2 W. E. Alkins and M. Cook — Variation of Sphceria 



axes length, width, and thickness being noted for each shell ; 



the position of the axes was as defined when dealing with 



Sph. lacustre. Each was determined to the nearest one-tenth 



of one millimetre, and from the observed data the value of 



,, ,. Width , Thickness , 1 , 



the ratios r and — -— was calculated. 



Length Length 



The correlation of each pair of measured axes has been 



studied, as has that of the two ratios just mentioned. 



Results. 



(a) Length, Width, and Thickness Distribution. The 

 distribution of length, width, and thickness is shewn in Table I 

 (in all the distribution and correlation tables a class-interval of 

 o'5 mm. has been adopted as most convenient). The corre- 

 sponding curves are all perfectly normal, very slightly 

 asymmetrical, distribution curves, and suggest at once a high 

 correlation of the three dimensions. The similarity of the 

 three frequency polygons is borne out by the close agreement 

 of the coefficients of variation of the three variables — for 

 length, 12*42; for width, 12*92; and for thickness, 1484. 



TABLE I. 



Distribution of Length, Width, and Thickness. 



Length 



Number of 



Width 



Number of 



Thickness 



Number of 



mm. 



Specimens 



mm. 



Specimens 



mm. 



Specimens 



4-5 



5 



5-0 



1 



2-5 



2 



50 



12 



5-5 



4 



3 



13 



5-5 



36 



6 



9 



3 5 



43 



6 



94 



6 5 



16 



4-0 



108 



6-5 



156 



7-0 



40 



4-5 



179 



70 



85 



7'5 



82 



5-0 



90 



7'5 



58 



8-0 



104 



5-5 



45 



8-0 



32 



8-5 



95 



6-0 



18 



8-5 



17 



9 



62 



6-5 



2 



9 



5 



9 5 

 10-0 

 10-5 

 110 

 11-5 



40 



19 



21 



6 



1 







(b) Correlation of Length and Width. The correlation 

 table for length and width is given in Table II. The value 

 of the coefficient of correlation, as would be expected from 



