+---------------------+---------+---------+----------+------------+ | | | | | IN | | | STRUVE. | ENCKE. | MEAN. | SEMI-DIAM. | | | | | | OF SATURN. | +---------------------+---------+---------+----------+------------+ | Equatorial radius | ´´ | ´´ | ´´ | | | of the planet | 8·9955 | | | | | Ext. semi-diameter | | | | | | of exterior ring | 20·047 | 20·2225 | 20·13475 | 2·23830 | | Int. semi-diameter | | | | | | of exterior ring | 17·644 | 18·0190 | 17·83150 | 1·98230 | | Ext. semi-diameter | | | | | | of interior ring | 17·237 | 17·3745 | 17·30575 | 1·92380 | | Int. semi diameter | | | | | | of interior ring | 13·334 | 13·3780 | 13·35600 | 1·48470 | | Breadth of interval | 00·407 | 00·6445 | 00·52575 | 0·05844 | +---------------------+---------+---------+----------+------------+ The period of a satellite revolving at the distance, 1·9238, the interior limit of the interval =10h. 50m. 16s. One-sixth of the period of Dione =10 56 53 One-third " Enceladus =10 59 22 One-half " Mimas =11 18 32 One-fourth " Tethys =11 19 36 And the period of a satellite at the distance, 1·9823, the exterior limit of the interval =11 28 3 The interval, therefore, occupies precisely the space in which the periods would be commensurable with those of the four members of the system immediately exterior. Particles occupying this portion of the _primitive_ ring would always come into conjunction with one of these satellites in the same parts of their orbits. Such orbits would become more and more eccentric until the matter moving in them would unite near one of the apsides with other portions of the ring. _We have thus a physical cause for the existence of this remarkable interval._ CHAPTER XIII. THE ASTEROID RING BETWEEN MARS AND JUPITER.