Page:Popular Science Monthly Volume 59.djvu/465

Rh ancestral intermediate condition; i. e., they correspond to the right and left-hand polygons of Fig. 7. Consequently we may expect them to he skew in opposite directions and so we find them to he. For example, Bateson has measured the horns on the heads of 343 rhinoceros beetles; the frequency curve is shown in Fig. 8. The left-hand polygon has a skewness of $$+$$ 0.48; the right-hand polygon of -0.03. One might infer that the right-hand form, the long-horned beetles, had diverged less from the ancestral condition than the short-horned beetles. Again, my pupil, Mr. Garber, has obtained a bimodal distribution polygon in the length of the chinch bug's wing (Fig. 9). The

short-winged form has a skewness of +.44; the long winged form of -.43. In this case also the ancestral form lies between the present modes. It is obvious that we may get cases in which two modes, representing conditions in different places, have moved, to different extents, in the same direction. Thus the index (breadth ÷ length) of the shell of Littorina, a marine snail, as measured by Bumpus, has at Newport a mode of 90; at Casco Bay of 93. The skewness is positive in both •places and greater (+.24) at the more southern point than at Casco Bay (+.13). This result indicates that the Littorina came from a more northern home, for which we have confirmatory historical evidence, and that these ancestral races were rounder, having an index