or combination of tribes acknowledging that name. The Beni Nizâr embraced many subordinate tribes, numbering, as Sprenger thinks, in the time of Mahomet, some five or six million souls, and connected mostly by no other tie than the common name. They spread over the whole of Northern Arabia and Mesopotamia: but the Beni Modhar, or branch to which Mahomet belonged, had their seat chiefly on the shore of the Red Sea. Descending the line, each progenitor's name represents a gradually diminishing affiliation of tribes. Thus the Beni Nizâr (tribe of Nizâr, the patriarch of the race) include the distant stocks of Bekr and Taghlib. The Beni Modhar (son of Nizâr) exclude these, while embracing the numerous groups sprung from Modhar through Cays Aylân,—which latter again are excluded from the branch next in descent bearing the appellation of Beni Khindif;—and so on till the circle is narrowed to the families descended from Fihr, that is, the "Coreish." 

Each tribe had thus its central column of descent; and the more remote the progenitor, the more numerous the tribes ranging under his name. This central column was termed by traditionists, "The Genealogical Tree," Amûd al nasab): and with this stem, every clan of the race supposed to spring from the common patriarch was connected, by assigning its descent from some of the successive progenitors; the common appellation of the group of sub-tribes thus affiliated together being generally assumed as the name of such progenitor. It became necessary, therefore, to provide that the number of links in the tree of a sub-tribe reaching up to the progenitor under whom it branched off from the main tribe, should correspond with the number of links in the parent stem. For example, as there are eighteen generations between Mahomet and Modhar, it follows that in the family tree of the Beni Suleim descended from Aylân son of Modhar, there must be seventeen links. These removes are termed Cúdûd (close relations) in the technical language of the genealogists; and as they were drawn out merely to square with a theory, so they were no doubt filled up generally in an arbitrary manner. If real names were not forthcoming for a gap, names were invented, and so the synchronism maintained.