its mean distance, the motion would be uniform, and the periodic time unaltered, because the planet would arrive at the apsides or extremities of the major axis at the same instant, and would have the same velocity, whether it moved in the circular or elliptical orbit, since the curves coincide in these points; but, in every other part, the elliptical motion would either be faster or slower than the circular or mean motion. The difference between the two is called the equation of the centre, which consequently vanishes at the apsides, and is at its maximum ninety degrees distant from these points, or in quadratures, where it measures the eccentricity of the orbit, so that the place of a planet in its elliptical orbit is obtained by adding or subtracting the equation of the centre to or from its mean motion.
The orbits of the planets have a very small inclination to the plane of the ecliptic in which the earth moves; and, on that account, astronomers refer their motions to this plane at a given epoch as a known and fixed position. The paths of the planets, when their mutual disturbances are omitted, are ellipses, nearly approaching to circles, whose planes, slightly inclined to the ecliptic, cut it in straight lines passing through the centre of the sun; the points where an orbit intersects the plane of the ecliptic are its nodes. The ascending node of the
