boas] THE CEPHALIC INDEX 46 1
tend to be too small. This is definitely shown to be the case when the transversal diameter differs from the norm.
The variabilities of the arrays show that the reduction of vari- ability of capacity is greatest. This proves that the four linear measurements which we have treated largely determine the capacity. The variability of the length and height of skull is very slightly reduced. This shows that these measurements are largely influenced by causes which we have not included in our considerations. The same is true of the bizygomatic diameter of the face. When we compare the reduction in variability of the linear measurements as determined by c y and as determined by the quadruple correlation, we find the following :
Variability of Array.
Determined by c. Determined by Quadruple Correlation. 1 O.84 O.79
b 0.74 0.54
h 0.90 0.78
z 0.87 0.69
This comparison proves that breadth, height, and bizygomatic diameter have an insignificant effect upon length as compared with the effect of capacity. The great reduction of variability for breadth of head and bizygomatic diameter is due to the intimate correlation between these two values.
It follows from these considerations that while the cephalic index is a convenient practical expression of the form of the head, it does not express any important anatomic relation. On the other hand, the relation between capacity and head diameters is found to be of fundamental importance, and among these the relation between transversal diameter and capacity is most sig- nificant. Since in measurements on the living we are unable to measure capacity of the head, it is necessary to find a substitute. It would seem that circumferences are the most available means for judging cranial size. Therefore such circumferences should be included in all anthropometrical schedules designed to investigate racial characters.
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