Vibrations upon the Form of Certain Sponge- Spicules. 581 



or practically 2/5. Other combinations of the observations give a result in 

 close agreement, and we- do not consider it necessary to give further detailed 

 calculations of the value of n, which can easily be verified by the reader by 

 reference to the figures. 

 The interpolation formula 



0-074 + 0-3 (4w + l)/(4w + 2) 



for the nodal position, with n = 2/5, becomes 



0-074 + (0-3x 13/18)'= 0-291. 



This calculation is also typical, and will not be given for each individual 

 case, except in its final result. 



The ten specimens are shown in figs. 5-14, which are reproduced to scale- 

 These should be compared with fig. 4, which has just reached the critical 

 stage, but in which no whorls have yet appeared. 



Fig. 4. Fig. 5. 



Fig. 6 



Fig. 7. 



Fig. 8. 



Fig. 9. 



The details of these cases are as follows.: — 



Fig. 5. — Calculations for this spicule are given above. Its length in the 

 drawing is 74'0 mm. and its thickest part is exactly in the middle. The 

 whorls are very near the critical stage {i.e., their first appearance), and the 

 median one is slightly displaced from the centre towards the other, i.e., it 



vol. lxxxix. — b. 3 c 



