necessary for the crossing of different species must constantly occur, and yet the species remain distinct. The same is true of many hermaphrodite species of marine animals living in great numbers together; the water is full of the sperm of several species, and the conditions of cross-contact of sexual elements are constantly present, and yet species remain substantially distinct.
It is evident, therefore, that in close-breeding, and in the crossing of varieties of different degrees of divergence, there is, first, a less than average result, then an average, then better than an average, then this better result quickly reaches a maximum and again declines, crosses the line of average and becomes bad, and finally infinitely bad, or dies out. In the human species it is probable that the crossing of those varieties called national varieties, even strong national varieties, produces good results; but the crossing of varieties so divergent as those called primary races is probably bad—these approaching too nearly the nature of different species.
The general law of the effect of breeding may therefore be graphically represented by the following diagram, in which the absciss A B represents the level of average result, distance on this absciss from the middle point a represents the divergence of crossing varieties, and ordinates positive and negative represent the result of crossing, whether good or bad. Further, the middle point a represents no divergence or identical individuals, the distance b b individual differences, c c divergence constituting slight varieties, d d strong varieties, f f races, and g g species. By inspection of the figure it is seen that close-breeding (a) produces negative ordinates or bad results, then going from this
point the curve crosses the line of average at b b, then the ordinates become positive and reach maximum at d d, or strong varieties, then again crosses the line of average and becomes negative at f f, indicating the bad effect of crossing races, and finally becomes infinitely negative before it reaches g g, showing the practical infertility of crossing different species under natural conditions.
If I am right in this view, then the mixing of primary races is bad, and such mixed races, as weaker varieties in the struggle for life, must perish. There is one possibility which may save these races. Admitting the fact of deterioration as an immediate result of universal crossing of existing races, it is possible that by judicious crossing again of the slight varieties which must eventually arise in the mixed race, this