For simplicity’s sake I will assume that in place of eight there were four original classes.  This will illustrate the principle equally well, and be far less involved.

Let A, B, C, and D represent the names of the four classes—­to one of which every native belongs.

1.  The first law is that—­Natives belonging to class A may only intermarry with class B, and natives belonging to C may only intermarry with class D.

2.  The progeny of a man and woman of intermarrying classes is of a different class from either father or mother.

Thus a man of class B marries a woman of class A, but their offspring (male or female) is of class D.

Let Am represent a male of class A.

Let Af represent a female of class A, and similarly Bm, Bf, &c.

Let Ap represent progeny who belong to class A, and similarly Bp, Cp,
Dp.

Law 2 may now be set down as under—­

Af + Bm       Am + Bf       Cf + Dm       Cm + Df
-------       -------       -------       -------
Dp            Cp            Bp            Ap

3.  The first law holds good with the progeny of these combinations, i.e., Dp can only marry one of class C—­though neither the father nor mother of Dp could marry into class C; similarly for Cp, &c.

4.  Dp recognises as father or mother all members of classes A and B; similarly Cp, &c.

This explains the seeming absurdity of the answer one receives from natives to questions concerning their relationships to others.  An old man, for instance, may point out a young girl and say, “That one my mother,” for the girl belongs to the same class as his actual father or mother.

5.  All the progeny of classes A and B are brothers and sisters; similarly C and D.

Thus taking Dp2 to represent the progeny of an Ap and a Bp

Af + Bm          Ap + Bp
---------        -------
Dp               Dp2

All of class Dp recognise class Dp2 (though of another generation) as brothers and sisters.  For this reason there is no absurdity in a small boy pointing out a very aged woman as his sister.

6.  A man may have as many wives as he can get, so long as these laws are adhered to.

Let us now see what degrees of kindred are prohibited by these laws.

Let us take the case of a man of class A. He can only marry a woman of class B, whose parents must therefore have belonged to classes C and D her mother being a C and her father a D.

Therefore his wife’s mother and father belong to classes with which he may not intermarry.

Therefore a man may not marry—­

1.  His mother-in-law. 2.  The sister of his wife’s mother. 3.  The sister of his wife’s father. 4.  Nor the sister of any one of the three. 5.  Nor can he marry his sister.

But he may marry—­

His wife’s sisters (sisters by blood or tribal class).

And as far as I can see, no law prevents a man from marrying his grandmother should he so desire.