It would naturally be supposed that with each succeeding degree of
relationship the ratio of same-name to different-name cousin marriages
would increase in geometrical proportion, viz. first cousins, 1:3;
second cousins, 1:9; third cousins, 1:27, etc., but on the other hand
there is the tendency for families of the same name to hold together
even in migration as may be proved by the strong predominance of
certain surnames in nearly every community. So that the ratio or
same-name to different-name second cousin marriage may not greatly
exceed 1:4. Beyond this degree any estimate would be pure guesswork.
However the coefficient of attraction between persons of the same
surname would undoubtedly be well marked in every degree of kinship,
and conversely there are few same-name marriages in which some
kinship, however remote, does not exist.

The proportion of mixed generation cousin marriages (1-1/2 cousins,
2-1/2 cousins, etc.) is always smaller than the even generation
marriages of either the next nearer or more remote degrees. For
example, a man is more likely to marry his first or his second cousin
than either the daughter of his first cousin, or the first cousin of
one of his parents, although such mixed generation marriages often
take place.

The conclusions, then, in regard to the frequency of consanguineous
marriage in the United States may be summarized as follows:

1. The frequency varies greatly in different communities, from perhaps
.5 per cent of first cousin marriages in the northern and western
states to 5 per cent, and probably higher, in isolated mountain or
island communities. The average of first cousin marriage in the United
States is probably not greater than one per cent.