4. The next point to be noted is, that the cumulative divergence of type thus induced can take place only in as many different lines as there are different _cases_ of isolation. This is a point which Mr. Gulick has not expressly noticed; but it is one that ought to be clearly recognized. Seeing that isolation secures the breeding of similar forms by exclusion (immediate or eventual) of those which are dissimilar, and that only in as far as it does this can it be a factor in organic evolution, it follows that the resulting segregation, even though cumulative, can only lead to divergence of organic types in as many directions as there are cases of isolation. For any one group of intergenerants only _serial_ transformation is possible, even though the transformation be cumulative through successive generations in the single line of change. But there is always a probability that during the course of such _serial transformation in time_, some other case of isolation may supervene, so as to divide the previously isolated group of intergenerants into two or more further isolated groups. Then, of course, opportunity will be furnished for _divergent transformation in space_--and this in as many different lines as there are now different homogamous groups. That this must be so is further evident, if we reflect that the evolutionary power of isolation depends, not only on the _preventing_ of intercrossing between the isolated portion of a species and the rest of that species, but also upon the _permitting_ of intercrossing between all individuals of the isolated portion, whereby the peculiar average of qualities which they as a whole present may be allowed to assert itself in their progeny--or, if the isolation has been from the first discriminate, whereby the resulting homogamy may thus be allowed to assert itself. Hence any one case of either species of isolation, discriminate or indiscriminate, can only give rise to what Mr. Gulick has aptly called "monotypic evolution," or a chain-like series of types arising successively in time, as distinguished from what he has called "polytypic evolution," or an arborescent multiplication of types arising simultaneously in space.