480 
Proceedings of the Royal Society of Edinburgh. [Sess. 
If the parents be 
elements from the same parents are 
a, a 
b, b 
and 
c, c 
d, d 
then the offspring having two 
P. 
Q. 
R. 
a, a 
c, c 
a, b 
d, d 
b,b 
c, d 
which represent different things according as dominance exists or not ; for 
if dominance exist R is included among those having apparently two pairs 
of dominant zygotes, while if the hybrid is distinct it is grouped with 
P and Q as containing two units from the same parent. 
11. In addition to the methods just given Professor Pearson has also 
discovered two methods of determining correlation by means of what he 
calls contingency. It is not necessary to go fully into this part of the 
question. The manner in which the results given by these methods differ 
from those just considered is illustrated in the subjoined table. They are 
not in general suitable for simple Mendelian cases, as they depend for 
success on the number of divisions being much more numerous than these 
tables give. 
Table showing the Correlation Coefficients calculated by different Methods 
WHERE ONE, TWO, OR THREE DOMINANT ZYGOTES OCCUR IN ONE PARENT AND A 
like Number of Recessive in the other. 
Product 
Method. 
Mean Square 
Contingency. 
Mean 
Contingency. 
Fourfold Table. 
A* 
B* 
c* 
One zygote 
•333 
•32 
•37 
•5 
Two zygotes . 
•333 
•33 
•41 
•46 
•46 
Three zygotes 
•333 
•32 
*39 
•42 
•42 
•45 
* See par. 9. 
Results of Assortive Mating. 
12. With the same notation as just used the most general form of 
correlation under a Mendelian system for assortive mating between husband 
and wife, if the standard deviation of each is equal, is the following : — 
Husbands. 
Wives. 
(a, a). 
(a, b). 
(b, b>. 
Totals. 
(a, a) . 
m 
2r 
n 
m + n + Qr 
(a, b) . 
2 r 
4p 
2 r 
4(r +p) 
(b, b) . 
n 
2 r 
m 
m + 2 r + n 
Totals . 
m + 2r + n 
4 (r+p) 
m + Zr + n 
