FACTOR RELATIONS IN QUANTITATIVE INHERITANCE 183 



TABLE XXXIII. FREQUENCY DISTRIBUTIONS FOR COROLLA LENGTH IN A CROSS 

 BETWEEN VARIETIES OP Nicotiana longiflora CAV. (After East) 



That the results of experiments in size inheritance may be explained 

 by a multiple factor hypothesis is apparent from the explanation which 

 follows. For the sake of simplicity we will assume that two races A 

 50 and B = 100 differ by five pairs of genetic factors which display an 

 equal effect in size production. The genetic formula for Race A may 

 be represented by aabbccddee; and the contrasted Race B by AABBCCDD- 

 EE. We assume that the factors display no dominance, that their effect 

 is equal and cumulative, and that a dominant factor gives a character 

 expression greater by 5 than the corresponding recessive factor. By 

 crossing two such races an F\ of the genetic constitution AaBbCcDdEe 

 is obtained, which on the above . assumptions has a size equal to 75. 

 Selfing such a hybrid we would secure, in case these factors displayed 

 independent segregation, the following series of phenotypes: 



50 55 60 65 70 75 80 85 90 95 100 

 1 10 45 120 210 252 210 120 45 10 1 



These values are merely the coefficients obtained by expanding the 

 binomial (a + 6). 10 If these values be plotted, they give an approxima- 

 tion to the usual form of normal variability curve as shown by the 

 polygon representing expansion of this binomial in Fig. 15, and this 



