Mr. Hartland gives in this readable and convenient form a restatement of the facts and arguments leading to the conclusion that the earliest ascertainable method of deriving kinship is through the woman only, and that patrilineal reckoning is a later development. The matriarchal theory had hardly been seriously considered up to the seventh decade of the nineteenth century, when Bachhofen and McLennan broke new ground with Das Mutterrecht and Primitive Marriage. The theory was elaborated by Professor Giraud-Teulon in 1884 and corroborated by Professor Robertson Smith in the following year. At the close of the nineteenth century the work of Professor Baldwin Spencer and Mr. Gillen among certain primitive tribes in the centre of Australia and then a more extensive examination of the aborigines of North America gave an impetus to the attack on the universal priority of maternal kinship. Mr. Hartland exhibits and summarizes the evidence for matrilineal kinship in different parts of the world, and concludes that wherever in the Eastern hemisphere there exists a concurrence of matrilineal and non-matrilineal features in the same society, the matrilineal features are always the more archaic, which raises a strong presumption that this is also true of the Western.