_AB_ showing both dominant characters. _Ab_ " dominant _A_ and recessive _b_. _aB_ " recessive _a_ and dominant _B_. _ab_ " both recessive characters _a_ and _b_. The numerical ratio in which these classes appeared were also regular and approached the ratio 9_AB_ : 3_Ab_ : 3_aB_ : 1_ab_. But on cultivating these plants and allowing them to fertilise themselves it was found that the members of the RATIOS 1 _ab_ class produce only _ab_’s. 3 {1 _aB_ class may produce either all _aB_’s, {2 _or_ both _aB_’s and _ab_’s. RATIOS 3 { 1 _Ab_ class may produce either all _Ab_’s, { 2 _or_ both _Ab_’s and _ab_’s. { 1 _AB_ class may produce either all _AB_’s, { 2 _or_ both _AB_’s and _Ab_’s, 9 { 2 _or_ both _AB_’s and _aB_’s, { 4 _or_ all four possible classes again, namely, { _AB_’s, _Ab_’s, _aB_’s, and _ab_’s, and the average number of members of each class will approach the ratio 1 : 3 : 3 : 9 as indicated above. The details of these experiments and of others like them made with _three_ pairs of differentiating characters are all set out in Mendel’s memoir. Professor de Vries has worked at the same problem in some dozen species belonging to several genera, using pairs of varieties characterised by a great number of characters: for instance, colour of flowers, stems, or fruits, hairiness, length of style, and so forth. He states that in all these cases Mendel’s principles are followed. The numbers with which Mendel worked, though large, were not large enough to give really smooth results[10]; but with a few rather marked exceptions the observations are remarkably consistent, and the approximation to the numbers demanded by the law is greatest in those cases where the largest numbers were used. When we consider, besides, that Tschermak and Correns announce definite confirmation in the case of _Pisum_, and de Vries adds the evidence of his long series of observations on other species and orders, there can be no doubt that Mendel’s law is a substantial reality; though whether some of the cases that depart most widely from it can be brought within the terms of the same principle or not, can only be decided by further experiments. [10] Professor Weldon (p. 232) takes great exception to this statement, which he considerately attributes to “some writers.” After examining the conclusions he obtained by algebraical study of Mendel’s figures I am disposed to think my statement not very far out.