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] attended to by D Alembcil, and showed that the annual variation of the precession causes a corresponding variation in the length of the tropical year, which at present is about 9 or 10 seconds shorter than it was in the time of Hippar- chus. He proved that the secular inequalities of the motions of the earth and moon have no sensible effect in displacing the axis of the earth s rotation ; and he deter mined the nutation of the lunar orbit corresponding to the nutation of the terrestrial equator. Physical astronomy is also indebted to Laplace for a complete theory of the system of Jupiter s satellites, from which Delambre constructed a set of tables representing the motions of these bodies with all desirable accuracy. And when to these numerous and most important researches we add the mathematical theories of molecular attrac tion, and the propagation of sound, together with many great improvements in analysis, and reflect, besides, that he is the author of the Mecanique Celeste, the Systeme du Monde, and the Theorie des Probabilites, we shall not hesitate to rank him next to Newton among the greatest benefactors of the mathematical and physical sciences. By the brilliant discoveries of Laplace, the analytical solution of the great problem of physical astronomy was completed. The principle of gravitation, which had been found by Newton to confine the moon and the planets to their respective orbits, was shown to occasion every apparent irregularity, however minute, in the motions of the planets and satellites ; and those very irregularities which were at first brought forward as objections to the hypothesis have been ultimately found to afford the most triumphant proofs of its accuracy, and have placed the truth of the Newtonian law beyond the reach of all future cavil. Such is the state to which analysis has now attained, that the geometer embraces in his formulae every circumstance which affects the motions or positions of the different bodies of the planetary system ; and the conditions of that system being made known to him at any given instant of time, he can determine its conditions at any other instant in the past or future duration of the world. He ascends to remote ages to compare the results of his theories with the most ancient observations ; lie passes on to ages yet to come, and predicts changes which the lapse of centuries will hardly be sufficient to render sensible to the observer. But notwithstanding the comparative perfection to which the theory of astronomy has been brought, it is still far from having reached the limit beyond which further refinement becomes superfluous. The masses of the planets, and some other elements, remain to be determined with still greater precision, by a diligent comparison of the analytical formulae with good observations ; and the labours of the geometer may still be beneficially employed in giving greater simplicity to the calculus, or in extending its power over subjects which have hitherto eluded its grasp. The observation of periodic comets that complete their revolutions in comparatively short intervals of time, opens up an interesting field for speculation and research, and will doubtless be the means of throwing light on some curious and as yet very obscure points, respecting the appearances, motions, and physical constitution of those strange bodies. In the other departments of astronomy, also, numerous questions still remain to be discussed, the solution of which will occupy and reward the future labours of astronomers, and in which much progress has been made during the present century, by means of the powerful instruments now employed at the great observatories of every civilised country, and the improved methods of analysis brought to bear upon the results of observation. The curious pheno mena of double and multiple stars, some of which are found to form connected systems of bodies revolving about one another, or a common centre of motion, the variable stars, the proper motions of the stars, the translation of the solar system in space, the progressive condensation of nebulae, are subjects still in a great measure new ; for it is only of late years that observers have begun to direct the requisite attention towards them, or indeed have been in possession of instruments of sufficient power and delicacy to observe and measure the minute changes which take place beyond the boundaries of our own system. The discoveries in astronomy during the present century have been so brilliant and numerous, and the progress in every department is so rapid, and involves so many details, that it would be impossible to give here a detailed account of that progress. Moreover, there is a reason for not attempt ing this, in the circumstance that we have brought the history of our subject as far as is possible without consider ing the work of men still living. For although some to whom the astronomy of the present day is indebted, and not a few who must always be regarded as among the leading astronomers of the century, have passed away, yet the consideration even of their work would necessarily introduce the discussion of the labours of those whoso labours are still in progress. It seems on all accounts better, therefore, to content ourselves with the discussion of the various results obtained during recent years, without attempting the invidious task of apportioning to the several workers their relative positions.

—Apparent Motion of the Star-sphere.

When we look at the heavens on a clear night, we perceive a concave hemisphere on which are strewn multitudes of bright points. As we watch these hour after hour, we find that they are carried round precisely as though they were fixed on the interior surface of a spherical shell turn ing on a fixed axis. New groups are seen to rise above the eastern horizon, while those above the western horizon descend and finally disappear. Turning towards the south, we see that the groups of stars which pass above the horizon somewhat to the east of the south attain but a slight elevation when at their highest in the south, and then descending set as far to the west of the south point as they had risen to the east of it. Turning to the north, we see that there are groups of stars which remain visible the whole night, wheeling around a fixed point, and describing circles of greater or less magnitude according as they are at a greater or less distance from that point. Supposing our stand point to be in or near London, the point thus remaining fixed is due north, and about 51 1 above the horizon, therefore, about 38 from the point directly overhead. If the heavens be observed night after night, similar phenomena are seen ; and we recognise the uni formity of the motion of the (imaginary) star-sphere about its (imaginary) axis ; for in any assigned interval, on any night in the year, the star-sphere turns by the same amount. It is soon found that the rate of turning is such that a complete rotation is effected in the course of about one day. But before many days have passed we find that this uniform turning motion does not corre spond exactly to our common day. For though on several successive nights the stars may appear to be nearly in the same situation with respect to the horizon at any assigned hour, yet before long (or even in twenty-four hours if exact observation be made) it is found that the stars occupy the same position, not at the same hour on successive nights, but about four minutes earlier night after night. Thus, in the course of about fifteen days, the star-sphere has gained one hour s rotation ; in about thirty days, two hours rotation, and so on : until in the 