ceptions of dynamics, in which, indeed, he has but handed down to us the theory of the ancients, without any infusion of original ideas.20 In so far, his various propositions are to be regarded as showing the state of the science in the earliest ages. They comprise only a few vague generalities concerning the principle of motion and the nature of equilibrium, not more obscure than fallacious, and confine themselves to mere elementary knowledge. Yet, in one passage, the philosopher seems to have a dim perception of the law of gravitation, affirming that heavy bodies descend to the centre of the universe, and that the velocity of their descents is in the ratio of their weights. But ancient science, though it could jump at conclusions, rarely groped for the cause, and in the greatest days of Greece, there was no meditative Newton to solve the problem of the falling apple. Far from penetrating such mysteries, Aristotle was perplexed by the spectacle of a small power, through the medium of the lever, moving considerable weights, in addition to the intervening weight of the lever itself; and could only explain the phenomenon by assuming, what was

20 Questiones Mechanicæ.

wholly false, that the motive force impelled the lever with greater facility, in proportion to its distance from the fulcrum, considering that it was diffused through a larger space, because the end furthest from the centre

described a greater circle. By a curious mode of reasoning, the shorter arm of the lever was declared to operate with more power on superior forces, or what naturally exceeds it in resistance, than the other; and this vague definition remained unshaken till the science was based on new and more durable principles by Archimedes. Even then, dynamics can hardly be said to have advanced; and the primary law of motion was unknown. The great Syracusan, by his natural sagacity rather than experiment, ascertained the true proportion of the force employed by certain machines to the resistance in the case of equilibrium; but he evinces no knowledge of the principle of the composition of forces, in respect to the precise conditions of equilibrium in machines of every description. On the other hand, it is almost certain that he was not cognisant of any means of calculating the motion of bodies, and instead of believing that it was naturally uniform, and rectilineal, concluded, with the primitive philosophers,

that it must be circular, the circle being regarded as the prescribed form of every revolution of nature. The science of dynamics, indeed, remained stationary, and we are at a loss to comprehend how the Romans could have constructed such complicated machines as those described in the pages of Vitruvius, when we find that it is only recent times so recent as the middle of the seventeenth century—that discovered the law regulating the mutual collision of bodies. This, after an unsuccessful investigation by Des Cartes, was simultaneously accomplished by Wren, Wallis, and Huygens, to whom the task had been confided by the Royal Society, and the dynamical enigmas of ancient and latter times were now swept away, leaving exposed the broad foundations of the whole science, as regards both equilibrium and motion. But Archimedes, without solving the law, fully understood the powers of the lever; and his well-known challenge to Hiero, to give him a place to stand on, and he would move the world, is an imperishable exposition of his opinions. During the siege of Syracuse, levers and cranes formed his most effective artillery, and, with their aid, the Roman galleys, on nearing the city walls, were raised

from the water, and dashed in pieces on the rocks, while the more distant were reached by his burning-glasses, and enveloped in flames.21

Hydrodynamics, which is also a branch of mechanical science, was better understood by the ancients, and as widely practised. It refers to bodies in the fluid condition, in the phenomena exhibited by pressure, equilibrium, cohesion, motion, and resistance, showing, in a precise and definite manner, how the laws of these varied forces must be applied to the construction of machines, in connexion with water, whether the object be to raise the limpid element from a depth, or to use it as a first mover or primary agent. This great river of knowledge parts, as it were, into two streams, the one comprehending all that relates to pressure, equilibrium, and cohesion, and which is called Hydrostatics; the other affecting the actual motion of fluids, the resistance they offer to moving bodies, and their application to mechanical power, and which bears the appellation of Hydraulics.

An apt illustration of the knowledge acquired by the ancients of the motion of fluids is furnished by the Clepsydræ, or water

21 Hist. of Rome.

clocks, which were constructed on the principle of regulating the passage of the water by the size of the emitting aperture, and by the dimensions of the superincumbent column. As water-clocks preceded the invention of sun-dials, they prove that some of the leading doctrines of Hydrodynamics were perfectly understood at a very remote era. The form originally assumed by the Clepsydræ presented two inverted cones, the uppermost solid, and the other, which contained the water, hollow, and marked down its length into twelve equal divisions, which, as the fluid descended, announced the flight of the successive hours. The momentum was imparted by the solid cone, and, according to the depth of penetration attained by this primitive pendulum, the flow of the water was more or less rapid-the clock was fast or slow!

The shadoof, in the form still used in Egypt, is another specimen of the hydraulic science of the ancients. It is such a machine as might be expected in a rude age, when man was but little raised from barbarişm, being composed merely of buckets, carefully secured to a pole, with which they are raised, when full, from the river, and the contents poured into a duct, designed to irrigate the land.