Manchester Memoirs, Vol. Ivii. (191 3), No. 10. 17 



height. The significance of this fact must be considered 

 in relation with the geological history of the shells. 



It will probably have seemed to many that the occur- 

 rence of the whole range of shell-forms here described in 

 a single mass of material is incompatible with Hyatt's 

 assertion that the same series of forms at Steinheim con- 

 stitutes a stratigraphical sequence, in which the discoid 

 types occur at the lowest and the high-spired forms at 

 I the highest horizons. Nevertheless a perusal of his paper 

 and a consideration of the manner in which his material 

 was collected and investigated must result in the convic- 

 tion that his assertion is substantially correct. His state- 

 ment is not, however, that each type occurs at one horizon 

 only, but merely that the discoid forms alone are found at 

 the lowest horizons, while the turreted types appear later 

 and finally predominate. Now this is just what our study of 

 the present material has led us to anticipate, viz., that the 

 species was originally discoid, a turreted tendency having 

 subsequently appeared and gradually increased in degree, 

 so that the most recent form is one with a fairly high 

 spire. Could this form be isolated, it would doubtless 

 show a comparatively small range of perfectly sym- 

 metrical variation. Among the actual shells, however, 

 each of the preceding types still finds expression, but the 

 frequency of the occurrence of each type would seem to 

 be inversely proportional to the remoteness of the type in 

 the ancestry of the existing forms, presumably according 

 to an exponential law. This hypothesis at least appears 

 to give the simplest and most satisfactory explanation of 

 the facts concerning the distribution of the existing 

 varieties. 



The alternative is to assume that the maximum 

 frequency as determined by inheritance should occur 

 among shells of truly mean height, and that the observed 



