228 Prof. K. Pearson. On the Ancestral Gametic [Apr. 2, 



precisely those which it was pointed out in 1896 would lead to a knowledge 

 of the parental constitution* replacing that of the ancestry. 



(6) The striking point, however, of the present investigation is that the 

 values now shown theoretically to exist for the aucestral gametic correlations 

 in a simple Mendelian mixture are very close to those determined for 

 somatic characters in biometric investigations, whereas the somatic correla- 

 tions for a Mendelian population, if we maintain intact the principle 

 of absolute dominance, appear theoretically to be too low. 



Thus the value for parental correlation in man, horse, dog and cattle is 

 about 05, and for the grandparental correlation lies between 025 and - 30 ; 

 but this tendency in the grandparent to some slight excess on the Mendelian 

 gametic value must not be given too much weight. 



(7) It seems desirable to consider how far the results in my paper of 

 1904 for the somatic correlations are modified if we assume for our popu- 

 lation 



p 2 (A A) + 2pq (Aa) + q 2 (aa), 



and do not make p = q. 



Assuming the principle of dominance to be absolute, I enquire what is 

 the proportion of offspring possessing the dominant character! (i.e. (AA) 

 or(Aa)) supposing the nth parent to possess it (i.e. to be (AA) or (Aa)); 

 and again, what is the proportion possessing the dominant character, 

 supposing the nth parent does not possess it (i.e. to be aa). 



Percentage of dominant offspring. 

 2" — Ijj (p -L- 2o) 2 4- (fi 



nth parent dominant in somatic character... 100 x ^ , , 1 — — ^— , 

 * 2 n - l (j) + q) 2 (p + 2q) 



nth parent recessive in somatic character ...100 x - — P ( + -ff) PI (p + 9g) ^ 



2»- 1 (p + qy(p + 2q) 



From this it follows that the correlation which is equal to the regression is 



J_ g 

 2 n ~ 1 p + 2q 



If p = q } this is g 9 3-i , in agreement with the conclusion of my memoir 



of 1904. But unless qj (p + 2q) = f, i.e. the number of pure dominants in the 

 population be vanishingly small (as well, of course, as the number of impure 

 dominants !), this is not a series to which the form p, p 2 , p 3 . . . applies, and 

 when we judge (as we must in most instances in man) by the somatic and 

 not the unknown gametic constitution, the ancestry does matter. 



* As a matter of fact, a knowledge of the gametic constitution of the ancestry in any 

 generation would be equally sufficient with that of the parents, 

 t It is assumed that A is dominant over a. 



