completely died away. " So long as society was organised on the basis of mother-right, my mother's totem was also mine, and consequently I could not marry a woman of the same totem without committing incest. If, during so long a period, the maternal totem has marked all who bore it with a special seal w^hich has rendered them matrimonially taboo to me, if the violation of this taboo has, during a long series of generations, roused in the conscience the movement of disgust and horror of which incestuous unions are the object, it is easy to con- ceive that these traditional sentiments, these inveterate repug- nances cannot have vanished by enchantment, by virtue only of the adoption of a new mode of filiation. The fact that the civil and religious status of the children was no longer framed on the same principle could not suffice miraculously to transform a mentality so powerfully constituted. The prejudices con- solidated by long usage survived the causes which had engendered them ; and the maternal totem, conserving something of its old character, continue to give rise to the same matrimonial interdiction as in the past. The public conscience refused to admit that the members of class Ai could henceforth marry those of Bx ; and as they could not marry in any other class, all marriage became impossible to them." A way out of this impasse had to be found. It was found by dividing each of the primary classes, A and B (so to say) vertically into two, in such a way that the totem clans were divided between the new- classes and the same totems did not appear in both halves of either of the primary classes. There was thus created a double cleavage. The primary classes A and B remained each divided horizontally by generations into A and A\, B and B\. They now became divided vertically by totems into A and Aa, B and Bb, making in the second generation A\ and Aa\^ Bi and Bbi. The risk of marrying into the mother's totem- clan, and with it the horror of incest, the matrimonial taboo, ■was thus removed.
This is the hypothesis, and Prof. Durkheim proceeds to the task of proving it. He shows that among tribes, like the Narrinyeri and the Kurnai, in other parts of Australia, where male descent is the rule, marriage into the mother's totem-clan