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HISTORY OF PHYSICAL ASTRONOMY.

In the next place, were the irregularities due to a comet which cameinto collision with the planet, and suddenly changed the direction andquantity of its motion ? The effect of such a collision would be to throwthe planet out of the ellipse in which it was moving, into another ellipsehaving different elements. Its motion, therefore, previous to the epochof collision, and during an indefinite lapse of time afterwards, would he satis-fied by two distinct systems of elliptic elements, and consequently in neithercase ought there to appear any outstanding irregularities, when once theelements were duly corrected by means of observations relating exclusivelyto the ellipse under consideration. This hypothesis acquired some degreeof plausibility from the fact, that Bouvard succeeded in representing withtolerable accuracy, by means of an elliptic orbit, all the observations ofthe planet comprised between the years 1781 and 1820. In order,however, to justify its adoption, it would be necessary that this ellipseshould tally either with the observations anterior to 1781, or with thosesubsequent to 1820, conditions both of which had been found by astrono-mers to be incompatible with the actual motion of the planet.

It was manifest, then, that the irregularities must be occasioned bysome cause acting continuously upon the planet, and varying slowly in theintensity of its influence. This can be no other than a planet, and thequestion then arises: is it possible to assign the place in the heavenswhich it ought to occupy ? In the first place, it could not be situated withinSaturn , for, if so, it would disturb that planet to a greater extent than itdisturbs Uranus ; but this was contrary to fact, the perturbations whichit produces in the motion of Saturn being insensible. Secondly, was itsituated between Saturn and Uranus '? In that case, it would require tobe nearer Uranus than Saturn , and as its mass, in consequence, mustnecessarily be very inconsiderable, the perturbations produced by itwould be sensible only in conjunction. But the periodic times of the twoplanets would be very nearly equal. It followed, therefore, that theperturbations would be sensible only once during the period including allthe existing observations of Uranus . This conclusion, however, was atvariance with the actual character of the irregularities of the planet.The disturbing body must, therefore, he situated beyond Uranus . Itmust not be very near that planet, for its mass would then be incon-siderable, and its perturbations, as in the preceding case, would exhibita character inconsistent with observation. Nor must it be situated veryfar beyond Uranus; for, if it were so, its respective distances from Saturn and Uranus would be comparable with each other, and it would be im-possible to account for the irregularities of Uranus without developingsimilar irregularities of the same order of magnitude in Saturn ; but ofthese there did not exist any sensible traces. It manifestly followed,therefore, that the planet must be situated at some moderate distancebeyond Uranus . Now, according to Bodes law, the successive distances ofthe more remote planets are nearly double each other. Le Yerrier, there-fore, assumed as the basis of a first approximation, that the disturbingplanet was twice as distant from the sun as Uranus , and, arguing similarlyfrom analogy, he concluded that it revolved very nearly in the plane ofthe ecliptic. He was thus led to propound the subject of his researchesin the following form:— “Is it possible that the irregularities ofUranus may arise from the action of a planet situated in the ecliptic at amean distance double that of Uranus ? If such be the case, what is theactual position of this planet ? What is its mass ? and what are the ele-