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



the tapering form having had its expected effect in shifting the subsidiary- 

 whorl towards the centre. 



The general tendency of the subsidiary whorl is to be displaced rather 

 farther towards the centre of the spicule than is required by theory. No 

 correction has been made, however, for the curvature of the spicule, which 

 must in itself produce such a tendency, and of a magnitude in general agree- 

 ment with the observed discrepancies. This curvature 

 cannot be accurately determined, because the apparent 

 curvature must depend upon the position in which the 

 spicule happens to be lying. 



It must always be borne in mind, also, that the slight 

 increase in total length of the spicule which takes place 

 after the critical stage has been passed must tend to make 

 the position of the subsidiary whorl appear to approach the 

 centre. Owing to the continued deposition of silica upon 

 the shaft, which results in increase of both length and 

 thickness, the adult spicule is useless for purposes of 

 accurate mathematical investigation of the nodal points. 

 Nevertheless, it is easy to see that, due allowance being 

 made for the disturbing factors, the position of the whorls 

 in the adult spicule is approximately that required by theory. 

 There is surprisingly little variation in this respect, and 

 although we have seen hundreds, or perhaps thousands, of 

 adult individuals, we have never noticed a case which is 

 inconsistent with the vibratory theory. In view of the 

 relative scarcity of individuals at or near the critical stage, 

 the evidence afforded by the examination of large numbers 

 of adults, though it is impossible to carry out that examina- 

 tion with mathematical exactness, acquires considerable 

 importance. 



So far as we are aware, no case has as yet been satisfactorily established, 

 at any rate previously to the observations on Latrunculia above referred 

 to, in which the occurrence of vibrations during development influences the 

 final form of any part of an organism.* We have here a new factor in 



* Since this paper was written we have found a reference, in Prof. D'Arcy Thompson's 

 recently published work on 'Growth and Form,' p. 323, to a suggestion by FitzGerald, 

 that the patterns on the frustules of diatoms might be due to electro-magnetic vibrations. 

 We are not aware, however, that this suggestion has ever been supported by satisfactory 

 evidence. Prof. Thompson himself makes (p. 475) a similar suggestion with regard to the 

 skeleton of certain radiolarians, but without any attempt at mathematical analysis, 

 which, indeed, would be extremely difficult in such cases. 



Fig. 15. 



