Page:American Anthropologist NS vol. 1.djvu/519

 4^0 AMERICAN ANTHROPOLOGIST [n. s., i. 1899

that the development of the frontal sinuses and of the occipital protuberances does not depend upon the form of the inner cavity of the skull, but upon the general development of the skeleton. Since this is partly expressed by stature, we might expect that this influence would partly be eliminated by the introduction of stature in the series of correlations. Unfortunately this element cannot be introduced on account of lack of data. Furthermore, the errors of the values of multiple correlations are so great that it is not advisable to carry on the investigation of a series of no more than 57 skulls beyond quadruple correlations which may be considered approximately correct in their first decimal.

It is of great interest to note that when capacity is introduced in our consideration a compensatory growth is found to exist between breadth of head on the one hand, and height and length of head on the other. We find, therefore, as a result of our investigation, that the law of compensation which Virchow formulated after an analysis of the forms of skulls with pre- mature synostosis of sutures, holds good also in normal skulls. Among skulls belonging to the same type a breadth above the average is compensated by a height and a length below the average. The correlation between length and breadth is not an expression of a biological relation between the two measurements, but an effect of the changes which both undergo when the capacity of the skull increases or decreases. The cephalic index, therefore, is not the expression of a law of direct relation between length and breadth of the skull. The proportion between the diameters of the skull and its capacity, on the other hand, expresses an in- timate biological relation between these measurements. It appears that the diameters of the head must be considered as due to the tendency of the inner cavity of the skull, or more prob- ably of the brain, to assume a certain size and form in a given type of man, this form being expressed by the proportion of the diameters of the brain and its size. If one of the diameters dif- fers from the norm in being excessively large, the others will

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