Sir John Leslie used to attribute the stability of this tower to the cohesion of the mortar it is built with being sufficient to maintain it erect, in spite of its being out of the condition required by physics--to wit, that “in order that a column shall stand, a perpendicular let fall from the centre of gravity must fall within the base.” Sir John describes the Tower of Pisa to be in violation of this principle; but, according to later authorities, the perpendicular falls within the base. EARLY PRESENTIMENTS OF CENTRIFUGAL FORCES. Jacobi, in his researches on the mathematical knowledge of the Greeks, comments on “the profound consideration of nature evinced by Anaxagoras, in whom we read with astonishment a passage asserting that the moon, if the centrifugal force were intermitted, would fall to the earth like a stone from a sling.” Anaxagoras likewise applied the same theory of “falling where the force of rotation had been intermitted” to all the material celestial bodies. In Aristotle and Simplicius may also be traced the idea of “the non-falling of heavenly bodies when the rotatory force predominates over the actual falling force, or downward attraction;” and Simplicius mentions that “water in a phial is not spilt when the movement of rotation is more rapid than the downward movement of the water.” This is illustrated at the present day by rapidly whirling a pail half-filled with water without spilling a drop. Plato had a clearer idea than Aristotle of the _attractive force_ exercised by the earth’s centre on all heavy bodies removed from it; for he was acquainted with the acceleration of falling bodies, although he did not correctly understand the cause. John Philoponus, the Alexandrian, probably in the sixth century, was the first who ascribed the movement of the heavenly bodies to a primitive impulse, connecting with this idea that of the fall of bodies, or the tendency of all substances, whether heavy or light, to reach the ground. The idea conceived by Copernicus, and more clearly expressed by Kepler, who even applied it to the ebb and flow of the ocean, received in 1666 and 1674 a new impulse from Robert Hooke; and next Newton’s theory of gravitation presented the grand means of converting the whole of physical astronomy into a true _mechanism of the heavens_. The law of gravitation knows no exception; it accounts accurately for the most complex motions of the members of our own system; nay more, the paths of double stars, far removed from all appreciable effects of our portion of the universe, are in perfect accordance with its theory.[8] HEIGHT OF FALLS.