546 HEREDITY 



characters of each pair behaved independently of those of the 

 other pair, but all possible combinations 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 yellow: 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 

 niunber of individuals in each combination that occurred in the 

 Fi generation were in accord with mathematical laws governing 

 combinations. Representing the dominants, smooth and yellow, 

 by large iS and large Y, and the recessives, wrinkled and green, 

 by small w and small g, the combinations of S and w are SS + 2 

 Sw + vno, and the combinations 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 pairs of contrasting characters are considered separately. 

 Now (SS + 2Sw + WW) (YY + 2 Yg + gg = SSYY + 2 

 SYYw + YYww +2 = YgSS + 4 YSwg + 2 Ygww + SSgg + 2 

 ggSw + ggww, which are the different combinations and the 

 relative numbers of individuals in each combination obtained 

 when two pairs of contrasting characters are considered in 

 relation to each other. Since the dominants obscure the reces- 

 sives, 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 abo ve formula, are pure dominants, the 

 individuals having the constitution wwgg are pure recessives, 

 while the others are not pure. Thus the laws of mathematics 

 afford a way of expressing what Mendel discovered concerning 

 the behavio r of characters in inheritance. 



He crossed Peas having smooth yellow seeds and gray-brown 

 seed coats with Peas having wrinkled green reeds and white 

 seed coats, thus employing three pairs of contrasting characters. 

 He found also in this case that the pairs of contrasting characters 



