690 ON CONCRETIONS, SPICULES, ETC. [ch. 



by means of a rotation about the vertical axis*." It is, of course, 

 evident that the whole process is merely that which is familiar to 

 physicists as "close packing." It is a very simple case of what 

 Lord Kelvin used to call "a problem in tactics." It is a mere 

 question of the rigidity of the system, of the freedom of movement 

 on the part of its constituent cells, whether or at what stage this 

 tendency to shp into the closest propinquity, or position of minimmn 

 potential, will be found to manifest itself. 



Lastly, a curious case is presented by the so-called "chessman" 

 spicules of Latrunculia and of a few other sponges, where the spicular 

 shaft is thickened at regular intervals, and the thickenings grow 

 into whorled and flattened lobes. Dendy suggested that the 

 developing spicule is in a state of vibration (due perhaps to the 

 water-currents of the sponge), and that the whorls correspond to 

 nodes, or loci of comparative rest, where the formative cells tend 

 to settle down and do their work undisturbed. The position of 

 the nodes and internodes will depend on many circumstances, on 

 whether the spicule be a fixed rod or a free one, straight or curved, 

 uniform in section or tapering towards either end. In the free bar 

 there should tend, in any case, to be a node in the middle, and 

 two more at definite distances from either end. It so happens that 

 in the forms investigated there are only two whorls, the median 

 and one other; but J. W. Nicholson has calculated the positions 

 of these according to the vibration theory, and the theoretical 

 results are found to agree with those of observation very closely 

 indeed. That one of the whorls should be lacking might seem to 

 imperil the proof; but on the other hand among large numbers of 

 spicules no one was found to have its whorls in a position incon- 

 sistent with the theory, and there was the required agreement 

 between the shape of the spicule and the position of the whorls. 

 The absence of a third whorl is explained as due to a lack of the 

 necessary formative cells at that part of the spiculef. The theory 

 is in a way supported by recent work (by R. W. Wood of Baltimore 

 and others) on "supersonic vibrations," showing excessively rapid 



* Korschelt and Heider, p. 16. 



t A. Dendy and J. W. Nicholson, On the influence of vibration upon the form 

 of certain sponge-spicules, Proc. R.S. (B), lxxxix, pp. .'^73-587, 1917; A. Dendy, 

 The chessman spicules of the genus Latrunculia, etc., Journ. Quekett Microsc. Club, 

 xm, pp. 1-16, 1917. 



