viz NATURAL CROSSING 115 



subsequent years. Thus, the years would yield : 

 A, per cent., B, 10 per cent., C, 19 per cent, D. 27 'I per 

 cent, &c. 



Again, if we start with F! plants, all being identical, 

 allow no further crossing, and consider one allelomorphic 

 pair only, we shall obtain the following series, P denoting 

 homozygotes, and H denoting heterozygotes. A, 100 per- 

 cent H. B, 50 per cent. JET and 50 per cent. P. C, 25 

 per cent. H and 75 per cent. P., &c. In other words, 

 assuming the productivity of H and P to be equal, the 

 hybrid form will decrease to infinitely small proportions. 

 When two pairs of characters are involved, the rate of 

 decrease of H will be slower. Instead of a 1 : 2 : 1 ratio 

 in the year B, or 2 H : 2 P, we shall have the ratio of 

 1 : 1 : 2 : 2 : 4 : 2 : 2 : 1 : 1, or 12 H : 4 P, being 25 per cent. 

 instead of 50 per cent, of homozygote forms. 



Combining these two antagonistic processes, crossing 

 and segregation, we come to the following general 

 algebraic statement. 



For y pairs of simple allelomorphs involved in a cross 

 we obtain in F 2 : 



2?y homozygotes (P) from by individuals. 



Since crossing is renewed every year we can consider 

 this as a general value for purification. 



In each generation let xP become H, by crossing, and 

 yH become P, by segregation. 



Then the composition of the crop will be : 



1st Year : P only. 



2nd : (l 



3rd : {(l 

 4th. : l 



i 2 



Hence 



nth year: ^ 



