K. Pearson 
85 
Case 1. ^ = 1. 
^ (tt + «)= = -^bir- + -oOTra + •25a-, 
2x2 
TT^ 25 7o Dominance of protogenic determinants, 
air 50 Balanced heterogenic determinants, 
oP 25 Dominance of allogenic determinants. 
In this case it will be seen that the dominance of either determinant means 
a pure cell. The case is that of simple Mendelism and is the basis of a " pure 
gamete" theory. 
Case 2. p = 2. 
This gives 
TT^ 2-78 
■n'a 22-22 
[tt'' + 47ra + a^]-. 
= 25 Dominance of protogenic determinant, 
Tr'^a- 50'00 = 50 °/_, Balanced heterogenic determinants, 
ira' 22-221 
2-78 
= 2; 
Dominance of allogenic determinant. 
This case is of peculiar interest ; we get absolutely the Mendelian percentages, 
if the somatic character follows the preponderance of a given pure race determinant, 
using preponderance here in a simple numerical sense. Further, the protogenic 
25 per cent, would apparently breed true to the somatic character of the pure 
protogenic race, if the somatic character of the balanced heterozygote were, as is 
occasionally asserted to be the case, indistinguishable from that of the protogenic 
race. The peculiar suggestiveness of this result lies in the exact Mendelian 
properties arising on a simple view of dominance apart from any hypothesis of 
the pure gamete. There exists a latent allogenic determinant in the heterogenic 
chromosome of a large percentage of the 25 per cent, with dominant protogenic 
character. This, if judicious cross-breeding were adopted, might be rendered 
manifest in some, if only a small number, of the grandchildren of the offspring 
of the hybrids. 
Case 3. p = 3. 
( 3 ly 
^ 4('^'+97r=a-|-97ra=+a»)=. 
(6 0^ 
29-5 '7o Dominance of protogenic determinant, 
7r« 0-25 7„ 
TT^a 4-50 7o 
tt'ol' 24-75 
TT^a' 41-00 41 Balanced heterogenic determinants, 
IT- a' 24-75 7 1 
7ra' 4-50 °/ 
a? 0-25 7J 
29-5 7o Dominance of allogenic determinant. 
