GROWTH AND MORPHOLOGICAL CHARACTERS. 51 



classes in an arithmetical progression derived from the exponents of the 

 first term of the binomial, i. e., n, n — 1, n — 2, n — 3, .... n — n. 

 The total individuals in the series would be 2". 



Had the same heterozygous Fi hybrids been mated to the larger 

 parent instead of the smaller, the distribution of classes in the resulting 

 F2 generation would appear as follows: 



ABC + AbC + ABc + Abe + aBC + aBc + abC + abc Fi gametes. 



ABC + ABC larger parent gametes. 



AABBCC + AABbCC + .AABbCc + AaBbCc ' 



AABBCc AaBBCc } . . . F2 zygotes. 



AaBBCc AaBbCC 



1(6D) + 3(5D) + 3(4D) + 1(3D) F2 distribution of classes 



It is apparent here that the coefficients of the classes are again 

 derived from the expansion of (l + l)^ but, unlike the previous illus- 

 tration, we find the dominant factor represented in the classes in an 

 arithmetical progression, the first term of which is equal to twice the 

 number of allelomorphic pairs. Hence, for "n" allelomorphic pairs 

 we would theoretically derive a series as follows : 



l(2nD)+n[(2n-l)D] + H(^[(2n-2)D]+ "^"7_^j^"3-'^ [(2n-3)D] 

 + . . . . +nf{2n-(n-l)}Dj + l(2n-n)D. 



The gist of all this is that the F2 generations of which we are speaking 

 would theoretically show a range from the larger to the smaller parent 

 with the mode in center when the F2 has been produced by mating the 

 Fi individuals inter se. An F2 generation produced by mating the Fi 

 to the smaller parent shows a range from the Fi to the smaller parent, 

 with the mode half way between these. An F2 generation produced by 

 mating the Fi to the larger parent shows a range from the Fi to the 

 larger parent with the mode half way between. 



This is, briefly, the theory of multiple factors as applied to size- 

 inheritance. If, after sufficiently numerous experiments with plants 

 and animals, it is found to be applicable to such complex cases, it will 

 show that segregation into apparently continuous classes is really dis- 

 continuous, or, in other words, Mendelian. 



At present we know of no adequate hypothesis, other than the 

 Mendelian, by which to explain the uniform Fi generation, the more 

 variable F2 generation, the recovery of parental types, and the tendency 

 for certain recombinations to breed true while others split up again. 

 There is a small number of cases of size-inheritance in which a Men- 

 delian explanation seems well justified. It is logically defensible to 

 resort to this explanation when possible, since it fits a large number of 

 cases involving qualitative characters. However, it is too early to 

 insist that size-inheritance is universally Mendelian, for the number of 

 crucial experiments is few. 



