HISTORY OF PHYSICAL ASTRONOMY.

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important methods of Euler , Clairaut , D’Alembert , and Lagrange; but inrespect to which it has been beautifully remarked by an eminent philo-sopher* that the immortal author might be amply justified in using thewords of the prince of antiquity, “ et quorum pars magna fui.”

The third period, although distinguished less by intellectual triumphsthan by the profusion of its accumulated treasures, notwithstandingexhibits some results which may vie in splendour with the most brilliantefforts of genius in any age. The sublime theory of the variation ofarbitrary constants was carried by Lagrange to a state of perfection whichwill command the admiration of geometers to the latest posterity, and wassubsequently applied with success to all the great problems of the systemof the world. The vast treasures of analysis which had been amassed bythe geometers of the eighteenth century supplied inexhaustible stores forthe improvement and extension of 1#ie several parts of the theory of gravi-tation; and, as the objects of research were now of a still more evanescentcharacter than they had been in the preceding period, the labours of theastronomer were characterized by a suitable degree of refinement. Theannals of science do not contain the record of more delicate operationsthan those which have been conducted in the present age for the purposeof determining the ellipticity of the earth by means of the pendulum.The elements of the planetary orbits have also been determined withunexampled precision, a circumstance which has been attended with thetwofold advantage of improving the tables of astronomy, and exhibiting, inbold relief, the existence of outstanding irregularities. By these meansthe long inequalities in the earth and moon, besides various phenomenaof minor interest, have been detected and accounted for by the theory ofgravitation. A similar process led to a clear definition of the anomalies ofUranus , and suggested those immortal investigations which established theexistence of an exterior planet.

The future prospects of physical astronomy are in accordance with itspast triumphs. The theories of the smaller planets and comets, and theinverse problem of planetary perturbation, still continue to offer to thegeometer extensive subjects of interesting research. The theories of thesecondary systems are also still in an imperfect condition. It is true thatthe moon and the system of Jupiter ’s satellites have formed the subjects ofelaborate research, and that their complex perturbations have been studiedwith a degree of success which leaves little further to be desired; but sointricate are the various parts of physical astronomy, and so difficult is it forthe geometer to bring them within the reach of his analysis, that methodsof investigation devised for any particular problem become totally uselesswhen applied to others apparently similar to it. In the secondary systemsof Saturn, Uranus , and Neptune , difficulties will doubtless occur to thegeometer, which can only be vanquished by methods of analysis peculiarlyadapted to each specific case. But the planetary system does not holdout the exclusive prospect of future advancement in the study of Celestial Mechanics . Already the sublime truth announced by Newton, that every par-ticle of matter in the universe attracts every other particle with a force vary-ing reciprocally as the squares of their mutual distances, has been realisedin the motions of those vast bodies which roll in space at an inconceivabledistance beyond the limits of the solar system. The recent researches ofastronomers on the motions of Double Stars have established this importantfact beyond all doubt. An unlimited field of speculation is here presented