476 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Professor Pearson, the same correlation coefficients are represented by ^t, 
T \, etc. The well-known correlations found by observation have no 
obvious relation to either of these sets of figures, and if Mendel’s law is 
proved to be efficient, some means of reconciling theory and observation must 
be found. In the subsequent pages the various factors which influence 
correlation will be considered under different heads. 
Influence of the Different Methods of Calculating Correla- 
tion Coefficients on the Values Deduced if Mendelian 
Principles hold. 
6. When the typical correlation table for parent and offspring given by 
Mendelian theory is considered it is evident that it shows several properties. 
If, say, the population consist of 
(a, a), (a, b), (b, b), 
then it may be tabulated in two ways : 
Pure (a, a) containing two a elements ; 
Hybrid (a, b) „ one a element ; 
Pure (b, b) ,, no a element ; 
or if the hybrid (a, b) resemble (a, a) in appearance we have (a, a) + (a, b) 
not having a pair of b zygotes and (b, b) possessing a pair of b zygotes. 
Both these forms have linear regression, and in consequence the product 
method of determining correlation is valid. The case already given may 
be repeated. Taking x equal to y the correlation of parent and offspring 
reduces to the following simple form : — 
Parent. 
Offspring. 
(a, a). 
(a, b). 
(b, b). 
Totals. 
(a, a) . 
1 
1 
2 
(a, b) . 
1 
2 
1 
4 
(b, b) . 
1 
1 
2 
Totals . 
2 
4 
2 
8 
This table shows obvious symmetry, has evidently linear regression, and 
gives a correlation coefficient between parent and offspring of r = *5. But 
if the table is further condensed, that is, if (a, a) and (a, b) are considered 
as one class we have instead : — 
