





OF PARENTS BY THOSE OF THE CHILDREN. (203) 11 
are divided into classes according to the increasing value of the average 
index of parents that we may see whether in families of parents with a 
low index, the proportion of the numbers of children in the two groups 
is different. The last line of the tables IIa and Illa gives the result of 
all the parents together. The indication of the children in both groups 
is more or less arbitrary. The number in parentheses of column II de- 
notes that this number might also have been taken. 
_ From table Ila it is obvious that there are totally too many hetero- 
zygotes by far; the proportion is 1 : 5(4.5). For the different subdi- 
visions this proportion differs but little. This again indicates the exist- 
ence of hereditary variations. In table IIIatherearealsotoomanyheter- 
ozygotes, however nearly twice fewer than in table IIa. Here, too, for 
the different subdivisions the numbers expressing the proportion do 
not diverge much. 
It is remarkable that table II, containing the families in which the 
indices of children upwards surpass those of parents contains so much 
more cases, 70 families with 293 children, than table III in which the 
indices of children downward surpass those of parents, 46 families with 
177 children. If in heredity the heterozygotes were intermediate, we 
should as often find an upward-surpassing as a downward. If however 
the high index is more or less dominant over the low one and if there is 
moreover a large variability in the heterozygotes, then from this the 
found result is to be explained. 
For explaining the tables II and III we have given two examples 
(p. 8). If both P-forms have the indices 80 and 75 and if they repre- 
sent the formulae DR x RR = DR + RR, then of children the 
heterozygotes will vary from 85—75, the homozygous dolichocephalic 
ones will vary little. So there will be an upward-surpassing by the indices 
of children. The contrary case, that, according to the formula DR x 
DD = DR + DD, the indices of parents are 80 x 85, will in the first 
place show a downward-surpassing. According to this formula with 
dominance of the high index, there may however also be an upward- 
surpassing. We supposed that the index 80 of one of the parents was a 
| heterozygote of the P-forms 75 and 85; it may, also be that the index 
80 is a heterozygote of one of the P-forms 80 and 90. As there is dom- 
inance of brachycephaly with a large variability of the heterozygotes, 
the extreme variation that the P-form has here, will rarely be found 
among the children; they will oftener vary in the regions of 85 and 90. 
