136 Proceedings of the Koyal Physical Society. 



respect, 22 individuals having fewer than, and 138 individuals having more 

 than, the normal number. The tables further show that this variation is 

 most marked in the perradial canal system. (It is worthy of remark that 

 the perradial canals are first in order of development in the larval stage.) 

 Here, as in the case of the tentaculocysts, the great tendency is towards an 

 increase in the number. Thus, these 160 abnormal specimens have altogether 

 a total of 994 perradials instead of the normal 640. This is an increase of 

 over 55 per cent. On the other hand, the interradials give a total of 671 

 eanals, or less than 5 per cent, increase. The perradials range for a single 

 individual from 2 to 12, and the interradials from 2 to 7, while the thousand 

 specimens give an average of 8 - 385 perradial and interradial canals instead of 

 the normal 8. The following are the numbers : — 



1 individual had 4 branched radial canals. 



J- » >! « » I) 



*■ )j jj o ,, ,, 



19 7 



840 „ „ 8 (normal) „ ,, 



26 „ „ 9 



42 „ „ 10 



18 „ „ 11 



32 „ „ 12 



6 „ „ 13 



10 „ „ 14 



1 1 ^ 



3 „ „ 16 



On calculating the curve l of the canals we find that the following are 

 the main factors, and that the curve is asymmetric and of limited range 

 in both directions (Pearson's Type I). 



The Mean (M.), 



The Standard Deviation (o-) ; . 

 The Coefficient of Variability (C.V.), 

 The Probable Error of Mean (P.E.M), . 

 The Probable Error of Standard Deviation, 



8-385 



1-148 



0437 



= ± 0-245 



= ± 0173 



5. Note on Twinning. 



It has been said that there was found perfect correlation between the 

 number of branched radial canals and the number of marginal sense-organs. 

 Put this requires some qualification, for in ten individuals two adjacent 

 tentaculocysts occurred at the outer end of a single radial canal (Fig. 2). 



1 Karl Pearson, "Contributions to the Mathematical Theory of Evolution,'.' PMl. Trans. 

 Roy. Soc. London, 1894, et seq. 



(!. B. Davenport, "Statistical Methods with special reference to Biological Varia- 

 tion.' London and New York, L899. 



