HISTORY OF PHYSICAL ASTRONOMY.

m

to the centre of gravity of the earth and moon, diverge most from eachother. Now the amount of this divergence depends on the relativedistances of the earth and moon from their common centre of gravity,and these again depend on the relative masses of the two bodies. Hence,when the maximum value of the inequality is determined by observationand the mass of the earth is at the same time known, the mass of themoon becomes known also. Now Delambre inferred, from a great numberof observations on the sun, that the maximum value of the lunar equationwas 7".5. This result gave Laplace for the value of the moon’smass.

The third method which Laplace employed for determining the moon’smass is suggested by the inequality of nutation. This inequality beingdue to the action of the moon on the terrestrial spheroid, it is clear that acomparison of its observed value with the formula for it, furnished bytheory, will lead to a knowledge of the moon’s mass. Laplace assumedthe maximum value of nutation to he 9".6, as estimated by Maskelyne,and hence inferred that the moon’s mass was equal to -Jq-.

Comparing together these different results he finally fixed upon asthe most probable value of the mass.

The researches of succeeding astronomers generally lead to the con-clusion that the real value of the moon’s mass is somewhat less thanthe estimate of Laplace. It is fortunate that this is a point, in whichgreat precision is not called for by the existing state of science.

CHAPTER XI.

Theory of the Perturbations of the larger Planets.—Theory of Mercury_Researches

of Le Verrier.—Theory of Venus.—Determination of its Mass.—Theory of the

Earth Solar Tables.—Delambre-Long Inequality depending on the Action of

Venus discovered by Mr. Airy.—Theory of Mars. -—Evaluation of its Mass.—Theoryof Jupiter.—Calculation of the Terms of the Long Inequality involving the FifthPowers of the Eccentricities.— Researches of Plana.—Correction of the value of Ju­ piter ’s Mass_Theory of Saturn.—Researches relative to the determination of its

Mass.—Theory of Uranus. —Its anomalous Irregularities.—Discovery of an ExteriorPlanet by means of them.—Theory of the Smaller Planets.—Hansen..—Lubbock.—

Theory of Comets_Researches on the Motion of Encke’s Comet_Hypothesis of a

Resisting Medium._Perturbations of Halley’s Comet calculated.—Satellites of Jupiter,

Saturn , and Uranus.—Determination of the Mass of Saturn’s Ring, by Bessel.—Libration of the Moon.—Nicollet.—Theory of the Figure of the Earth. —Researchesof Ivory on the Attraction of Elliptic Spheroids.—Experiments with the Pendulum. —.Mean Density of the Earth.—Motion of the Earth about its Centre of Gravity.—Poisson—Researches on the Tides.—Oscillations of the Atmosphere.—Experimentsof Colonel Sabine.

Although the methods devised by the mathematicians of the last centuryfor the purpose of computing the effects of planetary perturbation were com-plete in so far as the more important bodies of the system were concerned,there still remained, even in this part of the theory, various points whichcalled for further investigation. The masses of the planets in some casesrequired to be determined upon more satisfactory principles, or by means