ONE:This proposition argues the expediency of reducing the proportions of mill gearing and increasing its speed, a change which has gradually been going on for fifty years past; but there are opposing conditions which make a limit in this direction, such as the speed at which bearing surfaces may run, centrifugal strain, jar, and vibration. The object is to fix upon a point between what high speed, light weight, cheapness of cost suggest, and what the conditions of practical use and endurance demand."What is it now you have got?" Leona asked.
THREE:35
THREE:Marine and railway engineering have engrossed the best talent in the world; investigation and research has been expended upon these subjects in a degree commensurate with their importance, and it would be hard to suggest a single want in the many able text-books that have been prepared upon the subjects. Marine and railway engineering are sciences that may, in a sense, be separated from the ordinary constructive arts, and studied at the end of a course in mechanical engineering, but are hardly [61] proper subjects for an apprentice to take up at the beginning.The cry that rose to her lips was stifled, a firm hand grasped her arm, another was laid tightly over her mouth.
THREE: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, Cyrn, 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.
