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APPENDIX.

Mr. Adams in England, and M. Le Verrier in Trance, undertook aboutthe same time to investigate the irregularities of Uranus upon the suppo-sition of their being produced by the action of an exterior planet, and, in-dependently of each other, arrived at a very approximate determination ofthe position of the disturbing body. Upon this ground, therefore, they areseverally entitled to the honour associated with the theoretical discoveryof the planet Neptune . With respect to Le Verrier’s researches onthe limits of the orbit of the disturbing body, they have not beenborne out by the results of actual observations; but this circumstance,attributable in all probability to the intricacy of the subject andthe imperfect state of analysis, does not in the slightest degree impugn hisclaims to the great discovery just mentioned. The American astronomersand mathematicians have more especially distinguished themselves by theirlabours in connexion with the planet Neptune , since the epoch of its phy-sical discovery. The results that have been deduced from Bond’s oliserva-tions of the satellite of Neptune and the mathematical researches ofWalker and Peirce, unquestionably exhibit a degree of consistency withthe actual observations of Uranus and Neptune which has not been paral-leled by any similar efforts on this side of the Atlantic, while at the sametime they tend to throw much interesting light on the theory of bothplanets. The peculiar views which Prof. Peirce was led to entertain,respecting the researches of the distinguished geometers to whom thetheoretical discovery of Neptune is due, may perhaps be attributed to hishaving devoted his attention too exclusively to the analytical formulae re-presenting the action of the planets, without taking into sufficient con-sideration the mode in which the disturbing forces directly operate. Theseviews were announced by Prof. Peirce in a spirit of candour and mode-ration highly honourable to his character as a philosopher. They are be-yond all doubt erroneous, but the trifling inadvertence into which he wasthus betrayed does not detract from the merit of his more substantiallabours in connexion with the theory of Uranus and Neptune .

IY.

REMARKS ON THE LUNAR INEQUALITY TERMED THE EVECTION.

One of the most remarkable instances of perturbation which occursin the solar system is the inequality in the moon’s longitude termed theevection. So long as the moon was observed merely in eclipses, this in-equality continued to escape the notice of astronomers. When Hippar­ chus , however, after having constructed the astrolabe, succeeded in deter-mining the position of the moon in quadratures, he found that the resultscould not be generally reconciled with the existing theory of hermotion. That great astronomer, having no similar observations of themoon anterior to his own accessible to him, was unable to arrive at a defi-nitive conclusion respecting the anomaly; but he formally pointed out itsexistence, and executed a series of valuable observations with the view ofaiding future astronomers in their researches on the subject. It is wellknown that the discovery of the law of this famous inequality is due toPtolemy . The account which he has given of the inequality as it pre-sented itself to his observations *, would seem to imply a law of variation* Syntaxis, lib. V., cap. ii.