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



For any suitable spicule the value of n may be determined by direct 

 measurement of the varying transverse diameter in the magnified drawing. 

 For this purpose, it is essential, as already stated, to obtain specimens which 

 have just reached the critical stage (when the whorls are only commencing to 

 develop). In such cases very accurate measurements are possible. Moreover, 

 progressive changes in the position of the actual nodes, caused by the fact 

 that the more developed spicule may not be exactly similar to its original 

 shape when the whorls commenced to form, cease in these circumstances to 

 be a disturbing factor. The fact that the whorls on the oxydiscorhabd appear 

 first as very thin, sharply defined rings, makes it possible also to determine 

 their position with considerable accuracy. 



An account is given below of the quantitative examination of ten specimens 

 of the oxydiscorhabd, at or near its critical stage of development, from the 

 standpoint of the vibratory theory. It is necessary, in view of the preceding 

 account of the biological history of the spicule, merely to show that the 

 positions of the two actually occurring whorls are in accordance with the 

 theory of vibrations of non-uniform bars already outlined. The absence of 

 the third whorl has already been explained. 



The magnification adopted for each of the specimens was, as already stated, 

 about 1075, and the measurements were all made upon the enlarged drawings, 

 the actual dimensions- of which will alone be quoted. 



If the curve of any spicule is of the form 



y = Ax n , 



and if 2yi, 2y 2 are breadths at distances Xi, x 2 from the end, 



2y 1 /2y 2 = (x 1 /x 2 y 

 or n = (log 2y x — log 2y 2 )/(log x x — log x 2 ). 



A series of values can be found for n by such measurements and a mean 

 value taken. For example, for the first of the ten spicules (fig. 5), measure- 

 ments are shown in the following Table : — 



Breadth (2jr). 



Distance from end (x). 



mm. 



mm. 



2-6 



34 



2 3 



27 



2-1 



20-5 



1-5 



9 



From the third and fourth pairs of observations of position and breadth 



quoted in the Table 



n _ log 21 -log 1-5 _ 0-322-0-176 = 0146 

 log 20-5 -log 9-0 1-311-0-954 0-357 



