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CONTENTS.
on the Theory of Jupiter and Saturn.—Invariability of the Mean Distances of thePlanets.—Oscillations of the Eccentricities and Inclinations.— Stability of thePlanetary System. 47
CHAPTER V.
Irregularities of Jupiter and Saturn.—Researches of Lambert.—Lagrange.—Circum-stances which determine the Secular Inequalities in the Mean Longitude.—Laplace’s Investigation of the Theory of Jupiter and Saturn.—His Discovery ofthe physical cause of the Long Inequality in their Mean Motions.—Accelerationof the Moon ’s Mean Motion.— Halley.—Dunthorne.— Failure of Euler andLagrange to account for the Phenomenon.—Its explanation by Laplace.—SecularInequalities in the Moon ’s Perigee and Nodes.—Inequalities depending on theSpheroidal Figure of the Earth.—Parallactic Inequality.
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CHAPTER VI.
Theory of the Figure of the Earth.—Newton.— Huygens.—Maclaurin.—Clairaut.—Attraction of Spheroids.—D’Alembert—Legendre.—Theory of Laplace.—Motion of the Earth about its Centre of Gravity.—Nutation.—Bradley.—Investi-gation of Precession and Nutation, by D’Alembert. —The Tides.—EquilibriumTheory.—Researches of Laplace.—Stability of the Ocean.—Libration of theMoon.—Galileo.— Hevelius.—Newton.— Cassini.—Newton’s Explanation of theMoon ’s Physical Libration.—Researches of Lagrange.—Combination of the Prin-ciple of Virtual Velocities with D’Alembert’s Principle.—Laplace investigates theEffect of the Secular Inequalities of the Mean Motion upon the Libration inLongitude.—His Theory of Saturn’s Rings .......
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CHAPTER VII.
Jupiter ’s Satelites.—Galileo.—Simon Marius.—Ilodierna.—Borelli.—Cassini.— Hisfirst Tables.—He is invited to France. —He publishes his second Tables.—HisRejection of the Equation of Light.—Researches of Maraldi I.—He discoversthat the Inclination of the second Satellite is variable.—Bradley’s Discoveries.—Maraldi II.—His Discoveries relative to the third andfourth Satellites. —He adoptsthe Equation of Light.—Wargentin.—-He discovers the Inequalities in Longitude of the first and second Satellites. —He remarks that the third Satellite has twoEquations of the Centre.—Motion of the Nodes of the fourth Satellite.—Inclina-tion of the third Satellite.—Libratory Motion of the Nodes.—Inclination of thefourth Satellite. 76
CHAPTER VIII.
Physical Theory of the Satellites.—Newton.—Euler.—Walmsley.—Bailly computesthe Perturbations of the Satellites.—Researches of Lagrange.—He obtains foreaeli Satellite four Equations of the Centre and four Equations of Latitude. —His mode of representing the Positions of the Orbits.—Inutility of his Theory inthe Construction of Tables.—Laplace.—His Explanation of the constant Rela-tions between the Epochs and Mean Motions of the three interior Satellites. —Hecompletes the Physical Theory of the Satellites.—Delambre.— He calculatesTables on the Basis of Laplace’s Theory —He determines the Maximum Value ofAberration by means of the Eclipses of the first Satellite.—Agreement of hisResult with Bradley’s.— Conclusions derivable from it.
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