White[253] supposes a colony composed of an equal number of blacks and whites; then he tries to find out what will happen in the course of time, by supposing that a thirtieth part of them die and are born each year. He arrives, by his calculations, at the following results: in sixty-five years the number of blacks, whites, and mulattos will be equal; in ninety-one years the whites will only form one-tenth of the total population, and the blacks one-tenth; in three centuries, there would not remain one hundredth part of them, either black or white. This proposition is true, theoretically speaking; it is practically false: it rests upon what we may call an unstable equilibrium. In the physical world we may, by care, happen to put an ellipsoid in a state of equilibrium on the extremity of its greater axis, or a cone on its apex; these are also unstable equilibria, but the least cause intervening, the smallest movement, and the balance is instantly destroyed. If we admit into White’s theory a birth which does not take place, or an unproductive union, the conclusions are overturned at once; a part of the new generation will preserve the primitive type,[254] and this portion will be much more considerable than White imagined. When the facts of arrest of development, quoted above, are not sufficient to prove that a mongrel breed cannot subsist by itself, can we anywhere find one? Do we find a people preserving for centuries a medium type between two other types which gave it birth? We see them nowhere,--just as little as we see a race of mules. The fact is that such a hybrid race, intermediate to two defined types, can only have a subjective and ephemeral existence. The definition of the word _type_, both in natural history and in the particular case in which we are engaged, is rather a difficult matter, and which we can _feel_ much better than we can express it in writing. When we have seen a certain number of men belonging to one race, the mind, without any particular study, takes from each a number of general characteristics, and forms from them a sort of ideal being, to which it refers the real beings which it may henceforth see, and with which it identifies those who have a sufficient amount of similarity with this being.[255] We have seen in the preceding chapter that, as regards historic times at least, a type invariably reproduces itself through time and space, when it does not succumb to the new climate in which it is about to live. If we admit, however, that two types may have met with a harmony of influences, a medium in which they can both live, we say that--even with all the care that may be taken to mix them--we shall always find, whatever White may say, black people and white people, if these races were black and white originally; and this by reason of laws which we think we can shape, and whose demonstration will be as positive as that of the domain of history.