by many must in reality occur--namely, differential or non-equivalent nuclear division--for otherwise it would be unintelligible how the ids of the new variety, if they once attain a majority in the tree, could give place in an individual branch to a majority of the ancestral ids. Only differential nuclear division, in the manner of a reducing division, can be the cause of this. Of course this implies only a dissimilar or differential distribution of the ids between the two daughter-nuclei, not a splitting up of the individual ids into non-equivalents. That in free Nature bud-variations left to themselves can ever become permanent varieties is probably an unlikely assumption, because of the inconstancy of their seeds which only breed true in rare cases; nor is it likely that such variations as the copper-beech, the weeping ash, and so on could hold their own in the struggle for existence with the older species; but there is certainly nothing to prevent our assuming that, in certain circumstances, saltatory variations, when they have a germinal origin, may become persistent varieties and may even lead to a splitting of the species. This may happen, for instance, when the variations remain outside the limits of good and bad, and thus are neither of advantage to the existence of the species nor a drawback thereto. In the next chapter we shall discuss the influence of isolation upon the formation of species, and it will be seen that in certain conditions even indifferent variations may be preserved, and that saltatory variations, as for instance in the evolution of species of land-snails or butterflies, may have materially contributed to bring this about. I should like to emphasize still more the part played by saltatory variations arising from germinal selection in the origin of secondary sexual characters. As soon as personal selection, whether sexual or ordinary, prefers as useful in any sense a saltatory variation, it is not only preserved and becomes a character of a variety, but it may increase, and we have to ask whether such sudden variations are frequently of a useful kind, especially when not individual characters alone, but whole combinations of them are implicated. If we may judge from the sports of the flowers and the leaves of plants, transformations useful to the species as a whole rarely occur suddenly, that is, they occur only in a few out of very numerous sports; they are much more frequently indifferent, although quite visible and often conspicuous variations.