| Saturn and its System | 91 |
force. Now this could be true, either because the force had a restraining effect to this end, or because it had no effect upon the inclination at all. Laplace jumped to the conclusion that the first was the case, for he tells us, apropos of Saturn and his next to outer satellite, that we see “that Saturn's action can retain this satellite in very nearly the same plane; and much more so those satellites which are inferior to it, as well as the rings.”[1]
He made the mistake of post hoc ergo propter hoc. Tisserand is more guarded when he says: “Ainsi, l'inclinaison de l'orbite d'un satellite sur l'anneau demeure constante et toujours très petite si elle l'a été seulement à un moment donné.” This is so; but it is true, not because the force has an effect upon the inclination, but precisely because it has none. The spherical ellipse found by Tisserand, t. iv., ch. vi., to represent the change of inclination in the case of the satellites of Saturn, is the curve of the combined precessions due to each of the perturbing forces, the equatorial protuberance, the ring, the sun, and the other satellites.
Effect of tidal crest.Impotent on the inclination as the equatorial protuberance is, there is another protuberance which is not so impotent. For consider what effect the tide-raising force of an outside body would have upon the plastic matter of another rotating in a plane tilted to the orbital plane of the first. As we saw in Chapter II., the effect would be to raise two bosses or ansæ in the equatorial
- ↑ See Laplace, Book IV., § 26. At the time, Hyperion was undiscovered and the “next to outer satellite” in consequence different.
