EVOLUTION 457 



ancestry, were it only for a few generations, we should 

 sensibly eliminate regression or create a stock of excep- 

 tional men (see p. 481). This is precisely what is done 

 by the breeder in selecting and isolating a stock until it 

 is established. 



Turning back for a moment to our correlation table 

 for fathers and sons, we can obtain its regression line and 

 deduce the coefficient of correlation between the stature 

 of father and son. This is the quantity which enables us 

 to predict the average degree of resemblance, or it is the 

 quantitative measure of heredity that we have been seek- 

 ing. Thus to determine cross or direct heredity between 

 any pair of relatives, we have only to form a correlation 

 table and ascertain the quantity r considered on our p. 397. 

 This is the coefficient of heredity. For example, in the 

 above case, r—.^g6, a rather high value.^ The formula 

 giving the probable stature of the son of a father of given 

 stature, i.e. the regression equation (p. 401), is : — 



Stature of son — 69".2 5 = .446 x (stature of father 

 — 69". 1 1), or stature of son = 38".45 -f- .446 x stature of 

 father. The reader must not expect, however, that this 

 result will apply to every individual case. If he does, his 

 disappointment will be great. Of the individual we can 

 assert nothing as certain, only state the probable. The 

 individual varies owing to the variability of the gametes, 

 and we know nothing of the particular gametes, which 

 fused to give the stirp, of which he is the product. All 

 we know in heredity is what degree of resemblance there 

 is on the average, and if the reader will apply our formula 

 to fifty English middle-class fathers of the same height, 

 he will find that their sons have an average height differ- 

 ing but little from that indicated by the formula. The 

 statistician dealing with heredity is like the physicist 

 dealing with the atom, he can say little or nothing of the 



1 I attribute this high value to the influence of assortative mating. In 

 upwards of looo families recently dealt \\ith, in which the correlation between 

 stature in father and mother was about three times as great as in this series 

 (see p. 431), I found the correlation between father and son to reach even 

 the value .5 ! In fact, the influence of homogamy on heredity can be shown 

 to be very great. 



