HISTORY OF PHYSICAL ASTRONOMY. 187

comet by means of these data alone, or even to affirm that the revolutionsubsequent to 1750 would be longer or shorter than the preceding revolu-tion. In 1812 the Academy of Turin proposed as the subject of a prize,the perturbations of Halley’s comet. The prize was awarded to Damoi-seau, whose investigation was subsequently published in the Turin Me-moirs for 1817. He determined the value of the major axis, at the timeof its perihelion passage in 1759, by computing the action of the planetson it throughout the preceding revolution. Setting out, then, from thecomplete elements of 1759, he computed the alterations they would sufferthroughout the time which would elapse until the comet would againarrive in perihelion. The method he employed in his researches isfounded on the variation of elements, and coincides essentially with thatexplained by Lagrange in 1780. He did not, however, adopt the modeof proceeding suggested by that geometer for the superior part of theorbit, preferring to execute the whole of the calculations by the saferthough more laborious process of mechanical quadratures. In computingthe perturbations of the major axis from 1682 to 1759, he changed theelements only once, but, in performing a similar operation upon all theelements throughout the revolution subsequent to 1759, he used the cor-rected elements at every 30° of eccentric anomaly. The planets whoseaction he took into account in his original memoir were Jupiter , Saturn ,and Uranus ; and his final result relative to the time of return w'as, thatthe comet would pass its perihelion on the 16th November, 1835. Dis-covering on a subsequent occasion that the Earth would exercise a sensibledisturbance on the comet after it had passed its perihelion in 1759, hecomputed the derangement arising from this cause, and found that itwould have the effect of shortening the next revolution to the extent of12 days. Hence, according to his previous conclusion, the passage of theperihelion would take place on the 4th November.

The researches of Encke having rendered probable the existence of aresisting medium, the return of Halley’s comet was anxiously lookedforward to by astronomers, under the impression that it would tlirow T somelight upon this interesting question. It was principally with this objectin view that the Academy of Sciences of Paris proposed the perturbationsof Halley’s comet as the subject of a prize. After twice offering theprize without obtaining any competitors, the Academy finally awarded it,in 1829, to M. Pontecoulant. The details of this geometer’s researcheswere published in the sixth volume of the Memoires des Savans Etrangers.He assumed, as the basis of his calculations, the elements of Burchardtfor 1682 and 1759, and computed the perturbations by a process similarto that employed by Damoiseau. He found that the comet would pass itsperihelion on the 7th of November, 1835. In the Connaissance des Tempsfor 1837 * he corrected this result by taking into account the action ofthe Earth before the perihelion passage of 1759, and by emploj’ing, insteadof Bouvard’s value of Jupiter ’s mass,-that which Nicolai had recentlydeduced from the perturbations of Juno. His final conclusion was thatthe comet would pass its perihelion on the morning of the 14th of No-vember, 1835.

The perturbations of Halley’s comet formed also the subject of pro-found investigations by Lehmann and Rosenberger, two German mathe-

* Published in 1834.