HISTORY OF PHYSICAL ASTRONOMY.

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forming a 'barrier to his researches, on the contrary, conduced to theirsimplification. He found the greatest value of the inequality to amountto 806", or 14' 56," and its period to upwards of 675 years. This in-equality is manifestly similar to several others of long duration, to whichwe have already had occasion to allude, but it differs from them in so far asI the particulars relative to it are not susceptible of being tested by observa-tion, on account of the short time that has elapsed since the discovery ofthe planet. As it was desirable to verify the calculations of Le Verrier ,M. Cauchy determined the value of the inequality by a method of his own,and obtained a result which completely accorded with that of the originaldiscoverer.

The researches on the perturbations of the smaller planets gave rise toan interesting discusssion among astronomers respecting the essentialnature of the principle of gravitation. In 1826, Nicolai having com-pared the analytical expressions for the perturbations of Juno by Jupiter,with fifteen observed oppositions of the planet, met with such discordancesas induced him to suppose that the absolute attraction of Jupiter on thesun and on the planet were unequal, or, in other words, that the totalj amount of attraction exerted by one body upon another depended on thequality of the matter contained in the attracted body, as well as upon itsquantity. This doctrine, being at variance with the fundamental principleof gravitation, attracted a considerable degree of attention on the occasionof its first announcement; but the subsequent researches of astronomershave served to shew that it is untenable. Bessel, for this purpose, made agreat number of experiments with pendulums, composed of different sub-stances, such as ivory, glass, marble, meteoric stones, &c.; but he wasunable to discover in the times of oscillation any indication that the in-tensity of the terrestrial attraction depended on the quality of thependulous body.

The theory of Comets depends on the solution of two problems of capitalimportance. The one relates to the investigation of the species of conicsection, in which the comet moves, and the determination of the elementsof the orbit; the other relates to the calculation of the effects produced bythe disturbing action of the planets. Both of these problems have largelyoccupied the attention of geometers, from the establishment of the theoryof gravitation by Newton , down to the present day. The first solution ofthe problem for determining the orbit of a comet, by means of observa-tions on its motion, was given by Newton in the Principia. It wasfounded on the supposition, that the species of conic section, described bythe comet, is a parabola. This assumption conduced much to the simplifi-cation of the problem, nor did it entail any sensible error on the ultimateresults, when the eccentricity of the orbit is very great. On the otherhand, the solution was defective, inasmuch as it assigned no means ofascertaining the value of the mean distance in the case of the orbit beingreally elliptic. This element could only be determined by means of therelation between it and the periodic time, the latter being deduced from] the interval comprised between two successive appearances of the comet.ii Various solutions of the same problems have been given by geometers> since Newton ’s time, some of which are independent of any assumptionwith respect to the form of the orbit. The most celebrated of the latterclass are those of Laplace and Gauss.

The researches on the perturbations of comets offer difficulties pre-cisely analogous to those which occur in the theory of the smaller planets.