38 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [vol.xii. 



them, the spine index would decrease downstream, but as there is an increasing index down- 

 stream it shows that the height of the spines increases more rapidly than the distance be- 

 tween the spines. This law, in general terms, is true for all of the upper Tennessee system. 



d. Summary of the Laws of Quantitative Variation. 



The Powell River shells are relatively narrow in the headwaters and become progressively 

 wider in groups 2, 3, and 4, and near the mouth again return to the narrow modal condition. 

 The shells of the headwater groups 1, 2, and 3 have a high degree of globosity, with modes at 

 75 or 77 per cent. Groups 4 and 5 show a progressive decline. Therefore globosity of the shell 

 progressively declines downstream. Spinosity shows a general progressive downstream change. 

 The headwater shells are relatively smooth but the change in spine height is not uniformly 

 progressive because group 4, instead of group 3, as might be anticipated, is the transitional 

 series from the relatively smooth to the strongly spinbse kinds. The distance between the 

 spines is less in the headwaters (groups 2 and 4) than downstream (as in groups 3 and 5). This 

 is a progressive change toward increase in distance between them, except in the case of group 3, 

 which was also exceptional with regard to spine height. Spine index shows a rather uniform 

 progressive change from a low index in the headwaters to a higher index downstream. 



In general, then, there is a progressive change from the headwaters downstream, as follows : 

 From a greater diameter of the shell to less; from a high degree of globosity to one of a less degree; 

 from a spineless to relatively long spines; from a narrow space between the spines to a wider 

 space; and from a relatively low spine index to one of a higher degree. The change from the 

 smooth to the spmose shell is relatively abrupt, as shown by the modes, but there is a perfect 

 series of individual intergradations. 



The Clinch shells are relatively wide in the headwaters and soon become relatively narrow 

 and remarkably stable in all the downstream series. Group 8 is exceptional and is even narrower 

 than the narrow headwater and downstream (groups 1 and 5) series from the Powell. The 

 degree of globosity of the shell shows a progressive decline from the headwaters downstream. 

 This change is nearly uniform, except that groups 8 and 10 have the same modal condition. 

 The height of spines shows the same degree of progressive increase from smooth shells to 

 strongly spinose ones, group 10 also again lagging in its modal condition. The distance between 

 spines shows a rather uniform progressive change toward a downstream increase in the dis- 

 tance between spines, and gi'oups 7 and 8 are the transitional steps between the extremes. 

 The spine index shows a progressive change from a lower to a higher index, except the lagging 

 of group 10. 



In general, then, thei'e is a progressive change from the headwaters downstream of the 

 same general character as in the Powell. In the Clinch, group 10 is a downstream group with 

 the characters usually found farther upstream. 



As in the Powell, the transition from the smooth to the spinose shells is relatively abrupt, as 

 shown by the modes, but all degrees of individual intergradations are found between these two 

 kinds. 



The Holston sheUs do not change so regularly downstream as those of the Powell and 

 Clinch, and consequently it is much more difficult to summarize their general relations. There 

 is a much greater diversity in the shells. This is clearly due to the distracting influence of the 

 South Fork of the Holston, as shown by group 14, and by the \mique occurrence of smooth 

 shells far from the headwaters, as Ln groups 15 and 16, from near Rogersville. In general, the 

 relations are about as foUows: The comparatively wide and globular shells from the head- 

 waters (group 12) are relatively smooth and change downstream to (group 13) a relatively 

 wide and globular shell, with low close set spines, a relatively higher spine index, and thus 

 grade into group 14, which has the greatest shell width for the Holston, a moderate (71 per 

 cent) degree of globosity of the shell, very long spines, very wide apart (the widest for the Hol- 

 ston and wider than those of the Powell and Clinch), and a moderate (17 per cent) spine index. 

 Continuing downstream group 15 shows a transitional stage to group 16 in width of the shell, 

 an increase in globosity of the shell (due to the reappearance of smooth shells), a reduction in 

 spine height and the presence of smooth shells, a reduction of the space between the spines, and 



