Astronomers could only recognize one solution of such a difficulty. It was impossible to doubt that there must be some other planet in addition to the bodies at that time known, and that the perturbations of Uranus, hitherto unaccounted for, were due to the disturbances caused by the action of this unknown planet. Arago urged Leverrier to undertake the great problem of searching for this body. But the conditions of the search were such that it must be conducted on principles wholly different from any search which had ever before been undertaken for a celestial object. For this was not a case in which mere survey with a telescope might be expected to lead to the discovery. There are in the heavens many millions of stars, and the problem of identifying the planet, if indeed it should lie among these stars, seemed a very complex matter. Of course, it is the abundant presence of the stars which causes the difficulty. The materials available to the mathematician for the solution of this problem were to be derived solely from the discrepancies between the calculated places in which Uranus should be found, taking into account the known causes of disturbances, and the actual places in which observation had shown the planet to exist. Here was, indeed, an unprecedented problem, and one of extraordinary difficulty. Leverrier, however, faced it, and, to the astonishment of the world, succeeded in carrying it through to a brilliant solution. After many trials, Leverrier ascertained that, by assuming a certain size, shape, and position for the unknown planet’s orbit, and a certain value for the mass of the hypothetical body, it would be possible to account for the observed disturbances of Uranus. Gradually it became clear to his perception, not only that the difficulties in the movements of Uranus could be thus explained, but that no other explanation need be sought for. And now for an episode in this history which will be celebrated so long as science shall endure. It is nothing less than the telescopic confirmation of the existence of this new planet, which had previously been indicated only by mathematical calculation. Great indeed was the admiration of the scientific world at this superb triumph. Here was a mighty planet, whose very existence was revealed by the indications afforded by refined mathematical calculation. At once the name of Leverrier, already known to those conversant with the more profound branches of astronomy, became everywhere celebrated. When, in 1854, Arago’s place had to be filled at the head of the great Paris Observatory, it was universally felt that the discoverer of Neptune was the suitable man to assume the office. Leverrier died on Sunday, September 23, 1877, in his sixty-seventh year. * * * * *