First comet whose periodicity, without comparison with previous dates, has been determined by calculation and verified by observation–M. Le Verrier demonstrates that it has nothing in common with the comet of Lexell–Slight eccentricity of Faye's comet and great perihelion distance–Dates of its return–Perturbations in the movements of Faye's comet inexplicable by gravitation alone : a problem to be solved

A communication by Arago, published in 1844, in the Comptes Rendus of the Academy of Sciences, gives an account of the first researches relative to the fourth periodical comet, which we here subjoin :–

‘This body was discovered at the Observatory of Paris by M. Faye, on November 22, 1843. This young astronomer hastened to calculate its parabolic elements. But as the number of observations increased M. Faye perceived that a parabola was quite inadequate to represent the series of positions occupied by the comet, and announced that he should determine its elliptic orbit, as soon as the state of the sky should have permitted him to pursue his observations of the new comet in regions so far removed from those in which it had first appeared that no doubt could possibly exist as to the certainty of his results. M. Faye therefore applied himself to the multiplying of observations, which had become extremely difficult to obtain, on account of the indistinctness of the comet. Matters were in this stage when a letter from Schumacher informed him that Dr. Goldschmidt, a pupil of Gauss, had already calculated an elliptic orbit, having used the observations made at Paris on November 24, and those of December 1 and 9, made at Altona.’