THE MECHANISM OF HEREDITY 73 



the F2 Mendelian expression for N allelomorphic pairs 

 when dominance is complete is the expanded bionominal: 



(3 + l)» or (3/4 4-1/4)** 

 N==l (3 + 1)1 = 34-1 



iV = 2 (3 + 1)2 = 32 4-34-34-1=- 94- 34-3 + 1 

 iV = 3 (3 + 1)3 = 33 + 3(32) 2+3(3)41 = 27 + 9 + 9 + 9 

 + 3 + 3+3 + 1 



Likewise, the expanded bionomial (V2 + %)^" gives the 

 numerical relationships when dominance is absent and N 

 represents the number of allelomorphic pairs. The ex- 

 pression is (% + i/2)^" instead of {1/2 + 1/2)" because it is 

 supposed that the presence of any allelomorphic pair in 

 the heterozygous condition produces one-half the visible 

 effect on the character that is produced when the heredi- 

 tary factors are present in the homozygous condition. 

 When N is very large the frequencies with which the dif- 

 ferent classes occur form a regular curve called the nor- 

 mal curve of error. This is the curve that is produced 

 when the errors in any physical measurement are sim- 

 ilarly plotted, using as classes any constant deviation 

 from the average, as a^ 2a, 3a, etc. This same curve is 

 also produced when one plots the fluctuations of many 

 organic characters produced by the infinite complexity of 

 external conditions. 



If no non-heritable fluctuations intervened to obscure 

 the class to which any particular zygote belongs, there- 

 fore, one should expect the following classes in Fn when 

 parents of different sizes differing in N allelomorphic 

 pairs are crossed. The extremes represent the grand- 

 parental types in each case, and the intermediate classes 

 theoretically divide the difference between the parents 

 into aliquot parts. It should be noted, however, that this 



