SUMMARY OF MENDELISM 547 



behaved independently of each other, and that the combinations 

 in the F 2 generation were of many kinds. The combinations in 

 this case also agreed quite well with the mathematical laws of 

 combinations, when a large number of the F 2 individuals were 

 taken into account. The kinds of combinations and their pro- 

 portions follow quite well the general algebraic formula (a + b) n, 

 in which n represents the number of characters involved. Thus 

 (a + 5) 2 expanded gives a 2 + 2 a6 + 6 2 which is in accord with 

 the 1 : 2 : 1 ratio, the ratio expressing the inheritance of two 

 contrasting characters. The formula (a + 6) 4 gives the com- 

 binations when plants are crossed that have two pairs of con- 

 trasting 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 combinations. This means that, by 

 crossing in a certain way, the desirable characters of different 

 varieties may be brought together, or undesirable characters 

 eliminated, and thereby plants of a more desirable type produced. 



Summary of Mendelism. Mendel's discoveries concerning 

 the distribution of characters in hybrid offspring and his explana- 

 tion as to why characters are so distributed may be summarized 

 as follows: (1) in a pair of contrasting characters one of the 

 characters (dominant) commonly expresses itself to the exclusion 

 of the other (recessive) ; (2) characters do not blend but behave 

 as units, separating completely from one another; (3) the se- 

 gregation of characters is due to the fact that gametes are pure 

 in respect to the genes for the characters of contrasting pairs, 

 that is, gametes contain the genes for only one and not for both 

 characters of a contrasting pair; (4) half of the gametes of a 

 hybrid have the genes for one of the contrasting characters and 

 the other half of the gametes have the genes for the other con- 

 trasting character; and (5) the probable combinations of the two 

 kinds of gametes in fertilization give 3 dominants to 1 recessive, 

 the recessive and one of the dominants being pure. 



Importance of Mendelism. Mendel's discoveries have com- 

 pletely revised our methods of investigating and ideas concerning 



