454 



POPULAR SCIENCE MONTHLY. 



understood, but at present it seems probable that we get symmetrical 

 polj^gons 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 gath- 

 ered 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 



100 120 130 160 180 200 220 24-0 £60 280 300 



FiG.8. Polygon OF FREtjuENCiES OF i-EXGTHS IN Fig. 9. Folyijon of fkequenhy of 



MILLIMETERS OF CEPHALIC BONES OF 343 RHINOCE- LENGTHS OF WING, IN HUNDREDTHS OF A 

 ROS BEETLES. FROM DATA OF BATESON. 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 -f- 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 origi- 

 nal, ancestral, condition. The cases in which the frequency curve is 

 bimodal frequently signify that two races are arising out of a former 



