═════════════════════╤═══════════╤═══════════ GENERATION │THEORETICAL│ ACTUAL │ NUMBER │ NUMBER ─────────────────────┼───────────┼─────────── I │ 2│ 2 II │ 4│ 4 III │ 8│ 8 IV │ 16│ 14 V │ 32│ 24 VI │ 64│ 44 VII │ 128│ 74 VIII │ 256│ 116[2] IX │ 512│ 177[2] X │ 1024│ 256[2] XI │ 2048│ 342[2] XII │ 4096│ 533[2] ═════════════════════╧═══════════╧═══════════ A series of forty royal families gives the following averages:— ═══════════════════════════════╤══════════ GENERATION │ AVERAGE │ NUMBER ───────────────────────────────┼────────── I │ 2.00 II │ 4.00 III │ 7.75 IV │ 13.88 V │ 23.70 VI │ 40.53 ═══════════════════════════════╧══════════ When we compare these conditions in the thickly populated parts of modern Europe and of America, with their unstable population, with the conditions among primitive tribes, it becomes at once apparent that the total number of ancestors of each type in small communities must be much less than the number of ancestors in the modern states just referred to. A characteristic example is presented by the Eskimo of Smith Sound in North Greenland. From all we know, it seems extremely unlikely that this community ever consisted of more than a few hundred individuals. From what we know about the history of Eskimo communities, we might much rather assume that originally it consisted of a very few families only. The community has been cut off from the outer world for very long periods; and while there may have been accessions of new individuals from outside once each century, on the whole it has remained completely isolated. It is therefore obvious that the ancestry of this group cannot contain anything like the million of people required by the theory, but that all the individuals must be interrelated through their remote ancestry.