Chapter Xxi, When the Earth Is in _d_, It Will Come Nearer to Its First

movent, that is, to the sun which is in t; that is to say, the earth is nearer to the sun in the midst of winter when it is in d, than in the midst of summer when it is in b; and, therefore, during the winter the sun is in its Perigæum, and in its Apogæum during the summer. And thus I have shown a possible cause of the eccentricity of the earth; which was to be done.

I am, therefore, of Kepler's opinion in this, that he attributes the eccentricity of the earth to the difference of the parts thereof, and supposes one part to be affected, and another disaffected to the sun. And I dissent from him in this, that he thinks it to be by magnetic virtue, and that this magnetic virtue or attraction and thrusting back of the earth is wrought by immateriate species; which cannot be, because nothing can give motion but a body moved and contiguous. For if those bodies be not moved which are contiguous to a body unmoved, how this body should begin to be moved is not imaginable; as has been demonstrated in art. 7, chap. IX, and often inculcated in other places, to the end that philosophers might at last abstain from the use of such unconceivable connexions of words. I dissent also from him in this, that he says the similitude of bodies is the cause of their mutual attraction. For if it were so, I see no reason why one egg should not be attracted by another. If, therefore, one part of the earth be more affected by the sun than another part, it proceeds from this, that one part hath more water, the other more dry land. And from hence it is, as I showed above, that the earth comes nearer to the sun when it shines upon that part where there is more water, than when it shines upon that where there is more dry land.

9. This eccentricity of the earth is the cause why the way of its annual motion is not a perfect circle, but either an elliptical, or almost an elliptical line; as also why the axis of the earth is not kept exactly parallel to itself in all places, but only in the equinoctial points.

Now seeing I have said that the moon is carried about by the earth, in the same manner that the earth is by the sun; and that the earth goeth about the sun in such manner as that it shows sometimes one hemisphere, sometimes the other to the sun; it remains to be enquired, why the moon has always one and the same face turned towards the earth.

Suppose, therefore, the sun to be moved with simple motion in the little circle f g h i, (in fig. 4) whose centre is t; and let ♈ ♋ ♎ ♑ be the annual circle of the earth; and a the beginning of Libra. About the point a let the little circle l k be described; and in it let the centre of the earth be understood to be moved with simple motion; and both the sun and the earth to be moved according to the order of the signs. Upon the centre a let the way of the moon m n o p be described; and let q r be the diameter of a circle cutting the globe of the moon into two hemispheres, whereof one is seen by us when the moon is at the full, and the other is turned from us.

The diameter therefore of the moon q o r will be perpendicular to the strait line t a. Wherefore the moon is carried, by reason of the motion of the earth, from o towards p. But by reason of the motion of the sun, if it were in p it would at the same time be carried from p towards o; and by these two contrary movents the strait line q r will be turned about; and, in a quadrant of the circle m n o p, it will be turned so much as makes the fourth part of its whole conversion. Wherefore when the moon is in p, q r will be parallel to the strait line m o. Secondly, when the moon is in m, the strait line q r will, by reason of the motion of the earth, be in m o. But by the working of the sun's motion upon it in the quadrant p m, the same q r will be turned so much as makes another quarter of its whole conversion. When, therefore, the moon is in m, q r will be perpendicular to the strait line o m. By the same reason, when the moon is in n, q r will be parallel to the strait line m o; and, the moon returning to o, the same q r will return to its first place; and the body of the moon will in one entire period make also one entire conversion upon her own axis. In the making of which, it is manifest, that one and the same face of the moon is always turned towards the earth. And if any diameter were taken in that little circle, in which the moon were supposed to be carried about with simple motion, the same effect would follow; for if there were no action from the sun, every diameter of the moon would be carried about always parallel to itself. Wherefore I have given a possible cause why one and the same face of the moon is always turned towards the earth.

But it is to be noted, that when the moon is without the ecliptic, we do not always see the same face precisely. For we see only that part which is illuminated. But when the moon is without the ecliptic, that part which is towards us is not exactly the same with that which is illuminated.

10. To these three simple motions, one of the sun, another of the moon, and the third of the earth, in their own little circles f g h i, l k, and q r, together with the diurnal conversion of the earth, by which conversion all things that adhere to its superficies are necessarily carried about with it, may be referred the three phenomena concerning the tides of the ocean. Whereof the first is the alternate elevation and depression of the water at the shores, twice in the space of twenty-four hours and near upon fifty-two minutes; for so it has constantly continued in all ages. The second, that at the new and full moons, the elevations of the water are greater than at other times between. And the third, that when the sun is in the equinoctial, they are yet greater than at any other time. For the salving of which phenomena, we have already the four above-mentioned motions; to which I assume also this, that the part of the earth which is called America, being higher than the water, and extended almost the space of a whole semicircle from north to south, gives a stop to the motion of the water.

This being granted, in the same 4th figure, where l b k c is supposed to be in the plane of the moon's monthly motion, let the little circle l d k e be described about the same centre a in the plane of the equinoctial. This circle therefore will decline from the circle l b k c in an angle of almost 28½ degrees; for the greatest declination of the ecliptic is 23½, to which adding 5 for the greatest declination of the moon from the ecliptic, the sum will be 28½ degrees. Seeing now the waters, which are under the circle of the moon's course, are by reason of the earth's simple motion in the plane of the same circle moved together with the earth, that is to say, together with their own bottoms, neither outgoing nor outgone; if we add the diurnal motion, by which the other waters which are under the equinoctial are moved in the same order, and consider withal that the circles of the moon and of the equinoctial intersect one another; it will be manifest, that both those waters, which are under the circle of the moon, and under the equinoctial, will run together under the equinoctial; and consequently, that their motion will not only be swifter than the ground that carries them; but also that the waters themselves will have greater elevation whensoever the earth is in the equinoctial. Wherefore, whatsoever the cause of the tides may be, this may be the cause of their augmentation at that time.

Again, seeing I have supposed the moon to be carried about by the simple motion of the earth in the little circle l b k c; and demonstrated, at the 4th article of chapter XXI, that whatsoever is moved by a movent that hath simple motion, will be moved always with the same velocity; it follows, that the centre of the earth will be carried in the circumference l b k c with the same velocity with which the moon is carried in the circumference m n o p. Wherefore the time, in which the moon is carried about in m n o p, is to the time, in which the earth is carried about in l b k c, as one circumference to the other, that is, as a o to a k. But a o is observed to be to the semidiameter of the earth as 59 to 1; and therefore the earth, if a k be put for its semidiameter, will make fifty-nine revolutions in l b k c in the time that the moon makes one monthly circuit in m n o p. But the moon makes her monthly circuit in little more than twenty-nine days. Wherefore the earth shall make its circuit in the circumference l b k c in twelve hours and a little more, namely, about twenty-six minutes more; that is to say, it shall make two circuits in twenty-four hours and almost fifty-two minutes; which is observed to be the time between the high-water of one day and the high-water of the day following. Now the course of the waters being hindered by the southern part of America, their motion will be interrupted there; and consequently, they will be elevated in those places, and sink down again by their own weight, twice in the space of twenty-four hours and fifty-two minutes. And thus I have given a possible cause of the diurnal reciprocation of the ocean.

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.

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.

Vol. 1. Lat. & Eng. C. XXVI. Fig. 1-5 ]

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