292 PROF. K. PE ARSON - ON THE MATHEMATICAL THEORY OF EVOLUTION. 
considered whether there is not, at any rate in many characteristics, an actual and 
not apparent male prepotency. It is, perhaps, needless to point out the sensible, if 
small, modifications introduced into inheritance by assortative mating. 
Lastly, we note in Table XIV. the increasing tendency to “breed truer” as we 
select (i.) mother, (ii.) father, and (iii.) both mother and father. 
(9.) On Some Points connected with Morbid. Inheritance. 
(a.) On the Skippmg of Generations. —It must be carefully borne in mind that the 
formulae we have discussed make not the least pretence to explain the mechanism of 
inheritance. All they attempt is to provide a basis for the quantitative measure 
of inheritance—a schedule, as it were, for tabulating and appreciating statistics. 
At the same time we may reasonably ask whether our formulae are wide enough to 
embrace certain of the more isolated and remarkable features of heredity. Let the 
subscripts 1, 2, 3, 4 refer respectively to father, mother, son, daughter. Thus, cr 3 
would be the S.D. of the son population. h 2 a deviation of a mother from the mean 
of mothers, r u the correlation coefficient of fathers and daughters, and so on. Now 
if we consider the general form for single correlation : 
_ i / p 2 rxy y 2 \ I 
- _ v /) " ' v'* cr'cr'' ' (t"*J 1 — '/' 2 
Z - ZqC , 
we may give any values whatever to cr' and a", and any value to r, which is less than 
unity, and deduce the theoretical results. Let us suppose r to be of finite value, but 
that o" is very small as compared with a'. Then the regression of y on x = h'rcr a' 
will be very small, while the regression of x on y = li'ra jcr" will be large. On the 
other hand, the deviation in y will never be very remote from its mean. All this is 
perfectly true whatever be the value of r. 
Now let us apply this to some secondary sexual characteristic, say hair on the 
face. A very small amount of hair on the woman’s face, with a very large amount of 
hair on the man’s face, is compatible with a large value of r ; a small amount of hair 
on the woman’s face may be accounted for by a low mean and very small standard 
deviation. The regression from father to daughter will be expressed by 
>h = r 14 ^ h, 
°i 
or, since oq is extremely small, the daughter will hardly differ sensibly from the 
mean small hairiness of women. The regression from daughter to daughter’s son 
will be 
