I have now tried to show the dependence of special features of the classificatory system of relationship upon special social conditions. If I have succeeded in this I shall have gone far towards the accomplishment of one of the main purposes of these lectures. They have, however, another purpose, viz., to inquire how far we are justified in inferring the existence of a social institution of which we have no direct evidence when we find features of the nomenclature of relationship which would result from such an institution. I have now to enter upon this part of my subject, and I think it will be instructive to take you at once to a case in which I believe that an extraordinary form of marriage can be established as a feature of the past history of a people, although at the present moment any direct evidence for the existence of such a marriage is wholly lacking. When I was in the interior of Viti Levu, one of the Fijian islands, I discovered the existence of certain systems of relationship which differed fundamentally from the only Fijian systems previously known. Any features referable to the cross-cousin marriage were completely absent, but in their place were others, one of which I have already mentioned, which brought into one class relatives two generations apart. The father’s father received the same designation as the elder brother, and the son’s wife was called by the same term as the mother. As I have already said, my first conclusion was that these terms were the survivals of forms of social organisation resembling the matrimonial classes of Australia, but as soon as I had worked out the explanation of the Pentecost system, it became evident that the Fijian peculiarities would have to be explained on similar lines. At first I thought it probable that the difference between the Pentecost and Fijian systems was due to the difference in the mode of descent in the two places. For long I tried to work out schemes whereby a change from the matrilineal descent of Pentecost to the patrilineal condition of Fiji could have had as one of its consequences a change from a correspondence in nomenclature between the mother’s mother and the elder sister to one in which the common nomenclature applied to the father’s father and the elder brother. It is an interesting example of the strength of a preconceived opinion, and of some measure of the belief in the impossibility of customs not practised by ourselves, that for more than two years I failed to see an obvious alternative explanation, although I returned to the subject again and again. The clue came at last from the system of Buin, in the island of Bougainville, recorded by Dr. Thurnwald.[16] The nomenclature of this system agreed with that of inland Fiji in having one term for the father’s father and the elder brother, but since the people of Buin still practice matrilineal descent, it was evident that I had been on a false track in supposing the correspondence to have been the result