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Dreisen announced to the world the discovery of an other asteroid, which was named Astrea. Before twa years had rolled round, the same indefatigable observer discovered a sixth member in this wonderful group,

which was called Hebe. His success induced other observers to undertake a similar examination, and in a very short time the researches of Mr. Hind of London, were rewarded by the discovery of a seventh and eighth asteroid, which were named Iris and Flora.

Thus have we no less than eight of these minute worlds, revolving in orbits so nearly equal, that for weeks and months these miniature orbs may sweep along in space, almost within hail of each other. Let us now return to an examination of the hypothesis of Olbers, that these are the fragments of a world of large size, which once occupied an orbit intermediate between those of Mars and Jupiter.

If any internal convulsion could burst a world and separate its fragments, it is readily seen that the fragments of largest mass would move in orbits more nearly coincident with that of the original planet, while the smaller fragments would revolve in orbits greatly inclined to the primitive one. This condition is wonderfully fulfilled among the asteroids. The larger planets, Ceres and Vesta, revolve in orbits with small inclinations to the ecliptic, while the smaller objects are in some instances found to move in planes with very great inclinations. The force necessary to burst a planet, and to give to its fragments certain orbits, has been computed by Lagrange, and he finds that in case any fragment is projected with an initial velocity one hundred and twenty-ono times greater than that of a cannon ball, it would become a direct comet, with a parabolic orbit, while a primitive velocity one hundred and fifty-six times greater than that of a cannon ball would cause the fragments to revolve with a retrograde motion in the curve of a parabola. Any less powerful force would cause the fragment to revolve in ellipses; and it is probable that the force which operated to produce the asteroids was not more than twenty or thirty times greater than that of a cannon ball. Although the theory of Olbers has received new accessions of strength from the discovery of every new asteroid, it would be wrong to regard it as one of the demonstrated truths of astronomy. In the mean time, powerfil efforts are making to scour the heavens, and a method of observation has been proffered to the Academy of sciences, of Paris, by which all the visible fragments may be discovered within a period of four years. Should this plan, which contemplates a division of the heavens among different astronomers, be adopted, volunteers have already presented themselves, and the most interesting results may be anticipated.

From this curious branch of astronomical inquiry we turn to one of still deeper interest. In the examinations for new planets, thus far, the telescope has been the sole instrument of research. Conjectures based upon analogical reasoning, it is true, guided the instrumental examinations, but the mind had never dared to rise to the effort of reasoning its way analytically to the exact position of an unknown body. It has been reserved for our own day to pro• duce the most remarkable and the boldest theorizing

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which has ever marked the career of astronomical science. I refer to the analytic effort to trace out the orbit, define the distance, and weigh the mass of an unknown planet as far beyond the extremest known planet as it is from the sun.

I am fully aware of the difficulties by which I am surrounded, when I invite your attention to this complex and intricate subject; and I know how utterly impossible it is, in a popular effort, to do any kind of justice to the intricate and involved reasoning of the great geometers, who have not only rendered themselves, but the age in which we live, illustrious by their efforts to resolve this, the grandest problem which has ever been presented for human genius.Trusting to your close attention, I shall attempt to exhibit some faint outline of the train of reasoning and the kind of research employed in rescuing an unknown world from the viewless regions of space in which it has been tracing its unknown orbit for ages commensurate with the existence of the great system of orbs of which it constitutes a part.

After the discovery of the planet Uranus, by Sir William Herschel, geometers were not long in fitting it with an orbit which represented in the outset, with accuracy, its early movements. With this orbit it became possible to trace its career backwards, and to define its position among the fixed stars for fifty or one hundred years previous to the date of its discovery. This was actually done, with the hope of finding that the place of the planet had been observed and recorded by some astronomer, who ranked it among the fixed stars. This hope was not disappointed. The planet, believed to be a fixed star, had been seen and observed no less than nineteen different times, by four different observers, through a period running back nearly one hundred years previous to the discovery of its planetary character by Herschel. These remote observations were of the greatest value as data for the determination of the elements of its elliptic orbit, and for the computation of the mean places, which might serve to predict its position in coming years.

A distinguished astronomer, M. Bouvard, of the Paris Academy of Sciences, about thirty years ago, undertook the analytic investigation of the movements of Uranus, and a computation of exact tables. He was met, however, by difficulties which, in the state of knowledge as it then existed, with reference to this planet, were absolutely insurmountable. He found it quite impossible to obtain any orbit which would pass through the places of the planet determined after its discovery, and through those positions which had been fixed previous to that epoch. In this dilemma it became necessary to reject the old observations as less reliable than the new ones, and the learned computer leaves the problem for posterity to resolve, carefully abstaining from any absolute de. cision in the case.

His orbit, based upon the new or modern observations, and his tables being computed, it was hoped that the theoretic places of the planet would thereafter coincide with the observed places and that all discrepancies which might not be fairly chargeable to errors of observation, would be removed. In this ex. pectation, however, the astronomical world was disappointed ; and while the tables of Bouvard failed absolutely to represent the ancient observationu, in a few years they were but little more truthful in giving the positions actually filled by the planet under the telescope. The discrepancies between the theoretic and actual places of the planet began to attract attention many years since. As early as 1838, Mr Airy, Astronomer Royal of England, on a comparison of his own observations with the tables, found that the planet was out of its computed track, by a distance as great as the moon's distance from the earth, and that it was actually describing an orbit greater than that pointed out by theory. It seemed that this remote body was breaking away from the sun's control, or that it was operated on by some unknown body deep sunk in space, and which thus far had escaped the scrutinizing gaze of man.

These deviations became so palpable as to attract general attention, and various conjectures were made with reference to their probable cause.

Some were disposed to regard the law of gravitation as somewhat relaxed in its rigorous application to this remote body; others thought the deviation attributable to the action of some large comet, which might sway the planet from its course; while a third set of philosophers conjectured the existence of a large satellite revolving about Uranus, and from whose attraction the planet was caused to swerve from the computed orbit. These conjectures were not sustained by any show of reasoning, and were of no scientific value.

Such was the condition of the problem when it was undertaken by a young French astronomer, not quite unknown to fame in his own country, but comparatively at the beginning of his scientific career. The

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