understood, but at present it seems probable that we get symmetrical polygons when the organ measured is not undergoing evolution and, on the other hand, that unsymmetrical polygons indicate evolutionary progress. Also the direction of skewness is probably determined by the direction of evolution. At present, however, we can only say that in many cases the skew polygon tails off (or is skew) in the direction from which the race is evolving. This conclusion, which I believe to be new, is based upon certain results of experiments as well as upon data gathered from material which had developed under natural conditions. Of this material the most important for our purpose is that in which two polygons have apparently arisen by a splitting off from the original polygon of the two extremes which now form two distinct and widely separated types. The first case (Fig. 7) is derived from the common
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| Fig. 8. Polygon of frequencies of lengths in millimeters of cephalic bones of 343 rhinoceros beetles. From data of Bateson. | Fig. 9. Polygon of frequency of lengths of wing, in hundredths of a millimeter, for a lot of chinch bugs. | |
white daisy. In the figure the full-line polygon gives the frequency distribution of the ray-flowers in a collection of wild daisies. This polygon has a skewness of 1.18. The left-hand, dot-and-dash, polygon gives the ray frequences in the descendants of 12-or 13-rayed wild plants. The positive skewness is increased as a result of this selection to 1.92. The right-hand polygon gives the ray frequencies in the descendants of the 21-rayed plants, a single highly aberrant case of 32 rays being omitted. The skewness is —0.13. In this case we have experimental evidence that curves are skew towards the original, ancestral, condition. The cases in which the frequency curve is bimodal frequently signify that two races are arising out of a former
