There remains now the question of fecundity. The causes which determine the increase or the decay of a population are so multifarious, and for the most part so foreign to ethnological influences, that we cannot without committing grave errors, estimate the degree of fecundity of different races, in comparing for each of them, the number of births and deaths. It appears, nevertheless, very probable that all the races are not equally prolific, and the mind easily perceives that there must be between them notable differences. It is, therefore, unnecessary that in order a mixture should be eugenesic the fecundity of the cross-breed should be _absolutely equal_ to that of individuals of pure blood. Had it been demonstrated by strict numbers, that a mixed race, by the simple fact of intermixture breeds less rapidly than the two parent races, and were it demonstrated that it presents a greater number of cases of sporadic sterility, it would by no means result from it that this mixed race is incapable of maintaining itself and increasing by itself. The intermixture would cease to be eugenesic if the fact of sterility became sufficiently general to render the births diminishing with every new generation, so that at length the gaps caused by death could no longer be filled and the race would prove inevitably destined, sooner or later, to become extinct. Thus, even if it were demonstrated that the offspring of an intermixture between Celts and Kimris are somewhat less prolific than the ancestors of the pure races, and that the mixed populations increased less rapidly than the others; the Kimro-Celtic hybridity would not on that account cease to be eugenesic, provided the _relative_ sterility did not descend beneath the degree when the sterility becomes _absolute_, that is to say, when the fecundity becomes insufficient. But the departments in which history and ethnology prove that the intermixture has been pushed to the extreme point, the population far from having diminished, has increased since the revolution, namely, since the establishment of new territorial divisions, as rapidly as in the rest of France, and it appears to me as certain that the intermixture of Kimris and Celts either between themselves, or with the Romans and Germans, constitute examples of eugenesic hybridity.