First we have tribes in which each person is born into one or other of two social divisions usually called 'phratries.' Say that the names of the phratries mean Eagle Hawk and Crow.

Each born Crow must marry an Eagle Hawk; each born Eagle Hawk must marry a Crow.

The names are derived through the mothers.

One obvious result is that no two persons, brother and sister maternal, can intermarry; but the rule also excludes from intermarriage great numbers of persons in no way akin to each other by blood, who merely share the common phratry name, Crow or Eagle Hawk.
In each phratry are smaller sets of persons, each set distinguished by the name of some animal or other natural object, their 'totem.' The same totem is never found in both phratries.

Thus a person marrying out of his or her phratry, as all must do, necessarily marries out of his or her totem.
The same arrangements exist among tribes which derive phratry and totem names through the father.
This derivation of names and descent through the father is regarded by almost all students, and by Mr.J.G.Frazer, in one passage of his latest study of the subject, as a great step in progress.