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THREE:Modern turbine wheels have been the subject of the most careful investigation by able engineers, and there is no lack of mathematical data to be referred to and studied after the general principles are understood. The subject, as said, is one of great complicity if followed to detail, and perhaps less useful to a mechanical engineer who does not intend to confine his practice to water-wheels, than other subjects that may be studied with greater advantage. The subject of water-wheels may, indeed, be called an exhausted one that can promise but little return for labour spent upon it��with a view to improvements, at least. The efforts of the ablest hydraulic engineers have not added much to the percentage of useful effect realised by turbine wheels during many years past.

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THREE:6

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THREE:Not only oratory and literature, but philosophy and science were cultivated with renewed vigour. The line between philosophy and sophisticism was not, indeed, very distinctly drawn. Epict��tus severely censures the moral teachers of his time for ornamenting their lectures with claptrap rhetoric about the battle of Thermopylae or flowery descriptions of Pan and the Nymphs.406 And the professed declaimers similarly drew on a store of philosophical commonplaces. This sort of popular treatment led to the cultivation of ethics and theology in preference to logic and metaphysics, and to an eclectic blending of the chief systems with one another. A severer method was inculcated in the schools of Athens, especially after the endowment of their professors by Marcus Aurelius; but, in practice, this came to mean what it means in modern universities, the substitution of philology for independent enquiry. The question was not so much what is true as what did Plato or Aristotle really think. Alexandrian science showed something of the same learned and traditional character in the works of Ptolemy; but the great name of Galen marks a real progress in physiology, as well as a return to the principles of Hippocrates.

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THREE:A learner should, in fact, consider the application and operative conditions of gearing as one of the main parts of the subject, and the geometry or even the construction of wheels as subsidiary; in this way attention will be directed to that which is most difficult to learn, and a part for which facilities are frequently wanting. Gearing may be classed into five modifications��spur wheels, bevel wheels, tangent wheels, spiral wheels, and chain wheels; the last I include among gearing because the nature of their operation is analogous to tooth wheels, although at first thought chains seem to correspond more to belts than gearing. The motion imparted by chains meshing over the teeth of wheels is positive, and not frictional as with belts; the speed at which such chains may run, with other conditions, correspond to gearing.

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