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HISTORY OP PHYSICAL ASTRONOMY.

effect of Jupiter ’s eccentricity. The maximum value which he assigned tothe aberration of light would have given him 16 m 20 s * for the greaterequation—a result which would have been much more conformable toobservation than the quantity he actually employed. It is surprising thathe should have overlooked the importance of his great discovery in furnish-ing an independent means of calculating this equation.

The irregularities in the motions of the satellites were the cause ofmuch perplexity to Bradley. The second satellite, especially, presentedanomalies which could not be accounted for either by a circular or anelliptic orbit. Sometimes it deviated from its mean place to so great an ex-tent, and in so short a time, as to be incompatible with a small eccentricity ;while, on the contrary, other observations rendered it impossible that theorbit should differ much from a circle. He discovered that the threeinterior satellites piassed through the irregularities of their motions in 437days; the errors returning at the close of this period in the same orderand magnitude as before. He considered that about the middle of thisperiod tlie inequality of the second satellite might amount to 30 or 40minutes. He remarked that the period of the inequalities correspondedto that which brought back the satellites to the same position relativelyto each other, and to the axis of Jupiter 's shadow; and he henceinferred, with his usual sagacity, that the inequalities resulted from themutual attraction of the satellites. “ While we carefully attend,” says he,“ to future observations, by means of which the theory of the satellites maybe established, a posteriori, let us hope that some rival of the great Newton,relying upon the sure and tried principle of gravitation, will achieve thenoble task of investigating a priori the effects of their mutual attraction.”Bradley retained the inclinations of the three interior satellites at 2° 55',as fixed by Cassini; but he reduced that of the fourth to 2° 40'. Thiswas a happy alteration; Delambre’s tables make it 2° 40' 42" for the sameepoch. He also discovered that the orbit of the fourth satellite is eccentric ;and he fixed the maximum value of the equation of the centre at 48 m .

Maraldi II. devoted much of his time to researches on the satellites, andeffected some very important improvements in the theory of their motions.In a memoir, which appeared in the volume of the Academy of Sciences for 1732, he proved that the inclination of the third satellite is variable;and he also established the eccentricity of the fourth satellite. Withrespect to the first of these points, he found that the durations of theeclipses of the satellites had been continually diminishing ever since theyear 1093. It was impossible to explain this constant diminution by aneccentricity in the orbit, since the effect of such a supposition would be toproduce sometimes a diminution; and at other times an increase in theduration of the eclipse. Nor would a motion of the nodes suffice for thispurpose; for he shewed that the utmost change in their position whichcould possibly occur would not exceed 3°, and this would occasion a changeof only 10 s in the duration of eclipses at the limits; whereas observa-tion shewed it to amount to 16 m 44 s . Besides, upon this suppo-sition, the same variation ought to have manifested itself at the nodes asat the limits ; hut the duration of eclipses varied only to a very smallextent when they happened in the former of these positions. The observ-ations, therefore, could only be reconciled together by admitting that the

* Strictly speaking, the equation is equal only to half this quantity ; but in the tablesof the satellites the coefficients are doubled in order to render the results always additive.