When once the reader understands this fact—insisted on by Spencer and Gillen—he becomes convinced, becomes mathematically certain that the chance distribution of conceptional totemism did not and could not thus array the totems of the Arunta. This present arrangement, and this alone, makes the Arunta associations with totemic names non-exogamous. I proceed to give further evidence of Spencer and Gillen. "Whilst every now and then we come across traditions, according to which, as in the case of the Achilpa," (Cats) "the totem is common to all classes[54] we always find that in each totem one moiety of the tribe predominates,[55] and that, according to tradition, many of the groups" (totem groups) "of ancestral individuals consisted originally of men or women or of both men and women, who all belonged to one moiety. Thus in the case of certain Okira or Kangaroo groups we find only Kumara and Purula; in certain Udnirringita or Wichetty Grub groups we find only Hulthara and Panunga, in certain Achilpa or 'Wild Cat' (groups) 'a predominance of Kumara and Purula, with a smaller number of Bulthara and Panunga.'[56] At the present day no totem is confined to either moiety of the tribe, but in each local centre we always find a great predominance of one moiety, as for example at Alice Springs, the most important centre of the Wichetty Grubs, amongst forty individuals, thirty-five belong to the Bulthara and Panunga and only five to the other moiety of the tribe."[57]
Here the great majority—thirty-five to five—of the members of the totem belong to one of the two main exogamous divisions. Outside of the Arunta nation and Kaitish all the Grubs would belong to one main exogamous division. It is mathematically certain that chance could not bring thirty-five to five members of a given totem—or, "a great majority" in each case—into one or other phratry.
Consequently the chance distribution of totems on the present conceptional Arunta system has not caused this uniform phenomenon. It follows that the totems of the Arunta were at one time hereditary, and were arranged, some exclusively in one, some exclusively in the other moiety, so that no person could marry into his or her own totem. The fortuitous system of conceptional distribution then arose out of the Arunta philosophy of spirits and emanations, and out of the churinga nanja usage, and has now detached a small minority of members of each totem from their original phratry and lodged them in the other. Members of every totem can therefore find legal spouses of their own totem in the phratry not their own, and may marry them. And thus these Arunta associations with totemic names are now non-exogamous. But they have been exogamous totem kins. Mr. Frazer finds what he calls totemism without exogamy in parts of Melanesia.[58] I need not here repeat my arguments, given in Anthropos, vol. v. (1910) pp. 1092-1108, to prove that the so-called "totems" in this case are only animal or vegetable "familiars" of individuals. Thus the great example of "totem clans" so-called, without exogamy, is put out of action. The Arunta "clans" are not clans, and the Arunta have had exogamous totem clans like other people.
[45] J. A. F. pp. 269, 270.
[46] Secret of the Totem, p. 125.
[47] Secret of the Totem, p. 23.
[48] Native Tribes of South-East Australia, p. 153.
[49] T. and E., vol. iv. pp. 3, 4.
[50] What, follows I have already said in Anthropos, 1910.
[51] Northern Tribes, p. 175.