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THREE:That something had been cast overboard, tied to the float, was obvious to Larry, Dick and Sandy.Lalage struck out boldly into the street followed by Balmayne. There was only one thing uppermost in his mind, one great project that filled his untutored brain. A great wrong had been done, and he was to right it by blood. There was no crime about this, it had been the custom of his race for centuries.

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THREE:1. The distance to which power is to be transmitted.

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THREE:As a means for transmitting power, shafts afford the very important advantage that power can be easily taken off at any point throughout their length, by means of pulleys or gearing, also in forming a positive connection between the motive-power and machines, or between the different parts of machines. The capacity of shafts in resisting torsional strain is as [46] the cube of their diameter, and the amount of torsional deflection in shafts is as their length. The torsional capacity being based upon the diameter, often leads to the construction of what may be termed diminishing shafts, lines in which the diameter of the several sections are diminished as the distance from the driving power increases, and as the duty to be performed becomes less. This plan of arranging line shafting has been and is yet quite common, but certainly was never arrived at by careful observation. Almost every plan of construction has both advantages and disadvantages, and the best means of determining the excess of either, in any case, is to first arrive at all the conditions as near as possible, then form a "trial balance," putting the advantages on one side and the disadvantages on the other, and footing up the sums for comparison. Dealing with this matter of shafts of uniform diameter and shafts of varying diameter in this way, there may be found in favour of the latter plan a little saving of material and a slight reduction of friction as advantages. The saving of material relates only to first cost, because the expense of fitting is greater in constructing shafts when the diameters of the different pieces vary; the friction, considering that the same velocity throughout must be assumed, is scarcely worth estimating.There is, indeed, nothing more nobly characteristic of the Hellenic spirit, especially as organised by Socrates, than its capacity not only for communicating, but for awakening ideas; thus enabling all the nations among which it spread to realise the whole potential treasure of theoretical and practical energy with which they were endowed. And, from this point of view, we may say that what seems most distinctively proper to Rome��the triumphant consciousness of herself as a world-conquering and world-ruling power��came to her from Greece, and under the form of a Greek idea, the idea of providential destiny. It was to make his countrymen understand the fateful character and inevitable march of her empire that Polybius composed his great history; it was also by a Greek181 that the most successful of her early national epics was sung; and when at last her language was wrought into an adequate instrument of literary expression��thanks also to Greek rhetorical teaching,��and the culture of her children had advanced so far that they could venture to compete with the Greeks on their own ground, it was still only under forms suggested by Stoicism that Virgil could rewrite the story of his country��s dedication to her predestined task.

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THREE:In working out his theory of logic, the point on which Bacon lays most stress is the use of negative instances. He seems to think that their application to reasoning is an original discovery of his own. But, on examination, no more seems to be meant by it than that, before accepting any particular theory, we should consider what other explanations of the same fact might conceivably be offered. In other words, we should follow the example already set by Aristotle and nearly every other Greek philosopher after Socrates. But this is not induction; it is reasoning down from a disjunctive proposition, generally assumed without any close scrutiny, with the help of sundry conditional propositions, until we reach our conclusion by a sort of exhaustive process. Either this, that, or the other is the explanation of something. But if it were either that or the other, so and so would follow, which is impossible; therefore it must be this. No other logic is possible in the infancy of enquiry; but one great advantage of experiment and mathematical analysis is to relieve us from the necessity of employing it.Bruce was allowed to take his own way, a result he had not confidently expected. The vulgar curiosity of the passing crowd annoyed him. Standing outside the vestry hall was a carriage and a pair of horses. Leona Lalage, seated inside, smiled brilliantly on Bruce and his companion, and the footman opened the door.

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THREE:"Ah, I knew you would listen to reason; I knew there was nothing so vile and degraded that you would not do to save yourself. Answer me the question, then. Tell me at once where I can find Leona Lalage?"The intricacy of the subject renders it a difficult one to deal with except by the aid of diagrams, and as such mechanism may be inspected in almost any machine fitting shop, attention is called to the subject as one of the best that can be chosen for demonstration by diagrams. Problems of these variable speed movements are not only of great interest, but have a practical importance not found in many better known problems which take up time uselessly and have no application in a practical way.

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THREE:Such is the mild and conciliatory mode of treatment at first adopted by Plato in dealing with the principal representative of the Sophists��Protagoras. In the Dialogue which bears his name the famous humanist is presented to us as a professor of popular unsystematised morality, proving by a variety of practical arguments and ingenious illustrations that virtue can be taught, and that the preservation of social order depends upon the possibility of teaching it; but unwilling to188 go along with the reasonings by which Socrates shows the applicability of rigorously scientific principles to conduct. Plato has here taken up one side of the Socratic ethics, and developed it into a complete and self-consistent theory. The doctrine inculcated is that form of utilitarianism to which Mr. Sidgwick has given the name of egoistic hedonism. We are brought to admit that virtue is one because the various virtues reduce themselves in the last analysis to prudence. It is assumed that happiness, in the sense of pleasure and the absence of pain, is the sole end of life. Duty is identified with interest. Morality is a calculus for computing quantities of pleasure and pain, and all virtuous action is a means for securing a maximum of the one together with a minimum of the other. Ethical science is constituted; it can be taught like mathematics; and so far the Sophists are right, but they have arrived at the truth by a purely empirical process; while Socrates, who professes to know nothing, by simply following the dialectic impulse strikes out a generalisation which at once confirms and explains their position; yet from self-sufficiency or prejudice they refuse to agree with him in taking their stand on its only logical foundation.

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