[Footnote 62: As this argument is a rather difficult one to follow, while its theoretical importance is very great, I add here the following briefer exposition of it, in a series of propositions; being, with a few verbal alterations, a copy of what I wrote on the subject about twenty years back. Some readers may find this easier to follow than the fuller discussion in the text:-- _Can Sterility of Hybrids have been Produced by Natural Selection?_ 1. Let there be a species which has varied into _two forms_ each adapted to certain existing conditions better than the parent form, which they soon supplant. 2. If these _two forms_, which are supposed to coexist in the same district, do not intercross, natural selection will accumulate all favourable variations till they become well suited to their conditions of life, and form two slightly differing species. 3. But if these _two forms_ freely intercross with each other, and produce hybrids, which are also quite fertile _inter se_, then the formation of the two distinct races or species will be retarded, or perhaps entirely prevented; for the offspring of the crossed unions will be _more vigorous_ owing to the cross, although _less adapted_ to their conditions of life than either of the pure breeds. 4. Now, let a partial sterility of the hybrids of some considerable proportion of these two forms arise; and, as this would probably be due to some special conditions of life, we may fairly suppose it to arise in some definite portion of the area occupied by the two forms. 5. The result will be that, in that area, the hybrids (although continually produced by first crosses almost as freely as before) will not themselves increase so rapidly as the two pure forms; and as the two pure forms are, by the terms of the problem, better suited to their several conditions of life than the hybrids, they will inevitably increase more rapidly, and will continually tend to supplant the hybrids altogether at every recurrent severe struggle for existence. 6. We may fairly suppose, also, that as soon as any sterility appears some disinclination to _cross unions_ will appear, and this will further tend to the diminution of the production of hybrids. 7. In the other part of the area, however, where hybridism occurs with perfect freedom, hybrids of various degrees may increase till they equal or even exceed in number the pure species--that is, the incipient species will be liable to be swamped by intercrossing.