Periodical comets which have not been seen again; long periods; circumstances unfavourable to observation ; motions possibly disturbed by perturbations–Elliptic orbits determined by calculation–Uncertainty of return under these different hypotheses.

The nine comets of which we have just given an account are up to the present time the only comets which can be considered as certainly belonging to our system. But they are not the only comets which regularly perform their revolutions round the sun. Of the numerous comets moving in apparently elliptic orbits some, we shall now see, have been regarded as new apparitions of comets previously observed, the great resemblance of their parabolic elements having caused their periodicity to be suspected. But either their return to perihelion has not yet taken place, or circumstances favourable to observation have not occurred; or, an equally likely hypothesis, they may have been disturbed in their courses by the vicinity of the planetary masses, producing perturbations powerful enough to change their periods, or even to cast them out of the sphere of the sun's attraction, of which perhaps until then they had formed for a time a part.

Other comets, which have not been assimilated to comets already observed, have elliptic orbits determined by calculation; but for the reasons that we have just enumerated they have not been seen again ; that is to say, they have periods much too long, or they have been subjected to disturbing causes.