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HISTORY OF PHYSICAL ASTRONOMY.

recognised as an established truth in physical astronomy. The subjectwas one well adapted to the searching powers of a Laplace or a Poisson ,and in their countryman, M. Le Vender, astronomy found on the presentoccasion a worthy representative of these illustrious geometers. Themode of proceeding which Le Vender proposed to adopt in this inquirywas first to determine the effect produced by Jupiter on Lexell ’s comet,from its discovery in 1770 until the action of the planet ceased to besensible, and then to trace back the elements of Faye’s comet through thevarious revolutions comprised between the appearance of that body in 1843,and the epoch down to which he had conducted his researches on Lexell ’scomet. If the ultimate elements of Faye’s comet, when thus determined,were found to coincide with those of Lexell ’s for the same epoch, it mightthen be concluded that the two comets were identical; but on the otherhand, if they exhibited discordances which could not be accounted for byany admissible supposition of errors, whether of observation or calculation,it must necessarily follow that the comets were two distinct bodies. Le Verrier found that the ultimate results would be very much affected bythe errors in the original elements of both comets, for the effects of theseerrors continually increased with the lapse of time, insomuch that in someinstances a very small variation of the fundamental elements would besufficient to alter entirely the character of Jupiter ’s influence. The in-vestigation was therefore much more complicated and the conclusions lessdefinite than might have been expected if the data had been more precise.Le Verrier having submitted to a careful discussion the observations of1770 on Lexell ’s comet, determined by means of them the elements ofthe orbit, and then investigated the action of Jupiter on the comet. Hefound that, when the latter arrived within the sphere of the planet’s in-fluence, it was. compelled to deviate from its elliptic orbit, and describedan hyperbola round the planet. The errors of the elements might evenbe such that, after the action of the planet ceased to be sensible, the cometwould still continue to move in an hyberbola, and in that case would neveragain return to the solar system. Le Verrier computed the elements ofthe comet for the time when it quitted the sphere of Jupiter ’s influence,and then compared the results with the elements of Faye’s comet, thelatter being traced up to the same epoch through the various revolutionsanterior to its appearance in 1843. Pie found that, upon any possiblesupposition of the errors of observation, the elements of Faye’s comet couldnot be reconciled with those of Lexell ’s, and he therefore came to theconclusion that they were two distinct bodies.

It is possible that Faye’s comet may have originally emerged from theboundless regions of space describing a parabola or hyperbola having thesun in the focus, but that on its arrival within the sphere of Jupiter ’s in-fluence it was thrown into a new orbit by the powerful action of thatplanet, and was permanently fixed in the solar system. If the funda-mental elements of the comet were mathematically accurate, this questionmight be decided, at least for any determinate period, by tracing back thecomet through the various revolutions anterior to 1843. The errors,however, with which the elements are affected by the inevitable errors ofobservation, impart so indeterminate a character to the results, that, evenif the comet had been so introduced into the solar system, it would havebeen impossible to ascertain the exact time when this event happened.But although the question does not admit of a definitive solution, onaccount of the circumstance to which we have just alluded, still it is pos-