Vibrations upon the Form of Certain Sponge- Spicules. 585 



Fig. 14 — The spicule shown in this figure is practically a double cone, of 

 length 77'5 mm. The median whorl is at a distance of 40 mm. from the end 

 more remote from the subsidiary whorl, instead of the theoretical distance 

 \ (77 - 5), or 38 - 75 mm. It is therefore displaced towards the subsidiary 

 whorl to the extent of l - 25 mm. The distance of the subsidiary whorl from 

 the nearer end should be 0324 x 77 - 5 mm., or 240 mm., whereas actual 

 measurement gives a distance of 23 - mm. The displacement is therefore 

 1 mm. in the same direction as that of the median whorl. 



In attempting to estimate the value of the coincidence between the actual 

 positions of the whorls on the spicule as determined by observation, and the 

 theoretical positions of the nodes as determined by calculation, several 

 possible sources of error have to be considered. In the first place, we have 

 to make allowance for inaccuracies in the drawings which form the basis of 

 the measurements. Such inaccuracies may be expected to arise, partly from 

 the difficulty of making an exact tracing of a very fine line by aid of the 

 camera lucida and partly from the fact that the spicule does not lie absolutely 

 horizontal, one end usually being at a slightly higher level than the other. 



We have to remember also that a zone of comparative rest, in which there 

 is but little variation in the amplitude of vibration, extends for some 

 distance on either side of each node, and that the formative cells can hardly 

 be expected to be possessed of the power of determining the exact position of 

 least movement with absolute accuracy. Evidence that they exhibit varia- 

 tions in this respect is suggested by those cases in which the median whorl 

 is shifted a little to one side or other of the central point of the shaft. In 

 such cases, however, the subsidiary whorl also tends to be shifted in the same 

 direction, as though the two rings of formative cells which, on the analogy 

 of Latrunculia bocagei, may be assumed to exist, were perhaps linked together, 

 a state of things which, supposing that the cells in question form a sheath 

 around the spicule (as in Latrunculia), is very likely to occur. It seems 

 not impossible that alterations of surface tension may be responsible for the 

 dislocation of such a sheath as a whole. 



On the whole, it is somewhat surprising to find how close the agreement 

 between the observed and calculated positions of the whorls really is. In 

 order to demonstrate this agreement as clearly as possible, we have 

 indicated, by means of arrows at the side of each spicule, in figs. 5-14, 

 the calculated positions of the nodes for that particular case. 



It might be argued that the possible sources of discrepancy are so great 

 as to render mathematical treatment of the subject valueless. That this is 

 not the case, however, is shown by the fact that there is a demonstrable 

 correlation between the shape of the spicule and the position of the whorls, 



