In the Australian system, however, which distinguishes clan and totem, and therefore, as we may suppose, still exemplifies, on the whole, an uninterrupted development, we find also a third form of exogamous relationship. This last form of exogamy seems to be the one which is most common in Australia, whereas, of course, it has no place in the pure clan exogamy of the American Indians. The system indicated in diagram II, in which children belong directly to the clan of the mother in maternal descent and to that of the father in paternal descent, may be designated as limited exogamy with direct maternal or paternal descent. There developed from this a third system, in which, while the children are counted to the clan of the parent who determines descent, they nevertheless become members of a different totem group. Thus arises a limited exogamy with indirect maternal or paternal descent, as represented in diagram III.

A man of clan A and totem group l may marry only a woman of clan B and totem group p; the children, however, do not belong to the totem p, but to another specifically defined totem group, q, of clan B.

The way in which these various forms of exogamy affect the marriage relations of the children that are born from such unions is fairly obvious. Turning first to form I—unlimited exogamy—it is clear that, in the case of maternal descent, which here appears to be the rule, none of the children of the mother may marry except into the clan of the father; in paternal descent, conversely, they may marry only into the clan of the mother. Marriage between brothers and sisters, thus, is made impossible. Nor may a son marry his mother where maternal descent prevails, or a daughter her father in the case of paternal descent. In the former case, however, the marriage of father and daughter would be permitted, as would that of mother and son in the latter. The marriage of a son or daughter with relatives of the mother who belong to the same clan is not allowed in the case of maternal descent. The son, for example, may not marry a sister of his mother, nor the daughter a brother of the mother, etc. Since it is maternal descent that is dominant in the case of unlimited exogamy, the most important result of the latter is doubtless its prevention of the marriage of brother and sister, in addition to that of a son with his mother. The system of paternal descent, of course, involves a corresponding change in marriage restrictions.

What, now, are the results of form II—limited exogamy with direct maternal or paternal descent? It is at once clear that such exogamy prohibits all the various marriage connections proscribed by unlimited exogamy. Marriage between brothers and sisters is rendered impossible, as is also, in the case of maternal descent, that between a son and his mother or the relatives in her clan. Marriage between father and daughter, however, is permitted. Where paternal descent prevails, these latter conditions are reversed. Although forms I and II are to this extent in complete agreement, they nevertheless show a very important difference with respect to the prohibitions which they place on marriage. In unlimited exogamy, a man is at liberty to marry into any totem that belongs to the clan with which his own has exogamous relations; in limited exogamy, however, he may marry into only one of the totems of such a clan. Thus, the circle within which he may select a wife is very materially reduced. Limited exogamy with direct maternal or paternal descent, accordingly, means a reapproach to endogamy. The wife must be chosen from an essentially smaller group, narrowed down, in the case of maternal descent, to the more immediate relatives of the father, or, in paternal descent, to those of the mother. Such a condition is not at all a strict form of exogamy, as is maintained by some ethnologists, but is, on the contrary, something of a return to endogamy. This point is of decisive importance in determining the motives of the remarkable institution of exogamy.

What are the conditions, finally, which obtain in form III—limited exogamy with indirect maternal or paternal descent? It is at once obvious that marriage between brother and sister is here also excluded. Furthermore, another union is prohibited which was permitted in form II. For son and daughter, in the case of maternal descent, no longer belong to the totem group of the mother, p, but pass over into another group, say q. Not only, therefore, is a son prevented from marrying his mother because they both belong to the same clan, but a father is forbidden to marry his daughter because he may take only a woman of group p, to which his wife belongs. No less true is this of the son, who now likewise belongs to group q, and may therefore no longer marry a female relative of his father's, since the group q into which he has entered has exogamous connections with another totem group of the paternal clan, say with m. With this change a step to a stricter exogamy is again taken; the earlier restrictions on marriage remain, and the possibilities of marriage between relations are further reduced by changing the totem of the children. Cousins may not marry each other. Thus, the limits of exogamy are here narrower than those, for example, which obtain in Germany. It is evident that such limitations might become a galling constraint, particularly where there is a scarcity of women, as is the case, for the most part, in Australia. This has led some of the Australian tribes to the remarkable expedient of declaring that a man is not to be regarded as the son of his father, but, in the case of maternal descent, as the son of his paternal grandfather—a step which practically amounts to transferring him into the totem of his father and allowing him to enter into marriage with his mother's relatives. This circumvention, reminding one of the well-known fictions of Roman law, may have its justification in the eyes of the Australians in the fact that they draw practically no distinction between the various generations of ancestors.

