CONTENTS.

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CHAPTER IX.

PAGE

Secular Variationsof the Planets.—Elements of the Terrestrial Orbit.—Variations ofthe Eccentricity . — Motion of the Aphelion.—Obliquity of the Ecliptic. —Its secu-lar Variation computed by Theory.—Euler.—Lagrange.—Laplace.—Influence ofthe displacement of the Ecliptic on the length of the tropical Year.—Indirect Action

of the Planets on the terrestrial Spheroid Its effect in restricting the Variations of

the Obliquity of the Ecliptic and the length of the tropical Year.—Invariable Planeof the Planetary System.—Theory of Comets.—Hevelius.—Borelli.—Dbrfel.—Subjection of the Motions of Comets to the Theory of Gravitation by Newton.—Halley. — Clairaut. —Researches of Lagrange on Cometary Perturbation.— Lexel’sComet.—Its perturbations investigated by Laplace.—Publication of the MecaniqueCeleste.—General Reflections on the Progress of Physical Astronomy . . 97

CHAPTER X.

Variation of the Mean Distances of the Planets. ^ Researches of Poisson.—TheTheory of Planetary Perturbation resumed by Lagrange and Laplace.—Uni-formity of the results arrived at by these Geometers.—The General Theory ofthe Variation of Arbitrary Constants established by Lagrange.—Researches ofPoisson on this subject.—Death of Lagrange.—Researches of Modern Geometerson the Theory of Perturbation.—Method of Hansen.—Developement of thePerturbing Function.—Burchardt.—Binet.—New Methods devised for obtainingthe coefficients of the Perturbing Function. — Secular Inequalities of the Planets .

— Researches of Le Verrier.—Theory of the Moon.— Irregularities of the Epoch.

—Equation of Long Period.—Researches of Damoiseau, Plana, and Carlini.—Lunar Tables calculated by means of the Theory of Gravitation.—Researches ofLubbock and Poisson.—Reduction of the Greenwich Observations.—Discoveryof the True Cause of the Irregularities of the Moon ’s Epoch, by Hansen.—Re-searches for the purposes of determining the Value of the Moon ’s Mass . . 109

CHAPTER XL

Theory of the Perturbations of the larger Planets.—Theory of Mercury.—Re-searches of Le Verrier.—Theory of Venus.—Determination of its Mass.—Theoryof the Earth.—Solar Tables.—Delambre.—Long Inequality depending on theAction of Venus discovered by Airy.—Theory of Mars.—Evaluation of itsMass.—Theory of Jupiter.—Calculation of the Terms of the Long Inequalityinvolving the Fifth Powers of the Eccentricities.—Researches of Plana.—Cor-rection of the value of Jupiter ’s Mass.—Theory of Saturn.—Researches relative tothe determination of its Mass.—Theory of Uranus. —Its anomalous Irregularities.

—Discovery of an Exterior Planet by means of them.—Theory of the SmallerPlanets.—Hansen. — Lubbock.—Theory of Comets.—Researches on the Motion ofEncke’s Comet.—Hypothesis of a Resisting Medium.—Perturbations of Halley’sComet calculated.—Satellites of Jupiter, Saturn , and Uranus.—Determination ofthe Mass of Saturn’s Ring, by Bessel.—Libration of the Moon.—Nicollet.—Theoryof the Figure of the Earth. —Researches of Ivory on the Attraction of Elliptic Sphe-roids.—Experiments with the Pendulum. —Mean Density of the Earth.—Motionof the Earth about its Centre of Gravity.—Poisson.—Researches on the Tides .

— Oscillations of the Atmosphere.—Experiments of Colonel Sabine . . . 123

CHAPTER XII.

Introductory Remarks.—Ancient Observations of Uranus. —Calculation of Tablesof the Planet by Delambre. — Tables of Bouvard.—Irregularities of the Planet. —

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