Karl Pearson and David Heron 
211 
are assumed to hold. If every possible father be mated with every possible 
mother so as to insure random mating, we have the contingency table for father 
and offspring : 
Father. 
(A A) 
(Aa) 
(aa) 
Totals 
(-1-1) 
21 {21' + ni) 
m(Zl' + m') 0 
(21 + vi) (2l'+vi) 
(Aa) 
c 
21 (m'+Zn') 
i 
2m(l' + m' + n') . 2»(2Z'-fem') 
\ZV {m+2n)+2vi (l + m+n) 
\ + 2n'(2l + m) 
(aa) 
0 
m (m' + 2n') 
f 
2n (m' + 2n') 
(m + 2n) (m' + 2n') 
Totals 
41 (I' + m' + nf) 
4m (l'+m' + n') 
4n (I' + rri + n') 
4 (l + m+n) x (I' + m' + n) 
be 
.(B 
O 
Now there are four points at which we can make a fourfold classification, a, /3, 
7 and 8, and these will give tables for which the association and colligation in 
Mr Yule's sense can be calculated. Now we will suppose 
N = I + m + n and N ' = V + m! + n 
to remain constant, so that the total population is the same. Then if we divide 
at a no selection of (A A) or "dominant" fathers will affect the coefficient of asso- 
ciation ; if we divide at /3 or 8, Mr Yule's coefficients are unity, or there is perfect 
relationship between parents and offspring, and if we divide at 7, no selection of 
recessives will affect the Yulean association. What light can Mr Yule's coefficients 
possibly throw on Mendelian inheritance, when for two possible divisions they 
make the parental relationship perfect and for the other two they give substantial 
values of the relationship, but render it completely independent of selections, 
which in reality widely influence the relationship of parent and offspring, if we 
proceed by the theory of discrete units ? If we accept — which the present writers 
do not — the theory of dominance and assert that (AA) and (Aa) are somati- 
cally identical, and represent one somatic character, then 7 is the only reasonable 
division to make, and the typical Mendelian table becomes : 
Father. 
(A A), (Aa) 
(aa) 
Totals 
(AA), (Aa) 
4(1 + m) N' - m (m + 2n') 
2n{2N' -(vi + 2ri)} 
4NN' - (m + 2n) (vi + 2ii) 
(aa) 
m (vi + 2n') 
2n (m' + 2n') 
(m+2a) (m' + 2n') 
Totals 
4(l + m) N 1 
4nN' 
4NN' 
o 
•21—2 
