This idea was supported by the system of relationship of the Dieri of Australia which possesses at least one feature similar to those of Pentecost, a fact I happened to remember at the time because Mr. N. W. Thomas[13] had used it as the basis of a reductio ad absurdum argument to show that terms of relationship do not express kinship. The interest of the Pentecost system seemed at first to lie in the possibility thus opened of bringing Melanesian into relation with Australian sociology, a hope which was the more promising in that the people of Pentecost and the Dieri resemble one another in the general character of their social organisation, each being organised on the dual basis with matrilineal descent. When in Pentecost, however, I was unable to get further than this, and the details of the system remained wholly inexplicable.

The meaning of some of the peculiarities of the Pentecost system became clear when I reached the Banks Islands; they were of the same kind as those I have already considered as characteristic of these islands. When I had discovered the dependence of these features upon the marriage of a man with the wife of his mother’s brother, it became evident that not only these, but certain other features of the Pentecost system, were capable of being accounted for by this kind of marriage. The peculiar features of the Pentecost system could be divided into two groups, and all the members of one group could be accounted for by the marriage with the mother’s brother’s wife. All these features had the character in common that persons of the generation immediately above or below that of the speaker were classed in nomenclature with relatives of the same generation.

The other group consisted of terms in which persons two generations apart were classed with relatives of the same generation. Since the first group of correspondences had been explained by a marriage between persons one generation apart, it should have been obvious that the classing together of persons two generations apart might have been the result of marriage between persons two generations apart. The idea of a society in which marriages between those having the status of grandparents and grandchildren were habitual must have seemed so unlikely that, if it entered my mind at all, it must have been at once dismissed. The clue only came later from a man named John Pantutun, a native of the Banks Islands, who had been a teacher in Pentecost. In talking to me he often mentioned in a most instructive manner resemblances and differences between the customs of his own island and those he had observed in Pentecost. One day he let fall the observation with just such a manner as that in which we so often accuse neighbouring nations of ridiculous or disgusting practices, “O! Raga![14] That is the place where they marry their granddaughters.” I saw at once that he had given me a possible explanation of the peculiar features of the system of the island. By that time I had forgotten the details of the Pentecost system, and it occurred to me that it would be interesting, not immediately to consult my note-books, but to endeavour to construct a system of relationship which would be the result of marriage with a granddaughter, and then to see how far my theoretical construction agreed with the terminology I had recorded. The first question which arose was with which kind of granddaughter the marriage had been practised, with the son’s daughter or with the daughter’s daughter, and this was a question readily answered by means of a consideration arising out of the nature of the social organisation of Pentecost.

The society of this island is organised on the dual basis with matrilineal descent in which a man must marry a woman of the opposite moiety. Diagram 3, in which A and a stand for men and women of one moiety, and B and b for those of the other moiety, shows that a marriage between a man and his son’s daughter would be out of the question, for it would be a case of A marrying a. It was evident that the marriage, the consequences of which I had to formulate, must have been one in which a man married his daughter’s daughter.

Diagram 3.

It would take too long to go through the whole set of relationships, and I choose only a few examples which I illustrate by the following diagram:

Diagram 4.

This diagram shows that if A marries e, c, who previous to the marriage had been only the daughter of A, now becomes also his wife’s mother; and D, who had previously been his daughter’s husband, now becomes his wife’s father. Similarly, F, who before the new marriage was the daughter’s son of A, now becomes the brother of his wife, while f, his daughter’s daughter, becomes his wife’s sister. Lastly, if we assume that it would be the elder daughters of the daughter who would be married by their grandfathers, e, who before the marriage had been the elder sister of F and f, now comes through her marriage to occupy the position of their mother’s mother.