NOTES. 



469 



NOTE 66, pp. 19, ib., 20. In fig. 15 the central force is greater than the exact law 

 of gravity; therefore the curvature Ppa is greater than Pp A the real ellipse ; 

 hence the planet p comes to the point a, called the aphelion, sooner than if 

 it moved in the orbit PpA, which makes the line PSA advance to a. In 



Fig. 15. 



. 16. 



fig. 16, on the contrary, the curvature Ppa is less than in the true ellipse, so 

 that the planet p must move through more than the arc PpA, or 180<> before it 

 comes to the aphelion a, which causes the greater axis P S A to recede to o. 



NOTE 67, pp. 19, 20. 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 P'SA', 

 P"S A", &c., till by this direct motion it 

 has accomplished a revolution, and then 

 it begins again ; so that the motion is per- 

 petual. 



NOTE 68, p. 19. Sidereal revolution. The 

 consecutive return of an object to the same 

 star. 



fit- 17. 



\ 



NOTE 69, p. 19. Tropical revolution. The consecutive return of an object to 

 the same tropic or equinox. 



NOTE 70, p. 20. The orbit only bulges, #c. 

 In fig. 18 the effect of the variation in the 

 excentricity is shown where PpA is the el- 

 liptical orbit at any given instant; after a 

 time it will take the form Pj/ A, in conse- 

 quence of the decrease in the excentricity 

 CS; then the forms Pp"A, Pp"'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. 



NOTE 21, pp. 21, 22. The ecliptic is the apparent path of the sun in the 

 heavens. See Note 46. 



