Research Bulletin No. 2 
inches. Of the 182 zygotes 16 to 20 inches high, only or 3.3 
per cent, will breed true; 48, or 26.4 per cent, give progenies with 
four-inch ranges; 48, or 26.4 per cent, give progenies with eight 
inch ranges ; 64, or 35.2 per cent, give progenies with twelve-inch 
ranges; and 16, or 8.7 per cent, give progenies with sixteen-inch 
ranges. The old biometrical idea that the class of greatest 
frequency is the type of the population toward which all selected 
individuals tend to revert is therefore erroneous. It is true, 
however, that if a large number of size factors were heterozygous 
in the F 3 generation, the grandparental types would be recovered 
so infrequently that practically there would be a sort of blended 
inheritance. One could obtain races that bred comparatively 
true for all of the grades intermediate between the parents, but 
the nearer he was working for an absolute blend the easier would 
be his work when he was able to raise only a few individuals in 
each generation. He could, nevertheless, cross extreme sizes and 
expect to recover either grandparental size combined with any 
other good quality possessed by the other grandparent if he could 
deal with sufficiently large numbers. 
Passing now to the question of back crosses, the interesting 
problem arises as to whether the ¥ 1 crossed with either parent 
gives data which are easier to analyze than are those obtained 
from breeding the F x 's inter sc. When parents representing a 
single allelomorphic difference in a qualitative character are 
crossed, the (i F 1 X the recessive parent" gives heterozygous 
dominants and homozygous recessives in equal numbers. It is 
easier to determine a 1:1 ratio than a 3:1 ratio: therefore 
baekcrossing is a popular method in genetics. But in the cases 
we are discussing, no aid to factoral analysis is obtained from 
baekcrossing. Baekcrossing F 3 with either parent gives a 
frequency curve exactly like that obtained from breeding the F, 
individuals inter se. When crossed with the small parent, the 
distribution of the progeny is from the size of the small parent 
on the one hand to the size of the F t on the other ; when crossed 
with the large parent, the distribution is from the size of the F T 
on the one hand to the size of the large 1 parent on the other. The 
frequencies of the classes between these extremes is found by ex- 
panding the binomial (| + -i) n instead of H + i^ 2n n<Si i s done in 
the case of interbreeding the F x individuals. 
Unfortunately one can never meet in practice a ease as simple 
as our hypothetical one. The first perplexing factor is environ 
mental influence. External conditions influence the whole 
development of both plants and animals, but nowhere is their 
effect so great as on size characters. In studying the heredity 
of size characters, therefore, one is not only confused by the fact 
