TABLE I.—The Satellites of Saturn.
| Name. | Sidereal Revolution. | Mean Apparent Distance. | |||
|---|---|---|---|---|---|
| d. | h. | m. | s. | ″ | |
| Mimas | 0 | 22 | 37 | 22·9 | 26·78 |
| Enceladus | 1 | 8 | 53 | 6·7 | 34·38 |
| Tethys | 1 | 21 | 18 | 25·7 | 42·57 |
| Dione | 2 | 17 | 41 | 8·9 | 54·54 |
| Rhea | 4 | 12 | 25 | 10·8 | 76·16 |
| Titan | 15 | 22 | 41 | 25·2 | 176·55 |
| Hyperion | 22 | 12? | 213·3? | ||
| Japetus | 79 | 7 | 53 | 40·4 | 514·52 |
The late Professor Bessel devoted much attention to the theory of Titan, whose mean distance he found to be 20·706 equatorial radii of the primary. Struve's measurements of the ring are given in the second column of the following table. Sir John Herschel, however, regards the Russian astronomer's interval between the rings as "somewhat too small."[29] This remark is confirmed by the measurements of Encke, whose results are given in column third. The fourth contains the mean of Struve's and Encke's measurements; and the fifth, the same, expressed in equatorial radii of Saturn.
TABLE II.—The Rings of Saturn.
| Struve. | Encke. | Mean. | In 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 of the period of Enceladus | =10 | 59 | 22 |
| One-half of the period of Mimas | =11 | 18 | 32 |
| One-fourth of the period of 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.