Abstract
LONDON.
Royal Society, May 24.Sir J. J. Thpmson, president, in the chair.Prof. A. Dendy and Prof. J. W. Nicholson: The influence of vibrations upon the form of certain sponge-spicules. It has been suggested recently by one of the authors that the positions of the whorls which appear on certain siliceous spicules in the genus Latrunculiamay be determined by vibrations to which the spicule is subjected at a certain stageof its development, corresponding, in fact, with the nodal points of a vibrating rod. The object of the present communication is to describe a similar case in a closely allied, but hitherto undescribed, genus, and to subject it to mathematical analysis with the view of testing this vibratory theory. The problem was to determine the degree of coincidence betwen the actual positions of the whorls on the spicule and the positions which would be occupied by the nodes in a vibrating free-free rod of shape similar to that of the shaft of the spicule at the moment when the nodes are beginning to develop (i.e. at the critical stage). The general problem is that of the nodes in a rod composed of two equal portions, each formed by the rotation of the curve y c X between x o and x = 1 about its axis, and the positions of the nodes are expressed as functions of the index n by the interpolation formula. All the spicules examined correspond very closely with this law of shape for values of n between and i. Details of ten cases at or near the critical stage are given in the paper, and the conclusion is arrived at that the positions of the whorls, although subject to slight mdi- vidual variations due to various disturbing factors, agree so accurately with the theoretical positions of the nodes as to leave little doubt as to the influence of transverse vibrations in determining them. An efficient cause of such vibrations may be found in the water currents which circulate with considerable force through the canal system of the sponge.Prof. J. W. Nicholson: The lateral vibrations of bars of variable section. The paper contains a discussion of the lateral vibrations of a bar composed of two equal halves and free at each end. Each half consists of a portion of the solid generated by the revolution of the curve y = Ax about its axis, and the fundamental frequencies and positions ¢f the corresponding nodes are investigated for various values of n between o and i.
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Societies and Academies . Nature 99, 318–320 (1917). https://doi.org/10.1038/099318b0
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DOI: https://doi.org/10.1038/099318b0