298 



JOURNAL OF CONCHOLOGY, VOL. I4, NO. ID, APRIL, I915. 



I have not set out at length the range of variation within each 

 group for each of these particulars, but in general it is similar to the 

 variation in Banstead helvetica which has been already described 

 ijupra p. 232). The number of rows, for example, in the Marple 

 series varies from 36 to 44, from Tremadoc from 36 to 42, from 

 Bicknor from 37 to 43. The number of marginals is 9J to 12 from 

 Marple, 9 to 13 from Bicknor, 10 to 13 from Tremadoc. The 

 existence of this variability makes it necessary to enquire what degree 

 of difference in the average figures is significaiit of a real difference 

 between the various groups. The twenty specimens from Bicknor, 

 for example, differ in several particulars from the twenty specimens 

 from Marple, and it is conceivable that if other twenty examples from 

 Bicknor had been examined the results would have agreed with those of 

 the Marple group. Statistical enquiry has, however, discovered certain 

 principles which prevail in the varial)ility of live things, and knowing 

 the variability of these radular properties and taking into considera- 

 tion the number of specimens examined, we can state approximately 

 the difference which must be present between two averages before we 

 can regard it as indicative of a respectable distinction. The necessary 

 differences in the present case are roughly as follows : number of 

 rows 2"o, number of marginals o'8, length of radula o"2 mm., width 

 0*05 mm., area 0*2 sq. mm.j total teeth 90. Borderline cases, of 

 course, occur in which the presence of any real difference is doubtful. 

 The Marple helvetica accordingly have fewer rows than the Banstead 

 specimens, but not necessarily more than those from Tremadoc or 

 less than those from Bicknor ; the Tremadoc helvetica correspondingly 

 have fewer rows than those from Banstead and probably less than 

 those from Bicknor, but the average does not differ from the Marple 

 average by an amount large enough to be regarded as significant. 



Table III. 



Locality. 



Banstead compared with Bicknor 

 ,, ,, Tremadoc 



,, ,, Marple 



Bicknor compared with Tremadoc 

 ,, ,, Marple 



,, ,, Banstead 



Tremadoc compared with Marple 

 ,, ,, Banstead 



,, ,, Bicknor 



Marple compared with Banstead 

 ,, ,, Bicknor 



,, ,, Tremadoc 



