SCT. IL ELLIPTICAL MOTION. 9 



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 equi- 

 nox (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 ap- 

 parent path of the sun, in two. points diametrically oppo- 

 site 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 lon- 

 gitude (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 center 

 (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 eccentricity (N. 52) of the orbit ; so that the place 

 of a planet in its elliptical orbit is obtained, by adding or 

 subtracting the equation of the center to or from its 

 mean longitude. 



The orbits of the planets have a very small obliquity 

 or inclination (N. 53) 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 angular distance of a planet 

 from the plane of the ecliptic is its latitude (N. 54) ; 

 which is south or north, according as the planet is south 

 or north of that plane. When the planet 10 in the plane 



