Growth and variation in maize. 167 



We may assume that plants of the constitution aabb will remain 

 relatively small throughout the season, i. e., that they will have a mean 

 quintile position of TO. Further the AABB plants will remain relati- 

 vely large or will have a mean quintile value of 5"0. If we assume 

 that each tactor has the same value in increasing the mean quintile 

 value of a plant, then the addition of any one factor will tend to raise 

 the mean quintile position of the plant one quintile. Each type of 

 plant will then have the theoretical mean quintile position shown in 

 column three of table 23. 



If a frequency distribution of these mean quintile positions is 

 made using the same class units as those in the observed data it 

 is found that the frequency of each class occurs in the Tatio of 

 1:4:6:4:1. In percentage figures the ratios are 6"25 : 25-0 : 37'5 

 : 25*0: 6-25. Now the observed frequencies taking all the series to- 

 gether as given in table 16 are, for the same classes, 29 : 29 : 43 : 35 : 27. 

 In percentages these are in the ratio 17'8 : 17'8 : 26"4 : 2r.'S : 16'6. 

 It is clear from the two percentage ratios that they are not at all related 

 and that our supposition does not fit the facts. 



However, there is no a priori reason why each pair of factors 

 should have the same effect upon the plants. It is entirely conceivable 

 that the precense of the factor A, for example, has only one-half or 

 one-third the effect of the presence of the factor B. Applying this 

 principle it has been assumed as before that plants aabb would have 

 a mean quintile position of 1-0. If one A were present it would in- 

 crease the mean quintile position 0'5 of a quintile or to 1'5 quintile. 

 Two A's would of course have twice the effect of one. If one B were 

 present the mean quintile position would be increased I'S quintiles or 

 to a value of 2-5 quintiles. According to this scheme the theoretical 

 mean quintile position of each class of plants is that given in the last 

 column of table 23. Putting these into a frequency distribution as be- 

 fore we get the theoretical distribution given in table 24. The obser- 

 ved percentage frequencies are also given in this table. These latter 

 frequencies are the total percentage frequencies for all three series as 

 given in table 16. 



From this table it is seen that the two percentage distributions 

 correspond very well indeed. As a matter of fact if Elderton's test 

 for the goodness of fit is applied to these two distributions it is found 

 that the probability, P ) 0-9626. This means that in a series of random 

 samples, from material following the theoretical law, we could expect 



