No. 422.] QUANTITATIVE STUDY OF VARIATION 12! 
Aster prenanthoides Muhl. — The frequency polygons for all 
the heads counted in this species are shown in Figs. 16, 17, 
and 18, All are multimodal, but by doubling the classes in 
Fig. 17, which represents the variation in the rays, the curve 
becomes monomodal with negative skewness, the mode being 
on 26-27 and the mean on 28.037993. 
Doubling the classes in Fig. 16 still leaves three modes in 
the frequency polygon of the bracts. These modes occur on 

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IG. 6. — Aster nove-anglie L. Bract curve of 199 heads. Classes doubled. Mean = 44.030150 = 
jui sue eae x aee 37, 43, 47, 575 € = 5.212961 + 176248. 
40-41, 44-45, and 48-49. Fig. 18 shows the curve of the disk 
florets to have two nearly equal modes on 48-49 and 52-5 3- 
The correlation of rays and bracts in the 658 or a 
counted (Fig. 19) is expressed by the coefficient 77 
+ .007820, and that of the rays and disk florets (Fig. 20) by 
770316 + .008042. 
