Half Races and Half Curves. 29 



the further they deviate from the type of the species. 

 Fig. I gives a couple of examples at A and B. A gives 

 the number of petals of Caltlia palustris in a locality not 

 far from Hilversum; the flowers, where the species is 

 pure, are pentamerous. But in this place there occurred 

 flowers with 5-8 petals in the following proportions : 



Flowers with 5 6 7 8 Petals. 



Relative number 72% 21% 6% 1% 



Weigelia aniabilis, also, has normally pentamerous 

 flow^ers ; but it often varies in a minus direction. I found 

 in 1145 flowers on three bushes in our garden (Fig. IB): 



Number of slips in the corolla 3 4 5 



Number of flowers 61 196 888 



Half curves differ from the half of a normal curve 

 because the height of the mean, i. e., the number of nor- 

 mal cases, is too great. Such curves do not display the 

 variability of the character given by the highest ordinate, 

 but that of another character which is concealed in the 

 normal flowers.^ 



Half- or unilateral curves are widely distributed in 

 nature. Where they occur they point to the existence 

 of half races. Nevertheless middle races can, under cer- 

 tain circumstances, as we have already pointed out (p. 20) 

 exhibit half curves; just as, on the other hand, the half 



* Half curves are therefore compound curves. Their apex cor- 

 responds to the mean value of the normal character ; their flank is the 

 expression of the semi-latent character. If the normal character, in 

 the material at our disposal, does not vary it has no curve of its own, 

 which accounts for the absence of a flank on the other side. This 

 for example is the case for curves based on numbers, when the nor- 

 mal number is constant or practically constant as in the case of the 

 three-leaved clover or pentamerous flowers. If the normal character 

 is distinctly, though slightly, variable, as in the case of data based on 

 measurements, the half curve has a flank on the other side, but it is 

 very steep. I do not propose to pursue this point any further here, 

 since it is merely my object to show that half curves are only a 

 special case of asymmetrical curves. 



