No. 2.] SNAILS OF THE GENUS 10— ADAMS. 27 



QUANTITATIVE VARIATION OF 10. 



1. VARIATION IN SHELL DIAMETER. 



The quantitative study of variation is a subject which has received very little attention 

 from the students of fresh-water moUusca, and even quaUtative studies of variation in these 

 animals have rarely been considered from a geographic and environmental point of view. The 

 character of the variation in lo is of such a nature that some quantitative method seemed 

 essential for comparative studies. It was found diflGlcult to secure adequate series for this 

 purpose, not only on account of the large number of individuals needed, but also on account of 

 the difficulty of securing perfect specimens. On account of the thin edge of the peristome it is 

 quite Hable to injury, especially during shipment. In several locaUties dead weathered shells 

 from the sites of Indian camps had to be utilized, and such shells are very frequently injured. 

 Often a small number of individuals is found toward the Umit of range, and the smallness of 

 such series tends to introduce errors in quantitative studies. Perhaps the greatest source of 

 error is due to the fact that it is practically impossible to sort the shells into homogeneous series, 

 on account of the imperfection of the specimens, their graduated age, the intergradations from 

 one extreme form into another, and to irregularities of development. 



The dimensions of the shell were measured upon the last whorl. The diameter of the shell 

 was determined by spreading the caliper from near the upper angle of the aperture to the oppo- 

 site side of the shell. The length of the aperture was measured from the upper angle to the 

 end of the canal. All measurements were made in millimeters, and tenths were estimated. 



The entire series of shells will be discussed by groups and rivers in the following order: 

 Powell, Clinch, Holston, NoHchucky, French Broad, and Tennessee; and in general from the 

 headwaters progressively downstream. It should be borne in mind that we are dealing with 

 averages, modes or the prevailing class of the same dimension, or other maxima, and for brevity 

 this is assumed in the discussion. 



a. Powell River. 



Group 1 . This is composed of a very large series from the headwaters and contains numer- 

 ous young, and small-sized shells, which are largely smooth or with low spines, plate 28. 



By reference to the platted curve, plate 6, group No. 1, it is seen that the mode occurs at 

 15.5 mm. A diameter of 15.5 mm. may be taken to indicate the normal size of adult shells. 

 The numerous young clearly explain the skewness of the lower side of the curve, and its uniform 

 lower slope is an expression due in part to the completeness in the series from young to adults. 



Group 2. These shells are from about 10 miles farther downstream than the preceding 

 group. Young shells are not abundant among this series, plate 29. 



The curve, plate 6, No. 2, shows by its narrowness and single mode at 17.5 mm. that the 

 shells have a greater average diameter or are larger by 2 mm. than in the preceding group. 

 The skewness on the lower left side is in harmony with that of the preceding group. 



Group 3. This series is from about 25 to 30 miles below the preceding group. It is a series 

 of fairly mature shells, plate 30. 



The curve, plate 6, No. 3, shows a large proportion of relatively large shells with a maxima 

 at 17.5 and 18.5 mm., making them, as a group, the largest shells in the Powell Kiver. The 

 occurrence of these large shells, not the farthest downstream, but in the vicinity of Cumberland 

 Gap, is a point of interest. 



Group 4. Roughly estimated, this group was found about 30 miles below the preceding 

 and in the vicinity of Cumberland Gap, plate 31. 



As shown in plate 6, No. 4, the curve is broadly truncated with a broad apex ranging from 

 16.5 to 18.5 mm., and thus includes within its range the modes of groups 2 and 3. The skewness 

 on the lower left side is marked. This is quite a variable group, as is shown by the breadth of 

 the curve and the broad apex. 



Group 5. Roughly estimated, this series is from about 30 miles downstream from the 

 preceding group and about 100 miles from group 1. They are from the region of the lower 

 course of the PoweU, plates 32 and 33. 



