How to discover the periodicity of an observed Comet and predict its return –First method: comparison of the elements of the orbit with those of comets that have been catalogued –Resemblance or identity of these elements; presumed period deduced from it–Second method: direct calculation of elliptic elements – Third method.

There are, however, a certain number of comets of whose return astronomers are certain, and the time of whose apparition they can calculate. The prediction of the probable epoch at which these comets will be situated in regions of the heavens where they will be visible from the earth, and the determination of their perihelion passage, can be effected more or less accurately. These are the comets whose orbits, when calculated from a sufficient number of observations, prove to be neither parabolas nor hyperbolas, but, on the contrary, are closed and elliptic, and such that the comet thenceforth continues to describe them in regular periods; in a word, they are periodical comets Newton treated the orbits of comets as parabolic, merely in order to so represent the arc, always very short, described in the neighbourhood of the perihelion, when the comparatively small distance of the comet from the sun renders observations possible. In his opinion comets were bodies of regular periods, and which described ellipses, certainly very elongated, but in all respects similar to the planetary orbits.