On the whole however it seems simplest to regard the matter as one in which the rights are determined by no considerations of inheritance or descent but simply by the rule that the property in the woman remains vested in the body of purchasers.  For it must be remembered that not only an own but also a tribal sister may be given in exchange for a wife.  From this it follows that, theoretically at any rate, the contracting parties are corporations rather than individuals, and in this case the death of the individual on whose behalf the transaction has been effected does not extinguish the proprietary rights acquired by handing over a woman, standing in the relation of sister to the one corporation, in exchange for another woman standing in the relation of sister to the other corporation.

If this solution is correct, it is unnecessary to go into the complicated question of the relation of brother-inheritance to matriliny and patriliny.  For it is by no means clear that it is an exemplification of the former rather than the latter principle.  It may, of course, be argued that brothers succeed as children of the same mother; but against this must be set the fact that they are also children of the same father; for uncertain paternity can only be a vera causa where pirrauru and similar customs are found; and even here the pre-eminence of the primary husband might well be held to determine the legal paternity of the children, which is, of course, especially in Africa, a matter of potestas rather than procreation.  However this may be, the position of the widow does not appear to invalidate the guardianship origin of matriliny.

We now turn to the question of why male tends to take the place of female descent.  The possible factors are (1) authority in the family, (2) the rise of chieftainship and inheritance generally, and (3) the organisation of the family group.  Of the authority of father or mother over the children, there is not much trace in Australia except in the most youthful period of the pre-adult life.  It is for example exceptional for a parent to correct a child.  As to who decides in cases of infanticide we have unfortunately too little information to be able to generalise.  Only in one important step—­that of betrothal—­have we anything like adequate information, and the interrelations between rule of descent and potestas are found to be in this case sufficiently clear, though it is not clear on what principle it is decided who shall exercise the right.

Taking first tribes with matrilineal descent, we find that the Barkinji, the Wakelbura, the Dieri, and in some cases the Wollaroi, assign the right of betrothal to the mother or mother’s brother[19].  In other cases, transitional forms, the father, his elder brother, or the girl’s brothers decide, or else the parents or two of these persons jointly[20].  Among the Mukjarawaint the betrothal rested in part with the paternal grandparents[21]; it may be noted that the grandfather had to decide also whether a child should be brought up or killed.  Among the Kuinmurbura it falls to the mother’s brother’s son or the father’s sister’s son, who is, apparently, entitled to marry the girl himself[22].