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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.

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Every one remembers the classification of water-wheels met with in the older school-books on natural philosophy, where we are informed that there are three kinds of wheels, as there were "three kinds of levers"namely, overshot, undershot, and breast wheelswith a brief notice of Barker's mill, which ran apparently without any sufficient cause for doing so. Without finding fault with the plan of describing water-power commonly adopted in elementary books, farther than to say that some explanation of the principles by which power is derived from the water would have been more useful, I will venture upon a different classification of water-wheels, more in accord with modern practice, but without reference to the special mechanism of the different wheels, except when unavoidable. Water-wheels can be divided into four general types.5. The loss of power during transmission.
Expose
ONE:Attention has been called to this case as one wherein the conditions of operation obviously furnish true data to govern the arrangement of machinery, instead of the determinable strains to which the parts are subjected, and as a good example of the importance of studying mechanical conditions from a practical and experimental point of view. If the general diameter of a shaft is based upon the exact amount of power to be transmitted, or if the diameter of a shaft at various parts is based upon the torsional stress that would be sustained at these points, such a shaft would not only fail to meet the conditions of practical use, but would cost more by attempting such an adaptation. The regular working strain to which shafts are subjected is inversely as the speed at which they run. This becomes a strong reason in favour of arranging shafts to run at a maximum speed, provided there was nothing more than first cost to consider; but there are other and more important conditions to be taken into account, principal among which are the required rate of movement where power is taken off to machines, and the endurance of bearings.

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TWO:(1.) Into what classes can gearing be divided?(2.) What determines the wearing capacity of gearing?(3.) What is the advantage gained by employing wooden cogs for gear wheels?(4.) Why are tangent or worm wheels not durable?

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TWO:"You wouldn't force her to confess?"

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TWO:Drilling, more than any other operation in metal cutting, requires the sense of feeling, and is farther from such conditions as admit of power feeding. The speed at which a drill may cut without heating or breaking is dependent upon the manner in which it is ground and the nature of the material drilled, the working conditions may change at any moment as the drilling progresses; so that hand feed is most suitable. Drilling machines arranged with power feed for boring should have some means of permanently disengaging the feeding mechanism to prevent its use in ordinary drilling.

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TWO:

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TWO:No little astonishment was therefore created by an interview which I published with Dr. van der Goot of The Hague, who did so much excellent work in the Red Cross Hospital at Maastricht. He also had come to believe all these stories, and as everybody always mentioned a large hospital in Aix-la-Chapelle, which was said to be full of similarly mutilated soldiers, Dr. van der Goot went to that91 town to see for himself. The chief medical officer of that hospital in a conversation stated that not one single case of that sort had been treated in his institution nor in any of the other local hospitals where he was a visiting physician. At a meeting of the medical circle just lately held he had not heard one word, nor had any one colleague, about the treatment of similar cases.
FORE:Hetty was deeply interested. Was this another mere coincidence or was Bruce acting here like a puppet in the hands of the mysterious person who seemed to be pulling the strings in the drama? Anyway, it strengthened her hands.

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FORE:Plato had, in truth, a conception of science which no knowledge then attainedperhaps one may add, no knowledge ever attainablecould completely satisfy. Even the rigour of mathematical demonstration did not content him, for mathematical truth itself rested on unproved assumptions, as we also, by the way, have lately discovered. Perhaps the Hegelian system would have fulfilled his requirements; perhaps not even that. Moreover, that the new order which he contemplated might be established, it was necessary to begin by making a clean sweep of all existing opinions. With the urbanity of an Athenian, the piety of a disciple, and the instinct of a great dramatic artist, he preferred to assume that this indispensable task had already been done by another. And of all preceding thinkers, who was so well qualified for the undertaking as Socrates? Who else had wielded the weapons of negative dialectic with such consummate dexterity? Who had assumed such a critical attitude towards the beliefs of his contemporaries? Who had been so anxious to find a point of attachment for every new truth in the minds of his interlocutors? Who therefore could, with such116 plausibility, be put forward in the guise of one who laid claim to no wisdom on his own account? The son of Phaenaret seemed made to be the Baptist of a Greek Messiah; but Plato, in treating him as such, has drawn a discreet veil over the whole positive side of his predecessors teaching, and to discover what this was we must place ourselves under the guidance of Xenophons more faithful report.

