SECT, ii.] ELLIPTICAL MOTION. 1 1 



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 ter- 

 restrial 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, esti- 

 mated 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 dif- 

 ference between the two is called the equation of the centre 

 (K 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 qua- 

 dratures (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. 



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 is in the plane of the ecliptic, its latitude. 



