4o8 



Journal of Agricultural Research 



Vol. V, No. 10 



Out of these 1 1 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-I- 1)^. 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. 



Tabi,^ IV. — Third-generation segregating families in groups of four plants 



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 1 1 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. Four 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 i constant short-podded to i 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 



