TWO: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.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.
