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THREE:The latter seems a plausible theory, and perhaps a correct one; but there are two facts in connection with the operation of reaction water-wheels which seem to controvert the latter and favour the first theory, namely, that reaction wheels in actual practice seldom utilise more than forty per cent. of useful effect from the water, and that their speed may exceed the initial velocity of the water. With this the subject is left as one for argument or investigation on the part of the reader.

THREE:��Don��t!�� Sandy spoke sharply. ��Don��t go in there!��

THREE:We have endeavoured to show that Aristotle��s account of the syllogism is redundant on the one side and defective on the other, both errors being due to a false analysis of the reasoning process itself, combined with a false metaphysical philosophy. The same evil influences tell with much greater effect on his theory of applied reasoning. Here the fundamental division, corresponding to that between heaven and earth in the cosmos, is between demonstration and dialectic or experimental reasoning. The one starts with first principles of unquestionable validity, the other with principles the validity of which is to be tested by their consequences. Stated in its most abstract form, the distinction is sound, and very nearly prefigures the modern division between deduction and induction, the process by which general laws are applied, and the process by which they are established. Aristotle, however, committed two great mistakes; he thought that each method corresponded to an entirely different order of phenomena: and he thought that both were concerned for the most part with definitions. The Posterior Analytics, which contains his theory of demonstration, answers to the astronomical portion of his physics; it is the doctrine of eternal and necessary truth. And just as his ontology distinguishes between the Prime Mover himself unmoved and the eternal movement produced by his influence, so also his logic distinguishes between infallible first principles and the truths derived from them, the latter being, in his opinion, of inferior384 value. Now, according to Aristotle, these first principles are definitions, and it is to this fact that their self-evident certainty is due. At the same time they are not verbal but real definitions��that is to say, the universal forms of things in themselves as made manifest to the eye of reason, or rather, stamped upon it like the impression of a signet-ring on wax. And, by a further refinement, he seems to distinguish between the concept as a whole and the separate marks which make it up, these last being the ultimate elements of all existence, and as much beyond its complex forms as Nous is beyond reasoned truth.

THREE:Temperance and justice are very clearly distinguished in our minds. The one is mainly a self-regarding, the other mainly a social virtue. But it would be a mistake to suppose that the distinction was equally clear to Plato. He had learned from Socrates that all virtue is one. He found himself confronted by men who pointedly opposed interest to honour and expediency to fair-dealing, without making any secret of their preference for the former. Here, as elsewhere, he laboured to dissolve away the vulgar antithesis and to231 substitute for it a deeper one��the antithesis between real and apparent goods. He was quite ready to imagine the case of a man who might have to incur all sorts of suffering in the practice of justice even to the extent of infamy, torture, and death; but without denying that these were evils, he held that to practise injustice with the accompaniment of worldly prosperity was a greater evil still. And this conviction is quite unconnected with his belief in a future life. He would not have agreed with St. Paul that virtue is a bad calculation without the hope of a reward for it hereafter. His morality is absolutely independent of any extrinsic considerations. Nevertheless, he holds that in our own interest we should do what is right; and it never seems to have entered his thoughts that there could be any other motive for doing it. We have to explain how such a paradox was possible.These two fiends would not dare to do him any harm now. All the same, Hetty made up her mind not to go to bed. She had Mamie in her own room, the door of which she left purposely open. If the worst came to the worst she could ring the electric alarm on the top landing and rouse the household. Mamie was sleeping peacefully with her head on her hand.