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HISTORY OF PHYSICAL ASTRONOMY,

As the usual solutions of the Problem of Three Bodies completely fail inthis case, the effects of planetary disturbance are computed by the methodof mechanical quadratures. We have already mentioned that Lagrangefirst presented this method in a systematic form. In 1810, Besselpublished his famous researches on the comet of 1807. He concluded,from the observations, that the comet moved in an ellipse of greateccentricity. In computing the action of the planets on it, he resolvedthe disturbing force in the directions of the radius vector, of a perpen-dicular to it, and a perpendicular to the plane of the orbit. He thendetermined, by the method of quadratures, the values of the elementsfor every thirty days during which the comet was within the sphere ofplanetary influence. He assigns 1543 years as the most probable valueof the periodic time. A comet which appeared in 1815 was found byOlbers to revolve in an elliptic orbit with a period of about 72 years.The perturbations were computed by Bessel, whose researches on thesubject appeared in the Berlin Memoirs for 1813*. Fresh elementswere computed for every 25 days during which the comet was visible;for every year from 1815 to 1833, and for every two years throughout theremaining part of the orbit. He has fixed the 9th February, 1887, asthe time of the next return to perihelion. In 1818, a comet was dis-covered by Pons, the observed motion of which could not be reconciledwith the supposition of a parabolic orbit. M. Arago remarked thatits elements bore a strong resemblance to those of a comet whichappeared in 1805, and Olbers about the same time was led in a similarmanner to suspect its identity with a comet which appeared in 1795.Encke found that the observations might all be satisfied by supposingthe comet to move in an elliptic orbit, with a period of about three yearsand a half. He also computed the perturbations, taking into account theaction of all the planets, with the exception of Uranus and the smallbodies revolving between the orbits of Mars and Jupiter . The perturba-tions of Mercury were computed for every 4 days; those of Venus andthe Earth for every 12 days; and those of Mars, Jupiter, and Saturn forevery 36 days. This process was continued until the action of theplanets ceased to be sensible, after which the motion of the comet wasreferred to the centre of gravity of the sun and planetsf. The comet, onthe occasion of its perihelion passage in 1822, was not favourable forobservation in the northern hemisphere, but it was seen by Bumker atParamatta in New South Wales . A comparison of the earlier with themore recent observations seemed to indicate that the period of revolutionwas continually diminishing, and Encke was hence led to suspect theexistence of a resisting medium. The perihelion passage of 1825 wasnot favourable for deciding so delicate a question, but that of 1829 offeredpeculiar advantages for this purpose. In order to understand this, it isnecessary to remark that the axis of the comet lies almost in theplane of Jupiter ’s motion, and that the aphelion extends very nearlyto the orbit of that planet. Hence it is clear that, when Jupiter is in thatpart of his orbit which is in the neighbourhood of the comet’s aphelion,he will very much disturb the motion of the latter; and, if an erroneousvalue be assumed for his mass, the difference between the computed andobserved places of the comet may be very considerable, even inde-

* Airy’s account of the progress of Astronomy , British Association Report for 1832.

f Ibid.