Numerical calculations, where they are practicable, afford the only safe guide to this intricate field of inquiry. It does not suffice to show that tidal action would have been of the kind required--would have taken the right direction--for bringing about some apparently anomalous result. Proof must, besides, be forthcoming that the action would have been of adequate power. Plausible guesses on the subject may be entirely fallacious. The machine, even if properly constructed for the end in view, may work too feebly for its attainment. We are, for instance, assured that no difficulty connected with the sense of planetary rotation need impede acceptance of the theory of planetary origin from separated rings, since even if the embryo globes gyrated the wrong way at the outset, solar tidal friction would promptly have reduced them to conformity with the general current of movement. This is true in principle, but will it bear quantitative investigation? Many promising hypotheses have broken down under the weight of figures; whether this particular one is strong enough to survive their application remains to be seen. We are, indeed, sure of its validity as regards Mercury, but the efficacy of tidal friction decreases as the sixth power of increasing distance, and the actual rotation of Venus furnishes an enigma sufficiently perplexing to discourage scrutiny of its dimly discerned antecedent conditions. As regards the earth and the exterior planets, the question could only be answered with the help of information which is not forthcoming. The unexpected circumstance that the newly-discovered ninth Saturnian moon circulates from east to west can thus be no more than tentatively explained by invoking this agency of change. Admitting (as we seem bound to do) that satellites are the offspring of the planets they attend, there is no evading the conclusion that the small body under discussion was thrown off from a primary endowed with a rotation opposite to that now possessed by it. And the reversal must have been completely brought to pass before the eighth satellite, Japetus, came into existence. The crux is most arduous; there is no other resource for meeting it but to consider the effects on planetary rotation of solar tides, and this Professor W. H. Pickering, the discoverer of Phœbe, has done.[33] But a cause may be true without being sufficient; and close calculation will be needed to determine, in this instance, how the matter stands.