PREFACE.

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complete an accordance with observation as was manifest in his otherresearches on the lunar theory *. That Newton really was in possession ofa method adequate to a complete investigation of the subject, is renderedstill further probable by the recent researches of Mr. Adams, who, by theaid of geometrical considerations, analogous to those expounded with somuch elegance in the Principia, has obtained results relative to the move-ment of the lunar apogee, which present a complete accordance withobservation.

The fourth chapter is devoted to the early researches of geometers onthe perturbations of the planets and the stability of the planetary system.While occupied with the former of these subjects, the illustrious Euler devised a method of investigation which must be regarded as one of themost remarkable in the annals of science. It consisted in regarding theperturbations of a planet as arising from an incessant change in theelements of its elliptic motion. This fertile idea was destined to acquirean immense developement from the labours of succeeding geometers.

The sublime results which the analytical researches of Lagrange andLaplace have disclosed, relative to the stability of the planetary system,while they have served to invest astronomical science with additionalfeatures of interest, are entitled to be classed among the noblest triumphswhich the human mind has achieved in the investigation of the laws ofthe physical universe. The labour's of these great geometers, which wereof a kindred nature throughout their whole career, are on this occasionmore especially interlaced. As some misapprehension appears to havenot unfrequently arisen from this circumstance, I have endeavoured, by acareful reference to the volumes of the Academy of Sciences and otheroriginal sources, to exhibit the results independently arrived at by eachgeometer in the course of his researches on the subject.

The fifth chapter contains an account of the physical explanation of thegreat inequality in the mean longitudes of Jupiter and Saturn , and of thesecular inequality in the mean motion of the Moon , as well as an allusionto several points of minor importance in the Theory of Gravitation. Theirregularities in the mean longitudes of Jupiter and Saturn long continuedto form an inexplicable enigma to geometers. In vain did Euler employall the resources of his fertile genius in endeavouring to account for theirexistence by the principles of the Theory of Gravitation. Equally fruitlesswas the result of Lagrange’s application of his commanding powers ofanalytical research to the subject. It was reserved for Laplace to detectthe true origin of these anomalous phenomena in the mutual action ofthe two planets.

Perhaps a still more remarkable result, due to the same geometer, wasthe explanation of the secular inequality in the mean motion of the Moon .The records of certain eclipses of the Moon observed at Babylon aboutseven hundred years before the Christian era, when compared with obser-vations of similar phenomena by the Arabian astronomers about the tenth