RECENT RESEARCHES ©X TME SECULAR VARIATIONS OF THE PLANETARY 



ORBlTSr 



Bv John N. Stockwell. 



The reciprocal gravitatiou of matter produces disturbaiicea in tlie 

 motions of tlie heavenly bodie.Sj cansing them to deviate from the elliptic 

 paths which they would follow, if they were attracted only by tlie sun. 

 The determination of the amount by which the actual place of a planet 

 deviates from its true elliptic place at any time is called the problem 

 of planetary perturbation. The analytical solution of this problem has 

 disclosed to mathematicians the fact that the inequalities in the motions 

 of the heavenly bodies are produced in two distinct ways. Tlie first 

 is a direct disturbance in the elliptic motion of the body; and ilia 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, xiz : 

 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 inequalities in the planetary motions which are produced by the 

 direct action of the planets on each other, and depend for their amount 

 only on their distances and mutual configurations, are culled periodic 

 ineqmditics, because they pass through a complete cycle of values in a 

 comparatively short period of time; while those depending on the varia- 

 tion of the elements of the elliptic motion are produced with extreme slow- 

 ness, and require an immense number of ages for their full develo[)ment, 

 are called secular inequalities. The general theory of all the planetary 

 inequalities was completely developed by La Grange and La Place, 

 nearly a century ago; and the particular theory of each planet for the 

 periodic inequalities was given by La Place in the Mecanique Celeste. 



The determination of the periodic inecpialities of the planets has hith- 

 erto received more attention from astronomers than has been bestowed 

 upon the secular inequalities. This is owing in part to the immediate 

 re(iuirements of astronomy, and also in part to the less intricnte nature 

 of the jiroblem. It is true that an approximate knowledge of the secu- 

 lar inequalities is necessary in the treatment of the periodic inequalities ; 

 but since the secular inequalities are produced with such extreme slow- 

 ness, most astronomers have been content with the sn])position that 

 they are developed uniformly with the time. This supposition is sufii- 



* lutroductiou to ti luumoir to be puljlished in the " SDiithsouiiin Coiitributious to 

 Kuowled"'e." 



