The rings have usually been considered to be flat. At the time of their disappearance, however, knots have been seen upon them. It is as if their filament had suddenly been strung with beads. At the last occurrence of the sort in 1907, these beads were particularly well seen at several observatories, and were critically studied at Flagstaff. In connection with a new phenomenon detected there, that of a dark core in the shadow the rings threw across the planet’s face, an explanation suggested itself to account for both them and it: to wit, that the rings were not really flat, but tores; rings, that is, like an anchor ring, any cross-section of which would be of the nature of an oval flattened on its inner side. The cogency of the explanation consisted in its solution not only of the appearances but of the cause competent to bring those appearances about. For measurement showed that the knots were permanent in position, which, since the ring revolved, indicated that they extended all round it in spite of their not seeming to do so, and that their distances from Saturn were just what this cause should produce. The action observed was a corollary from the important principle of commensurability of orbital period. As we saw in the case of the asteroids, if two bodies be travelling round a third and their respective periods of revolution be commensurate, they will constantly meet one another in such a manner that great perturbation will ensue and the bodies be thrown out of commensurability of period. What has happened to the asteroids has likewise occurred in Saturn’s rings. The disturber in this case has been, not Jupiter, as with them, but one or other of Saturn’s own satellites. For when we calculate the problem, we find that Mimas, Enceladus, and Tethys have periods exactly commensurate with the divisions of the rings; in other words, these three inner satellites, whose action because of proximity is the greatest, have fashioned the rings into the three parts we know, called A, the outermost; B, the middle one; and C, the crêpe ring, nearest to the body of the planet. Mimas has been the chief actor, though helped by the two others, while Enceladus has further subdivided ring A by what is known as Encke’s division. Such has been the chief action of the satellites on the rings: it has made them into the system we see. But if we consider the matter, we shall realize that a secondary result must have ensued—when we remember that the particles composing the rings must be very crowded for the rings to show as bright as they do, and also that, though relatively thin, the rings are nevertheless some eighty miles through.