HISTORY OF PHYSICAL ASTRONOMY.

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"be hoped that the planet Neptune will he found to derange the motion ofSaturn to such an extent as to account for the errors of perturbationwhich arise from the assumption of the more probable value of Jupiter ’smass.

The theory of Saturn is so closely linked with that of Jupiter , that anyremarks relative to the perturbations of one of the planets are generallyapplicable to those of the other. The masses of the two planets have also beendetermined by similar methods. Newton obtained -jjjVt f° r the mass ofSaturn , by assuming that the period of the sixth satellite amounted to15 d .9453, and its greatest elongation to 3'.4"* * * § . The latter quantity,however, considerably exceeds the real value, and therefore the resultsderived from it were erroneous. Laplace supposed the elongation to beequal only to 2' 59", and hence inferred that the mass of the planet isequal to , t ; < Vg t- Bouvard obtained for the value of the mass by

means of the perturbations of Jupiter . This result is confirmed by theresearches of Bessel, who has been conducted to a mass equal to -rs'TJTi.Tby a careful measurement of the elongations of the sixth satellite.

In 1808, Bouvard published tables of Jupiter and Saturn , but they weresoon found to be vitiated by the errors in the theory of both planets, towhich allusion has already been made. This defect was remedied by theastronomer just cited, who in 1821 published tables of the planetsadapted to the corrected theory. Mr. Adams has recently discovered animportant error in the tables of Saturn . While engaged in researcheson the motion of that planet, he found that the calculated values of one ofthe terms of the perturbation in latitude were totally irreconcileable withthe formula from which they were professedly derived. He has explainedthe probable origin of this discordance, which is somewhat curious |.

Until very recently the theory of Uranus has occasioned much troubleto astronomers. Tables of the planet were published by Delambre in1790, and by Bouvard in 1821; but, notwithstanding the care andskill which had been employed in their construction on each of theseoccasions, it was found that they failed to represent the actual motion.Irregularities were indicated by the observations, which could not beaccounted for either by the principles of elliptic motion, or by the disturb-ing action of the other bodies of the system. Without prarsuing thisinteresting subject further at present, we shall merely state that theseanomalous errors in the motion of Uranus have led to the discovery a prioriof a new planet exterior to it. In the ensuing chapter we shall give adetailed account of the circumstances connected with this remarkableresult of the theory of gravitation.

Astronomers have not yet arrived at a sufficiently satisfactory resultrelative to the mass of Uranus . Sir William Herschel having announcedthat the fourth satellite revolved round the planet in 13 d .4559, and thatits greatest heliocentric elongation was equal to 44".23 §, Laplace henceconcluded that the mass of the planet was equal to T-gfnTlI- Bouvard, on

* Princip., liv. iii. prop. viii. cor. i. + Mec. Cel., liv. vi. chap. vi.

| The principal terras of the perturbation in latitude are—

9 7 .67 sin. (f-2 j>'-60°.29) + 28".i9 sin. (2 <p—4-f 66°.12)where <p <p' denote the mean anomalies of Saturn and Jupiter . In tabulating the last term,Bouvard appears to have employed ip-2tp' instead of 2 <p— 4 <p', so that the two termsmay be united in a single term, represented by 25".85 sin (<p— 2 <p' + 43’.88). Thecalculated values of this term were found by Mr. Adams to agree very closely with the table.

§ Phil. Trans., 1788. || Mec. Cel., liv. vi. chap. vi.

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