1649, the comet in passing through its node was situated in the close vicinity of Uranus, and hence must have been produced very considerable perturbations in the movement of the former. It should be looked for again in the year 1900. Lastly, there are two comets with nearly the same period of fifty-five years. The one was discovered in 1846 by De Vico, and should effect its first return in the year 1902; at its aphelion it withdraws to a distance nearly equal to the radius of the orbit of Neptune; it is thus an interior comet. The other comet of fifty-five years, which likewise does not pass beyond the orbit of Neptune, was discovered in 1873, by M. Coggia, at Marseilles; it is suspected to be identical with a comet observed by Pons in 1818.

SECTION III.

COMETS OF MEAN PERIOD.

Periodical comets exterior to the solar system; the type of this class is Halley's comet, which is the only comet of mean period whose return has been verified by observation-Enumeration of comets with periods between 69 and 200 years— Periods; aphelion and perihelion distances.

Or the comets belonging to this class Halley's comet is the type; but it is the only one of which we have several undisputed apparitions. When a comet is suspected to be identical with some other comet that has been previously observed, from the similarity of the parabolic elements, its return is probable; but as a rule great uncertainty attaches to the length of the period, even if, assuming the identity of the two comets, the perturbations be left out of the question. A third apparition is, therefore, generally necessary before the identity and real periodicity of a comet can be affirmed. And this third element up to the present time is wanting in the comets we are now engaged upon. But it will evidently suffice to prove a second apparition, when the elliptic elements have been calculated solely from observations of the first apparition. The following, in the order of their discovery, are the nine comets of mean period which we have to mention :—

The first on the list is the comet of 1532, observed by Apian and by Fracastoro, 'whose head,' says the latter observer, 'was three times larger than Jupiter, with a beard two

fathoms long.' According to the calculation of Olbers this comet has a period of 129 years, and is identical with a comet which appeared in 1661, and at several other remarkable epochs. Sir John Herschel mentions it in the following manner: 'In 1661, 1532, 1402, 1145, 891, and 243 great comets appeared, that of 1402 being bright enough to be seen at noonday. A period of 129 years would reconcile all these appearances, and should have brought back the comet in 1789 or 1790. That no such comet was observed about that time is no proof that it did not return, since, owing to the situation of its orbit, had the perihelion passage taken place in July it might have escaped observation.' Its next return should take place between 1918 and 1920.

A comet observed by the English astronomer Flamsteed, from the end of July to the commencement of September 1683, has, according to the elliptic elements calculated by Clausen, a period of about 190 years. This comet, whose return ought to have been observed about 1870, has failed to reappear; but the perturbation caused by the larger planets might occasion a delay of several delay of several years, and its re-appearance may still be expected. At its aphelion it recedes far beyond the orbit of Neptune, surpassing it by 497 millions of miles. A new discussion of the observations, however, by Mr. Plummer affords a presumption that the comet of 1683 describes a parabolic orbit, in which case it should be removed from the list of periodical comets.

About the years 1882 and 1887 search will have to be made for two comets, the first of which, discovered by Pons, in July 1812, has a period of about seventy-one years, and the second, discovered by Olbers, in March 1815, has a period of about seventy-four years, as calculated by Bessel. The return of the comet of 1815 to its perihelion would be accelerated two years by the perturbations of the planets. Then comes

the comet discovered in February 1846 by De Vico and Bond; a period of seventy-three years would bring it back to perihelion about the middle of the year 1919. Next we have the comet discovered by Brorsen (July 1847), with a period of seventy-five years, to return in 1922; that of Westphal (July 1852), with a period of sixty-one years, and next return in 1913; that of Secchi (comet I., 1853), whose period would be 188 years, and which, according to Mr. Hind, has a great resemblance to the comet of 1664. Lastly, the third comet of 1862, of whose connexion with the meteor stream of August 10 we shall have to speak in a later chapter. This comet has a period of about 120 years; its next appearance, therefore, should be expected about 1982.

We now append in order, according to the duration of their periodical revolutions, a list of the nine comets above enumerated. They would be ten in number, if Halley's comet, which we have taken as a type of this class (and be it noted that this division into classes is quite arbitrary), had not been placed amongst comets of verified return. We also add to this enumeration their greatest and least distances from the sun, expressed both in mean radii of the earth's orbit and in miles:

SECTION IV.

COMETS OF LONG PERIOD.

Periodical comets exterior to the known limits of the solar system-Distance to which the comet of longest calculated period recedes from the sun-The so-called comet of Charles V.: its apparitions in 1264 and 1556; its return predicted for the middle of the nineteenth century, between 1848 and 1860-Calculation of the perturbations; another comet lost or strayed-The great comet of 1680: the Deluge and the end of the world-Magnificent comets of 1811, 1825, and 1843.

Or the comets we are now about to mention, the periods of which have been calculated approximately, none certainly will be seen by anyone now living. One alone was expected about fifteen years ago; and if it really did return to its perihelion, in spite of all researches it was not observed, and it will not be visible again until after the lapse of three centuries.

We will begin by enumerating the comets, and will afterwards give some details about the most remarkable of them. The following tables contain the durations of their revolutions and their distances from the sun, expressed in radii of the terrestrial orbit: