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394   Life and Letters of Francis Galton

Problem.   October 25, 1909.

An array H, is made of husbands arranged in. estimated order of civic worth (see remarks below). Gauss's Law is supposed to apply throughout. Let the standard deviation of H which does not need measurement be unity. Cut off a segment G from the upper end of H, including 1/nth of the whole of H (1/n is here wanted only for the two values •02 and •04, to which the corresponding deviates in Sheppard's Table, Biometrika, Vol. v, p. 4, are 2.0537 and 1.7507). Make an array F in order of civic worth of all the male adult children of G as calculated from the formula for parental Heredity. It will be a skew array. Let the mean (or better the median) of all the values in F be f, and let the position of that value in the array H be 1/w of its length from the upper end. Required : the ratio of w to n for the two values of 1/n mentioned above, and consequently that of the deviates at those class-places (from Sheppard's Table).

Remarks.

A. It seems impossible to obtain a satisfactory numerical value of civic worth, but it is not more difficult to classify it by judgment, than it is to select recipients of honours, members of Council, etc., out of many eligible persons. Therefore the method here adopted is to compare class-places and to derive the corresponding deviates from Sheppard's Table.

B. Some law of fertility must be assumed that shall give limits to the possible error from ignorance of the true one. Perhaps the assumptions (i) that infertility so balances deviates that the F values are much the same as those of the children of parents at 1/nth of the array from the upper end, and (ii) that they are the same as those at 1/2nth of the same, might be adequate.