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ONE: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 earth��s 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.Some uphold the accusation on the ground of expressions in Belgian newspapers, collected in a German pamphlet. In my opinion these quotations have not the slightest value. Everyone will understand this who thinks of the excitement of journalists, whose country was suddenly and quite unexpectedly involved in a terrible war, and who felt now that as journalists they had to perform a great, patriotic duty. In their nervous, over-excited condition they sat at their desk and listened to the gossip of refugees about civilians taking part in the struggle. In their imagination they saw hordes of barbarians overrun their native soil, saw man and man, woman88 and woman, shoulder to shoulder, resisting the invader without regard for their own life. The thoughts of such journalists, whose very own country had been at war now for a few days, were not on severe logical lines; they found a certain beauty in that picture, and I can quite understand how some came to believe in it as a reality, and gloried in it.