1909-10.] The Significance of the Correlation Coefficient, etc. 499 
Parent. 
Offspring. 
Dominant. 
Recessive. 
Totals. 
Dominant . 
5 
1 
6 
Recessive . 
1 
1 
2 
Totals . 
6 
2 
8 
which when evaluated by the fourfold method gives r = - 53 as the correla- 
tion. As a matter of fact the table just quoted gives r = *54. 
If the highest ancestral coefficient is now examined we find some 
difference. The table for great-great-grandparental inheritance * — 
Great-great-grandparents. 
Offspring. 
Bay and 
Darker. 
Chestnut 
and Lighter. 
Totals. 
Bay and darker . 
497 
252 
749 
Chestnut and lighter . 
130 
99 
229 
Totals . 
627 
351 
978 
is marked by the presence of a great excess in chestnut horses. As before 
shown (par. 25), j* this tends to raise the correlation of parent and offspring. 
The effect of this, however, on succeeding generations may be here inquired 
into. In the case in point we have approximately one-third of the 
parentage recessive. The remaining two-thirds may be divided in two 
ways : it may be taken as of pure Mendelian composition, that is, we have 
one case of pure dominant and two of hybrid dominant ; on the other hand, 
considering that the pure horse may be a better animal than the hybrid, 
and therefore more likely to be chosen for breeding purposes, we may assume 
that the number of pure and of hybrid dominants is equal. The parentages 
on this hypothesis will then be : — 
2 (a, a) 4 (a, b) 3 (b, b) (A.) 
and 
2 (a, a) 2 (a, b) 2 (b, b) (B.) 
The former (A) will probably give the dominant in defect and the latter 
(B) in excess, so that some value between the results obtained on these two 
hypotheses may be taken as true. 
* Biometrika , vol. ii. p. 255. 
+ Of. also par. 4. 
