The mean distance of a planet from the sun is equal to half the major axis (N. 42) of its orbit: if, therefore, the planet described a circle (N. 43) round the sun at its mean distance, the motion would be uniform, and the periodic time unaltered, because the planet would arrive at the 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, or true motion (N. 44), would either be faster or slower than the circular or mean motion (N. 45). As it is necessary to have some fixed point in the heavens from whence to estimate these motions, the vernal equinox (N. 46) at a given epoch has been chosen. The equinoctial, which is a great circle traced in the starry heavens by the imaginary extension of the plane of the terrestrial equator, is intersected by the ecliptic, or apparent path of the sun, in two points diametrically opposite to one another, called the vernal and autumnal equinoxes. The vernal equinox is the point through which the sun passes in going from the southern to the northern hemisphere; and the autumnal, that in which he crosses from the northern to the southern. The mean or circular motion of a body, estimated from the vernal equinox, is its mean longitude; and its elliptical, or true motion, reckoned from that point, is its true longitude (N. 47): both being estimated from west to east, the direction in which the bodies move. The difference between the two is called the equation of the centre (N. 48); which consequently vanishes at the apsides (N. 49), or extremities of the major axis, and is at its maximum ninety degrees (N. 50) distant from these points, or in quadratures (N. 51), where it measures the excentricity (N. 52) of the orbit; so that the place of the planet in its elliptical orbit is obtained by adding or subtracting the equation of the centre to or from its mean longitude.