re 
SUMMARY. 
The present paper is a Mendelistic study of the headindex of 3600 
persons of about 360 families, of parents and children, also some 
including grandparents, parents and children. The biometric study 
of this material has been published elsewhere (1920b, 1920c). 
The material has been grouped in several tables according to Men- 
delian interpretation. | 
The tables I—III show that there is segregation (tab. I), that there 
are hereditary variations for the headindex (Fig. 1—3), that the head- 
indices of parents may have a very different hereditary composition 
(fig. 1a—3a) and that there are many families, where the indices of 
children surpass those of parents upward (tab. II) or downward (tab. 
III). The number of families of tab. II being so much larger than of 
tab. III indicates, that the high index (brachycephaly) is more or less 
dominant over the low one (dolichocephaly). 
It appears that there is a large non-hereditary variability (1919, 
192010): 
The index of children surpassing that of parents may be interpreted 
by the polymery-theory (NILSSON-EHLE), when it regards the indices 
of a single child. Tab. IIa and IIIa contain families, where the indices 
of all or nearly all children surpass that of parents. It is difficult to in- 
terpret these cases by the possibility of chance from the polymery- 
theory. Therefore we are compelled to accept in such cases the 
prepotence of parents. 
This notion is not unknown in the litterature of heredity (CASTLE, 
DAVENPORT, GOLDSCHMIDT). Yet there is a tendency to interpret more 
and more the phenomena of selection by multiple factors; also in the 
_sense of residual heredity (CASTLE 1919, 1920), of major and minor fact- 
ors, or of Nebenspaltungen. Prepotence indeed is no mendelian notion. 
We distinguish between selection based on prepotence and selection 
based on the combination, joining together, of multiple factors in a 
homozygous form. 
There are in the material only Se families where the head form of 
