The transition from the system of naming by patronymics to that of gentile names would not be made in a day or in a generation, and during the transition the usage would fluctuate: the descendants of Æneas might choose to be known as Ænæadæ rather than as the sons of Anchises, while the children of Æneas' brothers might retain the name of Anchisiadæ, because their fathers were less distinguished than their grandfather. The period of this fluctuation in usage may be assumed to have been long enough to allow of the requisite diversity of gentile names, while the fact that the number of _gentes_ is always fixed, however far back they can be historically traced, shows that the fluctuation at last hardened into unyielding custom. It was pointed out in the last paragraph but one that second cousins once removed (the great-grandchildren of a common house-father) might at one time belong to the same joint undivided family, and subsequently to different families, and that they might wish to continue, after their separation, to consider each other as relatives. Language afforded them no means of indicating their relationship, for there was no word in the original Aryan language for "cousin," much less for "second cousin." And before patronymics had been stereotyped into gentile names, it might seem that the Aryan system of naming at that time afforded no means of binding these relatives together either. But a certain Athenian custom may perhaps be taken, both as evidence of the existence of the desire in question, and as an indication of the means taken for gratifying it. At Athens it was the custom to name a child after its grandfather; and if we assume this practice to have obtained in Aryan times, we have here a ready means for indicating the fact that second cousins are related without the aid of a gentile name; for if I and my first cousin are both named after our common grandfather, then our children (who are second cousins once removed) will have the same patronymic, and therefore will be related, and thence again prohibited to marry. This may be illustrated by an imaginary pedigree, which will also serve to show how—when once patronymics, such as "John's son," became stereotyped into true family or gentile names, such as "Johnson"—all the _gentes_ of a tribe might be descended from a common ancestor. Thus:—