TO THE THEORY OF EVOLUTION. 
47 
Here we take for father and son r 13 = *5, for mother and son r 13 = *5, and for 
assortative mating, r 23 = *2. 
We have then to apply the general formulae (lxxxiii.) and (lxxxiv.) for the case of 
three variables. We have 
Aj = h 2 =h z = 1*64485 
A = & = & = *484,795 
< = = y/" = 1*644,850 
y 2 ' = v 9 " = y 8 "' = 1*705,532 
u/ = vf = v s '" = - *484,356 
< = < = V' = - 5*913,290 
Whence, after some arithmetical reduction, we find 
(Q - Q 0 )/Qo = 20*0389. 
But Q 0 = fu X ifo X yo N = goVo N. Hence Q = *00263 N. 
We must now distinguish between the absolute and relative production of excep¬ 
tional men by exceptional and non-exceptional parents. The exceptional pairs of 
parents are obtained by (xix.), whence we deduce, putting r = *2, h = Jc = 1*64485, 
ccd — be cl 
N 2 = N 
(d + b) (d + c) _ &_ 
N 2 ~ — N 
1 
400 
*002745. 
Whence the number of pairs of parents, both exceptional 
= *005245 N. 
Thus, *005245 N pairs of exceptional parents produce *00263 N exceptional sons, 
and *994755 N pairs of parents, non-exceptional in character, produce *04737 N 
exceptional sons, i.e ., the remainder of the N. The rates of production are thus as 
*5014 to *0476. Or : Pairs of exceptional parents produce exceptional sons at a rate 
more than ten times as great as pairs of non-exceptional parents. At the same time, 
eighteen times as many exceptional sons are born to non-exceptional as to exceptional 
parents, for the latter form only about \ per cent, of the community. 
The reader who will carefully investigate Illustrations II., VIII., and IX. will grasp 
fully why so many famous men are born of undistinguished parents, but will, at the 
same time, realise the overwhelming advantage of coming of a good stock. 
