Manchester Memoirs, Vol. lix. (191 5), No. 4. 5 



of just over 9, and that as a departure is made from this 

 mean in either direction, the numbers of individuals fall 

 off so regularly that a distribution curve is produced which 

 is remarkable for its high degree of symmetry. It is in fact 

 a very perfect, simple " continuous variation" curve and is 

 therefore to be accepted as proving that only one species 

 is embraced by the collection. The curve also indicates 

 that the species has been very constant, and has simply 

 varied about a 'mode' which shows no indication of hav- 

 ing moved, or of any tendency to move : in fact, whilst 

 there is remarkable variation in shell form and also in 

 other characters as will be noted later, yet these variations 

 were restricted within such limits that no vital departure 

 was made from the central type. It will be noted that in 

 the distribution curve shells which are long and narrow 

 are displaced to the left of the curve, and shells which are 

 short and broad to the right. 



Fig. 2 represents the distribution graph for -=. m a 



thousand individuals, and may be described in almost 

 similar terms to those applied to Fig. 1. We have a 



maximum of shells possessing, in this case, a mean yz 



ratio of about 1*65 and as a departure is made from the 

 mean in either direction there is a very regular falling off 

 in the numbers of individuals, producing as in the case of 

 Fig. 1., a remarkably symmetrical curve, indicating as 

 before, one species, which varied about a central type. In 

 this case shells which are long and thin are displaced to 

 the left of the curve, and shells which are short and thick, 

 to the right. 



The nature of the curves showing the distribution of 



"5 and yz indicates therefore that the distribution is quite 



normal, varies about a central type, and gives no indica- 



