289. The great excellency of the Newtonian philosophy, (for such it may be most fitly designated,) consists in the solid basis of mathematical demonstration on which its fundamental principles rest, and the innumerable physical proofs by which they are illustrated and confirmed. The great fact of the mutual attraction of bodies, had been previously ascertained; Kepler's celebrated laws, and Huygens' mechanical experiments, had gone far towards determining the ratio of this tendency; but the demonstration of the exact measure of the centripetal and centrifugal forces, and the phænomena resulting from them,--the proof that the law of gravitation pervades the whole system of nature, applying alike to the mightiest masses and the minutest particles of which it is composed,--the accurate delineation of the motions and orbits of the heavenly bodies, in conformity with this gravitating principle--all these are the glory of the new philosophy of which Newton was the founder. The demonstration of this astonishing fact having been obtained by the new method of analysis, it was the next object of this great practical philosopher to determine the extent of this mysterious law of nature, by the most careful astronomical observations and to prove by experiment, that those phænomena occurred which science had taught him to expect, and that the consequences which had been anticipated, really followed in the physical system. On the principle of the mutual attraction of the heavenly bodies, all those irregularities, or rather inequalities, of motion, observable in the planetary revolutions, which had long perplexed

astronomers, were satisfactorily explained - such as the librations and evection of the moon-the disturbing forces, mutually exerted by primary and secondary planets--the theory of the tides-and, above all, the precession of the equinoxes-with many other phænomena, which now constitute the chief objects of physical astronomy. Nor was it among the least of the discoveries resulting from the demonstration of this law, that the true configuration of the earth was ascertained, and some difficult problems were solved, connected with that fact; such as the cause of the slower vibration of the pendulum, and the diminished intensity of attraction, at the equator than at the poles.

290. But perhaps the most astonishing consequence of the discovery of the law of gravitation was, that it enabled the astronomer to estimate the magnitude and density of the planets. A rule of universal application was obtained, which was briefly this; "that in any two bodies (their distances being the same) their power of mutual attraction is in proportion to the quantity of matter they respectively contain; or, in other words, that they have a tendency to approach each other with velocities which are inversely as their quantities of matter." Applying this rule first to the moon, as the nearest of the planetary bodies, and subsequently to those more remote, Newton deduced, from an accurate observation of their distances compared with their velocity of motion, the mean density of each. Every succeeding year, and all the accumulated facts of modern science, have served but to confirm the

truth, and extend the application of these incontrovertible principles, and heighten our admiration of the genius and science of their inventor.

291. The preceding summary of the astronomical researches and discoveries of our great philosopher, cannot be more appropriately concluded, than by the following brief extract from another valuable work of the late Professor Playfair, in which they are all happily brought to bear on one point, and their mutual relation is distinctly traced.

"Thus it is found, that the laws of motion and the general properties of matter are the same in the heavens and on the earth; that the elliptical motions of the primary and secondary planets; the small deviations from those motions, whether in the places of the planets or in the form and position of their orbits; the facts which concern their figures, their rotation, and the position of their axis; and lastly, the oscillation of the waters which surround the earth, are all explained by one principle, that of the mutual gravitation of all bodies, with forces directly as their quantities of matter, and inversely as the squares of their distances.' The existence of this force was not assumed as an hypothesis, but deduced as a necessary consequence from the general facts or laws discovered by Kepler. We have thus arrived at the knowledge of a principle which pervades all nature, and connects together the most distant regions of space, as well as the most remote periods of duration."*

. Playfair's Outlines of Nat. Philos. II. p. 339.

II.

DYNAMICS AND MECHANICS.

SECT. I.

ON THE PROGRESS OF MECHANICAL SCIENCE DURING THE SIXTEENTH CENTURY.

292. THE Connexion is so intimate between all the practical sciences, that it might reasonably have been expected, (and facts have abundantly verified that expectation,) that the æra in which any one of these has remarkably flourished, would be characterized by a proportionate improvement in all the rest. It was scarcely possible that such brilliant discoveries should have been made in astronomy, as have been sketched in the preceding sections, without a simultaneous and corresponding progression in all the departments of mechanical science, whether it be regarded in the more abstract form of dynamics, or in the practical application of those general principles by various kinds of machinery. In like manner, we are prepared to expect that the same individuals, who have immortalized their names by astronomical researches and discoveries, would be those who occupy a prominent place in other departments of physical science, and especially in one so nearly allied as mechanics. That a more

distinct conception may be formed, by the juvenile reader, of the two great divisions of modern science, the history of which is now to be sketched, during a period in which they were rapidly progressive, it may not be improper just to state that the term dynamics is employed to describe that branch of physico-mathematical science, which treats abstractedly of the laws of matter and motion; or, in other words, which teaches the doctrine of moving forces: mechanics denotes that division of the science which reduces to practice the principles of dynamics, and illustrates them by experiment. The inventions of mechanical philosophy serve to exhibit the manner in which the moving forces act, the laws by which that action is regulated, and the effects that must necessarily result in any given case from their practical application.

293. It has been already stated, (§ 93,) that dynamics, considered as a science, was wholly unknown to the ancients. Nor did any material alteration take place in that of mechanics, from the æra of Achimedes, to the middle of the sixteenth century. The principles laid down by that great practical philosopher, and exemplified by his stupendous machinery, had been applied to various uses by a few scientific men, such as Gerbert, Friar Bacon, and some others, who lived, at distant intervals, during the middle ages. But no new discovery had been made,-no new theories invented,-no new problems solved, through the whole of that long series of years. The first who can be said to have taken a single step in advance, was Guido Ubaldi,