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. [Illustration: DIAGRAM 3. A = b | | +-------------+-------------+ | | B = a A = b | | +------+------+ +-------+-------+ | | | | A a B b ] 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: [Illustration: DIAGRAM 4. A = b | | D = c | | +-------+-------+ | | | e F f ] 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. When, after making these deductions, I examined my record of the Pentecost terms, I found that its terminology corresponded exactly with those which had been deduced. The wife’s mother and the daughter were both called _nitu_. The daughter’s husband and the wife’s father were both _bwaliga_. The daughter’s children were called _mabi_, and this term was also used for the brother and sister of the wife. Lastly, the mother’s mother was found to be classed with the elder sister, both being called _tuaga_.