Balanced Crosses 299 



vated, disregarding always the reverting off- 

 spring. At the end I counted the progeny of 

 the sixth and seventh generations and found 

 figures for their three groups of descendants, 

 which exactly correspond to Mendel's formula. 



Until now we have limited ourselves to the 

 consideration of single differentiating units. 

 This discussion gives a clear insight into the 

 fundamental phenomena of hybrid fertilization. 

 It at once shows the correctness of the assump- 

 tion of unit-characters, and of their pairing in 

 the sexual combinations. 



But MendePs law is not at all restricted to 

 these simple cases. Quite on the contrary, it 

 explains the most intricate questions of hybrid- 

 ization, providing they do not transgress the 

 limits of symmetrical unions. But in this realm 

 nearly all results may be calculated beforehand, 

 on the ground of the principle of probability. 

 Only one more assumption need be discussed. 

 The several pairs of antagonistic characters 

 must be independent from, and uninfluenced by, 

 one another. This premise seems to hold good 

 in the vast majority of cases, though rare excep- 

 tions seem to be not entirely wanting. Hence 

 the necessity of taking all predictions from Men- 

 del 's law only as probabilities, which will prove 

 true in most, but not necessarilv in all cases. 



