suddenly been increased by the addition of one more than normal, and the new vertebra is perfectly formed from the first. In cases of this sort we can easily understand that the inheritance must be either of one kind or the other, since intermediate conditions are impossible, when it comes to the question of one or not one; but if one individual had one and another six vertebræ, then it would be theoretically possible for the hybrid to have three. This brings us to a question that should have been spoken of before in regard to the inheritance of discontinuous variation. It sometimes occurs that a variation, which appears in other respects to be discontinuous, is inherited in a blended form. Thus the two kinds of variation may not always be so sharply separated as one might be led to believe. There may be two different kinds of discontinuous variation in respect to inheritance, or there may be variations that are only to a greater or a less extent inherited discontinuously; and it seems not improbable that both kinds occur. This diversion may not appear to have brought us any nearer to the solution of the difficulty that Darwin’s statement has emphasized, except in so far as it may show that the lines are not so sharply drawn as may have seemed to be the case. The solution of the difficulty is, I believe, as follows:— _The discontinuity referred to by Darwin relates to cases in which only a single step (or mutation) has been taken, and it is a question of inheritance of one or not one. If, however, six successive steps should be taken in the same direction, then when such a form is crossed with the original form, the hybrid may inherit only three of the steps and stand exactly midway between the parent forms; or it may inherit four, or five, or three, or two steps and stand correspondingly nearer to the one_ _or to the other parent. Thus while it may not be possible to halve a single step (hence one-sided inheritance), yet when more than one step has been taken the inheritance may be divided. There is every evidence that most of the Linnæan (wild) species that Darwin refers to have diverged from the parent form, and from each other, by a number of successive steps; hence on crossing, the hybrid often stands somewhere between the two parent forms. On this basis not only can we meet Darwin’s objection, but the point of view gives an interesting insight into the problem of inheritance and the formation of species._ The whole question of inheritance has assumed a new aspect; first on account of the work of De Vries in regard to the appearance of discontinuous variation in plants; and secondly, on account of the remarkable discoveries of Gregor Mendel as to the laws of inheritance of discontinuous variations. Mendel’s work, although done in 1865, was long neglected, and its importance has only been appreciated in the last few years. We shall take up Mendel’s work first, and then that of De Vries. Mendel’s Law[24]