PLANT HYBRIDIZATION BEFORE MENDEL 311 



"There Is therefore no doubt that, for the whole of the characters in- 

 volved in the experiments, the principle applied that the offspring of the 

 hybrid in which several essentially different characters are combined ex- 

 hibit the terms of a series of combinations, in which the developmental 

 series for each pair of differentiating characters are united. It is demon- 

 strated at the same time that the relation of each pair of different char- 

 acters in hybrid union is independent of the other differences in the two 

 original parental stocks." (p. 354.) 



The last sentence in the above is characteristic of Mendel's 

 type of experimental work, and demonstrates in small compass 

 the difference between his method of attack upon the problem of 

 heredity, and that of all of his predecessors. 



Mendel concludes that, where two or more characters are com- 

 bined in a cross, the offspring of the resulting hybrids form the 

 terms of a series of combinations, in which each pair of differen- 

 tiating characters is present, either as a pure dominant, or a pure 

 recessive, or a hybrid dominant. Moreover, if there is : 



One differentiating pair of characters in the parents, the number 

 of character-combinations, i.e., the number of terms of the series, 

 will be : 3^= 3. 



If there are : 



Two differentiating pairs of characters in the parents, the num- 

 ber of combinations will be : 3-= 9. 



If there are : 



Three differentiating pairs of characters in the parents, the 

 number of combinations will be : 3^= 27. 



Hence, generalizing, where "n" differentiating pairs of char- 

 acters are present in the parents, the number of combinations will 

 be 3". 



Moreover, the total number of individuals which constitute the 

 series will be 4", and the number of constant combinations will 

 be 2". 



To apply this rule to the case which Mendel worked upon, 

 with three differentiating pairs of characters, we have: 



^M z= 33 =: 27 (No. of possible character-combinations) 

 4« =3 43 =: 5^ (Individuals in the entire series) 

 2« z= 23 =: 8 (Constant character-combinations) 



"All constant combinations," Mendel says, "which in peas are possible 

 by the combination of the said seven differentiating characters, were 

 actually obtained by repeated crossing. Their number is given by 

 1" — 128. Thereby is simultaneously given the practical proof that the 



