Page:The Solar System - Six Lectures - Lowell.djvu/99



whose period is $$\textstyle \frac {1}{2}$$ that of Mimas. This distance falls almost exactly in the centre of Cassini's division.

Proceeding to the next simplest ratio, $$\textstyle \frac{1}{3}$$ of Mimas's period, the corresponding distance comes out 56,170 miles. This is the distance from the centre of the planet to the inner edge of ring B.

Again, $$\textstyle \frac{1}{4}$$ of the period of Mimas gives 46,370 miles. This is not far from the radius of the inner edge of the dark ring. So much for the action of Mimas.

The major axis of one half the period of Enceladus falls without the system, but the major axis of one third the period occurs at 72,090 miles. This is not far from the inner edge of Cassini's division. But the striking coincidence with Enceladus is that the distance corresponding to $$\textstyle \frac {2}{5}$$ of his period lies at 81,400 miles, or at Encke's division.

For Tethys, the only commensurable ratio is $$\textstyle \frac{1}{4}$$. To Tethys. This makes the distance fall at Cassini's division.

Thus Mimas, aided by Tethys, has been the divider of the rings into A, B, and C ; while Enceladus has subdivided A.

Not less interesting mechanically is Saturn's satellite system. Eight of these bodies are positively known, distanced from Saturn and diametered as follows :—