In the same way, in the now extinct Mount Gambier tribe, the phratries are Kumi and Kroki. Black Cockatoo (Wila) is in Kroki; in Kumi is Black Crestless Cockatoo (Karaal).[31] By Mr. Frazer's theory, which he probably no longer holds, a Cockatoo primary totem kin would throw off other kins, named after various other species of Cockatoo, and become a Cockatoo phratry, with several Cockatoo totem kins. The reverse is the fact: the two Cockatoos are in opposite phratries.

Again, among the Ta-ta-thi tribe, two species of Eagle Hawk occur as totems. One is in Eagle Hawk phratry (Mukwara), the other is in Crow phratry (Kilpara). This could not have occurred through Eagle Hawk "clan" splitting into other clans, named after other species of Eagle Hawk.[32]

In the Kamilaroi phratries two species of Kangaroos occur as totem kins, but the two Kangaroo totem kins are in opposite phratries.[33]

If Mr. Frazer's old view were correct, both species of Kangaroo would be in the same phratry, like the various kinds of Turtle in the Mohegan Turtle phratry. Again, in the Wakelbura tribe, in Queensland, there are Large Bee and Small or Black Bee in opposite phratries.[34]

On Mr. Frazer's old theory, we saw, a phratry is a totem kin which split into more kins, having for totems the various species of the original totem animal. These, as the two sorts of Bees, Cockatoos, Kangaroos, and so on, would on this theory always be in the same phratry, like the various kinds of Mohegan Turtles. But Mr. Frazer himself has collected and published evidence to prove that this is far from being usually the case; the reverse is often the case. Thus the argument derived from the Mohegan instance of the Turtle phratry is invalidated by the opposite and more numerous facts. The case of the Mohegan Turtle phratry, with various species of Turtles for totem kins within it, is again countered in America, by the case of the Wyandot Indians. They have four phratries. If these have names, the names are not given. But the first phratry contains Striped Turtle, Bear, and Deer. The second contains Highland Turtle, Black Turtle, and Smooth Large Turtle. If this phratry was formed by the splitting of Highland Turtle into Black and Smooth Turtles, why is Striped Turtle in the opposite phratry?[35] The Wyandots, in Ohio, were village dwellers, with female reckoning of lineage and exogamy. If they married out of the tribe, the alien was adopted into a totem kin of the other tribe, apparently changing his totem, though this is not distinctly stated.[36]

Thus Dr. Durkheim's theory of the segmentation of a primary totem "clan" into other "clans" of other totems is not aided by the facts of the Mohegan case, which are unusual. We more frequently find that animals of different species of the same genus are in opposite phratries than in the same phratry. Again, a totem kin (with female descent) cannot, we repeat, overpopulate its territory, for, as Dr. Durkheim says, an exogamous clan with female descent has no territorial basis. Nor can it segment itself without also segmenting its linked totem kin or kins, which merely means segmenting the local tribe. If that were done, there is no reason why the members of the two old "clans" in the new colony should change their totems. Moreover, in Dr. Durkheim's theory that cannot be done "while totemic beliefs are in vigour."

To recapitulate our objections to Dr. Durkheim's theory, we say (i.) that it represents human society as in a perpetual state of segmentation and resegmentation, like the Scottish Kirk in the many secessions of bodies which again split up into new seceding bodies. First, we have a peuplade, or horde, apparently (though I am not quite sure of the Doctor's meaning) permitted to be promiscuous in matters of sex. (ii.) That horde, for no obvious reason, splits into at least two "clans"—we never hear in this affair of more than the two. These two new segments select each a certain animal as the focus of a mysterious impersonal power. On what grounds the selection was made, and why, if they wanted an animal "god," the whole horde could not have fixed on the same animal, we are not informed. The animals were their "ancestors"—half the horde believed in one ancestor, half in another. The two halves of the one horde now became hostile to each other, whether because of their divergence of opinion about ancestry or for some other reason, (iii.) Their ideas about their animal god made it impossible for members of the same half-horde to intermarry, (iv.) Being hostile, they had to take wives from each other by acts of war. (v.) Each half-horde was now an exogamous totem kin, a "primary clan," reckoning descent on the female side. As thus constituted, "no clan has a territorial basis": it is an amorphous group, a floating mass. As such, no clan can overflow its territorial limits, for it has none.

(vi.) But here a fresh process of segmentation occurs. The clan does overflow its territory, though it has none, and, going into new lands, takes a new totem, though this has been declared impossible; "the totem is not a thing which men think they can dispose of at will, at least while totemic beliefs are in vigour." Thus the old "clans" have overflowed their territorial limits, though "clans" have none, and segments have wandered away and changed their totems, though, in the vigour of totemic ideas, men do not think that they can dispose of their totems at will, (vii.) In changing their totems, they, of course, change their blood, but, strange to say, they still recognise their relationship to persons not of their blood, men of totems not theirs, namely, the two primary clans from which they seceded. Therefore they cannot marry with members of their old primary clans, though these are of other totems, therefore, ex hypothesi, of different blood from themselves, (viii.) The primary clans, as relations all round grow pacific, become the phratries of a tribe, and the various colonies which had split off from a primary clan become totem kins in phratries. But such colonies of a "clan" with exogamy and female descent are impossible.

If these arguments are held to prove the inadequacy of Dr. Durkheim's hypothesis, we may bring forward our own.[37]