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 Caltha 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 5678 Petals. 
Relative number 72% 21% 6% 1% 
Weigelia amabilis, also, has normally pentamerous 
flowers ; 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 345 
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. 1 
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 
1 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. 
