46. In these situations of the globe of earth a line drawn from the sun to the center of the earth will be obliquely inclined toward the axis F G. Now suppose, that such a line drawn from the sun to the center of the earth, when in C or E, would be perpendicular to the axis F G; in which cases the sun will shine perpendicularly upon the equator, and consequently the line drawn from the center of the earth to the sun will cross the equator, as it passes through the surface of the earth; whereas in all other situations of the globe this line will pass through the surface of the globe at a distance from the equator either northward or southward. Now in both these cases half the circle O P will be in the light, and half in the dark; and therefore to every place in this circle the day will be equal to the night. Thus it appears, that in these two opposite situations of the earth the day is equal to the night in all parts of the globe; but in all other situations this equality will only be found in places situated in the very middle between the poles, that is, on the equator.
47. The times, wherein this universal equality between the day and night happens, are called the equinoxes. Now it has been long observed by astronomers, that after the earth hath set out from either equinox, suppose from E (which will be the spring equinox, if F be the north pole) the same equinox shall again return a little before the earth has made a compleat revolution round the sun. This return of the equinox preceding the intire revolution of the earth is called the precession of the equinox, and is caused by the protuberant figure of the earth.
49. Since the sun shines perpendicularly upon the equator, when the line drawn from the sun to the center of the earth is perpendicular to the earth’s axis, in this case the plane, which should cut through the earth at the equator, may be extended to pass through the sun; but it will not do so in any other position of the earth. Now let us consider the prominent part of the earth about the equator, as a solid ring moving with the earth round the sun. At the time of the equinoxes, this ring will have the same kind of situation in respect of the sun, as the orbit of the moon has, when the line of the nodes is directed to the sun; and at all other times will resemble the moon’s orbit in other situations. Consequently this ring, which otherwise would keep throughout its motion parallel to it self, will receive some change in its position from the action of the sun upon it, except only at the time of the equinox. The manner of this change may be understood as follows. Let A B C D (in fig. 120) represent this ring, E the center of the earth, S the sun, A F C G a circle described in the plane of the earth’s motion to the center E. Here A and C are the two points, in which the earth’s equator crosses the plane of the earth’s motion; and the time of the equinox falls out, when the straight line A C continued would pass through the sun. Now let us recollect what was said above concerning the moon, when her orbit was in the same situation with this ring. From thence it will be understood, if a body were supposed to be moving in any part of this circle A B C D, what effect the action of the sun on the body would have toward changing the position of the line A C. In particular H I being drawn perpendicular to S E, if the body be in any part of this circle between A and H, or between C and I, the line A C would be so turned, that the point A shall move toward B, and the point C toward D; but if it were in any other part of the circle, either between H and C, or between I and A, the line A C would be turned the contrary way. Hence it follows, that as this solid ring turns round the center of the earth, the parts of this ring between A and H, and between C and I, are so influenced by the sun, that they will endeavour, so to change the situation of the line A C as to cause the point A to move toward B, and the point C to move toward D; but all the parts of the ring between H and C, and between I and A, will have the opposite tendency, and dispose the line A C to move the contrary way. And since these last named parts are larger than the other, they will prevail over the other, so that by the action of the sun upon this ring, the line A C will be so turned, that A shall continually be more and more moving toward D, and C toward B. Thus no sooner shall the sun in its visible motion have departed from A, but the motion of the line A C shall hasten its meeting with C, and from thence the motion of this line shall again hasten the sun’s second conjunction with A; for as this line so turns, that A is continually moving toward D, so the sun’s visible motion is the same way as from S toward T.
49. The moon will have on this ring the like effect as the sun, and operate on it more strongly, in the same proportion as its force on the sea exceeded that of the sun on the same. But the effect of the action of both luminaries will be greatly diminished by reason of this ring’s being connected to the rest of the earth; for by this means the sun and moon have not only this ring to move, but likewise the whole globe of the earth, upon whose spherical part they have no immediate influence. Beside the effect is also rendred less, by reason that the prominent part of the earth is not collected all under the equator, but spreads gradually from thence toward both poles. Upon the whole, though the sun alone carries the nodes of the moon through an intire revolution in about 19 years, the united force of both luminaries on the prominent parts of the earth will hardly carry round the equinox in a less space of time than 26000 years.
[50.] To this motion of the equinox we must add another consequence of this action of the sun and moon upon the elevated parts of the earth, that this annular part of the earth about the equator, and consequently the earth’s axis, will twice a year and twice a month change its inclination to the plane of the earth’s motion, and be again restored, just as the inclination of the moon’s orbit by the action of the sun is annually twice diminished, and as often recovers its original magnitude. But this change is very insensible.
[51.] I shall now finish the present chapter with our great author’s inquiry into the figure of the secondary planets, particularly of our moon, upon the figure of which its fluid parts will have an influence. The moon turns always the same side towards the earth, and consequently revolves but once round its axis in the space of an entire month; for a spectator placed without the circle, in which the moon moves, would in that time observe all the parts of the moon successively to pass once before his view and no more, that is, that the whole globe of the moon has turned once round. Now the great slowness of this motion will render the centrifugal force of the parts of the waters very weak, so that the figure of the moon cannot, as in the earth, be much affected by this revolution upon its axis: but the figure of those waters are made different from spherical by another cause, viz. the action of the earth upon them; by which they will be reduced to an oblong oval form, whose axis prolonged would pass through the earth; for the same reason, as we have above observed, that the waters of the earth would take the like figure, if they had moved so slowly, as to keep pace with the moon. And the solid part of the moon must correspond with this figure of the fluid part: but this elevation of the parts of the moon is nothing near so great as is the protuberance of the earth at the equator, for it will not exceed 93 english feet.
52. The waters of the moon will have no tide, except what will arise from the motion of the moon round the earth. For the conversion of the moon about her axis is equable, whereby the inequality in the motion round the earth discovers to us at some times small parts of the moon’s surface towards the east or west, which at other times lie hid; and as the axis, whereon the moon turns, is oblique to her motion round the earth, sometimes small parts of her surface toward the north, and sometimes the like toward the south are visible, which at other times are out of sight. These appearances make what is called the libration of the moon, discovered by Hevelius. But now as the axis of the oval figure of the waters will he pointed towards the earth, there must arise from hence some fluctuation in them; and beside, by the change of the moon’s distance from the earth, they will not always have the very same height.
