SEGREGATION AND PURITY OF GAMETES 545 
behaved independertly of each other, but all possible combina- 
tions of them could be obtained. The F, generation of seeds 
contained smooth and yellow, wrinkled and yellow, smooth and 
green, and wrinkled and green seeds, and each kind of seeds 
occurred in a definite proportion of about 9 smooth and yel- 
low: 3 wrinkled and yellow: 3 smooth and green: 1 wrinkled 
and green. The wrinkled green seeds were pure recessives and 
bred true, and 1 out of 9 of the smooth yellow seeds was a pure 
dominant and thus bred true. All of the other seeds were not 
pure and various combinations again occurred in their offspring. 
The combinations and the number of individuals in each com- 
bination that occurred in the Ff, generation were in accord with 
mathematical laws governing combinations. Representing the 
dominants, smooth and yellow, by large S and large Y, and the 
recessives, wrinkled and green, by small w and small g, the com- 
binations of S and w are SS +2 Sw -+ ww, and the combina- 
tions of Y and g are YY +2 Yg+ gg. These combinations are 
simply the pure dominants, impure dominants, and recessives in 
the ratio of 1: 2:1 which occurs when a pair of contrasting 
characters’ is considered separately. Now (SS + 2 Sw + ww) 
(YY +2 Yg+qg) = SSYY +2 SYY¥w + YY¥ww + 2 ¥gSS + 
4YSwg +2 Yguw + SSgg + 2 ggSw + ggww, which are the dif- 
ferent combinations and the relative numbers of individuals 
in each combination obtained when two pairs of contrasting 
characters were considered in relation to each other. Since the 
dominants obscure the recessives, the apparent combinations 
with the relative number of individuals in each are 9 dominants, 
3 individuals with dominant yellow and recessive wrinkled, 3 
individuals with dominant smooth and recessive green, and 1 
individual with recessive wrinkled and green. The individuals 
having the constitution YYSS, as represented in above formula, 
are pure dominants, the individuals having the constitution 
wwgg are pure recessive, while the others are not pure. Thus 
the laws of mathematics afford a way of expressing what Mendel 
discovered concerning the behavior of characters in inheritance. 
He crossed Peas having smooth yellow seeds and gray-brown 
seed coats with Peas having wrinkled green seeds with white 
seed coats, thus employing three pairs of contrasting characters. 
He found also in this case that the pairs of contrasting characters 
behaved independently of each other, and that the combinations 
