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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.So far, however, we only stand on the threshold of Platonic love. The earthly passion, being itself a kind of generalisation, is our first step in the ascent to that highest stage of existence where wisdom and virtue and happiness are one��the good to which all other goods are related as means to an end. But love is not only an introduction to philosophy, it is a type of philosophy itself. Both are conditions intermediate between vacuity and fulfilment; desire being by its very nature dis218satisfied, and vanishing at the instant that its object is attained. The philosopher is a lover of wisdom, and therefore not wise; and yet not wholly ignorant, for he knows that he knows nothing. Thus we seem to be thrown back on the standpoint of Plato��s earliest agnosticism. Nevertheless, if the Symposium agrees nominally with the Apologia, in reality it marks a much more advanced point of speculation. The idea of what knowledge is has begun to assume a much clearer expression. We gather from various hints and suggestions that it is the perception of likeness; the very process of ascending generalisation typified by intellectual love.