i.] 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. 9j 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. 

 k\ in., and the distribution of their heights con- 

 forms 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 selec- 

 tion 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 1/( T 7 ?) 2 -I- (l *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 



