SEGREGATION AND PURITY OF GAMETES 545 



behaved independently of each other, l)iit all possible combina- 

 tions of them could be obtained. The F2 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 l)red 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 F2 generation were in accord with 

 mathematical laws governing combinations. Representing the 

 dominants, smooth and yellow, by large 8 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 + gg) = SSYY + 2 SYYw + YYww + 2 YgSS + 

 4 YSwg + 2 Ygwiv + 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 ]'F.S*S, as represented in above formula, 

 are pure dominants, the individuals having the constitution 

 wiogg 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 



