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304 also among the inhabitants of Porto Rico reveal a rapid change in cephalic index. This suggests that there are some powerful environmental and physiological factors in the cause complex that produces head form. As compared with heredity, these are minor factors, but still strong enough to produce modifications of several numerical units in the calculated indices. Certain empirical observations led Boas to assume a change of five to six units possible in a few generations. Unfortunately, all these observations have been upon Europeans, but it seems a fair assumption that if the principle is found to hold for one, it will also hold for the other.

In the earlier parts of this chapter we found evidences of homogeneity, and though there is a perplexing range of variation in head form, the question still remains as to whether these fluctuations are not mere pulsations around a single norm. If such they prove to be, then we have homogeneity in head form as well as in other characters. This is a difficult problem, but some approach to its solution can be made by statistical methods.

First, on a priori grounds we have a right to expect that, if more than one type of cephalic index exists here in the New World, the observed indices for the successive groups of natives will tend to cluster around separate nodes, or norms, when we treat them as a series. To apply this test, we have collected all the observations that the literature of the subject brought to our notice and combined them into a single series. For precision, we have tabulated the indices for skulls and living subjects separately, and for further check upon the result we have tabulated absolute skull measurements for length and breadth of head (p. 305).

Close inspection of these distributions suggests that the two for the cephalic index will be found to approximate the normal, or symmetrical type, found in homogeneous groups. Also, the series for absolute length and breadth of head show fairly symmetrical distributions. From all this one may suspect that there is, after all, but one type of head form for the New World.