Vibrations upon the Form of Certain Sponge- Spicules. 583 



being 44 and 42 mm. The subsidiary whorl is at 28'0 from the end, giving a 

 ratio 0-325. The value of n is 2/3, giving a theoretical ratio 0'310, which is 

 within 5 per cent, of the observed value. The displacement of the subsidiary 

 whorl from the theoretical position is again only 1 mm., and is probably to be 

 accounted for by the curvature of the spicule. 



Fig. 9. — The spicule appears to be absolutely conical, and the median 

 whorl is almost precisely central, coinciding with a marked primary central 

 thickening. The true distance of the subsidiary whorl from the end should 

 be 0'324 x 75 - 5, where 75 - 5 is the total length. This becomes 24 - 4, against, 

 the measured value 25 - 4. The displacement is again 1 mm. towards the 

 centre, as required either by curvature or slight subsequent growth at the 

 ends. 



Fig. 10. Fig. 11., Fig. 12. Tig. 13. Fig. 14. 



Fig. 10. — The lengths on the two sides of the primary central thickening 

 are 46 - and 47 - mm., indicating slightly unequal growth. The median 

 whorl coincides with the primary central thickening. The subsidiary whorl, 

 at 32 - mm. from the end, gives a ratio 0'344. It is not possible to 

 distinguish the spicule from a conical form, so that the theoretical ratio 

 in the absence of curvature would be 0'324, corresponding to a distance- 



