Manchester Memoirs, Vol. Ixv. (1921), No. 9 



Distribution of 



TABLE^ V, 



Width 



TABLE VI. 



Length 



Ratio. 



Distribution of 



Thickness 

 Length 



Ratio. 



Ratio 





Ratio 





Width 



No. of 



Width 



No. of 



Length 



Specimens 



Length 

 1-265 



Specimens 



1145 



1 



103 



1-165 



7 



1-285 



42 



1-185 



32 



1-305 



25 



1-205 



50 



1-325 



3 



1 -225 



120 



1-345 



2 



1-245 



115 







Ratio 



Thickness 



Length 



575 

 •595 

 •615 

 •635 

 •655 



No. of 



Specimens 



Ratio 



Thickness 



No. of 

 Specimens 



Length 



4 



5 



18 



50 



91 



675 

 •695 

 •715 

 •735 

 •755 



127 



125 

 55 

 22 



3 



In drawing up Tables V and VI a class interval of 002 has 

 been adopted] the more extended distribution with the class 

 interval 001 is included in Table VII. 



1 f~ i T"io"fh I hif^K'n' ^^ 



(/) Correlation of the Ratios ". ', . and — ^ V"- 



w ; Width Length 



An 



extended correlation table for the two ratios we have been 

 discussing is given in Table VII. While the correlation is 

 very far from precise, there is nevertheless a notable tendency 

 for high values of one index to be associated with high values 

 of the other. The coefficient of correlation has the value 

 + 0*448, which is almost exactlv the arithmetic mean of the 

 two values returned for Sph, lacustre (q.v.). . The equations of 

 regression are : — 



(a) 



(b) 



™ = o'927 + 0466 £, 



with the standard error ± 0*0283 ; 

 ? =0-141 + 0431 ^, 



with the standard error ± 0*0273. 



Summary. 



Measurements of length, width, and thickness of a series of 

 five hundred Sphcerium corneum (Linne) from the Ashton and 

 Guide Bridge Canal near Dukinfield Railway Station, Lanes., 

 have shewn that : — 



1. The correlation of each pair of variables (length, width, 

 and thickness) is high; the coefficient of correlation varies from 

 4- 0*925 in the case of length and thickness to + 0*96 in the 

 case of length and width. 



