When, therefore, a physiologist wishes to demonstrate the existence of that degree of hybridity which we have termed eugenesic, he selects two perfectly recognised distinct species of animals, crosses them, studies their breeds, and if he finds that they are indefinitely prolific, it is sufficient for him to affirm the existence of eugenesic hybridity--that is to say, that the physiological definition of the _species_ is unacceptable. But when a zoologist, in studying two races of animals, the specific determination of which is still contested, endeavours to establish that these two races are merely varieties of the same species, and when in order to weaken the differential anatomical characters pointed out by his adversaries, he invokes the physiological analogy exhibited by intermixture, we have a right to expect more than a partial demonstration. We must first prove that the intermixture of the two races constitutes a case of eugenesic hybridity; for if the cross-breed are not between themselves indefinitely prolific, it is certain that the two races are not of the same species. This first point being established, would not yet lead to any conclusion, since animals of different species may engender eugenesic breeds. He must, therefore, completely analyse all the phenomena of reproduction and prove that they are exactly the same in the parent races and in the hybrid race. It is not merely the sexual analogy but the sexual identity which must be rendered evident; for from his point of view, it is not sufficient that the two races in question should be homogenesic in some degree, they must be entirely homogeneous, and the least genital difference becomes an argument against the proposition he sustains. If the cross-breed, though very prolific, are less so than their parents, or less productive in their crossings than their direct alliances; or, finally, if the investigation of these crossings exhibits any functional inequality, it might become very probable that the two races do not belong to the same species. Such would also be the case if the cross-breed were less strong and vivacious than the individuals of the pure race, or if one of the crossings is more productive than the inverse crossing, as is observed in certain cases of hybridity, which approach more or less of _unilateral hybridity_. The existence of one of these phenomena might prove that the two races are not homogeneous, and might lead us to think that they are not of the same species.