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THREE:The extreme nicety with which gauging implements are fitted seems at first thought to be unnecessary, but it must be remembered that a cylindrical joint in ordinary machine fitting involves a precision almost beyond the sense of feeling, and that any sensible variation in turning gauges is enough to spoil a fit.

THREE:In front of me, behind me, on all sides, the guns boomed, clouds of dust and smoke filled the air, making it impossible to see much, which made the awe and terror endurable; but after the air became clear again, and the sun shed glowing light on the beautiful fields, it was terrible to think that all those dots in the plain were the bodies of young men, cruelly crushed by the infernal products of human ingenuity. It was agony to see here and there a body rising up, merely to fall down again immediately, or an arm waving as if invoking help.It was from mathematical science that the light of certainty first broke. Socrates had not encouraged the study of mathematics, either pure or applied; nor, if we may judge from some disparaging allusions to Hippias and his lectures in the Protagoras, did Plato at first regard it with any particular favour. He may have acquired some notions of arithmetic and geometry at school; but the intimate acquaintance with, and deep interest in them, manifested throughout his later works, probably dates from his visits to Italy, Sicily, Cyr��n��, and Egypt. In each of these places the exact sciences were cultivated with more assiduity than at Athens; in southern Italy they had been brought into close connexion with philosophy by a system of mystical interpretation. The glory of discovering their true speculative significance was reserved for Plato. Just as he had detected a profound analogy between the Socratic scepticism and the Heracleitean flux, so also, by another vivid intuition, he saw in the definitions and demonstrations of geometry a type of true reasoning, a particular application of the Socratic logic. Thus the two studies were brought into fruitful reaction, the one gaining a wider applicability, and the other an exacter method of proof. The mathematical spirit ultimately proved211 too strong for Plato, and petrified his philosophy into a lifeless formalism; but no extraneous influence helped so much to bring about the complete maturity of his constructive powers, in no direction has he more profoundly influenced the thought of later ages.