Karl Pearson 
267 
This gives nt once 
Here if the population were stable we should have 0-1 = 0-2, 1 and 2 representing 
as before mother and father. According to our present knowledge = r^g = '4 to 
•5, = say, •45, and r^o lies between 'lo and "25, say, "2. We have then 
cr^=a, X 1-5492 
and p^^, = p of our formulae on pp. 260 — 1, = '5809. 
(ii) We may suppose that the character is equally influential with the fertility 
of both sexes, but that there is no assortative mating. In this case ^^2 = 0, the 
coefficients of 
— and — must still be equal and we have at once 
0-] o-.. 
(iii) It is conceivable that the character affects the fertility in one sex only 
and that there is no assortative mating. In this case we may take x = ^-^, and if 
the population is stable (7^ = ctz, while p = •45. 
(iv) The character may be supposed to affect one sex only, but there may be 
assortative mating. In this case, returning to our formula on p. 259, r23 = 0 and 
X may be taken proportional to 
1 — rj.;- o"! 1 — ?'i2- (To ' 
or we may write 
which leads to 
= a, VI 
and 
vr 
or on the same assumptions as before : 
a^ = a,x -9798, and p = -.3674. 
In all these cases o-^ and p are of course the variability of offspring for the 
given character and their correlation with the parentage character on the as- 
sumption of one child to the parentage. We now proceed to discuss the constants 
of the offspring distribution as resulting from effective parentages, i.e. the quantities 
7?i2, ^2 and R of our p. 261. Here nio, is the reduced mean value of the character, 
Constants of Offspring Distribution. Illustration I. 
Hypothesis ... 
(i) 
(ii) 
(iii) 
(iv) 
•1260 
•1380 
•0976 
■0797 
22/0-. 
•9539 
•9445 
•9747 
•9818 
R/p 
•8976 
•9065 
•8805 
•8721 
