408 
Journal of Agricultural Research 
Vol. V, No. 10 
Out of these 11 segregating families, 5 show proportions with a greater 
deviation than the probable and 6 have a less deviation. The chances for 
deviations above and below the probable are theoretically equal. The 
greatest deviation is less than three times the probable. In 3 of the fam¬ 
ilies the calculated numbers occur, since fractions of plants are impossible. 
Of the other families 5 show an excess of long-podded and 3 an excess of 
short-podded plants. Hence, the ratios for the third generation conform 
closely to the theory of probability. However, a further test can be made. 
It seems that a perfectly random distribution, with three chances for 
long pods to one chance for short pods, should give for any number of 
equal groups of n plants each a frequency distribution of numbers of 
long-podded plants in the groups in classes from n to o which corre¬ 
sponds to the terms of the binomial (3 + 1 ) n . If all the segregating fami¬ 
lies of the third generation are divided into 76 consecutive groups of 4 
plants each in the same order as grown in the field, omitting the last 3 
plants out of the total of 307, we have the groups as given in Table IV. 
Table IV.— Third-generation segregating families in groups of four plants 
Groups. 
Deviations. 
irons. 
Found. 
Calculated. 
Long. 
4 
Short. 
O 
27 
24 
+3 
3 
I 
27 
32 
-5 
2 
2 
18 
16 
+2 
1 
3 
4 
4 
0 
0 
4 
0 
0 
0 
. 
There is, thus, a fair agreement of the actual figures with those calcu¬ 
lated for a random distribution with three chances for long to one chance 
for short pods. 
Of the random sample of 17 families from long-podded parents given 
in Table III, 11 families segregated into long podded and short podded, 
while 6 families were constantly long podded. The calculated nearest 
whole numbers are also 11 and 6. 
Eleven second-generation short-podded plants gave only short-podded, 
progeny. One of these has been grown to the fifth generation, giving 
only short-podded progeny. Pour second-generation long-podded plants 
which were constant in the third generation have been grown to the sixth 
generation on a field scale without throwing any short-podded progeny. 
Therefore, the whole of the second-generation plants were probably in 
the proportion of 1 constant short-podded to 1 constant long-podded to 2 
heterozygous long-podded plants. 
Now, we must assume, with Mendel, Correns, and Bateson, that this 
difference of long-podded and short-podded plants corresponds to a 
difference between the pollen grains and egg cells of the Florida velvet 
