10 BULLETIN 1468, U. S. DEPARTMENT OF AGRICULTURE 
The variability of the C-Wx linkage relationship seems to be no 
greater in the hybrids between Chinese maize and the Algeria pop 
corn used in these studies than in hybrids involving unrelated 
varieties. Thus the crossing over between C and Wx as reported 
by Bregger (#) has a standard deviation of 3.82 ±0.61, and that re- 
ported by Hutchison (9) has a standard deviation of 3.40 ±0.47. 
(Table 3.) There would seem, then, to be no reason to believe that 
the variability in crossing over between C and 7^ a? is in any way 
unique or that it is any greater in the material used by the writers 
than in that studied by others. 
CROSSOVER RATE MORE VARIABLE IN SOME PROGENIES THAN IN OTHERS 
A study of a number of progenies discloses the fact that not only 
do progenies differ in the mean rate of crossing over but also that the 
stability of the crossover rate varies, some progenies being much 
more variable in this respect than others. Biometrical constants for 
several progenies are given in Table 5. 
It will be seen that the progenies listed in Table 5, which are 
limited to those having not fewer than four plants, have standard 
deviations ranging from O.T8±0.19 to 11.00±1.66; or if the very low 
one be disregarded because only four plants are involved, the range 
is from 2.62±0.30 to 11.00±1.66. 
A comparison of the expected standard deviation — that is, 
\/pq/H, with the cr 50 corrected for the size of the population — shows 
that in most cases the variability of the crossover rate is significantly 
greater than that expected for the individual progenies. A single 
instance is found where the observed standard deviation (o- 50P ) is 
significantly less than the expected, and this is in a group of only 
four ears. There are several progenies with o- 502 > but slightly greater 
than the expected, but of the 48 groups 38 show a variability that ex- 
ceeds the expected by more than three times the probable error of the 
difference. The mean of the array of differences is 2.98 ±0.18, with 
the observed standard deviations exceeding the expected, and is 
clearly significant. 
There can be no question that in certain progenies the rate of 
crossing over is remarkably uniform and in others extremely vari- 
able, but in general the crossover rate is more variable than would 
be expected if the variability were due entirely to chance. 
The individual diversity among the plants of certain progenies 
with respect to the rate of crossing over is shown by the series of 
correlation coefficients in Table 6. The coefficients are all calculated 
by the formula v 
0-l 2 + 0"2 2 -0-l-2 2 
where a t and v 2 are the standard deviations of the two variables 
weighted by the number of seeds on the ear, and the <r\- 2 is the 
standard deviation of the array of differences between the paired ob- 
servations weighted by \/Ei. Although based on small numbers, 
the coefficients give definite evidence that progenies differ in a 
variety of ways with respect to crossing over. 
