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ONE:

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ONE:130Next in order are strains. As the cutting action is the source of strains, and as the resistance offered by the cutting tools is as the length or width of the edges, it will be found in the present case that while other conditions thus far have pointed to small proportions, there is now a new one which calls for large proportions. In displacing the metal between teeth of three-quarters of an inch pitch, the cutting edge or the amount of surface acted upon is equal to a width of one inch and a half. It is true, the displacement may be small at each cut, but the strain is rather to be based upon the breadth of the acting edge than the actual displacement of metal, and we find here strains equal to the average duty of a large planing machine. This strain radiates from the cutting point as from a centre, falling on the supports of the work with a tendency to force it from the framing. Between the rack and the crank-shaft bearing, through the medium of the tool, cutter bar, connection, and crank pin, and in various directions and degrees, this strain may be followed by means of a simple diagram. Besides this cutting strain, there are none of importance; the tension of the belt, the side thrust in bearings, the strain from the angular thrust of the crank, and the end thrust of the tool, although not to be lost sight of, need not have much to do with problems of strength, proportion, and arrangement.

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ONE:In their theory of cognition the Stoics chiefly followed Aristotle; only with them the doctrine of empiricism is enunciated so distinctly as to be placed beyond the reach of misinterpretation. The mind is at first a tabula rasa, and all our ideas are derived exclusively from the senses.37 But while knowledge as a whole rests on sense, the validity of each particular sense-perception must be determined by an appeal to reason, in other words, to the totality of our acquired experience.38 So also the first principles of reasoning are not to be postulated, with Aristotle, as immediately and unconditionally certain; they are to be assumed as hypothetically true and gradually tested by the consequences deducible from them.39 Both principles well illustrate the synthetic method of the Stoics��their habit of bringing into close16 connexion whatever Aristotle had studiously held apart. And we must maintain, in opposition to the German critics, that their method marks a real advance on his. It ought at any rate to find more favour with the experiential school of modern science, with those who hold that the highest mathematical and physical laws are proved, not by the impossibility of conceiving their contradictories, but by their close agreement with all the facts accessible to our observation.

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