boas] the cephalic index 455

is negative, R will be less than r. This will be the case when /j is larger than X t and /„ smaller than A n , or vice versa.

I think this effect of mixture is a sufficient explanation of the low value of the coefficient of correlation for Paris, where we find a very heterogeneous population embracing narrow- and long- headed subjects from northern France and very broad- and short- headed ones from southern France. The same explanation seems plausible for the Shuswap and the tribes of northern British Columbia. The high value for Eskimo skulls may be due to the fact that a number of female skulls were counted as male skulls. This would have the effect of raising the coefficient of correlation between the diameters of the head.

When the type is dis-homogeneous owing to mixed descent, the coefficient of correlation will depend upon the law of heredity. If the mixed race should range in a probability curve around a type intermediate between the parental types, we should expect to find the coefficient of correlation slightly influenced by mix- ture, if any. If the mixture should result in a tendency of rever- sion to either parental type, the effect would be similar to that observed in the case of mechanical mixture which was discussed before. Evidently in such cases the coefficient of correlation has no direct biological significance.

Ill

It is quite evident that both breadth and length of head are influenced by a great number of causes, some of which act upon both measurements in the same manner, while others may influence each in a peculiar way. Such causes may be investi- gated by determining their correlations with length and breadth of head separately. Thus, we may determine the correlation between capacity of skull, stature, dimensions of face, and the two diameters of the head. I have calculated a number of such correlations for adult males of a few Indian tribes with the following results :

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