NOTES. 605
Kayser, Handluch der Statik (1836), p. 460 :" Machines are divided also into simple and compound. Strictly speaking only the cord (!), the lever and the inclined plane are simple machines. It is customary, however, to treat along with these also those into which compound machines can be resolved. These simple machines are seven in number, viz., the cord, the lever, the pulley, the wheel and axle, the inclined plane, the wedge, and the screw. They are also called machine organs or mechanical powers. Many writers do not reckon the cord among them."
Riihlman, Mechanik (1860), p. 231 : " A machine of which no part is itself a machine is called simple, in the opposite case compound. The simple machines are the funicular machine, the lever, the pulley, the wheel and axle, the inclined plane and the wedge. Note : strictly speaking we need distinguish only three simple machines, the funicular machine, the lever, and the inclined plane, all the others may be resolved into these." This definition leaves something still wanting, and in itself it is a complete petitio principii. We have again the impossible derivation of the pulley from the lever.
Schrader, Elemente der Mechanik und Maschinenlehre (1860), p. 26 : " The different kinds of simple machines. The originals of all simple machines are the lever and the inclined plane. From the lever are derived the pulley and the wheel and axle, and from the inclined plane the wedge and the screw. Note : in the lever the moving piece rotates, in the inclined plane it moves in a straight path." The pulley is, as usual, quite wrongly placed.
[I am sony to say that the definitions of English authors have been no more satisfactory, as a rule, than those given above. Todhunter, for example, says : " The most simple machines are called mechanical powers ; by combining these, all machines, however complicated, are constructed. These simple machines . . . . are usually considered to be seven in number ; namely, the lever, the wheel and axle, the toothed-wheel, the pulley, the inclined plane, the wedge and the screw." We continually find, too, the loose expressions that the lever is a solid body "moveable about a fixed point," that it is "supported at one point" (as distinct from the w r heel, which is supported at an axis), and so on.] It is very remarkable that in all the examples we have given, with the exception of Langsdorf, the peculiarity of the screw as a simple machine is denied, although it is kinematically the general case of the three lower pairs, and ought therefore in every case to remain in the classification. The extra- ordinary confusion (for so we must call it) of ideas upon the subject arises from a peculiar misunderstanding which, so far as my experience goes, is very strongly rooted and may be only very slowly dislodged. It is that the simi- larity of the relations existing between the forces coming into action is mistaken for a similarity between the objects themselves. Because certain force-relations in the screw are conditioned similarly to those in the inclined plane, it does not follow that the two things are identical. Instead of ex- amining the things themselves, people have concerned themselves with certain of their properties. The importance of the latter indeed cannot be disputed, but they ought logically to be kept apart from the actual nature of the combination of bodies to which they belong. When, on the other hand, the more recent writers apparently do away with the simple machines altogether, but in reality introduce them as " exercises," " examples," "applications " and
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