546 HEREDITY 



in the F% generation were of many kinds. The combinations 

 in this case also agreed quite well with the mathematical laws 

 of combination, when a large number of the F 2 individuals 

 were taken into account. The kinds of combinations and their 

 proportions follow quite well the general algebraic formula 

 (a + 6)?, in which n represents the number of characters in- 

 volved. Thus (a + 6) 2 expanded gives a 2 + 2 ab + b z which is 

 in accord with the 1:2:1 ratio, the ratio expressing the inheri- 

 tance of two contrasting characters. The formula (a + 6) 4 gives 

 the combinations when plants are crossed that have two pairs 

 of contrasting characters. Of course the results obtained scarcely 

 ever exactly agree with the mathematical formula, and the more 

 individuals taken into account, the closer the agreement. 



As a result of his work with a number of pairs of characters, 

 Mendel showed that by means of repeated artificial fertilization, 

 the constant characters of different varieties of plants may be 

 obtained in all of the associations which are possible according 

 to the mathematical laws of combination. This means that, by 

 crossing in a certain way, the desirable characters of different 

 varieties may be brought together, and thereby plants of a more 

 desirable type produced. 



Mendel's Law. Mendel's discoveries and conclusions con- 

 cerning the way parental characters appear in hybrids and their 

 offspring constitute Mendel's law, and his discoveries may be sum- 

 marized as follows: (1) characters are of two kinds, dominant and 

 recessive; (2) characters do not blend but behave as units and 

 separate completely from one another; (3) gametes are, there- 

 fore, pure, never containing genes for both of a pair of contrast- 

 ing characters; (4) the offspring of a hybrid consist of dominants 

 and recessives in the ratio of three dominants to one recessive, 

 and the recessives and one-third of the dominants breed true, 

 while two-thirds of the dominants breed as hybrids, producing 

 offspring consisting of dominants and recessives and again in 

 the ratio 3:1; (5) when any number of pairs of characters 

 are considered, each pair behaves independently, and all com- 

 binations of characters according to the mathematical laws of 

 combination can be obtained. 



After eight years of work, Mendel published an account of 

 his remarkable discoveries, but unfortunately his publication 

 remained unnoticed until 1900, thirty-five years after its pub- 



