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FORE:An engineer may direct and control work without a knowledge of practical fitting, but such control is merely a commercial one, and cannot of course extend to mechanical details which are generally the vital part; the obedience that may thus be enforced in controlling others is not to be confounded with the respect which a superior knowledge of work commands.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.

FORE:I have been necessarily brief in my statement of Teichmüller��s theses; and to judge of them apart from the facts and arguments by which they are supported in the two very interesting volumes above named would be in the highest degree unfair. I feel bound, however, to mention the chief reasons which make me hesitate to accept his conclusions. It seems to me, then, that although Plato was moving in the direction of pantheism��as I have myself pointed out in more than one passage of this work��he never actually reached it. For (i.) he does not, like Plotinus, attempt to deduce his material from his ideal principle, but only blends without reconciling them in the world of sensible experience. (ii.) In opposing the perishable nature of the individual (or rather the particular) to the eternal nature of the universal, he is going on the facts of experience rather than on any necessary opposition between the two, and on experience of material or sensible objects rather than of immaterial souls; while, even as regards material objects, the heavenly bodies, to which he attributes everlasting duration, constitute such a sweeping exception to his rule as entirely to destroy its applicability. (iii.) Plato��s multiplied and elaborate arguments for the immortality of the soul would be superfluous were his only object to prove that the soul, like everything else, contains an eternal element. (iv.) The Pythagorean theory that the soul is a harmony, which Plato rejects, wouldxx have been perfectly compatible with the ideal and impersonal immortality which Teichmüller supposes him to have taught; for while the particular harmony perishes, the general laws of harmony remain. (v.) Teichmüller does not dispose satisfactorily of Plato��s crowning argument that the idea of life is as inseparable from the soul as heat from fire or cold from snow. He says (op. cit., p. 134) that, on this principle, the individual soul may still perish, just as particular portions of fire are extinguished and particular portions of snow are melted. Yes, but portions of fire do not grow cold, nor portions of snow hot, which and which alone would offer an analogy to the extinction of a soul.IX.