SELECTION ON THE VARIABILITY AND CORRELATION OF ORGANS. 
41 
Now let us see what happens if we select both parents moderately. As test cases, 
let us take /tj = /To = ’8 and '5, and for the extreme = 0. 
We have at once 
Ng = a- 3\/'68 + •32/r/(l + pi-:) .(Ixxv.), 
- 3 l‘i 3 = erg {A/ri (1 + P 13 )].. (Ixxvi.). 
Hence w^e deduce 
P12. 
Pi = P2 = 
•8. 
Pl = P2 = 
•5. 
/n = P2 
= 0. 
' 
2:3/^3. 
ri.3- 
^3/w3. 
ri3- 
Y3/0-3. 
ri3- 
•1 
•9515 
•3700 
•8764 
• 2865 
•8246 
0 
* 2 
•9G22 
•3991 
•8809 
• 3093 
•8246 
0 
•3 
•9727 
•4277 
•8854 
•3316 
•8246 
0 
•4 
•9832 
•4556 
•8899 
• 3535 
•8246 
0 
•5 
•9936 
•4831 
•8944 
•3750 
•8246 
0 
1 
1•0438 
•0131 
■9165 
•4762 
•8246 
0 
This table is very instructive. It shows us that selection and assortative mating- 
are factors of opposite influence; that if selection be only moderate, then with 
considerable assortative mating the coefficient of parental correlation may be 
increased, but if selection be stringent, then assortative mating cannot counteract, 
even if as high as ‘5, its destructive influence on parental correlation. 
For example, if Ave take parents remarkable for some intellectual or physical 
character, say with a variability only a A’ery small fraction of that of the general 
poj)ulation, then, however proportionately we might pair them, we should find their 
relationship to their children, as measured by the coefficient of correlation, Amry 
sensibly reduced beloAv that of the general population. I think aa’o have here the 
reason AAdiy Mr. Galtox’s Family Data, Avhich AA-ere draAvn from a rather narroAv 
class, and had only a small coefficient of assortative mating, give so much smaller 
parental correlation than my own Family Data, Avhich seem to me draAvn from a 
Avider class, and have a considerably higher assortative mating. 
It will be clear that Avith factors like assortatiAm mating, natural selection, artificial 
selection of breeders, unconscious selection of material from one class or one enAuron- 
ment, modifying our coefficients of heredity in one or another direction, AA^e can hardly 
hope for more in practical statistics than an approximation to the strength of the 
pure inheritance factor l^y dealing w-ith the average of as many races and characters 
as possible. 
* The Avork for Mr. Galton’s Family Data is given, ‘Phil. Trans.,’A, vol. 187, p. 270. My OAvn 
results are as yet unpuhlishecl. The average A'aluo is about -I.A, as compared with Mr. Gat.tox’s -.34 
VOL. CC.-A. 
G 
