Discovery of the comet and of its periodicity by D'Arrest--Return predicted by M. Yvon Villarceau for 1857; verification to within half a day-Importance of the perturbations caused by Jupiter-Research of MM. Yvon Villarceau and Leveau -Return of the comet in September 1870.

HERE, again, we have a periodical comet whose periodicity has been determined by calculation, and whose returns have been predicted and observed without the help of any comparison with previous comets. It bears the name of the astronomer who discovered it in 1851, and who recognised the periodicity of its orbit. M. Yvon Villarceau had drawn the same conclusion, and calculated the ephemeris for its next return to perihelion, which he announced for the end of 1857, a prediction verified to within twelve hours. The new comet was seen again at the Cape of Good Hope by Sir Thomas Maclear. its following return, which took place in 1864, astronomers were less fortunate, and were unable to perceive the comet, whose position in the heavens and distance from the earth were very unfavourable. In 1870 the perihelion passage of the comet took place on September 23; it was observed three weeks before by M. Winnecke, thanks. to the ephemeris calculated by MM. Yvon Villarceau and Leveau.

On

Of all the comets which have not failed to return to us,' says M. Yvon Villarceau, the comet of D'Arrest is perhaps the

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most interesting in regard to its perturbations. I do not think that any other comet has been so closely followed by Jupiter.' These perturbations, which the above-named astronomer had calculated for 1864, had increased by more than two months the duration of the first revolution, the comet being situated in 1862 at a distance from Jupiter equal to three-tenths of the distance of the sun from the earth, or at a distance of about twenty-seven millions of miles. They were calculated with great care by M. Leveau for the ensuing period, and it is doubtless owing to this great work, the labour of three years, that observations of the comet were rendered possible at its apparition in 1870. The comet, in fact, passed its perihelion on September 23 of that year. We enter into these details to show the difficulties of cometary astronomy, and how science is able, if not always to surmount them, at least to diminish them considerably.*

D'Arrest's comet describes its orbit in a little less than six years and a half (6·567 years), or in 2,398 days, only thirteen days more than the planet Sylvia. Next to Faye's comet, its orbit has the smallest eccentricity, or, in other words, the least elongated figure.

* [M. Leveau has since performed the calculations for the next revolution of the comet, and has given an ephemeris for every twentieth day throughout the year 1877. The perihelion passage is found to occur 1877, May 10-339 Paris mean time, and the comet will attain its maximum intensity of light about a fortnight later. It will be nearest to the earth in the middle of October, when its distance from us will be about one hundred and thirty millions of miles. It will probably be a very faint object.--ED.]

The period of Tuttle's comet is intermediate to that of Halley's comet and those of other periodical comets that have returned-Very elongated orbit of the comet of 13 years period-Previous observation in 1790; five passages not since observed-Next return in September 1885.

THE periodical comets of which we have just given an account, and that of Winnecke, which we shall next describe, may be considered, that of Halley excepted, as comets of short periods. Tuttle's comet, discovered sixteen years ago by the American astronomer of that name, is intermediate to Halley's comet of long period and the others. It performs its revolution in 133 years, or more exactly in 13 years 296 days, or about 5,044 days a period nearly two years longer than that which Jupiter occupies in his revolution. But it describes a very elongated orbit, so that at its aphelion it is removed from the sun a distance exceeding ten times its distance at its perihelion; it penetrates depths of space that are even beyond the orbit of Saturn; in fact, it attains the distance of nearly 955 millions of miles; at the perihelion it is about as far distant from the sun as is the earth.

Tuttle's comet was first observed in 1790 by Méchain, who discovered it, and by Messier, and it was the comparison of the parabolic elements of the comets that caused their identity to be recognised. From 1790 to 1858 there is an interval of sixty

eight years; that is to say, five times the duration of the periodic revolution of the comet, which must, therefore, have returned to its perihelion, without having been seen, in 1803, 1817, 1830, and 1844.

To the calculation of the elliptic elements, performed by M. Bruhns, we owe our knowledge of the exact period and the prediction of the return of the comet in the year 1871. It was, in fact, observed at Marseilles on October 13 of that year, and afterwards at Carlsruhe, at Paris, and at the Cape of Good Hope. It passed its perihelion on November 30. Leaving out of consideration the perturbations the comet may have to experience in the course of its present revolution, the next return of Tuttle's comet may be expected in the middle of September 1885. But, as with all other periodical comets, the date may be somewhat modified * under the influence of the planetary attractions, and the consequent disturbance of the orbit.

* Tuttle's comet, it should be observed, moves in an orbit the inclination of which is considerable-it exceeds 54°; consequently, in withdrawing from the sun and penetrating to the distances of the larger planets, Jupiter and Saturn, the comet moves further and further from the paths which they pursue. The disturbing influence of the masses of these planets upon the comet would, therefore, in any case, be inconsiderable.

SECTION IX.

WINNECKE'S PERIODICAL COMET.

Discovery of the periodicity of the third comet of 1819; calculation of its elliptic elements by Encke-Discovery of Winnecke's comet in 1858; its identity with the comet discovered by Pons-Return of the star to its perihelion in 1869; probable date of its next return in 1875.

IN 1819 Pons discovered, at Marseilles, a comet the elliptic elements of which were afterwards calculated by Encke; these elements assigned to it a period of 5 years. Now, in March 1858 M. Winnecke discovered, at the Observatory at Bonn, a new comet, whose parabolic elements, it was soon ascertained, bore considerable resemblance to those of the comet discovered by Pons. To determine if this identity were real, it was necessary to wait for the comet's return in 1863 and 1869. It was actually seen in the month of April of the latter year by M. Winnecke himself, and passed its perihelion on June 30. The date of its next return is, therefore, approximately fixed for the month of April 1875.* It will be requisite, however, as with all comets liable to approach Jupiter or the other planets, to allow for the perturbations it may have to undergo.

From its first apparition, in 1819, to its last, in June 1869, is an interval of fifty years, corresponding to nine revolutions. of the comet. Three passages only, as we have seen, have been

* [It was detected by M. Borrelly, at Marseilles, on the morning of February 2, 1875.-ED.]