Such an arrangement does not go far toward showing one's ancestry. Not a few Americans are in the tenth generation from their earliest forefathers on this side of the water. Hundreds of thousands are in the seventh, eighth or ninth generation. Let us reckon the number of our progenitors for ten generations. We had 2 parents, 4 grandparents, 8 great-grandparents, 16 great-great-grandparents, 32 ancestors of the sixth generation, 64 of the seventh, 128 of the eighth, 256 of the ninth, and 512 of the tenth generation. The number of ancestors for ten generations is thus 1,022. The different surnames represented among them may be as many as the number of ancestors of the earliest generation--i.e., 128 for eight generations, 256 for nine, and 512 for ten generations. The actual number is frequently lessened by the marriage of ancestors who bear the same surname. But the general significance of the numerical argument remains. Are we a descendant of the first John Smith, in the tenth generation and through a single line? Then the book on "The Smith Family" will only show 18 of our 1,022 ancestors, assuming that the wife of each of our ancestral Smiths is mentioned. If the wives are omitted, only 9 ancestors will be shown. And in the latter case the book shows our link with but one family and surname out of a possible 512. Or, if the book gives the maiden names of the wives of our nine ancestral Smiths, nine other family surnames out of the 512 will receive a bare mention. But none of these lines will be traced. The reader will now fully appreciate our reference to this kind of book as the "clan" genealogy. It shows the relationships, most of them quite distant, between the collateral branches of a single tribe; but it does _not_ exhibit the many lines of one's ancestry. The kind of book which accomplishes the latter object will come before us in the next chapter. Nevertheless, the "clan" genealogy has its place. The recognition of tribal relations has become popular, and family organizations, with the occasional function of a "family re-union," are rapidly increasing. Many of these organizations, embracing all the known descendants of a common ancestor, elect regular officers, and in a few cases the whole tribe has a legal status as a corporation. The tribal genealogy is also favored by many who hope to make a profit by the sale of their book. A fair-sized tribe is considered a promising field for such an enterprise. Among several thousand clansmen a considerable number, it is assumed, will purchase a copy of a book which traces one of their ancestral lines. When the project is well managed and the book properly exploited this hope is often realized very handsomely.