ONE:In the driving gearing of planing machines, conditions which favour the reversing movement are high speed and narrow driving belts. The time in which belts may be shifted is as their speed and width; to be shifted a belt must be deflected or bent edgewise, and from this cause wind spirally in order to pass from one pulley to another. To bend or deflect a belt edgewise there will be required a force in proportion to its width, and [133] the time of passing from one pulley to another is as the number of revolutions made by the pulleys.He put a hand on Sandys shoulder and the latter managed not to wince or draw away.
TWO:Thus, so far as was possible in such altered circumstances, did the Renaissance of the second century reproduce the271 intellectual environment from which Platos philosophy had sprung. In literature, there was the same attention to words rather than to things; sometimes taking the form of exact scholarship, after the manner of Prodicus; sometimes of loose and superficial declamation, after the manner of Gorgias. There was the naturalism of Hippias, elaborated into a system by the Stoics, and practised as a life by the new Cynics. There was the hedonism of Aristippus, inculcated under a diluted form by the Epicureans. There was the old Ionian materialism, professed by Stoics and Epicureans alike. There was the scepticism of Protagoras, revived by Aenesidmus and his followers. There was the mathematical mysticism of the Pythagoreans, flourishing in Egypt instead of in southern Italy. There was the purer geometry of the Alexandrian Museum, corresponding to the school of Cyrn. On all sides, there was a mass of vague moral preaching, without any attempt to exhibit the moral truths which we empirically know as part of a comprehensive metaphysical philosophy. And, lastly, there was an immense undefined religious movement, ranging from theologies which taught the spirituality of God and of the human soul, down to the most irrational and abject superstition. We saw in the last chapter how, corresponding to this environment, there was a revived Platonism, that Platonism was in fact the fashionable philosophy of that age, just as it afterwards became the fashionable philosophy of another Renaissance thirteen centuries later. But it was a Platonism with the backbone of the system taken out. Platos thoughts all centred in a carefully considered scheme for the moral and political regeneration of society. Now, with the destruction of Greek independence, and the absorption everywhere of free city-states into a vast military empire, it might seem as if the realisation of such a scheme had become altogether impracticable. The Republic was, indeed, at that moment realising itself under a form adapted to the altered exigencies of the time; but no Platonist could as yet recognise272 in the Christian Church even an approximate fulfilment of his masters dream. Failing any practical issue, there remained the speculative side of Platos teaching. His writings did not embody a complete system, but they offered the materials whence a system could be framed. Here the choice lay between two possible lines of construction; and each had, in fact, been already attempted by his own immediate disciples. One was the Pythagorean method of the Old Academy, what Aristotle contemptuously called the conversion of philosophy into mathematics. We saw in the last chapter how the revived Platonism of the first and second centuries entered once more on the same perilous path, a path which led farther and farther away from the true principles of Greek thought, and of Plato himself when his intellect stood at its highest point of splendour. Neo-Pythagorean mysticism meant an unreconciled dualism of spirit and matter; and as the ultimate consequence of that dualism, it meant the substitution of magical incantations and ceremonial observances for the study of reason and virtue. Moreover, it readily allied itself with Oriental beliefs, which meant a negation of natural law that the Greeks could hardly tolerate, and, under the form of Gnostic pessimism, a belief in the inherent depravity of Nature that they could not tolerate at all.But a profounder analysis of experience is necessary before we can come to the real roots of Platos scheme. It must be remembered that our philosopher was a revolutionist of the most thorough-going description, that he objected not to this or that constitution of his time, but to all existing consti254tutions whatever. Now, every great revolutionary movement, if in some respects an advance and an evolution, is in other respects a retrogression and a dissolution. When the most complex forms of political association are broken up, the older or subordinate forms suddenly acquire new life and meaning. What is true of practice is true also of speculation. Having broken away from the most advanced civilisation, Plato was thrown back on the spontaneous organisation of industry, on the army, the school, the family, the savage tribe, and even the herd of cattle, for types of social union. It was by taking some hints from each of these minor aggregates that he succeeded in building up his ideal polity, which, notwithstanding its supposed simplicity and consistency, is one of the most heterogeneous ever framed. The principles on which it rests are not really carried out to their logical consequences; they interfere with and supplement one another. The restriction of political power to a single class is avowedly based on the necessity for a division of labour. One man, we are told, can only do one thing well. But Plato should have seen that the producer is not for that reason to be made a monopolist; and that, to borrow his own favourite example, shoes are properly manufactured because the shoemaker is kept in order by the competition of his rivals and by the freedom of the consumer to purchase wherever he pleases. Athenian democracy, so far from contradicting the lessons of political economy, was, in truth, their logical application to government. The people did not really govern themselves, nor do they in any modern democracy, but they listened to different proposals, just as they might choose among different articles in a shop or different tenders for building a house, accepted the most suitable, and then left it to be carried out by their trusted agents.
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