Some Australian tribes are divided into four exogamic groups. The laws of exogamy demand that a member of the first group must marry a member of the second group, and a member of the third group one of the fourth group. CUNOW explains these customs by showing that when custom provides that a man in a tribe that is divided into two exogamic units, and in which only members of the same generation are allowed to intermarry, conditions like those found in Australia will naturally develop, if each group has a name, and one set of names are used for the first, third, fifth, generations, and another set of names for the second, fourth, sixth, generations, etc. If we should designate the two tribal divisions by the letters A and B, the generations by 1 and 2, the names of the four divisions would be A1, A2, B1, B2; and in marriages in which is placed first the sex that determines the group to which the offspring belongs, we find that— A1 must marry B1, and his children are A2 B1 " " A1, " " " " B2 A2 " " B2, " " " " A1 B2 " " A2, " " " " B1 ------------------------------------------------------------------------ IX. SUMMARY I MAY now be allowed to pass once more briefly over the whole ground that we have covered. First of all, we tried to understand the reasons for our belief in the existence of gifted races and of others less favorably endowed, and found that it was based essentially on the assumption that higher achievement is necessarily associated with higher mental faculty, and that therefore the features of those races that in our judgment have accomplished most are characteristics of mental superiority. We subjected these assumptions to a critical study, and discovered little evidence to support them. So many other causes were found to influence the progress of civilization, accelerating or retarding it, and similar processes were active in so many different races, that, on the whole, hereditary traits, more particularly hereditary higher gifts, were at best a possible, but not a necessary, element determining the degree of advancement of a race. The second part of the fundamental assumption seemed even less likely. Hardly any evidence could be adduced to show that the anatomical characteristics of the races possessing the highest civilization were phylogenetically more advanced than those on lower grades of culture. The various races differ in this respect; the specifically human characteristics being most highly developed, some in one race, some in another. Furthermore, it appeared that a direct relation between physical habitus and mental endowment does not exist.