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HISTORY OF PHYSICAL ASTRONOMY.

appearance previous to the year 1844. The planet Jupiter , which in allprobability chained it down orginally to the system, will one day act uponit with equal intensity, but in an opposite direction, and we may reasonablypresume that, when it has escaped from his influence, it will again fly offinto infinite space, describing a parabola or hyperbola.

The theory of Jupiter ’s satellites has not received any material improve-ment since the publication of the Mecanique Celeste . In 1817 Delambrepublished new tables of the satellites founded on all the eclipses that hadbeen observed from 1660 down to the commencement of the present century.These were succeeded by Damoiseau's tables which appeared in 1836.

The satellites of Saturn have hitherto occupied the attention of geometersonly in a very small degree. This has chiefly arisen from the small pro-gress made by astronomers in determining by observation the elements oftheir motions, and in tracing, a posteriori, the more considerable in-equalities resulting from their mutual perturbation. We have seen astriking proof of the utility of observation for both these purposes, in thehistory of Jupiter ’s satellites. The influence of the spheroidal figure ofSaturn is clearly indicated by the positions of the ring and the orbits ofthe interior satellites, which coincide almost with the plane of his equator.As the satellites recede from their primary, the disturbing action of thesun increases relatively to that occasioned by the spheroidal figure of theplanet, and the orbits commence to deviate sensibly from the plane of hisequator, and to incline towards that of the ecliptic. The sixth, or Huy-genian satellite, which is the brightest of all, and therefore the mostfavourable for observation, has formed the subject of an elaborate investi-gation by Bessel. From the motion of the apsides of this satellite, heconcluded that the mass of the ring amounted to of the planet’s mass.He also obtained for the latter a value agreeing very nearly with thatdeduced by Bouvard from the equations of condition employed in the con-struction of Jupiter ’s tables. Some valuable observations of the satelliteswere made by Sir John Herscliel in the course of his residence at theCape of Good Hope . From those of the sixth satellite he derived elementswhich agreed very nearly with the values assigned by Bessel for the epochof 1830, taking into account the variation of each element during the inter-mediate period. He also computed the epochs and mean motions of theother satellites, and obtained results which accorded very well with thosededucible from the earlier observations of Sir William Herschel .

If the theory of Saturn ’s satellites is still in its infancy, the remarkapplies with still greater force to the satellites of Uranus . These bodiescan only be rendered visible by means of the most powerful telescopes, andtherefore it may naturally be presumed that a considerable time will elapsebefore a correct theory of their motions be formed. When their elementsare once determined by observation, they will offer peculiar interest to thegeometer in consequence of their motions being retrograde and the planesof their orbits being nearly perpendicular to the plane of the ecliptic.

The consummate researches of Lagrange left little to be accomplishedin the theory of the Libration of the Moon. Poisson applied his powers ofanalysis to this interesting subject, but the results at which he arrived hadonly the effect of confirming those obtained by the illustrious geometerjust mentioned *. Although the mean motions of the moon with respect torotation and revolution be both equal to each other, still the inequalities

* Connaissance des Temps, 1821-22. The researches of Poisson are principallydirected to the inequalities in the inclination and node of the lunar equator.