to which only a single individual has access at the same time. Then a very slight difference in muscular power will either accomplish or fail in producing the desired effect, and the ultimate effect (say in repelling an attack on a fortress under relatively primitive conditions) will be entirely incommensurate with the additional strength required to produce it. So we may readily understand how a slightly greater mechanical aptitude might render one race able to launch a remarkable series of inventions for which another, by barely missing the required degree of development, would be forever debarred. This is only a special form of the Darwinian doctrine of the survival value of small variations, applied not to the question of the struggle for existence (with which, nevertheless, it may be most intimately related), but to the creation of new cultural values. This aspect of the subject naturally leads to another that is closely connected with it and is essential to an understanding of the entire question. Mental endowment is a variable phenomenon within any particular people or tribe. However democratic may be our ideals, the doctrine that all individuals are born equal in point of ability can no longer be seriously maintained. Every race must, therefore, be regarded not as representing a single point of mental development, but as a continuum of mental values with a certain range of variation. In comparing the different races we must, accordingly, apply the canons used by statisticians in comparing series of variable measurements. Here a matter of vital importance challenges our attention. Two series may have the same average value and yet differ considerably in range. Now it is obvious that, where the number of individuals considered is small, excessive values are less likely to occur than in a larger series. In a gathering of a hundred men, we are not likely to find a man above 6 feet 6 inches in height; the average stature of all New Yorkers will probably not be any greater than that of one hundred men selected at random, yet in the entire city we shall find a number of individuals of gigantic stature. When we apply this fact to our special problem we see at once that extraordinary deviations from the norm cannot be expected to occur in a tribe of 500 or even 5,000, while among the vast populations of India, China or the Caucasian countries of America and Europe such favorable variants are likely to occur with considerable absolute frequency. These variations, as has already been suggested, need not even be excessive to produce significant cultural results. Again, we may urge the principle of minimal variations. A _little_ greater energy or administrative talent may be just sufficient to found a powerful state; a _slightly_ greater amount of logical consistency may lead to the foundation of geometrical reasoning or of a philosophical system; a _somewhat_ keener interest, above the purely utilitarian one, in