10 ORBITS OF THE PLANETS. SECT. II. 



of the ecliptic, its latitude 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 lati- 

 tude of a planet cannot be obtained by direct observa- 

 tion, but are deduced from observations made at the 

 surface of the earth, by a very simple computation. 

 These two quantities, 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 determina- 

 tion of its elliptical motion, the nature and position of its 

 orbit must be ascertained by observation. This depends 

 upon seven quantities, called the elements of the ortyt 

 (N. 57). These are, the length of the major axis, and 

 the eccentricity, 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 perihelion ; the 

 inclination of the orbit to the plane of the ecliptic, and 

 the longitude of its ascending node ; these give the po- 

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

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

 longitude 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 as- 

 certaining all the circumstances 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 center of the sun (N. 58). The 

 orbits of the recently discovered planets deviate 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. 



Were the planets attracted by the sun only, they 

 would always move in ellipses, invariable in form and 

 position ; and because his action is proportional to his 



