1904.] serve to Test various Theories of Inheritance. 279 



tion which has been isolated and intra-bred for some generations 1 

 If not, it would very possibly exhibit " segregation " in the second 

 generation ; thus if there were any Aryan or other non-Jewish 

 blood in the immediate ancestry, this might be induced by a segrega- 

 tion tendency increasing the variability in the offspring of such pairs. 

 Further apparent segregation would arise in the case of any unfaith- 

 fulness, and this might be correlated with physical dissimilarity. 

 Shortly, we want a good deal further information as to the nature of 

 these particular American East European Jews. But quite apart 

 from all this, the forty-eight families had only 158 children or an 

 average of less than 3 3. Now, some families must have had four 

 and five children and Dr. Boas gives the standard deviation of all the 

 separate families, or he must have found a standard deviation here 

 and there on the basis of at least two and possibly even fewer 

 individuals ! * I do not think standard deviations so found can be 

 of any value at all. Further, and most important, he has not determined 

 the standard deviation about the mean of the individual family, which 

 he ought to have done, but about the theoretical average mean of all 

 families having a father and mother of the given characters. Now the 

 individual family has all its ancestors in common beside the father and 

 mother and hence its mean is not in our previous notation : 



m + E/c — x + E^— y, 



the value used by Dr. Boas, but the much longer expression given by 

 the general formula for " Ancestral Heredity." f It is only when we 

 take the average results for all families of parents x and ?/, that the 

 other ancestral terms will disappear, and we reach the above result 

 His only method of reaching an approximation to the mean of an 

 individual family, would be to actually find it from the family itself, 

 and then investigate the standard deviation from this mean. \ This he 

 has not done, and I think we must doubt, even if he had done it, the 

 validity of means and variabilities based upon two to four individuals. 

 Still his memoir is very suggestive, and it seems to me that the investi- 

 gation of a large series of head measurements in parents, and, if 

 possible, adult children, say, in 1000 families forming a homogeneous 

 population, would be of great value. 



* I have shown in ' Bionietrika,' vol. 1, p. 399, that the values of the standard 

 deviation found from two individuals will, on the average, only be about 0'563 of 

 its true value. Similar large reductions occur if it be found from three to four 

 individuals, and so on. This is quite apart from the large probable errors intro- 

 duced by paucity of numbers. 



f ' Eoy. Soc. Proc.,' vol. 62, p. 394. 



X There would, I take it, certainly be correlation between x—y and the omitted 

 ancestral terms in the family mean. 



x 2 



