540 PROCEEDINGS OF THE AMERICAN ACADEMY. 



We have thus far considered only cases of cross-breeding between 

 parents differing in a single character. We have seen that in such cases, 

 no new forms, except the unstable hybrid form, are produced. But 

 when the parent forms crossed differ in two or more characters, there 

 will be produced in the second and later hybrid generations individuals 

 possessing new combinations of the characters found in the parents ; 

 indeed all possible combinations of those characters will be formed, and 

 in the proportions demanded by chance. Thus when parents are crossed 

 which differ in two characters, A and B, let us designate the dominant 

 phase of these characters by A, B, the recessive phase by a, b. The 

 immediate offspring resulting from the cross will all be alike, AB(ab),* 

 but the second and later generations of hybrids will contain the stable 

 (i. e. pure) classes, AB, Ab, aB, ab, in addition to other (unstable, or 

 still hybrid) forms, namely AB(ab), A(a)b, and aB(b). In every six- 

 teen second-generation offspring there will be, on the average, one of 

 each of the stable combinations. Two of these combinations will be 

 identical with the parent forms, the other two will be new. 



But the difficulty of establishing a stable (i. e. pure) race is greater in 

 this case than in that of one variable character. Only the individual 

 which possesses both recessive characters can at once be set aside as pure. 

 For to each of the stable individuals possessing one dominant and one 

 recessive character, there will be two other individuals, exactly like it in 

 appearance, but hybrid in one of the two characters. The one pure 

 individual can be distinguished from the two impure individuals only 

 by breeding tests. 



Again, nine out of every sixteen of the second-generation hybrids will 

 possess the two dominant characters, and so will be in appearance 

 exactly like their parents, the first-generation hybrids. But only one of 

 the nine will be pure with reference to those characters. Of the remain- 

 ing eight, four will be hybrid in one character, and four will be hybrid 

 in both characters exactly like the entire first generation of offspring. 



The greater the number of separately variable characters involved 

 in a cross, the greater will be the number of new combinations obtain- 

 able ; the greater, too, will be the number of individuals which it will 

 be necessary to raise in order to secure all the possible combinations ; 

 and the greater, again, will be the difficulty of isolating the pure (i. e. 



* This is Mendel's use of lower-case letters to designate recessive characters, 

 with which I have combined the use of a parenthesis when a character by nature 

 recessive is not visible in the individual. 



