302 H. S. WILLIAMS PERSISTENCE OF FLUCTUATIKG VARIATIONS 



were also reduced to the percentage ratio of width to length to obtain 

 the index ratio E^. 



The index E^ was obtained by comparing the length of the muscular 

 scar with the length of the shell ; this ratio reduced to percentage was 

 ratio index E^. 



Eeasons for Selection of Ehipidomella for Study 



A word of explanation may be here offered as to the reasons for select- 

 ing the genus Ehipidomella and the particular dimensions for measure- 

 ment. Eliipidomella was chosen because it offered a number of distinct 

 morphologic characters which at a glance could be seen to fluctuate, as 

 well as others which seemed to be repeated with great precision and were 

 alike for all the specimens. The specimens were also well preserved or 

 else left clear impressions when the shell was dissolved from the rock. 



There was no other genus represented in these rocks so closely related 

 to Ehipidomella as to furnish any doubt as to the proper reference of the 

 specimens to the genus. Schizophoria, in young specimens, might pos- 

 sibly be confused with young specimens of Ehipidomella if only the 

 exterior were in evidence ; but no case arose in which the generic relations 

 were not evident. Also Ehipidomella is fairly well represented in num- 

 ber of specimens for the majority of the faunules showing the recurrent 

 Tropidoleptus fauna. 



The particular characters and dimensions chosen for measurement were 

 selected because of their fitness to furnish accurate measurements and 

 because they well represent the general and particular fluctuating char- 

 acters of the shells. 



Form of Shell, Eatio Index E^ 



It was observed that the various described species of the genus differ 

 most conspicuously in the shape of the shell. While this shape is made 

 up of a large number of details, differences in any one of them appear 

 to affect the proportion between width and length, and for this reason 

 these dimensions were chosen for measurement. Sy taking these two 

 diameters and reducing them to a percentage scale, a ratio index was 

 obtained which expresses by a single number the particular form fluctua- 

 tion of each specimen on a common scale, whatever the size of the shell. 

 This ratio index E^ furnishes, therefore, not only a mathematical ex- 

 pression for the shape of an individual shell, but it is a means by which 



