CHARACTERS IN AN UPLAND-EGYPTIAN COTTON HYBRID. 39 
(5) In certain cases individuals should be produced in F 2 that show a more extreme 
deviation than is found in the frequency distribution of either grandparent. 
For 31 of the 39 characters the F 2 frequency distribution of 
Holdon X Pima extended beyond the combined distributions of the 
grandparental races in one or both directions. For 3 characters half 
or more of the F 2 distribution lay outside the combined distributions 
of the grandparents (figs. 3-41). 
(6) Individuals from various points on the frequency curve of an F 2 population 
should give F 3 populations differing markedly in their modes and means. 
For all of the characters determined in F 3 the means of the progenies 
which gave, respectively, the highest and the lowest mean differed 
by an amount not less than 12 times the probable error of the 
difference (Table 8) . The coefficients of correlation between the F 2 
value and the F 3 progeny mean for the several characters ranged from 
0.35 to 0.87, the average value of the coefficient having been 0.66. 
For 17 of the 18 characters the parent-offspring coefficient of correla- 
tion was not less than four times its probable error (Table 9). 
(7) Individuals from either the same or from different points on the frequency 
curve of an F., population should give F 3 populations of diverse variabilities extending 
from that of the original parents to that of the F 2 generation. 
The F 3 progenies of Holdon X Pima w r hich gave, respectively, the 
highest and the lowest coefficient of variation or standard deviation 
showed, for every character, a significant difference in variability. 
The least variable of the F 3 progenies was significantly more variable 
than the less variable parental race in only 2 of the characters and 
was significantly more variable than the more variable parental race 
in none of the characters. The most variable of the F 3 progenies 
was at least equal in variability to the F 2 population in all of the 
characters (Table 10). There was a tendency, although with many 
exceptions; to less variability in the F 3 progenies of individuals at 
either extreme of the F 2 frequency distribution than in the F 3 progenies 
of intermediate F 2 individuals (Table 11). 
(8) In generations succeeding the F 2 the variability of any family may be less but 
never greater than the variability of the population from which it camel 
In the present case, for 3 of the characters, the most variable F 3 
progeny gave a coefficient of variation or standard deviation which 
was apparently significantly higher than that of the entire V, 
population (Table 10). To this extent the eighth postulate is not 
fulfilled. But, as was pointed out by East (16, p. 174), complications 
due to linkage may affect the result. Furthermore, "when dealing 
with small populations one should not place too much confidence in 
the probable error calculated for any particular biometrical constant." 
The latter consideration should not be overlooked in view of the 
small size of the Holdon X Pima F 3 populations. 
It was pointed out in discussing the frequency distributions for 
bract connation index and midlock furrow index that some of the 
F 2 plants had the margins of their involucral bracts connate to a 
much greater extent than in Pima, the parent which has the niort; 
connate bracts, and that midlock furrows much longer than those 
of Holdon, the parent in which this character appears, were found in 
