The measured deviations of Uranus at the different points of its orbit were the sole data available for the discovery of the new planet. We have to fit the orbit of the unknown globe, as well as the mass of the planet itself, in such a way as to account for the various perturbations. Let us, for instance, assume a certain distance for the hypothetical body, and try if we can assign both an orbit and a mass for the planet, at that distance, which shall account for the perturbations. Our first assumption is perhaps too great. We try again with a lesser distance. We can now represent the observations with greater accuracy. A third attempt will give the result still more closely, until at length the distance of the unknown planet is determined. In a similar way the mass of the body can be also determined. We assume a certain value, and calculate the perturbations. If the results seem greater than those obtained by observations, then the assumed mass is too great. We amend the assumption, and recompute with a lesser amount, and so on until at length we determine a mass for the planet which harmonises with the results of actual measurement. The other elements of the unknown orbit--its eccentricity and the position of its axis--are all to be ascertained in a similar manner. At length it appeared that the perturbations of Uranus could be completely explained if the unknown planet had a certain mass, and moved in an orbit which had a certain position, while it was also manifest that no very different orbit or greatly altered mass would explain the observed facts. These remarkable computations were undertaken quite independently by two astronomers--one in England and one in France. Each of them attacked, and each of them succeeded in solving, the great problem. The scientific men of England and the scientific men of France joined issue on the question as to the claims of their respective champions to the great discovery; but in the forty years which have elapsed since these memorable researches the question has gradually become settled. It is the impartial verdict of the scientific world outside England and France, that the merits of this splendid triumph of science must be divided equally between the late distinguished Professor J.C. Adams, of Cambridge, and the late U.J.J. Le Verrier, the director of the Paris Observatory.