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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.It has been doubted, we think with insufficient reason, that Lucretius was acquainted at first hand with Empedocles.204 But, by whatever channel it reached him, the enthusiasm of Empedocles and the Eleates lives in his verse no less truly than the inspiration of Aeolian music in the song of his younger contemporary, Catullus. The atomic theory, with its wonderful revelations of invisible activity and unbroken continuity underlying the abrupt revolutions of phenomenal existence, had been the direct product of those earliest struggles towards a deeper vision into the mysteries of cosmic life; and so Lucretius was enabled through his grasp of the theory itself to recover the very spirit and passion from which it sprang.205
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TWO:Even M. Vacherot, with all his anxiety to discover an Oriental origin for Neo-Platonism, cannot help seeing that this attack on the Gnostics was inspired by an indignant reaction of Greek philosophy against the inroads of Oriental superstition, and that the same character belongs more or less to the whole system of its author. But, so far as we are aware, Kirchner is the only critic who has fully worked out this idea, and exhibited the philosophy of Plotinus in its true character as a part of the great classical revival, which after producing the literature of the second century reached its consummation in a return to the idealism of Plato and Aristotle.522

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TWO:CHAPTER VIII. WATER-POWER.Ren Lalage bowed his head and wept after the manner of his nation. He had offered Prout a far more valuable clue than he had expected. All sorts of possibilities were opening out before the eyes of the detective.
THREE:We have seen how Plato came to look on mathematics as217 an introduction to absolute knowledge. He now discovered a parallel method of approach towards perfect wisdom in an order of experience which to most persons might seem as far as possible removed from exact sciencein those passionate feelings which were excited in the Greek imagination by the spectacle of youthful beauty, without distinction of sex. There was, at least among the Athenians, a strong intellectual element in the attachments arising out of such feelings; and the strange anomaly might often be seen of a man devoting himself to the education of a youth whom he was, in other respects, doing his utmost to corrupt. Again, the beauty by which a Greek felt most fascinated came nearer to a visible embodiment of mind than any that has ever been known, and as such could be associated with the purest philosophical aspirations. And, finally, the passion of love in its normal manifestations is an essentially generic instinct, being that which carries an individual most entirely out of himself, making him instrumental to the preservation of the race in forms of ever-increasing comeliness and vigour; so that, given a wise training and a wide experience, the maintenance of a noble breed may safely be entrusted to its infallible selection.134 All these points of view have been developed by Plato with such copiousness of illustration and splendour of language that his name is still associated in popular fancy with an ideal of exalted and purified desire.

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THREE:I will, in connection with this subject of patterns and castings, suggest a plan of learning especially applicable in such cases, that of adopting a habit of imagining the manner of moulding, and the kind of pattern used in producing each casting that comes under notice. Such a habit becomes easy and natural in a short time, and is a sure means of acquiring an extended knowledge of patterns and moulding.Nothing animate or inanimate in nature is uniform; plants, trees, animals, are all different; even the air we breathe and the temperature around us is constantly changing; only one thing is constant, that is time, and to this must we go for all our standards.

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THREE:

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TWO: THREE:Plotinus seems to have begun his career as a public teacher soon after taking up his residence in Rome. His lectures at first assumed the form of conversations with his private friends. Apparently by way of reviving the traditions of Socrates and Plato, he encouraged them to take an active part in the discussion: but either he did not possess the authority of his great exemplars, or the rules of Greek dialogue were not very strictly observed in Rome; for we learn from the report of an eye-witness that interruptions were far too frequent, and that a vast amount of nonsense was talked.408 Afterwards a more regular system of lecturing was established, and papers were read aloud by those who had any observations to offer, as in our own philosophical societies.
TWO:But although the Germans are afraid to let the truth be known, there is no reason why I should withhold my evidence. On the contrary, I will try to do everything I can to make public opinion do justice to the unfortunate Belgians, trodden down and insulted, falsely and vilely libelled by their oppressors, and accused of offences of which they never were guilty.
On the whole, an appearance of candour would be best. She would go straight to Prout, who had the Corner House tragedy in hand, and tell him everything, at least everything that Lawrence had found out. She never guessed for a moment that this was exactly what the novelist expected her to do, in fact, he had apparently told all he knew to gain this end. Also, at his suggestion, Isidore had blurted out the fact that Prout had succeeded in laying Leon Lalage's brother by the heels."Perhaps I have something to say to you," Hetty said between her teeth.Great crowds walked the long way to Tirlemont. They were constantly threatened by German soldiers, who aimed their rifles at them; passing officers commanded from time to time that some should stay behind, and others were shot. Especially did the clerics amongst the refugees suffer a great deal;145 many were not only scandalously scoffed at, but also maliciously injured. The greater part of the Germans showed a strong anti-Catholic bias, in particular against the clergy, whom they accused of having incited the people against them."Then why should a woman like that encumber herself----"The famous theses of Gorgias were quoted in a former chapter as an illustration of the tactics pursued by Greek Humanism in its controversy with physical science. They must be noticed again in the present connexion, on account of their bearing on the development of scepticism, and as having inaugurated a method of reasoning often employed in subsequent attacks, directed, not against the whole of knowledge, but against particular parts of it. The scepticism of Protagoras rested on the assumption that there is an external reality from the reaction of which with mind all our perceptions proceed. Neither of these two factors can be known apart from the other, and as both are in a constant flux, our knowledge of the resulting compound at one time does not show what it has been or will be at another time. But Gorgias altogether denied the existence of any objective reality; and he attempted to disprove it by an analytical instead of a synthetic argument, laying down a series of disjunctive propositions, and upsetting the different alternatives in succession. Existence must be either something or nothing, or both together; and if something, it must be either finite or infinite, or both, and either one or many, or both. His argument against an infinite existence is altogether futile; but it serves to illustrate the undeveloped state of reflection at that period. The eternity of the world is confounded with its unlimited extension in space: and this hypothesis, again, is met by the transparent quibble that the world, not being in any one place, must be nowhere or not at all. And the alternative that the world has not always existed is refuted by the unproved assumption, which, apparently, no Greek philosopher ever thought of disputing, that nothing can begin without being caused by something else. Still, however contemptible such reasonings may seem,131 it is obvious that in them we have the first crude form of the famous antinomies by which Kant long afterwards sought to prove the impossibility of a world existing in space and time apart from a percipient subject, and which have since been used to establish in a more general way the unknowability of existence as such. It will also be observed that the sceptical arguments respectively derived from the relativity of thought and from the contradictions inherent in its ultimate products are run together by modern agnostics. But no reason that we can remember has ever been given to show that an idea is necessarily subjective because it is self-contradictory.
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