r.] ANTECEDENTS. 31

is based on that by which the relative frequency of different "runs of luck " is calculated.

I now proceed to apply this law. I have 62 cases in which the heights of both parents are given numerically, whence it appears that- (1) the average height of the fathers is between 5 ft. 9 in. and 5 ft. 94 in., and that their distribution conforms closely to the law of frequency of error, the" probable error" of the series being 1.7 in. (2) The average height of the mothers is 5 ft. 42 in., and the distribution of their heights conforms fairly to the above-mentioned law, the " probable error " of the series being 1.9 in. It follows from the well-known properties of the law in question, that if there had been no sexual selection in respect of height, the sum of the heights of the two parents would also conform to the law of frequency of error, and that the probable error

of the series would be V(1.7)2 +(1'9)2 = 2.5 in.

(3) I find that the heights in question do con

form pretty closely to the law in question, and

that the probable error of the series is 2.3 in.,

which differs so slightly from the value obtained

by calculation, on the supposition of there having