1904.] serve to Test various Theories of Inheritance. 263 



theory was developed with special reference to certain characters in 

 man and hound, which were said to be alternative, i.e., the offspring, 

 if the parental types were different, took after one or other parent. 

 Quite recently Dr. Franz Boas* has published a very suggestive paper 

 on ''Heredity in Head Form." He propounds a theory that the 

 cephalic index in man is a case of alternative inheritance, and that 

 the offspring take after one or other parent. His theory is less general 

 than my theory of 1899, because he excludes from consideration the 

 reversion to grandparents or higher ancestry. It is more general 

 than mine, in that he assumes imperfect and not perfect correlation 

 between the groups of offspring and the individual parents whom they 

 respectively follow. This I consider a distinct gain. But the neglect 

 of ancestry, other than the immediate parents, renders the application 

 of his theory to so-called Mendelian phenomena absolutely impossible. 

 Thus, when a white mouse is crossed with a grey mouse the hybrid 

 generation can hardly be considered as made up of two groups taking 

 respectively after white and grey parents. In the following, or 

 segregating generation, it is possible to consider the groups as a result 

 of reversion to grandparental or higher ancestral types ; it is not 

 possible to deal with them on Dr. Boas's more limited theory. Hence, 

 I think he errs in terming his theory a generalised form of Mendel's 

 Law. It is a theory of alternative inheritance, and no such theory 

 which stops at resemblance to the paternal and maternal types can 

 describe the fundamental phenemenon of segregation in the second 

 generation. We must deal with reversion to higher ancestors, whether 

 such reversion be physiologically brought about by the purity of the 

 gamete or by any other process. 



A general theory of alternative inheritance may cover Mendelian 

 phenomena ; a theory of the individual dominance of either parent in 

 one or another group of offspring, a theory of what I have defined as 

 intermittent unit prepotency, cannot do so.f Still, Dr. Boas considers 

 that he has evidence for his theory in the inheritance of cephalic 

 index in man, and it seems to me that his paper indicates the manner 

 in which it may be possible to still further generalise my results of 

 1899. It is clear, however, that we badly need some criterion to 

 distinguish between these competing theories in the case of measure- 

 ments of the inheritance of any given character. Since none of the 

 three theories referred to is essentially based on the determination of 

 the type of the offspring from the parental types,! we are thrown back 



* ' The American Anthropologist' (JST.S.), vol. 5, pp. 530 — 538. 

 t ' Biometrika,' vol. 2, p. 389. 



X Dr. Boas, I think, has not fully understood my theory of the midparent. He 

 repeatedly speaks of the mid parental value of a character and of the offspring 

 clustering round this value on the theory of " G-alton and Pearson." There is abso- 

 lutely no antagonism between my theory and the stature of Americo-European 

 half-bloods exceeding both parental types. My midparent is based solely on 



U 2 



