518 FRETS, THE INDEX CEPHALICUS. 
but for the same length-, resp. breadtn-class the Scottish material 
is more dolichocephalic than the Dutch. 
From tab. 14—17 it appears that with increasing headiengiië 
also the headbreadth regularly increases. But with increasing head- 
length, the headbreadth increases relatively less than the head- 
length (tab. 14) 1). This is the reason that with increasing headlength 
the index falls: for dolichocephaly cooperate larger length and 
smaller breadth. 
In the same way we find for headbreadth that with increasing 
breadth, the headlength regularly increases. The index increases 
also. So with increasing headbreadth, the headlength increases 
relatively less than the headbreadth or with other words for brachy- 
cephaly larger breadth and smaller length cooperate (tab. 14). 
In the index two influences are active: lengthening and narrowing 
for dolichocephaly, and enlarging and shortening for brachycephaly. 
So in grouping material according to lengthclasses we do not find 
(tab. 14 last two columns) for all classes the same mean index 
(f. i: in my material 80.1, the general mean index), because the 
influence of narrowing displays itself. And with breadthclasses 
the influence of shortening causes the increase of the headindex 
with increasing headbreadth. The cause of this result may be seen 
in the principle of compensational growth. Length and breadth 
are both factors of the capacity of the head. So we find as a 
tendency, that an increasing length is accompanied by a relatively 
narrowing, an increasing breadth by a relatively shortening of 
the head (See also p. 522). 
TSCHEPOURKOWSKY (1905, p. 286) remarks that we do not find 
between the lengths and the breadths of skulls in the same race 
a relation which is in accordance with the principle of compen- - 
sational growth. I suppose that in the sense as is illustrated here, 
he will not deny, that it is valid (See also p. 522). 
Boas in his interesting paper on the cephalic index (1899) con- 
cludes, that, ,among skulls belonging to the same type, the 
correlation between length and breadth is not an expression of 
a biological relation between the two measurements, but an effect 
1) For tab. 14 the mean breadth, resp. length has been calculated from 
the mean index of each length-resp. breadthclass. Also for the general mean index. 

