HISTORY OF PHYSICAL ASTRONOMY.
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second order is equal only to 1".07; and all those depending on the termsof the third and fourth orders are less than 0".l * * * § .
The researches of geometers on the perturbations of Mars have not ledto any interesting results; they form a striking contrast in this respectwith those memorable researches in connexion with the same planet bymeans of which Kepler was conducted to his great discoveries relative tothe fundamental laws of the motions of the planets and the forms of theirorbits. The perturbations produced by this planet in the motions of theother bodies of the system are so small as to render the determination ofits mass exceedingly difficult. Laplace effected this object by the aid ofthe hypothetic principle that the densities of the planets vary in the in-verse ratio of their mean distances from the sun. In this manner he ob-tained T.'STii.oiio f° r t ^ le mass of the planet*. Delambre, by comparingLaplace’s formula of the Earth 's perturbations with the solar observationsof Bradley and Maskelyne, was induced to fix the mass at ■ 2 , 3 T 67 r 2 <>' t-Burchardt by a similar process obtained -orf-sh.'STT f° r its true value l.The accordance between these results is sufficiently satisfactory; but Mr.Airy has inferred from his researches on the solar theory that Delambre’sestimate should be diminished in the proportion of 22 to 15. It is for-tunate, as in the case of Mercury , that the disturbing effects of thisplanet are so insignificant as to dispense with the necessity of extremeaccuracy.
In the theory of Jupiter the most important point is the long ine-quality depending on the action of Saturn . This inequality is mainlycontained among the terms of the third order relative to the eccen-tricities and inclinations; but Laplace suspected that the terms in-volving the fifth powers of the eccentricities might also be sensible.Burchardt performed the laborious operation of calculating these terms,hut unfortunately he applied them with the wrong sign. Laplace soonafterwards noticed this circumstance in a supplement to the third volumeof the Mecanique Celeste, and he shewed that, when it was duly taken intoaccount, the theory would present a most satisfactory accordance with aconjunction of Jupiter and Saturn observed by Ibyn Jounis, at Cairo ,towards the close of the eleventh century. That astronomer has assigned1439" as the excess of Saturn’s geocentric longitude over that of Jupiter on the 31st October, 1087, at 16 h mean time of Paris . Now, when theplaces of the two planets were calculated by theory for the same epochprevious to the detection of Burchardt’s error, the excess of longitude wasfound to amount only to 729". When the effect of that error, however,was subsequently taken into account by Laplace , the same quantity rose to1117". The difference between this result of theory and the recordedexcess of longitude amounts to 322" or 5' 22", a quantity which fallsconsiderably within the errors of the observations of the Arabianastronomers.
* Mec. Cel., liv. vi. chap. ix. et x.; Theorie Analytique du Systeme du Monde, liv.chap. xiv. et xv. The largest inequalities in Venus and the Earth depending on theterms of the third order are due to the disturbing action of Mercury . The reciprocal
action of these planets occasions analogous inequalities in the motion of Mercury , themaximum effect of Venus amounting to 8", but that of the Earth only to 0".5.
f Mec. Cel., liv. vi. chap. vi. } Tables du Soleil, 180G.
§ Connaissance des Temps, 1816. Pontecoulant attributes this value to Bessel(Theorie Analytique du Systeme du Monde, tome iii. p. 346); but as it is less thanDelambre’s exactly by Jth, which was the correction obtained by Burchardt, it is clear thatwe ought to read for Bessel’s name that of the last-mentioned astronomer.
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