MICHIGAN ACADEMY OF SCIENCE. G3 



used both adult and yomiji- shells. The genus 7o may not vary in this 

 manner, but he makes no mention as to whether he determined this 

 point. If fact, it seems to me that some of the remarkable variability 

 curves obtained by him may be due to such a cause as the preponder- 

 ance of specimens of certain ages. 



EXPLANATION OF THE FIGURES. 



Figure 1. Variation in the Mean Ratios of each Length. 



L. Length of the shells in each vertical column in mm. 



N. Number of shells of each length, i. e., in each vertical column. 



M. Mean ratio (1/av) of shells of each length. 



The numbers along the left hand side of the plate ai'e the ratios 

 represented by each horizontal line. 



The numbers scattered throughout the plate are the frequencies of the 

 square in which they occur, i. e., the figure 1 in the lower left hand 

 corner indicates that there was one shell, 13 mm. long, with a ratio be- 

 tween 2.1.5 and 2.20. 



The zigzag line represents the means, plotted by ''the method of rec- 

 tangles,"^ while the continuous curve rejn'esents the probable variatioii 

 of the ratios. 



Figure 2. Variation of the Shells of Single Lengths. 



1. Shells 22 mm. long (points represented by oj. 



2. Shells 23 mm. long (points represented by x). 



These curves are plotted by the "method of loaded ordinates."'"' 

 The numbers at each point represent the frequency of each group. 

 The numbers along the top of the plate represent the ratios of each 

 group. 



Ann Arbor, Mich., April, 1010. 



^C. B. Davenport, Statistical Metliods with special reference to Biological Variation, 

 New York, 1899, p. 13. 

 2Ibid., p. 12. 



