The cause why the moon hath always one and the same face turned towards the earth.
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.
The cause of the tides of the ocean.
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[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.