23. SUPPOSE in the first place, the line, in which the two planes intersect each other, to be perpendicular to the line which joins the earth and sun. Let T (in fig. 98, 99, 100, 101.) represent the earth; S the sun; the plane of this scheme the plane of the earth’s motion, in which both the sun and earth are placed. Let A C be perpendicular to S T, which joins the earth and sun; and let the line A C be that, in which the plane of the moon’s orbit intersects the plane of the earth’s motion. To the center T describe in the plane of the earth’s motion the circle A B C D. And in the plane of the moon’s orbit describe the circle A E C F, one half of which A E C will be elevated above the plane of this scheme, the other half A F C as much depressed below it.
24. NOW suppose the moon to set forth from the point A (in fig. 98.) in the direction of the plane A E C. Here she will be continually drawn out of this plane by the action of the sun: for this plane A E C, if extended, will not pass through the sun, but above it; so that the sun, by drawing the moon directly toward it self, will force it continually more and more from that plane towards the plane of the earth’s motion, in which it self is; causing it to describe the line A K G H I, which will be convex to the plane A E C, and concave to the plane of the earth’s motion. But here this power of the sun, which is said to draw the moon toward the plane of the earth’s motion, must be understood principally of so much only of the sun’s action upon the moon, as it exceeds the action of the same upon the earth. For suppose the preceding figure to be viewed by the eye, placed in the plane of that scheme, and in the line C T A on the side of A, the plane A B C D will appear as the straight line D T B, (in fig. 102.) and the plane A E C F as another straight line F E; and the curve line A K G H I under the form of the line T K G H I.
Now it is plain, that the earth and moon being both attracted by the sun, if the sun’s action upon both was equally strong, the earth T, and with it the plane A E C F or line F T E in this scheme, would be carried toward the sun with as great a pace as the moon, and therefore the moon not drawn out of it by the sun’s action, excepting only from the small obliquity of the direction of this action upon the moon to that of the sun’s action upon the earth, which arises from the moon’s being out of the plane of the earth’s motion, and is not very considerable; but the action of the sun upon the moon being greater than upon the earth, all the time the moon is nearer to the sun than the earth is, it will be drawn from the plane A E C or the line T E by that excess, and made to describe the curve line A G I or T G I. But it is the custom of astronomers, instead of considering the moon as moving in such a curve line, to refer its motion continually to the plane, which touches the true line wherein it moves, at the point where at any time the moon is. Thus when the moon is in the point A, its motion is considered as being in the plane A E C, in whose direction it then essaies to move; and when in the point K (in fig. 99.) its motion is referred to the plane, which passes through the earth, and touches the line A K G H I in the point K. Thus the moon in passing from A to I will continually change the plane of her motion. In what manner this change proceeds, I shall now particularly explain.