tribe a tabu of the mother’s as well as of the father’s totem.  That being so, it is natural to suppose that the new marriage organisation according to male descent might be modified to take account of this fact.  By dividing the classes and arranging that one member of a couple should be debarred not only from intermarrying with the class of his mother, for which the four-class system also provides, but also from intermarrying with the second member of the same couple too, this result was attained, in the view of Dr Durkheim.

It remains however to be established that this segregation of totems is actually found in the tribes in question.  For the Warramunga Spencer and Gillen distinctly state[136] that the arrangement is dichotomous, in which case the alleged result would not be brought about.  The Anula and Mara are exceptional tribes with direct male descent; it is hardly likely that the eight-class system spread from them.  The Mayoo have not yet been reported on by an expert.  Finally some of the tribes have not even the dichotomous arrangement of totems but distribute them in both phratries.  The basis of the hypothesis, therefore, is hardly established.

Singularly enough, Dr Durkheim[137] expresses his adherence to a previous theory of his own as to the method of effecting the change from female to male descent in four-class tribes.  This he supposes to have been done by transferring one of the two classes from each phratry to the opposite one; and in the former discussion (Annee Soc. V, 82 sq.) he showed that this procedure would result in scattering the totems through both phratries, as we find them to be in the case of the Arunta.  It is therefore singular to find that he adheres to this theory when his new hypothesis demands that the totems, so far from being more widely distributed, should be actually confined to the members of one couple.  Beyond the Urabunna custom in intertribal marriages, however, which is hardly decisive evidence, there does not appear to be any proof that the transference from one phratry to the other ever took place.

The further support claimed by Dr Durkheim for his hypothesis from the alleged male descent of the totem in tribes where female descent of the class names prevails, rests on too uncertain a basis to make it necessary to deal with it at length; some criticism of the evidence will be found elsewhere.

We have seen above that the Dieri rule is precisely parallel to that of the eight-class tribes in practice; it is however expressed, not by a class system, but by enacting that people standing in a certain degree of kinship or consanguinity shall marry.  If Dr Durkheim’s theory of the origin of the eight-class system is correct, it should also apply to the Dieri.  Now the rule that a man must marry his maternal great-uncle’s daughter clearly prevents intermarriage with one of the mother’s totem; but this cannot be the object of the rule, for it is prevented already by the phratry system.  Dr Durkheim’s theory therefore finds no support in the Dieri rule.