38 BULLETIN 1164, U. S. DEPARTMENT OE AGRICULTURE. 
three showed less variability in the progenies representing both ex- 
tremes of the F 2 distribution than in the progenies of intermediate 
F 2 individuals. The correlation between the percentage extremeness 
of the 22 F 2 parent individuals and the size of the coefficient of vari- 
ation or standard deviation of the corresponding F 3 progenies was 
determined for the characters in question and gave values for r (coef- 
ficient of correlation) as follows : 
Leaf index — 0.242±0.135 
Leaf lobe index - .418 ± .119 
Callus color - .106± .142 
In all cases the correlation is negative, as the theory requires, although 
only the coefficient for leaf lobe index appears to be significant, being 
3.5 times the probable error. 
The data as a whole indicate a tendency, although with many ex- 
ceptions, to less variability in the progenies of extreme than in the 
progenies of intermediate individuals of the second generation. As 
far as the evidence goes, it points to a greater degree of homozygosity 
at both ends of the F 2 distribution and hence strengthens the con- 
clusion that segregation has occurred. 
SUMMARY OF EVIDENCE OF F 2 SEGREGATION AFFORDED BY F 3 . 
Many of the characters determined on this hybrid of upland and 
Egyptian cottons are not size characters in the narrow sense, although 
nearly all of them resemble size characters in showing inheritance of 
the "blend" rather than of the sharply alternative type. In review- 
ing the evidence that segregation took place in the second generation, 
the data will be considered, therefore, in their relation to the eight 
requirements "which must be fulfilled in order to establish the valid- 
it v of the multiple-factor theory of size inheritance,'' as postulated 
by East 06, pp. 165-167). 
(1) Crosses between individuals belonging to races which * * * approach a. 
homozygous condition, should give Fj populations comparable to the parental races 
in uniformity. 
This condition was fulfilled for the hybrid here dealt with in 
respect to nearly all of the characters (Tables 2 and 3). 
(2) In all cases where the parent individuals may reasonably be presumed to 
approach complete homozygosis, F 2 frequency distributions arising from extreme 
variants of the F 1 population should be practically identical. 
This point was not adequately tested in the present case, but the 
evidence, such as it is, indicates that the requirement was met 
(P- 11). 
(3) The variability of the F 2 population from such crosses should be much greater 
than that of the F x population. 
The Holdon-Pima hybrid gave an F, coefficient of variation or 
standard deviation which was significantly higher than the correspond- 
ing constant of F x in 37 of the 38 characters compared (Table 2). 
(4) When a sufficient number of F 2 individuals are available, the grandparental 
types should be recovered. 
For 37 of the 39 characters determined in F 2 of the Holdon-Pima 
hybrid the frequency distribution of F 2 comprised the means of both 
grandparental populations, and for 33 characters both extremes of 
the combined arandparental distributions were recovered in F., (figs. 
3-41). 
