198 



PROCEEDINGS OF THE ACADEMY OF 



[Feb., 



Specimens of P. a. allcni from Albert Lea, Minn., the most northern 

 point from which I have seen the variety, those from Winfield, Henry 

 eounty, in southeastern and Des IMoines in central Iowa, are yellow or 

 whitish, small, averaging 23 mm. in diameter; 70 per cent, of those seen 

 measuring from 22 to 24 mm., the extreme of size being 21 and 26 mm., 

 these extremes represented by very few specimens, I have below 

 plotted the curve obtained from measuring the diameters of a lot of 

 50 specimens from Des IMoines, la., collected by Mr. T. Van Hyning. 

 The number of individuals is prol^ably sufficient to afford a perfectly 

 normal curve for the particular place these were obtained; but the 

 specimens from Albert Lea, Minn., and Winfield, la., though few in 

 number, are so similar that I would not expect much difference in 

 their curves.* 



Fig. 1, a-b, diameter variation curve of .50 shells of Polygyra albolabris aJleni 

 from Des Moines, la. ; c-d, 18 shells from Seligman, southwest- 

 ern Missouri. 



This contrasts strongly with the conditions in Avestern Arkansas. 



'' This curve is remarkably symmetrical, the average diameter of the lot. 

 obtained by dividing the sum of their diameters by the number of specimens, prac- 

 tically coinciding with the diameter of the greatest number of individuals, repre- 

 sented by the mode or highest point of the curve. Variation in size is about 

 equal toward both minimum and maximum. Of course it is understood that 

 exact measurements of the shells would efTace the angles of the "curve," espe- 

 cially'near the mode. I neglected fractions smaller than ^mm., as in organisms 

 of this size greater exactness would be mere pedantry. 



A widely different condition is seen in the other curve, in which the average 

 diameter is less than that of the greatest number of specimens. It must be 

 constantly borne in mind that tlie curve of the Seligman lot is probably widely 

 different from what a series of 50 or 100 specimens from that locality w^ould 

 produce; but still the absence of individuals between 22 and 25 mm. diameter, 

 together with the fact that other localities in western Arkansas show a large and 

 a small form, leads me to suspect that a sufficient series would form a bimodal 

 curve, the minor mode remote from the other, and probably near the 21 mm. 

 lien. 



