These tables give rise to many other observations, of which I shall only point out the principal. M. Pruner Bey carried his calculations to the third place of decimals; M. Broca to the fourth. I have gone no further than the second, that the eye may be more easily attracted by the series formed by these numbers, so important in the characterization of races. It should be remembered that the greater number are means taken from a certain number of crania. Were there a sufficient number of subjects for each race, and all the indices taken from each arranged in serial order, the distance from one to the other would undoubtedly be no longer 0·01, but would be diminished to 0·001, or even less. The insensible shades observed in passing from one individual to another would here be as remarkable as in the comparison of stature. There is no need to insist at any length upon the intercrossing, so strikingly betrayed by the two tables. We see that the same index places side by side the most dissimilar races, the South German with the Annamite, the Breton with the Kalmuck, the Belgian with the Tagal, the Parisian with the Malay, the Italian with the Maori, etc., and that by their several indices the white races are scattered throughout almost all the coloured races. I need not return to the consequences which may be drawn from these facts from a monogenistic point of view. The yellow and black races are not so widely separated as the white; the former are either brachycephalic or mesaticephalic, the latter all dolichocephalic, with the exception of the Aëtas. I have shown that the latter belong to a group of populations extending from the Andaman and Philippine Islands to Torres Strait in Melanesia, penetrating New Guinea, and forming a special _branch_ in the midst of the Melanesian Negro population. The case appears to be somewhat similar in Africa. This discovery, entirely contrary to the ideas generally maintained till the present time, is due to M. Hamy. This excellent investigator recognized brachycephaly in six skulls taken from the Paris collections, and obtained from Cape Lopez, or the mouths of the Fernand Yaz. Shortly afterwards, M. Duchaillu having brought from the same districts ninety-three skulls, the measurements of which were made public by Englishmen, M. Hamy calculated the indices, and found that twenty-seven of these crania were brachycephalic or mesaticephalic. There is then every indication that the Negro _stock_ in Africa presents a special _branch_ corresponding to the Negritoes. This result is confirmed by Schweinfurth, who places the Niams-Niams and some neighbouring tribes amongst the brachycephali. We see that the horizontal cephalic index cannot serve as a starting point in the classification of human races, as Retzius imagined it might. We also see, however, that all the value which was attributed to it by its author, is preserved in the characterization of secondary groups.