A. MATHEMATICS AND ASTRONOMY. 39 



the problem; but, aside from any considerations connected 

 with the immediate needs of practical astronomy, the study 

 of the secular inequalities is one of the most interesting and 

 important departments of the science, because their indefinite 

 continuance in the same direction would ultimately seriously 

 affect the stability of the planetary system. Lagrange and 

 Laplace have, however, shown that the secular inequalities 

 are themselves periodic, requiring many centuries in which 

 to complete their cycles. The exact computation of these 

 inequalities has been undertaken, both by the former astron- 

 omers and by Pontecoulant, and subsequently with greater 

 accuracy by Le Verrier. But Stockwell has approached the 

 problem with the advantage of the most recent discoveries 

 in astronomy and accurate knowledge of the motions of the 

 planets, and has given to the whole work of computation a 

 system such that it is now possible to determine the secular 

 variations of the planetary elements with less labor, perhaps, 

 than would answer for the accurate determination of a com- 

 et's orbit, which latter is a matter of perhaps ten hours' com- 

 putation. Stockwell has computed anew, with the utmost 

 accuracy, the numerical values of the secular changes of the 

 elements of all the known planets. Li reference to the earth 

 and its orbit, he says: "The secular motions w^hich take 

 place in the case of the spherical earth are so modified by the 

 actual condition of the terrestrial globe, that changes in the 

 position of the equinox and equator are now produced in a 

 few centuries that would otherwise require a period of many 

 thousand years." This consideration is of much importance 

 in the investigation of the reputed antiquity and chronology 

 of those ancient nations which attained some proficiency in 

 the science of astronomy, and the records of whose astronom- 

 ical labors are the only remaining monuments of a highly in- 

 tellectual people, of whose existence every trace has long 

 since passed away. 



The grand problem which yet remains to be solved is thus 

 clearly stated by Stockwell : A system of bodies moving in 

 eccentric orbits is manifestly one of stability ; on the other 

 hand, a system of bodies moving in circular orbits is one of 

 unstable equilibrium. It would seem, then, that between 

 the two supposed conditions a system might exist which 

 possesses a greater degree of stability than either, the idea 



