324 LAPLACE. 



established with complete evidence that the planetary 

 ellipses are perpetually variable ; that the extremities of 

 their major axes make the tour of the heavens ; that, in- 

 dependently of an oscillatory motion, the planes of their 

 orbits experienced a displacement in virtue of which 

 their intersections with the plane of the terrestrial orbit 

 are each year directed towards different stars. In the 

 midst of this apparent chaos there is one element which 

 remains constant or is merely subject to small periodic 

 changes ; namely, the major axis of each orbit, and con- 

 sequently the time of revolution of each planet. This is 

 the element which ought to have chiefly varied, accord- 

 ing to the learned speculations of Newton and Euler. 



The principle of universal gravitation suffices for pre- 

 serving the stability of the solar system. It maintains 

 the forms and inclinations of the orbits in a mean con- 

 dition which is subject to slight oscillations ; variety does 

 not entail disorder ; the universe offers the example of 

 harmonious relations, of a state of perfection which New- 

 ton himself doubted. This depends on circumstances 

 which calculation disclosed to Laplace, and which, upon 

 a superficial view of the subject, would not seem to be 

 capable of exercising so great an influence. Instead of 

 planets revolving all in the same direction in slightly 

 eccentric orbits, and in planes inclined at small angles 

 towards each other, substitute different conditions and 

 the stability of the universe will again be put in jeopardy, 

 and according to all probability there will result a fright- 

 ful chaos.* 



* The researches on the secular variations of the eccentricities and 

 inclinations of the planetary orbits depend upon the solution of an 

 algebraic equation equal in degree to the number of planets whose 

 mutual action is considered, and the coefficients of which involve the 

 values of the masses of those bodies. It may be shown that if the 



