462 Variation and Correlation of the Human Skull 
It will be seen at once from these results that if an individual tends to brachy- 
cephaly he will also tend to hypsicephaly. Further, we ask, are the brachycephalic 
races hypsicephalic and the dolichocephalic races chamaecephalic ? Again we want 
our interracial coefficients of correlation to answer this problem satisfactorily. 
If we turn to the correlation between the indices and the lengths they do not 
involve, we find : 
(a) For both sexes in Naqadas brachycephaly is associated with hypsi- 
cranial characters. Among the French there is practically no association at all. 
(b) For both sexes of the Naqadas hypsicephaly is associated with platy- 
cranial characters. On the other hand, for both sexes in the French, hypsicephaly 
is united with stenocranial characters. 
(c) In both races platycephaly is associated with brachycranial characters — 
the association vanishing, however, for the Naqada males, and being more marked 
for the French. 
Lastly turning to the relations between the indices and the absolute lengths 
they involve, we conclude that 
(d) Dolichocephaly and chamaecephaly in both races are associated with 
macrocranial characters. 
(e) Brachycephaly is associated with platycranial characters in both races. 
(/") Hypsicephaly is associated in both races with hypsicranial characters. 
In (d), (e) and (/) the association is really produced entirely or almost entirely 
by the spurious correlation. 
Here, again, a whole range of racial problems are suggested which can only be 
dealt with by interracial correlation investigations. 
It should be noted that throughout the above statements we have used 
technical terms for brevity in an intraracial sense. 
By dolichocephalic, chamaecephalic and stenocephalic crania within the race 
we understand those of individuals having their B/L, HjL and BjH indices below 
the racial mean ; by brachycephalic, hypsicephalic, platycephalic crania, those of 
individuals having the corresponding indices above the mean. By brachycranial, 
stenocranial and chamaecranial characters we describe those of individuals with 
cranial length, breadth and height below the racial mean, and by macrocranial, 
platycranial and hypsicranial characters those of individuals with length, breadth 
and height above the racial mean. As soon as we can find interracial means — 
means of racial means — we shall be able to use these terms also in an interracial 
sense, which will be somewhat less arbitrary than that of the Frankfurter 
Verstandigung ; that concordat really fixes rough numbers to represent unknown 
interracial results. 
Here we must conclude for the present our discussion of the correlation of 
cranial characters. We see that except where one of the characters is capacity, 
