The analytical formularies, contained in such works as La Place's 'Mecanique Celeste,' exhibit to the eye of the mathematician a record of all the evolutions of the bodies of the solar system in ages past, and of all the changes they must undergo in ages to come. Such has been the result of the combination of transcendent mathematical genius and unexampled labor and perseverance, for the last century. The learned societies established in various centres of civilization have more especially directed their attention to the advancement of physical astronomy, and have stimulated the spirit of inquiry by a succession of prizes, offered for the solutions of problems arising out of the difficulties which were progressively developed by the advancement of astronomical knowledge. Among these questions, the determination of the return of comets, and the disturbances which they experience in their course, by the action of the planets near which they happen to pass, hold a prominent place. In 1826, the French Institute offered a prize for the determination of the exact time of the return of Halley's comet to its perihelion in 1835. M. Pontecoulant aspired to the honor. "After calculations," says he, "of which those alone who have engaged in such researches can estimate the extent and appreciate the fastidious monotony, I arrived at a result which satisfied all the conditions proposed by the Institute. I determined the perturbations of Halley's comet, by taking into account the simultaneous actions of Jupiter, Saturn, Uranus, and the Earth, and I then fixed its return to its perihelion for the seventh of November." Subsequently to this, however, M. Pontecoulant made some further researches, which led him to correct the former result; and he afterwards altered the time to November fourteenth. It actually came to its perihelion on the sixteenth, within two days of the time assigned.