206 THE EVOLUTION THEOKY 



a blended inheritance ; in another the child takes after the father oi" 

 after the mother ; in a third, and this probably occurs most frequently, 

 the child resemljles the father in some characters and the mother in 

 others. 



But how then does Galton's curv^e of frequency of variations 

 come about ? Why does the mean of any character occur by far the 

 most frequently, and why does the frequency of a variation diminish 

 regularly in proportion to its approximation to either extreme ? 

 To this it is answered : Because the process of mingling through 

 amphigony goes on through numerous generations, and thus an 

 elimination of chance, and the establishment of an average, must 

 be brought about. 



But this does not quite suffice to explain matters, for experience 

 shows that asynnnetrical frequency-curves of variations also occur, 

 even in species with sexual reproduction. As De Vries has recently 

 shown, there are also ' half-Galton curves,' that is, curves which sud- 

 denly break off at their highest point. We must conclude from this 

 that the frequency of the different variations depends not only on their 

 degree, but also on the greater or less facility with which they 

 arise from the constitution of the species. 



This consideration can be readily elucidated with the help of 

 Amnion's exposition, and especially of his graphic representation of the 

 ' playground of variations.' If we think of the indifferent variations 

 occurring in any cliaracter of a species as arranged in a series ascend- 

 ing from the smallest to the largest, this line may be regarded as the 

 abscissal-axis, and from it ordinates may be drawn which express the 

 frequency of the variation in (juestion by the differences in their 

 length. If the tips of these ordinates be united, w^e have the curve 

 of frequency (Fig. 120, ^), which according to Galton ought to be 

 .symmetrical, and in most cases really is so. Amnion calls the space 

 between the smallest and the lai'gest variations the ' variation-play- 

 ground,' that is, the playground within which all variations are equally 

 advantageous to the species. This is not co-extensive with the variation- 

 area, for there may be more marked deviations below the beginning 

 or above the upper end of the variation-playground, but these, being- 

 disadvantageous, fall under the shears of personal selection. The 

 variation-playground may also be called the area of indulgence of 

 variation, because tlie variations falling within it are spared from the 

 eliminating activity of selection, or the variation-area of survivors, 

 because on an average only those survive whose variations do not 

 overstep tlie limits of this area. 



Tins implies that variations below U (the lower limit of the 



