

FRETS, THE INDEX CEPHALICUS. 521 
more brachycephalic than the male and it appears that this diffe- 
. rence is larger than the difference for the same lengthclasses. 
(tab. 18). So the head of the female is relatively shorter than that 
of the male and the head of the male is relatively wider than that 
of the female; the first difference is larger than the second. From 
this, it proceeds that the index of the female is, for my material, 
more brachycephalic than for the male. We see the same for the 
Scottish material of TocHER (p. 514-517). 
Our result is that as to sex the head of the female is relatively 
narrower and shorter than the male — the first difference being 
smaller than the second —in my Dutch and in TocHER’s Scottish 
material; therefore the head of the female is a little more brachy- 
cephalic than that of the male. And as to race the head is relativily 
narrower and longer in TocHER’s Scottish than in my Dutch 
material; so the index is much more dolichocephalic in the Scottish 
than in the Dutch material. 
We have found that there are several influences that determine 
the index. We may introduce a normai index, but we shall often 
want to know (f.i. with inquiries of heredity) the different analytical 
moments of it (influence of sex, of headlength, of headbreadth, of 
Stature, of age). It remains to be investigated if these relations occur 
in the same way in other races. 
The correlation of headlength and headbreadth; of headlength, 
resp. headbreadth and headindex (tab. 19) I have calculated by 
means of the formel of Bravais according to the indications of 
JOHANNSEN (1913, p. 309). These results affirm the results of our 
calculations (p.511) about the relation of headlength, resp. head- 
breadth and fndex: we find that the correlation of headlength and 
index is negative and of headbreadth and index positive. And the 
positive correlation of headbreadth and index is somewhat larger 
than the negative one of headlength and index. In my material we also 
observe that the females are somewhat more highly correlated 
than the males. Similar results were got by MACDONELL (1904, p. 
239 and tab. 20 p. 524) 
