all whites have a capacity of the skull greater than 1550 cc., while 27 per cent of the negroes and 32 per cent of the Melanesians have capacities above this value. If we were to assume a direct relation between size of brain and ability,—which, as we have seen before, is not admissible,—we might, at most, anticipate a lack of men of high genius, but should not expect any great lack of faculty among the great mass of negroes living among the whites, and enjoying the advantages of the leadership of the best men of that race. On the other hand, we find characteristics in different races so far apart and so little variable, that an overlapping is entirely or practically excluded. Examples of these are the frizzly hair of the negro as compared with the straight hair of the Mongol; the elevation and narrowness of the nose of the Armenian, and the flatness of the negro nose; the differences in pigmentation of the North European and of the Central African. Investigations on the character of variability, which have been based on the measurements of the body, on social and economic phenomena, and also on variable physical phenomena, such as meteorological data, have resulted in the discovery that almost always the same law nearly covers the distribution of the numerical values of the observations (Lock, Bowley). [Illustration: FIG. 1.] It has been shown that the values which represent the phenomenon are so distributed that certain numerical values occur very frequently, and that the greater the difference between an observation and the value at which the greatest number of cases are found, the less will be the number of these observations. The character of this distribution is shown in Fig. 1, in which the horizontal line represents the numerical values of the observations, while the vertical distances represent the frequency of that observation to which the vertical distance belongs. In the theoretical distribution which is represented in Fig. 1, the following values of the stature of a number of men are found:— 1415-1455 mm. 5 cases 1455-1495 mm. 11 cases 1495-1535 mm. 44 cases 1535-1575 mm. 135 cases 1575-1615 mm. 325 cases 1615-1655 mm. 607 cases 1655-1695 mm. 882 cases 1695-1735 mm. 1000 cases 1735-1775 mm. 882 cases 1775-1815 mm. 607 cases 1815-1855 mm. 325 cases 1855-1895 mm. 135 cases 1895-1935 mm. 44 cases 1935-1975 mm. 11 cases 1975-2015 mm. 5 cases