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    BRORSEN'S COMET IN 1842.—In September, 1846, it was pointed out by Mr. Hind (Astron. Nach. No. 582) that the comet of short-period discovered by Brorsen at Kiel on February 26 preceding must have approached very near to the planet Jupiter about May 20, 1842, possibly within 0.05 of the earth's mean distance, and it was surmised that an entire change of orbit might have been produced at that time. In 1857 D'Arrest examined this point more closely, applying the formulæ of the Mécanique Céleste to determine the elements priar to the encounter with the planet. His results were published in Astron. Nach. No. 1087. Adopting good elements for 1846, but without taking account of perturbations, since the comet left the sphere of activity of Jupiter after the near approach, he inferred that the closest proximity occurred May 20.6924 Berlin mean time, the distance between the two bodies being then 0.05112; that for April 19.5 the inclination of the comet's orbit was 40° 51′, or 10° greater than in 1846, and that the perihelion distance was greater than 1.5, instead of 0.65 at the time of Brorsen's discovery, and it was considered that the comet would not be visible when the radius-vector was much over unity; hence, perhaps, our ignorance of its existence before the year 1846. Thus the question has remained until within the last two years. Our object now is to record the results of a much more complete investigation of the effect of the comet's encounter with Jupiter, by Herr Harzer, forming the subject of an inaugural dissertation in the University of Leipsic in 1878. He adopts the definitive elements of Prof. Bruhns for 1846, with a small correction te the mean motion indicated by the observations at the comet's reappearance in 1868, and calculates backward with great care the perturbations of Mercury, Venus, the Earth, Mars, Jupiter, and Saturn to 1842, July 16.5, when the distance from Jupiter was 0.305; the total perturbations in the interval 1846, February 25.5 —1842, July 16.5 are as follows:—Mean anomaly, − 1° 58′ 32″.6; mean sidereal motion, + 4″.391; longitude of perihelion, + 9′ 52″.8; ascending node, + 24′ 35″.4; inclination, + 1° 48′ 31″.4; angle of eccentricity, + 56′ 30″.0. From the ecliptical co ordinates of the comet with respect to Jupiter at the latter date and the variations of these relative co-ordinates, the hyperbolic elements of the orbit about the planet are obtained and the perijove is found to have taken place May 27.28488 M.T. at Berlin, when the distance was 0.054714. The hyperbolic elements are assumed to 1842, April 7.5, when the distance between comet and planet was 0.30334, and the radius of the sphere of attraction 0.27149. The elements are then again referred to the sun, and thus the following figures defining the comet's orbit before this near approach to Jupiter, result:—

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