HEREDITY 521 



the number of individuals which belong to the series, and 2" the number of 

 unions which remain constant. The series therefore embraces, if the original 

 stocks differ in four characters, 3* = 81 classes, 4* = 256 individuals, and 

 2 4 = 16 constant forms ; or, which is the same, among each 256 offspring of 

 the hybrids (differing in four characters) there are 81 different combinations, 

 1 6 of which are constant. 1 



All constant combinations which in peas are possible by the combina- 

 tion of the said seven differentiating characters were actually obtained by 

 repeated crossing. Their number is given by 2 7 = 128. Thereby is simul- 

 taneously given the practical proof that the constant characters which appear 

 in the several varieties of a group of plants may be obtained in all the asso- 

 ciations which are possible, according to the (mathematical) laws of combina- 

 tions, by means of repeated artificial fertilization. 



All this has a distinct bearing upon the question of varieties, 

 and its general trend is that changes effected by crossing tend 

 not to remain constant ; that is, that a union of dissimilar char- 

 acters by this means is practically impossible. 



It will be noted that Mendel makes no prediction as to what 

 hybrids or crossed forms will look like, but only as to their 

 " essential constitution " and breeding powers. 



Gametic purity. This raises the whole question of gametic 

 purity as the most fundamental question involved in Mendel's 

 law. If BR, when bred with BR, in actual experience produces 

 not more BR's but rather B 2 + 2 BR -f R 2 , then it raises an 

 interesting point as to the real nature of the germs arising from 

 the crossed parents BR. 



If the characters B and R had made a real union, or blend, in 

 the germ, such a distribution among the offspring would be 

 impossible. The crossed or blended forms would themselves 

 breed true, that is to their own type. If they do not breed true, 

 then we conclude that the real cross, or blend, has not been 

 made, and that in some way the characters B and R must remain 

 distinct in the germinal matter of the mixed parent ; that is to 

 say, the distribution of the offspring of hybrid parents into two 

 classes, pure forms and hybrids, instead of one form all hybrids, 

 is possible only upon the assumption that the two characters 

 remain distinct in the parents and in the germ cells thrown off 

 by them, so that the elements are still capable of uniting under 



1 The student may test this formula by making the complete expansion. 

 See Bateson, Mendel's Principles of Heredity, p. 64. 



