PEE FACE.

*V

century, seemed to indicate tliat the Moon ’s angular velocity round theEarth was subject to a slow acceleration. This fact was confirmed beyondall doubt by the observations of modern astronomers; but its existenceseemed absolutely irreconcilable with the results to which geometers wereconducted by their researches on the Theory of Gravitation. The physicalcause of this acceleration continued to escape the analytical scrutinies ofEuler , Lagrange, and Laplace, until at length the sagacity of the last-mentioned geometer led to its detection.

The sixth chapter is devoted to an account of the labours of geometerson the Figure of the Earth , the Precession of the Equinoxes, theLibration of the Moon , and other kindred subjects. By an ingeniousapplication of his researches on the attraction of spheroids, Newton rigor-ously determined the ellipticity of the Earth , upon the supposition of itsdensity being uniform, and of the figure of an oblate spheroid being com-patible with the conditions of equilibrium of a fluid mass. The truth ofthe last-mentioned supposition was afterwards demonstrated by Maclaurin with all the elegance and rigour of the ancient geometry. With respect tothe internal structure of the Earth , the ellipticity deduced from themeasurement of arcs of the meridian was totally at variance with thesupposition of its homogeneity. It was reserved for Clairaut to determinethe ellipticity on the more probable hypothesis of the strata increasing indensity towards the centre of the Earth .

The Precession of the Equinoxes is beyond doubt the most remark-able of all the perturbative effects by which the planetary system is cha-racterised. Its original discovery as a sidereal phenomenon is due to thegreat astronomer Hipparchus . The explanation of its true characterwas first given by Copernicus , who shewed that it might arise from aconical motion of the Earth ’s axis. The question relative to the physicalcause of this singular movement continued to be involved in impenetrablemystery, until at length Newton discovered its origin in the disturbingaction of the Sun and Moon upon the redundant matter accumulated roundthe terrestrial equator. The subsequent discovery of the Nutation of theEarth ’s Axis by Bradley introduced a new cause of complication intothe subject. The complete solution of the problem of the Earth ’s motionround its centre of gravity, by a rigorous application of the principles ofMechanical Science, was reserved for D’Alembert . The subject of theLibration of the Moon , which is noticed in the same chapter, exhibitsanother striking illustration of the comprehensive character of the Theoryof Gravitation in assigning the physical explanation of the various phe-nomena relative to the movements of the celestial bodies. The researchesof Newton on this subject were perfected by Lagrange, who succeeded inobtaining results which accorded in a most satisfactory manner with thosededuced from observation.

The seventh and eighth chapters embrace a somewhat detailed historyof the theory of Jupiter ’s satellites. In the seventh chapter I have givenan account of the original discovery of these bodies by the illustrious