100 BOTANICAL GAZETTE [SEPTEMBER 
If we assume that the discs used in pedigree 15 differ from the 
spheres by the possession of a single dominant flattening factor A, 
which increases the index by 1.50, that in pedigree 19 the disc type 
possesses in addition to this a second dominant flattening factor B, 
which increases the index by 0.75, and that in pedigree 1 the sup- 
plementary flattening factor (which we may call C) is smaller and 
can increase the index by only 0.25, we would obtain approximately 
the shapes which we actually find in the F,. The original sphere 
type has an index of 0.97. The disc in pedigree 15 would thus have 
an index of 0.97 plus 1.50, or 2.47, as compared with the 2.48 which 
was found. The F, and F, types would be expected to repeat these 
indices, a condition which they come reasonably close to doing. 
In pedigree 19, however, the parent disc (AB) would have an index 
of 0.97 plus 1.50 plus 0.75, or 3.22, as compared with the 3.28 
observed. The F, should be approximately the same. In the F, 
three-quarters of the spheres would be aB, 0.97 plus 0.75, and the 
other quarter ab, 0.97 only, giving a mean for the whole sphere 
group of 1.53. Similarly, three-quarters of the discs would be AB 
or 3.22, and one-quarter Ad or 2.47, giving a mean for the disc group 
of 3.03. These indices are close to the actual figures. The same 
general situation would occur in pedigree 1, factor C being present 
instead of A, and the original disc type being AC. In table II the 
actual indices and the theoretical expectations are both presented. 
It will be noted that this hypothesis does not explain the fact 
that the F, discs are in every case flatter than the pure types. The 
numbers involved are also much too small to prove such a hypoth- 
esis. They certainly seem to indicate, however, that in two of 
the disc types more than one factor is responsible for the shape dif- 
ference between it and the sphere, and that these two factors are of 
unequal effect. 
This is probably a rather simple case of shape inheritance. 
Indeed, other pedigrees at present in process of completion indicate 
that shape inheritance in squashes is often much more complex, 
involving a considerable number of factors, some of which also - 
show lack of dominance. In GrortH’s' work with tomatoes, 4 
* Grotu, B. H. A., Some results in size inheritance. N-.J. Agric. Exp. Sta. Bull. 
278. pp. 92. pls. 34. 1915. 
