We take it to be unnecessary even to say that, the revolution of the satellites of these two planets being retrograde and anomalous, the rotation of their principals must be retrograde and anomalous also. Before going any farther we have something to say about the anomalous position of the orbit of Neptune, which is certainly not the position sought for by M. Leverrier; in fact, the elements employed by him in his calculations to discover a perturbing planet--whose existence may be said to have been known--are so different from the elements of the one actually discovered, that there would be nothing out of reason in saying that Neptune is not the perturber that was sought for, but only an instalment of the perturbing force. It may raise a storm in some quarters to say so, but the fact remains the same, or it must be confessed that mathematics is a more elastic science than it professes to be. He has not the power of attraction required to produce the perturbations in the movements of Uranus which gave rise to the search for an outer planet. M. Leverrier made his calculations under the belief that a planet of 1/9300th part of the mass of the sun was required to produce the perturbations that had been observed in the orbital motion of Uranus; whereas the planet discovered has only 1/20,000th of that mass--not one-half of what was required. On the other hand, the semi-axis major of the orbit of the planet discovered is found to be 30·037 instead of 36·154 (Bode's law measures) used for the search; which greater proximity to the sun, it is true, increases its power of attraction 1·449 times, but as its mass is only 0·465 per cent. of what was expected, the attractive force would amount to less than 0·68 per cent. of what was required. Then the question comes to be, Where did the wanting 0·32 per cent. of attractive force come from? And the answer is that some astronomers have been searching for another planet to make up the weight, with more or less diligence, ever since the deficiency came to be recognised. But all that we want to have to do with the question is to suggest a very plausible reason for the anomalous position of the orbit of Neptune.