For the Mendelian principle of heredity asserts a proposition absolutely at variance with all the laws of ancestral heredity, however formulated. In those cases to which it applies strictly, this principle declares that the cross-breeding of parents _need_ not diminish the purity of their germ-cells or consequently the purity of their offspring. When in such cases individuals bearing opposite characters, _A_ and _B_, are crossed, the germ-cells of the resulting cross-bred, _AB_, are each to be bearers either of character A or of character _B_, not both. Consequently when the cross-breds breed either together or with the pure forms, individuals will result of the forms _AA_, _AB_, _BA_, _BB_[61]. Of these the forms _AA_ and _BB_, formed by the union of similar germs, are stated to be as pure as if they had had no cross in their pedigree, and henceforth their offspring will be no more likely to depart from the _A_ type or the _B_ type respectively, than those of any other originally pure specimens of these types. [61] On an average of cases, in equal numbers, as Mendel found. Consequently in such examples it is _not_ the fact that each ancestor must be brought to account as the Galton-Pearson Law asserts, and we are clearly dealing with a physiological phenomenon not contemplated by that Law at all. Every case therefore which obeys the Mendelian principle is in direct contradiction to the proposition to which Professor Weldon’s school is committed, and it is natural that he should be disposed to consider the Mendelian principle as applying especially to “alternative” inheritance, while the law of Galton and Pearson is to include the phenomenon of blended inheritance. The latter, he tells us, is “the most usual case,” a view which, if supported by evidence, might not be without value. It is difficult to blame those who on first acquaintance concluded Mendel’s principle can have no strict application save to alternative inheritance. Whatever blame there is in this I share with Professor Weldon and those whom he follows. Mendel’s own cases were almost all alternative; also the fact of dominance is very dazzling at first. But that was two years ago, and when one begins to see clearly again, it does not look so certain that the real essence of Mendel’s discovery, the purity of germ-cells in respect of certain characters, may not apply also to some phenomena of blended inheritance. The analysis of this possibility would take us to too great length, but I commend to those who are more familiar with statistical method, the consideration of this question: whether dominance being absent, indefinite, or suppressed, the phenomena of heritages completely blended in the zygote, may not be produced by gametes presenting Mendelian purity of characters. A brief discussion of this possibility is given in the Introduction, p. 31.