But the most important discoveries of Galileo were those which relate to the times of descent, the spaces descended, and the velocities acquired when bodies fall by the action of gravity. He made observa tions on the motions of pendulums, and determined that the times of their vibrations are proportioned to the square roots of their lengths ; he also gave theorems for the composition of two motions, when both are uniform, when both are accelerated, and when one is uniform and the other accelerated. Nor should we omit to state that he was the first to obtain expressions for the strength of materials in resisting the strains to which they are subject. It deserves notice moreover that Galileo, in opposing the arguments of one of his contemporaries con cerning the law of the descent of bodies by gravity, makes a supposition that the spaces descended with the accelerated motion may be divided Into equal parts, each so small that the motion during the time of describing it may, without sensible error, be considered as uniform; an hypothesis corresponding exactly to that which, agreeably to the principles of the modern analysis, is now employed In investigations concerning variable motions.
The theory of the motions of fluids was, apparently, first cultivated In Italy by CasteLli, who wrote on the subject in 1638 ; and about the same tine Torricelli, having discovered the existence of a space void of air In the upper part of a tube filled with mercury, its open end being immersed in a vessel of that fluid, was enabled to refute the ancient notion that nature abhorred a vacuum. The latter was subse quently led to the conclusion that the pressure of the atmosphere is the cause of the support of a column of mercury in a tube, and also of the ascent of water in pumps. Both of these writers were pupils of Gafileo ; and, soon after the time of this philosopher, the French mathematicians Descartes, Pascal, Fermat, and Roberval, prosecuted with ardour the new science, as that of mechanics was called. Among the fruits of their researches may be named the determination of the centres of oscillation and percussion in a body or system of bodies vibrating about a fixed axis. The impulse given by Galileo, being thus continued by a succession of men of talent both in Italy and France, caused the science to advance with an accelerated movement, and soon put it in a condition to embrace all the subjects of terrestrial physics.
The mechanics of that age was not however entirely emancipated from the trammels of a false philosophy ; and the theory of Descartes, concerning the communication of motion when bodies strike each other, is remarkable on account of the metaphysical principle which it involves. In speaking of the collision of bodies, he gives as a reason why the same momentum should exist after as before the impact, that it depends on the divine immutability. God having created a certain
quantity of motion to serve as the cause of all the operations of nature, that quantity, he conceives, can never be increased or diminished. Yet there is some reason to think that Descartes had better notions concerning the phenomena of collision, for he states correctly, iu one of Cis letters, that the motion of a body when it strikes another which is at rest becomes divided between the two masses, and that the resulting velocity is diminished as the mass is augmented. The chief feature in the physics of Descartes is his supposition that the planets revolve about the suu in vortices of mther, the particles of which, having acquired a certain degree of centrifugal force, act on the planets and prevent them from falling together in the centre of the system. He supposed that the like vortices surround each planet : but the particles of rather, having less specific gravity than the bodies on the surface of the planet, the tendency of these bodies to that surface prevails over the force by which the either causes them to recede from thence.
The laws of the collision of bodies, which had been in vain attempted by Descartes, were at length, and nearly at the same time, discovered by the English mathematicians Wallis and Sir Christopher Wren, and by Huyghens on the Continent. The first of these, in his treatise De Motu' (1670), divides bodies into such as are hard and such as are elastic, and he explains the phenomena attending the shock of bodies of both kinds. In that of hard bodies he adopts as an hypothesis that the body struck destroys as much motion in the striking body as the latter communicates to it ; and in elastic bodies he considers the forces of compression and restitution to be proportional, in each, to the velocities before the shock. The name of Huyghens has become celebrated from the discovery of the properties of cycloidal curves, and the attempt to make the lower extremity of a clock-pendulum vibrate in an arc of that kind, in order that the times of vibration might be equal, whatever were the extent of the arc described. This attempt did not succeed ; but, being led in the course of his inquiries to inves tigate the position of the centre of oscillation in a compound pendulum, Huyghens found that when several pendulous bodies descend by gravity and afterwards re-ascend by the acquired velocities, in whatever way they may act upon each other, their common centre of gravity cannot rise higher than the point from wheuce it descended. This proposition is considered as proved from the fact that, if it were otherwise, the centre of gravity might by mechanical means be made to rise con tinually higher, and thus perpetual motion might ensue : but this is impossible.