Ill] 



Representation of F^ Generation 



59 



upper expression Indicates the nature of the female gamete, 

 the lower one that of the male orametc : 



The constitution of each of the sixteen types which are 

 produced in F^ is thus displayed, and since A is dominant 

 over a, and B over b, the visible appearance of F^ is 



(^AB : 2iAb : ^aB : lad. 



Similarly when three pairs of factors are concerned, 

 Aa, Bd, Cc, the F^ type will exhibit them all, and be in 

 appearance ABC. In /% there must then be eight visibly 

 distinct types, and the ratios in which they severally appear 

 will be as follows : 



2jABC+gaBC+^ABc^()AbC+2>^bc + 2)^Bc 



-\- 2i^dC + labc. 



I am obliged to a mathematical friend for the following 

 scheme by which the number of types and the ratios in 

 which each will appear are given for any number of pairs 

 of factors, one factor of each pair being dominant and the 

 other recessive. 



4 = 3 + 1 



i6 = (3 + 1)' = 3' + 3 + 3 + 1=9 + 3 + 3 + 1 



64 = (3 + i)' = 3' + 3-3' + 3. 3+1 =27 + 27 + 9+^ 



256 = (3+1/ =3' + 4 -3' + 6. 3"' + 4. 3 + I 



= 81 +27 + 27 + 27 + 27 



+9+9+9+9+9+9 



+3+3+3+3 

 + 1. 



