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"What's the theory here, sir?" Prout asked respectfully.

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Next 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.Returning to our more immediate subject, we must observe that the Pythagoreans did not maintain, in anticipation of modern quantitative science, that all things are determined by number, but that all things are numbers, or are made out of numbers, two propositions not easily distinguished by unpractised thinkers. Numbers, in a word, were to them precisely what water had been to Thales, what air was to Anaximenes, the absolute principle of existence; only with them the idea of a limit, the leading inspiration of Greek thought, had reached a higher degree of abstraction. Number was, as it were, the exterior limit of the finite, and the interior limit of the infinite. Add to this that mathematical studies, cultivated in Egypt and Phoenicia for their practical utility alone, were being pursued in Hellas with ever-increasing ardour for the sake of their own delightfulness, for the intellectual discipline that they supplieda discipline even12 more valuable then than now, and for the insight which they bestowed, or were believed to bestow, into the secret constitution of Nature; and that the more complicated arithmetical operations were habitually conducted with the aid of geometrical diagrams, thus suggesting the possibility of applying a similar treatment to every order of relations. Consider the lively emotions excited among an intelligent people at a time when multiplication and division, squaring and cubing, the rule of three, the construction and equivalence of figures, with all their manifold applications to industry, commerce, fine art, and tactics, were just as strange and wonderful as electrical phenomena are to us; consider also the magical influence still commonly attributed to particular numbers, and the intense eagerness to obtain exact numerical statements, even when they are of no practical value, exhibited by all who are thrown back on primitive ways of living, as, for example, in Alpine travelling, or on board an Atlantic steamer, and we shall cease to wonder that a mere form of thought, a lifeless abstraction, should once have been regarded as the solution of every problem, the cause of all existence; or that these speculations were more than once revived in after ages, and perished only with Greek philosophy itself.
THREE:But the yachts boat, with its motor hastily started, and coldlost way as the engine sputtered and died!

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ONE:"Where do you come from?" was his first question.

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An interesting study in connection with modern shaping machines is the principle of various devices called 'quick return' movements. Such devices consist of various modifications of slotted levers, and what is known as Whitworth's quick return motion.It is not proposed at this time to treat of the construction of machinery for transmitting power, but to examine into the conditions that should determine which of the several plans of transmitting is best in certain caseswhether belts, gearing, or shafts should be employed, and to note the principles upon which they operate. Existing examples do not furnish data as to the advantages of the different plans for transmitting power, because a given duty may be successfully performed by belts, gearing, or shaftseven by water, air, or steamand the comparative advantages of different means of transmission is not always an easy matter to determine.
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