584 The Sniitksoman Institution 



VARIATIONS OF THE ORBITS OF EIGHT PLANETS 



The following summaries from the paper ^ itself will give an 

 idea of its scope and of some of its principal results. 



The reciprocal gravitation of matter produces disturbances 

 in the motion of the heavenly bodies, causing them to deviate 

 from the elliptic paths they would follow if they were attracted 

 only by the sun. 



The inequalities in the motions of the heavenly bodies are 

 produced in two distinct ways. The first is a direct disturb- 

 ance in the elliptic motion of the body, and the second is 

 produced by reason of a variation of the elements of its elliptic 

 motion. The elements of the elliptic motion of a planet are 

 six in number — viz., the mean motion of the planet and its 

 mean distance from the sun, the eccentricity and inclination 

 of its orbit, and the longitude of the node and perihelion. 

 The first two are invariable ; the other four are subject to 

 both periodic and secular variations. The periodic inequali- 

 ties pass through a complete cycle of values in a compara- 

 tively short period of time ; while the secular inequalities 

 are produced with extreme slowness. The general theory 

 of all the planetary inequalities was completely developed by 

 Lagrange and Laplace nearly a century ago. Owing to the 

 immediate requirements of astronomy, more attention has 

 been bestowed upon the periodic than on the secular inequali- 



1 Stockwell, John N.,"The Secular Vari- and right ascension," 1872, in Volume xviii 

 aliens of the Elements of the Orbits of tlie of the " Smithsonian Contributions to Know- 

 Eight Principal Planets, Mercury, Venus, the ledge." The expense of printing this paper 

 Earth, Mars, Jupiter, Saturn, Uranus, and was met by the gift of $1200 from Mr. Leon- 

 Neptune, with tables of the same ; together hard Case of Cleveland, Ohio, who preferred 

 with the obliquity of the ecliptic and the pre- at that time that his name should not be 

 cession of the equinoxes in both longitude mentioned. 



