Although it frequently happens that the children belong to the kin which through one of the parents or otherwise exercises the supreme authority in the family, it is far from being the case that there is invariable agreement between the principles on which kinship and authority are determined.  Three main types of family may be distinguished:  (1) patripotestal, (2) matripotestal, (a) direct, and (b) indirect, in which the authority is wielded by the father, mother, and mother’s relatives, in particular her brothers, respectively.  Innumerable transitional forms are found, some of which will be mentioned in the next chapter, which deals with the rule of descent by which membership of natal groups is determined.

Turning now to kinship organisations, we find that the most widely distributed type is the totem kin, in fact, if we except the Hottentots and a few other peoples among whom no trace of it is found, it is difficult to say where totemism has not at one time or another prevailed.  It is found as a living cult to-day among the greater part of the aborigines of North and South America, in Australia, and among some of the Bantu populations of the southern half of Africa.  In more or less recognisable forms it is found in other parts of Africa, New Guinea, India, and other parts of the world.  In the ancient world its existence has been maintained for Rome (clan Valeria etc.), Greece, and Egypt, but the absence of information as to details of the social structure renders these theories uncertain.

Aberrant cases apart, totemism is understood to involve (1) the existence of a body of persons claiming kinship, who (2) stand in a certain relation to some object, usually an animal, and (3) do not marry within the kin.

Passing over the classes, which are peculiar to Australia and will be fully dealt with below, we come to a more comprehensive form of kinship organisation in the phratries.  These are a grouping of the community in two or more exogamous divisions, between which the totem kins, where they exist, are distributed.  The essential feature of a phratry is that it is exogamous; its members cannot ordinarily marry within it, and, where there are more than two phratries, there may exist rules limiting their choice to certain phratries.[4]

This dual or other grouping of the kins is widely found in North America, the number of phratries ranging from two among the Tlinkits, Cayugas, Choctaws, and others, to ten among the Moquis of Arizona.  As in Australia, the totem kins bearing the same eponymous animal as the phratry are usually, e.g. among the Tlinkits, found in the phratry in question.  Exceptions to this rule are found among the Haida, where both eagle and raven are in the eagle phratry.