eccentricity of the earth, or, according to the ancients, of the sun, not by diminishing the quantity of the same eccentricity, (because the true measure of that quantity is the difference by which the summer arch exceeds the winter arch), but by taking for the centre of the ecliptic of the great orb the point c nearer to f, and so placing the whole great orb as much nearer to the ecliptic of the fixed stars towards ♋, as is the distance between c and i. For seeing the whole great orb is but as a point in respect of the immense distance of the fixed stars, the two strait lines ♎ ♈ and a b, being produced both ways to the beginnings of Aries and Libra, will fall upon the same points of the sphere of the fixed stars. Let therefore the diameter of the earth m n be in the plane of the earth's annual motion. If now the earth be moved by the sun's simple motion in the circumference of the ecliptic about the centre i, this diameter will be kept always parallel to itself and to the strait line g l. But seeing the earth is moved in the circumference of an ellipsis without the ecliptic, the point n, whilst it passeth through ♎ ♑ ♈, will go in a lesser circumference than the point m; and consequently, as soon as ever it begins to be moved, it will lose its parallelism with the strait line ♑ ♋; so that m n produced will at last cut the strait line g l produced. And contrarily, as soon as m n is past ♈, the earth making its way in the internal elliptical line ♈ l ♎, the same m n produced towards m, will cut l g produced. And when the earth hath almost finished its whole circumference, the same m n shall again make a right angle with a line drawn from the centre i, a little short of the point from which the earth began its motion. And there the next year shall be one of the equinoctial points, namely, near the end of ♍; the other shall be opposite to it near the end of ♓. And thus the points in which the days and nights are made equal do every year fall back; but with so slow a motion, that, in a whole year, it makes but 51 first minutes. And this relapse being contrary to the order of the signs, is commonly called the precession of the equinoxes. Of which I have from my former suppositions deduced a possible cause; which was to be done.
According to what I have said concerning the cause of the eccentricity of the earth; and according to Kepler, who for the cause thereof supposeth one part of the earth to be affected to the sun, the other part to be disaffected; the apogæum and perigæum of the sun should be moved every year in the same order, and with the same velocity, with which the equinoctial points are moved; and their distance from them should always be the quadrant of a circle; which seems to be otherwise. For astronomers say, that the equinoxes are now, the one about 28 degrees gone back from the first star of Aries, the other as much from the beginning of Libra; so that the apogæum of the sun or the aphelium of the earth ought to be about the 28th degree of Cancer. But it is reckoned to be in the 7th degree. Seeing, therefore, we have not sufficient evidence of the ὁτί (that so it is,) it is in vain to seek for the διότι (why it is so.) Wherefore, as long as the motion of the apogæum is not observable by reason of the slowness thereof, and as long as it remains doubtful whether their distance from the equinoctial points be more or less than a quadrant precisely; so long it may be lawful for me to think they proceed both of them with equal velocity.
Also, I do not at all meddle with the causes of the eccentricities of Saturn, Jupiter, Mars, and Mercury. Nevertheless, seeing the eccentricity of the earth may, as I have shewn, be caused by the unlike constitution of the several parts of the earth which are alternately turned towards the sun, it is credible also, that like effects may be produced in these other planets from their having their superficies of unlike parts.
And this is all I shall say concerning Sidereal Philosophy. And, though the causes I have here supposed be not the true causes of these phenomena, yet I have demonstrated that they are sufficient to produce them, according to what I at first propounded.
