Comets appear in all regions of the heavens–Effects of parallax–Apparent motion of a comet, in opposition and in perihelion, moving in a direction opposite to the earth–Hypothetical comet of Lacaille; calculations of Lacaille and Olbers concerning the maximum relative movement of this hypothetical comet and the earth.

The orbits which the planets describe about the sun are not circles, but oval curves, termed ellipses; these ellipses differ but little from circles; that is to say, their eccentricities are small. Moreover, the planes of the orbits in which they move are inclined at small angles to the plane of the ecliptic. Hence it follows that their apparent paths are confined to a comparatively narrow zone of the heavens, which zone is called the zodiac. If we imagine these curves pressed down, as it were, upon the ecliptic they will appear as nearly concentric circles described about the sun, and so disposed as not to intersect each other. The distances of the earth and of each of the planets vary according to the position occupied by these bodies in their respective orbits; but these variations are confined within very narrow limits, and hence it follows that the velocities of the planets change so slightly that the difference is all but imperceptible. The mean diurnal motion of Mercury, which of all the planets moves the most rapidly, amounts to only 4°5′