Fig. 16.
Note 67, pp. [16], [17]. Motion of apsides. Let P S A, fig. 17, be the position of the elliptical orbit of a planet, at any time; then, by the action of the disturbing forces, it successively takes the position Pʹ S Aʹ, Pʺ S Aʺ, &c., till by this direct motion it has accomplished a revolution, and then it begins again; so that the motion is perpetual.
Fig. 17.
Note 68, [p. 17]. Sidereal revolution. The consecutive return of an object to the same star.
Note 69, [p. 17]. Tropical revolution. The consecutive return of an object to the same tropic or equinox.
Note 70, [p. 17]. The orbit only bulges, &c. In fig. 18 the effect of the variation in the excentricity is shown where P p A is the elliptical orbit at any given instant; after a time it will take the form P pʹ A, in consequence of the decrease in the excentricity C S; then the forms P pʺ A, P pʹʹʹ A, &c., consecutively from the same cause; and, as the major axis P A always retains the same length, the orbit approaches more and more nearly to the circular form. But, after this has gone on for some thousands of years, the orbit contracts again, and becomes more and more elliptical.
Fig. 18.