230 PROCEEDINGS OF THE AMERICAN ACADEMY. 



For the possible combinations of two sets of gametes each G and W 

 are represented by their product GG-\- '2GW + WW, or simplified as 

 already explained, G+2G(W) + W. 



The principle illustrated by these examples is, as pointed out by 

 Bateson (:02), the most fundamental and far-reaching of the Mendelian 

 ideas. It is known as the law of segregation, or " splitting" (de Vries, 

 :00) of the parental characters at gimete formation, or as the " principle 

 of gametic purity" (Bateson, :02). Dominance is purely a secondary 

 matter ; it may or may not occur along with segregation, though the 

 latter can be more easily demonstrated in cases where it is associated 

 with the former. The principle of gametic purity just stated rests upon 

 the assumption that gamete-formation is the reverse of fertilization. In 

 fertilization, gametes A and B unite to form a zygote AB; when this 

 zygote in turn forms gametes, they will be again A and B. From a 

 knowledge of the somatic form alone of pure As and Bs, one can make 

 no trustworthy prediction as to the form of AB. — Here is the funda- 

 mental error of the" law of ancestral heredity " as stated by Galton ('97) 

 or Pearson (:03). — ABmay have invariably the somatic form of A or of 

 B (cases of simple dominance, as of gray over white in mice) ; or it may 

 have sometimes the form of A, sometimes that of B (cases of alternative 

 dominance — see Tschermak (:02) — ) ; or, finally, the somatic form of 

 AB may be different from both that of A and that of B (cases like that 

 of the gray hybrid formed by the cross of black-white with white mice). 

 But, no matter what the somatic form of AB is, we may with confidence 

 predict that its gametes will be essentially pure As and pure Bs, and the 

 two will be produced in proportions approximately equal. This is the 

 Mendelian expectation in all cases of alternative inheritance. Whether 

 it applies to other cases also, and if so to what extent, is not yet known. 

 For the present we may confine our attention to the case which afforded 

 a basis for the " law of ancestral heredity," namely alternative color- 

 inheritance among mammals. 



In Table II are given the Mendelian predictions for the inheritance 

 of complete albinism in the various generations and matings of von 

 Guaita's mice. These predictions are based upon the fact repeatedly 

 observed that complete albinism behaves as a recessive character in 

 heredity with reference to a pigmented character of any sort (gray, 

 black, or spotted). Predictions are not made for the other color cate- 

 gories separately, because their relations to each other are not entirely 

 clear from von Guaita's experiments. It seems probable, however, that 

 they bear one toward another relations of alternative dominance. This 



