8 BULLETIN 1468, U. S. DEPARTMENT OF AGRICULTURE 
but the error from this source is small. The formula for the dif- 
ference between plus and minus variations is given by Haldane (8) 
as 0.3033(1— 2/?) /w, to be added to the probable error in excess 
and subtracted from the probable error in defect. 
For a discussion of the variability of percentages, see Wright (18). 
To determine whether the variability in a series of observed ratios 
is greater than the expected in random samples from a single popu- 
lation, the observed standard de viation is compared with the stand- 
ard deviation of the mean ratio, -yjpq/n. Where the number on which 
the individual ratios is based varies, Yule (19) has been followed and 
the harmonic mean of the numbers (H) taken for the value of n. 
The formula for the expected standard deviation in a series of 
ratios (expressed as percentages), if the variations are due only to 
errors of sampling, is^/pq/H, where £>— the mean percentage, q= 
100— p, andZZ=2V7s-, n being the number on which the individual 
percentage is based and N the number of percentages in the series. 
All linkage values have been calculated from the coefficient of 
association, Q. The merits and limitations of this method have been 
outlined by Collins (5). It was applied to the studies in hand and 
even to the back crosses, because by this method the crossover values 
are not distorted by differential death rates of zygotic classes, ex- 
cept in the event that the death rate of a combination of characters 
differs from the combined death rate of the single characters. The 
Bridges (3) method of balanced viability could not be used without 
introducing the element of individual diversity. 
The formulae for determining the rate of crossing over p from Q 
for the several gametic combinations that occurred in these studies 
are given in Table 2. The calculations were greatly facilitated by a 
series of curves plotted from the equations. 
VARIABILITY OF CROSSOVER RATE 
VARIABILITY NOT UNIQUE IN C-Wx LINKAGE NOR IN CHINESE-ALGERIA MAIZE 
HYBRIDS 
That the variability found in the rate of crossing over between 
C and Wx is not unique for this pair of linked genes is shown by the 
results obtained by Emerson and Hutchison (6) with the B-Lg 6 fac- 
tor pair, where standard deviations of 4.48 ±0.49 and 4.49 ±0.49 were 
found in the male and female gametes respectively. These are 
standard deviations comparable with those for the C-Wx factors 
shown in Table 3. 
These authors also report on a series of plant reciprocals involv- 
ing the C->Sh genes, where standard deviations of 1.93±0.21 and 
2.45 ±0.26 were found in the male and female gametes. Although 
both of these standard deviations are lower than most of those ob- 
tained with the C-Wx genes shown in Table 5, there are several 
progenies in this table with comparable standard deviations. 
c B is a factor for plant color, and Lg is a factor for liguleless leaves. 