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FORE:

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FORE:In working to regular scales, such as one-half, one-eighth, or one-sixteenth size, a good plan is to use a common rule, instead of a graduated scale. There is nothing more convenient for a mechanical draughtsman than to be able to readily resolve dimensions into various scales, and the use of a common rule for fractional scales trains the mind, so that computations come naturally, and after a time almost without effort. A plain T square, with a parallel blade fastened on the side of the head, [80] but not imbedded into it, is the best; in this way set squares can pass over the head of a T square in working at the edges of the drawing. It is strange that a draughting square should ever have been made in any other manner than this, and still more strange, that people will use squares that do not allow the set squares to pass over the heads and come near to the edge of the board.There was no time to be lost, for she could hear Balmayne coming down the garden. And then a happy inspiration came to her. From her head she removed the gold and ornamented dagger, with its long steel pin. She stooped down. . .

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FORE:

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FORE:

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FORE:"S?ur Eulalie!... S?ur Eulalie!... You ... you ... are a ... cousin ... of ... S?ur Eulalie?""Horrible!" I sighed. "Have they not yet hit the bridge?"

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FORE:

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FORE:Low banks favored them.

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TWO:

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THREE:But Jove all-bounteous! who, in cloudsFor that fog the seaplane was making at full speed.

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THREE:The third thesis maintains that, granting the world to exist and to be knowable, one man cannot communicate his knowledge to another; for, the different classes of sensations being heterogeneous, a visual or tactual impression on our consciousness cannot be conveyed by an auditory impression on the consciousness of someone else. This difficulty has been completely overcome by the subsequent progress of thought. We cannot, it is true, directly communicate more132 than a few sensations to one another; but by producing one we may call up others with which it has become associated through previous experience. And the great bulk of our knowledge has been analysed into relations of co-existence, succession, and resemblance, which are quite independent of the particular symbols employed to transmit them from one mind to another.220

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THREE:Two passages in Aristotles writings have been supposed to give evidence of his admiration for Alexander. One is the description of the magnanimous man in the Ethics. The other is a reference in the Politics to an ideal hero, whose virtue raises him so high above the common run of mortals that their duty is to obey him as if he were a god. But the magnanimous man embodies a grave and stately type of character quite unlike the chivalrous, impulsive theatrical nature of Alexander,177 while probably not unfrequent among real Hellenes; and the god-like statesman of the Politics is spoken of rather as an unattainable ideal than as a contemporary fact. On the whole, then, we must conclude that the intercourse between these two extraordinary spirits has left no distinct trace on the actions of the one or on the thoughts of the other.

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THREE:"She was bad, utterly bad from a child," he said. "She was a distant connexion of the family. As a girl she set us all aflame with her beauty. She was the vainest and most cruel girl in the village. If she could rob another girl of her lover she was happy, and happier still in flinging him aside after. She was delighted when she could breed a quarrel between two friends and get them to fight.
TWO:It is a matter of courtesy in the usages of a shop, and one of expediency to a learner, to ask questions from those who are presumed to be best informed on the subject to which the questions relate; and it is equally a matter of courtesy to ask questions of different workmen, being careful, however, never to ask two different persons the same question, nor questions that [169] may call out conflicting answers.

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Evidently Jeff either caught his thought or decided on a course through his own quick wit.The voice ceased; nothing more could be heard but the humming of the wire. Bruce swished into the dining-room and huddled on his coat.There the German authorities detained me for a full week, by prohibiting me to return: "for the sake of your own safety," they told me courteously. During the day I was busy enough, and in the evenings I enjoyed the pleasant company of the three fathers of the Sacred Heart who had remained in the137 mission house, and with whose photographic instrument I took many a snapshot of the Louvain ruins.
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