Of these 10,198 marriages, 211, or 2.07 per cent were between persons bearing the same surname. Applying Darwin's formula we would have 5.9 as the percentage of first cousin marriages in colonial New York. This figure is evidently much too high, so in the hope of finding the fallacy, I worked out the formula entirely from American data. To avoid the personal equation which would tend to increase the number of same-name first cousin marriages at the expense of the same-name not first cousin marriages, I took only those marriages obtained from genealogies, which would be absolutely unbiassed in this respect. Out of 242 marriages between persons of the same name, 70 were between first cousins, giving the proportion:
| Same-name first cousin marriages All same-name marriages | = | _70_ 242 | = | .285 |
as compared with Darwin's .57. So that we may be fairly safe in assuming that not more than 1/3 of all same-name marriages are first cousin marriages. Taking data from the same sources and eliminating as far as possible those genealogies in which only the male line is traced, we have it:
| __Same-name first cousin marriages__ Different-name first cousin marriages | = | _24_ 62 | = | __1__ 2-7/12 | = | __1__ 2.583 |
This is near the ratio which Darwin obtained from his data, and which he finally changed to 1/4. I am inclined to think that his first ratio was nearer the truth, for since we have found that the coefficient of attraction between cousins would be so much greater than between non-relatives, why should we not assume that the attraction between cousins of the same surname should exceed that between cousins of different surnames? For among a large number of cousins a person is likely to be thrown into closer contact, and to feel better acquainted with those who bear the same surname with himself. But since the theoretical ratio would be about 1/4 it would hardly be safe to put the probable ratio higher than 1/3, or in other words four first cousin marriages to every same-name first cousin marriage. Our revised formula then is:
| __All same-name marriages__ All first cousin marriages | = | _3_ 1 | X | _1_ 4 | = | .75 |
Instead of Mr. Darwin's .35.
Taking then the 10,198 marriages, with their 2.07 per dent of same-name marriages, and dividing by .75 we have 2.76 per cent, or 281 first cousin marriages.
In order to arrive at approximately the percentage of first cousin marriages in a nineteenth-century American community I counted the marriage licenses in Ashtabula County, Ohio, for seventy-five years, (1811-1886). Out of 13,309 marriages, 112 or .84 per cent were between persons of the same surname. Applying the same formula as before, we find 1.12 per cent of first cousin marriages, or less than half the percentage found in eighteenth-century New York. This difference may easily be accounted for by the comparative newness of the Ohio community, in which few families would be interrelated, and also to that increasing ease of communication which enables the individual to have a wider circle of acquaintance from which to choose a spouse.
Adopting a more direct method of determining the frequency of cousin marriage, I estimated in each of sixteen genealogical works, the number of marriages recorded, and found the total to be 25,200. From these sixteen families I obtained 153 cases of first cousin marriage, or .6 per cent. Allowing for the possible cases of cousin marriage in which the relationship was not given, or which I may have over-looked, the true percentage is probably not far below the 1.12 per cent obtained by the other method.