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HISTORY OF PHYSICAL ASTRONOMY.

I

satellite would lie reduced to the simple consideration of a material particle jattracting the body at that point. This, however, is not the real case of !nature ; for observation shews that the figure of the planet is That of anoblate spheroid, whose axes are to each other nearly as 13 to 14. Thiscircumstance causes the law of his attraction to deviate from the inversesquare of the distance, and hence originates a disturbing force whichpowerfully deranges the motions of the satellites.

Newton, in the third book of the Prineipia, considers the disturbingaction of the'sun upon Jupiter ’s satellites, and attempts to determine theinequalities of their motions by the principles of the lunar theory. In thismanner he found that the nodes of the fourth satellite had a retrogrademotion upon the plane of Jupiter ’s orbit, the annual quantity of whichamounted to 5'* * * § . We have seen that this result was subsequently contra-dicted by observation; the actual motion having been discovered byastronomers to be direct. The phenomenon in question does not, in fact,depend so much upon the sun as upon the third satellite and the ellipticityof Jupiter ; causes of disturbance which were not taken into account byNewton.

Euler, in 1748, first remarked that the spheroidal figure of Jupiter would occasion an irregularity in the law of his attraction f. Walmsley, in1758]:, shewed that the disturbance hence arising would produce a motionof the nodes and apsides of each satellite. In 1703 Euler communicated amemoir to the Academy of Berlin , in which he examined the perturbationsof a satellite revolving round a planet of a spheroidal figure. lie shewedthat when the satellite revolved in the plane of the planet’s equator the jaction of the protuberant matter generally occasioned a progressive motion Iof the apsides. As the orbit of the satellite became more inclined to this ]plane, the motion of the apsides continually diminished, and it ceasedaltogether when the angle of inclination was equal to 54° 44'. From this ;position the motion of the apsides was regressive, and it continued toincrease until the orbit of the satellite was perpendicular to the plane ofthe equator.

Bailly§, about the same time, employed Clairaut ’s theory of the moon iin researches on the perturbations of the satellites. He discovered, by asimple analysis, that the mutual attraction of the three interior satellitesoccasioned those inequalities in their motions which produced a regularreturn of their eclipses at the end of 437 days. We have seen thatBradley was the first astronomer who threw out a suspicion of this fact.These inequalities are precisely analogous to the lunar variation, the onlydifference being, that the disturbing body is in each case one of the satel-lites themselves, and not the sun. In the theory of the first satellitethe principal disturbing body is the second, for the exterior satellites aretoo remote to exercise any sensible influence, and the effect of Jupiter ’sellipticity is equally inappreciable, because the orbit of the satellite issituated in the plane of his equator, and at the same time does not pos-sess any eccentricity. It is clear, then, that by comparing the coefficientof the equation furnished by theory with the magnitude of the inequality,

* Prineipia, lib. iii. prop. 23. Newton, in the same proposition, makes the in-equality of the fourth sateliite depending on the disturbing action of the sun, and, similarto the lunar variations, equal to 5 ' 12".

t Recherches des Inegalites de Jupiter et de Saturne. Prix de l’Academie, tome vii.

} Phil. Trans., 1758.

§ Born at Paris in 1736 ; perished by the guillotine in 1793.