SEQUEL TO THE EPOCH OF NEWTON. 445 



Thus the secular inequalities of the celestial motions, like all the 

 others, confirm the law of universal gravitation. They are called " sec- 

 ular," because ages are requisite to unfold their existence, and because 

 they are not obviously periodical. They might, in some measure, be 

 considered as extensions of the Newtonian theory, for though Newton's 

 law accounts for such facts, he did not, so far as we know, foresee such 

 a result of it. But on the other hand, they are exactly of the same 

 nature as those which he did foresee and calculate. And when we 

 call them secular, in opposition to periodical, it is not that there is any 

 real difference, for they, too, have their cycle ; but it is that we have 

 assumed our mean motion without allowing for these long inequalities. 

 And thus, as Laplace observes on this very occasion, 30 the lot of this 

 great discovery of gravitation is no less than this, that every apparent 

 exception becomes a proof, every difficulty a new occasion of a triumph. 

 And such, as he truly adds, is the character of a true theory, — of a 

 real representation of nature. 



It is impossible for us here to enumerate even the principal objects 

 which have thus filled the triumphal march of the Newtonian theory 

 from its outset up to the present time. But among these secular 

 changes, w r e may mention the Diminution of the Obliquity of the Eclip- 

 tic, which has been going on from the earliest times to the present. 

 This change has been explained by theory, and shown to have, like all 

 the other changes of the system, a limit, after which the diminution 

 will be converted into an increase. 



We may mention here some subjects of a kind somewhat different 

 from those just spoken of. The true theoretical quantity of the Pre- 

 cession of the Equinoxes, which had been erroneously calculated by 

 Newton, was shown by D'Alembert to agree with observation. The 

 constant coincidence of the Nodes of the Moon's Equator with those 

 of her Orbit, was proved to result from mechanical principles by La- 

 grange. The curious circumstance that the Time of the Moon's rota- 

 tion on her axis is equal to the Time of her revolution about the earth, 

 was shown to be consistent with the results of the laws of motion by 

 Laplace. Laplace also, as we have seen, explained certain remarkable 

 relations which constantly connect the longitudes of the three fhst 

 satellites of Jupiter ; Bailly and Lagrange analyzed and explained the 

 curious librations of the nodes and inclinations of their orbits ; and 

 Laplace traced the effect of Jupiter's oblate figure on their motions, 



30 Sysl. du Monde, 8vo, ii. 37. 



