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now, usually, called by his name. The persevering labours of Kepler conspiring with the fortunate invention of the telescope, at length succeeded, however, in annihilating every impediment, and prepared the way for the present theory of the universe.

It will, also, be seen that the discoveries of the above astronomers were, by Newton, proved to be necessary consequences of a principle of nature which exists, identically, in the fall of a stone to the ground, in the tendency of the moon to the earth, and in those of the planets to the sun; and it is to be observed that from researches, founded on this principle alone, which were begun by our great philosopher, and extended after his death by the mathematicians of the continent, result the modern tables of the celestial movements. These exhibit, chiefly, the mean or uniform velocity which each planet would have if it moved in an undisturbed circular orbit; the first inequality of velocity, commonly called the equation of the centre, which expresses the variation arising from the movement in a supposed elliptical orbit; and the effects of the several perturbations produced by the attractions of other planets, by which the motion of each, both in longitude and latitude, is rendered still further variable; besides these, the tables contain the variable distances of the earth and planets from the sun, the movements of the apsides and nodes of their orbits, and all the corresponding elements of the satellites.

Hitherto the improvements in analysis, by which the formulæ relating to the lunar and planetary motions were investigated, have been accompanied by corresponding ameliorations in the instruments of observation; and thus, the constant coefficients of the variable terms which enter into the formulæ have been obtained with considerable accuracy. But, that instruments more capable than those already in use, of determining accurately the places of celestial bodies by observation, should hereafter be constructed, seems very uncertain. Instruments of great magnitude, though they afford superior optical powers, and are susceptible of more minute graduations than those of smaller size, are more than the latter subject to partial expansions or contractions, from inequalities in the material, and to derangements, from the strains produced by changing their

directions during the observation; and these evils, necessarily, place a limit to their useful dimensions. But we may add that the errors in the observed places of stars, arising from imperfection of vision and from inappreciable variations in the state of the atmosphere, too often render useless the skill displayed in the design, and the accuracy attained in the execution of the magnificent instruments produced by modern art.

A history of the progress of astronomy would, probably, be thought incomplete if the actual state of the science were not described. Therefore, after exhibiting an outline of the researches of Kepler and of the planetary theory of Newton, the last, in all probability, to be recorded, some account has been given of the recent discoveries made in the heavens; of the operations undertaken to ascertain the figure of the earth; and of the nature of the instruments employed in observation: and a chapter has been added, containing a statement of the subjects to which the modern analysis has been applied in investigating, by the theory of gravitation, the formulæ for representing the celestial movements.

The Writer has not atteinpted, in the Work, to trespass on the domain of natural theology; and he only solicits the reader's indulgence while he remarks that astronomy affords the most striking evidences of the infinite power and intelligence of the Deity. The former is manifested in the incalculable number and vast magnitudes of the bodies in the universe, and the distances to which their attractive influences extend; the latter, in the proportion established between the intensities of the moving forces acting on each, by which, while in constant oscillation between opposing attractions, the planets constitute systems capable of an endless duration. That inconceivable tendency of all the particles of matter to approach each other, can only be considered as the result of a principle originally communicated to them purposely to be the bond by which the different parts of the universe might be held together. But, because this tendency, if it acted alone, would have caused all the particles to unite in one mass; the Divine Power, which gave existence and a law of attraction to matter, must, also, have been exerted in causing the unions of portions of that matter in many distinct

masses constituting suns and planets, in establishing the former as centres of particular systems, and in applying to each of the latter an impulsive force by which it is enabled to revolve about the common centre of the system to which it was made to belong. Here, then, are several independent actions which, since they are combined together to work out certain useful ends, necessarily exclude the possibility of a fortuitous occurrence. And though the profound geometer may determine the direction of the impelling force and the position of the point of application by which, for any planet, the particular motion in the orbit and the observed obliquity in the axis of rotation might be obtained; he is as incapable as the rudest peasant of shewing, from natural causes, what communicated the force, or why, among the infinite number of possible directions and intensities, those should have been given which, alone, are capable of producing the phenomena of summer and winter, of day and night, in unceasing alternation.

It is evident that the science of astronomy may be treated in two very different ways. The observed circumstances, in respect of time and place, which attend the recurrence of celestial phenomena, by affording data for anticipating the repetition of the like phenomena in times to come, permit the laws which regulate the movements of the sun, moon and planets to be determined: or the existence of a law of nature, according to which material bodies may act on each other, being assumed ; from this may be deduced formulæ expressing both the mean and variable movements, and agreeing with those obtained from a comparison of observations. An astronomy formed from observation of the heavens is the subject of many excellent and well known English works; but the other, or that which is properly denominated Physical Astronomy, though now, perhaps, gaining ground, has, hitherto been but little studied in this country. If the first work of the kind, the “ Principia” of the illustrious Newton, and the essays of Simpson and Robison, be excepted, reference can only be made to the treatises of the late Mr. Woodhouse, the learned researches of Ivory, Herschell, Airy, and Lubbock; and the valuable but, as yet, unfinished transla

tions of the Mécanique Céleste, by Bowditch and Mrs. Somerville.

To a treatise on astronomy founded on either of the two principles above mentioned the following Work will, it is hoped, serve as a convenient introduction; it may be considered as holding an intermediate place with respect to the voluminous histories of M.M. Bailly and Delambre and, be it said, while acknowledging the merits of such as the elegant essay of Dr. Adam Smith, or that recently published in the Library of Useful Knowledge, the very general outlines which have, occasionally, been given of the origin and progress of the science.

Royal Military College, Sandhurst,

May 20, 1833.

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