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on the lunar theory, our imperfect attempt to trace the history of physicalastronomy is now brought to a close. A review of the progress of thissublime department of science from its origin to its present advancedstate exhibits three periods, severally characterized by distinctive fea-tures, and separated by well-defined outlines. The first of the seperiodsextends from the commencement of Newton ’s career to about the middleof the eighteenth century. It comprehends the establishment of thetheory of gravitation by that immortal philosopher, the general propaga-tion of its principles, and the efforts pursued by geometers with a view toits future development. The appearance of the Principia in 1089, is oneof those conspicuous landmarks in the annals of science which enable thereader to group together a multitude of subordinate events, and to pursuehis way with comparative ease along the intricate path of physical re-search. Guided by the maxims of a cautious philosophy in establishinghis fundamental principles, and relying on the conclusions of a sublimegeometry, the offspring of his own genius, Newton has in that w'ork un-folded the mechanism of the material universe, and traced with completesuccess the agency of gravitation in all the grand phenomena of theplanetary movements. The dim perceptions of Copernicus , the moresearching and comprehensive but equally ineffectual speculations of Kepler ,the sober conjectures of Borelli, and the acute surmises of Hooke, werenow proved by demonstrative reasoning to be so many indistinct andscattered glimpses of one all-pervading principle which the author had theglory of first revealing to the world. The multitude of complex andapparently unconnected phenomena, which astronomers had detected bymeans of persevering efforts, prosecuted throughout a long successionof ages, now assumed the character of subordinate truths flowing from onecommon source. The sagacious generalizations of Hipparchus audPtolemy among the ancients, and the equally admirable efforts of TychoBrahe and Kepler among the moderns, were finally emancipated fromthe empiricism which characterizes mere mathematical inductions, andnow stood forth invested with all the grandeur of natural laws. Thegeneral adoption of the theory of gravitation which took place towardsthe close of the period we are considering, affords a lesson at once interest-ing and instructive. Slow at first to admit principles which presentedthemselves in the austere garb of the ancient geometry, and violated thecherished creations of fancy, the human mind, notwithstanding, was unableeffectually to resist the force of demonstrative reasoning, and finally wasconstrained to bow before the simple majesty of truth. By a rationalexposition of their more salient features, the principles of the theory ofgravitation were brought home to the understandings of persons unusedto processes of scientific inquiry with a power of conviction which the morerefined investigations of modern times are calculated only in a smalldegree to strengthen. With respect to the geometer, the impressionproduced on his mind by the discoveries of Newton was of a totally differentcharacter. Far from recognising a theory already complete in all its parts,he discovered, in the pages of the Principia , an inexhaustible mine ofprofound research, and already descried, in the dim perspective of futurity,the magnificent expansion which the sublime principles therein expoundedwere destined to acquire. But, to use the language of an illustrious livingphilosopher, the geometry of Newton was like the bow of Ulysses, whichnone but its master could bend *. The efforts of geometers during this

* Herschel’s Discourse on the Study of Natural Philosophy, p 273.