ing period, the new period amounting to 27,937 days; this increase arose from two antagonistic causes 1. An increase of 135 days, 34 being due to the action of Jupiter. 2. A diminution of 66 days, 30 being due to the action of Saturn, Uranus, and of the Earth. The duration of this last pericd was found equal to seventysix years and 135 days, or seventy-six years and four months and a half. An equal period would bring the next time of perihelion passage to March 29, 1912. But this date will be subject to modification by the perturbations incident to the journey. Jupiter will exercise a considerable retarding influence, and the revolution which the comet is now accomplishing will be shorter than any yet observed-it will be 27,217 days; that is to say, hardly seventy-four years and six months. This brings the next apparition, according to the calculations of Pontécoulant, to May 24, 1910, about nine o'clock in the morning.* If, on the contrary, we look back into the past and consult old chronicles and records, we shall find several apparitions of Halley's comet, the dates of which are as follows, some nearly certain, others somewhat doubtful: June 8, 1456. Halley had already given notice of this apparition. In December 1301. According to the researches of E. Biot and Laugier. * The elements of the orbit calculated for this epoch by the same mathematician give the 16th of May, 1910, about 11 P.M. In addition to these dates Mr. Hind gives the following as corresponding probably to former apparitions of the same comet: 1223, 912, 837, 608, 530, 373, 295, 218. The period which these apparitions lead us to infer (notably those of 1456, 1378, 760, 451) amounts to about seventy-seven years and a quarter, which is longer in a marked degree than that of the three or four last revolutions.* M. Laugier asks if this diminution which we are obliged to admit is not due to the same cause as that which has been assigned to account for the similar diminution undergone by Encke's comet; that is to say, the resistance of the ether; or if, as Bessel thought, it was due to a dispersion or loss of matter abandoned by the comet in the course of its successive revolutions. These are questions of high interest, and we shall recur to them again. * From the year 12 B.C. to the year 1835, 1,847 years have elapsed, a period comprising twenty-four revolutions of Halley's comet. The mean duration would thus be 76 years 350 days. SECTION III. ENCKE'S COMET; OR, THE SHORT PERIOD COMET. Discovery of the identity and periodicity of the comets of 1818, 1805, 1795, and 1786; Arago and Olbers-Encke calculates the ellipse described by the comet-Dates of twenty returns up to 1873-Successive diminution of the period of Encke's comet. IN 1818 Pons, one of the most indefatigable of observers and comet-seekers, discovered at Marseilles a comet which passed its perihelion on the 27th of the following January. The elements of the new comet, when compared with those of comets already catalogued, gave reason to suppose that it had been observed in 1805. Arago remarked this to the Board of Longitude when Bouvard presented the parabolic elements of the new comet; and Olbers, on making the same remark in Germany, added that it was doubtless the same comet which had been observed in 1795 and 1786. We subjoin the elements of the comets of 1818 and 1805: 'The resemblance was too striking not to produce attempts The elliptic to determine the periodicity of the new comet. elements of the orbit were calculated by Encke, astronomer at the Observatory of Gotha, and for this reason the comet received the name of Encke's comet; but it is also sometimes called the short-period comet, in contradistinction to Halley's comet, whose period of revolution is so much longer. The comet of Encke, in fact, describes its orbit in about 1,210 days, or three years 114 days. If we only consider,' says Poisson, 'the rapidity of its successive revolutions, this body might be regarded as a planet, but it continues to have a place assigned to it amongst comets, because of the appearances which it presents, and because it is not visible to us throughout its entire orbit.' In fact, at the time when Poisson wrote his report the belief in the extreme elongation of all cometary orbits still existed, and it seemed improbable that a comet should have so short a period of revolution. But successive observations of its return removed all doubt, and soon new periodical comets were discovered, which justified the possibility of cometary orbits, comparable in point of their relatively slight eccentricity with the orbits of the planets themselves. The first return of the short-period comet to its perihelion. took place towards the end of May 1822. Encke calculated the epoch of its return, and computed an ephemeris; then, taking into account the perturbations which must have been experienced by the comet in the course of its preceding revolution, owing to its passage near to Jupiter, he showed that its period would be lengthened about nine days, and that the comet would be invisible in Europe; and in fact it was only observed in the southern hemisphere (in Australia). We extract from the Annuaire du Bureau des Longitudes for 1872 the epochs of the perihelion passages of the comet from its discovery in 1818 up to its last and next passage: By adding to the preceding the previous apparitions of 1786, 1795, and 1805 we have in all twenty observed returns; but since the first date twenty-seven consecutive revolutions have really taken place. Now, if the exact intervals between the perihelion passages be noted, and the durations of the corresponding periods deduced from them, we have the following table, which was calculated by Encke: The above list testifies to a fact of the highest importance: the period of the comet is continually diminishing. Will it continue always to diminish; and if so, what law does this continual alteration of the orbit follow? A diminution in the periodical time of a body cannot take place, according to the laws of Kepler, without a corresponding diminution in the length of the major axis, or mean distance of the comet from |