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 
