THREE:For disadvantages there is, on the other hand, a want of uniformity in fittings that prevents their interchange from one part of a line shaft to the othera matter of great importance, as such exchanges are frequently required. A line shaft, when constructed with pieces of varying diameter, is special machinery, adapted to some particular place or duty, and not a standard product that can be regularly manufactured as a staple article by machinists, and thus afforded at a low price. Pulleys, wheels, bearings, and couplings have all to be specially prepared; and in case of a change, or the extension of lines of shafting, cause annoyance, and frequently no little expense, which may all be avoided by having shafts of uniform diameter. The bearings, besides being of varied strength and proportions, are generally in such cases placed at irregular intervals, and the lengths of the different sections of the shaft are sometimes varied to suit their diameter. With line shafts of uniform diameter, everything pertaining to the shaftsuch as hangers, couplings, pulleys, and bearingsis interchangeable; the pulleys, wheels, bearings, or hangers can be placed at pleasure, or changed from one part of the shaft to another, or from [47] one part of the works to another, as occasion may require. The first cost of a line of shafting of uniform diameter, strong enough for a particular duty, is generally less than that of a shaft consisting of sections varying in size. This may at first seem strange, but a computation of the number of supports required, with the expense of special fitting, will in nearly all cases show a saving.Meanwhile a new and powerful agency was about to interpose with decisive effect in the doubtful struggle. This was the study of mathematics. Revived by the Arabians and never wholly neglected during the Middle Ages, it had profited by the general movement of the Renaissance, and was finally applied to the cosmical problem by Galileo. In this connexion, two points of profound philosophical interest must be noted. The first is that, even in its fall, the Aristotelian influence survived, to some extent, both for good and for evil. To Aristotle belongs the merit of having been the first to base astronomy on physics. He maintains the earths immobility on experimental no less than on speculative grounds. A stone thrown straight up in the air returns to its starting-point instead of falling to the west of it; and the absence of stellar385 parallax seems to show that there is no change in our position relatively to the heavenly bodies. After satisfying himself, on empirical considerations, that the popular astronomy is true, he proceeds to show that it must be true, by considerations on the nature of matter and motion, which, although mistaken, are conceived in a genuinely scientific spirit. Now Galileo saw that, to establish the Copernican system, he must first grapple with the Peripatetic physics, and replace it by a new dynamical theory. This, which he could hardly have effected by the ordinary mathematical methods, he did by borrowing the analytical method of Atomism and applying it to the measurement of motion. The law of falling bodies was ascertained by resolving their descent into a series of moments, and determining its rate of velocity at successive intervals; and curvilinear motions were similarly resolved into the combination of an impulsive with an accelerating force, a method diametrically opposed to that of Bacon, who would not even accept the rough analysis of the apparent celestial motions proposed by Greek astronomers.
