Manchester Memoirs, Vol. Ixv. (192 1), No. 8 

 TABLE I. 



Length, Width, and Thickness Distribution. 





Length 





Width 



Thickness 







Length No. of 



Width 



No. of 



Thickness No. of 





mm. 



Specimens 



mm. 





Specimens 



mm. Specimens 







4-0 



3 



4-5 





1 



2-5 4 







4-5 



3 



5-0 





3 



3-0 8 







5 



9 



5-5 





5 



3-5 20 







5 5 



20 



6-0 





8 



4-0 57 







6-0 



31 



6 5 





10 



4-5 89 







6-5 



65 



7-0 





26 



5-0 1 22 







7-0 



58 



75 





38 









7-5 



11 



8-0 





55 













8-5 





47 













9-0 





1 







Mean, mm. ... 



6-39 



7 '65 



4-21 



Standard 











Deviation, mm. 



0-713 





0-879 



0-535 



Coefficient of 











Variation 



11-16 





11-48 



12-71 



In all the distribution and correlation work a class interval 

 of o"5 mm. has been adopted as the most satisfactory. The 

 three distribution curves are all very similar, and suggest at 

 once that the correlation of each pair of variables is high. 

 The resemblance of the curves is borne out by the fact that the 

 coefficients of variation (Pearson) of the three dimensions for 

 the whole series of shells are practicallv identical for length, 

 1 1" 16; for width, 11 '48; and for thickness, 1271. 



(b) Correlation of Length and Width. A full correlation 

 table for length and width is given in Table II (the two 

 specimens distinguished in this and the following table are 

 the two to which reference is made later in the sections dealing 

 with the ratio distribution and correlation). It is obvious 

 from a glance at this table that the correlation of the two 

 dimensions is high, and this is confirmed by the high value 

 of the correlation factor (r) — + 0*950. 



The equations of regression are : — 

 (a) L = 0*49 + 0771 W, 



with a standard error of 



(b) W = 0*17 + 1 171 L; standard error, 

 where L = length, \ 

 W = width, J 



? The regressions throughout have been assumed to be recti- 

 linear. 



± 0222 ; 



± 0*2735 



in mm. 



