604 NOTES.
For we find wheels of the simplest possible form, consisting, namely, of nothing but a nave and radial spokes, in primitive water-lifting wheels, where the horizontal wheel-shaft was driven from a vertical one (cf. Fig. 50 of Ewbank's Hydraulic and Other Machines, 16th Edition, New York, 1870). The screw-wheels for parallel axes, the invention of which has been ascribed to an Englishman, White, are to be found in primitive Indian cotton ginning rollers (see a drawing in Leigh's Modern Cotton Spinning, London, 1873, as well as several complete machines in the Indian Museum, London). We may note also that toothed- wheels having intersecting axes, in the forni of crown- wheel and pinion, have received more extensive application and attention in mill work, almost down to our own time, than spur-wheels. The latter, indeed, appear to come last in order, so that the real sequence of historical develop- ment is exactly the reverse of what we might expect, a hint that we must never confound what actually and practically lies nearest to us with what is geometrically simplest.
46 (P. 238.) From the Arabic sakai, to water or supply water ; sakka, a water-carrier in eastern countries.
46 (P. 275.) It is not uninteresting to compare the different statements on this subject. We may give a few specimens of them :
Poppe, Maschinenkunde (1821), p. 81 : "The lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw are included under the name simple machines, simple engines (Rusttzeuge) or mechanical powers. From these all machines, even the most complicated, are constructed. Since, however, the theory of the wheel and axle and of the pulley is based upon the law of the lever, and the theory of the wedge and the screw upon the law of the inclined plane, we may reduce the number of simple machines to two, the lever and the inclined plane."
Here it is clearly and emphatically stated that all machines, " even the most complicated," are formed from the simple machines, and that the latter may be reduced to two. Read, however, the following :
Langsdorf, Maschinenkunde (1826), i. p. 277 : "Even in the older text- books we find machines divided into simple and compound, the latter being those which are formed by a combination of several of the former. The simple machines are limited to the lever, the pulley, the inclined plane, the wedge, the screw, and the wheel and axle. The immoveable inclined plane should not, however, be included, it is no more a machine than is the slope of a mountain. We do indeed find a moveable inclined plane in the wedge ; inclined plane and wedge are not then machines of two different kinds. I put in their place the roller. . . . ." Here, then, it is said to be wrong to treat the inclined plane as a simple machine, while before it was treated as the foundation of several others.
Gerstner, Handbuch der Mechanik (1831), i. p. 73 : "Machines are com- monly divided into simple and compound. The simplest machine, which we shall first consider, is the lever. We shall then proceed to the wheel and axle, the pulley and the pulley-tackle (!), the inclined plane, the screw and the wedge. All these machines are simple machines ; compound machines consist always of a combination of several simple ones, after which, therefore, their treatment will come."
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