In calculating the elements of Halley’s comet, former astronomers have in general adopted the parabolic hypothesis, neglecting the reciprocal of the semi-axis major; and even in the more recent investigations of its orbit, no accurate value of this quantity has been employed. Mr. Lubbock, perceiving the serious effect which an error in the semi-axis major would occasion in the determination of the other elements, renewed these very laborious calculations, assuming as the value of this quantity that given by M. Pontécoulant, in his “Théorie analytique du Systême du Monde;” taking also into account the alterations which the elements of the comet have undergone by the action of the planets, and likewise the effect of precession upon the longitude of the node, and of the perihelion. The author takes this opportunity of correcting the very erroneous statements that have been made respecting the results of his investigations, especially with regard to the time of the perihelion passage, which is, of course, very different from that of its actual appearance to spectators on the earth; although these two epochs are frequently confounded with one another.
IV. Observations of Halley's Comet, after its Perihelion Passage