174 Plant-Breeding 



If the numbers in which the forms belonging to these 

 classes appear, be compared, the ratios of 1, 2, and 4 are 

 evidently unmistakable. The numbers 32, 65, 138 present 

 very fair approximations to the ratio numbers of 33, 66, 132. 



The developmental series consists, therefore, of nine 

 classes of which four appear therein always once and are 

 constant in both characters; the forms RY, ry resemble 

 the parental forms, the two others present combinations 

 between the conjoined characters R, r, F, y, which com- 

 binations are likewise possibly constant. Four classes 

 appear always twice, and are constant in one character 

 and hybrid in the other. One class appears four times, 

 and is hybrid in both characters. Consequently the off- 

 spring of the hybrids, if two kinds of differentiating char- 

 acters are combined therein, are represented by the ex- 

 pression RY Ry rYry 2 RYy 2rYy 2 RrY 



This expression is indisputably a combination series 

 in which the two expressions for the characters R and r, 

 y and Y are combined. We arrive at the full number of 

 the classes of the series by the combinations of the ex- 

 pressions. 



The following, quoted from East, has reduced the 

 above to a mathematical expression : "The numerical rela- 

 tions found are approximately the following series : AB, 

 Ab, aB, ab, 2 ABb, 2 aBb, 2 Aab, 2 AaB, and 4 AaBb. This 

 is really a combination by multiplication of the two series 

 (A 2Aa a) x (B 2 Bb b) = AB Ab aB 

 - ab 2 ABb 2 aBb 2 Aab 2 AaB 4 AaBb. 

 The two pairs of characters behave independently of each 

 other and as if chance only governed their combinations. 



