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40 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. 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 of a change in the mode of descent. Once turned into a fresh path by the necessity of showing how the correspondence could have arisen out of a matrilineal condition, it was not long before I saw how it might be accounted for in a very different way. I saw that the correspondence would be the natural result of a form of social organisation in which it was the practice to marry a grandmother, viz., the wife of the father's father. Not only did this form of marriage explain the second peculiar feature of the Fijian system,