The Inheritance of Quantitative Characters in Maize 113 
meter plant would almost surely not have 9 stalks and the 
9-stalked plant would not be 26 decimeters tall, unless about 
65,000 F 2 plants, instead of 256. were grown. To be sure of 
getting one 9-stalked plant, let us grow four times the number 
indicated in Table 1, or approximately 1,000 F 2 plants. Since 
over 70 per cent of all the F 2 plants are from 16 to -20 decimeters 
tall, the chances are that the one 9-stalked plant will be from 16 
to 20 centimeters tall — if taller so much the better. Let us sup- 
pose that it is 18 decimeters tall like the F 1 plants. 
On selfing this one 9-stalked. 18-decimeter plant, what will be 
obtained in F 2 ? We can be sure that the progeny will all be of 
the 9-stalked type. Table 1 shows that out of the 70 18-decimeter 
plants, 6 (group III) will breed true, 48 (group XI) will have 
an F 3 range from 14 to 22 decimeters, and 16 (group XV) will have 
an F 3 range from 10 to 26 decimeters. If then the 9-stalked F 2 
plant belonged in group XV for height, we would have an even 
chance of getting one 9-stalked. 26-decimeter plant by growing 
only 256 F 3 individuals and would be fairly sure of getting it by 
growing 1,000 F r plants. In short, we would accomplish with 
2,000 F 2 and F 3 plants what we would have had only an even 
chance of accomplishing with 65.000 F 2 plants or what would 
have required perhaps 250.000 F 2 plants to make its accomplish- 
ment fairly sure. If. however, as is much more likely, the 
9-stalked, 18-decimeter F 2 plant belonged in group XI in height, 
its F 3 progeny, while breeding true to the 9-stalked condition, 
would have a range from 14 to 22 decimeters. Since all the 
individuals of group XI are heterozygous in only two factors, an 
F 3 generation of 16 plants would afford an even chance — and 50 
plants make fairly sure — of getting one 9-stalked, 22-decimeter 
plant. But also, since all the F 2 individuals of group XI lack 
one of the four height factors, the one 22-decimeter F 3 plant 
must be homozygous for three factors and lack the fourth, like 
the F 2 plants of group IV. and will, therefore, breed true to this 
height. There will then be no possibility of producing a 26-deci- 
meter type from it directly any more than from an F 2 18-deci- 
meter plant belonging to group III. which would of course breed 
true to that height. Crossing between different F ? , types must 
then be resorted to. 
We have assumed that a 9-stalked. 22-decimeter plant has 
been produced as described above by selection from 1.000 F, and 
50 F 3 plants. From the same 1,000 F 2 plants a 26-decimeter. 
5 stalked plant could also have been selected and would of 
course have bred true to the 26-decimeter height. It would 
possibly also have bred true to the 5-stalked condition (if be- 
longing to group III for number of stalks), or possibly would 
