64 Mendel's Experiments 



parents differ in three characters results therefore according 

 to the following expression : 



ABC + ABc + AbC + Abe + aBC + aBc + abC + abc + 

 2 ABCc + 2AbCc + 2 aBCc + 2 abCc + 2 ABbC+ 2 ABbc + 

 2 aBbC+ 2 aBbc + 2AaBC + 2 AaBc + 2 AabC+2 Aabc + 

 4 ABbCc+4, aBbCc + 4, AaBCc + 4 AabCc + AaBbC + 

 4 AaBbc + 8 AaBbCc. 



Here also is involved a combination series in which the 

 expressions for the characters A and #, B and b, C and e, 

 are united. The expressions 



A + 2Aa + a 



C+2Cc + c 



give all the classes of the series. The constant combinations 

 which occur therein agree with all combinations which are 

 possible between the characters A, B, C,a,b,c\ two thereof, 

 ABC and abc, resemble the two original parental stocks. 



In addition, further experiments were made with a 

 smaller number of experimental plants in which the re- 

 maining characters by twos and threes were united as 

 hybrids : all yielded approximately the same results. There 

 is therefore no doubt that for the whole of the characters 

 involved in the experiments the principle applies that the 

 offspring of the hybrids in which several essentially different 

 characters are combined represent the terms of a series of 

 combinations, in which the developmental series for each pair 

 of differentiating characters are associated. It is demon- 

 strated at the same time that the relation of each pair of 

 different characters in hybrid union is independent of the 

 other differences in the two original parental stocks. 



If n represent the number of the differentiating charac- 

 ters in the two original stocks, 3" gives the number of terms 