The three forms of exogamy, accordingly, agree in prohibiting the marriage of brothers and sisters and, in so far as maternal descent may be regarded as the prevailing system, the marriage of a son with his mother. Both these prohibitions, doubtless, and especially the latter, reflect a feeling which was experienced by mankind at an early age. The aversion to the marriage of a son with his mother is greater than that to the marriage of brother and sister or even that of father and daughter. Consider the tragedy of Œdipus. It might, perhaps, be less horrible were it father and daughter instead of son and mother who were involved in the incestuous relation. Marriages between brothers and sisters have, of course, sometimes occurred. Thus, as has already been remarked, the Peruvian Incas ordained by law that a king must marry his sister. In the realm of the Ptolemies, likewise, the marriage of brother and sister served the purpose of maintaining purity of blood, and even to-day such marriages occur in some of the smaller despotic negro states. The custom is probably always the result of the subjugation of a people by a foreign line of rulers. Indeed, even the Greeks permitted marriage between half-brothers and half-sisters.

Though these natural instincts were less potent in early times than in later culture, they may not have been entirely inoperative in the development from original endogamy to exogamy. Nevertheless, one would scarcely attempt to trace to the blind activity of such instincts those peculiar forms of exogamy that appear particularly among the Australian tribes. On the contrary, we would here also at once be inclined to maintain that the reverse is true, thus following a principle that has approved itself in so many other cases. The aversion to marriage with relatives has left its impress on our present-day legislation, not so much, indeed, in the positive form of exogamy, as in the negative form which forbids endogamy within certain limits. This aversion, however, is not the source so much as it is the effect—at least in great measure—of the exogamous institutions of early culture. All the more important is the question concerning the origin of these institutions. This question, in fact, has already received much attention on the part of ethnologists, particularly since the beginning of the present century, when it has become more and more possible to study the tribal organization of the Australians. Here, however, we must distinguish between the general theories that have been advanced concerning the causes of exogamy as such—theories which date back in part even to a fairly early period—and hypotheses concerning the origin of the various forms of exogamy.

Exogamy as such has generally been approached from a rationalistic point of view. It has been regarded as an institution voluntarily created to obviate the marriage of relatives, and is supposed to have arisen contemporaneously with another institution of like purpose, namely, tribal division. This view is championed, among other scholars, by the able American sociologist, Lewes Morgan, in his book "Ancient Society" (1870), and even by Frazer in his comprehensive work "Totemism and Exogamy" (1910), which includes in its survey all parts of the earth. Frazer says explicitly: 'In the distant past, several wise old men must have agreed to obviate the evils of endogamy, and with this end in view they instituted a system that resulted in exogamous marriage.' Thus, the determinant motive is here supposed to have been aversion to the marriage of relatives. According to Morgan's hypothesis—an extreme example of rationalistic interpretation—the aversion was due to a gradually acquired knowledge that the marriage of relatives was injurious in its effects upon offspring. The entire institution, thus, is regarded as a eugenic provision. We are to suppose that the members of these tribes not only invented this whole complicated system of tribal division, but that they foresaw its results and for this reason instituted exogamous customs. Were people who possess no names for numbers greater than four capable of such foresight, it would indeed be an unparalleled miracle. Great social transformations, of which one of the greatest is unquestionably the transition from the primitive horde to totemic tribal organization, are never effected by the ordinances of individuals, but develop of themselves through a necessity immanent in the cultural conditions. Their effects are never foreseen, but are recognized in their full import only after they have taken place. Moreover, as regards the question of the injurious effects resulting from the marriage of relatives, authorities even to-day disagree as to where the danger begins and how great it really is. That the Australians should have formed definite convictions in prehistoric times with reference to these matters, is absolutely inconceivable. At most, they might have felt a certain instinctive repugnance. Furthermore, if these institutions were established with the explicit purpose of avoiding marriage between relatives, the originators, though manifesting remarkable sagacity in their invention, made serious mistakes in their calculations. For, in the first place, the first two forms of exogamy only partially prevent a union which even endogamous custom avoids, namely, that between parents and children; in the second place, the transition from unlimited to limited exogamy with direct maternal or paternal descent does not involve an increased restriction of marriage between relations, but, as we have already seen, marks a retrogression, in the sense of a reapproach to endogamy.