Note 185, [p. 145]. Mr. Wheatstone’s principle is, that when vibrations producing the forms of figs. 1 and 2, [plate 3], are united in the same surface, they make the sand assume the form of fig. 3. In the same manner, the vibrations which would separately cause the sand to take the forms of figs. 4 and 5, would make it assume the form in fig. 6 when united. The figure 9 results from the modes of vibration of 7 and 8 combined. The parts marked a a are in different states of vibration from those marked b b. Figs. 1, 2, and 3, [plate 4], represent forms which the sand takes in consequence of simple modes of vibration; 4 and 5 are those arising from two combined modes of vibration; and the last six figures arise from four superimposed simple modes of vibration. These complicated figures are determined by computation independent of experiment.
Note 186, [p. 146]. The long cross-lines of fig. 46 show the two systems of nodal lines given by M. Savart’s laminæ.
Fig. 46.
Note 187, [p. 146]. The short lines on fig. 46 show the positions of the nodal lines on the other sides of the same laminæ.
Note 188, [p. 146]. Fig. 47 gives the nodal lines on a cylinder, with the paper rings that mark the quiescent points.
Fig. 47.
Fig. 48.