576 Profs. A. Dendy and J. W. Nicholson. Influence of 



Since the spicule continues to grow after the whorls have appeared, 

 it is obvious that the only measurements of any value for our purposes 

 are those made upon spicules on which the whorls are only just com- 

 mencing their development. We may call this the critical stage. After 

 it has passed, the distance between the two whorls will not increase, but the 

 distance between the subsidiary whorl and the end of the spicule increases 

 considerably. It will be observed that, as in the case of the Latruncvlia 

 spicule, only one subsidiary whorl is formed, and we may attribute the 

 absence of a second one to the same cause, viz., the absence of the necessary 

 formative cells. 



Before proceeding to discuss the position of the whorls, it is desirable to 

 say something about the way in which the measurements were made. The 

 spicules were first drawn with a camera lucida, under a Zeiss microscope, 

 with an F objective and a No. 4 eyepiece, giving a magnification of about 

 1075 diameters. The outline was corrected without the camera, and 

 measurements were made upon the finished drawing. In making the 

 measurements and calculations, the absolute dimensions of the drawing, 

 and not those of the spicule itself, have been employed. 



It will be observed that the case is a different one from that of the 

 Latruncvlia spicule, for the ends of the rod are not weighted, and the 

 vibrations must be those of the free-free type. It is safe to assume that 

 any vibrations that occur must be transverse ones, for, whereas it is easy to 

 see how transverse vibrations might be induced by sudden alterations of 

 pressure upon a slender elastic rod lying in the almost liquid mesogloea in 

 the immediate neighbourhood of the canals through which water is flowing, 

 it is extremely improbable that vibrations of any other type would be set up. 



The positions of the nodes in a transversely vibrating rod of uniform 

 section are, of course, well known, but, apparently, no investigator has 

 hitherto determined, either by experiment or calculation, the corresponding 

 positions in the case of a rod having the form of a double cone or paraboloid, 

 or some form intermediate between these two, such as is exhibited by the 

 oxydiscorhabd. It was therefore necessary in the first instance to arrive at a 

 general formula, by means of which this problem could be solved, and then 

 to calculate the theoretical positions of the nodes in each spicule examined. 

 The degree of accuracy with which the positions found by actual measure- 

 ment agree with those determined by calculation, based upon the form of 

 the spicule, affords the best possible test of the truth of the vibratory theory. 



The lateral vibrations of a bar of uniform cross-section and material are 

 investigated very fully in Lord Eayleigh's treatise,* and we may quote, for 

 * ' Theory of Sound.' vol. 1, p. 256. 



