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HISTORY OF PHYSICAL ASTRONOMY.

announcement that the comet, a little before its perihelion passage, wouldcross the plane of the ecliptic at a distance of only 20,000 miles from theEarth ’s orbit, and near the place where the latter would then be moving.The results of exact calculation were sufficient, however, to dissipate allfears on this point, for it was found that the comet would cross the eclipticon the 20th October, 1832; hut that the Earth would not arrive at thesame place until the 30th November. This comet returned agreeably toprediction, and has subsequently reappeared in 1839 and 1840. On thelast-mentioned occasion it underwent a singular transformation, havingseparated into two distinct comets, which continued to travel together ata mutual distance of 3' or 4' daring the whole period of their visibility.One of these objects was a little fainter than the other, but each of themexhibited the distinctive features of a comet. The tails w r ere parallel toeach other, and extended in a direction perpendicular to the line joiningthe centres of the nuclei. This extraordinary change in the constitutionof the comet appears to have taken place very suddenly. It was first ob-served in Europe on the 15th of January, 1840, by Mr. Challis of Cam-bridge, and M. Wichmann of Kcenigsberg; but it was afterwards foundthat it had been seen on the 12th of the same month by LieutenantMaury, at the Observatory of Washington , in the United States . M.Plantamour of Geneva determined the elements of each comet by obser-vation, and then computed the perturbations occasioned by the Earth ,Jupiter, and Mars. The motions of both comets, when calculated by thisprocess, agreed very closely with their observed motions for the wholeperiod during which they were visible. M. Plantamour found that theabsolute distance between each nucleus was constantly the same, and wasequal to about two-thircls of the radius of the lunar orbit.

The approaching return of Halley’s comet in 1835 excited a lively in-terest in the scientific world, and a strong desire was felt that the pertur-bations of its elements should be computed. The data necessary for thispurpose are the elements of the comet corresponding to the time of itsperihelion passage in 1759. These are readily deducible from the obser-vations of that year with the exception of the major axis. This elementmay be determined by assuming as the major axis corresponding to theperihelion of 1682 the value indicated by the time of revolution between1682 and 1759, supposing the comet to move in an ellipse, and thenapplying to it the perturbations it would suffer from the action of theplanets during the same period. But these perturbations cannot becomputed without a knowledge of the fundamental values of the otherelements. It is clear, then, that in order to obtain a complete set ofdata for calculating the perturbations of the comet relative to its perihelionpassage in 1835, the geometer must possess a knowledge of the perihelionelements for 1682. In the Connaissance des Temps for 1819, Burchardthas given the elements for 1682 and 1759. His results relative to 1682are founded on the observations of Flamstead, and those relative to 1759on the observations of Messier.

A comparison of the three revolutions of this comet comprised betweenthe years 1531, 1607, 1682, and 1759, affords a striking indication of thepowerful perturbations which it experiences from the action of the planets.The first of these periods includes 27,811 days; the second 27,352 days;and the third 27,937 days: thus the first exceeds the second by 469 days,and falls short of the third by 126 days. It was clearly impossible, there-fore, to arrive at any accurate conclusion relative to the next return of the