Let A, B, C, Fig. 62, page 294, represent the earth in different positions in its orbit, M, a superior planet, as Mars, and N R, an arc of the concave sphere of the heavens. First, suppose the planet to remain at rest in M, and let us see what apparent motions it will receive from the real motions of the earth. When the earth is at B, it will see the planet in the heavens at N; and as the earth moves successively through C, D, E, F, the planet will appear to move through O, P, Q, R. B and F are the two points of greatest elongation of the earth from the sun, as seen from the planet; hence, between these two points, while passing through its orbit most remote from the planet, (when the planet is seen in superior conjunction,) the earth, by its own motion, gives an apparent motion to the planet in the order of the signs; that is, the _apparent_ motion given by the _real_ motion of the earth is _direct_. But in passing from F to B through A, when the planet is seen in opposition, the apparent motion given to the planet by the earth's motion is from R to N, and is therefore _retrograde_. As the arc described by the earth, when the motion is direct, is much greater than when the motion is retrograde, while the apparent arc of the heavens described by the planet from N to R, in the one case, and from R to N, in the other, is the same in both cases, the retrograde motion is much swifter than the direct, being performed in much less time. [Illustration Fig. 62.] But the superior planets are not in fact at rest, as we have supposed, but are all the while moving eastward, though with a slower motion than the earth. Indeed, with respect to the remotest planets, as Saturn and Uranus, the forward motion is so exceedingly slow, that the above representation is nearly true for a single year. Still, the effect of the real motions of all the superior planets, eastward, is to increase the direct apparent motion communicated by the earth, and to diminish the retrograde motion. This will be evident from inspecting the figure; for if the planet _actually_ moves eastward while it is _apparently_ carried eastward by the earth's motion, the whole motion eastward will be equal to the sum of the two; and if, while it is really moving eastward, it is apparently carried westward still more by the earth's motion, the retrograde movement will equal the difference of the two.