12 CEBITS OF THE PLANETS. [SECT. n. 



is zero: it is then said to be in its nodes (N". 55). The 

 ascending node is that point in the ecliptic through which 

 the planet passes, in going from the southern to the northern 

 hemisphere. The descending node is a corresponding point 

 in the plane of the ecliptic diametrically opposite to the 

 other, through which the planet descends in going from the 

 northern to the southern hemisphere. The longitude and 

 latitude of a planet cannot be obtained by direct observation, 

 but are deduced from observations made at the surface of 

 the earth, by a very simple computation. These two quan- 

 tities, however, will not give the place of a planet in space. 

 Its distance from the sun (N. 56) must also be known ; and, 

 for the complete determination of its elliptical motion, the 

 nature and position of its orbit must be ascertained by ob- 

 servation. This depends upon seven quantities, called the 

 elements of the orbit (N. 57). These are, the length of 

 the major axis, and the excentricity, which determine the 

 form of the orbit ; the longitude of the planet when at its 

 least distance from the sun, called the longitude of the peri- 

 helion ; the inclination of the orbit to the plane of the ecliptic, 

 and the longitude of its ascending node ; these give the posi- 

 tion of the orbit in space ; but the periodic time, and the 

 longitude of the planet at a given instant, called the longi- 

 tude of the epoch, are necessary for finding the place of the 

 body in its orbit at all times. A perfect knowledge of these 

 seven elements is requisite for ascertaining all the circum- 

 stances of undisturbed elliptical motion. By such means it 

 is found, that 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 

 (N. 58). The orbits of the recently discovered planets de- 

 viate more from the ecliptic than those of the ancient planets : 

 that of Pallas, for instance, has an inclination of 34 37' 50'2" 

 to it ; on which account it is more difficult to determine their 

 motions. 



