PREFACE.

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Galileo , and of the labours of subsequent astronomers in establishingthe laws of their complicated movements. The eighth chapter exhibits aview of the researches of geometers, having for their object the explana-tion of these laws by the Theory of Gravitation. Some of the mostcurious effects of perturbation occur in this beautiful system. The resultsare mainly due to Lagrange and Laplace. The powerful character ofthe analysis which Laplace employed in these researches, is remarkablyexhibited in the determination of the ellipticity of Jupiter by means ofthe derangements which the redundant matter accumulated round theequator of the planet occasions in the motions of the satellites. Theillustrious geometer even boldly asserted, that the result thus derivedfrom theory was entitled to greater reliance than that obtained by directmeasurement with the micrometer!

The ninth chapter commences with a brief notice of the labours ofgeometers on some of the more hidden effects of perturbation. One ofthe most interesting of these is the gradual diminution of the obliquityof the ecliptic, occasioned by the disturbing action of the planets onthe earth. The sublime results arrived at by Lagrange and Laplace,relative to the stability of the planetary system, assure us that such adiminution will not continue indefinitely, but that after a certain limit ofobliquity has been attained, the angle contained between the planes of theecliptic and the equator will then commence to open out. This processwill continue until the obliquity attains a certain maximum value, whenthe increase will be converted again into a diminution, and thus theinclination of the two planes will continually oscillate between fixedlimits prescribed by the intensity of the disturbing forces. It follows asa necessary consequence, that the climate of any particular country willnot undergo an essential change from this cause, such as would inevitablyensue if the equator and ecliptic were ever to coincide, or to form witheach other an angle of ninety degrees. Thus the more profoundly doesanalysis penetrate into the operations of nature, the more admirable is theharmony which appears to pervade her various arrangements.

The subject of Comets was one of the severest tests to which the Theoryof Gravitation was submitted during the early period of its history. Thesebodies seemed to be so destitute of any coherent structure, and at thesame time so capricious in their movements, that the attempt to makethem the groundwork of strict investigation was long considered to beattended with insuperable difficulties. Newton, however, perceived, withcharacteristic sagacity, that, however evanescent might be the physicalconstitution of Comets , their material structure would subject them to theinfluence of the principle of Gravitation; and, in pursuance of this idea,he framed a theory of their movements, according to which they allrevolved in orbits resembling one or other of the conic sections, having thesun in the common focus. The apparition of the great comet of 1680 fur-nished him with the means of obtaining a complete verification of his theory.By a rigorous discussion of its observed positions he demonstrated incon-