8 (200) SURPASSING UPWARD AND DOWNWARD OF THE INDICES 
From the curves of the figs 2 and 3 it is obvious, that, when the in- 
dices of parents are increasing, the utmost values of the indices of 
children are also increasing. 
ei 

N 
i 
Ne 
ZEN N 
ur Et 0 ED VAAT 
AA 
NZA Kef 
VMV EAU ET 
EEE HA V6 A ER WAN PN 
PPE AA 
[\ 
FRE TEEN 
RER 
iN 
N | \ 
Diagram of 45 families of tab. III. Where upper- and underline conflue 
there is but one child measured. 
The tables I—III must be taken together. Accepting for the explan- 
ation of the indices of children of the cases of table I that both parents 
are heterozygous (Aa), then the phenomenon ofthe upward-surpass- 
ing of the indices of parents through those of children may be 
explained by accepting that one of the parents is heterozygous and 
the otheı homozygous for the low index (aa x Aa = aa + Aa), 
and downward by accepting that one of the parents is homozygous for 
the high index (AA x Aa = AA + Aa). For the cases of table II the 
low index (aa) forms the fixed point, whilst the variability of the heter- 
ozygotes causes the possibility of the upward surpassing of the child- 
ren s indices; for table III the fixed point is formed through the high 
index (AA) and the variability of the heterozygotes can explain the 
surpassing of the indices in downward direction 1). According to these 
formulae the indices of the parents will often differ rather much; not 
always, because there is a large non-hereditary variability for the het- 
erozygotes with possibly some dominance of the high index. 
This result can be explained by an example. Suppose the parents 


*) We previously leave aside wether one factor or many ones, working in the same 
sense, define the characteristic (p. 15 and Frets, 1919, p. 356 and 1920a, p. 1—6). 
