Page:The Kinematics of Machinery.djvu/615

 NOTES.

�593

�Reuleaux's beautifully made models are now (May 1876) at the Exhibition of Scientific Apparatus at South Kensington, where they will remain during the summer. By drawing the triangle ABC with its centroid upon paper, arid the duangle with its centroid upon tracing paper, the rolling of the centroids and the relative motion of the elements can both be tolerably well followed. By this method I have found it very easy not only to examine the motion, but also to draw series of point-paths for these higher pairs of elements.]

16 (P. 125.) For drawing these and similar roulettes I use a special three- legged compass, made for me by Herr J. Kern of Aarau (Switzerland). The third leg is jointed and its length also can be altered, so that obtuse as well as acute-angled triangles can be taken up, which could not be done with the old form of three-legged compass.

17 (P. 125.) What a strong hold this idea has obtained is shown, for example, in the following passage from Weissenborn's Cyclischen Kurven, (Eisenach 1856) p. 3 : " If the

circle described about m Q roll upon that described about M, and if the describing point B describe the curve B P x P 2 as the inner circle rolls upon the arc B b, then evidently, if the smaller circle be fixed and the larger one rolled upon it in a direction opposite to that of the former rotation, the point of the great circle which at the beginning of the operation coincided with B describes the same line B P x P 2. This "evidently" expresses the usual notion, and the one which is suggested by a hasty pre- judgment of the case. In point of fact B describes the pericy- cloid B B' B", which certainly differs

��FIG. 445.

�sufficiently from the hypocycloid

�B P! P 2.

Centroids are also of very great assistance in understanding planetary movements, and are well suited to remove the difficulties which commonly occur in connection with their '* real " and " apparent " motions. (I have a very instructive model for this purpose in the kinematic collection at Berlin.) If we test the ideas held by the majority of people upon this matter, we shall perceive how true a remark of Poinsot's (in the Memoir already referred to) still is, " Mais s'il s'agit du mouvement d'un corps de grandeur sensible et de figure quelconque, il f aut convenir qu'on ne s'en f ait qu'une id4e tres-obscure."

]8 (P. 129.) These curves have often engaged the attention of mathe- maticians. Of. Schlomilch's Zeitschrift, vol. ix., p. 209, Durege, Ueber einige besondere Arten cyMischer Kurven.

K Q Q

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