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The story begins with the finding of Phœbe, the ninth satellite of Saturn, by Professor W. H. Pickering, of Harvard Observatory. He found it by examining photographs of Saturn, with the stars all round it; and as he was able to identify it on a number of such photographs taken on different days, he calculated an orbit for it so as to be able to find it again when wanted. You remember the case of the little planet Ceres, which had been observed for so short a time that astronomers despaired of finding it again, until Gauss showed them how to calculate the orbit—even from a very few days' observations? Professor Pickering was luckier than Piazzi; he had quite enough observations to calculate the orbit so he thought; but the trouble was that when he looked for the little satellite in its expected place (after the Sun had hidden it, as it hid Ceres) he could not find it anywhere! This was very puzzling indeed. Of course the little satellite might have been destroyed in the meantime by some unknown agency, but this did not seem likely; it seemed much more likely that he had made a mistake, and so indeed he had—the mistake of thinking that the satellite was travelling round Saturn in the usual way, like satellite A in Fig. 54. It is really travelling like satellite B, and when Professor Pickering persuaded himself, very reluctantly, to try this other supposition, he, to his great delight, found the little satellite in its calculated place. You may wonder why he made any supposition at all when he had actual observations to go upon; it would take too long to explain it here, but I may remind you that both Adams and Leverrier, in their cal-