Page:In the high heavens.djvu/225

 have invented the methods by which the nature of the solar system could be studied. The results at which they arrived are not a little remarkable. They have computed how much the planets act and react upon each other, and they have shown that in consequence of these actions the orbit of each planet gradually changes its shape and its position. But the crowning feature of these discoveries is the demonstration that these changes in the orbits of the planets are all periodic. The orbits may fluctuate, but those fluctuations are confined within very narrow limits. In the course of ages the system gradually becomes deformed, but it will gradually return again to its original position, and again depart therefrom. These changes are comparatively so small that our system may be regarded as substantially the same even when its fluctuations have attained their greatest amplitude. These splendid discoveries are founded upon the actual circumstances of the system, as we see that system to be constituted.

Take, for instance, the eccentricities of the orbits of the planets around the sun. Those eccentricities can never change much; they are now small quantities, and small quantities those eccentricities must for ever remain. The proof of this remarkable theorem partly depends upon the fact that the planets are all revolving around the sun in the same direction. If one of the planets we have named were revolving in an opposite direction to the rest, the mathematical theory would break down. We should have no guarantee that the eccentricities would for ever remain small, as they are at present. In a similar manner, the planets all move in orbits whose planes are inclined to each other at very small angles. The positions of